Lenses, devices, methods and systems for refractive error

Abstract

Lenses, devices, methods, and / or systems for addressing refractive error are provided. Lenses, devices, methods, and / or systems may be used to correct, address, mitigate, or treat refractive errors, providing excellent vision at distances, including from far to near, without significant ghosting. Refractive errors may result, for example, from myopia, hyperopia, or presbyopia, with or without astigmatism. Certain embodiments of the disclosed lenses, devices, and / or methods include those that address foveal and / or peripheral vision. Exemplary lenses within the scope of certain embodiments include contact lenses, corneal onlays, corneal inlays, and lenses for intraocular devices (both anterior and posterior chambers), accommodating intraocular lenses, electro-active spectacle lenses, and / or refractive surgery.

Description

[Technical Field]

[0001] Certain disclosed embodiments include lenses, devices, and / or methods for modifying or controlling the wavefront of light entering the eye, particularly the human eye.

[0002] Certain disclosed embodiments are directed to lens, device, method, and / or system configurations for correcting or treating refractive error.

[0003] Certain disclosed embodiments are directed to lens, device, method, and / or system configurations for addressing refractive error while providing excellent vision from far to near distances without significant ghosting.

[0004] Certain disclosed embodiments include lenses, devices, and / or methods for correcting, treating, reducing, and / or addressing refractive error, particularly in the human eye. Refractive error may result, for example, from myopia or hyperopia, with or without astigmatism. Refractive error may result from presbyopia, alone or in combination with myopia or hyperopia and with or without astigmatism.

[0005] Certain disclosed embodiments of lenses, devices, and / or methods include embodiments that address foveal vision, certain embodiments address both foveal and peripheral vision, and certain other embodiments address peripheral vision.

[0006] Exemplary lenses in the field of certain embodiments include contact lenses, corneal on-lays, corneal inlays, and lenses for intraocular devices (both anterior and posterior chambers).

[0007] Exemplary devices within the scope of certain disclosed embodiments include accommodating intraocular lenses and / or electro-active spectacle lenses.

[0008] Exemplary methods within the scope of certain embodiments include methods for altering the refractive state and / or wavefront of light entering the eye and received by the retina of the eye (e.g., refractive surgery, corneal ablation), methods for designing and / or manufacturing lenses and optical devices, surgical methods for altering the refractive state of the eye, and methods for controlling stimuli for developing eye growth.

[0009] This application is related to Australian Provisional Application No. 2012 / 901,382, entitled "Devices and Methods for Refractive Error Control," filed on April 5, 2012, which is incorporated herein by reference in its entirety. This application claims priority to PCT Application No. PCT / AU2013 / 000354, entitled "Lenses, Devices, Methods and Systems for Refractive Error," filed April 5, 2013, U.S. Application No. 13 / 857,613, entitled "Lenses, Devices and Methods for Ocular Refractive Error," filed April 5, 2013, U.S. Application No. 2013202694, entitled "Lenses, Devices, Methods and Systems for Refractive Error," filed April 5, 2013, and Australian Provisional Application No. 2012 / 904,541, entitled "Lenses, Devices, and Methods for Ocular Refractive Error," filed October 17, 2012. Each of these Australian provisional applications is incorporated herein by reference in its entirety. Additionally, US Pat. Nos. 7,077,522 and 7,357,509 are each incorporated herein by reference in their entirety. [Background technology]

[0010] In order to clearly perceive an image, the optical structure of the eye must focus the image on the retina. Myopia, commonly known as nearsightedness, is an optical disorder of the eye in which an on-axis image is focused in front of the fovea of ​​the retina. Hyperopia, commonly known as farsightedness, is an optical disorder of the eye in which an on-axis image is focused behind the fovea of ​​the retina. Focusing an image in front of or behind the fovea of ​​the retina produces a low-order aberration of defocus. Another low-order aberration is astigmatism. The eye may also have higher-order optical aberrations, including, for example, spherical aberration, coma, and / or trefoil. Many people who experience naturally occurring refractive errors are progressive (gradual increase in refractive error). Progression is particularly prevalent in people with myopia.

[0011] Schematic diagrams of eyes exhibiting myopia or hyperopia and astigmatism are shown in Figures 1A-1C, respectively. In a myopic eye 100, a parallel incident light beam 102 passes through the eye's refractive elements, i.e., the cornea 104 and the lens 106, to a focal point 108 in front of the retina 110. Thus, the image on the retina 110 is blurred. In a hyperopic eye 120, a parallel incident light beam 122 passes through the eye's refractive elements, i.e., the cornea 124 and the lens 126, to a focal point 128 beyond the retina 110, also blurring the image on the retina 110. In an astigmatic eye 140, a parallel incident light beam 142 passes through the eye's refractive elements, i.e., the cornea 144 and the lens 146, to a focal point 128, again blurring the image on the retina 110. In an astigmatic eye 140, a parallel incident light beam 142 passes through the eye's refractive elements, i.e., the cornea 144 and the lens 146, to two foci, a tangential focus 148 and a sagittal focus 158. In the example of astigmatism shown in Figure 1C, the tangential focus 148 is in front of the retina 160, while the sagittal focus 158 is behind the retina 160. The image on the retina in the case of astigmatism is called the circle of least confusion 160.

[0012] At birth, human eyes are generally hyperopic; that is, the axial length of the eyeball is too short for its optical power. With age, from childhood through adulthood, the eyeball continues to grow until its refractive state stabilizes. Because eye elongation in developing humans is controlled by a feedback mechanism known as the emmetropization process, the position of the focal point relative to the retina plays a role in controlling the rate of eye growth. Deviations from this process likely result in refractive errors such as myopia, hyperopia, and / or astigmatism. While ongoing research explores the causes of deviations in emmetropization from stabilizing at emmetropia, one theory is that optical feedback may play a role in controlling eye growth. For example, Figure 2 illustrates a case in which the emmetropization process would be altered under the feedback mechanism theory. In FIG. 2A , a parallel incident light beam 202 passes through a negative refractive element 203 and the eye's refractive elements (cornea 204 and lens 206) to form an image at a focal point 208 that overshoots the retina 210. The resulting blurred image on the retina, called hyperopic defocus, is an example of defocus that may promote eye growth under this feedback mechanism. In contrast, as seen in FIG. 2B , a parallel incident light beam 252 passes through a positive refractive element 253 and the eye's refractive elements (cornea 254 and lens 256) to form an image at a focal point 258 in front of the retina 210. This resulting blurred image on the retina, called myopic defocus, is believed to be an example of retinal-induced defocus that will not promote eye growth. Therefore, it has been proposed that the progression of myopic refractive error can be controlled by positioning a focal point in front of the retina. In the case of astigmatic systems, the spherical equivalent, i.e., the midpoint between the tangential and sagittal foci, may be positioned in front of the retina. However, these proposals do not provide a complete explanation or solution, especially in the case of progressive myopia.

[0013] Several optical device designs and refractive surgery methods have been proposed to control eye growth during emmetropization. Many are based on improvements to the previously summarized idea that foveal imagery provides the stimulus to control eye growth. In humans, the eye grows and lengthens during emmetropization, but cannot shorten. Thus, during emmetropization, the eye grows and lengthens to correct hyperopia, but cannot shorten to correct myopia. Proposals have been made to address the progression of myopia.

[0014] In addition to the optical strategies proposed to combat the development and progression of refractive errors, particularly in myopia, there is also interest in strategies involving non-optical interventions, such as pharmacological agents such as atropine or pirenzepine.

[0015] Another ocular condition is presbyopia, in which the eye's ability to accommodate is reduced or the eye loses its ability to accommodate. Presbyopia may be experienced in combination with myopia, hyperopia, astigmatism, and higher-order aberrations. Different methods, devices, and lenses have been proposed to address presbyopia, including in the form of bifocal, multifocal, or progressive addition lenses / devices that provide two or more focal points to the eye simultaneously. Common types of lenses used for presbyopia include single-vision reading glasses, bifocal or multifocal glasses, center-near or center-distance bifocal and multifocal contact lenses, concentric (ring-type) bifocal contact lenses, or multifocal intraocular lenses.

[0016] Additionally, sometimes, removal of the eye's lens is necessary, for example, in patients suffering from cataracts. The removed natural lens may be replaced by an intraocular lens. Accommodating intraocular lenses allow the eye to control the refractive power of the lens, for example, through haptics extending from the lens to the ciliary body.

[0017] Masking has been proposed as a method for improving the depth of focus of the eye. However, masking is an undesirable property because it results in a loss of light to the eye, which at least degrades the contrast of the image projected onto the retina. Furthermore, these characteristics present challenges for implementing contact lenses and / or intraocular lenses on the lens, for example.

[0018] Some problems with existing lenses, devices, methods, and / or systems are that they attempt to correct refractive error but sacrifice quality of vision at different distances and / or introduce ghosting and / or distortion. Therefore, what is needed are lenses, devices, methods, and / or systems for reducing and / or addressing refractive error, e.g., myopia, hyperopia, or presbyopia, with or without astigmatism, without incurring at least one or more of the drawbacks described herein. Other solutions will become apparent as described herein. Summary of the Invention

[0019] Certain embodiments are directed to various ophthalmic lenses, devices, and / or methods for providing an aberration profile. Characteristics of the aberration profile and / or methods for identifying the aberration profile are described for myopic, hyperopic, and / or presbyopic eyes. Additionally, ophthalmic lenses, devices, and methods for providing an aberration profile are disclosed for an ophthalmic eye with astigmatism.

[0020] In certain embodiments, the ophthalmic lens has an optical axis and an aberration profile centered on the optical axis, the aberration profile having a focal length and including at least one of a first-order spherical aberration component C(4,0) and a second-order spherical aberration component C(6,0). The aberration profile provides a retina image quality (RIQ) with a through-focus slope that degrades in the direction of ocular growth and an RIQ of at least 0.3. The RIQ is the Visual Strehl Ratio measured along the optical axis at a wavelength selected from the range of 540 nm to 590 nm, inclusive, over a spatial frequency range of 0 cycles / degree to 30 cycles / degree, inclusive, for at least one pupil diameter in the range of 3 mm to 6 mm. In other embodiments, the RIQ measure may be different, for example, in some embodiments the RIQ measure may be a simple Strehl ratio in the spatial domain, a simple Strehl ratio in the frequency domain, a visual Strehl ratio with inclusion of the cosine of the phase transfer function, a visual Strehl ratio with a weighted contrast sensitivity function, a multifocal effect ratio, a metric obtained from two-dimensional correlation analysis in the spatial domain, a metric obtained from two-dimensional correlation analysis in the frequency domain, or one of many phase reversals in the frequency domain.

[0021] In certain embodiments, the lens includes an optical axis and an aberration profile centered on the optical axis, the aberration profile providing a focal length including C(2,0) Zernike coefficient terms, a peak visual Strehl ratio within a through-focus range (a "first visual Strehl ratio"), and a visual Strehl ratio that remains at or exceeds a second visual Strehl ratio throughout a through-focus range that includes the focal length, the visual Strehl ratio measured over a spatial frequency range from 0 cycles / degree to 30 cycles / degree, inclusive, at a wavelength selected from the range of 540 nm to 590 nm, inclusive, for at least one pupil diameter in the range of 3 mm to 5 mm, the first visual Strehl ratio being at least 0.35, the second visual Strehl ratio being at least 0.10, and the through-focus range being at least 1.8 diopters.

[0022] In certain embodiments, the lens includes an optical axis and an aberration profile centered on the optical axis, the aberration profile providing a focal length including C(2,0) Zernike coefficient terms, a peak RIQ within a through-focus range (a "first RIQ"), and an RIQ that remains at or exceeds a second RIQ throughout a through-focus range that includes the focal length, wherein the RIQ is a visual Strehl ratio measured over a spatial frequency range of 0 cycles / degree to 30 cycles / degree, inclusive, and at a wavelength selected from the range of 540 nm to 590 nm, inclusive, for at least one pupil diameter in the range of 3 mm to 5 mm, wherein the first visual Strehl ratio is at least 0.3 and the second visual Strehl ratio is at least 0.10, and the through-focus range is at least 1.8 diopters. In other embodiments, the RIQ measure may be different; for example, in some embodiments, the RIQ criterion may be one of a simple Strehl ratio in the spatial domain, a simple Strehl ratio in the frequency domain, a visual Strehl ratio in the spatial domain, a visual Strehl ratio in the frequency domain, a visual Strehl ratio with a weighted contrast sensitivity function, a multifocal effect ratio, a metric obtained from a two-dimensional correlation analysis in the spatial domain, a metric obtained from a two-dimensional correlation analysis in the frequency domain, or a number of phase reversals in the frequency domain. In certain embodiments, a method for a presbyopic eye includes identifying a wavefront aberration profile for the eye, the wavefront aberration profile including at least two spherical aberration terms greater than C(4.0). A prescribed focal length of the aberration profile is determined taking into account the spherical aberration, the prescribed focal length being at least +0.25D relative to a focal length for a C(2,0) Zernike coefficient term of the wavefront aberration profile. The method includes fabricating an ophthalmic device, lens, and / or corneal profile for the eye to affect the wavefront aberration profile.

[0023] In certain embodiments, a method for a myopic eye includes identifying a wavefront aberration profile for the eye and applying or prescribing the aberration profile. The wavefront aberration profile includes at least two spherical aberration terms, and a prescribed focal length of the aberration profile is determined taking into account the spherical aberration, and the prescribed focal length is at least +0.10D relative to a focal length for a C(2,0) Zernike coefficient term of the wavefront aberration profile. The wavefront aberration profile also provides degraded retinal image quality in a direction posterior to the retina.

[0024] Certain embodiments are directed to a method for a hyperopic eye, the method including identifying a wavefront aberration profile for the eye and applying or prescribing the aberration profile. The wavefront aberration profile includes at least two spherical aberration terms, and a prescribed focal length of the wavefront aberration profile is determined taking into account the spherical aberration. At the prescribed focal length, the wavefront aberration profile provides improved retinal image quality in a direction posterior to the retina.

[0025] In certain embodiments, a computing device includes an input for receiving a first combination of aberrations, one or more processors for calculating a second combination of aberrations for one or more optical surfaces, and an output for outputting the second combination of aberrations, where the calculated second combination of aberrations is combined with the first combination of aberrations to provide an overall combination of higher order aberrations (HOAs), as disclosed herein. In certain embodiments, the computing device can be used to generate a power profile, an aberration profile, a wavefront ablation profile, or a combination thereof. These calculations can then be used for contact lenses, corneal inlays, corneal onlays, single and dual element intraocular lenses (anterior and / or posterior chamber), accommodative intraocular lenses, wavefront ablation for corneal refractive surgery techniques, and other suitable devices and / or applications.

[0026] The aberration profiles disclosed herein may be used on the optic zone of a lens, a portion of the optic zone of a lens, or a significant portion of the optic zone of a lens. The extent to which the optic zone of a lens includes an aberration profile may depend on the particular application of the disclosed embodiments. In particular applications, the aberration profiles disclosed herein may be used on at least two, three, or four portions of the optic zone of a lens. These multiple portions may be separate, overlapping, or a combination thereof. The multiple portions of the aberration profile used on one or more portions of the optic zone of a lens may have the same aberration profile or power profile, substantially the same aberration profile or power profile, different aberration profiles or power profiles, or a combination thereof. In certain embodiments, the aberration profiles disclosed herein may be used on at least 10%, 20%, 30%, 40%, or 50% of the optic zone of a lens. In certain embodiments, the aberration profiles and / or power profiles disclosed herein may be used in between 5% and 10%, between 5% and 30%, between 5% and 50%, between 5% and 75%, between 5% and 95%, between 50% and 95%, or between 60% and 99% of the optical zone of the lens. An ophthalmic lens, the lens comprising an optical axis and an aberration profile associated with the optical axis and a focal length, the aberration profile comprising four or more high-order aberrations, the lens configured to provide the visual performance of a correctly prescribed single vision lens at at least a far viewing distance and to provide minimal ghosting at far, intermediate, and near distances, the lens also configured to provide a Strehl ratio at the focal length of at least 0.2 and a through-focus slope of the Strehl ratio that decreases at the negative power end of the through-focus range, the Strehl ratio measured substantially along the optical axis over a spatial frequency range of 0 cycles / degree to 30 cycles / degree, inclusive, and at a wavelength selected from the range of 540 nm to 590 nm, inclusive, for at least a portion of an optical zone diameter of 3 mm to 6 mm.

[0027] The particular high-order aberration profiles and resulting through-focus retinal image quality described and / or claimed have the advantage, among other things, that they allow for ghosting to be minimized at a variety of distances from far, intermediate, and near.

[0028] The particular at least three higher-order aberration terms described and / or claimed and the resulting through-focus retinal image quality have, among other advantages, the ability to minimize ghosting at a variety of distances from far, intermediate, and near.

[0029] The particular at least four higher-order aberration terms described and / or claimed and the resulting through-focus retinal image quality have, among other advantages, the ability to minimize ghosting at a variety of distances from far, intermediate, and near.

[0030] The particular high-order aberration profiles and resulting through-focus retinal image quality described and / or claimed have the advantage, among other things, that they provide improved visual acuity at a variety of distances from far, intermediate, and near.

[0031] The particular high-order aberration profiles and resulting through-focus retinal image quality described and / or claimed have the advantages that, among other things, they provide improved visual acuity at a variety of distances from far, intermediate, and near, and minimize the occurrence of ghosting.

[0032] The particular high-order aberration profiles described and / or claimed and the resulting RIQ of at least 0.3 and through-focus RIQ slope that degrades in the direction of eye growth have the advantage, among other things, that they allow for minimized ghosting at a variety of distances from far, intermediate, and near, and have the potential to attenuate myopia progression.

[0033] The particular high-order aberration profiles described and / or claimed and the resulting RIQ of at least 0.3 and through-focus RIQ tilt improving in the direction of eye growth have the advantage, among other things, that they allow for minimized ghosting at a variety of distances from far, intermediate, and near, and have potential correction for hyperopia.

[0034] The particular high-order aberration profiles described and / or claimed, including at least four spherical aberration terms selected from the group C(4,0) to C(20,0), have the advantage that, among other things, they improve visual acuity, enable minimized ghosting at a variety of distances from far, intermediate, and near, and provide a lens with potential correction for hyperopia.

[0035] The particular high-order aberration profiles described and / or claimed, and the resulting first visual Strehl ratios of at least 0.35, second visual Strehl ratios of at least 0.1, and through-focus ranges of at least 1.8D, have the advantage, among other things, that they provide improved visual acuity at distances ranging from far and intermediate distances and / or enable ghosting to be minimized at distances ranging from far and intermediate distances.

[0036] The particular high-order aberration profiles described and / or claimed, and the resulting first visual Strehl ratios of at least 0.35, second visual Strehl ratios of at least 0.1, and through-focus ranges of at least 2.25D, have the advantage, among other things, that they provide improved visual acuity at distances ranging from far, intermediate, and near distances, and / or enable ghosting to be minimized at distances ranging from far, intermediate, and near distances.

[0037] The particular high-order aberration profiles described and / or claimed, and the resulting retinal image quality of multifocal lenses, have the advantage, inter alia, that they provide visual performance at intermediate and far distances that is at least substantially equivalent to the visual performance of a correctly prescribed single vision lens at far viewing distances, and that is configured to allow for minimized ghosting at far, intermediate, and near distances.

[0038] The particular high-order aberration profiles and resulting retinal image qualities described and / or claimed have the advantage, among other things, that they allow ghosting to be minimized at a variety of distances from far, intermediate, and near.

[0039] The particular high-order aberration profiles and resulting retinal image qualities described and / or claimed have the advantage, among other things, that they allow ghosting to be minimized at a variety of distances from far and intermediate distances.

[0040] The particular two or more higher order aberration profiles described and / or claimed having one or more of the following components: 1st order spherical aberration C(4.0), 2nd order spherical aberration C(6.0), 3rd order spherical aberration C(8.0), 4th order spherical aberration C(10.0), 5th order spherical aberration C(12.0), 6th order spherical aberration C(14.0), 7th order spherical aberration C(16.0), 8th order spherical aberration C(18.0), and 9th order spherical aberration C(20.0), and a resulting through-focus slope of the visual Strehl ratio such that the sloped visual Strehl ratio decreases in the direction of eye growth, have the advantages that, among other things, they allow for improved visual acuity at distances, minimized ghosting, and have the potential to attenuate the progression of myopia.

[0041] The particular aberration profiles described and / or claimed, consisting of at least two spherical aberration terms and a defocus term, have the advantage, among other things, that they provide a lens with visual performance at near viewing distances that is within 2 units of the visual performance of a properly prescribed single vision lens at distance viewing distances.

[0042] The particular aberration profiles described and / or claimed, consisting of at least two spherical aberration terms and a defocus term, have the advantage, inter alia, that they provide multifocal lenses with visual performance on a visual analog scale at near viewing distances having a score of 9 or higher in 25%, 30%, 35%, 40%, 45%, 50%, or 55% of a representative sample of presbyopes.

[0043] The particular high-order aberration profiles described and / or claimed, selected at least in part from the group including spherical aberration coefficients C(4,0) to C(20,0), have the advantage, among other things, that they provide correction of up to 1 diopter of astigmatism without substantially using rotationally stable toric lens design features.

[0044] The particular described and / or claimed high-order aberration profiles, selected at least in part from the group including spherical aberration coefficients C(4,0) to C(20,0), have the advantage, among other things, that they provide an increase in the depth of focus of the eye by modifying retinal image quality over a predetermined distance range.

[0045] The described and / or claimed intraocular lens system, comprising a first lens, a second lens, and at least three higher-order aberration terms, has the advantage, inter alia, of providing improved visual acuity along a substantially continuous range of viewing distances, including near, intermediate, and far distances, that is substantially equivalent to the visual performance of a correctly prescribed single vision lens at far viewing distances.

[0046] The described and / or claimed power profiles, which transition between a maximum value and a minimum value, where the maximum value is within 0.2 mm of the center of the optical zone and the minimum value is no more than 0.3 mm, 0.6 mm, 0.9 mm or 1.0 mm from the maximum value, and where the amplitude of the transition between the maximum value and the minimum value is at least 2.5D, 4D, 5D or 6D, have the advantage, inter alia, that they provide a lens configured to provide visual performance over intermediate and far distances that is at least substantially equivalent to the visual performance of a correctly prescribed single vision lens at far viewing distances, and the lens is configured to provide minimal ghosting at far, intermediate and near distances.

[0047] Further embodiments and / or advantages of one or more embodiments will become apparent from the following description, given by way of example, and with reference to the accompanying drawings, in which: [Brief explanation of the drawings]

[0048] These and other features, aspects, and advantages of the present disclosure will become better understood with regard to the following description, appended claims, and accompanying drawings. [Figure 1A] 1A-1C are schematic diagrams of an eye showing myopia, hyperopia, and astigmatism, respectively. [Figure 1B] 1A-1C are schematic diagrams of an eye showing myopia, hyperopia, and astigmatism, respectively. [Figure 1C] 1A-1C are schematic diagrams of an eye showing myopia, hyperopia, and astigmatism, respectively. [Figure 2A] 1A and 1B are schematic diagrams of hyperopic and myopic defocus induced in the retina, respectively. [Figure 2B] 1A and 1B are schematic diagrams of hyperopic and myopic defocus induced in the retina, respectively. [Figure 3] FIG. 10 illustrates a two-dimensional through-focus point spread function calculated at the retinal plane in the absence of high-order aberrations (HOAs), and in the presence of spherical aberration HOA, vertical coma, and horizontal trefoil, according to certain embodiments. [Figure 4]10A-10C are graphs of the interaction of first-order spherical aberration with horizontal coma, vertical coma, horizontal trefoil, and vertical trefoil, respectively, in accordance with certain embodiments. [Figure 5] 10A-10C are graphs of the interaction of first-order spherical aberration with horizontal coma, vertical coma, horizontal trefoil, and vertical trefoil, respectively, in accordance with certain embodiments. [Figure 6] 10A-10C are graphs of the interaction of first-order spherical aberration with horizontal coma, vertical coma, horizontal trefoil, and vertical trefoil, respectively, in accordance with certain embodiments. [Figure 7] 10A-10C are graphs of the interaction of first-order spherical aberration with horizontal coma, vertical coma, horizontal trefoil, and vertical trefoil, respectively, in accordance with certain embodiments. [Figure 8] 10 is a graph illustrating the magnitude of myopic progression under an optical feedback mechanism for eye growth of primary spherical aberration versus primary vertical astigmatism versus primary horizontal astigmatism according to certain embodiments. [Figure 9] 10 is a graph illustrating the magnitude of myopia progression of primary spherical aberration versus secondary vertical astigmatism versus secondary horizontal astigmatism according to certain embodiments. [Figure 10] 1 is a graph illustrating myopia progression on a binary scale of primary versus secondary spherical aberration in accordance with certain embodiments. [Figure 11] 1 is a graph illustrating myopia progression on a binary scale of first order spherical aberration versus third order spherical aberration in accordance with certain embodiments. [Figure 12] 1 is a graph illustrating myopia progression on a binary scale of first order versus fourth order spherical aberration in accordance with certain embodiments. [Figure 13] 1 is a graph illustrating myopia progression on a binary scale of first order spherical aberration vs. second order spherical aberration vs. third order spherical aberration according to certain embodiments. [Figure 14] 10A-10C illustrate exemplary designs of aberration profiles providing negative and positive gradients RIQ in the direction of eye growth according to certain embodiments. [Figure 15] 1 is a workflow diagram for myopia (progressive or non-progressive) according to certain embodiments. [Figure 16]1 is a workflow diagram for a hyperopic eye (progressive or non-progressive) toward emmetropia, according to certain embodiments. [Figure 17] 1A-1C illustrate exemplary designs of power profiles for correcting lenses across the optical zone diameter to affect the optical feedback mechanism for myopia, according to certain embodiments. [Figure 18] 1A-1C illustrate exemplary designs of power profiles for correcting lenses across the optical zone diameter to affect the optical feedback mechanism for myopia, according to certain embodiments. [Figure 19] 1A-1C illustrate exemplary designs of power profiles for correcting lenses across the optical zone diameter to affect the optical feedback mechanism for myopia, according to certain embodiments. [Figure 20] 1A-1C illustrate exemplary designs of power profiles for correcting lenses across the optical zone diameter to affect the optical feedback mechanism for myopia, according to certain embodiments. [Figure 21] 1A-1C illustrate exemplary designs of power profiles for correcting lenses across the optical zone diameter to affect the optical feedback mechanism for myopia, according to certain embodiments. [Figure 22] 1A-1C illustrate exemplary designs of power profiles for correcting lenses across the optical zone diameter to affect the optical feedback mechanism for myopia, according to certain embodiments. [Figure 23] 1A-1C illustrate exemplary designs of power profiles for correcting lenses across the optical zone diameter to affect the optical feedback mechanism for myopia, according to certain embodiments. [Figure 24] 1A-1C illustrate exemplary designs of power profiles for correcting lenses across the optical zone diameter to affect the optical feedback mechanism for myopia, according to certain embodiments. [Figure 25]1A-1C illustrate exemplary designs of power profiles for correcting lenses across the optical zone diameter to affect the optical feedback mechanism for myopia, according to certain embodiments. [Figure 26] 10A-10C illustrate exemplary designs of power profiles for correcting lenses across the optical zone diameter to affect the optical feedback mechanism for hyperopia, according to certain embodiments. [Figure 27] FIG. 1 shows the global through-focus retinal image quality (TFRIQ) of the aberration profile corresponding to a single focal length lens. [Figure 28] FIG. 10 shows the global TFRIQ of the first aberration profile (iteration A1), which may have application for progressive myopia. [Figure 29] FIG. 1 illustrates a power profile of a lens for providing a first aberration profile (iteration A1) according to certain embodiments. [Figure 30] FIG. 10 illustrates the global TFRIQ of a second aberration profile (iteration A2), which may also have application for progressive myopia, according to certain embodiments. [Figure 31] FIG. 10 illustrates the full chord diameter power profile of a second aberration profile (iteration A2) in accordance with certain embodiments. [Figure 32] FIG. 10 illustrates the global TFRIQ of the third and fourth aberration profiles (iteration C1 and iteration C2), which may have application for a hyperopic eye, in accordance with certain embodiments. [Figure 33] FIG. 10 illustrates the global TFRIQ of the third and fourth aberration profiles (iteration C1 and iteration C2), which may have application for a hyperopic eye, in accordance with certain embodiments. [Figure 34]10A and 10B show power profiles across optical cord diameters for third and fourth aberration profiles (iteration C1 and iteration C2), which may have application for hyperopic eyes in accordance with certain embodiments. [Figure 35] 10A and 10B show power profiles across optical cord diameters for third and fourth aberration profiles (iteration C1 and iteration C2), which may have application for hyperopic eyes in accordance with certain embodiments. [Figure 36] 1 shows the retinal image quality (RIQ) of seven aberration profiles over a 2.5D through-focus range, corresponding to three exemplary aberration profiles (Iteration B1, Iteration B2, Iteration B3) obtained after optimizing central distance or central near (aspheric multifocal and concentric ring / annulus type bifocal) and through-focus performance according to certain embodiments. [Figure 37] FIG. 37 illustrates the power profile of a contact lens across the optical zone diameter to provide the TFRIQ described in FIG. 36, according to certain embodiments. [Figure 38] FIG. 37 illustrates the power profile of a contact lens across the optical zone diameter to provide the TFRIQ described in FIG. 36, according to certain embodiments. [Figure 39] FIG. 37 illustrates the power profile of a contact lens across the optical zone diameter to provide the TFRIQ described in FIG. 36, according to certain embodiments. [Figure 40] FIG. 37 illustrates the power profile of a contact lens across the optical zone diameter to provide the TFRIQ described in FIG. 36, according to certain embodiments. [Figure 41] FIG. 37 illustrates the power profile of a contact lens across the optical zone diameter to provide the TFRIQ described in FIG. 36, according to certain embodiments. [Figure 42] FIG. 37 illustrates the power profile of a contact lens across the optical zone diameter to provide the TFRIQ described in FIG. 36, according to certain embodiments. [Figure 43] FIG. 37 illustrates the power profile of a contact lens across the optical zone diameter to provide the TFRIQ described in FIG. 36, according to certain embodiments. [Figure 44] FIG. 10 illustrates on-axis TFRIQ for three exemplary embodiments (iterations B1, B2, and B3) for presbyopia across four pupil diameters (3 mm to 6 mm), according to certain embodiments. [Figure 45] FIG. 10 illustrates on-axis TFRIQ for three exemplary embodiments (iterations B1, B2, and B3) for presbyopia across four pupil diameters (3 mm to 6 mm), according to certain embodiments. [Figure 46] FIG. 10 illustrates on-axis TFRIQ for three exemplary embodiments (iterations B1, B2, and B3) for presbyopia across four pupil diameters (3 mm to 6 mm), according to certain embodiments. [Figure 47] FIG. 10 shows an on-axis TFRIQ for central distance or central near concentric designs across four pupil diameters (3 mm to 6 mm), according to certain embodiments. [Figure 48] FIG. 10 shows an on-axis TFRIQ for central distance or central near concentric designs across four pupil diameters (3 mm to 6 mm), according to certain embodiments. [Figure 49] FIG. 10 shows the on-axis TFRIQ of a central distance or central near aspheric multifocal design across four pupil diameters (3 mm to 6 mm), according to certain embodiments. [Figure 50] FIG. 10 shows the on-axis TFRIQ of a central distance or central near aspheric multifocal design across four pupil diameters (3 mm to 6 mm), according to certain embodiments. [Figure 51] FIG. 1 illustrates a monocular correction approach for presbyopia according to certain embodiments, in which different high-order aberration profiles are provided to the right and left eyes, thereby resulting in different through-focus optical and / or visual performance (desired vergence) for the right and left eyes, to provide a combined add power range of 1.5D and 2.5D on the negative side of the through-focus curve. [Figure 52]FIG. 1 illustrates a monocular correction approach for presbyopia according to certain embodiments, in which different high-order aberration profiles are provided to the right and left eyes, thereby resulting in different through-focus optical and / or visual performance (desired vergence) for the right and left eyes, to provide a combined add power range of 1.5D and 2.5D on the negative side of the through-focus curve. [Figure 53] FIG. 1 illustrates a monocular correction approach for presbyopia according to certain embodiments, in which different high-order aberration profiles are provided to the right and left eyes, thereby resulting in different through-focus optical and / or visual performance (desired vergence) for the right and left eyes, to provide a combined add power range of 1.5D and 2.5D on the positive side of the through-focus curve. [Figure 54] FIG. 1 illustrates a monocular correction approach for presbyopia according to certain embodiments, in which different high-order aberration profiles are provided to the right and left eyes, thereby resulting in different through-focus optical and / or visual performance (desired vergence) for the right and left eyes, to provide a combined add power range of 1.5D and 2.5D on the positive side of the through-focus curve. [Figure 55] 5A-5C show the global TFRIQ of three further iterations of the aberration profile (iterations A3, A4, and A5 shown in FIGS. 56, 57, and 58, respectively) to provide substantially constant retinal image quality across a horizontal field of view from 0 degrees to 30 degrees, in accordance with certain embodiments. [Figure 56] FIG. 10 illustrates the generation of an on-axis RIQ for iteration A3, according to certain embodiments. [Figure 57] FIG. 10 illustrates the generation of an on-axis RIQ for iteration A4, according to certain embodiments. [Figure 58] FIG. 10 illustrates the generation of an on-axis RIQ for iteration A5, according to certain embodiments. [Figure 59]FIG. 10 illustrates an exemplary design of a power profile correcting a contact lens with an anti-phase profile (iteration E1 and iteration E2), according to certain embodiments. [Figure 60] FIG. 10 illustrates an exemplary design of a power profile correcting a contact lens with an anti-phase profile (iteration E1 and iteration E2), according to certain embodiments. [Figure 61] FIG. 10 illustrates on-axis TFRIQ for iterations E1 and E2 with three different levels of intrinsic first-order spherical aberration for a candidate eye, according to certain embodiments. [Figure 62] FIG. 10 illustrates on-axis TFRIQ for iterations E1 and E2 with three different levels of intrinsic first-order spherical aberration for a candidate eye, according to certain embodiments. [Figure 63] FIG. 10 illustrates on-axis TFRIQ for iterations E1 and E2 with three different levels of intrinsic first-order spherical aberration for a candidate eye, according to certain embodiments. [Figure 64] FIG. 1 shows the TFRIQ performance measure (depth of focus) for 78 exemplary aberration profiles (Appendix A) including combinations of spherical aberration terms. The Y-axis of the graph shows the "Q" performance metric, and the X-axis shows the through-focus range of -1.5D to +1D. In this example, calculations were performed for a 4mm pupil. The solid black line shows the through-focus performance of combinations without spherical aberration modes, while the gray line shows 78 combinations including at least one higher-order spherical aberration term. The 78 combinations were selected for performance on the negative side of the through-focus curve, according to certain embodiments. [Figure 65] FIG. 57 illustrates the TFRIQ of one exemplary combination from FIG. 56 including only positive spherical aberration compared to a combination without any spherical aberration, in accordance with certain embodiments. [Figure 66]FIG. 1 shows the TFRIQ performance measure (depth of focus) for 67 exemplary aberration profiles (Appendix C) including combinations of spherical aberration terms. The Y-axis of the graph shows the "Q" performance metric, and the X-axis shows the through-focus range of -1.5D to +1D. In this example, calculations were performed for a 4mm pupil. The solid black line shows the through-focus performance of combinations without spherical aberration modes, while the gray line shows 67 combinations including at least one higher-order spherical aberration term. These 67 combinations improve performance on the positive side of the through-focus curve, according to certain embodiments. [Figure 67] 1 is a workflow diagram for presbyopia in accordance with certain embodiments. [Figure 68] FIG. 1 illustrates the power profile of a toric prescription for an astigmatism / presbyopia contact lens according to certain embodiments. [Figure 69] 1A-1C illustrate exemplary lens power profiles obtainable from exemplary combinations of spherical aberration terms according to certain embodiments. [Figure 70] FIG. 1 illustrates a lens power profile converted to an axial thickness profile for a contact lens according to certain embodiments. [Figure 71] FIG. 1 shows an example of an axial power profile (iteration G1) of a lens across the full cord diameter, according to certain embodiments, which is an illustration of one of a set of designs whose performance is substantially independent of the candidate eye's inherent spherical aberration. [Figure 72] 1 illustrates an example TFRIQ, referred to as iteration G1, at a 4 mm pupil diameter in accordance with certain embodiments. The Y-axis shows the RIQ performance metric, and the X-axis shows the through-focus range from -1 D to +1.75 D. The four different legends, namely, solid black line, solid gray line, dashed black line, and double solid line, represent four different levels of spherical aberration in a sample of the aberrant population at a 5 mm pupil diameter. [Figure 73]1 illustrates an example TFRIQ, referred to as iteration G1, at a 5mm pupil diameter in accordance with certain embodiments. The Y-axis shows the RIQ performance metric, and the X-axis shows the through-focus range from -1D to +1.75D. The four different legends, namely, solid black line, solid gray line, dashed black line, and double solid line, represent five different levels of spherical aberration in a sample of the aberrant population at a 5mm pupil diameter. [Figure 74] FIG. 10 shows an example of an axial power profile (iteration J1) of a lens across a half-chord diameter, according to certain embodiments, which is an illustration of one of a set of designs for an intraocular lens used to restore vision at distances including far and near distances after removal of the intraocular lens. [Figure 75] FIG. 10 shows an example of an axial thickness profile (iteration J1) of a lens across a half-chord diameter, according to certain embodiments, which is an illustration of one design set for an intraocular lens used to restore vision at distances including far and near distances after removal of the intraocular lens. [Figure 76] FIG. 1 shows the power profiles of 11 different contact lenses across half-chord diameters; these 11 different designs (iterations K1-K11) represent several designs of commercially available lenses. [Figure 77] FIG. 1 shows the power profiles of four different lenses across half-chord diameters; these four different designs (iterations R1-R4) are illustrative of certain embodiments. [Figure 78] Figure 7 shows the normalized absolute magnitude of the amplitude spectrum of the fast Fourier transform of 11 different contact lenses (iterations K1 to K11) as a function of spatial frequency in cycles / mm. These are the 11 lenses presented in Figure 76. [Figure 79]1 shows the normalized absolute magnitude of the amplitude spectrum of the fast Fourier transform of four different lens designs (iterations R1-R4) as a function of spatial frequency in cycles / mm. These four designs are illustrative of certain embodiments. [Figure 80] FIG. 7 shows the absolute first derivative of 11 different contact lenses (iterations K1-K11) as a function of half-chord diameter (mm). These are the 11 lenses presented in FIG. 76. [Figure 81] 1 shows the absolute first derivative of four different contact lenses (iterations R1-R4) as a function of half-chord diameter (mm). These four designs are illustrative of certain embodiments. [Figure 82] 1 shows the average subjective ratings measured on a visual analog scale for distance visual acuity for a sample of the affected presbyopic population, where lenses H-K are four examples of specific embodiments and lenses A-G are commercially available lenses. [Figure 83] 1 shows the mean subjective ratings measured on a visual analog scale for intermediate vision for a sample of the affected presbyopic population, where lenses H-K are four examples of specific embodiments and lenses A-G are commercially available lenses. [Figure 84] 1 shows the mean subjective ratings measured on a visual analog scale for near vision for a sample of the affected presbyopic population, where Lenses H-K are four examples of specific embodiments and Lenses A-G are commercially available lenses. [Figure 85] 1 shows the mean subjective ratings measured on a ghosting analogue scale for distance vision for a sample of the affected presbyopic population, where lenses H-K are four examples of specific embodiments and lenses A-G are commercially available lenses. [Figure 86]1 shows the mean subjective ratings measured on a ghosting analog scale for near vision for a sample of the affected presbyopic population, where Lenses H-K are four examples of specific embodiments and Lenses A-G are commercially available lenses. [Figure 87] 1 shows the mean subjective ratings measured on a visual analog scale for overall visual acuity for a sample of the affected presbyopic population, where lenses H-K are four examples of specific embodiments and lenses A-G are commercially available lenses. [Figure 88] 1 shows the mean subjective ratings measured on a ghost-free analog scale for distance vision for a sample of the affected presbyopic population, where Lenses H-K are four examples of specific embodiments and Lenses A-G are commercially available lenses. [Figure 89] 1 shows the mean subjective ratings measured on a ghost-free analog scale for near vision for a sample of the affected presbyopic population, where Lenses H-K are four examples of specific embodiments and Lenses A-G are commercially available lenses. [Figure 90] 1 shows the mean subjective ratings measured on a ghosting analog scale for combined distance and near visual acuity for a sample of the susceptible presbyopic population. Lenses H-K are four examples of specific embodiments, while lenses A-G are commercially available lenses. [Figure 91] 1 shows the mean subjective ratings measured on a visual analog scale for cumulative visual performance, including distance, intermediate, and near visual acuity, and freedom from ghosting at distance and near, for a sample of the affected presbyopic population. Lenses H-K are examples of specific embodiments, while lenses A-G are commercially available lenses. [Figure 92] Figure 1 shows the percentage of people whose subjective rating of distance visual acuity on a visual analog scale was greater than 9. Data was obtained from a sample of the affected presbyopic population. Lenses H-K are illustrative of specific embodiments, while Lenses A-G are commercially available lenses. [Figure 93]Figure 1 shows the percentage of people whose subjective rating score on a visual analog scale for intermediate vision was greater than 9. Data was obtained from a sample of the affected presbyopic population. Lenses H-K are illustrative of specific embodiments, while Lenses A-G are commercially available lenses. [Figure 94] Figure 1 shows the percentage of people whose subjective rating of near visual acuity on a visual analog scale was greater than 9. Data was obtained from a sample of the affected presbyopic population. Lenses H-K are illustrative of specific embodiments, while Lenses A-G are commercially available lenses. [Figure 95] Figure 1 shows the percentage of people whose subjective assessment of overall visual acuity on a visual analog scale was greater than 9. Data was obtained from a sample of the affected presbyopic population. Lenses H-K are illustrative of specific embodiments, while Lenses A-G are commercially available lenses. [Figure 96] Figure 1 shows the percentage of people whose subjective rating of distance visual acuity on a ghosting analog scale exceeded a score of 3. Data was obtained from a sample of the affected presbyopic population. Lenses H-K are illustrative of specific embodiments, while Lenses A-G are commercially available lenses. [Figure 97] Figure 1 shows the percentage of people whose subjective rating score on a ghosting analog scale for near visual acuity was greater than 3. Data was obtained from a sample of the affected presbyopic population. Lenses H-K are illustrative of specific embodiments, while Lenses A-G are commercially available lenses. [Figure 98] Figure 1 shows the percentage of people whose subjective rating score on a visual analog scale for cumulative visual acuity was greater than 9. The cumulative visual acuity rating was obtained by averaging the distance, intermediate, near, and total visual acuity ratings, as well as the absence of ghosting at distance and near. Data was obtained from a sample of the affected presbyopic population. Lenses H-K are illustrative of specific embodiments, while Lenses A-G are commercially available lenses. [Figure 99]

[0023] Figure 1 shows the mean objective measures of high-contrast visual acuity for a sample of the anomalous presbyopic population. Measures were obtained using a 6-meter test distance and presented on the logMAR scale. Lenses H-K are illustrative of specific embodiments, while lenses A-G are commercially available lenses. [Figure 100]

[0023] Figure 1 shows the mean objective measures of contrast sensitivity for a sample of the affected presbyopic population. Measures were obtained using a 6-meter test distance and presented on the logMAR scale. Lenses H-K are illustrative of specific embodiments, while lenses A-G are commercially available lenses. [Figure 101]

[0023] Figure 1 shows mean objective measures of low-contrast visual acuity for a sample of the affected presbyopic population. Measures were obtained using a 6-meter test distance and presented on the logMAR scale. Lenses H-K are illustrative of specific embodiments, while lenses A-G are commercially available lenses. [Figure 102]

[0023] Figure 1 shows the mean objective measures of intermediate visual acuity for a sample of the affected presbyopic population using a 70 centimeter test distance. Measures are presented on the logMAR scale. Lenses H-K are illustrative of specific embodiments, while lenses A-G are commercially available lenses. [Figure 103]

[0023] Figure 1 shows the mean objective measures of near visual acuity for a sample of the affected presbyopic population using a 50 centimeter test distance. Measures are presented on the logMAR scale. Lenses H-K are illustrative of specific embodiments, while lenses A-G are commercially available lenses. [Figure 104]

[0023] Figure 1 shows the mean objective measures of near visual acuity for a sample of the affected presbyopic population using a 40 centimeter test distance. Measures are presented on the logMAR scale. Lenses H-K are illustrative of specific embodiments, while lenses A-G are commercially available lenses. [Figure 105]

[0023] Figure 1 shows the mean objective measures of combined visual acuity for a sample of the affected presbyopic population. The combined visual acuity includes a distance measure, a 70 cm intermediate measure, and a 50 cm near measure. The measures are presented on the logMAR scale. Lenses H-K are examples of specific embodiments, while lenses A-G are commercially available lenses. [Figure 106] FIG. 1 shows the mean objective measures of combined visual acuity for a sample of the affected presbyopic population. The combined visual acuity includes a distance scale of 6 meters, an intermediate scale of 70 cm, and a near scale of 50 cm. The scales are presented on the logMAR scale. Lenses H-K are examples of specific embodiments, while lenses A-G are commercially available lenses. [Figure 107] Figure 1 shows the percentage of people whose subjective rating score on a visual analogue scale for ghosting at distance or near equaled 1. Data was obtained from a sample of the affected presbyopic population. Lenses H-K are illustrative of specific embodiments, while lenses A-G are commercially available lenses. [Figure 108] Figure 1 shows the percentage of people whose subjective rating score on a visual analogue scale for ghosting at distance or near was less than 2. Data was obtained from a sample of the affected presbyopic population. Lenses H-K are illustrative of specific embodiments, while lenses A-G are commercially available lenses. [Figure 109] 1 illustrates the power profiles of three exemplary embodiments across half-chord diameters. The power profiles of the three designs start at approximately 3D in the center and gradually decrease to 0D power at half-chord diameters of 0.5 mm, 0.75 mm, and 1 mm. [Figure 110] Figure 109 shows the real part of the optical transfer function (for a 4 mm optic zone diameter) as a function of spatial frequency for the lens profile disclosed in Figure 109. The neural contrast sensitivity function is also plotted as a function of spatial frequency to facilitate evaluation of the effect of the designed positive power at the center of the lens on the optical transfer function. [Figure 111] 1 illustrates the power profiles of three exemplary embodiments across half-chord diameters. The power profiles of the three designs start at approximately 6D in the center and gradually decrease to 0D power at half-chord diameters of 0.5mm, 0.75mm, and 1mm. [Figure 112] Figure 112 shows the real part of the optical transfer function (for a 4 mm pupil diameter) as a function of spatial frequency for the lens profile disclosed in Figure 111. The neural contrast sensitivity function is also plotted as a function of spatial frequency to facilitate evaluation of the effect of the designed positive power at the center of the lens on the optical transfer function. [Figure 113] 1 shows the power profiles of three exemplary embodiments across half-chord diameters. The power profiles of the three designs start at approximately 10D in the center and gradually decrease to 0D power at half-chord diameters of 0.5mm, 0.75mm, and 1mm. [Figure 114] Figure 115 shows the real part of the optical transfer function (for a pupil diameter of 4 mm) as a function of spatial frequency for the lens profile disclosed in Figure 114. The neural contrast sensitivity function is also plotted as a function of spatial frequency to facilitate evaluation of the effect of the designed positive power at the center of the lens on the optical transfer function. [Figure 115] Figure 115 shows the power profiles of several exemplary embodiments across the half-chord diameter with varying positive powers ranging from +3D to +7D with varying zone widths ranging from 0.25mm to 1mm of the half-chord of the lens. Figure 115 shows the through-focus image quality ("Q" metric) of five exemplary combinations with high-order aberrations (T1-T5), including symmetric high-order aberrations. [Figure 116] FIG. 1 shows the power profiles of two exemplary embodiments of contact lens designs (N41 and N42) across half-chord diameters. [Figure 117]

[0023] Figure 1 shows the through-focus image quality ("Q" metric) of two exemplary contact lenses (N41 and N42) calculated for a 3mm pupil diameter. The solid and double lines represent the through-focus image quality of two exemplary designs, N41 and N42, where one design is used in one eye and the other design is used in the fellow eye. The dashed lines represent binocular performance. [Figure 118] FIG. 10 shows the through-focus retinal image quality of two exemplary designs N41 and N42 calculated at a 3 mm pupil diameter. [Figure 119] Figure 1 shows measured power profiles of 10 commercially available contact lens designs across half-chord diameters. These power profile measurements were obtained with a commercially available Hartmann-Shack based power mapping system, Optocraft (Optocraft GmbH, Germany). [Figure 120] Figure 1 shows measured power profiles of 10 commercially available contact lens designs across half-chord diameters. These power profile measurements were obtained with a commercially available Hartmann-Shack based power mapping system, Optocraft (Optocraft GmbH, Germany). [Figure 121] Figure 1 shows measured power profiles of 10 commercially available contact lens designs across half-chord diameters. These power profile measurements were obtained with a commercially available Hartmann-Shack based power mapping system, Optocraft (Optocraft GmbH, Germany). [Figure 122] Figure 1 shows measured power profiles of 10 commercially available contact lens designs across half-chord diameters. These power profile measurements were obtained with a commercially available Hartmann-Shack based power mapping system, Optocraft (Optocraft GmbH, Germany). [Figure 123]Figure 1 shows measured power profiles of 10 commercially available contact lens designs across half-chord diameters. These power profile measurements were obtained with a commercially available Hartmann-Shack based power mapping system, Optocraft (Optocraft GmbH, Germany). [Figure 124] FIG. 1 illustrates the power profiles of 12 exemplary embodiments of contact lens designs across half-chord radii. [Figure 125] FIG. 1 illustrates the power profiles of 12 exemplary embodiments of contact lens designs across half-chord radii. [Figure 126] FIG. 1 illustrates the power profiles of 12 exemplary embodiments of contact lens designs across half-chord radii. [Figure 127] FIG. 1 illustrates the power profiles of 12 exemplary embodiments of contact lens designs across half-chord radii. [Figure 128] FIG. 1 illustrates the power profiles of 12 exemplary embodiments of intraocular lens designs across half-chord diameters. [Figure 129] FIG. 1 illustrates the power profiles of 12 exemplary embodiments of intraocular lens designs across half-chord diameters. [Figure 130] FIG. 1 illustrates the power profiles of 12 exemplary embodiments of intraocular lens designs across half-chord diameters. [Figure 131] FIG. 1 illustrates the power profiles of 12 exemplary embodiments of intraocular lens designs across half-chord diameters. [Figure 132] FIG. 10 illustrates the through-focus image quality ("Q" metric) of eight illustrative example combinations with high-order aberrations, including both symmetric and asymmetric high-order aberrations. [Figure 133]FIG. 12 illustrates the through-focus image quality ("Q" metric) of two illustrative example combinations. The solid line with triangle symbols represents the through-focus image quality obtained when -1.25 DC at 90 degrees of astigmatism is combined with various levels of defocus. The solid line with circle symbols represents the through-focus image quality when -1.25 DC at 90 degrees of astigmatism is combined with various levels of defocus with the high-order aberration combinations described in Table 12.1. [Figure 134] Figures 12.2 and 12.3 show the real part of the optical transfer function as a function of spatial frequency for three sets of exemplary aberration combinations. In these figures, the solid lines represent a candidate eye with -1D of defocus with no other high-order aberrations, and the double lines represent the candidate eye when defocus is corrected and the high-order aberrations are left uncorrected. The triple lines represent one set of high-order aberration combinations #1, #2, and #3 described in Table 12.2. [Figure 135] Figures 12.2 and 12.3 show the real part of the optical transfer function as a function of spatial frequency for three sets of exemplary aberration combinations. In these figures, the solid lines represent a candidate eye with -1D of defocus with no other high-order aberrations, and the double lines represent the candidate eye when defocus is corrected and the high-order aberrations are left uncorrected. The triple lines represent one set of high-order aberration combinations #1, #2, and #3 described in Table 12.2. [Figure 136] Figures 12.2 and 12.3 show the real part of the optical transfer function as a function of spatial frequency for three sets of exemplary aberration combinations. In these figures, the solid lines represent a candidate eye with -1D of defocus with no other high-order aberrations, and the double lines represent the candidate eye when defocus is corrected and the high-order aberrations are left uncorrected. The triple lines represent one set of high-order aberration combinations #1, #2, and #3 described in Table 12.2. [Figure 137] FIG. 1 shows the power profiles of two exemplary embodiments of contact lens designs (N11 and N12) across half-chord diameters. [Figure 138]1 shows the through-focus image quality ("Q metric") of two exemplary contact lenses (N11 and N12) calculated for a pupil diameter of 3 mm. The solid and double lines represent the through-focus image quality of the two designs N11 and N12 when each design is used to correct a pair of eyes. The dashed line represents the binocular performance when both eyes are combined and functioning together. DETAILED DESCRIPTION OF THE INVENTION

[0049] The present disclosure will now be described in detail with reference to one or more embodiments, some examples of which are illustrated and / or supported in the accompanying drawings. The examples and embodiments are provided by way of example and are not to be construed as limiting the scope of the disclosure.

[0050] Moreover, features illustrated and described as part of one embodiment can be used by themselves to provide other embodiments, and features illustrated and described as part of one embodiment can be used with one or more other embodiments to provide still further embodiments, It will be understood that the present disclosure is intended to cover these variations and embodiments, as well as other variations and / or modifications.

[0051] It will be understood that as used herein, the term "comprise" and any of its derivatives (e.g., comprises, comprising) is considered to include the features it refers to and does not exclude the presence of any additional features, unless otherwise stated or implied. Features disclosed in this specification (including the appended claims, abstract, and drawings) may be replaced by alternative features serving the same, equivalent, or similar purpose, unless expressly stated otherwise.

[0052] The headings used in the detailed description are provided solely for ease of reference by the reader and should not be used to limit the subject matter found throughout this disclosure or the claims. Headings should not be used when interpreting the scope of the claims or the limitations of the claims.

[0053] As defined herein, an aberration profile may be an arrangement of one or more aberrations in a one-dimensional, two-dimensional, or three-dimensional distribution. The arrangement may be continuous or discontinuous. An aberration profile may be provided by an arrangement of one or more power profiles, power patterns, and power distributions in a one-dimensional, two-dimensional, or three-dimensional distribution. The arrangement may be continuous or discontinuous. The aberrations may be rotationally symmetric or rotationally asymmetric.

[0054] As used herein, the terms "over a range of dioptric distances" and "range of dioptric distances" refer to a range of distances corresponding to equivalent diopter units. For example, a linear range of 100 cm to 50 cm corresponds to a range of dioptric distances of 1D to 2D, respectively.

[0055] The optical and / or visual performance of the human eye may be limited by one or more optical and / or visual factors. Some of these factors may include monochromatic and polychromatic optical wavefront aberrations and retinal sampling, which may impose a Nyquist limit on spatial acuity. Some other factors may include the Stiles-Crawford effect and / or scattering. These factors, or a combination of these factors, may be used to determine retinal image quality (RIQ) according to certain embodiments. For example, retinal image quality (RIQ) may be obtained by measuring the wavefront aberrations of the eye with or without a corrective lens in place, with appropriate adjustments, if necessary, using factors such as the Stiles-Crawford effect. As disclosed herein, various methods for determining RIQ may also be used, such as, but not limited to, the simple Strehl ratio, point spread function, modulation transfer function, complex modulation transfer function, phase transfer function, optical transfer function, the Strehl ratio in the spatial domain, the Strehl ratio in the Fourier domain, or combinations thereof.

[0056] As used herein, visual acuity may be used as a measure of an aspect of visual performance. Visual acuity testing assesses the limit when a visual target, such as a letter, i.e., the letter "E" ("illiterate" E) or the letter "C" (Landolt C), or some other target, can no longer be resolved, identified, or correctly reported by the patient undergoing visual acuity testing. The limit is related to one or more of the spatial frequency of the visual target (how finely spaced the visual target details are) and the contrast of the visual target, among other factors. The limit of visual acuity may be reached when the contrast of the image of the visual target, produced by the optical structure of the eye with or without additional optical devices, is too low to be discerned by the visual system (including the retina, visual pathway, and visual cortex).

[0057] The eye model used to evaluate the performance of certain exemplary embodiments is the Escudero-Navarro eye model, which has lens surface modifications to make it substantially aberration-free. However, the present disclosure is not limited to a particular eye model. Other eye models may also be used to evaluate the performance of the embodiments disclosed herein. Some examples of such eye models are as follows: a) a single refractive surface reduced model eye comprising an anterior corneal surface and a retinal surface, with an intraocular fluid of a specific refractive index separating the two surfaces; b) A miniature model eye with two refractive surfaces that can be formed by adding a posterior corneal surface to the model eye described in (a); c) A miniature model eye with three refractive surfaces that can be formed by adding two lens surfaces to the model eye described in (a), wherein the refractive index between the two lens surfaces is substantially greater than the refractive index of the intraocular fluid; d) a model eye with four refractive surfaces, such as the Lotmar model eye, the Liou-Brennan model eye, or the Gullstrand model eye; e) one of the model eyes described in (a)-(d), wherein one of the disclosed surfaces may be substantially spherical; f) one of the model eyes described in (a) to (d), wherein one of the surfaces may be substantially aspherical; g) one of the model eyes described in (a) to (d), wherein one of the surfaces may be substantially aspherical; h) one of the model eyes described in (a) to (d), wherein one of the surfaces may be substantially non-coaxial or tilted; (i) a modified model eye (d) in which the refractive index between the lens surfaces may be considered to have a gradient refractive index; and (j) A personalized model eye based on measured characteristic properties of a particular human eye or a selected group of human eyes.

[0058] The performance of some exemplary embodiments may be evaluated without ray tracing through a combination of optical device, lens, and selected model eye, but alternatively using Fourier optics, in which a wavefront defined at the posterior surface of the lens is propagated to retinal space by applying a two-dimensional Fourier transform.

[0059] Section 1: Retinal Image Quality (RIQ) A wavefront aberrometer, such as a Shack-Hartmann instrument, may be used to measure the optical properties of a candidate eye with or without refractive correction, a model eye with or without refractive correction, and identify a measure of retinal image quality (RIQ). In some instances, the model eye used may be a physical model that is anatomically and optically equivalent to the average human eye. In certain instances, RIQ may be calculated by optical computational methods such as ray tracing and / or Fourier optics. Several measures of RIQ are described herein.

[0060] (A) Strehl ratio Once the wavefront aberrations of a candidate eye are obtained, the image quality at the retina of the eye can be determined by calculating a simple Strehl ratio, as set forth in Equation 1. In certain applications, the image quality at the retina of the eye can be characterized by calculating the simple Strehl ratio shown in Equation 1. The Strehl ratio can be calculated in both the spatial domain (i.e., using the point spread function shown in Equation 1(a) below) and the Fourier domain (i.e., using the optical transfer function shown in Equation 1(b) below). The Strehl ratio measure is constrained between 0 and 1, with 1 associated with the best achievable image quality. In certain embodiments, the image quality produced by a lens and / or device at its focal length can be calculated without the use of a model eye. For example, Equations 1(a) and 1(b) can also be used without a model eye. Strehl ratio in the spatial domain TIFF0007618639000001.tif26155 formula 1a Strehl ratio in the frequency domain TIFF0007618639000002.tif19159 formula 1b

[0061] (B) Monochromatic RIQ U.S. Patent No. 7,077,522 B2 describes a visual acuity metric called the sharpness metric. This metric can be calculated by convolving a point spread function with a neutral quality function. Furthermore, U.S. Patent No. 7,357,509 describes several other metrics that measure the optical performance of the human eye. One such RIQ measure is the visual Strehl ratio calculated in the frequency domain. In certain applications, the RIQ measure is characterized by the visual Strehl ratio calculated in the frequency domain. The frequency domain visual Strehl ratio is described by Equation 2, which is constrained between 0 and 1, with 1 associated with the best achievable image quality at the retina. This metric addresses monochromatic aberrations. Monochromatic RIQ in the frequency domain TIFF0007618639000003.tif983 formula 2

[0062] The RIQ measure, Monochromatic Visual Strehl Ratio, correlates highly with objective and subjective visual acuity. In certain disclosed embodiments, this measure can be used to describe RIQ. However, other measures and alternatives described herein can be used in the design of optical devices, lenses, and / or methods.

[0063] (C) Multicolor RIQ The visual Strehl ratio defined by Williams above addresses monochromatic light. To accommodate polychromatic light, a metric called polychromatic retinal image quality (polychromatic RIQ) has been defined, which includes chromatic aberration weighted by spectral sensitivity for selected wavelengths. The polychromatic RIQ measure is defined in Equation 3. In certain applications, the polychromatic RIQ measure can be used to describe the RIQ characterized by Equation 3. multicolor RIQ TIFF0007618639000004.tif9118 formula 3

[0064] (D) Monochromatic Global RIQ The visual Strehl ratio or monochromatic RIQ, also described herein in Subsection B, primarily addresses on-axis visual acuity. As used herein, unless the context clearly requires otherwise, "on-axis" refers to one or more of the optical axis, visual axis, or papillary axis. To accommodate wide-angle views (i.e., peripheral vision), a metric called Global Retinal Image Quality (GRIQ) is defined, which includes a range of visual eccentricities. The monochromatic GRIQ scale is defined by Equation 4: In certain applications, the polychromatic RIQ scale is characterized by Equation 4: Monochromatic global RIQ in the frequency domain TIFF0007618639000005.tif1615 formula 4

[0065] (E) Multicolor Global RIQ As another form of RIQ metric that accommodates polychromatic light and wide angle viewing (i.e., peripheral vision), a metric called polychromatic global retinal image quality (GRIQ) is defined, which includes the range of chromatic aberration and field eccentricity weighted by spectral sensitivity for selected wavelengths. The polychromatic GRIQ scale is defined by Equation 5: In a specific application, the polychromatic GRIQ scale is characterized by Equation 5: Multicolor Global RIQ TIFF0007618639000006.tif1416 formula 5

[0066] In formulas 1 to 5, f specifies the spatial frequency to be tested, which is F min ~F max (which indicates the boundary limits on spatial frequency content), e.g., F min = 0 cycles / degree, F max = 30 cycles / degree, f x and f y specifies the spatial frequencies to be tested in the x and y directions, CSF(fx ,f y ) denotes the contrast sensitivity function, which in the symmetric form is CSF(F) = 2.6(0.0192 + 0.114 * f) * e -(0.114*f)^1.1 can be defined as FT, in one form of expression, denotes a 2D Fourier transform, for example a 2D Fast Fourier Transform; A(ρ,θ) and W(ρ,θ) denote the pupil amplitude function across the pupil diameter and the wavefront of the test case, respectively; Wdiff(ρ,θ) denotes the wavefront in the diffraction-limited case, ρ and θ are normalized polar coordinates, where ρ represents the radial coordinate and θ represents the angular coordinate or azimuth; λ denotes the wavelength, α indicates the viewing angle, φ indicates the meridian angle, S(λ) denotes the spectral sensitivity.

[0067] The wavefront can be written, for example, as a set of standard Zernike polynomial functions up to a desired order, as described below. TIFF0007618639000007.tif1652In the above formula, a i denotes the i-th coefficient of the Zernike polynomial, Z i (ρ,θ) denotes the i-th Zernike polynomial term, "k" represents the highest term in the expansion.

[0068] These polynomials may be represented in the Optical Society of America format, the Malacara format, or other available Zernike polynomial expansion formats. Besides the Zernike method of constructing the wavefront and / or wavefront phase, other non-Zernike methods of wavefront construction, such as Fourier expansions, Taylor expansions, Bessel functions, even polynomials, odd polynomials, sums of sines, sums of cosines, super conics, Q-shaped aspheres, B-splines, wavelets, or combinations thereof, may similarly be employed. Spectral sensitivity functions may be selected for use in Equation 5 from, for example, a population average, a particular lighting condition, such as photopic, mesopic, or scotopic conditions, a subpopulation average, such as a particular age group, or specific individuals or combinations thereof.

[0069] (F) Global RIQ metric integrating impetus impetus exposure time Factors described herein for RIQ variations include one or more of wavefront aberration, chromaticity and spectral sensitivity, the Stiles-Crawford effect of the first kind, and optical and / or visual performance within the peripheral retina. Another factor that may be included is the amount of time spent in various accommodation states on average each day (daily amount of precision work), also known as myopia-induced exposure time T(A). This provides the following GRID variations: TIFF0007618639000008.tif1560 formula 6

[0070] (G) Possible other RIQ scales As described herein, other measures of RIQ may also be used in the design of devices, lenses, and / or methods. One example of an alternative RIQ measure is the simple modulation transfer function (MTF). Referring to Equation 2, the polychromatic MTF is formed by calculating the modulus of the real part of the optical transfer function and further eliminating the step of convolution with the CSF function. The monochromatic MTF is formed when S(λ) is also removed from Equation 2.

[0071] Other measures of RIQ used in the design of devices, lenses, and / or methods may include the multifocal effect ratio. Referring to Equation 2, the multifocal effect ratio metric may be calculated by dividing the RIQ metric of the design by the RIQ metric obtained for a monofocal lens. This multifocal effect ratio may be further calculated at various dioptric vergence values, thereby providing a through-focus multifocal effect ratio.

[0072] One other RIQ measure used in the design of devices, lenses, and / or methods may include none of the phase reversals. The number of phase reversals metric may be obtained from the phase transfer function. The phase transfer function is obtained as the inverse tangent angle of the imaginary part of the optical transfer function divided by the real part of the optical transfer function. A nonlinear optimization routine may be developed to find a design solution that reduces the number of phase reversals to the range of dioptric vergence.

[0073] Another measure of RIQ that may be used in devices, lenses, and / or methods is to include information of the phase transfer function in the calculation of the monochromatic RIQ or visual Strehl ratio. For example, one way to include phase transfer information in the visual Strehl ratio calculation is to convolve the real part of the optical transfer function in Equation 2 with the cosine of the phase transfer function described in Equation 7. Monochromatic RIQ in the frequency domain using PTF TIFF0007618639000009.tif867 expression 7

[0074] Another measure of RIQ that may be used in the design of devices, lenses, and / or modules is to include weighted contrast sensitivity function and weighted phase transfer function information in the monochromatic RIQ calculation. Monochromatic RIQ in the frequency domain with weighted PTF and CSF TIFF0007618639000010.tif940 formula 8 In the above equation, a and b are the CSF(f x , f y ) and PTF(f x , f y ) is the weight given to

[0075] Another measure of RIQ that may be used in the design of devices, lenses, and / or modules is to include the individualized contrast sensitivity function of a particular human eye. Monochromatic RIQ in the frequency domain for specific human eyes TIFF0007618639000011.tif938 formula 9

[0076] In the above equation, Indv_CSSF is the contrast sensitivity function of the particular human eye to which the optical device, lens, and / or method is being applied.

[0077] Another measure of RIQ that may be used in the design of a device, lens, and / or module is to include a two-dimensional correlation analysis in the spatial domain. Two-dimensional correlation analysis in the spatial domain is performed by obtaining a correlation coefficient when the point spread function of the optimized design is correlated with the point spread function of the refractive-limited system. Such correlation coefficients may be obtained for a large number of configurations spanning a variety of pupil diameters and / or distance ranges. The obtained correlation coefficients range from -1 to 1, with values ​​close to -1 indicating a high negative correlation, values ​​close to 0 indicating a low correlation, and values ​​close to 1 indicating a high positive correlation. For the correlation analysis, a simulated image obtained by convolving the point spread function with an object in image space may be used for the correlation analysis.

[0078] Another measure of RIQ that may be used in the design of a device, lens, and / or module is to include a two-dimensional correlation analysis in the frequency domain. Two-dimensional correlation analysis in the frequency domain is performed by obtaining a correlation coefficient when the point spread function of the optimized design is correlated with the optical transfer function of the refractive-limited system. Such correlation coefficients may be obtained for multiple configurations spanning a variety of pupil diameters and / or distance ranges. The obtained correlation coefficients range from -1 to 1, with values ​​close to -1 indicating a high negative correlation, values ​​close to 0 indicating a low correlation, and values ​​close to 1 indicating a high positive correlation. For the correlation analysis, one of the following input variables may be selected: the real part of the optical transfer function, the imaginary part of the optical transfer function, the modulation transfer function, and the phase transfer function.

[0079] Section 2: Through-Focus RIQ RIQ can also be considered to be anterior and / or posterior to the retina. RIQ anterior and / or posterior to the retina is referred to herein as "through-focus RIQ," abbreviated herein as TFRIQ. Similarly, RIQ at and / or around the retina may also be considered over a particular range of focal lengths (i.e., during eye accommodation, which, in addition to changes in focal length, causes changes in the refractive properties of the eye). Certain embodiments may consider not only RIQ at the retina, but also changes in through-focus RIQ. This is in contrast to approaches that may consider only RIQ at the retina and / or the integral or sum of RIQ measures at or around the retina. For example, certain embodiments of the lenses, devices, and / or methods disclosed herein are designed to change RIQ, or provide control over the change or degree or rate of change, in a direction anterior to the retina (i.e., from the retina toward the cornea) and / or in a direction posterior to the retina for eyes with particular refractive properties. Certain embodiments can also be designed to vary the RIQ for a given focal length or to provide control over changes or variations in RIQ. For example, several candidate lens designs can be identified through varying RIQ in an anterior direction to the retina, and then a single design or subset of designs can be identified taking into account the variation in RIQ as the focal length changes. In certain embodiments, the process described above is reversed. In particular, a set of designs is selected based on the change in RIQ at the retina for a given focal length. Selection within the set is then made with reference to TFRIQ. In certain embodiments, a single evaluation process is performed that combines consideration of TFRIQ and the change in RIQ at the retina for a given focal length. For example, an average measure of RIQ as the focal length changes can be used to identify designs. The average measure gives more weight to certain focal lengths (e.g., thus, distance, intermediate, and near vision can be weighted differently).

[0080] For example, an average measure of RIQ as focal length varies may be used to identify designs that may be used with a particular device, lens, and / or method disclosed herein. For example, a measure of RIQ averaged over a range of focal lengths. The average measure may be a weighted average measure that gives greater weight to, or emphasizes, certain focal lengths (e.g., distance, intermediate, and near vision), and therefore may be weighted differently.

[0081] RIQ can also be considered anterior and / or posterior to the retina. RIQ anterior and / or posterior to the retina is referred to herein as "through-focus RIQ," abbreviated herein as TFRIQ. Similarly, RIQ at and / or around the retina may also be considered over a particular range of focal lengths. For example, upon accommodation of the eye, which causes a change in the refractive properties of the eye, its focal length also changes. Certain embodiments may consider not only RIQ at the retina, but also through-focus RIQ changes. This is in contrast to approaches that may consider only RIQ at the retina and / or the integral or sum of RIQ measures at or around the retina. For example, certain embodiments of the lenses, devices, and / or methods disclosed herein are designed to change RIQ, or provide control over the degree or rate of change, in a direction anterior to the retina (i.e., from the retina toward the cornea) and / or in a direction posterior to the retina for eyes with particular refractive properties. Certain embodiments can also be designed to vary the RIQ for a given focal length or to provide control over changes or variations in RIQ. For example, several candidate lens designs can be identified through varying RIQ in an anterior direction to the retina, and then a single design or subset of designs can be identified taking into account variations in RIQ as focal length changes. In some embodiments, the process described above is reversed. In particular, a set of designs is selected based on changes in RIQ at the retina for a given focal length. Selection within the set is then made with reference to TFRIQ. In some embodiments, a single evaluation process is performed that combines considerations of TFRIQ and changes in RIQ at the retina for a given focal length. For example, an average measure of RIQ as focal length changes can be used to identify designs that may be used with particular devices, lenses, and / or methods disclosed herein. The average measure gives greater weight to particular focal lengths (e.g., thus, distance, intermediate, and near vision can be weighted differently).In certain embodiments, the through-focus RIQ and / or change in RIQ at the retina for a given focal length are considered for one or more of: i) on-axis; ii) integrated around-axis, e.g., a region corresponding to or approximating the pupil size, with or without considering the Stiles-Crawford effect; iii) off-axis (off-axis refers to a specific location, set of locations, and / or the entirety of locations on the retina outside the fovea, which may be locations where light is focused at a field angle greater than about 10 degrees); and iv) a combination of one or more of i)-iii). In certain applications, the field angle is greater than about 15 degrees, greater than about 20 degrees, greater than about 25 degrees, greater than about 30 degrees, or greater.

[0082] Although the description herein refers to quantitative measures of RIQ, qualitative measures can be used as well to assist the aberration profile design process beyond quantitative measures. For example, the visual Strehl ratio at a particular through-focus location is calculated or determined based on the point spread function. As can be seen from the example images referenced in the following section, the point spread function can be visually evaluated. This provides a way to qualitatively evaluate through-focus.

[0083] In some embodiments, the image quality produced by the lens and / or device at that focal length is calculated without using a model eye. The image quality produced by the lens and / or device may be calculated in front of and / or behind the focal length of the lens and / or device. The image quality in front of and / or behind the focal length may be referred to as through-focus image quality. The through-focus range has negative and positive powers relative to the focal length.

[0084] Section 3: Aberrations and through-focus affecting image quality at the retina The influence of low-order aberrations on RIQ and TFRIQ is known in the art. The use of corrective low-order aberrations represents a conventional method of refractive error correction for the eye. Therefore, the identification of an aberration profile composed of low-order aberrations for correcting defocus and astigmatism will not be described in detail herein.

[0085] The effect of higher order aberrations (HOAs) on image quality is illustrated from the through-focus two-dimensional point spread function (300) in Figure 3. In Figure 3, the rows show the point spread function for a selection of aberrations, and the horizontal axis shows the degree of defocus in diopters for the associated aberration.

[0086] An exemplary HOA with respect to image quality is shown in Figure 3 according to a specific embodiment. This is illustrated by the through-focus two-dimensional point spread function 300 shown in Figure 3. In Figure 3, the rows show the point spread functions for a selection of aberrations, and the horizontal axis shows the degree of defocus in diopters for the particular associated aberration.

[0087] The point spread function 302 without high-order aberrations (in the illustrated exemplary image of the retina of an eye with only myopia or hyperopia), the point spread function 306 with only vertical coma, and the point spread function 308 with only horizontal trefoil remain symmetric with respect to positive and negative defocus. With respect to positive and negative first-order spherical aberration, either alone 304 or in combination with coma and / or trefoil 310, the through-focus of the point spread function is asymmetric with respect to positive and negative defocus. For certain HOAs, positive and negative defocus have unequal effects on image quality. It can be seen that these unequal effects are more pronounced for spherical aberration. HOAs that exhibit asymmetric effects with respect to RIQ, visual acuity, and / or contrast sensitivity have application in some of the lenses, devices, and / or methods disclosed herein.

[0088] The interaction between HOAs and defocus affects TFRIQ. Some HOAs interact favorably with defocus, improving RIQ, while others interact unfavorably, degrading RIQ. The most common higher-order ocular aberrations measured include spherical aberration, coma, and trefoil. Beyond these, the HOA profiles achieved by some multifocal optical designs induce significant wavefront aberrations, often expressed in terms of up to the tenth order of Zernike polynomial expressions.

[0089] Roughly speaking, terms closer to the center of a Zernike pyramid are often more influential or useful, measured in terms of resulting optical effects, compared to edge / corner terms. This is because terms farther from the center have a relatively larger flat area on the wavefront compared to terms whose angular frequency is closer to zero. In certain applications, the Zernike terms with the highest or substantially highest likelihood of interacting with defocus are, for example, terms with even radial orders having zero angular frequency components, i.e., 4th, 6th, 8th, and 10th Zernike coefficients, which represent 1st, 2nd, 3rd, and 4th order spherical aberrations. Other Zernike coefficients representing other orders of spherical aberration can also be used.

[0090] The above description of aberrations identifies some of the aberrations that affect the retinal RIQ and through-focus RIQ. The description is not, and is not intended to be, an exhaustive description of the various aberrations that affect the retinal RIQ and through-focus RIQ. In various embodiments, additional aberrations that affect the retinal RIQ and / or through-focus RIQ are contemplated, and relevant aberrations are identified taking into account the current refractive state of the ocular system (meaning the eye together with any lenses or optical devices that affect the wavefront received by the retina) and the target retinal RIQ / through-focus RIQ.

[0091] Section 4: Optimizing RIQ When designing and / or selecting the required change in the refractive state of the eye, measurements of RIQ and through-focus RIQ are typically performed for certain disclosed embodiments. In particular, finding the magnitude and sign of defocus that interacts with one or more of the relevant aberrations to produce an acceptable RIQ and through-focus RIQ is typically performed. A search is performed for the best or at least acceptable combination of RIQ and through-focus RIQ. In certain embodiments, the combination selected is determined by evaluating the RIQ and through-focus RIQ and selecting a combination that is suitable, substantially optimized, or optimized for the application. In certain embodiments described herein, a merit function S=1 / RIQ is used for this purpose. In certain embodiments, an approximation of the merit function S=1 / RIQ can be used for this purpose.

[0092] Identifying the aberration coefficients that optimize or substantially optimize RIQ at the retina can be achieved in certain embodiments by finding the minimum or substantially minimum value of the function S. Considering the RIQ optimization routine over a certain range of dioptric distances (through focus) adds complexity to the optimization process. Various methods can be used to address this complexity.

[0093] One example, according to certain embodiments, is the use of a nonlinear unconstrained optimization routine over a selected set of Zernike SA coefficients as variables. Automatic and / or human-mediated random elements can be incorporated to shift to different locations, thereby finding alternative local minima of the function S. The criteria by which the optimization routine evaluates performance can be a combination of retinal RIQ and maintaining through-focus RIQ within predefined limits of retinal RIQ. The limits can be defined in various ways, such as a specific range around a value for retinal RIQ. The range can be fixed (e.g., plus or minus 0.15 for the visual Strehl ratio or similar measure) or can vary (e.g., within a predefined rate of change as the distance from the retina increases). In certain embodiments, the range can be fixed to one or more of the following ranges: plus or minus 0.05, plus or minus 0.1, or plus or minus 0.15. These ranges can be used with one or more of the simple Strehl ratio, the point spread function, the modulation transfer function, the phase transfer function, the optical transfer function, the Strehl ratio in the Fourier domain, or a combination thereof.

[0094] As described in more detail herein, the objective function for TFRIQ may, in at least certain embodiments, vary depending on whether the objective of the merit function is to provide TFRIQ with a slope that provides a stimulus that inhibits ocular growth of the candidate eye, or to provide TFRIQ with a slope that provides a stimulus that promotes ocular growth, under the description of optical feedback for emmetropization. In certain other applications, such as correction to improve presbyopia, the objective of the merit function is to provide TFRIQ with a slope that is acceptably low in magnitude or substantially equal to zero. In certain other presbyopic embodiments, an acceptably low magnitude slope for TFRIQ can be considered from one or more of: a) a TFRIQ slope of approximately zero; b) a TFRIQ slope equal to zero; c) a TFRIQ slope greater than zero / diopter and less than 0.25 / diopter; d) a TFRIQ slope greater than -0.25 / diopter and less than 0 / diopter; e) a TFRIQ slope greater than 0 / diopter and less than 0.5 / diopter; or f) a TFRIQ slope greater than -0.5 / diopter and less than 0 / diopter.

[0095] Another approach is to limit the number of possible combinations of aberration profiles. One way to limit the possible aberration values ​​is to specify that the Zernike coefficients may only have values ​​corresponding to 0.05 μm focus increments or another increment interval. In certain embodiments, the Zernike coefficients may have values ​​corresponding to increments of about 0.01 μm, about 0.02 μm, about 0.03 μm, about 0.04 μm, or about 0.05 μm. In certain embodiments, the Zernike coefficients may have values ​​corresponding to increments of 0.01 μm, about 0.02 μm, about 0.03 μm, about 0.04 μm, or about 0.05 μm. In certain embodiments, the Zernike coefficients can have values ​​corresponding to increments selected within one or more of the following ranges: 0.005 μm to 0.01 μm, 0.01 μm to 0.02 μm, 0.02 μm to 0.03 μm, 0.03 μm to 0.04 μm, 0.04 μm to 0.05 μm, or 0.005 μm to 0.05 μm. The intervals can be selected taking into account available computational resources. By limiting the number of allowable coefficient values, it is possible to simulate the performance of a significant portion of the aberration profiles formed by combinations of Zernike coefficients, and accordingly, aberration profiles with the best or acceptable on-axis and through-focus RIQs can be identified. The results of this process can be used to constrain a more fine-tuned analysis, for example, by returning the optimization routine with coefficient values ​​within a small range around the identified candidate combination of high-order aberrations.

[0096] Section 5: Control of emmetropic stimulation by optical feedback A person can be identified as at risk for developing myopia based on, for example, one or more of the following indicators: whether the person's parents experienced myopia and / or hyperopia, their ethnicity, lifestyle factors, environmental factors, the amount of precision work, etc. Other indicators or combinations of indicators can be used in accordance with certain embodiments as well. For example, a person can be identified as at risk for developing myopia if one or both of the person's eyes have retinal RIQ that improves in the direction of eye growth. RIQ can be obtained with or without currently used refractive correction (e.g., with or without a current prescription for glasses or contact lenses). In certain embodiments, improving RIQ in the direction of eye growth can be used alone or in conjunction with one or more other indicators, such as the other indicators listed herein.

[0097] From one perspective, the emmetropization process can be described under an optical feedback mechanism based on the RIQ at the retina and / or the gradient of TFRIQ in the anterior-posterior direction relative to the retina. According to this perspective on emmetropization, the candidate eye is stimulated to grow to a position where the merit function S of an optimization routine is minimized or substantially minimized. Under this description of the emmetropization process, at least for human eyes, if the location of a local or global minimum of the merit function S is posterior to the retina, the eye can be stimulated to grow longer in certain embodiments. In yet another application, the substantial minimum of the merit function optimization routine can be a local or global minimum. In other applications, if the location of a local or global minimum of the merit function S is posterior to the retina or if the through-focus RIQ improves posterior to the retina, the eye can be stimulated to grow longer. For example, if the location of a local or global minimum of the merit function S is located on or anterior to the retina, the eye may remain the same length.

[0098] The following description describes how selected combinations of HOAs can affect changes in through-focus RIQ. These aberrations can be easily incorporated into lenses, optical devices, and / or used in ways that change the aberration profile of the wavefront of incoming light received by the retina.

[0099] In certain embodiments, these aberration characterizations can be readily incorporated into lenses, optical devices, and / or used in methods to alter the aberration profile of the wavefront of incoming light received by the retina. This provides a mechanism by which certain embodiments can alter the refractive state of a candidate eye. In certain embodiments, lenses, optical devices, and / or methods will include at least the aberration characteristics of the embodiments to alter the refractive state of a candidate eye.

[0100] As described in more detail herein, achieving a target TFRIQ can, in certain embodiments, be considered together with achieving or obtaining an on-axis RIQ that is substantially close to the target on-axis RIQ at the retina for a particular focal length, which is typically distance vision. In certain applications, one or more of the following, referred to as distance vision, are for objects farther than 6 meters. In other applications, the target TFRIQ can be considered for another focal length, such as intermediate or near vision, instead of distance vision. In some applications, intermediate vision can be defined as a range of approximately 0.5 to 6 meters. In some applications, near vision can be defined as a range of approximately 0.3 to 0.5 meters.

[0101] As described in more detail herein, achieving a target TFRIQ is generally considered to mean achieving or obtaining an on-axis RIQ at the retina that is substantially close to the target on-axis RIQ for a particular focal length, which is distance vision. One or more of the following, referred to as distance vision, are objects farther than 6 meters. In some applications, the target TFRIQ may be considered for another focal length in lieu of distance vision, such as intermediate vision or near vision. In some embodiments, intermediate vision may be defined as a range of approximately 0.5 to 6 meters. In some applications, near vision may be defined as a range of approximately 0.3 to 0.5 meters.

[0102] For the examples described herein, RIQ was assessed or characterized using the visual Strehl ratio, shown in Equation 2:

[0103] (A) First-order spherical aberration, coma, and trefoil The interactions between first-order spherical aberration, coma, and trefoil and their effects on ocular growth can be described or characterized by using a wavefront phase function defined using the defocus, first-order spherical aberration (PSA), coma, and trefoil terms of the standard Zernike expansion. Other methods are also possible.

[0104] The pupil size was fixed at 4 mm and the calculations were performed at 589 nm wavelength. To evaluate the effect of the aberration profile on eye growth, it was assumed that the location of the minimum of the function S above on the posterior side of the retina provides the stimulus for eye growth to that location, and that if the minimum of the function S is on or in front of the retina, there is no stimulus for eye growth. In other words, it is assumed that the image formed on the retina provides the stimulus for growth to minimize the function S. The range of values ​​of PSA, horizontal and vertical coma, and horizontal and vertical trefoil used in the simulations was: PAS=(-0.30,-0.15,0.00,0.15,0.30)μm Horizontal frame = (-0.30,-0.15,0.00,0.15,0.30)μm Vertical coma = (-0.30, -0.15, 0.00, 0.15, 0.30) μm horizontal trefoil = (-0.30, -0.15, 0.00, 0.15, 0.30) μm, and Vertical trefoil = (-0.30, -0.15, 0.00, 0.15, 0.30) μm is.

[0105] For a total of 3125 combinations tested, it was observed that, overall, spherical aberration primarily dominates the direction of RIQ improvement.

[0106] Figures 4-7 show the eye growth stimulation resulting from TFRIQ for combinations according to certain embodiments, particularly for a selection of the combined effect of PSA with horizontal coma and vertical coma and the combined effect of PSA with horizontal trefoil and vertical trefoil. Figures 4-7 are on a continuous scale, with white (0) indicating no progression and gray-black transitions indicating the amount of progression in diopters.

[0107] FIG. 4 shows a graph 400 of the interaction of primary spherical aberration and horizontal coma. The gray plot indicates the amount of myopic progression stimulated by the combination of these two aberrations, with white 402 indicating no progression stimulus and shading toward black 404 indicating a myopic progression stimulus (to -0.8D in this case) resulting from PSA combined with horizontal coma. FIG. 5 shows a graph 500 of myopic progression as a function of the interaction of primary spherical aberration and vertical coma. As in FIG. 4, the white areas 502 indicate no progression stimulus and the dark areas 504 indicate a progression stimulus. FIG. 6 shows a graph 600 of the interaction of primary spherical aberration and horizontal trefoil. FIG. 7 shows a graph 700 of myopic progression as a function of the interaction of primary spherical aberration and vertical trefoil. For the combinations shown in FIGS. 4-7, approximately 52% of the combinations provide a stimulus that promotes eye growth.

[0108] The stimulus for eye growth can therefore be removed by controlling the refractive state of the eye to be within one or more of the white regions in Figures 4-7. This can be achieved, for example, by designing a lens or optical device that, when applied, modifies the refractive properties of the eye, such that the retina of the eye experiences a through-focus RIQ that does not substantially improve or does not improve in the direction of eye growth (posterior to the retina), or that decreases in the direction of eye growth.

[0109] Although trefoil and coma within the range of -0.30 to 0.30 μm for a 4 mm pupil do not appear to significantly affect the direction of growth (the maximum progressive effect is only -0.1 D), positive PSA appears to accelerate growth, while negative PSA appears to inhibit growth. Thus, PSA appears to have a dominant effect. Therefore, at least in eyes with a positive PSA and optionally either coma or trefoil, adding a negative PSA can inhibit ocular growth under the explanation of optical feedback for emmetropization. Naturally, providing a negative PSA to an eye or removing at least a positive PSA can remove the stimulus for ocular growth. The ocular coma and trefoil may be left unchanged or, optionally, partially or completely corrected (preferably within the range of -0.30 to 0.30 μm).

[0110] (B) Interaction of spherical aberration and astigmatism To illustrate the interaction between spherical aberration and astigmatism, a wavefront phase function was defined using these aberrations (including both horizontal / vertical and diagonal components) and defocus. Figures 8-13 (unlike Figures 4-7) are on a binary scale - in the above formula, white (1) indicates a test case that results in a stimulus for progression (i.e., increased eye growth), and black (0) indicates a candidate combination that results in no or very little progression (i.e., no stimulus or stop signal for eye growth). The scale is unitless. Figures 8-13 illustrate certain disclosed embodiments.

[0111] 8 is an illustration showing a graph 800 illustrating the magnitude of myopia progression for PSA versus the primary oblique astigmatic (POA) component versus the primary horizontal / vertical astigmatic (PHV) component. In this example, graph 800 shows combinations of PSA and astigmatism that may result in a stimulus for myopia progression (white) and combinations that will not result in a stimulus for myopia progression (black). Neither POA nor PHV appears to have a significant impact on the effect of PSA.

[0112] 9 is an illustration showing a graph 800 illustrating the magnitude of myopia progression for PSA versus secondary oblique astigmatic (SOA) versus secondary horizontal / vertical astigmatic (SHV) components, according to certain embodiments. In this example, neither SOA nor SHV appears to have a significant impact on the effect of PSA.

[0113] The stimulus for eye growth can therefore be removed by controlling the refractive state of the eye to be within one or more of the white regions of FIGS.

[0114] From the exemplary Figures 8 and 9, it appears that the primary and secondary astigmatism components, when combined with PSA, have a slight effect on improving or inhibiting eye growth. Therefore, when considering these aberrations, this indicates that priority can be given to PSA. Furthermore, it can be determined whether the eye has a high level of POA, PHV, SOA, and / or SHV. If this is the case, in this example, correcting these aberrations (by reducing or substantially eliminating them) can help to remove the stimulus for eye growth.

[0115] (C) Higher-order spherical aberration In the case of the naked eye or a single-vision spectacle-corrected eye, a fourth-order Zernike expansion can be used to describe or characterize the wavefront at the exit pupil. However, this may not necessarily be the case when, for example, contact lenses are used for correction, and in particular in the case of multifocal contact lenses (both aspheric and concentric), a significant amount of fifth-order or higher HOAs may be used. Multifocal contact lenses can be described, for example, using up to about tenth or twelfth order Zernike polynomials. In such cases, the magnitude and sign of higher-order spherical aberrations (besides PSA) begin to play an important role.

[0116] To represent the interactions between the first-, second-, third-, and / or fourth-order spherical aberrations of the standard Zernike expansion, the wavefront phase was defined using these terms and defocus. Several combinations of HOAs predicted from modeled data for these multifocal contact lenses were used. A select set of these HOAs demonstrating the interactions to produce peak RIQ was obtained using a dedicated nonlinear optimization routine. Calculations were performed for a 4mm pupil and at a wavelength of 589nm. It was observed that at least the first three modes of the innate spherical aberration of the eye played a role in governing the direction of the stimulus for eye growth, and in some cases, higher modes of spherical aberration also played a role. In certain applications, these roles were significant.

[0117] The results described below relate to secondary spherical aberration (SSA), tertiary spherical aberration (TSA), and quaternary spherical aberration (QSA), although spherical aberrations having higher orders can be similarly used with embodiments of the lenses, devices, and / or methods described herein.

[0118] For four types of spherical aberration, the effect of HOA combinations was investigated using a range of -0.3 μm to 0.30 μm. These ranges for these types of aberrations do not necessarily correspond to the normative distribution of aberrations associated with the eye. This is because the occurrence of these higher-order aberrations is not necessarily associated with the eye, but with the optical device (multifocal contact lens) alone or in combination with the eye. Furthermore, the range of -0.3 μm to 0.30 μm is only used to demonstrate the effect, but larger or smaller ranges can be used when determining the HOA combination to provide the aberration profile of a lens or optical device or to implement by a surgical procedure.

[0119] 10-12 are illustrations showing the stimulation for myopia progression as a function of PSA together with SSA, TSA, and QSA, respectively, according to certain embodiments. In this example, the scheme is a binary color plot, with white (0) indicating wavefront aberration combinations that provide stimulation for myopia progression under the feedback mechanism described herein, and black (1) indicating combinations that prevent myopia progression. From these graphs, it is clear that higher orders of spherical aberration affect the stimulation for eye growth. In this example, approximately 82% of the combinations investigated suggest stimulation for eye growth. The interaction of spherical aberration terms depends on their respective signs and their respective magnitudes.

[0120] FIG. 10 is an illustration showing a graph 1000 illustrating the presence of a stimulus for myopia progression depending on the combination of PSA and SSA, according to certain embodiments. In FIG. 10, it can be seen that when a PSA in the range of −0.3 μm to 0.20 μm is combined with a negative SSA in the range of 0.00 μm to −0.30 μm, there is little or no improvement in RIQ in the direction of eye growth, and therefore no myopia progression is predicted (region indicated by 1004). However, when a PSA in the range of 0.20 μm to 0.30 μm is considered together with a negative SSA in the range of approximately −0.10 μm, it appears to worsen progression, as indicated by region 1002. Overall, the sign of the SSA appears to have a dominant effect on the effect of wavefront aberrations and the resulting retinal image quality. In this example, a negative SSA of significant magnitude (i.e., greater than −0.20 μm) predicts a protective effect against myopia progression when combined with either a positive or negative PSA, when PSA and SSA are the only two HOAs involved in the wavefront aberration of the candidate eye.

[0121] 11 is an illustration showing a graph 1100 illustrating the presence of a stimulus for myopia progression depending on the combination of PSA and TSA, according to certain embodiments. When PSA and TSA have the same sign and TSA is approximately 4 / 5 the magnitude of PSA, as shown in rectangular box 1106, no or little myopia progression is predicted (black area). However, in this example, myopia progression can be expected for other combinations of PSA and TSA, for example, as shown in areas 1102 and 1104.

[0122] 12 is an illustration showing a graph 1200 illustrating the presence of a stimulus for myopia progression depending on the combination of PSA and QSA, according to certain embodiments. When PSA and TSA have opposite signs and QSA is approximately 4 / 5 the magnitude of PSA, as shown in the black-dominated area 1204, no myopia progression is predicted. However, for other combinations of PSA and QSA (e.g., as shown in the white areas 1202, 1206), myopia progression may be expected.

[0123] 13 is an illustration showing a graph 1300 illustrating the presence of a stimulus for myopia progression according to a combination of PSA, SSA, and TSA, according to certain embodiments. The scheme is a binary color plot, where 1 (white) indicates a wavefront aberration combination that is favorable for myopia progression, and 0 (black) indicates a combination that prevents myopia progression (i.e., provides no stimulus for eye growth). TIFF0007618639000012.tif115139

[0124] The majority of the black circles 1304, with a few exceptions, are within the region dominated by negative SSA. Furthermore, combinations of PSA and TSA with the same sign, combined with negative SSA, appear to provide a protective effect against myopia progression. Combinations of PSA, SSA, TSA, and QSA (including the black region shown in FIG. 13) that have a protective effect against myopia progression under the explanation of optical feedback of emmetropization can be summarized as shown in Table 1.

[0125] The majority of the open circles 1302, with a few exceptions, are within the region dominated by positive SSA. Furthermore, combinations of PSA and TSA with the same sign, combined with positive SSA, can provide a treatment effect for hyperopia. The combinations of PSA, SSA, TSA, and QSA (including the open areas shown in FIG. 13) that have a treatment effect for hyperopia under the explanation of emmetropization optical feedback can be summarized as shown in Table 2. TIFF0007618639000013.tif127139

[0126] Thus, when designing an eye-modifying lens, optical device, or method, aberrations can be selected to provide a protective effect against eye growth, for example, for myopia, or to provide a combination of the above-mentioned aberrations that promote eye growth, for example, for hyperopia, which can be applied in combination with any required correction for myopic or hyperopic defocus.

[0127] From the above discussion, it is clear that spherical aberration, including first-order SA terms, second-order SA terms, third-order SA terms, and fourth-order SA terms, affect RIQ and through-focus RIQ. Furthermore, it has been found that much higher orders of spherical aberration can also affect RIQ and through-focus RIQ. In various embodiments, different combinations of spherical aberrations are used, including embodiments that use a combination of two or more spherical aberrations that provides a required or acceptable through-focus RIQ along with a required or acceptable RIQ at a particular focal length (e.g., distance vision). In certain embodiments, one or more characterizations of spherical aberration can be used as well.

[0128] Section 6: Instantaneous gradient of image quality The above description of the stimulus for eye growth can be explained under an optical feedback mechanism based on the location of the peak on-axis RIQ. In certain examples, another possible alternative approach to describing the stimulus for eye growth is by the gradient of the TFRIQ at the retina. In some embodiments, the lens, method, and / or device utilizes the gradient or slope of the RIQ to control myopia progression with or without astigmatism. In other embodiments, the lens, method, and / or device utilizes the gradient or slope of the RIQ to treat hyperopia with or without astigmatism. The gradient or slope of the RIQ may be considered in terms of one or more of the following RIQ variants, each of which is described herein: a) monochromatic RIQ with or without considering the effect of accommodation; b) polychromatic RIQ with or without considering the effect of accommodation; c) global RIQ; d) RIQ taking into account a myopia-inducing exposure time signal; and e) global RIQ with a myopia-inducing exposure time signal.

[0129] In certain embodiments, the lenses, devices, and / or methods disclosed herein can be applied to provide stimulation under this optical feedback mechanism of emmetropization. Embodiments for addressing ocular growth under the optical feedback mechanism of emmetropization (e.g., addressing myopic progression or attempting to stimulate ocular growth to correct hyperopia) can use aberrations to affect one or both of the location of the minimum or substantial minimum of the function S relative to the retina and the slope of the function S through the retina.

[0130] In the following description, it is assumed that a positive TFRIQ gradient (increasing RIQ behind the retina) provides a stimulus for the onset and progression of myopia, while a negative TFRIQ gradient slows or stops myopia progression. Figure 14 is an illustration showing plots of RIQ for two different cases 1402 and 1404 as a function of through-focus in the direction behind the retina, according to certain embodiments. The cases are two different combinations of PSA, SSA, and TSA that produce the same or substantially the same retinal RIQ. As can be seen, both sets of selected aberrations produce similar image quality at the retina (defocus=0) with the introduction of defocus (in the direction of eye growth), but the retinal image quality for test case 1402 gradually increases, indicating a stimulus for eye growth, while test case 1404 shows that the retinal image quality further deteriorates in the direction of eye growth, resulting in no stimulus for growth at all.

[0131] From the results described herein showing the effect of HOAs on image quality and the resulting myopia progression, it is possible to determine relevant HOA combinations that can be used in lenses, optical devices, and / or implemented using optical surgery, which, in combination with ocular aberrations as needed, result in a combination of HOAs that inhibits or slows ocular growth for the treatment of myopia progression. To slow ocular growth in myopia, compensatory optical devices and / or surgical procedures can be used, which, in combination with the ocular optical design, can result in a combination of HOAs that results in a negative slope of TFRIQ as shown in Example 1404 (FIG. 14). To treat hyperopia in certain applications, compensatory optical devices and / or surgical procedures can be used, which, in combination with the ocular optical design, can result in a combination of HOAs that results in a positive slope of TFRIQ as shown in Example 1402 (FIG. 14).

[0132] When an aberration profile has a variable RIQ across the through-focus range, the slope of the through-focus RIQ at a particular focal length can be modified by selecting an appropriate defocus term C(2,0) for the RIQ profile under consideration. For example, if the slope is positive at a first level of through-focus and negative at a second level of through-focus, the slope at the retina of the recipient's eye can be selected by selectively introducing defocus at the first or second level. Examples of aberration profiles with variable RIQ slope at different levels of defocus are provided herein in connection with embodiments of aberration profiles for application to presbyopia. Many of the embodiments describing presbyopia can be applied to provide stimuli that retard and / or accelerate eye growth under the description of the emmetropization optical feedback mechanism described herein. Young people typically have progressive myopia and therefore may not experience presbyopia. Thus, the selected aberration profile may place less emphasis on achieving a high RIQ over a wide through-focus range and more emphasis on achieving the highest RIQ at the retina for distance vision, combined with providing a negatively sloped RIQ profile through the retina (i.e., decreasing RIQ in the direction of eye growth).For young, hyperopic patients, the selected aberration profile may again place less emphasis on achieving a high RIQ over a wide through-focus range and more emphasis on achieving the highest RIQ at the retina for distance vision, combined with providing a positively sloped RIQ profile behind the retina (in the direction of eye growth).

[0133] In certain embodiments, lenses, devices, and / or methods can incorporate an aberration profile that provides an eye with progressive myopia or an eye identified as at risk for developing myopia with i) an acceptable on-axis RIQ and ii) a through-focus RIQ with a degrading slope in the direction of ocular growth. In certain embodiments, the scale of acceptable on-axis RIQ may be considered from one or more of an on-axis RIQ of 0.3, an on-axis RIQ of 0.35, an on-axis RIQ of 0.4, an on-axis RIQ of 0.45, an on-axis RIQ of 0.5, an on-axis RIQ of 0.55, an on-axis RIQ of 0.6, an on-axis RIQ of 0.65, or an on-axis RIQ of 0.7. In certain embodiments, a candidate myopic eye may be considered with or without astigmatism.

[0134] In certain embodiments, lenses, devices, and / or methods can incorporate an aberration profile that provides an eye with hyperopia with i) an acceptable on-axis RIQ and ii) a through-focus RIQ with a slope that improves in the direction of ocular growth. In certain embodiments, the scale of acceptable on-axis RIQ may be considered from one or more of an on-axis RIQ of 0.3, an on-axis RIQ of 0.35, an on-axis RIQ of 0.4, an on-axis RIQ of 0.45, an on-axis RIQ of 0.5, an on-axis RIQ of 0.55, an on-axis RIQ of 0.6, an on-axis RIQ of 0.65, or an on-axis RIQ of 0.7. In certain embodiments, a candidate hyperopic eye may be considered with or without astigmatism. In certain embodiments, the gradient or slope of the RIQ may be considered in terms of one or more of the following variants of RIQ, each of which is described herein: a) monochromatic RIQ with or without taking into account the effect of accommodation, b) multichromatic RIQ with or without taking into account the effect of accommodation, c) global RIQ, d) RIQ taking into account a myopia-inducing exposure time signal, and e) global RIQ with a myopia-inducing exposure time signal.

[0135] In certain embodiments, slope over a range of field angles may be considered, and / or variation in RIQ may be considered for a range of pupil sizes. An aberration profile may be selected that provides an average modal or substantially uniform slope over a range of field angles, such as 10 degrees, 20 degrees, 30 degrees, or 40 degrees, that inhibits or promotes eye growth (and / or cancels any existing aberrations in the eye that promote or inhibit eye growth, respectively). Average slope over a range of pupil sizes or at a modal pupil size may also be considered. Alternatively, a design may be selected that has either a positive or negative slope of through-focus RIQ for a range of field angles and / or for a range of pupil sizes.

[0136] In some embodiments, the image quality produced by a lens and / or device at its focal length is calculated without using a model eye. The image quality produced by a lens and / or device may be calculated in front of and / or behind the focal length of the lens and / or device. The image quality in front of or behind the focal length may be referred to as through-focus image quality. The through-focus range has a negative power end and a positive power end relative to the focal length. For example, in a through-focus range of -1.5D to +1.5D, -1.5D to 0D is considered the negative power end, while 0D to +1.5D is considered the positive power end. In some embodiments, the through-focus slope along the negative power end may be considered, while in other embodiments, the through-focus slope along the positive power end may be considered.

[0137] Section 7: Aberration Design or Selection Process In some embodiments, determining the aberration profile required for the lens, optical device, and / or resulting from the procedure includes first identifying the HOA present in the eye. In some embodiments, determining the aberration profile required for the lens, optical device, and / or resulting from the procedure includes first identifying the HOA present in the eye. Measurements can be performed using, for example, a wavefront eye exam using an aberrometer, such as a Shank-Hartmann aberrometer. The eye's existing HOA can then be taken into account. Additionally, one or more HOA effects inherent to the lens or optical device can be taken into account as well.

[0138] When the request is for a lens that provides a stimulus for or retards eye growth, these existing HOAs are then compared with HOA combinations that inhibit or retard myopia progression (e.g., as discussed above with reference to FIGS. 5-14) to determine one or more additional HOA combinations that may be needed to reduce, retard, or promote eye growth under the optical feedback mechanism of emmetropization. These additional combinations are then implemented in the design of the lens or optical device, or implemented using optical surgery. The flowcharts of FIGS. 15 and 16 provide summaries of suitable methods according to certain embodiments.

[0139] Alternatively, in certain applications, the eye's existing aberrations can be ignored, and an aberration profile providing the required through-focus RIQ gradient can be provided for the eye by a lens, or in certain applications, a removable lens, where a different aberration profile can be followed if necessary. The aberration profile of the lens and the aberration profile resulting from the eye combination can then be measured to determine whether the RIQ characteristics are acceptable (e.g., providing a specific through-focus RIQ gradient and acceptable RIQ for distance vision). Alternatively, different lenses can be placed on the eye, and objective and / or subjective visual acuity measures can determine which lens to select. If a lens is selected that provides stimulation to inhibit or promote eye growth regardless of the eye's existing aberrations, the selected aberration profile can be one with a generally higher value of spherical aberration so that the sign of the gradient does not change with low levels of HOA in the eye. In certain applications, the goal of the merit function optimization routine in searching for HOA combinations can be different. For example, when considering presbyopia, the goal can be a combination of aberrations that provides high RIQ over a wide through-focus range. When peripheral vision is useful, the objective can include high RIQ over a wide range of viewing angles. Thus, in various embodiments, the HOA is utilized to optimize for the goal of high RIQ at the retina in combination with one or more of low through-focus RIQ slope, low RIQ variation with pupil diameter, and high RIQ in peripheral vision.

[0140] In certain applications, an acceptably high RIQ may be considered to be an RIQ greater than 0.7, greater than 0.65, greater than 0.6, greater than 0.55, greater than 0.5, greater than 0.45, greater than 0.4, greater than 0.35, or greater than 0.3. In certain applications, an acceptably low change in RIQ with pupil diameter may be considered to be a change in RIQ between one or more of the following ranges: between 0 and 0.05, between 0.05 and 0.01, or between 0.1 and 0.15. In certain other applications, an acceptably low slope of through-focus RIQ may be considered to be from one or more of a slope less than zero, a slope equal to zero, a slope greater than zero, a slope near zero, a slope in the range of -0.5 to zero, a slope in the range of 0 to 0.5, a slope in the range of -1 to zero, a slope in the range of 0 to 1, a slope in the range of -1 to -0.5, or a slope in the range of 0.5 to 1. The provided high RIQ, low variation in RIQ, and low slope of TFRIQ can be combined in one or more combinations. For example, a combination of a high RIQ of 0.4 or greater, a low variation in RIQ with pupil diameter between 0 and 0.05, and a low slope of TFRIQ of approximately zero can be applied in some embodiments. In other applications, a combination of a high RIQ of 0.3 or greater, a low variation in RIQ with pupil diameter between 0 and 0.075, and a low slope of TFRIQ in the range of -0.25 to 0.25 or -0.5 to 0.5 can be applied.

[0141] The following examples were selected using the RIQ measure of Equation 2. An initial set of designs for analysis was found by calculating this RIQ for all combinations of SA Zernike coefficients up to order 10, or for a significant number of combinations. The coefficients used were constrained to be in the range of -0.3 μm to 0.3 μm, and to be values ​​that are multiples of 0.25 μm. In certain embodiments, the RIQ used may be based on an approximation or characterization of Equation 2.

[0142] Analysis of the initial set of designs included 1) identifying an optimized combination of Zernike coefficients that provided high RIQ around the retina and a negative slope of through-focus RIQ, 2) consideration of RIQ and through-focus RIQ at different pupil sizes and the change in RIQ and through-focus RIQ, and 3) consideration of RIQ across the horizontal field. The relative weight given to these evaluation stages may vary for a particular recipient. To identify the following example, the greatest weight was given to the first criterion.

[0143] Section 8: Optical design examples to address through-focus RIQ tilt Examples of designs for influencing the stimulus for eye growth under an optical feedback mechanism are provided herein. The following examples are rotationally symmetric. However, astigmatic and other non-rotationally symmetric designs can be created. When intentional decentration of a symmetric design is imposed so that the optical axis of a corrective contact lens coincides with a reference axis of the eye, such as the pupillary or visual axis, certain residual amounts of asymmetric aberrations, such as coma and trefoil, can be induced, which can be compensated for by selecting additional higher-order asymmetric terms. Figures 17-25 are illustrations showing power profile graphs of sample designs that provide RIQ for on-axis (i.e., at zero visual angle) visual acuity that degrades in the direction of eye growth, thus providing a stimulus for inhibiting eye growth under the account of the optical feedback mechanism of the emmetropization process, according to certain embodiments. The aberration profile graphs are described as the axial power variation in diopters across the optical zone diameter. The provided examples may have application for progressive myopia, whose spherical refractive error is -2D; this information is indicated by the double gray line on the power profile.

[0144] Figure 26 is an illustration detailing a sample design that can be used for hyperopia treatment, according to certain embodiments. This design was generated by taking as input parameters a specific aberration profile that would produce a positive gradient of TFRIQ in the direction of eye growth, as shown in Table 2, and optimizing the power profile (the anterior surface of the corrective contact lens) to achieve the required positive gradient. The lens design is described as the axial power variation in diopters across the optical zone diameter. The provided example may have application for non-progressive hyperopia, whose spherical refractive error is +2D; this information is indicated by the double gray line on the power profile.

[0145] As described herein, the exemplary power profiles shown in FIGS. 17-26 were selected based on the gradient of RIQ around the retina, according to certain embodiments. Across these examples, significant variations in RIQ values ​​can occur. These variations occur on axis, across pupil diameters, and at different viewing angles. Further selection criteria are the values ​​of RIQ and the variation of RIQ with viewing angle. In particular, selection can be made to maximize one or more of the on-axis RIQ, the RIQ across pupil diameters (with or without Stiles-Crawford light reduction), and the RIQ at different viewing angles. Furthermore, the recipient's pupil size can also be used as a selection criterion—for example, a first aberration profile may better suit a first recipient with a normal pupil size of 4 mm, while a second aberration profile may better suit a second recipient with a normal pupil size of 5 mm. A "normal" pupil size can optionally be selected taking into account lifestyle factors, such as the amount of time a person spends indoors or outdoors. Further examples referenced below incorporate these selection criteria, but first, to provide a point of comparison, the RIQ performance of a single vision lens is described and shown in FIG.

[0146] 27 is an illustration showing a graph of a measure of the through-focus RIQ metric, according to certain embodiments, where RIQ is the visual Strehl ratio (monochromatic) in this case and in the examples below. RIQ can be obtained, for example, from a monofocal contact lens with a -2D power used to correct a recipient model myopic eye having only -2D. The horizontal (dependent) axis indicates through-focus in diopters. A zero (0) value on the horizontal axis represents the location of the focus of the monofocal lens, and the vertical (independent) axis indicates RIQ. Three plots are provided: one for the axis (circles), one for a 10-degree field of view (triangles), and one for a 20-degree field of view (triangles).

[0147] As used in this example described herein, the term "global" refers to consideration over a specific range of field angles, including zero. Therefore, the graph shows global through-focus RIQ because it includes plots over a specific range of field angles. A monofocal lens has axially symmetric RIQ at zero field angle, but asymmetric through-focus RIQ at non-zero field angles, including both 10 and 20 degrees. In particular, the graph shows that RIQ improves in the direction of eye growth at zero field angle, according to certain embodiments. Under the explanation of the optical feedback mechanism of emmetropization, peripheral and on-axis visual acuity provide stimuli for eye growth. In certain embodiments, the tilt of TFRIQ at the retina to control eye growth (reduced RIQ for negative tilt, i.e., myopia and positive tilt, or increased RIQ for hyperopia) may be over a range of field angles that may or may not include zero or on-axis field angles. An average measure of the tilt of TFRIQ (sometimes referred to as the average through-focus tilt of RIQ) may be used over a selection of field angles or ranges of field angles. For example, the tilt of the TFRIQ averaged between at least -20° and +20° viewing angles. Another example may average the tilt of the TFRIQ over at least -20°, 0°, and +20° viewing angles. A wider range of viewing angles may also be used, such as at least -30° and +30° viewing angles, or at least -40° and +40° viewing angles.

[0148] In certain embodiments, the average slope of the TFRIQ over a selection of field angles or ranges of field angles may be a weighted average slope of the TFRIQ that gives more weight, less weight, or the same weight to different field angles to emphasize or weight the contributions of different field angles depending on the application.

[0149] FIG. 28 is an illustration showing a graph of RIQ for a lens embodiment (labeled "Iteration A1") selected to address an optical feedback mechanism explanation for emmetropization in which eye growth is prevented (e.g., to address progressive myopia or to address the risk of developing myopia), according to certain embodiments. The data for FIG. 28 was prepared for a 4 mm pupil size and to address the same or substantially the same level of myopia for the monofocal iterations. Comparing FIG. 28 with FIG. 27, RIQ no longer improves in the direction of eye growth for non-zero field angles. In particular, RIQ has a strong tendency toward deterioration in the direction of eye growth for 10 degrees off-axis. While there is a slight improvement in RIQ around the retina at 20 degrees off-axis or substantially no change in RIQ at all, the overall effect is strongly biased toward deteriorating RIQ in the direction of eye growth. FIG. 29 shows the power profile resulting in the RIQ graph of FIG. 28.

[0150] Figure 30 is an illustration showing a graph of RIQ for a particular embodiment (Iteration A2) of the lens selected to address the optical feedback mechanism explanation of emmetropization. The data for Figure 30 was prepared for a pupil size of 5 mm.

[0151] 31 and 32 are illustrations showing RIQ graphs for two other embodiments of lenses (Iterations C1 and C2, respectively) selected to address the optical feedback mechanism explanation for emmetropization, but in this case to provide an RIQ that improves the direction of eye growth (e.g., to provide growth stimulation to the eye and correct hyperopia). Figures 31 and 32 show exemplary embodiments selected with different weightings for the selection criteria. In the power profile given in Figure 31, achieving a high on-axis RIQ is given more weight than achieving a high RIQ over a wide range of field angles.

[0152] In the power profiles presented in Figure 32, greater weight was placed on providing high RIQ over a wide range of field angles compared to achieving high on-axis RIQ. For certain applications, an acceptable high RIQ over a wide field angle is considered to be an RIQ greater than 0.6, greater than 0.55, greater than 0.5, greater than 0.45, greater than 0.4, greater than 0.35, or greater than 0.3. Table 3 lists the defocus and high-order aberration coefficients up to the 20th order in microns for a 5mm pupil diameter for the power profiles described above. TIFF0007618639000014.tif48140

[0153] Section 9: Application to presbyopia Presbyopia is a condition in which the eye gradually decreases with age in its ability to focus on near objects. The ability to focus on near objects can be referred to as accommodative ability. Pre-presbyopia is an early stage in which patients begin to complain of a decreased ability to focus on near objects. The ability to focus on near objects without the use of the lenses and / or devices disclosed herein is considered a non-presbyopic state. Certain embodiments are directed to providing lenses, devices, and / or methods configured to provide visual performance substantially comparable to pre-presbyopic and non-presbyopic visual performance over a range of distances with minimal ghosting.

[0154] For example, a close distance is in the range of 33 cm to 50 cm or 40 cm to 50 cm, a medium distance is in the range of 50 cm to 100 cm, 50 cm to 80 cm, or 50 cm to 70 cm, and a long distance is in the range of 100 cm or more, 80 cm or more, or 70 cm or more. Other distances or ranges of distances may also be used.

[0155] In certain applications, increasing the through-focus RIQ can provide one or more benefits in presbyopia. The decrease in the eye's ability to see near due to decreased accommodation can be partially compensated for and / or mitigated by using the increased through-focus of certain approaches described herein. Benefits may include visual performance that is close to or approaches the visual performance of a properly prescribed single-vision lens for near viewing distances.

[0156] Other benefits may include (i) visual performance at far and intermediate distances that is substantially equivalent to that of a properly prescribed single-vision lens for the far viewing distance; (ii) visual performance over intermediate and far distances that is at least substantially equivalent to that of a properly prescribed single-vision lens at the far viewing distance; iii) visual performance along a substantially continuous range of viewing distances, including intermediate and far distances, where the visual performance of the multifocal lens is at least substantially equivalent to that of a properly prescribed single-vision lens at the far viewing distance; and / or (iv) visual performance at far or intermediate distances that is substantially equivalent to that of a properly prescribed single-vision lens at the far viewing distance, with minimal or substantially minimal ghosting. In certain embodiments, the viewing distances over one or more of the following ranges, namely, near, intermediate, and far distances, may be continuous, substantially continuous, or continuous over a portion of one or more near distances, one or more intermediate distances, or one or more far distances. This may also be true for optical infinity. In certain embodiments, the continuum can be defined as a near range of 33 cm to 50 cm, 40 cm to 50 cm, or 33 cm to 60 cm, a mid-range range of 50 cm to 100 cm, 50 cm to 80 cm, or 50 cm to 70 cm, and a far range of 100 cm or greater, 80 cm or greater, or 70 cm or greater. According to certain disclosed lenses, the lenses are configured to provide visual performance along a continuum of viewing distances including near, intermediate, and far distances.

[0157] In some embodiments, the through-focus RIQ is further increased by employing a monocular optimization approach or using one or more of the monocular methods disclosed herein. The monocular optimization approach, in certain embodiments, is achieved by increasing the through-focus RIQ to optimize one eye for distance vision and the other eye for near vision. In certain embodiments, this optimization is by selecting different base powers for the lenses (i.e., effective refractive prescriptions). The increased through-focus (e.g., RIQ) for each lens allows the base powers to be separated or used between the two base powers without sacrificing or substantially reducing distance, intermediate, or near vision.

[0158] In certain embodiments, one or more of the monocular methods disclosed herein can be used to increase binocular through-focus RIQ or through-focus RIQ by using an aberration profile for one eye and a different aberration profile for the other eye. The increased through-focus RIQ of each lens optimizes one eye for distance vision and the other eye for near vision without substantially reducing distance, intermediate, and / or near vision, and with minimal or substantially minimal ghosting for the two aberration profiles.

[0159] In certain embodiments, one or more of the monocular methods disclosed herein can be used to increase binocular through-focus RIQ or through-focus RIQ by using an aberration profile and base power for one eye and a different aberration profile and base power for the other eye. The increased through-focus RIQ of each lens optimizes one eye for distance vision and the other eye for near vision without substantially reducing distance, intermediate, and / or near vision, and with minimal or substantially minimal ghosting for the two aberration profiles and base powers.

[0160] Under a monocular approach, in some embodiments, the selection of the aberration profile can give high priority to consideration of RIQ and through-focus RIQ at different pupil sizes (reflecting changes in the eye with different accommodation and illumination levels) and changes in RIQ and through-focus RIQ.

[0161] Similarly, lenses or optical devices can be designed as bifocal, multifocal, or omnifocal lenses, one or both of whose components incorporate the aberration profiles described herein to increase TFRIQ. Combinations of bifocal, multifocal, and omnifocal lenses, devices, methods, and procedures can be used synergistically in one eye or both eyes, with appropriate selection for each eye to improve binocular performance. For example, one eye can be biased for optimal vision for distance, while the other eye can be biased for optimal vision at near distances.

[0162] A combination of bifocal, multifocal, omnifocal lenses, devices, and / or monocular methods can increase visual performance by approximately 1, 1.25, 1.5, 1.75, 2, or 2.25 D over a particular range of diopter distances. For example, with reference to such a method of prescribing a bifocal lens, one eye may have distance visual acuity (RIQ, about 0.35, 0.4, 0.45, 0.5, or another selected value) in the upper quadrant of performance and near visual acuity (RIQ, about 0.1, 0.12, 0.15, 0.17, 0.2, or another selected value) in the lower quadrant of performance, and the other eye may have intermediate visual acuity (RIQ, about 0.35, 0.4, 0.45, 0.5, or another selected value) in the upper quadrant of performance and near visual acuity (RIQ, about 0.1, 0.12, 0.15, 0.17, 0.2, or another selected value) in the lower quadrant of performance.

[0163] Different base powers, power profiles, or aberration profiles can be selected such that when used in two different eyes, the through-focus RIQs overlap, increasing the binocular through-focus RIQ. For example, in certain embodiments, the base powers can be selected such that in combination the visual Strehl ratio is not less than 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.40, or another selected value between the combined RIQ profiles.

[0164] A) Example of presbyopia FIG. 36 shows a through-focus RIQ (in this case, visual Strehl ratio) graph for seven power profiles, according to certain embodiments. In this figure, the vertical axis (RIQ) is defined on a logarithmic scale. FIG. 36 was obtained for an eye with a 5 mm pupil size and no myopia or hyperopia or other high-order aberrations. One or more power profiles can be fitted to a myopic or hyperopic eye by incorporating an appropriate corrective defocus term that does not affect the high-order aberrations that define the power profiles used for FIG. 36.

[0165] The seven power profiles are a power profile that may appear in a conventional central distance aspheric multifocal lens (shown by a △ in Figure 36), a power profile that may appear in a conventional central near multifocal lens (shown by an X in Figure 36), a power profile that may appear in a central distance concentric bifocal lens (shown by a black ■ in Figure 36), a power profile that may appear in a central near concentric bifocal lens (shown by an open ◇ in Figure 36), and three iterations (Iteration B1, Iteration B2, Iteration B3) that include advantageous combinations of spherical aberrations (shown by a black circle, a capital + sign, and a pair of concentric circles in Figure 36, respectively).

[0166] The power profiles for each of these are shown in Figures 37-43. The central distance and central near aspheric multifocal lenses had central components extending to approximately 2 mm, with outer zone power beginning at a radius of approximately 1.8 mm. A linear transition was provided between the near and distance power zones. Both concentric bifocal lenses had a ring structure alternating between 2 diopters of additional power and no add power (also called base distance power).

[0167] Table 4 lists the defocus in microns and high-order spherical aberration coefficients up to 20th order for a 5 mm pupil diameter for each of the power profiles of three exemplary embodiments: Iteration B1 (FIG. 41), Iteration B2 (FIG. 42), and Iteration B3 (FIG. 43). TIFF0007618639000015.tif67130

[0168] Table 5 lists the defocus in microns and the high-order spherical aberration coefficients up to the 20th order for a 5 mm pupil diameter for each of the power profiles described: a central distance aspheric multifocal lens (Figure 37) and a central near aspheric multifocal lens (Figure 38). TIFF0007618639000016.tif78127

[0169] In an aspheric multifocal lens, the spherical aberration coefficients progressively decrease in absolute magnitude with increasing order. This contrasts with the power profiles of Iterations B1, B2, and B3, which include at least one higher-order spherical aberration with a coefficient absolute value greater than the absolute values ​​of the coefficients for the lower-order terms. This characteristic is present in one or more of the power profile embodiments described herein. It is noted from FIG. 36 that the central distance aspheric multifocal lens, according to certain embodiments, has a D of 0.23 at 0D, which is substantially inferior to the other power profiles. However, the performance of this lens, as measured by the RIQ metric, remains relatively constant over a wide through-focus range. For example, at -0.4 diopters, the RIQ is approximately 0.2, at 0.67 diopters, the RIQ is approximately 0.18, and at -1 diopter, the RIQ is approximately 0.12.

[0170] The central near aspheric multifocal lens has an RIQ of approximately 0.5 at 0D. With this exemplary design, the RIQ drops to approximately 0.24 at -0.67 diopters (still better than the central distance aspheric multifocal lens). However, beyond that value, the central near aspheric multifocal lens has a rapidly decreasing RIQ, as can be seen, with an RIQ value of approximately 0.08 at -1 diopter. Both concentric bifocal lenses (central distance and central near) have low RIQs of 0.13 and 0.21 at 0D. Both concentric bifocal lenses maintain their RIQ levels or higher over a range of approximately 1.1 diopters. TIFF0007618639000017.tif146122

[0171] Iterations B1, B2, and B3 have RIQs at 0D that are at least as good as the central near bifocal lens, and similarly, due to the eye's accommodation, have better RIQs across the TF range between -0.65D and 0.75D. For example, Iteration B2 has an RIQ of approximately 0.53 at -0.4 diopters, an RIQ of approximately 0.32 at -0.67 diopters, and an RIQ of approximately 0.13 at -1 diopter. The through-focus performance (RIQ) of Iterations B1, B2, and B3 can be further increased. This increase is achieved by shifting the curve to the left in FIG. 36. However, the performance of the central near aspheric multifocal lens cannot be shifted in this manner without substantially affecting performance due to the asymmetric RIQ (right side of FIG. 36) that decreases substantially more rapidly for plus powers in this example.

[0172] For example, three exemplary iterations have an RIQ of about 0.40 at +0.55 D. Combining the spherical aberration term with the +0.55 D defocus term will shift the RIQ value for distance vision to the value for +0.55 D in Figure 36. Considering iteration B2 again, the through-focus performance (RIQ) will be modified as follows: RIQ of about 0.4 for distance vision, RIQ of about 0.53 at -0.4 diopters, RIQ of about 0.64 at -0.67 diopters, RIQ of about 0.52 at -1 diopters, RIQ of about 0.40 at -1.1 diopters, and RIQ of about 0.15 at -1.5 diopters.

[0173] By shifting the distance vision point within the lens with a combination of HOAs that increases through-focus RIQ performance, lenses, devices, and / or methods that provide the combination of HOAs can have substantially improved through-focus performance. This is achieved while maintaining RIQ at least as good as that of a central near aspheric multifocal lens and substantially improved RIQ compared to a central distance aspheric multifocal lens. The amount of defocus plus power added to shift the RIQ curve is a matter of choice and represents a trade-off between distance and near vision RIQ. Table 6 shows the defocus (left-most column) and RIQ values ​​for the power profiles described above. Table 6 also shows the defocus values ​​shifted by +0.55D, which applies when Iterations B1, B2, and B3 are modified by this amount.

[0174] Figure 115 shows the through-focus retinal image quality for five exemplary combinations of high-order aberrations (T1-T5 shown in Table 6.1), including only symmetric high-order aberrations. The through-focus retinal image quality was calculated for the five exemplary high-order aberration combinations using the monochromatic RIQ (visual Strehl ratio) described in Equation 2. The T1, T4, and T5 combinations used a 3mm pupil diameter to obtain through-focus retinal image quality, while the T2 and T3 combinations used a 4mm pupil diameter. These calculations for specific pupil diameters and / or at specific retinal image qualities result in exemplary combinations. Other exemplary combinations are also considered using one or more of the image quality metric, pupil, and spatial frequency range to calculate through-focus retinal image quality. TIFF0007618639000018.tif129140

[0175] B) Effect of pupil size Figures 44-46 show the variation of through-focus RIQ with pupil size for Iteration B1, Iteration B2, and Iteration B3, respectively, according to certain embodiments. The exemplary RIQ profiles are relatively stable in that the RIQ maintains a combination of a relatively high RIQ (e.g., compared to a central distance aspheric multifocal lens) combined with a relatively wide through-focus range (e.g., compared to a central near aspheric multifocal lens). Figure sets 47, 48, and 49-50 show the variation of through-focus RIQ with pupil size for two concentric bifocal lenses and two aspheric multifocal lenses, respectively. From these figures, it can be seen that, by comparison, the changes in RIQ and through-focus RIQ performance are less stable for these lenses than for Iteration B1 (Figure 39), Iteration B2 (Figure 40), and Iteration B3 (Figure 41). Figures 39-50 are examples according to certain embodiments.

[0176] C) Monocular and / or binocular designs As described herein, iteration B2 (FIG. 40) can provide an RIQ of 0.4 or greater from distance vision to approximately 1.1 diopters of intermediate vergence. If an appropriate level of defocus is added to the same iteration while correcting the fellow eye, the TFRIQ can increase from 1.1 diopters up close, for example, to 2.2D target vergence. That is, the binocularly combined candidate eye can provide an RIQ of 0.4 or greater from the distance test distance all the way up to or substantially up to 2.2 diopters. Using this monocular design approach, and assuming the recipient accepts the monocular design, the combined through-focus performance can be substantially increased according to certain embodiments.

[0177] Referring to the through-focus profiles shown in Figures 51 and 52 described herein, under a monocular design approach, according to certain embodiments, one lens will be selected to have a base power that shifts the through-focus curve to the far left or slightly back to the left from the far left (starting at the -2.5D mark) (distance refractive prescription), and the other lens will be selected to have a base power that shifts the through-focus curve slightly to the left (starting at the -1.5D mark).

[0178] Figures 51 and 52 show the design TF RIQ (binocular "Q" correction) of two pairs of power profiles, according to certain embodiments. Each lens in the pair was designed to increase the RIQ in combination with the other lens in the pair. The defocus and high-order spherical aberration coefficients for these combinations are specified in Tables 7 and 8, respectively. TIFF0007618639000019.tif68134TIFF0007618639000020.tif74134

[0179] The power profiles described with respect to Tables 7 and 8 are examples of combinations of high-order aberrations that provide improved through-focus performance on the negative side of the through-focus function. Similarly, using this monocular design approach, the combined through-focus performance can also be substantially increased on the negative side of the through-focus function, provided that an appropriate level of defocus is added to the selected combination of high-order aberrations. Figures 53 and 54 show examples with a relatively constant RIQ (>0.35) over a certain range of defocus in the positive direction of the through-focus function, according to certain embodiments. The defocus and high-order spherical aberration coefficients for these combinations are specified in Tables 9 and 10, respectively. TIFF0007618639000021.tif74124TIFF0007618639000022.tif85119

[0180] FIG. 118 shows the through-focus retinal image quality of two exemplary designs N41 and N42, calculated at a 3 mm pupil diameter using the visual Strehl ratio as the retinal image quality metric described in Section 1. The power profile of the exemplary embodiment pair N41 and N42 as a function of the half-chord diameter of the optical zone is set forth in FIG. 117. This pair of lenses may be prescribed for a pair of eyes, with one design prescribed for a selected eye and the other design prescribed for the fellow eye. In this example, as seen in FIG. 118, the solid and double lines represent the through-focus retinal image quality of each of the two exemplary designs, N41 and N42, respectively. A pair of exemplary designs with different performance characteristics may be used in a method for correcting a pair of eyes. Using such an exemplary method may result in a combination and / or summation of the individual performances of each lens, which may occur at the visual cortex level in the brain. For example, the summed response for the embodiment pair N41 and N42 is represented by the dashed line in FIG. 118.

[0181] FIG. 138 shows the through-focus retinal image quality of two exemplary designs N11 and N12, calculated at a 3 mm pupil diameter using the visual Strehl ratio incorporating the cosine of the phase transfer function as the retinal image quality metric described in Section 1. The power profile of the exemplary embodiment pair N11 and N12 as a function of the half-chord diameter of the optical zone is described in FIG. 137. This pair of lenses may be prescribed for a pair of eyes, with one design prescribed for a selected eye and the other design prescribed for the fellow eye. In this example, as seen in FIG. 138, the solid and double lines represent the through-focus retinal image quality of each of the two exemplary designs, N11 and N12, respectively. A pair of exemplary designs with different performance characteristics may be used in a method for correcting a pair of eyes. Using such an exemplary method may result in the combination and / or summation of the individual performances of each lens, as predicted at the visual cortex level in the brain. For example, the summed response for the embodiment pair N11 and N12 is represented by the dashed line in FIG. 138.

[0182] Section 10: Designing for enhanced central vision Some embodiments may be used to selectively optimize visual performance under one or more defined viewing conditions. Such viewing conditions may include, but are not limited to, a specific viewing distance, a specific lighting condition, a specific visual task, or a combination thereof. Optical performance may include retinal image quality metrics described herein. For designs to enhance central vision, visual performance may include visual acuity and / or contrast sensitivity. For example, some of the disclosed embodiments may be utilized to create devices, lenses, and / or methods selectively optimized for one or more of high-contrast visual acuity, low-contrast visual acuity, contrast sensitivity, high illumination, low illumination, photopic vision (daytime viewing), mesopic vision, scotopic vision (nighttime viewing), distance viewing, computer viewing, near reading, or a combination thereof.

[0183] Section 10A: Designing for Peripheral Vision In some embodiments, when selecting a combination of HOAs to form a power profile, increased weighting can be given to peripheral vision, which may be applicable, for example, when the recipient plays a particular sport where peripheral vision is important.

[0184] Figure 55 shows a graph of RIQ (also known as the visual Strehl ratio) for three different power profiles that substantially equalize RIQ across the horizontal field, according to certain embodiments. RIQ measures were obtained for a 5mm pupil. The defocus and high-order spherical aberration coefficients for each power profile are shown in Table 11. TIFF0007618639000023.tif77125

[0185] Iteration A3 (FIG. 56), Iteration A4 (FIG. 57), and Iteration A6 (FIG. 58) produced an on-axis RIQ of approximately 0.5 over a field angle of zero to 30 degrees (which is 60 degrees combined across both the nasal and temporal fields if horizontal symmetry is assumed), according to certain embodiments. The on-axis RIQ was also approximately 0.5, which is lower than some other embodiments that allow for a degradation of RIQ below 0.5 with increasing field angle.

[0186] Thus, in certain embodiments, on-axis RIQ can be traded off against RIQ at high field angles. For example, RIQ can be allowed to drop to 0.2 at a 30-degree field angle (but remain above 0.5 for fields below 20 degrees), allowing for the selection of an HOA that increases on-axis RIQ beyond the value shown in FIG. 55. A power profile design for peripheral vision can be selected for lenses designed to provide RIQ gradients (providing stimuli to retard or accelerate eye growth under the account of optical feedback mechanisms for emmetropization) or for corrections / lenses for presbyopia (emmetropia, myopia, or hyperopia) or other eyes. In certain embodiments, the high field angle is one or more of a 10-degree, 20-degree, 30-degree, or 40-degree field of view. Other suitable high field angles can be used in certain applications as well.

[0187] Section 11: Positive and Negative Phase Selection For a particular recipient of the lenses, devices, and / or methods disclosed herein, a choice can be made between two power profiles of opposite phase. In this context, the term "opposite phase" identifies a power profile having a specific combination of high-order aberrations of the same or substantially the same magnitude relative to a desired pupil, while their signs are opposite to each other. Figures 59 and 60 show power profile iterations E1 and E2, which are examples of power profiles with opposite phases, according to certain embodiments. Table 12 reflects the magnitudes and signs of the high-order spherical aberration terms for iterations E1 and E2. The opposite-phase lenses described herein may result in the same or substantially the same on-axis peak RIQ. The through-focus RIQ of such a phase profile pair can be a mirror image or a substantially mirror image of each other across the Y-axis, as shown in Figure 61. However, this will result if the intrinsic high-order aberration profile is negligibly small (eg, for first order spherical aberration in the range -0.02 μm to 0.02 μm for a 5 mm pupil). TIFF0007618639000024.tif89121

[0188] The interaction between the candidate eye's intrinsic aberration profile and the selected phase profile may have a) improving or b) deteriorating effect on objective and / or subjective optical and / or visual performance. Because TFRIQ depends on the intrinsic aberration profile, for example, the selected phase profile may be useful to change the tilt of TFRIQ in a direction that would be favorable to the emmetropization process for a myopic or hyperopic eye, or alternatively, the same or similar phase profile may be used to alleviate presbyopic symptoms in a replacement candidate eye.

[0189] 62 and 63 show how the TFRIQ of the opposite-phase profile depends on the candidate eye's intrinsic ocular aberration (positive spherical aberration in this example) according to certain embodiments. Certain embodiments disclosed herein include providing lenses of the same or substantially the same design but with opposite phases and allowing the recipient to select a preferred phase. The selection process can be through objective evaluation of TFRIQ performance metrics and / or purely subjective preference through visually guided testing.

[0190] Section 12: Identifying and selecting combinations As described herein with respect to certain embodiments, by selecting an appropriate combination of desired on-axis RIQ for distance and HOA, it is possible to provide an appropriate through-focus RIQ that will enable better visual performance for distance, intermediate, and near vergence. This combination of high-order aberrations can include correction for the test candidate's unique aberration profile. Appendix A herein lists 78 combinations of high-order spherical aberration coefficients that provide both a useful high RIQ and the option of providing increased through-focus RIQ in the negative direction (left). Appendix A also lists combinations without any order of spherical aberration for comparison. Appendix B lists TFRIQ values ​​for the combinations listed in Appendix A. Calculations were performed for a 4 mm pupil diameter. However, the approach or method can be scaled to other appropriate and / or desired pupil sizes as needed or desired. For example, the method can be used with pupil sizes within one or more of the following ranges: 1.5-8 mm, 2-8 mm, 2.5-8 mm, 3-7 mm, 3-8 mm, 1.5-8 mm, and 3.5-7 mm. For example, the method can be used with pupil sizes of about 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6, 6.5, 7, 7.5, or 8 mm.

[0191] The TFRIQ measures of the 78 aberration combinations are shown in Figure 64, where the black lines show the symmetric RIQ resulting from combinations that have no higher-order aberrations, and the lighter lines (i.e., gray lines) show increased performance in the negative direction of the TFRIQ function for the 78 combinations that include higher-order spherical aberration terms.

[0192] Several observations can be made from Figure 64. The 78 profiles with higher-order spherical aberration terms provide increased through-focus performance in the negative direction, especially when an appropriate selection of negative power is made, shifting the plotted through-focus profile toward negative focus (left). The 78 profiles include a range where the RIQ is 0.1 or greater over at least 2 diopters. Several of the 78 profiles include a range where the RIQ is 0.1 or greater over at least 2.25 diopters. The 78 profiles include RIQs (visual Strehl ratio—monochromatic) that peak above 0.35. Many of the profiles include RIQs that peak above thresholds of 0.4, 0.5, 0.6, and 0.7, with some combinations resulting in peaks that exist above the 0.8 mark.

[0193] The spherical aberration terms range in combination from 1 (e.g., combination 77) to 9. In other embodiments, even higher orders of the spherical aberration terms can be added to create further combinations.

[0194] Combination 77 in Appendix A shows that by selecting a specific level of first-order spherical aberration, the aberration profile can be advantageously used for presbyopic eyes. For myopia, see U.S. Pat. No. 6,045,568. In contrast, according to certain embodiments, stimulation of retarding on-axis eye growth under the account of the optical feedback mechanism of emmetropization is achieved when the retina is located on the negative side of the graph shown in FIG. 65 (i.e., the focal length of the lens is longer than the eye). In other words, the aberration profile typically includes a C(2,0) term with additional negative power over the amount needed to correct myopia.

[0195] Appendix C lists 67 combinations of high-order spherical aberration coefficients that provide both a useful high RIQ and the option of providing increased through-focus RIQ in the positive direction (right side of Figure 66). Also listed in Appendix C are combinations without any order of spherical aberration, for comparison. Appendix D lists TFRIQ values ​​for the combinations listed in Appendix C. Again, calculations were performed for a 4 mm pupil diameter. However, the approach or method can be scaled to other suitable and / or desired pupil sizes as needed or desired.

[0196] The TFRIQ measures of the 67 aberration combinations are shown in Figure 66, where the black lines show the symmetric RIQ resulting from combinations that have no higher-order aberrations, and the lighter lines (i.e., gray lines) show increased performance in the positive direction of the TFRIQ function for the 67 combinations that include higher-order spherical aberration terms.

[0197] Several observations can be made from Figure 66. The 67 profiles with higher-order spherical aberration terms provide increased through-focus performance in the positive direction, especially when appropriate selection of negative power is made to shift the plotted through-focus profile toward negative focus (left). The 67 profiles include a range where the RIQ is 0.1 or greater over at least 2 diopters. Several of the 78 profiles include a range where the RIQ is 0.1 or greater over a D of at least 2.5D. Figure 67 shows an exemplary workflow diagram for identifying a power profile for application to a presbyopic eye, according to certain embodiments.

[0198] Section 13: Spherical aberration and astigmatism Iterations B1, B2, and B3 are described herein for emmetropic presbyopia. When considering astigmatic presbyopia, at least two different approaches can be employed. The first corrective approach is accomplished by considering the astigmatic refractive error as an equivalent sphere. In this method, the spherical equivalent prescription is derived by dividing the cylinder / astigmatic power by 2 (S=-C / 2). This is a very common approach often considered to address low to moderate amounts of astigmatism, e.g., up to -1.5D. When an equivalent sphere is utilized, the same or substantially the same iterations described herein, e.g., B1, B2, B3, can be used as the effective prescription once the defocus term is adjusted to fit the equivalent sphere.

[0199] The second method considers tailoring a toric prescription for both astigmatism and presbyopia. Figure 68 shows an exemplary embodiment including a toric power profile for treating both astigmatism and presbyopia. In this case, the prescription is made to correct an individual who has a -1D@90 astigmatism correction and needs additional power to enable near vision. As can be noted from the figure, the difference between the horizontal and vertical meridians is -1D, and this magnitude is set to correct the astigmatism in the above case, while the combination of higher-order spherical aberrations aims to alleviate presbyopic symptoms. Other suitable methods can similarly be used or incorporated into some of the disclosed embodiments.

[0200] The aberration profile of some exemplary embodiments with substantially rotationally symmetric terms may be selected to conceal and / or correct astigmatism down to at least -0.5DC, -0.75DC, -1DC, and -1.25DC. In some embodiments, the correction of astigmatism may be independent of the axis of the corrected astigmatism. In some embodiments, the selection of rotationally symmetric terms to conceal and / or correct astigmatism may be limited to at least 10th, 14th, 18th, or 20th order Zernike polynomial increases. In the current example shown in Table 12.1, a 5mm trend, a spatial frequency range of 0-25 cycles / degree, and the visual Strehl ratio as the through-focus retinal image quality metric were used. However, such calculations may also use a combination of pupil size, retinal image quality metric, and / or spatial frequency. Table 12.1 Defocus and construction spherical aberration coefficients for one exemplary embodiment that conceals approximately -1.25 DC astigmatism in any axis. Calculations were performed using a 5 mm pupil diameter and the visual Strehl ratio as the RIQ metric over a spatial frequency range of 0 to 25 cycles / degree. TIFF0007618639000025.tif112134

[0201] Section 13.A: Applications to Vision Improvement Some embodiments are directed to lenses, optical devices, and / or methods that include an aberration profile that is beneficial for improving vision for seeing a particular level of visual detail, such as for visual detail at a desired spatial frequency or in a desired range of spatial frequencies. The improved vision may take the form of improved retinal image quality, visual acuity, contrast sensitivity at the desired spatial frequency or range of spatial frequencies, and / or combinations thereof.

[0202] Visual acuity is sometimes used as a measure of an aspect of visual performance. Vision measurements assess a limit when a visual target, such as a letter, i.e., the letter "E" ("illiterate" E) or the letter "C" (Landolt C), or some other target, can no longer be resolved, identified, or correctly reported by the patient undergoing vision testing. The limit is related to one or more of the spatial frequency of the visual target (how finely spaced the visual target details are) and the contrast of the visual target, among other factors. The limit of visual acuity may be reached when the contrast of the image of the visual target, produced by the optical structure of the eye with or without additional optical devices, is too low to be discerned by the visual system (including the retina, visual pathway, and visual cortex). Because the retinal image contrast required to distinguish a retinal image increases as spatial frequency increases for targets of a range of fineness of detail (i.e., spatial frequency) (i.e., the finer the detailed target, the greater the contrast must be), the eye, or an eye with an optical device, can typically distinguish the finest details at the highest spatial frequencies, i.e., where the retinal image contrast is equal to or greater than the minimum contrast required to detect the detail.

[0203] In some embodiments, one way that vision may be improved is by increasing the contrast of the retinal image at a level of fineness of detail (i.e., spatial frequency) that is close to and / or slightly higher than the vision of the natural eye or an eye with an optical device.

[0204] Certain embodiments are directed to aberration profiles that increase contrast from slightly below or near the visual acuity of the natural eye, or the natural eye with a conventional optical device, to near or slightly above the visual acuity of the natural eye, or the natural eye with a conventional optical device.

[0205] In one exemplary embodiment, the eye may have a best-corrected visual acuity of 6 / 6 (or 20 / 20) (i.e., the best visual acuity achievable using the best correction with a conventional optical device for its refractive error, which may be myopia, hyperopia, astigmatism, or some combination thereof). This visual acuity level may be equated to a spatial frequency of 30 cycles per degree. That is, finer details and higher spatial frequency targets may produce retinal image contrast that is too low for the retina and visual system to distinguish. In this exemplary embodiment shown in FIG. 134, the optimized aberration combination provides a retinal image with enhanced (higher) contrast in the spatial frequency range from 20 cycles per degree to 60 cycles per degree, i.e., from slightly below the best-corrected visual acuity of the exemplary eye (corrected for defocus terms and uncorrected for high-order aberrations) to slightly above the best-corrected visual acuity of the exemplary eye. The increased contrast leads to an increase in the RIQ of the exemplary eye. The enhanced contrast in this range of spatial frequencies provided by the high-order aberrations of this exemplary embodiment may allow the exemplary eye to achieve better visual performance and / or improved visual acuity.

[0206] In yet another application, the eye may be amblyopic, i.e., suffer from amblyopia. Amblyopia is a vision condition in which, even with the best optical correction, the eye is unable to achieve the visual acuity normally achievable by a normal eye. An amblyopic eye may have very poor visual acuity, such as 6 / 9 (i.e., 20 / 30), 6 / 12 (i.e., 20 / 40), or even worse. Such eyes may benefit from improving their vision, including improving contrast at or near the limits of the amblyopic eye's visual acuity. Thus, exemplary aberration profiles may provide enhanced contrast and / or enhanced RIO (which may be either monochromatic or polychromatic RIQ) at a range of spatial frequencies depending on the eye's level of amblyopia. In some embodiments, the range of spatial frequencies for RIQ enhancement may be selected depending on the application, such as the visual needs of an individual patient or eye. For example, the spatial frequency range may be 5 to 15 cycles / degree, 10 to 15 cycles / degree, 10 to 20 cycles / degree, 15 to 20 cycles / degree, 15 to 25 cycles / degree, 20 to 25 cycles / degree, 20 to 30 cycles / degree, 25 to 30 cycles / degree, 25 to 35 cycles / degree, 30 to 35 cycles / degree, or 30 to 40 cycles / degree.

[0207] The fovea is the point on the retina that supports the sharpest vision. In most eyes with normal vision, the image of the object being "seen" is positioned on the fovea by rotation of the eye. This alignment of the visual object by the fovea is called "fixation." The retina's ability to reconstruct fine details decreases as one moves away from the fovea (central vision). Further into the peripheral retina (peripheral vision), visual acuity progressively worsens. Certain eyes exhibit extracentral fixation. Extracentral fixation is a visual phenomenon when the eye does not use foveal vision. When attempting to "see" an object, such eyes may position the image at some point on the peripheral retina. The range of visual angles relative to the central retina or fovea (which may be considered the optical axis of the eye, i.e., the model eye), at which the image is positioned by an extracentrally fixating eye, varies from eye to eye but is usually consistent within the same eye. This range of visual angles may range from on-axis (i.e., 0°) to 5° from the eye's optical axis, or from on-axis to 10° from the eye's optical axis. For eyes with a greater amount of off-center fixation, this range of visual angles may span from 5° from the optical axis of the eye to 15° from the optical axis of the eye. Alternatively, the range of visual angles may span from 10° from the optical axis of the eye to 20° from the optical axis of the eye.

[0208] Certain embodiments are directed to aberration profiles that provide a global RIQ (GRIQ) where the range of viewing angles over which GRIQ is achieved does not need to include the central on-axis or foveal visual point. Certain embodiments are directed to aberration profiles that enhance contrast from slightly lower or closer to the peripheral vision of an eye in the peripheral or off-center viewing range, or an eye with a conventional optical device, to slightly higher or closer to the peripheral vision of an eye in the peripheral or off-center viewing region, or an eye with a conventional optical device. For example, peripheral vision in some embodiments may be 20 / 80 (i.e., 6 / 24) or better at a 20-degree viewing angle. TIFF0007618639000026.tif149131

[0209] In another application, an off-central fixating eye may have a best-corrected peripheral vision of 6 / 18 (or 20 / 60) (i.e., the best vision achievable using the best correction using a conventional optical device for that refractive error, which may be myopic, hyperopic, or astigmatic, or some combination thereof, and whose vision is measured at the eye's off-central fixation visual point). This off-central fixation peripheral vision level may be equated to a spatial frequency of 10 cycles per degree. In some exemplary embodiments, the combination of high-order aberration profiles provides an enhanced (higher) contrast retinal image in a spatial frequency range from 10 cycles per degree to 20 cycles per degree, as seen in combination #2 of FIG. 135, i.e., a contrast slightly below or close to the peripheral vision of the measured best-corrected (peripheral) vision of the exemplary off-central fixating eye, to a contrast close to or slightly higher than the measured best-corrected (peripheral) vision of the exemplary off-central fixating eye.

[0210] In other applications, the angular range of off-center fixation may vary between 5° from the eye's optical axis and 15° from the eye's optical axis. In another embodiment, a combination of high-order aberration profiles provides an enhanced (higher) contrast retinal image in the spatial frequency range of 20 cycles per degree to 30 cycles per degree, as seen in combination #3 of FIG. 136. The aberration profile of the exemplary high-order aberration combination improved contrast, which may lead to an increase in GRIQ for the exemplary eye within a field angle selected to match the angular range of off-center fixation. When optimized high-order aberration combinations are configured for the exemplary eye such that they enhance contrast within a specific range of field angles and spatial frequencies selected to substantially match the angular range of off-center fixation, the exemplary eye can achieve better visual performance and improved contrast for the range of off-center fixation. TIFF0007618639000027.tif132132

[0211] Section 14: Implementation There are several methods that may be used to design or model the lenses and / or devices disclosed herein. One exemplary method for designing one or more optical devices is to (a) establish a group of target and performance requirements for one or more optical devices, including two or more of a focal length, an optical zone, an image quality at the focal length, and a through-focus image quality around the focal length, wherein the image quality is one of a monochromatic image zone, a polychromatic image zone, or a global image zone, wherein the image quality is calculated in the spatial domain or the Fourier domain, and wherein the image quality is calculated for at least a portion of the optical zone diameter between 3 mm and 8 mm. and for one of the spatial frequency ranges of 0-15 c / d, 0-20 c / d, 0-25 c / d, 0-30 c / d, 0-45 c / d, 0-60 c / d, 5-30 c / d, or 0-60 c / d; (b) defining a wavefront representation for one or more optical devices, the wavefront representation optionally being described using one or more of the following mathematical descriptions: Zernike polynomials, Fourier series, expanded even or odd polynomials, expanded aspheres, super conics, and Bessel series; and (c) optimizing the represented wavefront to substantially achieve target performance requirements for the one or more optical devices by using a nonlinear optimization calculation routine. In some other exemplary methods, optimization of the represented wavefront may be performed to achieve the performance requirements at at least one specific distance. In yet another exemplary method, optimization of the represented wavefront may be performed to achieve performance requirements at at least two specific distances.

[0212] In yet another exemplary method, optimization of the represented wavefront may be performed to achieve the performance requirements at at least three specific distances. In yet another exemplary method, optimization of the represented wavefront may be performed to achieve the performance requirements at at least four specific distances. In yet another exemplary method, the optimized specific distances may be separated by at least 0.5D. In yet another exemplary method, the optimized specific distances may be separated by at least 1D.

[0213] In yet another exemplary method, optimization of the represented wavefront may be performed to have a negative or positive slope of the through-focus image quality at the negative or positive end of the through-focus range. Other suitable methods for designing and / or modeling the lenses and / or devices disclosed herein may also be used.

[0214] Aberration profiles of the type described herein can be implemented in multiple lenses, ophthalmic devices, and / or methods. For example, contact lenses (hard or soft), corneal onlays, corneal inlays, and lenses for intraocular devices (both anterior and posterior chambers) can include combinations of the discussed aberration profiles. Techniques for designing lenses and achieving power profiles are known and will not be described in detail herein. Aberration profiles can be applied to spectacle lenses. However, because aberration profiles require alignment of the eye with the optical structure that provides the aberration profile, the benefits may only be apparent for one specific gaze direction. Recently, electro-active lenses have been proposed, which can track gaze direction and change the refractive properties of the lens in response. Using electro-active lenses, the aberration profile can move with the eye, which can increase the usefulness of the disclosed aberration profiles for spectacle lenses.

[0215] The aberration profile can be provided on a lens that is an intraocular lens. In some embodiments, the intraocular lens can include haptics that provide accommodation. In other embodiments, the lens can have a fixed focal length. The aberration profile can be provided on an auxiliary intracapsular lens.

[0216] In certain applications, one or more of the disclosed aberration profiles can be provided to an eye through computer-assisted surgery and / or methods of modifying the eye's power and / or aberration profile, such as implants, laser sculpting, laser ablation, thermokeratoplasty, and lens sculpting. Examples of such methods include radial keratotomy (RK), photorefractive keratotomy (PRK), thermokeratoplasty, conductive keratoplasty, laser assisted in-situ keratomileusis (LASIK), laser assisted in-situ epithelial keratomileusis (LASEK), and / or clear lens extraction. For example, refractive surgery or corneal ablation can be used to create the selected aberration profile. The desired power profile or desired change in corneal shape and / or power is subsequently determined or determined and input into the laser system for application to the patient's eye. Implant, laser ablation, and / or laser sculpting procedures can similarly be used to input desired profiles and / or aberration profiles into the lens itself to achieve the desired results, including but not limited to currently existing systems including wavefront-guided femtosecond lasers.

[0217] If an aberration profile is included in the lens, the aberration profile can first be converted into a lens thickness profile for input into computer-aided manufacturing. Considering as an example, the laser power profile D1 shown in FIG. 69, which is a combination of Zernike higher-order spherical aberration terms, is converted into an axial thickness or surface profile for the contact lens, taking into account the refractive index of the contact lens material (in this case, a contact lens material refractive index of 1.42). An exemplary thickness profile is shown in FIG. 70. In certain embodiments, the power profile or thickness profile features can be placed on the anterior surface, the posterior surface, or a combination of both, taking into account the refractive indices of the lens and cornea. Once one or more of the following parameters are determined: thickness profile, power profile, posterior surface shape, diameter, and material refractive index, one or more of the parameters are input into a computer-aided lathe or other manufacturing system that produces contact lenses. A similar approach can be adopted for other lenses and optical systems, such as intraocular lenses, anterior and / or posterior chamber lenses, corneal implants, refractive surgery, or a combination thereof.

[0218] An aberration profile can be selected and identified for a personalized custom lens. The process for designing the aberration profile can include measuring the wavefront aberrations of the eye and designing the aberration profile to achieve the through-focus RIQ profile described herein. The design process can include identifying the natural spherical aberration of the eye and designing an aberration profile for the lens, device, and / or method that, in combination with the spherical aberration of the eye, provides the required or desired RIQ profile. As described herein, the required or desired RIQ profile can vary depending on the application of the lens, for example, because different requirements may apply between individuals with progressive myopia and individuals with presbyopia. In some embodiments, other aberrations of the eye, such as astigmatism, coma, or trefoil, are ignored.

[0219] In other embodiments, these are taken into consideration. For example, as described herein, the presence of astigmatism influences the combination of aberrations that provide a through-focus RIQ that inhibits eye growth under the account of the optical feedback mechanism of emmetropization. In other embodiments, these aberrations are incorporated into the design. For example, when designing a lens, a base lens can be created that corrects defocus and one or more of astigmatism, coma, or trefoil. On top of this base profile, a spherical aberration profile is provided that is designed to achieve the profile described herein (in the sense of being used as an objective design). The spherical aberration profile can be selected using a trial-and-error or iterative convergence approach, for example, by identifying candidate profiles, calculating the through-focus RIQ, and evaluating whether the through-focus RIQ has an acceptable profile. In another approach, the aberration profile can be designed for the population average, mean, median, or other statistical expression or metric. One approach to designing a population mean, mean, median, or other statistical representation or metric is to normalize, customize, adjust, or optimize the design for pupil size.

[0220] In certain embodiments, aberration profiles, first derivatives of the power profile, second derivatives of the power profile, Fourier transforms of the power profile, descriptions of the power profile and image profile of the power profile, and / or other suitable or appropriate measures of one or more optical properties or one or more performance metrics for a lens, device, and / or method are provided, in part, by mathematical description or derivation, which allows a degree of precision when deriving and / or describing the aberration profiles, first derivatives of the power profile, second derivatives of the power profile, Fourier transforms of the power profile, descriptions of the power profile and image profile of the power profile for a lens.

[0221] However, in certain applications, lenses, devices, and / or methods may or may not have precision comparable to, commensurate with, or derived from mathematical calculations. For example, tolerances and imprecision introduced during manufacturing may or may not vary the lens profile. In certain embodiments, the power profile and / or aberration profile of the lens can be approximately measured using, for example, a wavefront aberrometer. From this, an approximate measure of the through-focus RIQ can be determined using, for example, the visual Strehl ratio. In certain embodiments, the power profile and / or aberration profile of the lens can be characterized using suitable equipment and / or techniques, such as, for example, Shack-Hartmann aberrometry, ray tracing, lens power mapping, focal length measurement, interferometry, phase contrast, ptychygraphy, a Foucault knife-edge system, or a combination thereof. From these characteristics, one or more of an aberration profile, a first derivative of the power profile, a second derivative of the power profile, a Fourier transform of the power profile, a description of the power profile and an image profile of the power profile, and / or other suitable or appropriate measures of one or more optical properties or one or more performance metrics can be measured, derived, or otherwise determined.

[0222] The aberration profile can be implemented in multiple lenses, devices, and / or methods according to certain embodiments. For example, a lens can be characterized by testing the lens with respect to ray tracing or a physical model eye having a focal length equal to or substantially equal to the focal length of the lens. The aberration profile of a lens, including high-order aberration profiles, results in an image on the retina, which can be quantified using one or more of the disclosed RIQ metrics. In certain embodiments, the model eye may have no or substantially no aberrations. In certain embodiments, the RIQ metric can be the visual Strehl ratio. In other embodiments, the pupil size can be selected from one or more of the following ranges: 2-8 mm, 2-7 mm, 2-6 mm, 3-6 mm, 3-5 mm, 4-6 mm, or 5-7 mm. In some other embodiments, the spatial frequency range can be selected from one or more of 0-30 cycles / degree, 0-60 cycles / degree, or 0-45 cycles / degree. In other embodiments, the selected wavelength for calculation of one or more RIQ metrics can be selected from one or more of 540 nm to 590 nm, inclusive; 420 nm to 760 nm, inclusive; 500 nm to 720 nm, inclusive; or 420 nm to 590 nm, inclusive. In certain embodiments, RIQ can be measured with respect to an on-axis model eye. In other applications, an off-axis model eye can be used to obtain other RIQ variants, such as global RIQ. Through-focus RIQ can be calculated with respect to a model eye by using a spherical lens in front of the model eye.

[0223] Certain embodiments disclosed herein are directed to a method of correcting vision whereby one or more lenses of the disclosed embodiments are prescribed according to one or more target refractive powers, an appropriate power profile, and the lenses are fitted to an eye to provide visual performance for the eye along a substantially continuous range of viewing distances, including intermediate and far distances, wherein the visual performance of the lenses is at least substantially equivalent to the visual performance of a correctly prescribed single vision lens at a far viewing distance.

[0224] Certain embodiments disclosed herein are directed to methods of correcting vision, whereby one or more lenses of the disclosed embodiments are prescribed according to one or more target refractive powers, an appropriate power profile, and the lenses are fitted to an eye to improve visual performance for the eye. In certain applications, one or more methods disclosed herein can be used according to certain embodiments to correct the vision of an eye, whereby the eye is affected by one or more of myopia, hyperopia, emmetropia, astigmatism, presbyopia, and certain optical aberrations.

[0225] Certain embodiments can be used in methods for correcting the vision of a pair of eyes, whereby one or both of the eyes with optical aberrations have at least one high-order aberration. Certain embodiments can be used in methods for correcting binocular vision, whereby two lenses of one or more embodiments disclosed herein are prescribed according to first and second target refractive powers, and first and second power profiles are selected, and the two lenses fitted to the pair of eyes improve the visual performance of the combined two eyes compared to the individual eyes separately. In certain methods disclosed herein, the first target refractive power is different from the second target refractive power.

[0226] Certain embodiments are directed to a method of correcting binocular vision, whereby a first target refractive power is selected to improve visual performance at a viewing distance that is at least one of far, intermediate, and near, and a second target refractive power is selected to improve visual performance at a viewing distance that is at least one of far, intermediate, and near, and the viewing distance at which the visual performance for the first target refractive power is selected is different from the viewing distance at which the visual performance for the second target refractive power is selected. In certain applications, one or more methods disclosed herein can be used to correct the vision of an eye, whereby the refractive state of the eye can be classified as one or more of myopia, hyperopia, emmetropia, regular astigmatism, irregular astigmatism, optical aberrations, presbyopia, and non-presbyopia, according to certain embodiments.

[0227] Certain embodiments are directed to a method of manufacturing a lens, wherein the lens is configured or designed according to a reference eye, whereby the configured lens characteristics are selected from one or more of focal length, refractive power, power profile, number of spherical aberration terms, magnitude of spherical aberration terms, whereby the reference eye is selected from one or more of an individual eye, both eyes of an individual person, a statistical representation of eyes, a sample of a population with an abnormality, a computational model of an eye, and / or a computational model of an eye of a population with an abnormality.

[0228] In certain embodiments, aperture size can be used to characterize the entrance pupil of the eye and / or a portion of the optical zone of the lens and / or device. In certain applications, an effective aperture size can be defined as an opening that is 1.5 mm, 2 mm, 3 mm, 4 mm, 5 mm, 6 mm, or 7 mm or greater, as opposed to a pinhole aperture, which typically has a diameter of, for example, less than 1.5 mm. For example, certain embodiments are directed to a lens having an optical axis, at least two optical surfaces, the lens configured to provide visual performance for a pre-presbyopic eye substantially equivalent to the visual performance of a single vision lens for a pre-presbyopic eye, and the lens has an aperture size greater than 1.5 mm.

[0229] Certain embodiments are directed to one or more methods of surgical correction of vision to improve visual performance. For example, a method for surgical correction may include (1) calculating one or more target corrections to the optical characteristics, power, and / or physical structure of an eye, the target corrections including at least one desired refractive power and at least one appropriate power profile, at least one aberration profile consisting of at least two spherical aberration terms and one defocus term, and visual performances along substantially continuous viewing distances including near, intermediate, and far distances, where the visual performances of the eye along the substantially continuous viewing distances are substantially equivalent to the visual performance of an eye wearing a correctly prescribed single vision lens for a far viewing distance; (2) inputting the desired corrections into an ophthalmic surgical system; and (3) applying the desired corrections to the eye via the ophthalmic surgical system. In certain applications, the visual performance of the eye is further characterized by minimal or no ghosting at near, intermediate, and far viewing distances.

[0230] In certain applications, the visual performance of a correctly prescribed single vision lens provides visual acuity for the eye that is best corrected visual acuity. In certain applications, best corrected visual acuity is visual acuity that cannot be substantially improved by further manipulation of the power of a correctly prescribed single vision lens. In certain applications, the aberration profile includes three or more spherical aberration terms and one defocus term.

[0231] Certain embodiments are directed to lenses that provide optical and / or visual performance substantially equivalent to, or better than, a correctly prescribed single focus at a distance viewing distance. As used in certain embodiments, correctly prescribed can refer to a prescribed single focus lens at a distance viewing distance that provides a visual acuity for an eye that is best corrected and cannot be substantially improved by further manipulation or adjustment of the lens power. As used in certain embodiments, appropriately, properly, or effectively prescribed can refer to a prescribed single focus lens at a distance viewing distance that provides a visual acuity for an eye that approximates best corrected visual acuity and cannot be substantially improved by further manipulation or adjustment of the lens power.

[0232] Certain embodiments are directed to one or more methods of surgical correction of vision to improve visual performance. For example, a method of correcting vision can include (1) calculating one or more target corrections for an eye, the corrections providing the eye with at least one optical characteristic, including at least one aberration profile, the aberration profile including at least two spherical aberration terms and one defocus term, and visual performance at intermediate and distant distances that is at least substantially equivalent to an eye fitted with a correctly prescribed single vision lens for a distance viewing distance, where the visual performance of the eye at a near viewing distance is within 2 units of the visual performance of an eye fitted with a correctly prescribed single vision lens at a distance viewing distance, as tested by a defined visual rating scale of 1 to 10 units; (2) inputting the desired corrections into an ophthalmic surgical system; and (3) applying the desired corrections to the eye via the ophthalmic surgical system. In certain applications, the visual performance further provides substantially minimized ghosting for the eye's visual acuity at near, intermediate, and far distances. In certain applications, substantially equivalent or better visual performance is determined at least in part by a visual rating scale of 1 to 10 units.

[0233] Certain embodiments are directed to one or more methods of surgical correction of vision to improve visual performance. For example, the vision correction method can include (1) calculating one or more target corrections for an eye, the corrections providing the eye with at least one optical characteristic, the at least one aberration profile, the aberration profile including at least two spherical aberration terms and one defocus term, and visual performance at intermediate and far distances substantially equivalent to or better than an eye fitted with a correctly prescribed single vision lens for the far viewing distance, further characterized by minimized ghosting for the eye's visual acuity at least at the far distance; (2) inputting the desired corrections into an ophthalmic surgical system; and (3) applying the desired corrections to the eye via the ophthalmic surgical system. In certain applications, minimized ghosting can be achieved by achieving a score of 2.4, 2.2, 2, 1.8, 1.6, or 1.4 or less on a 1-10 unit visual assessment ghosting scale.

[0234] Certain embodiments are directed to one or more devices and / or systems for surgical correction of vision to improve visual performance. For example, a device and / or system for correcting vision of an eye may include (1) an input module, (2) a calculation module, and (3) a delivery module, wherein the input module is configured to receive input related to vision correction of the eye, the calculation module is configured to calculate one or more target corrections for the eye, the corrections providing the eye with at least one target refractive power and at least one appropriate power profile, at least one aberration profile consisting of at least two spherical aberration terms and one defocus term, and visual performance along substantially continuous viewing distances including near, intermediate, and far distances, wherein the visual performance of the eye along the substantially continuous viewing distances is substantially equivalent to the visual performance of an eye wearing a correctly prescribed single vision lens for a far viewing distance, and the delivery module delivers the target corrections to the eye using the calculated target corrections for the eye calculated by the calculation module. In certain applications, the visual performance of the eye is further characterized by minimal or no ghosting at near, intermediate, and far distances.

[0235] In certain applications, a correctly prescribed single vision lens provides visual acuity for the eye that is best corrected visual acuity. In certain applications, best corrected visual acuity is visual acuity that cannot be substantially improved by further manipulation of the power of a correctly prescribed single vision lens. In certain applications, the aberration profile includes three or more spherical aberration terms and one defocus term. In certain applications, the delivery module can be an ophthalmic refractive surgery system, such as a femtosecond laser.

[0236] Certain embodiments are directed to one or more devices and / or systems for surgical correction of vision to improve visual performance. For example, a device and / or system for correcting vision of an eye may include (1) an input module, (2) a calculation module, and (3) a delivery module, wherein the input module is configured to receive input related to vision correction of the eye, the calculation module is configured to calculate one or more desired corrections for the eye, the corrections providing the eye with at least one optical characteristic, the at least one aberration profile, the aberration profile including at least two spherical aberration terms and one defocus term, and visual performance at intermediate and distant distances that is substantially equivalent to or better than an eye fitted with a correctly prescribed single vision lens for a distance viewing distance, where the visual performance of the eye at a near viewing distance is within 2 units of the visual performance of an eye fitted with a correctly prescribed single vision lens at a distance viewing distance, as tested by a defined visual rating scale of 1 to 10 units, and the delivery module utilizes the desired corrections for the eye calculated by the calculation module to deliver the desired corrections to the eye.

[0237] In certain applications, the visual performance further enables the eye's visual acuity to be evaluated at near, intermediate, and far distances with minimized ghosting. In certain applications, the substantially equivalent or better visual performance is determined at least in part by a visual rating scale of 1 to 10 units. In certain applications, the delivery module is an ophthalmic refractive surgery system, such as a femtosecond laser.

[0238] Certain embodiments are directed to one or more devices and / or systems for surgical correction of vision to improve visual performance. For example, a device and / or system for correcting the vision of an eye may include (1) an input module, (2) a calculation module, and (3) a delivery module, where the input module is configured to receive input related to the vision correction of the eye, the calculation module is configured to calculate one or more target corrections for the eye, the corrections providing the eye with at least one optical characteristic, the at least one aberration profile, the aberration profile including at least two spherical aberration terms and one defocus term, and visual performance at intermediate and far viewing distances that is substantially equivalent to or better than an eye fitted with a correctly prescribed single vision lens for the far viewing distance, the visual performance being characterized by minimized ghosting for the eye's vision at least at the far distance, and the delivery module utilizes the calculated target corrections for the eye calculated by the calculation module to deliver the desired corrections to the eye.

[0239] In certain applications, minimized ghosting is defined as having a score of 2.4, 2.2, 2, 1.8, 1.6, or 1.4 or less on a visual assessment ghosting scale of 1 to 10 units. In certain applications, the delivery module is an ophthalmic refractive surgery system, such as a femtosecond laser.

[0240] In certain embodiments, the lenses are configured to provide distance vision substantially equal to or better than that corrected by correctly prescribed lenses for distances over the diopter range of 0D to 2.5D or for refractive errors from infinity to 40cm, with minimal ghosting for emmetropia, myopia, hyperopia, and astigmatism.

[0241] For specific applications, the lenses substantially correct distance refractive errors, and the lenses are configured to allow myopia to be delayed without the visual acuity loss typically associated with multifocal contact lenses, for example, providing excellent visual acuity across a nasal-30-degree to temporal-30-degree field of view, providing a retinal image quality of 0.4 or greater for selected or averaged focal lengths from infinity to 40 cm, and providing lenses with an average retinal image quality of 0.3. When optimizing retinal image quality, such lenses provide highly clear, high-contrast images at selected distances, and the lenses provide excellent image quality and visual performance with minimal ghosting across a range of diopter distances from infinity to near for the correction of refractive errors, the treatment of presbyopia, and the control of myopia. The multifocal lenses are configured so that the overall visual performance of the multifocal lenses is at least substantially equivalent to or better than a correctly prescribed single-vision lens at distance viewing distances when tested according to a defined overall visual rating scale of 1 to 10 units.

[0242] In certain embodiments, such lenses provide the visual performance of the candidate eye along a substantially continuous range of viewing distances, including near, intermediate, and far distances, and the visual performance of the multifocal lens is at least substantially equivalent to the visual performance of a correctly prescribed single vision lens at far viewing distances.

[0243] In certain embodiments, the term minimal ghosting can refer to the lack of unwanted secondary images appearing at the image plane of an optical system. In certain embodiments, the term minimal ghosting can be used to refer to the lack of unwanted secondary images appearing on the retina of an eye. Conversely, the term no ghosting can refer to the lack of unwanted double images appearing on the retina of an eye. In certain embodiments, the term minimal ghosting can refer to the lack of unwanted double images perceived by a candidate eye. In other applications, minimized ghosting can refer to the lack of spurious out-of-focus images appearing along the side of a primary image in an optical system.

[0244] Section 14.A: Asymmetric HOA and Image Quality In certain embodiments, the selection of high-order aberrations that are optimized for the desired through-focus image quality may include, in addition to the rotationally symmetric high-order aberrations disclosed herein, asymmetric high-order aberrations from one or more of first-order horizontal astigmatism, first-order vertical astigmatism, second-order horizontal astigmatism, first-order horizontal coma, first-order vertical coma, second-order horizontal coma, second-order vertical coma, etc. In some other embodiments, the selection of asymmetric high-order aberrations may also include third-order asymmetric high-order aberrations, fourth-order asymmetric high-order aberrations, fifth-order asymmetric high-order aberrations, sixth-order asymmetric high-order aberrations, seventh-order asymmetric high-order aberrations, eighth-order asymmetric high-order aberrations, ninth-order asymmetric high-order aberrations. For example, Zernike coefficients represented by C(3,-1), C(3,1), C(5,-1), C(5,1), C(7,-1), C(7,1), C(9,-1), C(9,1), C(11,-1), (8,-2), (8,2), (10,-2), (10,2), (12,-2), (12,2), (14,-2), (14,2), etc. TIFF0007618639000028.tif149138

[0245] For example, the optimized high-order aberration combinations IC-1 through IC-8 shown in Table 12.4 are configured to provide the through-focus image quality shown in Figure 132. The calculations discussed in this section are performed using simple Strehl and visual Strehl ratios in the frequency domain as image quality metrics for pupil radii of 3 mm and 4 mm. In other embodiments, calculations utilizing other image quality metrics described in Section 1 may also be used with other pupil diameters ranging from 3 to 8 mm. TIFF0007618639000029.tif147133

[0246] Section 14.B: Non-coaxial / non-coaxial The eye contains various components and surfaces that combine to produce the eye's optical properties. In lens design, it is sometimes useful to assume that the eye, its components, and associated surfaces are coaxial. However, there are other instances in which the eye's components and associated surfaces may not be assumed to be coaxial. For example, the axis of the cornea may not be aligned with the center of the pupil. The axial misalignment may be translational and / or tilt. A combination of translational and tilt misalignment may also occur. When two or more landmarks (e.g., axes, centers, etc.) are misaligned (i.e., not coaxial, or "spaced apart") with respect to one another or relative to one another, the eye, or the eye-lens combination, is not symmetrical. The direction of misalignment may be superior (i.e., upward), inferior (i.e., downward), nasally (across the eye toward the patient's nose), or temporally (across the eye toward the patient's closer ear), or a combination of one or more of these directions.

[0247] In certain embodiments, a lens may include an optical zone that may be circular, elliptical, non-circular, non-elliptical, or a combination thereof, such as a contact lens. The optical zone may also be rotationally asymmetric and / or laterally (mirror image) asymmetric. With respect to optical and / or visual performance, the optical zone may have an optical axis, which is associated with the optical and / or visual performance provided by an aberration profile of the type described herein.

[0248] In some embodiments, the center, geometric center, or centroid (e.g., defined as the standard mathematical geometry definition of the center of gravity of a shape) of the optical zone may be spaced apart from its optical axis. Such embodiments may be beneficial for delivery of desired optical and / or visual performance to an eye that exhibits, at least in part, non-coaxial alignment of its components and / or associated surfaces. For example, the pupil region may be at least in part non-circular and at least in part non-coaxial / misaligned with the cornea of ​​the eye. Contact lenses for such exemplary embodiments may be beneficial for optical and / or visual performance when the optical axis of the contact lens remains substantially aligned with the optical axis of the eye, while the optical zone is non-coaxial. The amount by which the centroid of the optical zone and the optical axis of the contact lens may be spaced apart may be selected according to an individual eye, a population average, a representative value of a subpopulation, or a combination thereof, and may be at least 0.1 mm, 0.2 mm, 0.3 mm, 0.4 mm, 0.5 mm, 0.7 mm, or 1 mm. In some embodiments, the amount of spacing may be between 0.1 mm and 0.5 mm, 0.5 mm and 1 mm, 1 mm and 1.5 mm, 1.5 mm and 2.0 mm, or 2 mm and 3 mm.

[0249] For non-coaxial and non-coaxial lenses, the lens may include an optic zone and a carrier. The optic zone is one or more regions of the lens that provide desired optical performance, including, for example, an aberration profile of the type described herein. The lens carrier is one or more regions of the lens that are not intended to provide optical performance but may be configured to control the lens's interaction with the eye.

[0250] In some embodiments, the carrier may have a surface blend, thickness, thickness profile, edge profile, etc. to deliver a level of comfort to the contact lens wearer. Such carrier configurations may position the lens in a particular orientation or range of orientations, which may be beneficial for lenses with asymmetric amounts by ensuring substantial alignment of the lens when applied to the eye. Configurations may include prism ballast, lens edge truncation, dynamic thin zones, slab-off, double slab-off, horizontal iso-thickness, thin zone passages, etc. In such embodiments, the lens may include an optical zone and a carrier, and the center of gravity of the optical zone may be spaced apart from the optical axis, while the carrier may be configured to control the orientation of the lens. The amount by which the center of gravity of the optical zone and the optical axis of the lens may be spaced apart may be selected according to a representative value for an individual eye, a population average, or a subpopulation, and may be at least 0.1 mm, 0.2 mm, 0.3 mm, 0.4 mm, 0.5 mm, 0.7 mm, or 1 mm. In some embodiments, the amount of spacing may be between 0.1 mm and 0.5 mm, 0.5 mm and 1 mm, 1 mm and 1.5 mm, 1.5 mm and 2.0 mm, or 2 mm and 3 mm.

[0251] In certain embodiments, the lens may include an optical zone and a carrier, and the carrier's inner (closer to the optical zone) boundary, outer (closer to the outer edge of the lens) boundary, or both boundaries may be circular, elliptical, non-circular, non-elliptical, or a combination thereof. In some embodiments, the carrier and / or the optical zone may have multiple boundaries. The carrier may be rotationally asymmetric and / or laterally (e.g., mirror-image) asymmetric. In such embodiments, the carrier's center, geometric center, or centroid (e.g., defined as the standard mathematical geometry definition of the center of gravity of a shape) may be spaced apart (i.e., not co-located) from the optical axis associated with the optical zone of the contact lens. Alternatively, the carrier may be configured to control the orientation of the contact lens. Such embodiments may be beneficial because they provide desired optical and / or visual performance for eyes that exhibit, at least in part, non-coaxial alignment of their components and / or associated surfaces. For example, in the case of a contact lens that is applied to the eye by placement on the cornea, the cornea may be at least partially asymmetric and at least partially misaligned / non-coaxial with the optical axis of the eye. In such exemplary cases, the contact lens may be configured such that the center of gravity of the carrier is non-coaxial with the optical axis associated with the optical zone of the contact lens. The amount by which the optical axis and the center of gravity of the carrier of the contact lens may be separated may be selected depending on the representative values ​​of an individual eye, a population average, or a subpopulation, and may be at least 0.1 mm, 0.2 mm, 0.3 mm, 0.4 mm, 0.5 mm, 0.7 mm, or 1 mm. In some embodiments, the amount of separation may be between 0.1 mm and 0.5 mm, 0.5 mm and 1 mm, 1 mm and 1.5 mm, 1.5 mm and 2.0 mm, or 2 mm and 3 mm.

[0252] In certain embodiments, the lens may be a contact lens, which may include an optic zone and a carrier. The optic zone is one or more regions that provide optical performance, including, for example, the types of aberration profiles described herein. The carrier may be rotationally asymmetric and / or laterally (mirror image) asymmetric. In some embodiments, the carrier may have a surface blend, thickness, thickness profile, edge profile, etc., to deliver a level of comfort to the contact lens wearer. In other embodiments, the carrier may be configured to control the lateral position and / or rotational orientation of the contact lens. Such carrier configurations may position the contact lens in a particular orientation or a particular range of orientations. Configurations may include prism ballast, lens edge truncation, dynamic thin zone, slab-off, double slab-off, horizontal iso-thickness, thin zone passages, etc. In such embodiments, the lens may include an optical zone and a carrier, and the center, or geometric center, or centroid of the optical zone may be spaced apart (i.e., not co-located) from the center, geometric center, or centroid of the carrier, while the carrier may be configured to control the orientation of the contact lens. Such an arrangement may be beneficial for delivery of desired optical and / or visual performance to eyes exhibiting non-coaxial alignment of its components and / or associated surfaces. The amount by which the centroid of the optical zone and the centroid of the contact lens carrier may be spaced apart may be selected depending on the representative values ​​of an individual eye, a population average, or a subpopulation, and may be at least 0.1 mm, 0.2 mm, 0.3 mm, 0.4 mm, 0.5 mm, 0.7 mm, or 1 mm. In some embodiments, the amount of spaced apart may be between 0.1 mm and 0.5 mm, 0.5 mm and 1 mm, 1 mm and 1.5 mm, 1.5 mm and 2.0 mm, or 2 mm and 3 mm.

[0253] In certain embodiments, a lens may include an optic zone and a carrier, wherein the centroid, optical axis, of the optic zone and the center, geometric center, or centroid of the carrier are mutually spaced apart (i.e., not co-located) from one another, while the carrier may be configured to control the orientation of the contact lens. Such an arrangement may be beneficial in delivering desired optical and / or visual performance to an eye exhibiting non-coaxial alignment of its components and / or associated surfaces. The amount by which the optical axis associated with the optical zone, the centroid of the optical zone, and the centroid of the contact lens carrier may be spaced apart from one another may be selected depending on representative values ​​for an individual eye, a population average, or a subpopulation, and may be at least 0.1 mm, 0.2 mm, 0.3 mm, 0.4 mm, 0.5 mm, 0.7 mm, or 1 mm, and may vary pairwise (i.e., the amount by which the optical axis is spaced apart from the centroid of the optical zone may differ from the amount by which the optical axis is spaced apart from the centroid of the carrier, and either amount may differ from the amount by which the centroid of the optical zone is spaced apart from the centroid of the carrier). In some embodiments, the amount of spacing may be between 0.1 mm and 0.5 mm, 0.5 mm and 1 mm, 1 mm and 1.5 mm, 1.5 mm and 2.0 mm, or 2 mm and 3 mm.

[0254] Section 14.C: Prismatic Effects In some embodiments, an optical device may have a limited amount of optical tilt or prism term in addition to the designed aberration profile. Typically, it may be desirable to limit the amount of optical tilt or prism term so that it does not substantially interfere with vision. In some embodiments, tilt may be intentionally introduced, for example, to aid in rotational stabilization of toric contact lenses. Tilt may be unintentionally introduced, for example, due to manufacturing limitations. Typically, optical performance may not be affected by tilt. However, for certain ocular conditions, tilting the optical prism differently in one eye compared to the other eye may have a beneficial and / or therapeutic effect. In this case, a rotational stabilization feature may be included in the design.

[0255] Section 14D: Tear Film / Surface Treatment Subjective visual acuity assessment can be influenced by the on-eye comfort of a contact lens, and vice versa. Therefore, visual satisfaction can be enhanced by adding one or more features to a contact lens that increase perceived comfort. For a contact lens to provide acceptable fit and on-eye comfort, it may be desirable for the lens to be covered by a thin layer of tears on the anterior and posterior surfaces of the lens. Some embodiments may have one or more surfaces engineered to manipulate the tear film so that it contributes to the aberration profile. Certain materials and / or manufacturing processes may be used to manipulate the tear film. Such materials or manufacturing processes may be used with some of the disclosed embodiments. One or more surface treatments may be used to manipulate the tear film in some embodiments. For example, surface treatments may include one or more of the following: plasma treatment, layer-by-layer surface coating, addition of a wetting agent to the packing solution or contact lens, application of eye drops, or a combination thereof. Contact lenses without a pre-lens tear film may also provide consistent optical performance in accordance with some embodiments.

[0256] Section 15: An exemplary set of lens designs that are substantially independent of the eye's inherent spherical aberration The interaction between the inherent aberration profile of the candidate eye and the aberration profile of the selected combination of the design set may a) have an improving effect, b) have a deteriorating effect, or c) have no substantial effect at all on objective and / or subjective optical and / or visual performance.

[0257] The present disclosure provides embodiments directed to selecting any particular combination of positive and / or negative phase aberration profiles to achieve a particular goal for a candidate eye, which may be, for example, to change the slope of the through-focus RIQ in a direction that would be advantageous to the emmetropization process for a myopic or hyperopic eye, or alternatively, a similar approach or method may be used to reduce presbyopic symptoms in a replacement candidate eye.

[0258] Certain embodiments are directed to lenses, devices, and / or methods that enable the design of a lens that, when applied to a candidate eye, produces visual performance that is substantially independent of the candidate eye's aberration profile. Substantially independent means that, in certain applications, a lens is designed that provides acceptable and / or similar performance for multiple candidate eyes within a representative sample of a target population. In certain applications, a method for obtaining a target TFRIQ includes the use of a nonlinear unconstrained optimization routine and one or more other variables. The variables selected for the nonlinear unconstrained optimization routine can include a selected group of Zernike spherical aberration coefficients C(2,0) through C(20,0) and one or more other variables. The other variables can be, for example, the aberration profile of a representative sample of the target population.

[0259] A lens can be designed by selecting an optimization routine to evaluate the through-focus RIQ, which can include a) a target TFRIQ, b) a target TFRIQ within predefined limits, or c) a combination of a) and b). Iteration G1 (Figure 71) is one example of a lens design whose visual performance is independent of the candidate eye's intrinsic aberration profile.

[0260] Table 13 provides the remaining combinations of defocus terms and spherical aberration terms, denoted by Zernike coefficients C(2,0) through C(20,0), for example designs at optical zone or pupil diameters of 4, 5, and 6 mm. TIFF0007618639000030.tif76140

[0261] Figure 72 shows a graph of the through-focus performance of Iteration G1 for a 4 mm pupil size for a range of intrinsic spherical aberrations (and no other intrinsic aberrations) from -0.1 μm to +0.2 μm. Figure 73 shows the corresponding performance for a 5 mm pupil size. For both, the through-focus performance is relatively constant even with variations in intrinsic spherical aberration. Therefore, lenses of Iteration G1, lenses with similar characteristic aberration profiles, can be prescribed for a relatively large number of recipients in a population. The through-focus performance of Iteration G1 for both 5 mm and 4 mm pupil sizes is shown in Tables 14, 15, 16, and 17, respectively, for intrinsic first-order spherical aberrations of -0.10 μm, 0.00 μm, +0.10 μm, and +0.20 μm, all measured assuming a 5 mm pupil. TIFF0007618639000031.tif213163TIFF0007618639000032.tif154116TIFF0007618639000033.tif238157TIFF0007618639000034.tif175107

[0262] Section 16: Exemplary Design Sets for Intraocular Lenses The aberration profile can be used in intraocular lens applications according to certain embodiments. The aberration profile and / or power profile can be converted into an intraocular lens surface profile using one or more of the following parameters: thickness profile, power profile, aberration profile, anterior surface, posterior surface, diameter, and / or material refractive index. The surface profile is then provided to a computer-aided or other manufacturing process to produce the intraocular lens. The produced intraocular lens is configured at least in part based on the generated surface profile and / or surface profiles. In some embodiments, a supplemental intraocular lens can be implanted within the accommodating gel during a post-lens extraction procedure (e.g., a refill surgical procedure). The lens power profile (Iteration J) shown in FIG. 74 is a combination of Zernike high-order spherical aberration terms. According to certain embodiments, the power profile can be converted into an axial thickness profile (FIG. 75) for the intraocular lens, taking into account the refractive index of the intraocular lens material. In the above formula, the refractive index of the intraocular lens material is 1.475. Table 18 provides other combinations of defocus terms and spherical aberration terms, represented by Zernike coefficients C(2,0) through C(20,0), showing exemplary designs of intraocular lenses (FIG. 74) at 4 mm and 5 mm optical zone diameters. TIFF0007618639000035.tif70124

[0263] The aberration profiles disclosed herein may be used in multi-element intraocular lenses, such as phakic and pseudophakic intraocular lenses. The aberration profiles disclosed herein may be used in multi-element intraocular lens devices to restore accommodation. For example, the aberration profile may be implemented in one or more elements of a multi-element intraocular lens device by manipulating one or more of the following parameters in one or more of the elements: thickness profile, power profile, aberration profile, anterior surface, posterior surface, spacing between elements, and refractive index. The parameters are then provided to a computer-aided or other manufacturing process to produce the multi-element intraocular lens device. These processes may include lathing, molding, etching, ablation, and / or other methods. In certain embodiments, the profile may be created after the lens is implanted. The resulting intraocular lens is configured at least in part based on the aberration profile and / or the generated parameters.

[0264] Due to the multidimensional variable space within a multi-element intraocular lens, e.g., four surfaces in a two-element design, the greater number of degrees of freedom provides greater design flexibility and a greater number of design solutions. Furthermore, due to the dynamic configuration of the intraocular lens, the distance between elements changes from far focus to near focus, and performance may be altered and / or tailored by selecting appropriate aberration profiles at different surfaces of the multi-element intraocular lens. One advantage of the aberration profiles disclosed herein is that they can be used with multi-element intraocular lenses to provide different performance for distance, intermediate, and near vision. For example, elements may be configured for optimal visual performance in the distance range and an extended depth of focus in the near range. Visual performance may be visual acuity, contrast sensitivity, minimized ghosting, or a combination thereof.

[0265] Section 17: Descriptors for frequency profiles using Fourier transforms Fourier transform techniques can be used to characterize the power profiles of certain embodiments, and in particular, for certain bifocal or multifocal designs. For example, FIG. 76 plots power profiles for several commercially available bifocal and multifocal lenses. FIG. 77 plots power profiles for several bifocal or multifocal lenses according to several embodiments. FIG. 78 plots the Fourier transform of the power profiles for the commercially available bifocal and multifocal lenses of FIG. 76. FIG. 79 plots the Fourier transform of the power profile of FIG. 77. For both FIG. 78 and FIG. 79, the horizontal axis represents spatial frequency in cycles per millimeter (cycles / mm), and the vertical axis plots the normalized absolute value of the amplitude spectrum from the fast Fourier transform of the power profile. In these figures, normalization refers to rescaling each amplitude spectrum such that the maximum absolute value of the amplitude spectrum is rescaled to 1. For example, the normalized absolute value of the amplitude spectrum can be obtained by dividing the absolute value of the amplitude spectrum by the maximum absolute value of the amplitude spectrum.

[0266] A comparison of Figures 78 and 79 illustrates the distinction between certain embodiments and commercially available lenses plotted because the normalized absolute amplitude of the Fourier transform of both power profiles has a normalized absolute amplitude greater than 0.2 at one or more spatial frequencies at or above 1.25 cycles / mm. In contrast to the illustrated embodiment, Figures 77 and 79, none of the currently available lenses has a normalized absolute amplitude greater than 0.2 at one or more spatial frequencies at or above 1.25 cycles / mm. Certain embodiments, such as lenses, bifocal lenses, and / or multifocal lenses, can be characterized using Fourier transforms. For example, certain embodiments are directed to lenses with an optical axis and at least two surfaces, where the lens is characterized by a power profile having a normalized absolute amplitude of the Fourier transform of the power profile greater than 0.2 at one or more spatial frequencies at or above 1.25 cycles / mm. In certain applications, the lens is configured to have a power profile with a normalized magnitude absolute value of the Fourier transform of the power profile greater than 0.2 at one or more spatial frequencies at or above 1.25 cycles / mm.

[0267] Section 18: Descriptors of power profiles using first derivatives or rates of change of power First derivative methods can be used to characterize the power profiles of certain embodiments, and particularly for certain bifocal or multifocal designs. For example, Figure 76 plots power profiles for several commercially available bifocal and multifocal lenses. Figure 77 plots power profiles for several multifocal lenses according to several embodiments. Figure 80 plots the first derivative of the power profiles for commercially available bifocal and multifocal lenses of Figure 76. Figure 81 plots the first derivative of the power profiles of Figure 77. For Figures 80 and 81, the horizontal axis represents the half chord of the optical zone diameter, and the vertical axis plots the absolute value of the first derivative of the power profile.

[0268] A comparison of Figures 80 and 81 illustrates the distinction between the particular embodiment and the commercially available lens plotted because the power profile of the illustrated embodiment has at least five peaks in the absolute value of the first derivative, with at least five peaks whose absolute amplitudes are greater than 0.025 in 1D units per 0.01 mm. In contrast to the illustrated embodiment, Figures 80 and 81, no currently available commercially available lens has at least five peaks whose absolute first derivatives are greater than 0.025 in 1D units per 0.01 mm.

[0269] Certain embodiments, such as lenses, bifocal lenses, and / or multifocal lenses, can be characterized using the first derivative or rate of change of power. For example, certain embodiments are directed to lenses having an optical axis and at least two surfaces, the lenses having power profiles characterized such that the absolute value of the first derivative of the power profile has at least five peaks, with the absolute amplitude of at least five peaks being greater than 0.025 per 0.01 mm of 1D along the half chord. In certain applications, at least one power profile is characterized such that the absolute value of the first derivative of the power profile has at least five peaks, with the absolute amplitude of at least five peaks being greater than 0.025 per 0.01 mm of 1D along the half chord.

[0270] Section 19: Descriptors of frequency profiles using non-periodic functions Certain embodiments of the present disclosure have one or more power profiles that can be characterized by a non-periodic function over a significant portion of the lens's half-code optical zone. Certain embodiments are directed to lenses configured such that at least one power profile is non-periodic over a significant portion of the lens's half-code optical zone. In general terms, a non-periodic function is defined as a function that is not periodic. A periodic function is a function that repeats or replicates its value at regular intervals, often referred to as a period. For example, trigonometric functions (i.e., sine, cosine, secant, cosecant, tangent, and cotangent functions) are periodic because their values ​​repeat over intervals of 2π radians. A periodic function can also be defined as a function whose graphical representation exhibits translational symmetry. A function F(x) is said to be periodic with a period P (where P is a non-zero constant) if it satisfies the condition F(x + P) = F(x).

[0271] Section 20: Frequency profile descriptors using non-monotonic functions Certain embodiments of the present disclosure have one or more power profiles that can be characterized by a non-monotonic function over a significant portion of the lens's half-code optical zone. Certain embodiments are directed to lenses configured such that at least one power profile is non-monotonic over a significant portion of the lens's half-code optical zone. In general terms, a "monotonic" or "monotone" function is a function that is substantially non-increasing or substantially non-decreasing. A function F(x) is said to be non-increasing over an interval I of real numbers if F(b)≦F(a) for all b>a. In the above equation, a and b are real numbers and a subset of I. A function F(x) is said to be non-decreasing over an interval I of real numbers if F(b)≧F(a) for all b>a. In the above equation, a and b are real numbers and a subset of I.

[0272] Section 21: Frequency profile descriptors using non-monotonic and non-periodic functions Certain embodiments of the present disclosure have one or more power profiles that can be characterized by non-monotonic and non-periodic functions over a significant portion of the lens's half-code optical zone. Certain embodiments are directed to lenses configured such that at least one power profile is non-monotonic and non-periodic over a significant portion of the lens's half-code optical zone. In general terms, some functions can be both non-monotonic and non-periodic. Such functions, as described herein, have properties of both monotonic and non-periodic functions.

[0273] Certain embodiments, such as lenses, bifocal lenses, and / or multifocal lenses, can be characterized using a non-periodic function, a non-monotonic function, or a combination thereof. For example, certain embodiments are directed to lenses having an optical axis and at least two surfaces, the lenses having at least one power profile, the power profile characterized by a function that is non-monotonic, non-periodic, or a combination thereof over a substantial portion of the half-coded optical zone of the lens. In certain applications, the lenses are configured to have a power profile that is non-monotonic, non-periodic, or a combination thereof over a substantial portion of the half-coded optical zone of the lens.

[0274] Section 22: Lens power profile As is apparent from visual inspection of at least Figures 19, 20, 22-25, 29, 31, 34, 35, 39, 40, 41, 56-60, and 68, certain embodiments have a power profile having the following combination of features across the half-chord diameter: (i) A power profile with a moving average that increases with diameter and then decreases, or decreases with diameter and then increases. For certain contact lens embodiments, the moving average can be calculated over a 1 mm window from about 4 mm on-axis. Thus, by way of example, the average value can be calculated over a 1 mm range from on-axis and recalculated at intervals selected from the group of 0.2 mm, 0.4 mm, or 0.6 mm. (ii) A power profile that transitions between a local minimum and a local maximum within a 1 mm change in radius at least four times over a 4 mm half-chord. For example, referring to FIG. 22, the power profile begins with a local maximum on the axis and transitions to a local minimum at about a 1 mm radius, after which transitions between the local maximum and the local minimum occur at about 1.6 mm and about 2.3 mm. The power profile then may have a next local minimum at about 2.9 mm, a local minimum at about 3.1 mm, and a local maximum at about 4 mm, or may have a next local maximum at about 4 mm. In some examples, the power profile transitions at least six times over a 4 mm half-chord. For example, referring to FIG. 24, there are two transitions within the first 1 mm radius, two transitions within the second 1 mm radius, and two transitions in the region from 2 mm to 4 mm. In some examples, the power profile transitions at least 8 times over a 4 mm radial range (eg, FIG. 29), or at least 12 times over a 4 mm radial range (eg, FIG. 35), or at least 145 times over a 4 mm radial range (eg, FIG. 40). (iii) the power profile transitions smoothly for radii selected from the group of at least 3 mm, at least 3.5 mm, and at least 4 mm;

[0275] Thus, certain embodiments have a power profile having a combination selected from options in (i), (ii), and (iii), which power profile provides acceptable visual acuity for at least a subset of the population. These embodiments may have application for myopia, hyperopia, and / or presbyopia, with or without astigmatism. Other embodiments include: (iv) The on-axis power differs from the prescription by at least about 0.7D (see, eg, FIG. 22) or by at least about 1.5D (see, eg, FIG. 38). (v) The difference between the global maximum power and the global minimum power is between about 1.5 and 2.5 times the difference between any adjacent local minimum and local maximum within a radius of about 2.5 mm. In other words, the global maximum and global minimum are reached through a gradual change in the power profile that transitions itself between the local minimum and maximum. This includes combinations from the options listed above in this section 22, together with one or both of the following:

[0276] Section 23: Clinical Performance of Some Exemplary Embodiments Compared to Commercially Available Monofocal, Bifocal, and Multifocal Soft Contact Lenses In the following experimental clinical study, the performance of four exemplary embodiments described herein (manufactured in the form of soft contact lenses) was compared to seven commercially available lenses, including one monofocal product, one bifocal product, and five multifocal products, the details of which are set out in Table 19 herein. The study was approved by the ethics committee in Bellberry, South Australia.

[0277] Objective of the experiment: The purpose of this study was to evaluate four multifocal soft contact lenses according to specific embodiments and six commercially available bifocal and multifocal lens designs.

[0278] Study Design: The study design was a prospective, participant-masked, bilateral wear, crossover clinical trial with an overnight washout period between lens assessments. Lens wear duration was a maximum of 2 hours.

[0279] Participant Selection: Participants were included in the study if they met the following criteria: a) Able to read and understand English and give informed consent as indicated by signing the informed consent record. b) Male or female, at least 18 years of age (results reported herein are for participants over 45 years of age). c) Willing to comply with the wear and clinical trial visit schedule prescribed by the investigator. d) Have ocular health findings within normal limits that would not prevent the participant from safely wearing contact lenses. e) Correctable to at least 6 / 6 (20 / 20) or better with monofocal contact lenses in each eye. f) Have astigmatism correction of -1.5D or less. g) Have experience or are inexperienced contact lens wearers.

[0280] Participants were excluded from the study if they met one or more of the following criteria: a) Pre-existing visual irritation, injury, or condition (including infection or disease) of the cornea, conjunctiva, or eyelid that would preclude contact lens fitting and safe contact lens wear. b) Systemic diseases that have adversely affected ocular health, such as diabetes, Graves' disease, and autoimmune diseases such as ankylosing spondylitis, multiple sclerosis, Sjogren's syndrome, and systemic lupus erythematosus. Note: Conditions such as systemic hypertension and arthritis will not automatically exclude prospective participants. c) Use of or need for concurrent category S3 and above ophthalmic medications at the time of enrollment and / or during the clinical trial. d) The use of or need for systemic and / or topical medications that may alter normal ocular findings and / or are known to affect the participant's ocular health and / or physiological status or contact lens performance in either an adverse or beneficial manner at the time of enrollment and / or during the clinical trial. e) NB: Systemic antihistamines are permitted on an "as needed basis" when used prophylactically during the study and at least 24 hours before the clinical trial product is used. f) Ocular surgery within 12 weeks immediately prior to enrollment in this study. g) Immediately preceding corneal refractive surgery. h) Contraindications to contact lens wear. i) Known allergy or intolerance to any component of the clinical trial product. j) The researchers excluded people who the researchers felt would not be able to fulfill the clinical trial requirements. TIFF0007618639000036.tif119133

[0281] method: At each fitting visit, lenses were fitted to both eyes. After the lenses had settled, lens performance was assessed. Lens performance was evaluated as follows: 1.Visual acuity A logMAR chart was used to obtain measurements of visual acuity at a given distance under high lighting conditions. b. High-contrast visual acuity at 6 meters c. Low contrast visual acuity at 6 meters d. Contrast sensitivity using a Pelli-Robson equivalent chart (using Thomson software) at 6 meters. Text was held constant at 6 / 12 letter size while contrast decreased as a logarithmic function. e. A Hanks near point chart was used to measure visual acuity at 70 cm (intermediate), 50 cm, and 40 cm (near vision) under high lighting conditions. Because the Hanks near point chart was designed for use at a near distance of 40 cm, visual acuity equivalents for 50 cm and 70 cm were calculated. Both the intermediate and near visual acuity results were converted to equivalent logMAR. Includes:

[0282] Subjective Response Questionnaire: 1. Quality of distance, intermediate, and near vision on a visual analog scale of 1 to 10. 2. Evaluation of far and near ghosting on a ghosting analog scale of 1 to 10. 3. Overall assessment of visual acuity performance on a visual analogue scale of 1 to 10.

[0283] Figures 82-108 show the subjective and objective results from the clinical trials. Distance, intermediate, near, and overall visual acuity ratings were measured on a visual analog scale ranging from 1 to 10 in steps of 1, where 1 represented blurred and / or hazy vision and 10 represented clear and / or sharp vision. Distance and near ghosting visual acuity ratings were measured on a ghosting visual analog scale ranging from 1 to 10 in steps of 1, where 1 represented no ghosting and / or no double vision and 10 represented extreme ghosting and / or double vision. Lack of ghosting was calculated by subtracting the ghosting score from 11 points. Cumulative visual acuity results were obtained by averaging the distance, intermediate, and near visual acuity results. Cumulative ghosting results were obtained by averaging the ghosting at distance and near distances.

[0284] Section 24: Descriptor of power profiles using Zernike power polynomials Given a monochromatic wavefront W(ρ,θ) of an optical system, where ρ is the radial distance and θ is the angle in polar coordinates, the power distribution of the wavefront can be defined as follows: TIFF0007618639000037.tif1869In the above equation, "∂W / ∂r" represents the partial derivative of W(ρ,θ) along the radial distance "r".If a monochromatic wavefront W(ρ,θ) is chosen to be described as a finite series of standard Zernike polynomial expansions, the refractive power based on the wavefront may be represented by a set of basis functions and an original set of wavefront standard Zernike polynomial coefficients, as shown below. TIFF0007618639000038.tif1770In the above formula, r max corresponds to the pupil radius. TIFF0007618639000039.tif3886In the above formula, TIFF0007618639000040.tif23121In the above formula, TIFF0007618639000041.tif12380, otherwise where n and m are the radial and azimuthal components of the Zernike polynomial in double-index notation, and j is the Zernike coefficient delta in single-index notation.

[0285] For example, a list of rotationally symmetric Zernike power polynomial expansions up to order 10, i.e., five rotationally symmetric terms, is shown below: P = Z1 * 4 * 3^ (1 / 2) + Z2 * 5^ (1 / 2)*(24*R^2 - 12) + Z3 * 7^ (1 / 2)*(120*R^4 - 120*R^2 + 24) + Z4 * 9^ (1 / 2)*(360*R^2 - 840*R^4 + 560*R^6 - 40) + Z5 * 11^ (1 / 2)*(3360*R^4 - 840*R^2 - 5040*R^6 + 2520*R^8 + 60) Frequency distribution=(1 / r max ^2)*P

[0286] The terms Z1, Z2, Z3, Z4, and Z5 in the above Zernike power polynomial expansion represent the C(2,0) coefficient, the C(4,0) coefficient, the C(6,0) coefficient, the C(8,0) coefficient, and the C(10,0) coefficient, respectively.

[0287] The Zernike power polynomials described herein may be used to characterize the power profile of a particular embodiment. Figures 124-127 show power profiles designed for several exemplary embodiments. Figures 119-123 show the power profiles of several commercially available multifocal lenses measured with a commercially available Shack-Hartmann-based power profiling instrument named Optocraft (Optocraft GmbH, Germany). Default settings for multifocal lens use were used to obtain the measurement data for the commercially available lenses. The commercially available lenses were symmetrical, and only a cross-section of the power profile was exported for Zernike power polynomial fit analysis. In this example, the data density, i.e., the number of points used for fit analysis, was 400 points on the half-chord of the lens's optical zone, from 0 to 4 mm in 0.01 mm steps. The same data density was used when fitting the exemplary system values ​​to the Zernike power polynomials. The least squares method was used to optimize the best coefficients for the chosen degree / order of the symmetric radial Zernike power polynomial. Once the optimization routine was completed, a calculation routine was used to calculate two metrics: the coefficient of determination (R 2 ) and root mean square error (RMSE), the smaller the RMSE, the better the fit, and R 2 The higher the value, the better the fit. As used in this example, the best fit is a coefficient of determination (R) greater than 0.975. 2 ) and / or a fit with the lowest order mathematical function that produces a root mean square error (RMSE) of less than 0.15D. 2 In cases where it is not possible to fit a function that achieves the criteria of >0.975 and RMSE<0.15, the maximum R 2and / or the order of the function that produces the lowest RMSE is used to characterize the power profile. However, such a power profile in this example does not meet the criteria of the exemplary embodiment. Specific implementation values ​​may be characterized using radial Zernike power polynomials. The differences between the conventional multifocal lens and the exemplary embodiment are shown in Tables 20-23. As shown in Tables 20-23, the number of substantially non-zero symmetric Zernike power polynomial coefficients required to best fit the power profile of the exemplary embodiment is greater than the number of substantially non-zero symmetric Zernike power polynomial coefficients required to fit the power profile of the measured conventional multifocal lens. As used in this example, a best fit is defined as a coefficient of determination (R) greater than 0.975. 2 ) and / or a fit with the lowest order mathematical function that produces a root mean square error (RMSE) of less than 0.15D. 2 In cases where it is not possible to fit a function that achieves D > 0.975 and RMSE < 0.15, the maximum R 2 and / or the order of the function that yields the lowest RMSE is used to characterize the power profile. However, such a power profile in this example does not meet the criteria of the exemplary embodiment. As shown in Tables 20 and 21, the conventional lens is described by fewer than 20 coefficients that are non-zero (C(2,0) to C(40,0)), compared to the exemplary design, which is described by at least 20 non-zero coefficients. The R 2 As can be seen from the RMSE and RMSE values, the commercially available designs Multifocal 7 and Multifocal 8 were reproduced with RMSE > 0.25D using the Zernike power polynomial. In contrast, the R of exemplary embodiments 1-8 2 and RMSE values ​​were reproduced with RMSE<0.15D using the Zernike degree polynomial (Tables 22 and 23), provided that a sufficient number of coefficients were used in the calculation. TIFF0007618639000042.tif148122TIFF0007618639000043.tif125120TIFF0007618639000044.tif198140TIFF0007618639000045.tif198140 TIFF0007618639000046.tif198140TIFF0007618639000047.tif198140TIFF0007618639000048.tif153125TIFF0007618639000049.tif118121

[0288] In certain embodiments, a lens includes an optical axis and at least two surfaces, the lens having a power profile, the power profile may be reproduced using at least 30 or 40 non-zero symmetric Zernike power polynomial coefficients. In certain embodiments, the power profile may be reproduced using at least 28, 30, 40, 50, 60, 70, or 80 non-zero symmetric Zernike power polynomial coefficients. In certain embodiments, the power profile may be reproduced using between 30 and 40, between 30 and 50, or between 40 and 80 non-zero symmetric Zernike power polynomial coefficients. In certain embodiments, the power profile may be reproduced using between 30 and 80, between 30 and 70, or between 30 and 50 non-zero symmetric Zernike power polynomial coefficients. In some embodiments, one or more of the Zernike power polynomial coefficients may be zero, so long as the highest order Zernike power polynomial coefficient is non-zero or substantially non-zero. For example, a 20th order Zernike power polynomial may have 20th order Zernike power polynomial coefficients that are non-zero or substantially non-zero, while at the same time, 10th order and lower Zernike power polynomial coefficients may have zero values.

[0289] Section 25: Descriptor of power profiles using Fourier series The general form of the Fourier series expansion is shown below (rotationally symmetric): TIFF0007618639000050.tif1582 where i = 1 to n, where i is an integer and n is the order of the Fourier series being considered. C is a constant. ρ is the radial coordinate of the power profile. a i and b i are the coefficients of the ith order Fourier expansion.

[0290] The Fourier series described herein may be used to characterize the power profile of a particular embodiment. Figures 124-127 show power profiles designed for several exemplary embodiments. Figures 119-123 show the power profiles of several commercially available multifocal lenses measured with a commercially available Shack-Hartmann-based power profiling instrument named Optocraft (Optocraft GmbH, Germany). Default settings for multifocal lens use were used to obtain the measurement data for the commercially available lenses. The commercially available lenses were symmetrical, and only a cross-section of the power profile was exported for Fourier series fit analysis. In this example, the data density, i.e., the number of points used for fit analysis, was 400 points on the half-chord of the lens's optical zone, from 0 to 4 mm in 0.01 mm steps. The same data density was used when fitting the exemplary system values ​​to the Fourier series. A least-squares method was used to optimize the best coefficients for the chosen power or order of the Fourier series. Once the optimization routine is complete, the calculation routine calculates two metrics: the coefficient of determination (R 2 ) and root mean square error (RMSE), the smaller the RMSE, the better the fit, and R 2 The higher the value, the better the fit. As used in this example, the best fit is a coefficient of determination (R) greater than 0.975. 2 ) and / or a fit with the lowest order mathematical function that produces a root mean square error (RMSE) of less than 0.15D. 2 In cases where it is not possible to fit a function that achieves the criteria of >0.975 and RMSE<0.15D, the maximum R 2The order of the function that produces the lowest RMSE and / or the lowest power profile is used to characterize the power profile. However, such a power profile in this example does not meet the criteria of the exemplary embodiment. Tables 24-27 show the coefficients of the Fourier series expansion up to the 15th order obtained when the power profiles described in Figures 119 and 120 are best-fit to the Fourier series expansion described via a nonlinear least-squares optimization routine. In this example, the conventional lens is described by less than the fourth order of the Fourier series with non-zero coefficients. In contrast, the exemplary design requires at least the eighth order of the Fourier series with non-zero coefficients to be reproduced with an RMSE of <0.15D.

[0291] In certain embodiments, a lens includes an optical axis and at least two surfaces, the lens having a power profile, the power profile may be reproduced by using at least the 6th, 8th, 10th, 12th, and 15th orders of a Fourier series having substantially non-zero coefficients. TIFF0007618639000051.tif151123TIFF0007618639000052.tif198140TIFF0007618639000053.tif173104TIFF0007618639000054.tif164170 TIFF0007618639000055.tif154121TIFF0007618639000056.tif111119TIFF0007618639000057.tif150128TIFF0007618639000058.tif142164

[0292] Section 26: Effect of Plus Power Within the Optical Zone on the Optical Transfer Function Figures 109, 111, and 113 show power profiles as a function of half-chord diameter for several exemplary lens designs. The set of three designs shown in Figures 109, 111, and 113, respectively, have powers of approximately +3D, +6D, and +10D at the center of the half-chord, gradually decreasing to 0D at certain given points on the half-chord diameter of the lens. In Figures 109, 111, and 113, respectively, the points of intersection of the power profile with the x-axis occur at 0.5 mm (dashed black line), 0.75 mm (thick gray line), and 1 mm (thick black line) on the half-chord for the three different power profiles.

[0293] Figures 110, 112, and 114 show the modeled optical performance of the exemplary power profiles disclosed in Figures 109, 111, and 113, respectively. The modeled performance is measured and obtained with respect to the real part of the optical transfer function as a function of various spatial frequencies. The optical transfer function portion described in the equations disclosed in Section 1 was used to measure the optical performance of the profiles shown in these figures. Performance was modeled using a 4mm pupil diameter; however, other pupil diameters may also be used. The neural contrast sensitivity function is also plotted in Figures 110, 112, and 114 as a function of spatial frequency to facilitate measuring the impact of the designed plus power at the center of the lens on the optical transfer function. In the examples shown in these figures, the reduction in modulation of the real part of the optical transfer function as a function of spatial frequency was compared to the neural contrast sensitivity function to measure the impact on visual acuity. As shown in Figures 110, 112, and 114, when the plus power addition varying from +3D to +10D is limited to 0.5 mm of the half-chord diameter of the lens's optical zone, the reduction in contrast / modulation transmission at mid-spatial frequencies (i.e., 15 cycles / degree) is 0.8. In contrast, when the plus addition varying from +3D to +10D is greater than 0.5 mm or 0.75 mm of the half-chord, the reduction in contrast / modulation transmission at mid-spatial frequencies (i.e., cycles / degree) is 0.6. Thus, in some embodiments, the power profile may be optimized to have less impact on the optical transfer function by selecting a plus power variation ranging from +3D to +10D with a zone width ranging from 0.25 mm to 1 mm of the lens' half-chord. Such embodiments may include other features discussed in this disclosure.

[0294] Certain embodiments may have a power profile that includes an appropriate combination of the power profiles disclosed herein, such as the power profiles described in Section 22(i), Section 22(ii), or Section 22(iii). In some embodiments, the power profile may have varying powers ranging from +3D to +10D of additional plus power relative to the prescription power within an appropriate range in the half-chord of the high-g Cow zone. For example, in some embodiments, the appropriate range in the half-chord of the optical zone may be one of the following: 0-0.25mm, 0-0.5mm, or 0-0.75mm. Such a combination may provide acceptable visual acuity and / or minimized ghosting for at least a subset of the population.

[0295] Some embodiments are directed to lenses, methods, and / or devices including an optical axis, a power profile that transitions between a maximum value and its adjacent minimum value, where the maximum value is within 0.22 mm and the adjacent minimum value is within a distance from the center of the optical zone of the lens of at least 0.3 mm, 0.4 mm, 0.5 mm, 0.6 mm, 0.7 mm, 0.8 mm, 0.9 mm, or 1 mm, and the transition zone between the maximum value and its adjacent minimum value may be continuous, substantially continuous, smooth, substantially smooth, discontinuous, or some combination thereof. The amplitude of the transition zone between the maximum value and its adjacent minimum value is at least +2D, +2.25D, +2.5D, +2.75D, +3D, +3.25D, +3.5D, +4D, +4.5D, +5D, +5.5D, +6D, +6.5D, +7D, +7.5D, +8D, +8.5D, +9D, +9.5D, or +10D.

[0296] The subject matter claimed by the appended claims, as well as in accordance with the description set forth herein, particularly in the above-described embodiments and / or the examples below, covers all uses of the described lenses, devices, and / or any method uses covered by the descriptions, examples, and claims, except that the subject matter of the descriptions, examples, and claims may also cover the use of the described devices and any covered method uses, excluding such uses that involve or involve invasive steps that require professional medical expertise to be performed and represent a substantial physical intervention on the body that involves substantial health risks even when performed with the required professional care and expertise. Such excluded uses and / or steps of use are, for example, the implantation and / or modification of intraocular lenses, corneal inlays, corneal onlays, and corneal refractive surgical procedures, particularly within the human or animal body, in particular the removal of an intraocular lens from the lens of the eye, the removal of an intraocular lens, corneal inlay, corneal onlay from within a human or animal eye, the replacement of the lens with an intraocular lens, and / or the replacement of an intraocular lens, corneal inlay, and / or corneal onlay within the human or animal body.

[0297] However, the claimed subject matter covers all uses not falling within these exceptions, such as computational steps for calculating the correction of lenses and / or devices, computational steps for calculating, describing, and / or characterizing the power profile, aberration profile of lenses and / or devices, the ex vivo modification of lenses, such as contact lenses, spectacle lenses, corneal inlays, micro-onlays, or intraocular lenses (anterior and posterior chambers), in humans and / or animals; the application of the claimed methods and / or devices to model eyes formed by physical models that are optically equivalent to the eye; and the use of the methods and / or devices in optical computational methods such as ray tracing and / or Fourier optics.

[0298] Other exemplary embodiments are described in the following set of Examples A through X.

[0299] Example pair A: (A1) 1. An ophthalmic lens having an optical axis and an aberration profile centered on the optical axis, the aberration profile having a focal length and including high-order aberrations including at least one of a first-order spherical aberration component C(4,0) and a second-order spherical aberration component C(6,0), the aberration profile providing a retinal image quality (RIQ) with a through-focus slope that degrades in the direction of eye growth and an RIQ of at least 0.3 for a model eye having no or substantially no aberrations and an axial length equal to or substantially equal to the focal length, the RIQ being the visual Strehl ratio measured substantially along the optical axis over a spatial frequency range from 0 cycles / degree to 30 cycles / degree, inclusive, and at a wavelength selected from the range of 540 nm to 590 nm, inclusive, for at least one pupil diameter in the range of 3 mm to 6 mm.

[0300] (A2) 1. An ophthalmic lens having an optical axis and an aberration profile centered on the optical axis, the aberration profile having a focal length and including high-order aberrations including at least one of a first-order spherical aberration component C(4,0) and a second-order spherical aberration component C(6,0), the aberration profile providing a retinal image quality (RIQ) with a through-focus slope that degrades in the direction of eye growth and an RIQ of at least 0.3 for a model eye having no aberrations and an axial length equal to the focal length, the RIQ being the visual Strehl ratio measured substantially along the optical axis over a spatial frequency range from 0 cycles / degree to 30 cycles / degree, inclusive, at a wavelength selected from the range of 540 nm to 590 nm, inclusive, for at least one pupil diameter in the range of 3 mm to 6 mm.

[0301] (A3) 1. An ophthalmic lens having an optical axis, a focal length, and characterized by an aberration profile centered on the optical axis of the lens, the aberration profile including high-order aberrations including at least one of a first-order spherical aberration component C(4,0) and a second-order spherical aberration component C(6,0), the aberration profile providing a retinal image quality (RIQ) with a through-focus slope that degrades in the direction of eye growth and an RIQ of at least 0.3 for a model eye having no or substantially no aberrations and an axial length equal to or substantially equal to the focal length, the RIQ being the visual Strehl ratio measured substantially along the optical axis over a spatial frequency range from 0 cycles / degree to 30 cycles / degree, inclusive, and at a wavelength selected from the range of 540 nm to 590 nm, inclusive, for at least one pupil diameter in the range of 3 mm to 6 mm.

[0302] (A4) 1. An ophthalmic lens having at least one optical axis and at least one optical profile substantially about the at least one optical axis, the optical profile having at least one focal length and including one or more high-order aberrations, the profile providing a retinal image quality (RIQ) with a through-focus slope that improves in the direction of eye growth and an RIQ of at least 0.3 for a model eye that is substantially free of aberrations and has an axial length equal to or substantially equal to a desired focal length, the RIQ being measured substantially along the optical axis over a spatial frequency range of 0 cycles / degree to 30 cycles / degree, inclusive, at a wavelength selected from the range of 540 nm to 590 nm, inclusive, for at least one pupil diameter in the range of 3 mm to 6 mm.

[0303] (A5) 1. An ophthalmic lens having an optical axis and an aberration profile centered on the optical axis, the aberration profile having a focal length and including high-order aberrations including at least one of a first-order spherical aberration component C(4,0) and a second-order spherical aberration component C(6,0), the aberration profile providing a retinal image quality (RIQ) with a through-focus slope that improves in the direction of eye growth and an RIQ of at least 0.3 for a model eye having no or substantially no aberrations and an axial length equal to or substantially equal to the focal length, the RIQ being the visual Strehl ratio measured substantially along the optical axis over a spatial frequency range from 0 cycles / degree to 30 cycles / degree, inclusive, and at a wavelength selected from the range of 540 nm to 590 nm, inclusive, for at least one pupil diameter in the range of 3 mm to 6 mm.

[0304] (A6) 1. An ophthalmic lens having an optical axis and an aberration profile centered on the optical axis, the aberration profile having a focal length and including high-order aberrations including at least one of a first-order spherical aberration component C(4,0) and a second-order spherical aberration component C(6,0), the aberration profile providing a retinal image quality (RIQ) with a through-focus slope that improves in the direction of eye growth and an RIQ of at least 0.3 for a model eye having no aberrations and an axial length equal to the focal length, the RIQ being the visual Strehl ratio measured substantially along the optical axis over a spatial frequency range from 0 cycles / degree to 30 cycles / degree, inclusive, and at a wavelength selected from the range of 540 nm to 590 nm, inclusive, for at least one pupil diameter in the range of 3 mm to 6 mm.

[0305] (A7) 1. An ophthalmic lens having an optical axis, a focal length, and characterized by an aberration profile centered on the optical axis of the lens, the aberration profile including high-order aberrations including at least one of a first-order spherical aberration component C(4,0) and a second-order spherical aberration component C(6,0), the aberration profile providing a retinal image quality (RIQ) with a through-focus slope that improves in the direction of eye growth and an RIQ of at least 0.3 for a model eye having no or substantially no aberrations and an axial length equal to or substantially equal to the focal length, the RIQ being the visual Strehl ratio measured substantially along the optical axis over a spatial frequency range from 0 cycles / degree to 30 cycles / degree, inclusive, and at a wavelength selected from the range of 540 nm to 590 nm, inclusive, for at least one pupil diameter in the range of 3 mm to 6 mm.

[0306] (A8) An ophthalmic lens having at least one optical axis and at least one optical profile centered on the at least one optical axis, the optical profile having at least one focal length and including one or more high-order aberrations, the profile being substantially free of and providing a retinal image quality (RIQ) with a through-focus slope that improves in the direction of eye growth and an RIQ of at least 0.3 for a model eye having an axial length equal to or substantially equal to the desired focal length, the RIQ being measured substantially along the optical axis over a spatial frequency range of 0 cycles / degree to 30 cycles / degree, inclusive, at a wavelength selected from the range of 540 nm to 590 nm, inclusive, for at least one pupil diameter in the range of 3 mm to 6 mm.

[0307] (A9) A lens according to one or more of the examples in A above, wherein the focal length is a prescribed focal length for a myopic eye, which focal length is different from the focal length for the C(2,0) Zernike coefficient of the aberration profile.

[0308] (A10) A lens according to one or more of the examples in A above, wherein the focal length is a prescribed focal length for a hyperopic eye, which focal length is different from the focal length for the C(2,0) Zernike coefficient of the aberration profile.

[0309] (A11) The lens according to one or more of the examples in A above, wherein the high-order aberrations include at least two spherical aberration terms selected from the group C(4,0) to C(20,0).

[0310] (A12) The lens according to one or more of the examples in A above, wherein the high-order aberrations include at least three spherical aberration terms selected from the group C(4,0) to C(20,0).

[0311] (A13) The lens according to one or more of the examples in A above, wherein the high-order aberrations include at least four spherical aberration terms selected from the group C(4,0) to C(20,0).

[0312] (A14) The lens according to one or more of the examples in A above, wherein the high-order aberrations include at least five spherical aberration terms selected from the group C(4,0) to C(20,0).

[0313] (A15) The lens according to one or more of the examples in A above, wherein the high-order aberrations include at least six spherical aberration terms selected from the group C(4,0) to C(20,0).

[0314] (A16) The lens according to one or more of the examples in A above, wherein the high-order aberrations include at least seven spherical aberration terms selected from the group C(4,0) to C(20,0).

[0315] (A17) The lens of any one or more of Examples A above, wherein the magnitude of the included high-order aberrations is at least 0.01 μm over a 4 mm, 5 mm, or 6 mm pupil diameter.

[0316] (A18) A lens according to any one or more of the examples in A above, wherein the magnitude of the included high-order aberrations is at least 0.02 μm over a 4 mm, 5 mm, or 6 mm pupil diameter.

[0317] (A19) A lens according to any one or more of the examples under A above, wherein the magnitude of the included high-order aberrations is at least 0.03 μm over a 4 mm, 5 mm, or 6 mm pupil diameter.

[0318] (A20) A lens according to any one or more of the examples in A above, wherein the magnitude of the included high-order aberrations is at least 0.04 μm over a 4 mm, 5 mm, or 6 mm pupil diameter.

[0319] (A21) A lens according to any one or more of the examples in A above, wherein the magnitude of the included high-order aberrations is at least 0.05 μm over a 4 mm, 5 mm, or 6 mm pupil diameter.

[0320] (A22) A lens according to one or more of the examples in A above, wherein the magnitude of included high-order aberrations is at least 0.01 μm, 0.02 μm, 0.03 μm, or 0.04 μm over a 3 mm pupil diameter.

[0321] (A23) A lens according to any one or more of the examples in A above, wherein the average tilt across a horizontal visual field of at least -20 degrees to +20 degrees deteriorates in the direction of eye growth.

[0322] (A24) A lens according to any one or more of the examples in A above, wherein the average tilt across a vertical visual field of at least -20 degrees to +20 degrees deteriorates in the direction of eye growth.

[0323] (A25) A lens according to one or more of the examples in A above, wherein the tilt for a significant portion of the visual field angle across a horizontal field of view of at least -20 degrees to +20 degrees deteriorates in the direction of eye growth.

[0324] (A26) A lens according to one or more of the examples in A above, wherein the tilt for a significant portion of the visual angle tail across a vertical visual field of at least -20 degrees to +20 degrees deteriorates in the direction of eye growth.

[0325] (A27) The lens of one or more of Examples A above, wherein the aberration profile provides a RIQ of at least 0.3 at the focal length for a significant portion of pupil diameters in the 3mm to 6mm range.

[0326] (A28) The lens of any one or more of Examples A above, wherein the aberration profile provides a RIQ of at least 0.3 at the focal length for a significant portion of pupil diameters within the 4mm to 5mm range.

[0327] (A29) A lens according to one or more of the examples in A above, wherein the through-focus slope averaged over a horizontal field of view of at least -20 degrees to +20 degrees deteriorates in the direction of eye growth.

[0328] (A30) A lens according to one or more of the examples in A above, wherein the through-focus tilt averaged over a vertical field of view of at least -20 degrees to +20 degrees deteriorates in the direction of eye growth.

[0329] (A31) A lens according to one or more of the examples in A above, wherein the through-focus tilt deteriorates in the direction of eye growth for a significant portion of the field of view over a horizontal field of view of at least -20 degrees to +20 degrees.

[0330] (A32) A lens according to one or more of the examples in A above, wherein the through-focus tilt deteriorates in the direction of eye growth for a significant portion of the field of view over a vertical field of view of at least -20 degrees to +20 degrees.

[0331] (A33) A lens according to one or more of the examples in A above, wherein the aberration profile provides an RIQ with a through-focus slope that deteriorates in the direction of ocular growth when first order astigmatism is added to the aberration profile.

[0332] (A34) A lens according to one or more of the examples in A above, wherein the aberration profile provides an RIQ with a through-focus slope that improves in the direction of ocular growth when first order astigmatism is added to the aberration profile.

[0333] (A35) A lens according to one or more of the examples in A above, wherein the aberration profile provides an RIQ with a through-focus slope that deteriorates in the direction of ocular growth when secondary astigmatism is added to the aberration profile.

[0334] (A36) A lens according to one or more of the examples in A above, wherein the aberration profile provides an RIQ with a through-focus slope that improves in the direction of ocular growth when secondary astigmatism is added to the aberration profile.

[0335] (A37) RIQ is TIFF0007618639000059.tif24133 or characterized in that, in the above formula: Fmin is 0 cycles / degree and Fmax is 30 cycles / degree; CSF(x,y) denotes the contrast sensitivity function, CSF(F) = 2.6(0.0192 + 0.114f)e -(0.114f)^1.1 and In the above formula, f is F min ~F max Specify the spatial frequency to be tested in the range FT denotes 2D Fast Fourier Transform, e.g., 2D Fast Fourier Transform, A(ρ,θ) denotes the pupil amplitude function over the pupil radius, W(ρ,θ) denotes the wavefront of the test case measured for i=1 to 20; TIFF0007618639000060.tif1644, Wdiff(ρ,θ) denotes the wavefront in the diffraction-limited case, ρ and θ are normalized polar coordinates, where ρ represents the radial coordinate and θ represents the angular coordinate or azimuth; The lens of any one of examples A above, wherein λ denotes a wavelength.

[0336] (A38) RIQ is TIFF0007618639000061.tif24133 or characterized by the formula Fmin is 0 cycles / degree and Fmax is 30 cycles / degree; CSF(x,y) denotes the contrast sensitivity function, CSF(F) = 2.6(0.0192 + 0.114f)e -(0.114f)^1.1 and In the above formula, f is F min ~F max Specify the spatial frequency to be tested in the range FT denotes 2D Fast Fourier Transform, e.g., 2D Fast Fourier Transform, A(ρ,θ) denotes the pupil amplitude function over the pupil radius, W(ρ,θ) denotes the wavefront of the test case measured for i=1 to k; k is a positive integer, TIFF0007618639000062.tif1754, Wdiff(ρ,θ) denotes the wavefront in the diffraction-limited case, ρ and θ are normalized polar coordinates, where ρ represents the radial coordinate and θ represents the angular coordinate or azimuth; The lens of any one of examples A above, wherein λ denotes a wavelength.

[0337] (A39) 1. A lens comprising an optical axis and an aberration profile centered on the optical axis, the aberration profile providing a focal length for a C(2,0) Zernike coefficient term, a peak visual Strehl ratio within a through-focus range (a "first peak visual Strehl ratio"), and a visual Strehl ratio that remains at or above a second peak visual Strehl ratio throughout a through-focus range that includes the focal length, the visual Strehl ratio being measured on a model eye that is free or substantially free of aberrations, and measured along the optical axis over a spatial frequency range from 0 cycles / degree to 30 cycles / degree, inclusive, for at least one pupil diameter in the range of 3 mm to 6 mm, at a wavelength selected from the range of 540 nm to 590 nm, inclusive, the first visual Strehl ratio being at least 0.35, the second visual Strehl ratio being at least 0.1, and the through-focus range being at least 1.8 diopters.

[0338] (A40) A lens according to any one of Examples A above, wherein the first ocular Strehl ratio is at least 0.28 or 0.3.

[0339] (A41) A lens according to any one of Examples A above, wherein the first visual Strehl ratio is at least 0.4.

[0340] (A42) A lens according to any one of Examples A above, wherein the first visual Strehl ratio is at least 0.5.

[0341] (A43) A lens according to any one of Examples A above, wherein the first visual Strehl ratio is at least 0.6.

[0342] (A44) A lens according to any one of Examples A above, wherein the first visual Strehl ratio is at least 0.7.

[0343] (A45) A lens according to any one of Examples A above, wherein the first visual Strehl ratio is at least 0.8.

[0344] (A46) The lens of any one or more of Examples A above, wherein the second visual Strehl ratio is at least 0.08, 0.1, 0.12, 0.14, 0.16, 0.18, and 0.2.

[0345] (A47) A lens according to one or more of the examples in A above, wherein the through-focus range is at least 1.8 diopters.

[0346] (A48) A lens according to one or more of the examples in A above, wherein the through-focus range is at least 1.9 diopters.

[0347] (A49) A lens according to one or more of the examples in A above, wherein the through-focus range is at least 2 diopters.

[0348] (A50) A lens according to one or more of the examples in A above, wherein the through-focus range is at least 2.1 diopters.

[0349] (A51) A lens according to one or more of the examples in A above, wherein the through-focus range is at least 2.25 diopters.

[0350] (A52) A lens according to one or more of the examples in A above, wherein the through-focus range is at least 2.5 diopters.

[0351] (A53) A lens according to any one or more of the examples in A above, having a prescription focal length that is within 0.75 diopters of an edge of its through-focus range.

[0352] (A54) A lens according to any one or more of the preceding examples, having a prescription focal length located within 0.5 diopters of an edge of its through-focus range.

[0353] (A55) A lens according to any one or more of the preceding examples, having a prescription focal length located within 0.3 diopters of an edge of its through-focus range.

[0354] (A56) A lens according to any one or more of Examples A and B, having a prescription focal length located within 0.25 diopters of an edge of its through-focus range.

[0355] (A57) A lens according to one or more of the examples in A above, wherein the end of the through-focus range is the negative power end.

[0356] (A58) A lens according to one or more of the examples in A above, wherein the ends of the through-focus range are positive powers.

[0357] (A59) A lens according to one or more of the examples in A above, wherein the first visual Strehl ratio remains at or exceeds the second visual Strehl ratio over a through-focus range and over a range of pupil diameters of at least 1 mm.

[0358] (A60) A lens according to one or more of Examples A above, wherein the first visual Strehl ratio remains at or exceeds the second visual Strehl ratio over a through-focus range and over a range of pupil diameters of at least 1.5 mm.

[0359] (A61) A lens according to one or more of the examples in A above, wherein the first visual Strehl ratio remains at or exceeds the second visual Strehl ratio over a through-focus range and over a range of pupil diameters of at least 2 mm.

[0360] (A62) The lens of any one or more of Examples A above, wherein the combination of high-order aberrations includes at least one of first-order spherical aberration and second-order spherical aberration.

[0361] (A63) The lens according to one or more of the examples in A above, wherein the high-order aberrations include at least two spherical aberration terms selected from groups C(4,0) to C(20,0).

[0362] (A64) The lens according to one or more of the examples in A above, wherein the high-order aberrations include at least three spherical aberration terms selected from groups C(4,0) to C(20,0).

[0363] (A65) The lens according to one or more of the examples in A above, wherein the high-order aberrations include at least five spherical aberration terms selected from groups C(4,0) to C(20,0).

[0364] (A66) The lens of any one or more of the examples in A above, wherein the aberration profile is substantially described using only the spherical aberration Zernike coefficients C(4,0) to C(20,0).

[0365] (A67) The lens of any one or more of Examples A above, wherein the RIQ for all viewing angles over a horizontal field of view of at least -10 degrees to +10 degrees is at least 0.2, 0.25, 0.3, 0.35, or 0.4.

[0366] (A68) The lens of any one or more of Examples A above, wherein the RIQ for all viewing angles over a horizontal field of view of at least -20 degrees to +20 degrees is at least 0.2, 0.25, 0.3, 0.35, or 0.4.

[0367] (A69) The lens of any one or more of Examples A above, wherein the RIQ for all viewing angles over a horizontal field of view of at least -30 degrees to +30 degrees is at least 0.2, 0.25, 0.3, 0.35, or 0.4.

[0368] (A70) A lens according to one or more of the examples in A above, which does not substantially reduce the amount of light passing through the lens.

[0369] The lens according to one or more of the examples in A above, wherein the aberration profile is an aberration pattern.

[0370] (A72) 1. A method for a presbyopic eye, comprising: identifying at least one wavefront aberration profile for the eye, the at least one wavefront aberration profile comprising at least two spherical aberration terms; a prescribed focal length of a lens is determined taking into account the at least one spherical aberration, the prescribed focal length of the lens being at least +0.25D relative to a focal length for a C(2,0) Zernike coefficient term of the at least one wavefront aberration profile; and fabricating one or more of an ophthalmic device, a lens, and a corneal profile for the eye that affect the at least one wavefront aberration profile.

[0371] (A73) 1. A method for a myopic or emmetropic eye, comprising creating aberrations for the eye and applying or prescribing an aberration profile, the aberration profile having a focal length and including at least one of a first-order spherical aberration component C(4,0) and a second-order spherical aberration component C(6,0), the aberration profile providing for the eye a retinal image quality (RIQ) with a through-focus slope that degrades in the direction of eye growth and an RIQ of at least 0.3, the RIQ being the visual Strehl ratio measured along the optical axis at a wavelength selected from the range of 540 nm to 590 nm, inclusive, over a spatial frequency range of 0 cycles / degree to 30 cycles / degree, inclusive, for at least one pupil diameter in the range of 3 mm to 6 mm.

[0372] (A74) 1. A method for a hyperopic eye, comprising: creating aberrations for the eye and applying or prescribing an aberration profile, the aberration profile having a focal length and including at least one of a first-order spherical aberration component C(4,0) and a second-order spherical aberration component C(6,0), the aberration profile providing for the eye a retinal image quality (RIQ) with a through-focus slope that improves in the direction of eye growth and an RIQ of at least 0.3, the RIQ being the visual Strehl ratio measured along the optical axis at a wavelength selected from the range of 540 nm to 590 nm, inclusive, over a spatial frequency range of 0 cycles / degree to 30 cycles / degree, inclusive, for at least one pupil diameter in the range of 3 mm to 6 mm.

[0373] (A75) The method of any one or more of the method examples of A above, wherein applying or prescribing an aberration profile comprises providing a lens having an aberration profile including at least two spherical aberration terms selected from the group C(4,0) to C(20,0).

[0374] (A76) The method of any one or more of the method examples of A above, wherein applying or prescribing an aberration profile comprises providing a lens having an aberration profile including at least three spherical aberration terms selected from the group C(4,0) to C(20,0).

[0375] (A77) The method of any one or more of the method examples of A above, wherein applying or prescribing an aberration profile comprises providing a lens having an aberration profile including at least five spherical aberration terms selected from the group C(4,0) to C(20,0).

[0376] (A78) 10. A method for a myopic eye, comprising identifying a wavefront aberration profile for the eye and applying or prescribing the aberration profile, the wavefront aberration profile comprising at least two spherical aberration terms, a prescribed focal length of the lens being determined taking into account said spherical aberration, the prescribed focal length being at least +0.1 D relative to a focal length for a C(2,0) Zernike coefficient term of the wavefront aberration profile, and the wavefront aberration profile providing degraded retinal image quality in a direction posterior to the retina, as described in one or more of the example methods of A above.

[0377] (A79) 10. A method for a hyperopic eye, comprising identifying a wavefront aberration profile for the eye and applying or prescribing the aberration profile, the wavefront aberration profile comprising at least two spherical aberration terms, a prescribed focal length of the lens being determined taking into account said spherical aberration, the prescribed focal length being at least +0.1 D relative to a focal length for a C(2,0) Zernike coefficient term of the wavefront aberration profile, and the wavefront aberration profile providing improving retinal image quality in a direction posterior to the retina.

[0378] (A80) The method according to any one or more of the method examples of A above, wherein the prescribed focal length is at least +0.1D relative to the focal length for the C(2,0) Zernike coefficient term of the wavefront aberration profile.

[0379] (A81) 1. A method for a hyperopic eye, the method comprising identifying a wavefront aberration profile for the eye and applying or prescribing the aberration profile, the wavefront aberration profile comprising at least two spherical aberration terms, a prescribed focal length of a lens being determined taking into account said spherical aberrations, and at the prescribed focal length, the wavefront aberration profile provides improving retinal image quality in a direction posterior to the retina.

[0380] (A82) The method according to any one or more of the above method examples of A, wherein the lens does not substantially reduce the amount of light passing through the lens.

[0381] (A83) The method according to any one or more of the method examples of A above, wherein the aberration profile is an aberration pattern.

[0382] Example pair B: (B1) A multifocal lens having an optical axis and an effective near add power of at least 1D, wherein the optical characteristics of the multifocal lens are configured to have an aberration profile associated with the optical axis, the aberration profile consisting of a defocus term and at least two spherical aberration terms, the multifocal lens being configured to provide visual performance over intermediate and far distances that is at least substantially equivalent to the visual performance of a correctly prescribed single focus lens at a far viewing distance, and to enable ghosting at far, intermediate, and near distances to be minimized.

[0383] (B2) A multifocal lens according to any one or more of the method examples of B above, configured to provide at least 6 / 6 near visual acuity in individuals capable of achieving 6 / 6 visual acuity.

[0384] (B3) A multifocal lens according to any one or more of the method examples of B above, configured to provide at least acceptable visual performance at near distances.

[0385] (B4) A multifocal lens having an optical axis and an effective near add power of at least 0.75D, the optical characteristics of the multifocal lens being constructed or described at least in part based on an aberration profile associated with the optical axis, the aberration profile being comprised of a defocus term and at least two spherical aberration terms; the multifocal lens being configured to provide visual performance along a substantially continuous range of near viewing distances, the visual performance of the multifocal lens being at least substantially equivalent to the visual performance of a correctly prescribed single focus lens at a distance viewing distance; and the multifocal lens being configured to affect visual performance along a substantially continuous range of intermediate and far viewing distances, the visual performance of the multifocal lens being at least substantially equivalent to the visual performance of a correctly prescribed single focus lens at a distance viewing distance.

[0386] (B5) A multifocal lens having an optical axis, the optical characteristics of the multifocal lens being configured or described at least in part based on an aber...

Claims

1. A method for designing an ophthalmic lens having refractive error, the lens comprising: The optical axis, an aberration profile centered on the optical axis; and The prescription focal power; At least two optical surfaces; Equipped with The optical properties of the lens can be characterized by testing at least in terms of the following properties: 1st order spherical aberration C(4,0), 2nd order spherical aberration C(6,0), and higher order aberrations having four or more of the following components: 3rd order spherical aberration C(8,0), 4th order spherical aberration C(10,0), 5th order spherical aberration C(12,0), 6th order spherical aberration C(14,0), 7th order spherical aberration C(16,0), 8th order spherical aberration C(18,0), and 9th order spherical aberration C(20,0); the aberration profile, when tested on a model eye free of high order aberrations and having the refractive error, produces a retinal image quality (RIQ) with a through-focus slope such that the RIQ decreases in the direction of eye growth, the RIQ being determined by an optical Strehl ratio measured along the optical axis, the RIQ being measured on a model eye free of high order aberrations and at a wavelength selected from the range of 540 nm to 590 nm, inclusive, over a spatial frequency range of 0 cycles / degree to 30 cycles / degree, inclusive, for at least one pupil diameter in the range of 3 mm to 5 mm; The lens is ghost-free at close, intermediate and long distances, thereby (i) no undesirable images appear on the image plane of the optical system formed by said ophthalmic lens; (ii) no double image appears along the main image of the optical system formed by the ophthalmic lens; The present invention has any one of the following characteristics: a power profile of the Ophthalmic Lens is associated with the Optical Axis, the power profile having a transition between a maximum and a minimum, the maximum being within 0.2 mm of a center of the Optical Zone, the minimum being a distance of 0.3 mm or less from the maximum, and the amplitude of the transition between the maximum and the minimum being at least 2.5 D; The power profile of the ophthalmic lens comprises, over a half cord diameter: (a) a moving average is calculated over a 1 mm window that increases with diameter and then decreases, or decreases with diameter and then increases, from about 4 mm on-axis, the average being calculated over a range of 1 mm from on-axis and recalculated at intervals selected from the group of 0.2 mm, 0.4 mm, or 0.6 mm; and / or (b) having at least 4 transitions between local minima and local maxima within a 1 mm change in radius over 4 mm of the half-chord, or at least 6 transitions over 4 mm of the half-chord, or at least 8 transitions over a 4 mm radial range, or at least 12 transitions over a 4 mm radial range, or at least 15 transitions; and / or (c) a smooth transition to a radius selected from the group of at least 3 mm, at least 3.5 mm, and at least 4 mm; It has the following characteristics: The RIQ is In the above formula, Fmin is 0 cycles / degree and Fmax is 30 cycles / degree; CSF(x,y) denotes the contrast sensitivity function for the eye; In the above formula, x and y are F ｍｉｎ ~F ｍａｘ Specify the spatial frequency to be tested in the range The CSF(x) for the spatial frequency in the x direction is CSF(x) = 2.6(0.0192 + 0.114(x))e －（０．１１４（ｘ））＾１．１ and The CSF(y) for the spatial frequency in the y direction is CSF(y) = 2.6(0.0192 + 0.114(y))e －（０．１１４（ｙ））＾１．１ and FT denotes 2D fast Fourier transform, A(ρ,θ) denotes the pupil amplitude function across said pupil diameter; W(ρ,θ) denotes the wavefront of the test cases measured for i=1 to 20; and ai denotes the i-th coefficient of the Zernike polynomial, Zi(ρ,θ) denotes the i-th Zernike polynomial term, Wdiff(ρ,θ) denotes the wavefront in the diffraction-limited case, The method, wherein ρ and θ are normalized polar coordinates, ρ represents the radial coordinate, θ represents the angular coordinate or azimuth, and λ represents the wavelength.

2. 10. The method of claim 1, wherein the lens is further configured to provide the RIQ of at least 0.1 in the near range, the RIQ of at least 0.27 in the intermediate range, and the RIQ of at least 0.35 in the far range.

3. 10. The method of claim 1, wherein the lens is further configured to provide two or more of the RIQ of at least 0.1 in the near distance range, the RIQ of at least 0.27 in the intermediate distance range, and the RIQ of at least 0.35 in the far distance range.

4. The method of claim 1 , wherein the slope averaged over a horizontal field of view of at least −20 degrees to +20 degrees deteriorates in the direction of eye growth.

5. 2. The method of claim 1, wherein the slope averaged over a vertical field of view of at least -20 degrees to +20 degrees deteriorates in the direction of eye growth.

6. 2. The method of claim 1, wherein the aberration profile provides the RIQ with a through-focus slope that deteriorates in the direction of eye growth when primary or secondary astigmatism is added to the aberration profile.

7. 7. The method of claim 6, wherein the primary or secondary astigmatism is added to the desired aberration profile by modifying one or more of the terms C(2,-2), C(2,2), C(4,-2), C(4,2), C(6,-2), and / or C(6,2).

8. The method of claim 1 , wherein the visual Strehl ratio is at least 0.

3.

9. The method of claim 1 , wherein the transition between the maximum and minimum values ​​is one or more of continuous, discontinuous, monotonic, and non-monotonic.

10. A method for designing an ophthalmic lens having refractive error, the lens comprising: The optical axis, an aberration profile centered on the optical axis; and The prescription focal power; At least two optical surfaces; Equipped with The optical properties of the lens can be characterized by testing at least in terms of the following characteristics: 1st order spherical aberration C(4,0), 2nd order spherical aberration C(6,0), 3rd order spherical aberration C(8,0), 4th order spherical aberration C(10,0), 5th order spherical aberration C(12,0), 6th order spherical aberration C(14,0), 7th order spherical aberration C(16,0), 8th order spherical aberration C(18,0), and 9th order spherical aberration C(20,0); the aberration profile, when tested on a model eye free of high order aberrations and having the refractive error, produces a first RIQ that is the through-focus RIQ within a through-focus range, i.e., a peak RIQ, and that exceeds a second RIQ across the through-focus range, including a focal length, the first RIQ and the second RIQ being measured on a model eye free of high order aberrations and measured along the optical axis over a spatial frequency range from 0 cycles / degree to 30 cycles / degree, inclusive, for at least one pupil diameter in a range of 3 mm to 5 mm, at a wavelength selected from the range of 540 nm to 590 nm, inclusive; The lens is ghost-free at close, intermediate and long distances, thereby (i) no undesirable images appear on the image plane of the optical system formed by said ophthalmic lens; (ii) no double image appears along the main image of the optical system formed by the ophthalmic lens; The present invention has any one of the following characteristics: a power profile of the Ophthalmic Lens is associated with the Optical Axis, the power profile having a transition between a maximum and a minimum, the maximum being within 0.2 mm of a center of the Optical Zone, the minimum being a distance of 0.3 mm or less from the maximum, and the amplitude of the transition between the maximum and the minimum being at least 2.5 D; The power profile of the Ophthalmic Lens comprises, over a half cord diameter: (a) a moving average is calculated over a 1 mm window that increases with diameter and then decreases, or decreases with diameter and then increases, from about 4 mm on-axis, the average being calculated over a range of 1 mm from on-axis and recalculated at intervals selected from the group of 0.2 mm, 0.4 mm, or 0.6 mm; and / or (b) having at least 4 transitions between local minima and local maxima within a 1 mm change in radius over 4 mm of the half-chord, or at least 6 transitions over 4 mm of the half-chord, or at least 8 transitions over a 4 mm radial range, or at least 12 transitions over a 4 mm radial range, or at least 15 transitions; and / or (c) a smooth transition to a radius selected from the group of at least 3 mm, at least 3.5 mm, and at least 4 mm; It has the following characteristics: The RIQ is In the above formula, Fmin is 0 cycles / degree and Fmax is 30 cycles / degree; CSF(x,y) denotes the contrast sensitivity function for the eye; In the above formula, x and y are F ｍｉｎ ~F ｍａｘ Specify the spatial frequency to be tested in the range The CSF(x) for the spatial frequency in the x direction is CSF(x) = 2.6(0.0192 + 0.114(x))e －（０．１１４（ｘ））＾１．１ and The CSF(y) for the spatial frequency in the y direction is CSF(y) = 2.6(0.0192 + 0.114(y))e －（０．１１４（ｙ））＾１．１ and FT denotes 2D fast Fourier transform, A(ρ,θ) denotes the pupil amplitude function across said pupil diameter; W(ρ,θ) denotes the wavefront of the test cases measured for i=1 to 20; and ai denotes the i-th coefficient of the Zernike polynomial, Zi(ρ,θ) denotes the i-th Zernike polynomial term, Wdiff(ρ,θ) denotes the wavefront in the diffraction-limited case, The method, wherein ρ and θ are normalized polar coordinates, ρ represents the radial coordinate, θ represents the angular coordinate or azimuth, and λ represents the wavelength.

11. The method of claim 10 , wherein the lens is further configured to provide the RIQ of at least 0.1 in the near range, the RIQ of at least 0.27 in the intermediate range, and the RIQ of at least 0.35 in the far range.

12. 11. The method of claim 10, wherein the lens is further configured to provide two or more of the RIQ of at least 0.1 in the near distance range, the RIQ of at least 0.27 in the intermediate distance range, and the RIQ of at least 0.35 in the far distance range.

13. 11. The method of claim 10, wherein primary or secondary astigmatism is added to the desired aberration profile by modifying one or more of the terms C(2,-2), C(2,2), C(4,-2), C(4,2), C(6,-2), and / or C(6,2).

14. The method of claim 10 , wherein the first RIQ is at least 0.

3.

15. The method of claim 10 , wherein the second RIQ is at least 0.

1.

16. The method of claim 10 , wherein the through-focus range is at least 1.7D.

17. The method of claim 10 , wherein the transition between the maximum and minimum values ​​is one or more of continuous, discontinuous, monotonic, and non-monotonic.

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