Methods and devices for wavefront treatments of astigmatism, coma, presbyopia in human eyes

Abstract

To provide methods and devices for wavefront treatments of an eye's astigmatism, coma, and presbyopia.SOLUTION: Wavefront-engineered monofocal lenses, inducing spherical aberration into the eye's central pupil, provide vision correction beyond 20 / 20 acuity and improve quality of vision by eliminating image distortion caused by uncorrected astigmatism and coma in the eye. New presbyopia-correcting lenses, including Extended Depth of Focus (EDOF) bifocal, EDOF trifocal, and quasi-accommodating lenses, are disclosed for presbyopia corrections between +0.75 D to +3.25 D, and they are achieved by inducing a positive spherical aberration and a positive focus offset less than 3 Diopters in a central section plus a negative spherical aberration in an annular section within a central part of a monofocal lens.SELECTED DRAWING: Figure 5A

Description

[Technical Field]

[0001] Related application data This application is a continuation of U.S. provisional patent applications: 1) #62 / 920,859, filed May 20, 2019, by Junzhong Liang and Ling Yu, entitled "Wavefront monofocal lenses, wavefront bifocals, wavefront trifocals, and methods and devices of using spherical aberration to mitigate eye's astigmatism and focus errors," 2) #62 / 974,317, filed November 26, 2019, by Junzhong Liang and Ling Yu, entitled "Methods and devices for wavefront correction of astigmatism, coma, and presbyopia in human eyes," and 3) #62 / 995 / 872, filed February 18, 2020, by Junzhong Liang and Ling Yu, entitled "Wavefront monofocal, EDOF bifocal, EDOF trifocal, continuously-in-focus lenses and wavefront correction for astigmatism," This application claims priority from the International Application No. 2005 / 010999, filed on May 1, 2005, entitled "Coma, Presbyopia in Human Eyes," the disclosures of which are incorporated herein by reference.

[0002] This application relates to refractive correction of the human eye, including myopia, hyperopia, astigmatism, coma, and presbyopia, in the form of devices, methods, and applications. [Background technology]

[0003] Conventional refractive corrections for the human eye have historically been designed to correct specific refractive errors of the eye: focus error (myopia and hyperopia), astigmatism (cylindrical error), and in some cases spherical aberration. These refractive corrections are compromised for several reasons, including: 1) limitations in the selection of correctors for astigmatism correction, 2) limitations and errors in measuring the refractive error of the eye using subjective refraction, 3) manufacturing errors in ophthalmic lenses, and 4) coma or other higher order aberrations in some eyes.

[0004] Presbyopia is another factor that reduces human vision. Most people begin to notice the effects of presbyopia after age 40, when they begin to have difficulty seeing small print clearly. Devices for correcting presbyopia include reading glasses, bifocal / trifocal / progressive glasses, multifocal contact lenses, and diffractive bifocal / trifocal intraocular lenses (IOLs).

[0005] Invented by Benjamin Franklin in 1824, bifocals are eyeglasses with two different refractive powers. Bifocals have a baseline refractive power for distance vision defects, plus an additional refractive power on top of the baseline power for presbyopia correction. The two different refractive powers of bifocals are located in separate physical locations, e.g., the upper portion for distance vision and the lower portion for near vision. When people move their eyes up and down, the same optics in the lens are not used for distance and near vision correction. Because the eyes must use the same optics for viewing objects at both distance and near distances when the freedom to move the eyes up and down is lost due to the two different refractive powers, this split-optics design cannot be adopted for contact lenses, IOLs, implantable contact lenses (ICLs), corneal inlays, and surgical procedures.

[0006] Diffractive optics use grooved kinoform-shaped steps on a monofocal lens to generate 1) a first focus from the non-deviational "0" order diffraction for distance and 2) another focus from the deviational "1" order diffraction, producing simultaneous multiple focal points from the same incident light. Diffractive optics have been reported in progressive lenses (see U.S. Pat. No. 5,116,111) and trifocal IOLs (see U.S. Pat. Nos. 8,636,796 and 9,320,594).

[0007] The advantages of diffractive bifocal and trifocal IOLs include: 1) solving the problem of split optics for creating bifocal or trifocal lenses; and 2) enabling postoperative cataract patients to see at near and far distances without glasses. However, diffractive lenses (bifocal / trifocal IOLs) significantly degrade the quality of vision and are intolerable to most postoperative cataract patients. First, diffractive bifocal / trifocal IOLs cause nighttime symptoms such as halos and starbursts due to multiple images of bright objects at distance. Second, nighttime symptoms such as spider veins caused by diffractive rings projected onto the retina are common.

[0008] Diffractive optics cannot be applied to contact lenses because diffractive surfaces containing non-continuous, sharp edges (see Figure 1) can cause tissue damage to the corneal surface and disrupt normal tear flow across the cornea. Because both the split optics design in bifocal glasses and the diffractive optics in IOLs are not suitable for contact lenses, there are currently no reliable bifocal contact lenses in the prior art, despite the availability of many multifocal contact lenses on the market. Multifocal contact lenses that rely on pupil division for presbyopia correction have been reported (see U.S. Patent Nos. 6,808,262, 4,704,016, 4,898,461, 4,704,016, and 6,808,262). Given the physical optical system, e.g., the diffraction and interference of light rays traversing the pupil of the eye, both distant and near retinal images are uncertain.

[0009] The ultimate solution to correcting presbyopia for human vision is to restore accommodation to the eye's aging lens or replace the eye's optics with an accommodating IOL. Over the past two decades, significant efforts have been made to develop accommodating IOLs, followed by recent advances in achieving accommodation with fluid IOLs (see Figure 2). However, analysis of accommodative IOL data reveals at least three clinically significant problems. First, there are large fluctuations in focal power, as large as + / - 0.5 D, in both target accommodation states at distance near 0 D and near 3 D for eyes E13-401 (top right of Figure 2) and E15-301 (bottom right of Figure 2). Second, in the distance accommodation state, accommodative IOLs can produce a mean accommodation error of -1.0 D for eye E13-401 (top right of Figure 2) over a time scale of 0 to 5 seconds and for eye E02-411 (bottom left of Figure 2) over a time scale of 15 and 25 seconds. This large focus error can sometimes make it difficult to see clearly at long distances. Third, the accommodation range of the eye in Figure 2 varies from eye to eye, and for some eyes from moment to moment.

[0010] U.S. Patent No. 8,529,559 B2 and U.S. Patent Application No. 2011 / 0029073 A1 disclose a method and apparatus for inducing spherical aberration in the center of the eye's pupil for the treatment of presbyopia. While offering the benefit of extending the depth of focus of an ophthalmic lens, inducing spherical aberration with a corrective lens is believed to significantly reduce retinal contrast. It has also been proposed to induce spherical aberration of the opposite sign in the center of the eye's pupil to extend the depth of focus up to 3.5D. Unfortunately, the original design results in a significant reduction in contrast at distances. Summary of the Invention [Problem to be solved by the invention]

[0011] As a result, while many configurations and methods for vision correction are known in the art, these conventional methods and systems suffer from one or more of the drawbacks described herein above. [Means for solving the problem]

[0012] In a non-limiting embodiment, a wavefront technology monofocal lens for an eye, configured as an implantable or wearable lens, comprises: a) a baseline diopter power extending over an optical zone having a diameter of 5 mm to 8 mm for sphero-cylindrical correction; and b) at least one aspherical zone having at least one aspheric surface in a center of the monofocal lens having a diameter D0 of 2.5 mm to 4.5 mm, wherein the aspherical zone induces spherical aberration in the center of the pupil of the eye, and the spherical aberration or wavefront error induced in the center of the lens provides treatment for residual refractive error of the eye left uncorrected by the sphero-cylindrical correction, the residual uncorrected refractive error including astigmatism, focus error, coma, and higher order aberrations that are significant in the center of the pupil of the eye. In a non-limiting embodiment, a progressive lens for an eye, configured as an implantable or wearable lens, includes a baseline diopter power extending over an optical zone of 5 mm to 8 mm diameter for sphero-cylindrical correction, a positive focus offset φ1 of less than +2.0 D and more than +0.25 D in a central zone of diameter less than 2.5 mm and more than 1.8 mm, and at least two central aspherical zones at the center of the lens, each having an outer diameter of less than 4.5 mm and more than 2.5 mm, the central aspherical zones comprising at least one aspheric surface for inducing positive spherical aberration in a first zone and negative spherical aberration in a second zone, the first zone and the second zone being coaxial.In a non-limiting embodiment, a trifocal lens for an eye, configured as an implantable or wearable lens, includes a baseline diopter power extending over an optical zone of 5 mm to 8 mm diameter for sphero-cylindrical correction, a positive focus offset φ1 of less than +3.0 D and greater than +1.0 D in a central zone having a diameter D0 of less than 2.1 mm and greater than 1.65 mm, and at least two central aspherical zones in the center of the lens, each having an outer diameter of less than 4 mm and greater than 2.5 mm, the central aspherical zones being: The lens has at least one aspheric surface for inducing positive spherical aberration in a zone and negative spherical aberration in a second zone, the first and second zones being coaxial, and the focus offset φ1 induced in the central aspheric zone and the wavefront error from the induced spherical aberration create a trifocal lens, i.e., a first "distance" focus, a second focus with additional refractive power for "intermediate distance," and a third focus with additional refractive power for "near distance," and the positive focus offset φ1 in the central zone must be less than the total focus range of the trifocal lens.

[0013] In a non-limiting embodiment, a continuous focus (CIF) lens for the eye has an optical zone less than 8 mm in diameter that includes a multifocal structure that provides continuous foci for vision correction over a focal range of greater than 1.0 D, the multifocal structure having multiple foci that are closely adjacent to each other to provide substantially continuous foci, the multiple foci being achieved by using an aspheric surface to induce spherical aberration in a central portion of the lens less than 4 mm in diameter or by using diffractive optics to produce multiple foci simultaneously.

[0014] In a non-limiting embodiment, a wavefront implantable contact lens (ICL) for an eye comprises a haptic area for anchoring the ICL to the iris in the anterior chamber or for holding the ICL in place in the posterior chamber, and an optical lens area, the optical lens area including: i) a baseline diopter power extending across an optical area of 5 mm to 8 mm diameter for sphero-cylindrical correction; ii) a central area of 1.65 mm to 2.5 mm diameter that induces a positive spherical aberration and a positive focus offset φ1 less than +3.0 D and greater than +0.5 D; and iii) an annular area of less than 4.5 mm outer diameter that induces a negative spherical aberration, wherein wavefront errors from the induced spherical aberration and focus offset in the central and annular areas cause the optical lens to be either: i) a semi-accommodative continuous focus lens; ii) a wavefront progressive lens; or iii) a wavefront trifocal lens.

[0015] In one non-limiting embodiment, a method for correcting refractive error of an eye includes determining a refractive error of the eye, including at least a spherical power SPH, for distance vision correction; and performing refractive correction surgery with an extended depth of focus between a first focal power φ1 and a second focal power φ2, and setting a target spherical power SPH between the first focal power φ1 and the second focal power φ2 so that the post-operative eye maintains excellent visual acuity at distance even if future myopia progression occurs. [Brief explanation of the drawings]

[0016] [Figure 1] 1A-1C are cross-sectional views of a refractive bifocal IOL (top) and a diffractive trifocal IOL (bottom) in the prior art. [Figure 2] FIG. 1 illustrates an objective measurement of accommodation of an accommodative IOL in an eye according to the prior art. [Figure 3] FIG. 1 is a diagram showing parameters of a toric contact lens in the prior art. [Figure 4] FIG. 1 is a diagram showing specification parameters of a toric IOL in the prior art. [Figure 5A]FIG. 1 shows the point spread function of a hypothetical eye with 0D to 5 / 8D of astigmatism (CYL) and -0.5D to +0.5D of focus error (SPH) remaining uncorrected by a conventional monofocal contact lens or a conventional monofocal IOL for a pupil diameter of 3.5mm. [Figure 5B] Figure 1 shows the calculated retinal images of a hypothetical eye with 0D to 5 / 8D of astigmatism and -0.5D to +0.5D of focus error (SPH) left uncorrected by a conventional monofocal contact lens or a conventional monofocal IOL for a pupil diameter of 3.5mm. Tumbling E is calibrated for visual acuities of 20 / 16 (smallest letter), 20 / 20, 20 / 25, 20 / 30, and 20 / 40 (largest letter). [Figure 6A] This figure shows the point spread function of a hypothetical eye with 5 / 8D of astigmatism (CYL) left uncorrected by a monofocal contact lens or monofocal IOL and a focus error (SPH) of -0.5D to +0.5D, for a pupil diameter of 3.5mm. Additionally, six scenarios of spherical aberration for the corrected eye are provided, including 1) S1 = 0, meaning a perfect correction of the spherical aberration present in the natural eye; 2) S1 = -0.26, meaning no change in spherical aberration in the natural eye; and 3) S1 = -0.52, -0.78, -1.04, and -1.3, meaning more spherical aberration is induced in the eye. [Figure 6B] FIG. 6B shows a retinal image calculated from the point spread function for the case of FIG. 6A. [Figure 6C] Figure 1 shows the point spread function of a hypothetical eye with 5 / 8D of astigmatism (CYL) and focus error (SPH) ranging from -0.5D to +0.5D left uncorrected by a monofocal contact lens or monofocal IOL for a pupil diameter of 3.5mm. Additionally, six scenarios of spherical aberration in the eye are provided, including 1) S1 = 0, 2) S1 = 0.26, and 3) S1 = 0.52, 0.78, 1.04, and 1.3, which means more spherical aberration is induced in the eye. [Figure 6D] FIG. 6D shows a retinal image calculated from the point spread function for the case of FIG. 6C. [Figure 6E]The point spread function of a hypothetical eye with 3 / 8D of astigmatism (CYL) and focus error (SPH) ranging from -0.5D to +0.5D, left uncorrected by a monofocal contact lens or monofocal IOL, for a pupil diameter of 3.5mm, is shown. Additionally, six scenarios of spherical aberration in the eye are considered, including 1) S1 = 0, 2) S1 = -0.26, and 3) S1 = -0.52, -0.78, -1.04, and -1.3, which means more spherical aberration is induced in the eye. [Figure 6F] FIG. 6B shows a retinal image calculated from the point spread function for the case of FIG. 6E. [Figure 6G] Figure 1 shows the point spread function of a hypothetical eye with a pupil diameter of 3.5 mm, with no astigmatism left uncorrected by a monofocal contact lens or monofocal IOL (CYL=0D), and with a focus error (SPH) of -0.5D to +0.5D. Additionally, six scenarios of spherical aberration in the eye are considered, including 1) S1=0, 2) S1=-0.26, and 3) S1=-0.52, -0.78, -1.04, and -1.3, which means more spherical aberration is induced in the eye. [Figure 6H] FIG. 6C shows a retinal image calculated from the point spread function for the case of FIG. 6G. [Figure 6I] Figure 1 shows calculated retinal images of an acuity chart for a virtual eye in which only coma is left uncorrected by a conventional monofocal lens (left column) and a wavefront technology monofocal lens of one exemplary design (right column) for a pupil diameter of 3.5 mm. The coma of the eye is measured by Zernike polynomials with coefficient 1.0 micron for a pupil diameter of 6 mm. Three different orientations of coma are considered. [Figure 6J] Figure 1 shows calculated retinal images of an acuity chart for a virtual eye in which only coma is left uncorrected by a conventional monofocal lens (left column) and a wavefront technology monofocal lens of one exemplary design (right column) for a pupil diameter of 3.5 mm. The coma of the eye is measured by Zernike polynomials with coefficients of 1.5 microns for a pupil diameter of 6 mm. Three different orientations of coma are considered. [Figure 7]1 is a schematic diagram of a wavefront technology single vision lens in accordance with an embodiment of the present invention; FIG. [Figure 8A] Figure 1 shows point spread functions of a hypothetical eye comparing a conventional monofocal lens (left column) with an exemplary wavefront technology monofocal lens of the present invention (right column) for a pupil diameter of 3.5 mm. The eye is considered to have zero or fully corrected astigmatism (CYL=0). A focus error (SPH) of -0.5D to +0.5D remains uncorrected by the monofocal lens. [Figure 8B] 8B shows retinal images calculated from the point spread functions of FIG. 8A comparing a conventional monofocal lens (left column) and a wavefront technology monofocal lens with an exemplary design (left column). [Figure 8C] FIG. 8B shows the modulation transfer function (MTF) calculated from the point spread function of FIG. 8A comparing a conventional prime lens (top) and a wavefront technology prime lens (bottom) in an exemplary design. [Figure 9A] 2A shows the point spread function of a hypothetical eye with the exemplary wavefront technology monofocal lens of Table 2A for a pupil diameter of 3.5 mm. Astigmatism (CYL) from 0D to 5 / 8D and focus error (SPH) from -0.5D to +0.5D remain uncorrected by the wavefront technology monofocal lens. [Figure 9B] FIG. 2B shows the calculated retinal image of the same virtual eye with the exemplary wavefront technology monofocal lens of Table 2A for a pupil diameter of 3.5 mm (indoor vision test). [Figure 9C] FIG. 2B shows the calculated retinal image of the same virtual eye with a wavefront technology monofocal lens from Table 2A for a pupil diameter of 2.5 mm (daytime outdoor vision). [Figure 9D] FIG. 2 shows the calculated retinal image of a virtual eye with a wavefront technology monofocal lens of Table 2A for a pupil diameter of 5 mm (night vision). [Figure 9E] FIG. 1 shows the calculated retinal image of a virtual eye with a conventional single vision lens for a pupil diameter of 5 mm (night vision). [Figure 9F]Figure 2B shows the point spread function of a hypothetical eye with a wavefront monofocal lens of another exemplary design (Table 2B) for a 3.5mm pupil diameter. Astigmatism (CYL) between 0D and 5 / 8D and focus error (SPH) between -0.5D and +0.5D remain uncorrected by the wavefront monofocal lens. [Figure 9G] FIG. 9B shows a retinal image calculated from the point spread function for the case of FIG. 9F. [Figure 10A] Calculated point spread functions of a virtual eye with a "PureVision-low" multifocal lens from Bausch & Lomb for pupil diameters of 3.0 mm, 3.5 mm, 4.5 mm, and 5 mm. For simplicity, only CYL=0D is considered. [Figure 10B] FIG. 1 shows the calculated retinal image of a virtual eye with a "PureVisionlow" multifocal lens from Bausch & Lomb. [Figure 10C] 1 shows the point spread function of a virtual eye with an "Air Optix-med" multifocal lens from Alcon for pupil diameters of 3.0 mm, 3.5 mm, 4.5 mm, and 5 mm. For simplicity, only CYL=0D is considered. [Figure 10D] FIG. 1 shows the calculated retinal image of a virtual eye with an "Air Optix-med" multifocal lens from Alcon. [Figure 11] 1 is a schematic diagram of a wavefront bifocal, trifocal, continuous focus lens in accordance with one embodiment of the present invention. [Figure 12A] 1 shows the point spread functions of a virtual eye with an exemplary design of a wavefront progressive lens (WF Bifocal 1D) for pupil diameters of 3.0 mm, 3.5 mm, 4.5 mm, and 5 mm. For simplicity, the case CYL=0D is considered. [Figure 12B] FIG. 10B shows the retinal image calculated from the point spread function of FIG. 10A for a wavefront progressive lens of our design (WF Bifocal 1D). [Figure 12C]Figure 10 shows plots of calculated retinal contrast "through focus" for WF Bifocal 1D for a pupil diameter of 3.5 mm, and for pupil diameters of 3 mm to 5 mm at 20 / 20 and 20 / 40 lines. [Figure 12D] Figure 1 shows calculated retinal contrast for normal eyes at 20 / 25, 20 / 30, 20 / 40, and 20 / 60 in photopic (A) and mesopic (B) conditions from a study of over 250 eyes of US Navy pilots with 5% low-contrast visual acuity in photopic vision and 25% low-contrast visual acuity in mesopic vision. [Figure 12E] FIG. 10 shows plots of the calculated modulation transfer function (MTF) of WF Bifocal 1D at far distances of infinity (−0.25D), 4 meters (0D), and +0.25D focus error for pupil diameters of 3mm, 3.5mm, and 5mm. [Figure 13A] 1 shows the point spread function of a virtual eye with our wavefront EDOF Bifocal 3D design for pupil diameters of 3.0 mm, 3.5 mm, 4.5 mm, and 5 mm. For simplicity, we consider only the case CYL=0D. [Figure 13B] FIG. 13B shows the retinal image calculated from the point spread function of FIG. 13A with our wavefront EDOF Bifocal 3D lens. [Figure 13C] 10 shows plots of calculated retinal contrast "through focus" for EDOF Bifocal 3D for a pupil diameter of 3 mm, and for pupil diameters of 3 mm to 5 mm at the 20 / 20 and 20 / 40 lines. [Figure 13D] FIG. 10 shows plots of the calculated modulation transfer function (MTF) of EDOF Bifocal 3D at far distances of infinity (−0.25D), 4 meters (0D), and +0.25D focus error for pupil diameters of 3mm, 3.5mm, and 5mm. [Figure 13E]FIG. 1 shows the calculated retinal contrast at distance (A) and through focus for 20 / 20 vision (B) for our EDOF Bifocal 3D compared to a prior art wavefront design. [Figure 14A] 1 shows the point spread function of a virtual eye for one design of the wavefront "EDOF Trifocal 2.75D" for pupil diameters of 3.0 mm, 3.5 mm, 4.5 mm, and 5 mm. For simplicity, only the case CYL=0D is considered. [Figure 14B] FIG. 14B shows the retinal image calculated from the point spread function of FIG. 14A with a wavefront "EDOF Trifocal 2.75D" lens. [Figure 14C] FIG. 1 shows plots of calculated retinal contrast “through focus” for EDOF Trifocal 2.75D for a pupil diameter of 3 mm, and for pupil diameters of 3 mm to 5 mm at the 20 / 20 and 20 / 40 lines. [Figure 14D] FIG. 10 shows plots of the calculated modulation transfer function (MTF) of the EDOF Trifocal 2.75D at far distances of infinity (−0.25D), 4 meters (0D), and +0.25D focus error, for pupil diameters of 3mm, 3.5mm, and 5mm. [Figure 15A] 1 shows the point spread function of a virtual eye for one design of the wavefront quasi-accommodative continuous focus "QACIF2D" for pupil diameters of 3.0 mm, 3.5 mm, 4.5 mm, and 5 mm. For simplicity, only the case CYL=0D is considered. [Figure 15B] FIG. 15B shows the retinal image calculated from the point spread function of FIG. 15A with a wavefront QACIF2D lens. [Figure 15C] FIG. 10 shows plots of calculated retinal contrast “through focus” for QACIF2D for a pupil diameter of 3.5 mm, and for pupil diameters of 3 mm to 5 mm at the 20 / 20 and 20 / 40 lines. [Figure 15D]FIG. 10 shows plots of the calculated modulation transfer function (MTF) of QACIF2D at far distances of infinity (−0.25D), 4 meters (0D), and +0.25D focus error for pupil diameters of 3mm, 3.5mm, and 5mm. [Figure 15E] FIG. 1 shows plots of calculated retinal contrast "through focus" for QACIF2A for a pupil diameter of 3.5 mm, and for pupil diameters of 3 mm to 5 mm at the 20 / 20 line and the 20 / 40 line. [Figure 15F] FIG. 10 shows the calculated retinal image with a wavefront QACIF2D lens when CYL=½D. [Figure 15G] FIG. 10 shows the calculated retinal image with a wavefront QACIF2D lens when CYL=3 / 4D. [Figure 16] FIG. 1 provides a comparison of the wavefront monofocal / multifocal lenses of the present invention with conventional refractive monofocal and diffractive monofocal / multifocal lenses in terms of night vision and quality of vision affected by the incomplete correction of astigmatism and focus errors by these ophthalmic lenses. [Figure 17A] Figure 1 shows calculated retinal images for several exemplary wavefront multifocal lens designs of the present invention compared to a conventional refractive monofocal lens at night for a pupil diameter of 5mm at distances of infinity (-0.25D), 4 meters (0D), and a distance of +0.25D focus error. [Figure 17B] 1A and 1B show the image principle of a diffractive progressive lens (A) and the calculated components of the retinal image at distance for a diffractive progressive lens with additional refractive powers of +1.75D (B) and 3.5D (C), respectively. [Figure 17C] FIG. 1 shows calculated retinal images for a monofocal lens through focus, from −0.75D to +0.75D, and with 3 / 8D of uncorrected astigmatism. [Figure 18] FIG. 1 illustrates a liquid ophthalmic lens in accordance with one embodiment of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0017] 1. Single vision / toric lenses with Wavefront technology Focus error (SPH) and astigmatism (CYL) are refractive errors of the human eye that cause blurred images and reduce visual acuity and quality of vision.

[0018] Monofocal lenses, also known as single vision lenses, are the most common form of eyeglasses, contact lenses, implantable contact lenses, and IOLs. Types of monofocal lenses include spherical monofocal lenses, aspheric monofocal lenses, and toric monofocal lenses.

[0019] Spherical prime lenses use spherical surfaces on both the front and back surfaces and are used to correct focus errors in the eye, such as myopia and hyperopia.

[0020] Toric monofocal lenses utilize at least one toric surface to provide vision correction for astigmatism as well as the eye's focusing error.

[0021] 1A. Residual astigmatism left uncorrected by monofocal / toric ophthalmic lenses Correction of astigmatism with toric contact lenses typically begins at 0.75D, with incremental 0.5D increments. This is shown in Figure 3, which is the online order form for Air Optix toric contact lenses from Ciba Vision and Alcon Laboratories, Inc. IOL astigmatism correction also begins at approximately 0.75D. Figure 4 shows the specifications for the AcrySof® IQ toric IOL from Alcon Laboratories, Inc., along with guidelines for using these toric IOLs. The recommendation indicates that astigmatism between 0.75D and 1.0D may remain uncorrected with toric monofocal IOLs.

[0022] Causes of errors in astigmatism correction with contact lenses, implantable contact lenses (ICLs), and IOLs include: 1) uncorrected astigmatism with prescription when the eye has less than 0.75D of astigmatism as determined by refraction; 2) limited selection of toric powers with 0.5D increments for toric lenses; 3) limited selection of toric axis in 10-degree increments; and 4) rotation of the toric contact lens on the cornea or rotation of toric ICLs and IOLs with post-op settlement.

[0023] Therefore, astigmatism in the human eye is not adequately corrected by any of the existing monofocal or toric lenses, including contact lenses, IOLs, and ICLs. The eye's residual uncorrected astigmatism can be as much as 5 / 8D.

[0024] To study the effect of uncorrected astigmatism remaining in the eye with a conventional monofocal lens, we provide a simulation of the eye's point spread function in Figure 5A and a simulated retinal image of an acuity chart in Figure 5B.

[0025] The simulations considered two cases: perfect correction of astigmatism (CYL=0) and uncorrected astigmatism of 3 / 8D and 5 / 8D. Because uncorrected focus errors are also common for IOLs, ICLs, and contact lenses, uncorrected focus errors (SPH) of -0.5D, -0.25D, 0D, +0.25D, and +0.5D were also considered. Sources of error included: 1) the -0.25D myopic power difference between distance visual acuity at infinity and distance visual acuity at 4 meters on refraction testing; 2) limited selection of SPH powers for IOLs and ICLs; 3) errors in the SPH power of the ordered lenses; and 4) refractive errors of the eye.

[0026] Figure 5A shows the retinal image, or point spread function, of a point source in a hypothetical eye with a pupil diameter of 3.5 mm. Significant image blurring is evident in Figure 5A except for the case of perfect correction (SPH=0 and CYL=0). From the calculated point spread functions in Figure 5A, the corresponding retinal image of the eye's visual acuity chart in Figure 5B was calculated by convolving the calculated point spread functions in Figure 5A with a tumbling E visual acuity chart. The visual acuity chart consists of various sizes of letter E calibrated for visual acuity of 20 / 16 (smallest letter in the bottom row of each image in Figure 5B), 20 / 20, 20 / 25, 20 / 30, and 20 / 40 (largest letter in the top row of each image).

[0027] To illustrate the details of the point spread function, note that the total dimension size of the point spread function in FIG. 5A is 1 / 8 the total dimension size of the retinal image in FIG. 5B.

[0028] All simulated point spread functions in this disclosure have the same dimensional scale, and all simulated retinal images in this disclosure likewise have the same dimensional scale, with the dimensional scale of the point spread functions being 1 / 8 the size of the dimensional scale of the retinal images. Throughout this application, all simulations use the same visual acuity chart, consisting of various sized letter E's calibrated for visual acuity of 20 / 16 (the smallest letter in the bottom row of each image in FIG. 5B ), 20 / 20, 20 / 25, 20 / 30, and 20 / 40 (the largest letter in the top row of each image in FIG. 5B ).

[0029] The simulation results in Figures 5A and 5B show that conventional monofocal contact lenses, ICLs, and IOLs are far from adequate. The quality of vision is only good when both SPH and CYL are nearly perfectly corrected. There are several problems.

[0030] First, when astigmatism is not properly corrected, the blurring of the image caused by astigmatism, such as CYL=5 / 8D (third row in Figures 5A and 5B), makes it impossible to recognize the full set of 20 / 20 acuity letters (the second smallest letter on the chart) at any one of the five focal SPH settings. Because of this, people are most likely to have poor vision, and their best-corrected acuity is in the range of 20 / 40 or 20 / 30 (the largest or second largest letter on the chart) rather than the usual 20 / 20 acuity.

[0031] Second, even with perfectly corrected astigmatism (CYL=0, first row in Figures 5A and 5B), a focus error of + / -0.25D would blur vision so that the 20 / 16 character (the smallest character on the chart) could not be resolved. A focus error of + / -0.5D would completely blur vision for all characters from 20 / 40 to 20 / 16. This is significant because visual acuity is tested indoors at 4 meters, and a myopic SPH error of -0.25D occurs outdoors at infinity.

[0032] Third, when uncorrected astigmatism is combined with an uncorrected focus error of + / - 0.25D, or when the uncorrected focus error alone reaches the level of 0.5D, image distortion (structural changes between objects and their images) is clearly observed.

[0033] Finally, toric lenses suffer from the same problem due to their limited correction of astigmatism, as shown in FIGS.

[0034] 1B. Spherical aberration in the normal human eye In spherical aberration, parallel rays passing through the central region of a positive lens converge farther than rays passing through the edge of the lens. The optical system of the human eye is a positive lens, and spherical aberration is most pronounced around the pupil. Based on a study of 214 eyes, Zernike spherical aberration (2.236 * (6r 4 -6r 2+1)) was found to be +0.138±0.103 microns for a pupil diameter of 5.7 mm, where r is the normalized pupil radius (r=ρ / 2.85) and ρ is the pupil radius of the eye (J. Porter et.al., Monochromatic aberrations of the human eye in a large population, Journal of the Optical Society of America A, Vol.18, issue 8, pp.1793-1803(2001)).

[0035] Porter's mean Zernike spherical aberration W 12 (ρ)=0.138 * 2.236 * 6 * (r 4 -r 2 +1), the corresponding Seidel spherical aberration W(ρ) = 1.85 * r 4 =1.85 * (ρ / 2.85) 4 , or W(ρ)=0.0280ρ 4 From the Seidel spherical aberration W(ρ), the diopter power profile φ(ρ) is calculated as φ(ρ) = -(dW(ρ) / dρ) / ρ = -0.11 * ρ 2 where ρ is the polar radius in millimeters. 1) It is well known that the refractive power of the eye is higher at the periphery of the pupil than at the center of the pupil in the human eye; 2) Diopter power (-0.11±0.08D / mm 2 ) is 0.10±0.06 D / mm with opposite sign, provided by S. Plainis, DA Atchison and WN Charman, “Power Profiles of Multifocal Contact Lenses and Their Interpretation”, Optometry and Vision Sciences, vol.90, No.10, pp1066-1077. 2Since the diopter profile is close to that of the Zernike spherical aberration coefficients of Porter et al., it appears that the Zernike spherical aberration coefficients are a correction of the Zernike spherical aberration rather than the Zernike spherical aberration itself.

[0036] Therefore, the negative Seidel spherical aberration in a normal eye is W(ρ) = -1.85 * (ρ / 2.85) 4 =-0.0280ρ 4 , the corresponding focus profile across the pupil radius is φ(ρ)=0.11 * ρ 2 is.

[0037] It should also be mentioned that S. Plainis, D.A. Atchison, and W.N. Charman classify the Seidel spherical aberration of the eye as "positive," which contradicts the classical definition of optics (see Warren J. Smith, Modern Optical Engineering, 3rd Edition, p. 65). Positive spherical aberration is called overcorrection and is generally associated with diverging elements (negative lenses), while negative spherical aberration is called undercorrection and is generally associated with converging elements (positive lenses).

[0038] The human eye has negative spherical aberration, and the wavefront error due to the eye's negative spherical aberration can also be expressed as: W(ρ)=S1 * (ρ / r0) 4 where r0=0.5 * where D0 is the pupil radius, ρ is the polar radius in the pupil plane and has values between 0 and r0, and negative spherical aberration has a negative coefficient S1 (S1<0). Table 1 shows the spherical aberration of the eye in both microns (μm) and wavelength (lambda = 0.55 microns) for four different pupil diameters: 5.7 mm, 3.5 mm, 3 mm, and 2 mm. The mean spherical aberration of the human eye is -0.26 microns for a pupil diameter of 3.5 mm. [Table 1]

[0039] It can be seen clearly in Table 1 that the spherical aberration of the eye is negligible in the center of the pupil, being approximately λ / 20 for a 2 mm diameter pupil and only λ / 4 for a 3 mm diameter pupil, respectively. If the wavefront error is below λ / 4, the optical element is often considered to be diffraction limited or perfect. On the other hand, the mean spherical aberration of a normal human eye reaches 3.4 λ for a large pupil with a diameter of 5.7 mm in darkness, and is therefore noticeable in the deterioration of night vision.

[0040] Aspheric single vision lenses, which use at least one aspheric surface on the front and back surfaces, are also found in contact lenses and IOLs. The aspheric surfaces are used for two purposes: 1) to provide correction for the spherical aberration of the human eye, which is pronounced around the pupil, and 2) to eliminate spherical aberration in IOLs with large refractive powers. In either case, because the spherical aberration of the human eye and corrective lenses is small in the central optical zone, aspheric single vision lenses differ from spherical single vision lenses only along the outer lens periphery, approximately 3 mm in diameter.

[0041] 1C. Reduction of astigmatism by inducing spherical aberration in the center of the eye's pupil One aspect of the present invention describes a fundamental discovery regarding the benefits of inducing more spherical aberration in the center of the eye's pupil to improve the quality of ophthalmic lenses.

[0042] 6A shows the point spread functions of a hypothetical human eye with uncorrected astigmatism of CYL=5 / 8D and a pupil diameter of 3.5 mm, for six cases of spherical aberration in the eye: 1) S1=0 (first row from the left) when the spherical aberration in the eye is fully corrected by a conventional aspheric lens, 2) S1=-0.26 (second row from the left) when the spherical aberration in the eye is left unchanged by a spherical lens, and 3) S1=-0.52, -0.78, -1.04, and -1.34 when additional spherical aberration is induced in the eye by a wavefront technology lens. The wavefront technology monofocal lens of the present invention includes 1) a standard sphero-cylindrical correction over an optical zone with a diameter of 5 mm to 8 mm, and 2) spherical aberration induced in the center of the lens with a diameter of 2.5 mm to 4.5 mm. We simulate the visual acuity of an eye with a pupil diameter of 3.5mm, as this is the average pupil diameter of a normal human eye in clinical visual acuity tests. The simulation also considered different degrees of focus error (SPH): -0.5D, -0.25D, 0D, 0.25D, and 0.5D.

[0043] If the eye has 5 / 8D of astigmatism that remains uncorrected by a single vision contact lens, ICL, or IOL, the point spread function of the eye in Figure 6A clearly shows that it is larger in size when the spherical aberration of the eye is fully corrected with S1 = 0 or remains unchanged with S1 = -0.26. When more spherical aberration is induced in the center of the pupil, from S1 = -0.52 to S1 = -1.3, the point spread function of the eye becomes smaller and decreases in size.

[0044] From the point spread function in Figure 6A, we calculated the retinal image for an eye with uncorrected astigmatism of CYL = 5 / 8D and a pupil diameter of 3.5mm, with the visual acuity chart shown in Figure 6B. The best quality images for visual acuities of various spherical aberrations S1 = 0, -0.26, -0.78, -1.04, and -1.30 were identified and boxed.

[0045] Several findings emerge from the simulated retinal images in Figure 6B. First, with a conventional aspherical lens (S1 = 0, first column in Figure 6B) that corrects the eye's spherical aberration, image blurring makes it impossible to recognize the full set of 20 / 20 (the second smallest character on the chart, fourth row from the top) or even 20 / 25 acuity letters. When an uncorrected CYL = 5 / 8D is combined with SPH errors of ±0.25D and ±0.5D, poor visual acuity below 20 / 40 and image distortion are observed. Second, with a spherical lens (S1 = -0.26, second column in Figure 6A) that leaves the eye's spherical aberration uncorrected, image distortion is observed at all five focus settings. The best visual acuity quality is observed at a focus offset of +0.25D, where there is image distortion for all acuity letters from 20 / 16 to 20 / 30. All images at + / -0.25D and + / -0.5D are blurry and difficult to recognize characters below 20 / 40. Best-corrected visual acuity can be worse than 20 / 20, and the quality of the corrected visual acuity is poor due to image distortion caused by the phase shift in the phase transfer function. Third, with new types of wavefront aspheric lenses that induce more spherical aberration (S1 magnitude 0.52 microns or greater, S1 = -0.78, -1.04, and -1.30) in the center of the eye's pupil, visual acuity is improved in three ways: 1) best-corrected visual acuity improved to 20 / 20 or even 20 / 16, 2) quality of visual acuity improved by eliminating distortion, and 3) tolerance for errors in focus correction increased.

[0046] Similarly, Figures 6C and 6D show that wavefront aspheric lenses inducing positive spherical aberrations of S1 = 0.78, 1.04, and 1.30 microns for a pupil diameter of 3.5 mm also improve visual acuity, visual quality, and focus tolerance when the eye has 5 / 8D of uncorrected astigmatism.

[0047] Contrary to the common belief that inducing spherical aberration in the eye reduces best-corrected visual acuity, it has been shown for the first time that inducing spherical aberration in the center of the pupil of the eye can improve visual acuity and quality of vision in patients with 5 / 8D of uncorrected astigmatism with ophthalmic lenses (contact lenses / ICL / IOL), improving best-corrected visual acuity from 20 / 40 and 20 / 30 to 20 / 20 or better.

[0048] Having shown that inducing spherical aberration in the center of the eye's pupil with a wavefront technology monofocal lens can reduce 5 / 8D of uncorrected astigmatism and improve best-corrected visual acuity, we would like to examine the effect of induced spherical aberration on eyes with less uncorrected astigmatism, such as CYL=3 / 8D, or even CYL=0D, where the astigmatism is completely corrected.

[0049] Figure 6E shows the point spread functions of a hypothetical human eye with CYL=3 / 8D and a pupil diameter of 3.5 mm, considering the same six cases of spherical aberration: 1) S1=0 (first row from the left) when the spherical aberration of the eye is corrected by a conventional aspherical lens, 2) S1=-0.26 (second row from the left) when the spherical aberration of the eye remains unchanged by a conventional spherical lens, and 3) S1=-0.52, -0.78, -1.04, and -1.3 when additional spherical aberration is induced in the eye by a wavefront aspherical lens. We also consider eyes with various degrees of focus error: SPH=-0.5D, -0.25D, 0D, 0.25D, and 0.5D.

[0050] Similar to the results in Figures 6A and 6C, it is observed that inducing spherical aberration has the same effect as reducing the astigmatism for CYL=3 / 8D in Figure 6E: 1) the eye's point spread function increases in size when the eye's spherical aberration is fully corrected (S1=0, first column from the left) or remains unchanged (S1=-0.26, second column from the left). The eye's point spread function decreases in size when more spherical aberration is induced, for S1=-0.78, -1.04, and -1.3.

[0051] From the point spread function in Figure 6E, we calculated retinal images of the acuity chart for a virtual human eye shown in Figure 6F for a pupil diameter of 3.5 mm. The best quality images for acuity values of S1 = 0, -0.26, -0.78, -1.04, and -1.30 were identified and boxed.

[0052] When 3 / 8D of astigmatism is left uncorrected by the monofocal lens, similar findings are seen in Figures 6F (CYL=3 / 8D) and 6B (CYL=5 / 8D) and 6D (CYL=5 / 8D): A new class of wavefront aspheric lenses that induces more spherical aberration (S1=-0.78, -1.04, and -1.30) in the center of the pupil of the eye improves vision quality over conventional aspheric lenses (S1=0) and conventional spherical lenses (S1=-0.26) in three ways: 1) improvement in best-corrected visual acuity beyond 20 / 16, 2) elimination of distortion due to phase shift in the phase transfer function, and 3) increased tolerance for error in focus correction.

[0053] For a hypothetical eye with no or perfectly corrected astigmatism, Figure 6G shows the point spread function of the eye for a pupil diameter of 3.5 mm. The eyes with the most compact point spread functions are found for 1) a monofocal setting of SPH=0 when S1=0, 2) a bifocal setting of SPH=0, 0.25 when S1=-0.26, 3) a bifocal setting of SPH=0.25D, 0.50D when S1=-0.52 and S1=-1.04, and a trifocal setting of SPH=0, 0.25, 0.50D when S1=-0.78 and S1=-1.3.

[0054] Looking at the simulated visual acuity chart in Figure 6H, we can conclude that in rare cases (approximately 1 / 20), the new wavefront aspheric lenses, which induce more spherical aberration (S1 = -0.78, -1.04, and -1.30) in the center of the pupil, improve vision correction over conventional aspheric lenses (S1 = 0) and conventional spherical lenses (S1 = -0.26), even when the eye's astigmatism is fully corrected (CYL = 0) by monofocal / toric lenses, by 1) achieving the same best visual acuity of 20 / 16 or better with little loss in contrast while increasing tolerance for errors in focal power and 2) eliminating distortion due to phase shifts in the phase transfer function caused by small errors in focal correction.

[0055] It is also noted that the best quality is achieved when adding a focus offset beyond the spherical aberration induced in the pupil center.

[0056] In addition to the conventional baseline diopter power for spherocylindrical correction, wavefront technology monofocal lenses intentionally make the lens imperfect according to the conventional definition. The wavefront error introduced into the central optical zone of a wavefront technology monofocal lens can be expressed as: W(ρ,φ)=S1 * (ρ / r0) 4 -0.5 * φ * ρ 2 where r0=0.5 * D0 is the radius of the central aspheric zone, ρ is the polar radius in the pupil plane and has values between 0 and r0, φ is the focus offset in diopters, and S1 is the total spherical aberration induced in the monofocal lens by wavefront technology.

[0057] 1D. Reduction of coma by inducing spherical aberration in the center of the eye pupil Coma in the eye reduces the quality of vision. Wavefront correction of coma and higher-order aberrations has been demonstrated using adaptive optics by J. Liang, D.R. Williams, and D.T. Miller, "Supernormal vision and high-resolution retinal imaging through adaptive optics," Journal of the Optical Society of America A, Vol. 14, Issue 11, pp. 2884-2892 (1997). Wavefront correction of higher-order aberrations has also been proposed in U.S. Pat. No. 5,777,719.

[0058] Effective correction of ocular coma has not been demonstrated effectively in normal eyes with eyeglasses, contact lenses, and IOLs for a number of reasons. First, the coma of each eye must be measured individually. Second, the coma-correcting lenses (eyeglasses, contact lenses, IOLs) must be custom-made. Third, precise alignment of the lens position and orientation of the coma-correcting lenses relative to the eye must be achieved for eyeglasses, contact lenses, and IOLs to the ocular coma.

[0059] In one aspect of the present invention, FIGS. 6I and 6J illustrate the therapeutic treatment of coma by inducing additional spherical aberration in the center of the pupil of the eye.

[0060] Figure 6I shows calculated retinal images of the visual acuity chart for a virtual eye in which only coma remains uncorrected by a conventional monofocal lens (left column) and a wavefront technology monofocal lens (right column), which induces a spherical aberration (S1) of -0.78 microns for a 3.5 mm pupil diameter. The coma of the simulated eye is measured by a Zernike polynomial with a Zernike coefficient of 1.0 microns for a 6 mm pupil diameter. The unpleasant image blur and distortion caused by the eye's coma (left column) are effectively eliminated by the wavefront lens (right column).

[0061] Figure 6J shows the simulation results for a 6 mm pupil diameter where the Zernike coefficients for coma are increased from 1.0 microns to 1.5 microns. The effectiveness of using a wavefront lens to reduce significant coma remains clear.

[0062] 1E. Monofocal / Toric Contact Lenses, ICLs, and IOLs with Wavefront Technology U.S. Patent No. 8,529,559 B2 and U.S. Patent Application No. 2011 / 0029073 A1 disclose methods and devices for inducing spherical aberration in the center of the eye's pupil to correct presbyopia. Prior to the inventors' discovery in the present invention, it was widely believed that inducing more spherical aberration in the eye with a corrective lens would adversely affect image contrast. In the present invention, we have shown that in addition to increasing depth of focus, inducing spherical aberration in the center of the eye's pupil is also effective in improving the quality of vision correction: increasing best-corrected visual acuity (BCVA) and reducing astigmatism, coma, and focus errors that remain uncorrected by spherocylindrical correction.

[0063] FIG. 7 illustrates a wavefront technology monofocal lens for an eye. The lens 70 is configured as an IOL (75, 76) or contact lens (73, 74) or ICL and includes: 1) a baseline diopter power extending across an optical zone (71+72) having a diameter D1 of 5 mm to 8 mm for the correction of distance vision errors, including at least focus and / or cylindrical errors; and 2) at least a central aspheric zone (72) in the center of the lens, which uses at least one aspheric surface (73 or 74, 75, or 76) to induce spherical aberration at the center of the eye's pupil. The diameter D0 of the central aspheric zone is 2.5 mm to 4.5 mm. The baseline diopter power is typically specified as a spherocylinder correction. The wavefront error introduced in the aspheric zone provides treatment (or reduction) of residual refractive error remaining uncorrected in the eye by the baseline diopter power for distance vision errors. Refractive errors remaining uncorrected by the lens in the eye include astigmatism, focus errors (near or far vision), coma, and other higher-order aberrations significant enough to reduce visual acuity at least in the center of the eye's pupil. Residual uncorrected refractive errors further include presbyopic powers less than +1.0D. For presbyopic powers greater than 1.0D, such as 2D in U.S. Pat. No. 8,529,559 B2 and U.S. Patent Application Publication No. 2011 / 0029073 A1, corrected visual acuity deteriorates due to a significant reduction in image contrast for distance vision with a pupil diameter of approximately 3.5mm, resulting in a visual acuity worse than 20 / 20 at distance. Wavefront technology monofocal lenses can be fitted as contact lenses, intraocular lenses (IOLs), or accommodating intraocular lenses (AIOLs), implantable contact lenses (ICLs), or phakic IOLs.

[0064] In one embodiment, the central aspheric zone is further configured to induce an additional focus offset of between −0.75D and +1.25D in addition to the baseline diopter power.

[0065] In another embodiment, the spherical aberration induced in the central aspherical area is S1 * (ρ / ρ0) 4can be expressed as the wavefront error of ρ0=0.5 * D0 is the radius of the central aspheric zone, and ρ is the polar radius in the pupil plane, with values between 0 and ρ0, where ρ0 is between 1.25 mm and 2.25 mm.

[0066] In yet another embodiment, S1 is positive and has a magnitude of 0.78 * (D0 / 3.5) 4 greater than or negative and with a magnitude of 0.26 * (D0 / 3.5) 4 D0 is the diameter of the aspheric area. The spherical aberration of the corrected eye combined with a wavefront technology single vision lens is more than twice the statistical average of the spherical aberration of a normal human eye.

[0067] In addition to the conventional baseline diopter power for spherocylindrical correction, the wavefront technology monofocal lens of the present invention intentionally makes the monofocal lens imperfect according to the conventional definition. The wavefront error introduced into the central optical zone of the wavefront technology monofocal lens can be expressed as: W(ρ,φ)=S1 * (ρ / r0) 4 -0.5 * φ * ρ 2 where r0=0.5 * D0 is the radius of the central aspheric zone, ρ is the polar radius in the pupil plane and has values between 0 and r0, φ is the focus offset in diopters, and S1 is the total spherical aberration induced in the monofocal lens by wavefront technology. [Table 2]

[0068] In one exemplary embodiment to further tolerate uncorrected astigmatism and extend depth of focus, Table 2A shows the parameters of an exemplary wavefront design.

[0069] Figure 8A shows the point spread functions of a virtual eye with a pupil diameter of 3.5 mm, comparing a conventional monofocal lens (left column) with an exemplary wavefront technology monofocal lens (right column) with the induced spherical aberration and focus offset of Table 2A. The virtual eye is considered to have no astigmatism (CYL=0), leaving focus errors (SPH) between -0.5D and +0.5D uncorrected by the monofocal lens. It can be seen that, except for the full spherical correction at SPH=0, the point spread functions of the wavefront technology monofocal lens (right column) are more compact than those of the conventional monofocal lens (left column) for all cases of SPH=-0.5D, -0.25D, 0.25D, and 0.5D.

[0070] Figure 8B shows the retinal images calculated from the point spread functions for Figure 8A, comparing a conventional monofocal lens (left column) with a wavefront technology monofocal lens (right column). Additionally, Figure 8C shows the modulation transfer functions (MTFs) calculated from the point spread functions for Figure 8A for a conventional monofocal lens (top) and an exemplary design of a wavefront technology monofocal lens (bottom).

[0071] As expected for perfect correction of the extremely rare (e.g., <1 in 20 eyes) SPH (SPH=0) and CYL (CYL=0) cases, inducing spherical aberration with a wavefront lens significantly reduces retinal contrast at all frequencies, as seen in the image (middle row in Figure 8B) and MTF in Figure 8C. Retinal contrast with the wavefront lens decreases from 68% to 16% at 30 c / deg for 20 / 20, from 59% to 12% at 37.5 c / deg for 20 / 16, and from 47% to 5% at 48 c / deg for 20 / 12. It is important to note that this ideal case of SPH=0 and CYL=0 has little or no practical effect because perfect focus correction of both SPH and CYL is extremely rare, and the retinal contrast of a real eye is further degraded by third-order Zernike aberrations such as coma (see J Liang and DR Williams, "Aberrations and retinal image quality of the normal human eye", Journal of the Optical Society of America A, Vol. 14, Issue 11, pp. 2873-2883 (1997)). The formula for the average human optical modulation transfer function as a function of pupil diameter was published by AB Watson in Journal of Vision, 13(6):18, pp. 1-11 (2013).

[0072] SPH is usually not fully corrected due to 1) the -0.25D myopic difference between distance visual acuity at infinity and distance visual acuity at 4 meters on a visual acuity test, and 2) lens manufacturing errors or the eye's refractive error. When SPH = -0.25D and SPH = 0.25, as shown in Figure 8C, the retinal contrast is only approximately 1.2% at a spatial frequency of 37.5 cycles / degree, 2.1% at 20 / 16 acuity, and 48 cycles / degree at 20 / 12.5 acuity. Therefore, with a conventional single-vision lens perfectly corrected for both SPH and CYL, as shown in Figure 8B, the virtual eye would be unable to recognize letters with acuity of 20 / 16 or less. The MTF of a conventional single-vision lens is less than 2.5% across the entire spatial frequency range from 36 cycles / degree to 48 cycles / degree, limiting best-corrected visual acuity to less than 20 / 16.

[0073] This is quite different from our wavefront technology monofocal lenses. The wavefront design improves retinal contrast from less than 1.2% to 14% at SPH=-0.25D, to 5% at SPH=0.25D at 37.5 cycles / degree for 20 / 16 visual acuity, and to 11% at SPH=-0.25D at 48 cycles / degree for 20 / 12.5 visual acuity. Thus, the wavefront technology monofocal lenses allow the hypothetical eye to achieve best-corrected visual acuity of 20 / 16, or even 20 / 12.5 at SPH=-0.25D, as shown in FIG. 8B. It is also observed that when compared to conventional single vision lenses, our wavefront technology single vision lenses provide better visual acuity and improved image contrast and clarity at spatial frequencies higher than 24 cycles / degree (20 / 25 vision) at the small cost of slightly reduced retinal contrast at low spatial frequencies, such as 15 cycles / degree at 20 / 40 vision and 20 cycles / degree at 20 / 30 vision.

[0074] For SPH = -0.5D and SPH = 0.5D, the retinal contrast is nearly zero at 15 cycles / degree and 30 cycles / degree, as shown in Figure 8C. Therefore, the virtual eye cannot see 20 / 40 and 20 / 20 characters with a conventional monofocal lens, as shown in Figure 8B. It is also noteworthy that the 20 / 30 and 20 / 25 characters are distorted, as shown in Figure 8B, due to a phase inversion of the phase transfer function (PTF) between 15 and 31 cycles / degree. The phase inversion of the PTF shifts the position of the corresponding spatial frequency by half a cycle. In contrast, the wavefront technology monofocal lens allows the virtual eye to see all acuity characters from 20 / 40 to 20 / 16 without distortion, as shown in Figure 8B. For SPH = -0.5D, the wavefront technology monofocal lens can also see 20 / 12 characters with 11% retinal contrast at 48 cycles / degree. The elimination of the poor retinal image blurring seen with conventional single vision lenses by wavefront technology single vision lenses is achieved by 1) preventing nearly 100% loss of retinal contrast in the eye's MTF between 15 and 40 cycles / degree, and 2) eliminating the phase reversal of the eye's PTF seen with conventional lenses.

[0075] To study the correction of residual astigmatism, focus error, and its pupil diameter dependence of a monofocal lens with the exemplary wavefront technology shown in Table 2A, optical simulations are provided in Figures 9A-9D.

[0076] Figure 9A shows the calculated point spread function of a virtual human eye for a pupil diameter of 3.5 mm for the exemplary wavefront technology monofocal lens of Table 2A. Also, in Figure 9B for a pupil diameter of 3.5 mm (indoor vision test), the retinal image of the human eye for a tumbling E chart was calculated for different pupil diameters.

[0077] When comparing the retinal images obtained with the conventional single-vision lens of FIG. 5B and the wavefront lens of FIG. 9B under the same conditions with a pupil diameter of 3.5 mm, significant differences are observed in three aspects.

[0078] First, unlike the conventional monofocal lens in Figure 5B, the wavefront technology monofocal lens in Figure 9B shows astigmatism elimination. There is little or no difference in the retinal images calculated under different values of astigmatism (CYL) with the same focus error (SPH) in Figure 9B.

[0079] Second, wavefront technology monofocal lenses offer exceptional visual acuity: 1) 20 / 16 visual acuity can be achieved with a focus error tolerance of at least ±0.25D regardless of the eye's residual astigmatism, and 2) 20 / 20 visual acuity can be achieved with up to 5 / 8D of residual astigmatism and a focus error of ±0.5D.

[0080] Third, wavefront technology single-vision lenses improve the quality of vision by eliminating the image distortions of conventional lenses caused by residual focus error and / or residual cylindrical error, as shown in Figure 5B. In Fourier optics, image blurring in an optical system is characterized by 1) a loss of image contrast at various spatial frequencies of an object, as measured by the modulation transfer function (MTF), and 2) a phase shift or phase reversal between various spatial frequencies of an object, as measured by the phase transfer function (PTF). A phase reversal at a given spatial frequency results in a half-cycle position shift of the retinal image at that particular frequency. When a spatial frequency that is displaced by half a cycle is combined with an undisplaced spatial frequency of an object, the final retinal image is not only blurred but also distorted, resulting in distorted and difficult-to-read letters.

[0081] It can be concluded that wavefront technology monofocal lenses improve vision correction in most normal eyes, but may result in decreased visual acuity or contrast in a small group (e.g., 1 in 20) whose best-corrected visual acuity with monofocal lenses is 20 / 10.

[0082] Modern cameras use autofocus to dynamically correct focus errors and aspherical lenses and multiple lens elements to correct spherical aberration, astigmatism, and coma. Spherical aberration, by definition, degrades the image quality of an optical system, and this applies not only to camera lenses but also to the human eye, which has a larger pupil diameter at night. Using spherical aberration to improve visual acuity and vision quality seems counterintuitive, but makes perfect sense when considering the imperfect nature of ophthalmic correction in state-of-the-art IOLs and contact lenses, as shown in Figures 5A and 5B.

[0083] The quality of an ophthalmic lens for an eye must take into account visual acuity at different pupil diameters, e.g., 2.5 mm for outdoors and daylight, and 5 mm for night vision. Figures 9C and 9D show calculated retinal images of the same hypothetical eye when the pupil diameter is reduced to 2.5 mm or increased to 5 mm, respectively.

[0084] Compared to the calculated retinal image in Figure 9B for a pupil diameter of 3.5 mm, the retinal image in Figure 9C for a pupil diameter of 2.5 mm provides much better contrast and legibility of the acuity letters for each combination of astigmatism and focus error.

[0085] Simulating the retinal point spread function and retinal image for night vision is difficult because it is necessary to consider the high-order aberrations of the eye at night, which vary from eye to eye. For simplicity, we assume that the astigmatism and focus error that remains uncorrected by a monofocal lens are more significant than the high-order aberrations of the eye that are reasonable for 3 / 8D and 5 / 8D astigmatism and / or + / -0.25D and + / -0.5D focus errors.

[0086] Figures 9D and 9E show calculated retinal images of a virtual eye with an exemplary wavefront technology monofocal lens (Figure 9D) and a conventional monofocal lens (Figure 9E), respectively, for a 5mm pupil diameter. While the wavefront error of the wavefront technology monofocal lens does not exceed a 4mm pupil diameter, the uncorrected astigmatism and focus error are spread throughout the 5mm pupil diameter. Except for the rare case where SPH=0 and CYL=0, it is clear that the night vision performance of the exemplary wavefront technology monofocal lens for a 5mm pupil diameter is significantly superior to that of a conventional monofocal lens in terms of visual acuity and vision quality. The nighttime effect of Figure 9D (wavefront monofocal) compared to Figure 9E (conventional monofocal) appears more dramatic than the comparison of Figure 9B (wavefront monofocal) compared to Figure 5B (conventional monofocal) at a 3.5mm pupil diameter.

[0087] Therefore, when it is considered that astigmatism, coma, and focus errors remain uncorrected in the human eye by conventional single vision lenses, it can be concluded that spherical aberration at the center of the pupil is no longer a negative factor in designing ophthalmic lenses and eyepieces for vision devices.

[0088] In another exemplary embodiment of a wavefront technology monofocal lens, the wavefront errors introduced in the aspheric area are negative spherical aberration (S1<0) and negative focus offset. Table 2B shows the parameters of a second exemplary wavefront technology monofocal lens.

[0089] Figure 9F shows the calculated retinal image, point spread function, of a point source for a hypothetical human eye with a pupil diameter of 3.5 mm for a second exemplary wavefront technology monofocal lens. From the calculated point spread function in Figure 9F, we also calculated the retinal image of a tumbling E-chart, shown in Figure 9G. [Table 3]

[0090] The second exemplary wavefront technology monofocal lens in Table 2B, which uses negative spherical aberration (S1<0) and negative focus offset, shares similar advantages with the first wavefront technology monofocal lens in Table 2A, which uses positive spherical aberration (S1>0) and positive focus offset, with one obvious difference: the second exemplary wavefront technology monofocal lens (Table 2B) has better vision quality for positive focus errors SPH=0.25D and 0.50D, while the first exemplary wavefront technology monofocal lens (Table 2A) has better vision quality for positive focus errors SPH=0.25D and 0.50D.

[0091] In one embodiment of a wavefront technology monofocal lens, the induced total spherical aberration is negative (S1<0), and the induced focus offset φ is negative and has a magnitude less than 0.75D (φ>-0.75D). The induced negative spherical aberration (S1) is between -0.71 microns and -7.51 microns in the central aspheric zone, which scales to pupil diameters of 2.5mm to 4.5mm according to Table 2C, which shows the spherical aberration (S1) induced in the pupil for different radii r0 of the aspheric zone from 1.25mm to 2.25mm.

[0092] In another embodiment, the induced total spherical aberration is positive (S1>0) and the induced focus offset φ is positive and has a magnitude less than 0.75D (φ<0.75D). The induced positive spherical aberration (S1) is 0.71 microns to 7.51 microns at the central aspherical zone, which is scaled to pupil diameters of 2.5mm to 4.5mm according to Table 2C, which shows the spherical aberration (S1) induced in the pupil for different radii r0 of the aspherical zone from 1.25mm to 2.25mm. [Table 4]

[0093] In yet another embodiment, the induced spherical aberration can be further expressed as ρ nwhere n is an integer greater than or equal to 3. The wavefront error due to generalized spherical aberration is characterized by the generalized polynomial φ(ρ)=c3ρ 3 +c4ρ 4 +c5ρ 5 +c6ρ 6 ...In some cases, the induced spherical aberration can be further expressed as ρ n where n is an even integer greater than 4. [Table 5]

[0094] Further embodiments of wavefront technology monofocal lenses are provided in Table 2D. WFM-CL1 and WFM-CL2 are optimized for wavefront contact lenses in patients without presbyopia. WF-EDOF M1 and WF-EDOF M2 are optimized for wavefront EDOF monofocal lenses in patients with presbyopia correction and can be fitted to contact lenses, IOLs, and accommodative IOLs. Table 2E shows the spherical aberration induced in the central aspheric zone. [Table 6]

[0095] All of these designs (WFM-CL1, WFM-CL2, WF-EDOF M1, WF-EDOF M1) and the designs in Tables 2A and 2B can be used with implantable contact lenses (ICLs). ICLs share the same issues of limited lens selection (SPH or CYL), cylinder axis error, lens manufacturing error, refractive prescription error, and presbyopia. ICLs are less forgiving than contact lenses because they involve a surgical procedure.

[0096] In some embodiments, the wavefront technology monofocal lens is configured as a wavefront contact lens with a diameter of 9 mm to 16 mm and includes a front and a back surface, at least one of which is aspheric to induce spherical aberration in a central aspheric zone.

[0097] In one embodiment, the wavefront contact lens is configured to have a focus offset of +0.12D to +1.2D and a central pupil induced spherical aberration of 0.31 microns to 7.51 microns over a central aspheric area with a diameter of 2.5mm to 4.5mm.

[0098] In another embodiment, the wavefront contact lens is configured such that the spherical aberration induced at the center of the pupil is between -0.31 microns and -7.51 microns over a central aspheric area having a diameter between 2.5 mm and 4.5 mm, and the magnitude of the focus offset is less than 0.5D.

[0099] In yet another embodiment, the wavefront contact lens is further configured such that the spherical aberration (S1) induced in the central aspherical zone is determined individually based on the spherical aberration and other higher order aberrations measured in each individual eye.

[0100] In yet another embodiment, the wavefront contact lens further comprises correction of high order aberrations of the eye for therapeutic treatment, the high order aberrations of the eye being aberrations excluding astigmatism and focus errors of the eye.

[0101] In another embodiment, the wavefront monofocal contact lens is further configured as a toric contact lens.

[0102] In yet another embodiment, the back surface of the contact lens is further configured to have an aspheric shape at the periphery of the lens to prevent rotation of the lens on the eye if the lens is also a toric lens.

[0103] In some embodiments, the wavefront monofocal lens is configured as a wavefront monofocal intraocular lens (IOL) having a diameter of approximately 6 mm, e.g., 5 mm to 7 mm, and includes a front surface and a back surface, at least one of which is aspheric to induce spherical aberration in the aspheric zone. The wavefront monofocal IOL further includes a haptic zone.

[0104] In one embodiment, the wavefront monofocal IOL is configured to have a negative focal offset magnitude of less than 0.75D and an induced spherical aberration of between -0.31 microns and -7.5 microns over a central aspheric zone with a diameter of 2.5 mm to 4.5 mm.

[0105] In another embodiment, the wavefront monofocal IOL is configured with a focal offset of +0.25D to +1.20D and an induced spherical aberration of 0.31 microns to 7.5 microns over a central aspheric zone with a diameter of 2.5 mm to 4.5 mm.

[0106] In yet another embodiment, the wavefront monofocal IOL is further configured as a toric IOL.

[0107] In yet another embodiment, the wavefront monofocal IOL is configured as an accommodative IOL.

[0108] In some embodiments, wavefront technology monofocal lenses (contact lenses, IOLs, and accommodating IOLs, ICLs) are further configured to include aspheric areas outside the central aspheric area to a) correct spherical aberration in normal eyes at the pupil periphery, and b) correct spherical aberration at the pupil periphery of the human eye.

[0109] S. Plainis, DA Atchison, and WN Charman studied four major brands of multifocal contact lenses and published their findings in 2013 in “Power Profiles of Multifocal Contact Lenses and Their Interpretation,” Optometry and Vision Sciences, vol. 90, No. 10, pp. 1066-1077. They found five contact lenses that use aspheric surfaces to change spherical aberration when worn on the eye: Air Optix -low, -med, and -high from Alcon, and PureVision -Low and -High from Bausch & Lomb.

[0110] The "low" diopter profiles of PureVision from Bausch & Lomb and Air Optix from Alcon are approximately 6mm in diameter and φ(ρ)=0.67-0.18ρ, respectively. 2 and φ(ρ) = 0.54-0.15ρ 2 They are essentially the mean spherical aberration (0.112ρ 2) correction and aspheric lenses for positive focal offsets of +0.67D and +0.54D above the baseline correction for low-grade presbyopia correction. Consumers paid a premium to obtain these so-called multifocal contact lenses, but could actually purchase less expensive single-vision lenses with offset SPH powers of +0.50D or +0.75D in their prescriptions. Figures 10A and 10B show the calculated point spread function of the PureVision -low lens from Bausch & Lomb and the calculated retinal image of the visual acuity chart. There are two conclusions. First, as expected, the eye's best focus shifts from the baseline correction (SPH=0) to an add SPH=+0.67D across the lens, such that low-grade presbyopia of +0.5D to +1.0D is alleviated. At the same time, distance vision of -0.08D and +0.17D becomes severely blurred. Second, while providing correction of the eye's spherical aberration, these so-called multifocal contact lenses cannot be adapted as single vision lenses with wavefront technology as described in this invention because they 1) result in poor vision at distances as seen in Figures 10A and 10B, and 2) are unable to provide a reduction in the eye's uncorrected astigmatism for S1=0 as shown in Figures 6A-6H.

[0111] The diopter profile of Air Optix multifocal contact lenses marked "med" is φ(ρ) = 1.14-0.44ρ at the center of a 2.8mm diameter pupil. 2 The mean spherical aberration (0.112ρ) of the normal group of eyes was 2 After correction for the baseline focus error of each eye, this lens has a φ'(ρ)=1.14-0.33ρ 210C and 10D show the calculated point spread function and retinal image of the "Air Optix-med" lens, respectively. Acceptable visual acuity for indoor use with pupil diameters of 3 mm and 3.5 mm is +0.5D to +1.25D, with the best visual acuity set at around +0.5D. However, the "Air Optix-med" lens's presbyopia correction also comes at a high price: distance visual acuity of -0.25D to +0.25D. Additionally, as seen in FIGS. 10C / 10D, distance visual acuity at 0D and -0.25D is so poor that most people wearing Air Optix-med lenses would not be able to pass a driver's license test at 20 / 40 vision at around 6 meters, based on simulated results. Therefore, the "Air Optix-med" lens cannot be used with the wavefront technology single-vision lenses described in this invention. Even when these lenses are prescribed for off-label use, Air Optix med has the wrong combination of focus offset and induced negative spherical aberration.

[0112] The diopter profiles of the PureVision multifocal contact lenses (Bausch & Lomb) and Air Optix multifocal contact lenses (Alcon) marked with "high" are φ(ρ) = 1.93-0.50ρ at the center of pupils with diameters of 2.4 mm and 2.8 mm, respectively. 2 and φ(ρ) = 1.58-0.69ρ 2 The mean spherical aberration (0.112ρ) of the normal group of eyes was 2 After correction for the baseline focus error of each eye, these lenses have φ'(ρ) = 1.93-0.39ρ, respectively. 2 and φ'(ρ) = 1.58-0.58ρ 2The resulting diopter profile is 0.01. The PureVision and Air Optix multifocal lenses designated "high" cannot be adapted to the wavefront monofocal lenses described in this invention because their distance vision is reduced even more severely than with the Air Optix med lenses. Even when these lenses are prescribed for off-label use, the combination of focal offset and induced negative spherical aberration is incorrect.

[0113] 2. Wavefront Extended Depth of Focus (EDOF) Progressive Lenses Progressive lenses have two different refractive powers, usually providing a first focus for distance vision and a second focus for presbyopia correction.

[0114] Diffractive progressive lenses are available in IOLs with diopter separation between the two foci ranging from +1.75D to +4.0D. As previously mentioned, problems associated with diffractive multifocal IOLs include: 1) halo and starburst nighttime symptoms due to simultaneous bifocal images, 2) spiderweb nighttime symptoms associated with the diffractive structure, 3) ghost images of large distant objects caused by a lack of near focus, and 4) poor visual acuity and image distortion between foci due to focus error or astigmatism in the eye.

[0115] Because contact lenses cannot utilize the split-power designs of eyeglasses or the diffractive designs of IOLs due to their sharp diffractive surfaces, there are currently no progressive contact lenses that can provide presbyopic correction without significantly reducing distance vision. So-called multifocal contact lenses (Air Optix from Alcon and PureVision from Bausch & Lomb) are single-vision lenses, and Figures 10A-10D show that the patient's distance vision is significantly impaired and therefore cannot be qualified as progressive lenses.

[0116] Inducing spherical aberration of the opposite sign in the center of the pupil has been proposed in U.S. Patent No. 8,529,559 B2 and U.S. Patent Application No. 2011 / 0029073 A1. To obtain a desired depth of focus (DoF) of 3D for a presbyopia-correcting IOL, a focal offset of +4.0D (+1D greater than the desired DOF of +3.0D) is introduced into the central aspheric zone. This design results in a significant reduction in retinal contrast at distance for pupil diameters of 3mm or 3.5mm (indoor vision testing), which are the standard diameters used in IOL testing.

[0117] The Mini Well Ready IOL (S1fi SpA), designed based on inducing spherical aberration of opposite sign at the center of the pupil, uses a special configuration to solve the problem of low contrast at distance, providing an EDOF progressive lens with a high-contrast distance primary focus and a secondary extended depth of focus of +1.0D to +2.5D. However, the Mini Well Ready IOL also has at least one drawback: its depth of focus is 2.5D, far less than the 3D required for near reading at 33mm.

[0118] In one embodiment of the present invention, Table 3A describes two EDOF bifocal lenses, one labeled EDOF Bifocal 3D for high presbyopia correction of approximately 3D and the other labeled EDOF Bifocal 1D for low presbyopia correction of approximately +1.0D. Unlike the Mini Well Ready IOL, which has an extended depth of focus for near distances (see, "A New Extended Depth of Focus Intraocular Lens Based on Spherical Aberration," R Bellucci and MC Curatolo, J Refract Surg. 2017;33(6):389-394), our EDOF bifocal lenses have an extended depth of focus for distances, which increases the likelihood of achieving best-corrected distance vision of 20 / 20 with IOL / ICL surgery. [Table 7]

[0119] In a non-limiting embodiment, the EDOF progressive lens (110) of FIG. 11 for an eye is configured as an implantable or wearable lens and has: 1) a baseline diopter power extending over the optical zones (111, 112, 113) of the lens, including a central zone (111), an intermediate annular zone (112), and an outer annular zone (113), with a total diameter D2 of 5 mm to 8 mm, for the correction of distance vision defects; and 2) a diopter power of less than 2.5 mm in diameter. and 3) two aspheric zones (111 and 112) with outer diameters of less than 4.5 mm and greater than 2.5 mm covering at least the center of the eye's pupil, characterized in that at least one surface of the lens is aspheric to induce positive spherical aberration in the first zone (111) and negative spherical aberration in the second zone (112). The first and second zones are coaxial. In some embodiments, the second zone can be further configured to have a positive focal offset of less than 1.5D. The wavefront EDOF progressive lens can be configured as a contact lens, intraocular lens (IOL), accommodating intraocular lens (AIOL), ICL (implantable contact lens or posterior chamber phakic intraocular lens), or phakic IOL that functions in conjunction with the cornea and lens of the eye.

[0120] A first exemplary design provides an EDOF bifocal lens with an additional optical power of 1.0D + / - 0.25D between the two foci. The parameters of an exemplary wavefront bifocal lens (labeled "EDOF Bifocal 1D") are shown in Table 3A.

[0121] Assume an EDOF progressive lens has an optical zone diameter of 5mm to 8mm. The lens has a baseline diopter power that extends across the optical zone of the lens to correct distance vision defects in the same way as a single vision lens.

[0122] The progressive lens also has two aspherical zones covering the center of the eye's pupil, with an outer diameter D0 of 3.5 mm (radius 1.875). The aspherical zones are characterized in that at least one surface of the lens is aspherical to induce positive spherical aberration in the first zone and negative spherical aberration in the second zone. The spherical aberration induced by the aspherical zones is expressed as a wavefront error (OPD) across the eye's pupil, i.e. If ρ≦1.15, OPD(ρ)=0.7 * (ρ / r0) 4 If 1.15<ρ≦1.75, OPD(ρ)=-1.11 * (ρ / r1) 4 where ρ is the polar radius in the pupil plane. The positive spherical aberration of the first zone has a peak value of 0.70 microns at the boundary ρ=r0=1.15 mm. The negative spherical aberration of the second zone has a peak value of -1.11 microns at the boundary ρ=r1=1.75 mm. The aspherical zone covering the center of the eye's pupil has a diameter of 3.5 mm.

[0123] In addition to the baseline diopter power and the spherical aberration induced in the aspheric zone, there is a 1.0D positive focus offset in the central (first) zone and a 0.37D positive focus offset in the annular (second) zone.

[0124] The performance of a wavefront progressive lens was simulated. The calculated point spread functions (PSFs) for SPH = -0.25D to SPH = +1.5D are shown in Figure 12A, and the calculated retinal image of the visual acuity chart is shown in Figure 12B. The parameter SPH is used to specify the through-focus focus error of the eye. SPH = 0D specifies best-corrected visual acuity at 4 meters, a common distance for visual acuity testing in the United States. SPH = -0.25D specifies corrected visual acuity at infinity, which is -0.25D myopic when the target distance is 4 meters for traditional visual acuity testing. SPH = +1.0D specifies a +1.0D presbyopic correction. Four pupil diameters were considered: 3.0mm and 3.5mm for visual acuity testing and 4.5mm and 5.0mm for night vision testing.

[0125] Unlike the PSFs in Figures 10A and 10C, the calculated PSF of the WF Bifocal 1D lens in Figure 12A is observed to have a first focus covering a focus range of at least -0.25D to +0.25D and a second focus covering a focus range of +0.75D to +1.5D.

[0126] Figure 12C shows the calculated "through-focus" retinal contrast plots for the WF Bifocal 1D for a 3.5mm pupil and for 20 / 20 and 20 / 40 lines at pupil diameters of 3mm to 5mm. Our EDOF bifocal 1D works slightly differently from conventional progressive lenses in two ways. First, the first focus for distance vision has an extended depth of focus of -3 / 8D to +3 / 8D for visual acuity tests with pupil diameters of 3.0mm and 3.5mm. Second, the second focus for presbyopia correction of +0.75D to +1.5D has a gap for 20 / 20 vision at +1.25D. The calculated retinal image in Figure 12B confirms the wavefront progressive characteristics, as well as the slightly reduced visual acuity and field of view at +1.25D.

[0127] To estimate best-corrected visual acuity from the through-focus MTF in Figure 12C, we need to know the threshold contrast for each acuity line. Figure 12D shows the calculated retinal contrasts for normal eyes at 20 / 25, 20 / 30, 20 / 40, and 20 / 60, respectively, under photopic (A) and mesopic (B) conditions. These are unpublished data from J. Liang, D. Tanzer, and T. Brunstetter, who studied over 250 eyes of U.S. Navy pilots with normal uncorrected visual acuity ranging from 20 / 20 to 20 / 10. The photopic curve (A) above was derived from 1) each subject's best subjective visual acuity reading a 5% low-contrast acuity chart under photopic conditions, and 2) the calculated MTF for each eye during subjective testing of 5% low-contrast visual acuity. From Figure 12D (A), the mean threshold contrast for photopic vision is estimated to be less than 2% for 20 / 25 (24 cycles / degree), 20 / 30 (20 cycles / degree), and 20 / 40 (15 cycles / degree). The mesopic vision curve (B) was obtained from 1) each eye's best subjective visual acuity reading a 25% low-contrast chart under mesopic conditions and 2) the calculated MTF for each eye for the pupil diameter during subjective testing of 25% low-contrast visual acuity. From Figure 12D (B), the mean threshold contrast for mesopic vision is estimated to be approximately 5% to 6% for 20 / 25 (24 cycles / degree), 20 / 30 (20 cycles / degree), and 20 / 40 (15 cycles / degree).

[0128] Figure 12E shows plots of the calculated modulation transfer function (MTF) of the WF Bifocal 1D at infinity (-0.25D), 4 meters (0D), and a long distance of +0.25D focus error for pupil diameters of 3mm, 3.5mm, and 5mm. Figure 12E also shows the average MTF of a normal eye, labeled "Normal Eye," calculated based on the formula provided by AB Watson in Journal of Vision, 13(6):18, pp. 1-11 (2013), and the estimated MTF of a diffractive bifocal lens, labeled "Diffractive Bifocal 40%," calculated from the average MTF of a normal eye using a 50% bifocal lens. Diffractive bifocal lenses typically have approximately 20% energy loss that does not contribute to either the "0" or "1" order diffraction images. Our WF Bifocal 1D lenses provide better contrast than 50% diffractive multifocal lenses at distances, with no contrast loss at spatial frequencies above 20c / deg (characteristics below 20 / 30) and slight contrast loss at spatial frequencies below 20c / deg when compared to the normal human eye. This is especially true for the real eye, since our WF Bifocal 1D lenses can reduce the eye's uncorrected astigmatism and coma, which degrade vision quality with conventional single vision and diffractive multifocal lenses.

[0129] The data in Figures 12C and 12E reveal several findings for the EDOF bifocal 1D. First, this EDOF bifocal is expected to provide patients with visual acuity of 20 / 16 or better with relatively high contrast. Second, night vision at 4.5mm and 5mm pupil diameters is exceptional at distance. Therefore, a 1D presbyopic-correcting progressive lens can be invented with little or no loss of retinal contrast at distance. Another advantage of the Wavefront progressive lens is its tolerance for uncorrected astigmatism (approximately 0.5D).

[0130] In the exemplary design of "EDOF bifocal 3D" in Table 3A, this bifocal lens also has an aspherical region that covers the center of the eye's pupil. The spherical aberration induced in the aspherical region is represented as the wavefront error (OPD) across the eye's pupil, that is, When ρ < r0 = 1.1, OPD(ρ) = 1.0 * (ρ / r0) 4 When 1.1 < ρ ≤ r1 = 1.75, OPD(ρ) = -2.22 * (ρ / r1) 4 Here, ρ is the polar radius in the pupil plane. The positive spherical aberration of the first region has a peak value of 1.0 micron at the boundary ρ = r0 = 1.1. The negative spherical aberration of the second region has a peak value of -2.22 microns at the boundary ρ = r1 = 1.75.

[0131] In addition to the baseline diopter power and the spherical aberration induced in the aspherical region, there is a positive focus offset of 1.65D in the central (first) region and a positive focus offset of 1.15D in the annular (second) region.

[0132] The performance of the wavefront EDOF bifocal 3D was simulated, and the calculated point spread function (PSF) for SPH = -0.25D to SPH = +3.25D is shown in FIG. 13A, and the calculated retinal image of the visual acuity chart is shown in FIG. 13B. SPH = 0D specifies the best corrected visual acuity at 4 meters, which is a common distance for vision tests in the United States. SPH = -0.25D specifies the corrected visual acuity at infinity, and SPH = +3.0D specifies a presbyopia correction of +3.0D. Four pupil diameters of 3.0mm and 3.5mm for vision tests and 4.5mm and 5.0mm for night vision were considered.

[0133] It is observed that the calculated PSF of the WF Bifocal 3D lens in FIG. 13A has a first focus that covers an extended focus range of 0D to +1.25D and a second focus that covers a focus range of +2.75D to 3.25D. The focus at +2.25D is too narrow and too weak to be considered a focus region.

[0134] Figure 13C shows the calculated "through-focus" retinal contrast plots for the EDOF Bifocal 3D for a 3.5mm pupil diameter and for the 20 / 20 and 20 / 40 lines with pupil diameters from 3mm to 5mm. Our EDOF Bifocal 3D works slightly differently from conventional progressive lenses in two ways. First, the first focus for distance vision is an extended depth of focus from 0D to +1.25D for visual acuity tests with pupil diameters of 3.0mm and 3.5mm. Second, the second focus for presbyopia correction is from +2.75D to +3.25D. The calculated retinal images in Figure 13B confirm the EDOF progressive properties.

[0135] Figure 13D shows plots of the calculated modulation transfer function (MTF) of the WF Bifocal 3D at distances of infinity (-0.25D), 4 meters (0D), and +0.25D focus error for pupil diameters of 3 mm, 3.5 mm, and 5 mm. Figure 13D also shows the average MTF for a normal eye, labeled "Normal Eye," and the estimated MTF for a diffractive bifocal lens, labeled "Diffractive Bifocal 40%." Our WF Bifocal 3D provides comparable or better contrast than diffractive multifocal lenses at longer distances, with no contrast loss at spatial frequencies above 30 c / deg (characteristics below 20 / 20) and only slight contrast loss at spatial frequencies below 30 c / deg when compared to the normal human eye. This is especially true for the real eye, as our WF Bifocal 3D Lens can reduce the eye's uncorrected astigmatism and coma that degrade vision quality with conventional single vision and diffractive multifocal lenses.

[0136] Figures 13C and 13D show several findings for the EDOF bifocal 3D lens. First, this EDOF bifocal is expected to provide patients with 20 / 16 or better visual acuity with high contrast and extended depth of focus. Second, night vision with 4.5mm and 5mm pupil diameters is excellent at distance and near. Another advantage of this Wavefront progressive lens is its tolerance for up to 0.5D of uncorrected astigmatism.

[0137] Solving the problem of low contrast at distance using prior art wavefront designs (U.S. Pat. No. 8,529,559 B2 and U.S. Patent Application No. 2011 / 0029073 A1) is possible by finding an optimal solution using EDOF bifocal 3D to reduce the focus offset in the central aspheric zone to +1.65D, which is 1.35D less than the 3D total depth of focus of the wavefront progressive lens. In contrast, the central aspheric zone of the prior art wavefront design exhibits a focus offset of +4.0D, which is 1.0D more than the 3D total depth of focus. The significant improvement in contrast with our inventive EDOF bifocal 3D is plotted in Figure 13E, which shows retinal contrast at distance (A) and through-focus contrast at 20 / 20 acuity (B) comparing a prior art wavefront design (U.S. Pat. No. 8,529,559 B2 and U.S. Patent Application No. 2011 / 0029073 A1) with our new EDOF Bifocal 3D. Figure 13E is obtained with a lens diameter of 3 mm, the industry standard size for testing multifocal lenses.

[0138] In one embodiment, the spherical aberration induced in the aspheric area is expressed as a wavefront error across the pupil or OPD, i.e., If ρ≦r0, OPD(ρ)=S1 * (ρ / r0) 4 If r0<ρ≦r1, OPD(ρ)=(-S2) * (ρ / r1) 4 where ρ is the polar radius in the pupil plane, S1 is positive and represents the positive spherical aberration of the first area (111), and r0=0.5 * D0 is the radius of the first zone, greater than 0.87 mm and less than 1.25 mm. (-S2) is negative and represents the negative spherical aberration of the second zone, and r1 is the outer diameter of the second zone (112), less than 2.25 mm and greater than 1.20 mm. The second zone of the aspheric zone can be further configured to add a focal offset φ2, which is between -1.0D and +1.0D. In one embodiment, the positive spherical aberration S1 is greater than 0.20 microns and less than 1.50 microns. Table 3B shows the calculated positive spherical aberration for a wavefront progressive lens with a central aspheric zone diameter between 1.75 mm and 2.4 mm. In one embodiment, the magnitude of the negative spherical aberration (-S2) is greater than 0.25 microns and less than 6 microns. Table 3C shows the calculated negative spherical aberration of wavefront progressive lenses with annular aspherical zone outer diameters between 2.5 mm and 4.4 mm.

[0139] In yet another embodiment, the aspherical area further comprises ρ n where n is an integer greater than or equal to 3.

[0140] In some embodiments, the wavefront progressive lens is configured as a bifocal contact lens having a diameter between 9 mm and 16 mm. The wavefront progressive contact lens has a front surface and a back surface, at least one of which is aspherical at the center of the lens.

[0141] In one embodiment, the back surface of the wavefront EDOF progressive contact lens is further configured to have an aspheric shape at the periphery of the lens to prevent lens rotation on the eye when the lens is a toric progressive contact lens. [Table 8] [Table 9]

[0142] In some embodiments, the wavefront progressive lens is configured as a wavefront bifocal IOL with a diameter of 5mm to 7mm, and the aspheric surface is on the anterior or posterior surface of the IOL. In one embodiment, the wavefront bifocal IOL is further configured as an accommodating IOL.

[0143] In another embodiment, the wavefront progressive lens is configured as a wavefront corneal inlay having a diameter of approximately 6 mm or 5-7 mm, and the aspheric surface is the anterior or posterior surface of the corneal inlay.

[0144] 3. Wavefront EDOF trifocal lenses Diffractive trifocal IOLs not only provide a high rate of spectacle-free IOL surgery, but also allow the postoperative eye to see non-existent artifacts created by diffractive optics, such as 1) halos and starburst nighttime symptoms caused by simultaneous multiple images, 2) spider web nighttime symptoms associated with diffractive structures, and 3) ghost images of large distant objects caused by a lack of intermediate and near focus.

[0145] Inducing opposite-sign spherical aberration in the center of the pupil for a +3D presbyopia-correcting IOL has been proposed in U.S. Pat. No. 8,529,559 B2 and U.S. Patent Application No. 2011 / 0029073 A1. To obtain the desired 3D depth of focus (DoF), a focal offset of +4.0D greater than the desired DoF is introduced in the central aspheric zone. [Table 10]

[0146] The designs of U.S. Patent No. 8,529,559 B2 and U.S. Patent Application No. 2011 / 0029073 A1 suffer from at least three problems. First, the designs suffer from low contrast at distances, which was noted and addressed in the improved design of the Mini Well Ready IOL. Second, the original designs and the Mini Well Ready IOL are not trifocal lenses that satisfy the active lifestyles of patients who require excellent vision at distances for driving and watching TV, at intermediate distances (approximately 0.6 m) for working on a computer, and at close distances (approximately 0.3 m) for reading books or small print. Third, trifocal ophthalmic lenses with a full focal range of 2.0D to 2.5D for contact lenses, implantable contact lenses, and corneal inlays are also lacking because these lenses work in conjunction with the crystalline lens of the eye.

[0147] To address these issues, one aspect of the present invention provides a new class of wavefront EDOF trifocal lenses, as shown in Table 4A. First, we were able to create wavefront trifocal lenses with three foci: a first "distance" focus, a second "intermediate" focus with small add power, and a third "near" focus with large add power. These trifocal lenses provide functional vision at "distance," "intermediate," and "near" distances. Second, these trifocal lenses cover a wide presbyopia range of 2.25D to 3.25D, not only for IOLs but also for contact lenses, ICLs, and corneal inlays. Third, we solve the problem of low contrast at distance for 3D presbyopia correction by finding an optimal solution using a focus offset φ1 smaller than the total presbyopia range from the baseline diopter power to the "near" add power. Fourth, the trifocal lenses have an extended depth of focus at distance.

[0148] In one exemplary design of "EDOF Trifocal 2.75D" in Table 4A, this lens has two aspherical regions that cover the center of the eye's pupil, and its outer diameter is 3.0 mm. The aspherical regions are characterized in that at least one surface of the lens is aspherical to induce positive spherical aberration in the first region and negative spherical aberration in the second region, and the first region and the second region are coaxial. The spherical aberration induced in the aspherical regions is represented as the wavefront error (OPD) across the eye's pupil, that is, When ρ < r0 = 0.92, OPD(ρ) = 0.80 * (ρ / r0) 4 When 0.92 < ρ ≤ r1 = 1.5, OPD(ρ) = -2.2 * (ρ / r1) 4 Here, ρ is the polar radius in the pupil plane. The positive spherical aberration of the first region has a peak value of 0.80 microns at the boundary ρ = r0 = 0.92. The negative spherical aberration of the second region has a peak value of -2.2 microns at the boundary ρ = r1 = 1.5.

[0149] In addition to the baseline diopter power and the spherical aberration induced in the aspherical regions, there is a positive focus offset of +2.0 D in the central (first) region with a diameter of 1.75 mm (radius 0.875 mm).

[0150] The performance of EDOF Trifocal 2.75D was simulated, and the calculated point spread function (PSF) from -0.25D to +3.0D is shown in Fig. 14A, and the calculated retinal image of the visual acuity chart is shown in Fig. 14B. The parameter SPH is used to specify the focus error of the eye's through-focus. SPH = 0D specifies the best corrected visual acuity at 4 meters. SPH = -0.25D specifies the corrected visual acuity at infinity, which means that when the target far distance is 4 meters in the conventional visual acuity test, it is only -0.25D myopic. SPH = +3.0D specifies a presbyopia correction of +3.0D. Four different pupil diameters of 3.0 mm and 3.5 mm in the case of visual acuity test and 4.5 mm and 5.0 mm in the case of night vision were considered.

[0151] FIG. 14C shows plots of calculated "through-focus" retinal contrast for the EDOF Trifocal 2.75D for a 3.5 mm pupil diameter, 20 / 20 line, and 20 / 40 line.

[0152] From the calculated PSF in FIG. 14A and the “through-focus” plot in FIG. 14C, it can be observed that the EDOF Trifocal 2.75D has three distinct foci: a first focus covering an extended focal range of −0.25D to +0.75D for viewing at long distances, a second focus covering a focal range of +1.25D to +2.0D for intermediate distances, and a third focus of 2.25D to 3.0D for close distances.

[0153] Figure 14D shows plots of the calculated modulation transfer function (MTF) of the EDOF Trifocal 2.75D at distances of infinity (-0.25D), 4 meters (0D), and +0.25D focus error for pupil diameters of 3mm, 3.5mm, and 5mm. Figure 14D also shows the average MTF for a normal eye, labeled "Normal Eye," and the estimated MTF for a diffractive progressive lens, labeled "Diffractive Progressive 40%." Our EDOF Trifocal 2.75D provides comparable or better contrast than a diffractive multifocal lens at distances, with no contrast loss at spatial frequencies above 30c / deg (characteristics below 20 / 20) and some contrast loss at spatial frequencies below 30c / deg when compared to a normal eye. This is especially true for the real eye, as our EDOF Trifocal 2.75D Lens can reduce the eye's uncorrected astigmatism and coma that degrade vision quality with conventional single vision and diffractive multifocal lenses.

[0154] Figures 14C and 14D show several findings for the EDOF Trifocal 2.75D lens. First, the EDOF bifocal is expected to provide 20 / 16 or better visual acuity with relatively high contrast and extended depth of focus. Second, night vision with pupil diameters of 4.5mm and 5mm is excellent at distance and near. Another advantage of this Wavefront progressive lens is its tolerance for uncorrected astigmatism up to 0.5D.

[0155] Table 4A shows three other embodiments of EDOF trifocal lenses that solve the low contrast at distance problem of the designs of U.S. Patent No. 8,529,559 B2 and U.S. Patent Application No. 2011 / 0029073 A1 and provide the following features: 1) extended depth of focus for distance, 2) a second focus with presbyopia correction of +1.25D to +1.75D, and 3) a third focus that extends the total focus range from 2.25D to 3.25D. [Table 11] [Table 12]

[0156] The invention of wavefront trifocal lenses with high retinal contrast at distance is made possible by finding the optimal solution with low focal offsets of +1.62D and +2.7D in the central aspheric zone. These EDOF trifocal designs can be fitted with contact lenses, IOLs, accommodative IOLs, phakic IOLs, ICLs, and corneal inlays.

[0157] In some embodiments, the wavefront EDOF trifocal lens of FIG. 11 is configured as an implantable or wearable lens. It comprises: 1) a baseline diopter power extending across the optical zones (111, 112, 113) of the lens with a diameter D2 of 5 mm to 8 mm for the correction of distance vision defects, including focus and / or cylinder errors; 2) a positive focus offset φ1 of less than +3.0 D and more than +1.0 D in a central zone (111) with a diameter D0 of less than 2.1 mm and more than 1.65 mm; and 3) two central aspherical zones (111, 112) at least in the center of the lens, with an outer diameter of less than 4 mm and more than 2.5 mm, covering the center of the pupil of the eye, characterized in that at least one surface of the lens is aspherical to induce positive spherical aberration in the first zone (111) and negative spherical aberration in the second zone (112), and the first and second zones are coaxial. A wavefront error exceeding the baseline diopter power transforms the monofocal lens into a trifocal lens, i.e., a first "distance" focus, a second focus with additional refractive power for "intermediate distance," and a third focus with additional refractive power for "near distance," and the positive focus offset φ1 in the central zone must be less than the full focal range of the trifocal lens.

[0158] In one embodiment of a wavefront EDOF trifocal lens, the spherical aberration induced in the aspheric zone is expressed in terms of the optical path difference (OPD), or wavefront error across the pupil of the eye, i.e., If ρ≦r0, OPD(ρ)=S1 * (ρ / r0) 4 If r0<ρ≦r1, OPD(ρ)=(-S2) * (ρ / r1) 4 where ρ is the polar radius in the pupil plane; S1 is positive and represents the positive spherical aberration of the first zone with a peak value of S1 at the boundary ρ=r0, where r0 is the radius of the first zone and is greater than 0.82 mm and less than 1.1 mm; (-S2) is negative and represents the negative spherical aberration of the second zone with a peak value of (-S2) at the boundary ρ=r1, where r1 is the outer radius of the second zone and is greater than 1.2 mm and less than 2 mm.

[0159] In another embodiment, the positive spherical aberration S1 of the first zone is greater than 0.30 microns and less than 2 microns.

[0160] In yet another embodiment, the magnitude of the negative spherical aberration (-S2) is greater than 0.50 microns and less than 8.5 microns.

[0161] In yet another embodiment, the aspherical area further comprises ρ n where n is an integer greater than or equal to 3.

[0162] In yet another embodiment, the wavefront trifocal lens is further configured to add a focus error φ2 to a second zone of the aspheric zone, the focus error being between −1.0D and +1.0D.

[0163] In some embodiments, the wavefront trifocal lens is configured as a wavefront trifocal contact lens with a diameter of 9 mm to 16 mm, and the aspheric surface is the front or back surface of the contact lens. The back surface of the trifocal contact lens is further configured to have an aspheric shape at the periphery of the lens to prevent rotation of the lens on the eye if the contact lens is also a toric lens.

[0164] In another embodiment, the wavefront trifocal lens is configured as a wavefront trifocal IOL and has an optic zone of approximately 6 mm in diameter and 5 mm to 7 mm in diameter. The wavefront trifocal IOL has an anterior surface and a posterior surface, and at least one of the anterior surface or posterior surface is aspheric in the center of the lens.

[0165] 4. Quasi - Accommodating Lens Accommodating IOLs are currently troubled by one or more of the following drawbacks: 1) a narrow accommodation range insufficient for effective presbyopia correction; 2) insufficient control of artificial accommodation to freely achieve the desired accommodation state; 3) unstable vision due to large variations in artificial accommodation; 4) low vision due to uncorrected astigmatism of the eye.

[0166] In one aspect of the present invention, a new class of wavefront lenses for the eye, the quasi - accommodating continuous - focus (QACIF) lens, is disclosed. The QACIF lens has an optical zone with a diameter of less than 8 mm and provides a substantially continuous focus over a focal range of more than 1.0 D to 2 D. The 2 D focal range is smaller than the 3 D of the IOLs used in cataract surgery, but the QACIF lens with a 2 D focal depth is sufficiently good for the treatment of all presbyopic eyes without cataracts that use an ICL, phakic IOL, or contact lenses. The QACIF lens can be realized by a special multi - focus structure having a plurality of foci that are close enough to produce a substantially continuous focus. The multi - focus lens can be realized by 1) using an aspheric surface to induce spherical aberration in the central part of the lens with a diameter of less than 4 mm, or 2) using diffractive optics to produce simultaneous multiple foci.

[0167] In one exemplary design of the QACIF lens “QACIF2D” in Table 5A, the lens has two aspheric zones that cover the center of the eye's pupil, and its outer diameter is 3.5 mm. The aspheric zones are characterized in that at least one surface of the lens is aspheric to induce positive spherical aberration in the first zone and negative spherical aberration in the second zone, and the first zone and the second zone are coaxial. The spherical aberration induced in the aspheric zones is represented as the wavefront error (OPD) across the eye's pupil, that is, When ρ < r0 = 1.25, OPD(ρ)=1.0 * (ρ / r0) 4 When 1.25 < ρ ≦ r1 = 1.75, OPD(ρ)= - 1.11 * (ρ / r1) 4 where ρ is the polar radius in the pupil plane. The positive spherical aberration of the first zone has a peak value of 1.0 microns at the boundary ρ=r0=1.25 mm. The negative spherical aberration of the second zone has a peak value of -1.11 microns at the boundary ρ=r1=1.75 mm.

[0168] In addition to the baseline diopter power and the spherical aberration induced by the two aspheric zones, there is a positive focus offset of +1.25D in the central (first) zone with a diameter of 2.5mm (radius of 1.25mm) and a positive focus offset of +0.75D in the annular (second) zone with an outer diameter of 3.5mm (radius of 1.75mm).

[0169] The performance of the wavefront QACIF2D was simulated, and the calculated point spread function (PSF) is shown in Figure 15A, and the calculated retinal image of the visual acuity chart is shown in Figure 15B. The parameter SPH is used to specify the through-focus focus error of the eye. SPH = 0D specifies best corrected visual acuity at 4 meters. SPH = -0.25D specifies corrected visual acuity at infinity. SPH = +2.0D specifies +2.0D presbyopia correction. Four pupil diameters were considered: 3.0mm and 3.5mm for visual acuity testing, and 4.5mm and 5.0mm for night vision.

[0170] From the calculated point spread functions from SPH=-0.25D to SPH=+2.0D in Figure 15A, this lens produces three focal zones, one centered near 0D, one near +0.75D, and one near +1.75D with two peaks at +1.5D and +2.0D. For vision-test pupil diameters of 3mm and 3.5mm, these foci are close enough to create an extended depth of focus that nearly focuses the lens over the entire focal range SPH=-0.25D to SPH=2.0D, except for a relatively weak focus at SPH=+1.25D.

[0171] Figure 15C shows the calculated "through-focus" retinal contrast plots for the QACIF2D for a 3.5mm pupil diameter and for the 20 / 20 and 20 / 40 lines at pupil diameters from 3mm to 5mm. The QACIF lens can provide 20 / 20 or better visual acuity at first focus from -0.25D to 1.0D of extended depth of focus, and 20 / 20 or 20 / 25 at +1.50D to +1.75D. Visual acuity of 20 / 30 or better is expected at through focus from -0.25D to +2.0D. These findings may be contradicted by the calculated retinal image in Figure 15B. Thus, a nearly continuous focus lens is seen at all pupil diameters, with only slight degradation at +1.25D and +2.0D at a 3mm pupil diameter.

[0172] Figure 15D shows plots of the calculated modulation transfer function (MTF) of the QACIF2D at distances of infinity (-0.25D), 4 meters (0D), and +0.25D focus error for pupil diameters of 3 mm, 3.5 mm, and 5 mm. Figure 15D also shows the average MTF for a normal eye, labeled "Normal Eye," and the estimated MTF for a diffractive bifocal lens, labeled "Diffractive Bifocal 40%." Our QACIF2D provides better contrast than diffractive multifocal lenses at distances, with no contrast loss at spatial frequencies above 30 c / deg (characteristics below 20 / 20) and slight contrast loss at spatial frequencies below 30 c / deg when compared to a normal human eye. This is particularly true for real eyes, since our QACIF2D lens can reduce the uncorrected astigmatism and coma of the eye that degrade vision quality with conventional monofocal and diffractive multifocal lenses.

[0173] The QACIF2D lens is expected to provide patients with visual acuity of 20 / 16 or better with relatively high contrast, and night vision at 4.5mm and 5mm pupil diameters is exceptional.

[0174] Figures 15E and 15F show the calculated retinal images with the QACIF2D lens when the eye has ½D and ¾D of uncorrected astigmatism, respectively. It can be seen that the image in Figure 15E with 0.5D of uncorrected CYL is nearly identical to the image in Figure 15B with CYL=0. Even in the case of 0.75D of uncorrected astigmatism shown in Figure 15F, visual acuity is still good at +0.25D to +1.25D.

[0175] In addition to eliminating astigmatism, the QACIF2D is also independent of pupil diameters from 3mm to 5mm, as can be verified by the retinal images in Figures 15A / 15E / 15F and the through-focus plots (B) and (C) in Figure 15c. This is in stark contrast to the conventional lenses shown in Figures 5B and 10B, where the optical system is more sensitive to focus errors and astigmatism at larger pupil diameters.

[0176] Based on two basic characteristics of the exemplary lens: 1) excellent visual acuity of 20 / 20 or 20 / 25 from SPH=-0.25D to SPH=+2.0D, and 2) near independence from pupil diameter of 3mm to 5mm, this type of lens is classified as a 2.0D quasi-accommodative continuous focus (QACIF) lens, even without artificial accommodation of the AIOL.

[0177] ICLs or phakic IOLs with QACIF2D optics can treat all people over 45 years of age who are cataract-free, with myopia / hyperopia, astigmatism, and presbyopia, making them spectacle-independent and free from reading glasses.

[0178] Figure 15G shows another design of a semi-accommodative continuous focus lens, "QACIF2A." This results in a pupil-diameter-independent EDOF trifocal lens with an extended depth of field (DFO) of -0.25D to +0.5D, a second focus centered at +1.25D, and a third focus at +1.75D. QACIF2A can be used to supplement QACIF2D. When QACIF2A and QACIF2D are applied separately to two eyes, patients can expect visual acuity of 20 / 20 or better across the entire focus range of -0.25D to +2.0D and for all pupil diameters of 3mm to 5mm.

[0179] Two additional designs of QACIF lenses are also shown in Table 5A. They share similar features of nearly continuous focus over a 2.0D focus range and a high tolerance for uncorrected astigmatism.

[0180] In some embodiments, a wavefront quasi-accommodative continuous focus (QACIF) lens is configured as an implantable or wearable lens, the wavefront QACIF lens comprising: 1) a baseline diopter power extending across an optical zone of the lens with a diameter of 5 mm to 8 mm for the correction of distance vision defects, including focus error and / or cylindrical error; 2) a central aspheric zone having a positive focus offset φ1 and a positive spherical aberration S1, the positive focus offset φ1 being less than 2.0 D and greater than 0.75 D, and the positive spherical aberration S1 being greater than 0.25 microns and less than 2.75 microns, with the central aspheric zone having a diameter of less than 2.75 mm and greater than 1.9 mm; and 3) an annular aspheric zone outer diameter less than 4.5 mm and greater than 2.5 mm, which induces negative spherical aberration. The positive spherical aberration of the QACIF lens at the central aspheric area for diameters of 1.9 mm, 2.2 mm, and 2.75 mm was calculated and is shown in Table 5B.

[0181] The Wavefront QACIF lens is configured as a contact lens, an intraocular lens (IOL), an accommodating intraocular lens (AIOL), a phakic IOL, an ICL (implantable contact lens or posterior chamber phakic intraocular lens), or a corneal inlay.

[0182] In one embodiment, the annular aspherical zone outer than the central aspherical zone is further configured to have a positive focus offset greater than 0 and less than 1.5D. [Table 13] [Table 14]

[0183] In another embodiment, the spherical aberration induced in the aspheric area is expressed in terms of the optical path difference (OPD), or wavefront error across the pupil of the eye, i.e., If ρ≦r0, OPD(ρ)=S1 * (ρ / r0) 4 If r0<ρ≦r1, OPD(ρ)=(-S2) * (ρ / r1) 4 where ρ is the polar radius in the pupil plane, S1 is positive and represents the positive spherical aberration of the first zone with a peak value of S1 at the boundary ρ=r0, r0 is the radius of the first zone and is greater than 0.9 mm and less than 1.4 mm, (-S2) is negative and represents the negative spherical aberration of the second zone with a peak value of (-S2) at the boundary ρ=r1, and r1 is the outer radius of the second zone and is greater than 1.25 mm and less than 2.25 mm.

[0184] In yet another embodiment, the magnitude of the negative spherical aberration (-S2) is greater than 0.15 microns and less than 4.75 microns when the outer diameter of the annular aspherical zone is less than 4.5 mm and greater than 2.5 mm. The negative spherical aberration of the annular aspherical zone for diameters of 2.5 mm, 3.0 mm, and 3.75 mm was calculated and is shown in Table 5C.

[0185] In yet another embodiment, the aspherical area further comprises ρ n where n is an integer greater than or equal to 3.

[0186] In one embodiment, the wavefront QACIF lens is configured as a wavefront contact lens with a diameter of 9 mm to 16 mm, and the aspheric surface is the front or back surface of the contact lens, the back surface of the contact lens further configured to have an aspheric shape at the periphery of the lens to prevent rotation of the lens on the eye if the contact lens is also a toric lens. [Table 15]

[0187] In another embodiment, the wavefront QACIF lens is configured as a wavefront IOL and has an optic zone of approximately 6 mm in diameter and 5 mm to 7 mm in diameter. The wavefront IOL has an anterior surface and a posterior surface, at least one of which is aspheric in the center of the lens.

[0188] In yet another embodiment, the QACIF IOL is further configured as an accommodative IOL.

[0189] In yet another embodiment, the wavefront QACIF lens is configured as a wavefront ICL that is implanted between the iris and the lens of the eye, and the aspheric surface is the anterior or posterior surface of the wavefront ICL lens.

[0190] In another embodiment, the QACIF ICL is achieved through a change in optic thickness when the baseline power magnitude is less than 1.0D.

[0191] In yet another embodiment, the wavefront QACIF lens is configured as a wavefront corneal inlay that can be implanted in the cornea of the eye for vision correction, and the aspheric surface is the anterior or posterior surface of the wavefront corneal inlay.

[0192] In another aspect, a wavefront implantable contact lens (ICL) for an eye is disclosed, comprising: a) a haptic area for anchoring the ICL to the iris in the anterior chamber in the example of WO1999062434A1 or for holding the ICL in place in the posterior chamber in the example of U.S. Pat. No. 6,106,553; and b) a wavefront lens including: b1) a baseline diopter power extending over an optical area of 5 mm to 8 mm in diameter for sphero-cylindrical correction; b2) a central area of 1.65 mm to 2.5 mm in diameter that induces positive spherical aberration and a positive focal offset φ1 of less than +3.0 D and greater than +0.5 D; and b3) an annular area of less than 4.5 mm in outer diameter that induces negative spherical aberration. Wavefront errors from induced spherical aberration and focus offset in the central and annular zones cause the optical lens to be one of the following: 1) a semi-accommodative continuous focus lens, 2) a wavefront progressive lens, or 3) a wavefront trifocal lens.

[0193] In one embodiment, the wavefront ICL has a central aspheric area and an annular aspheric area to induce the required spherical aberration.

[0194] In yet another aspect, a method of refractive correction of an eye is disclosed, comprising: a) determining the refractive error of the eye, including at least a spherical power SPH for distance vision correction; and b) performing refractive correction surgery to provide the post-operative eye with an extended depth of focus from a first focal power φ1 to a second focal power φ2, such that the post-operative eye retains excellent vision at distance even when the eye has post-operative myopic progression of −0.5D to −1.25D. In one embodiment, the refractive correction surgery to provide the extended depth of focus includes implanting a wavefront ICL having an extended depth of focus. For example, if an ICL with a QACIF2D optic is implanted in the eye with a target distance distance of SPH=+0.75D instead of SPH=0D, the eye not only has post-operative 20 / 20 vision, but also has excellent vision in the focal range of −0.25D to +1.0D, as shown in FIGS. 15B / 15C . This is advantageous because 1) it can reduce postoperative myopia progression in young adults by up to 1 D, and 2) postoperative myopia progression of less than 1 D can beneficially begin after age 40, when the postoperative eye develops presbyopia.

[0195] 5. Advantages of Wavefront Single Vision, Progressive, Trifocal, and QACIF Lenses Although conventional monofocal and diffractive multifocal lenses may be excellent based on their optical design and laboratory test results, there are many issues with their performance when they are actually placed in or on the human eye.

[0196] The disclosed wavefront lenses (monofocal and multifocal) solve several fundamental problems of prior art monofocal / multifocal lenses: 1) eliminate the halos and starbursts associated with diffractive multifocal lenses, 2) eliminate the blurred zones between foci of multifocal lenses, 3) improve the quality of a patient's vision by eliminating the image distortions of traditional monofocal and diffractive multifocal lenses, and 4) increase the likelihood of achieving best corrected 20 / 20 vision by extending the 20 / 20 depth of focus and increasing tolerance for uncorrected astigmatism. This is shown in Figures 9B / 9G, 12C, 13C, 14C, and 15C.

[0197] FIG. 16A provides a comparison of the wavefront monofocal / multifocal lens of the present invention with conventional refractive monofocal and diffractive monofocal / multifocal lenses.

[0198] Figure 17A shows calculated retinal images at night with a pupil diameter of 5 mm for a wavefront multifocal lens of an exemplary design of the present invention compared to a conventional refractive monofocal lens. Three focus settings are considered: -0.25D for distance vision at infinity, 0D for a target visual acuity chart at 4 meters, and +0.25D for presbyopia at +0.25D. The angular dimension of each square in Figure 16B is 0.25 degrees of arc. Compared to the angular dimension of the sun in the sky (approximately 0.5 degrees of arc), the point spread function patterns at the three distances are very small: 1) approximately 1 / 12 times smaller for the conventional monofocal lens, and 2) 1 / 14 to 1 / 6 times smaller for our wavefront EDOF progressive, EDOF trifocal, and QACIF lenses.

[0199] Diffractive multifocal lenses are constructed as a single-focus lens plus a kinoform diffractive surface (see Figure 17B (A)). The retinal image of a diffractive multifocal lens consists of a diffraction image of diffraction order "0" without deviation for the designed distance vision correction, a diffraction image of diffraction order "1" with deviation with additional refractive power, and other "higher" diffraction images with deviation. Therefore, in addition to the in-focus image of diffraction order "0" affected by the wavefront error of the eye, there is also a defocused image of diffraction order "1" with focus error of "additional refractive power" shown in Figure 17B (C) for the additional refractive powers of +1.75D and +3.5D, respectively. Therefore, halos and starbursts are inevitably associated with diffractive multifocal lenses due to the defocused images of the near focus. In addition, nighttime symptoms associated with diffractive lenses can be caused by 1) light scattering and light shadows caused by the sharp-edge pattern and 2) diffraction patterns due to the discontinuous phase at each step of the kinoform.

[0200] Therefore, we can conclude that our wavefront multifocal lens has night vision performance similar to that of a monofocal lens with fully corrected focus error. The nighttime halos and starbursts of diffractive multifocal lenses are effectively eliminated. Furthermore, our wavefront multifocal lens outperforms conventional monofocal IOLs when the target distance visual acuity of the monofocal IOL is near 1 meter for alleviating presbyopia, rather than the best distance visual acuity of 4 meters.

[0201] Two other fundamental problems with conventional multifocal lenses are 1) blurred vision between foci and 2) poor visual quality associated with image distortion. From the through-focus calculated retinal image of a monofocal lens in Figure 10B, we can see that acceptable visual acuity has a short depth of focus of approximately + / - 0.25D for full correction of astigmatism (CYL = 0). However, if the eye has uncorrected astigmatism, the depth of focus is further reduced. Figure 17C shows the through-focus calculated retinal image of a monofocal lens from -0.75D to +0.75D with 3 / 8D of uncorrected astigmatism. We can conclude that 1) retinal image distortion occurs as soon as the focus error reaches 0.25D, and 2) the depth of focus for 20 / 20 is much smaller than + / - 0.25D. For a diffractive bifocal IOL with a diffraction efficiency of 40% at distance, the retinal image is similar to that in Figure 10B for CYL=0 and Figure 17C for CYL=3 / 8D, but with a reduction in contrast (1-40%) across all spatial frequencies. Thus, for a multifocal lens with an additional refractive power greater than 1.5D, one would expect blurred or distorted interfocal images for any focal length with a focus error of approximately 0.25D from either of the foci.

[0202] Complete blurring or distortion between foci is effectively resolved with our Wavefront progressive, trifocal, and QACIF lenses shown in Figures 9B / 9D / 9G, 15B / 15E, 12B, 13B, and 14B. Our Wavefront lenses for presbyopia provide continuous visual acuity of 20 / 40 or better across the entire focal range of each design.

[0203] 6. Liquid ophthalmic lenses In one embodiment of the present invention, Figure 18 discloses a liquid ophthalmic lens (180) comprising: 1) a liquid lens portion having a flexible bag formed by a front optical element (181) and a rear optical element (182) and a liquid (183) filling the flexible bag formed by the front and rear optical elements, 2) a solid optical element (184) immersed in the liquid in the liquid lens region and configured to change the refractive properties of the liquid lens, and 3) an attachment mechanism (185) for securing the solid optical element (184) to the flexible bag.

[0204] In one embodiment, the liquid lens portion is configured to be deformable between a disaccommodated state for a nominal optical power and an accommodated state for a different optical power, and the solid optical element (184) has a front and back surface and a refractive index n1 that is different from the refractive index of the liquid (n2).

[0205] Many mechanisms for surgically attaching a liquid lens to the eye exist in the prior art for controlling accommodation of the liquid lens. In one embodiment, the liquid ophthalmic lens further comprises haptics configured to deform in response to forces exerted by movement of the ciliary muscles of the eye, the haptics having an interior liquid volume in fluid communication with the liquid lens portion.

[0206] In yet another embodiment, the solid optic immersed in the liquid lens portion is an optically spherical lens configured to change the spherical power of the combined liquid lens. This design allows the same structure for the front and back elements of the liquid lens to accommodate a wide range of people with different IOL power requirements. The liquid lens has a 29D IOL power with a single structural design of the front (101), back (102), and liquid without the immersed solid optic. Its shape can be deformed to achieve a fixed accommodation range of up to 4.0D. If the immersed solid optic can be selected for a single optical power of +11.0D to -11.0D, the combination of the same structure of the liquid lens and the immersed lens achieves a focal range of +18D to +40D. One advantage of using a single structure for the deformable liquid lens is that it reduces potential variations in accommodation control due to different structures of the deformable liquid lens.

[0207] In yet another embodiment, the solid optic immersed in the liquid lens portion is an optically toric lens configured to add cylinder power to the liquid lens, allowing the liquid lens to be adapted to an accommodating toric IOL using the same structures of the accommodating IOL for the anterior and posterior elements.

[0208] In yet another embodiment, a solid optical element immersed in the liquid lens portion induces spherical aberration and a focal offset in a central region of the liquid lens having a diameter of approximately 3.5 mm, e.g., 2.2 mm to 4.5 mm, and the induced spherical aberration and focal offset result in a reduction of astigmatism, coma, focus error, and presbyopia that remain uncorrected by the liquid IOL when implanted in a human eye.

[0209] 7. Wavefront Corneal Implant for Presbyopia Correction In one aspect, a wavefront corneal implant configured for correcting presbyopia in an eye is disclosed. The wavefront corneal implant includes an optic having a diameter D1 between 2.0 mm and 4.5 mm. The optic has a base section of uniform thickness and an add-on section for refractive correction. The total thickness is between 10 microns and 50 microns. The add-on section induces wavefront errors in the eye, including: 1) a positive focal power φ1 of 1.0D to 2.5D in a central section having a diameter D0 between 1.5 mm and 2.5 mm; 2) a positive spherical aberration in the central section; and 3) a negative spherical aberration in an annular section outside the central section.

[0210] In one embodiment, the annular zone can further induce a focus error of between -1.0D and +1.0D.

[0211] Unlike conventional corneal inlays in the form of positive lenses, U.S. Patent Nos. 8,057,541 B2 and 8,900,296B, wavefront inlays using one of the wavefront bifocal, wavefront trifocal, and QACIF designs provide excellent visual acuity of 20 / 20 or better at distance and 20 / 20 or better at near with an additional refractive power of +1.0D to +2.5D.

[0212] The uniform thickness base section can be configured as parallel plates or with a radius of curvature of approximately 7.8 mm, like that of a normal cornea. In one embodiment, the add-on section is configured to vary in thickness only across the corneal implant.

[0213] In another embodiment, the corneal implant is made of a biocompatible material and is fabricated by a molding or lathing process.

[0214] In another embodiment, the corneal implant is made from human corneal tissue from a donor and is created through a process using laser ablation with UV light and / or laser cutting with a short pulse laser.

[0215] In another embodiment, the add-on optical zone of the corneal implant includes a thickness variation and a refractive index variation. The refractive index variation can be achieved using a short-pulse laser. The use of a refractive index variation in the corneal implant has the advantage that the refractive index variation is very small, within the range of 0.001 to 0.03, allowing for fine tuning of the wavefront map.

[0216] In yet another embodiment, the wavefront corneal implant is made of human corneal tissue from a donor through a process of laser ablation / ablation and changing the refractive index of the corneal tissue using a short pulsed laser.

[0217] In one embodiment, the add-on zone further comprises a baseline diopter power extending across the corneal implant for 1) conventional spherical correction or 2) spherocylindrical correction of distance vision aberrations.

[0218] In another embodiment, the add-on area of the corneal implant further comprises ρ n where n is an integer greater than or equal to 3.

[0219] 8. Wavefront Surgical Procedure for Presbyopia Correction in Human Eyes In one aspect of the present invention, a wavefront method of surgical procedure for correcting presbyopia in a human eye is disclosed, which includes: 1) using a first laser beam to create a central island at the center of the pupil with a diameter D1 between 2.0 mm and 4.5 mm, whose optical effect is represented by a wavefront error W1(r), and 2) using a second laser beam to change the refractive index at the center of the pupil by δn and a tissue depth distribution d(r). The combination of the effect of the central island W1(r) caused by the first laser and the gradient index (GRIN) optics created through laser writing with the second laser beam on the cornea results in a combined wavefront error that includes: a) a positive focal power φ0 of 1.0D to +2.50D in a central zone with a diameter D0 of 1.5mm to 2.5mm; b) a positive spherical aberration in the central zone; c) a negative spherical aberration in an annular zone outside the central zone; and d) a focus error of -1.0D to +1.0D in the annular zone.

[0220] In one embodiment, the wavefront procedure further includes using a first laser to generate a baseline refractive correction, or a conventional spherical or spherocylindrical correction, as needed for distance vision defects, where the baseline refractive correction is achieved by either tissue ablation using a UV beam or tissue removal using a short pulse laser.

[0221] 9. Wavefront lenses for contact lens fitting In one aspect of the present invention, a wavefront contact lens for testing human eyes is disclosed, which comprises: 1) a hypothetical, non-eye-specific, theoretical baseline diopter power extending over an optical zone between 5 mm and 9 mm in diameter; and b) at least a central aspheric zone between 2.2 mm and 4.5 mm in diameter at the center of the lens, which uses at least one aspheric surface to induce additional spherical aberration at the center of the eye's pupil.

[0222] In some embodiments, the virtual baseline diopter power comprises at least one of: a) an optically plano-concave with no optical power; b) a correction for astigmatism of the eye; c) a virtual sphero-cylindrical correction.

[0223] In one embodiment, the test contact lens further includes a focus offset in the central aspheric area.

[0224] In another embodiment, the central aspherical zone is configured to have at least one aspheric surface for inducing positive spherical aberration in a first zone and negative spherical aberration in a second zone, and the first zone and the second zone are coaxial.

[0225] In another aspect, a method for prescribing a contact lens is disclosed, comprising the steps of: 1) determining a spherocylinder correction for the contact lens, including astigmatism as specified by the spherical power SPH and / or CYL and AXIS; 2) placing a test contact lens, a wavefront contact lens, on a test eye, the test contact lens comprising: 2a) a hypothetical baseline diopter power extending over an optical zone having a diameter of 5-9 mm; and 2b) at least a central aspheric zone having a diameter D0 of 2.2 mm to 4.5 mm at the center of the lens, the test contact lens using at least one aspheric surface to induce additional spherical aberration at the center of the pupil of the eye; 3) subjectively updating the determined spherocylinder correction for the contact lens using a phoropter; and 4) prescribing a contact lens based on the updated spherocylinder correction and the optical properties of the wavefront contact lens placed on the test eye.

[0226] In yet another aspect, a system for prescribing contact lenses is described, comprising: 1) a wavefront module for measuring aberrations of the eye; 2) a processor module for determining 2a) a spherocylindrical correction of the contact lens, consisting of focus error SPH and / or astigmatism specified by CYL and AXIS, and 2b) determining at least an aspheric component having a diameter of 2.2 mm to 4.5 mm at the center of the lens to induce a spherical aberration in the eye to correct for a predicted residual refractive error of the eye under conventional spherocylindrical correction, 3) a phoropter module for subjectively updating the determined spherocylindrical correction of the contact lens by maintaining or changing at least the spherical power SPH; and 4) an output module for prescribing the contact lens based on the updated spherocylindrical correction and the aspheric component at the center of the lens.

[0227] In one embodiment, the estimated residual refractive error of the eye under conventional sphero-cylindrical correction includes astigmatism, coma, focus error, and presbyopia.

[0228] In another embodiment, subjectively updating the determined sphero-cylindrical correction of the contact lens further comprises placing a wavefront contact lens on the test eye, the wavefront contact lens including at least an aspherical component having a diameter of 2.2 mm to 4.5 mm in a central portion of the lens, the aspherical component of the lens inducing spherical aberration in the eye to be corrected. The system may further provide a choice between conventional contact lenses and wavefront contact lenses.

[0229] In yet another embodiment, at least an aspheric component in the center of the lens is determined for vision optimization with the objectives of: 1) increasing the contrast of the modulation transfer function at high spatial frequencies above 30 cycles / degree, improving best corrected visual acuity to 20 / 20 or better; and 2) eliminating image distortion, particularly eliminating phase reversal of the phase transfer function (PTF) at low spatial frequencies below 30 cycles / degree.

[0230] 10. Therapeutic treatments for higher-order aberrations of the eye Inducing spherical aberration in the center of the eye's pupil for vision correction is effective, resulting in the reduction of uncorrected astigmatism, focus error, coma, and presbyopia. Our wavefront technology lenses are also effective in improving the therapeutic correction of the eye's higher order aberrations.

[0231] In one aspect, a contact lens for therapeutic treatment of an eye is disclosed that comprises: a) a baseline wavefront refractive correction that includes focus error, astigmatism, and higher order Zernike aberrations such as coma and spherical aberration, extending across an optical zone of the lens between 5 mm and 8 mm in diameter for the correction of distance vision defects; and b) at least one aspheric zone in the center of the lens that induces spherical aberration in the center of the pupil of the eye to mitigate imperfections in the correction of distance vision defects.

[0232] In one embodiment, the imperfections in correcting distance vision aberrations include one or more of the following imperfections: 1) misregistration of the baseline wavefront correction with the eye's wavefront error, 2) limitations in correcting some aberrations in the baseline wavefront refractive correction, and 3) imperfections in measuring the baseline wavefront correction for distance vision aberrations.

[0233] In one embodiment, the therapeutic contact lens further comprises an optically clear outer zone having a diameter of between 6.0 and 13 mm.

[0234] In other embodiments, the therapeutic contact lenses are configured as EDOF monofocal lenses, EDOF bifocal lenses, EDOF trifocal lenses, and QACIF lenses.

[0235] 11. Methods and Apparatus for Improving the Vision Apparatus, Including the Eye Inducing spherical aberration in the center of the eye's pupil for vision correction has been found to be effective in correcting astigmatism, coma, focus errors, and presbyopia that remain uncorrected by conventional corrective lenses, and can also be applied to improve vision devices that include the eye as an image sensor.

[0236] In one aspect of the present invention, an improved vision device is disclosed that uses the human eye as an image sensor. The vision device includes: 1) an optical imaging module; and 2) an eyepiece module, which is a lens or group of lenses closest to the eye. Either the eyepiece or the optical imaging module induces spherical aberration at least in the center of the pupil of the human eye, with a diameter D0 between 2.2 mm and 4.5 mm.

[0237] In one embodiment, the vision device is one of a virtual reality (VR) device, a microscope, including a stereo microscope and a surgical microscope, a telescope, including a monocular or binocular, or vision goggles, including night vision goggles and gaming goggles.

[0238] In another embodiment, the optical image module provides one of: a) a microscopic view of a nearby object; b) a telescopic view of a distant object; c) an electronic display view.

[0239] In yet another embodiment, the eyepiece has a central aspheric area that induces spherical aberration in a small numerical aperture near the optical axis, covering eye pupil diameters up to 4.5 mm.

[0240] In yet another embodiment, the central aspherical area of the eyepiece further comprises a focus offset that exceeds the induced spherical aberration.

[0241] In one embodiment, the eyepiece has a central aspheric area to induce a wavefront error comprising: a) a positive focal power of +1.0D to +2.5D in a central area with a diameter D of 1.5mm to 2.5mm; b) additional positive spherical aberration in the central area; and c) negative spherical aberration in an annular area with an outer diameter of 2.5mm to 4.5mm outside the central area.

[0242] In yet another embodiment, the eyepiece further corrects for spherical aberration of the human eye around the pupil when the vision device is used with an eye pupil with a diameter greater than 4.5 mm.

[0243] In one embodiment, the eyepiece induces spherical aberrations of opposite signs in the observer's eye at least at the center of the pupil with a diameter D0 between 3.0 mm and 4.5 mm.

[0244] In another embodiment, inducing spherical aberration at least in the center of the observer's eye pupil is accomplished by adding a phase plate to a conventional eyepiece. The eyepiece may also provide a pupil tracker to assist in focusing for eyes with various degrees of myopia or hyperopia and in aligning the optical axis of the eyepiece with the center of the eye pupil.

[0245] In yet another embodiment, the vision device is further integrated with a surgical instrument or a head-mounted device.

[0246] Another aspect of the invention discloses an eyepiece for inducing spherical aberration in at least a central region of an optical system having a diameter D between 2.2 mm and 4.5 mm, the central region being the lens or group of lenses closest to the eye and having one aspheric surface. In one embodiment, the eyepiece also corrects spherical aberration in the human eye at the periphery of the pupil when the vision device is used with an eye pupil having a diameter greater than 4.5 mm.

[0247] Since its discovery in the 19th century, spherical aberration has been considered an optical defect that causes blurred images, such as astigmatism and coma. However, the present invention has shown that spherical aberration can be intentionally delivered to the center of the eye's pupil in a controlled manner by a lens to treat common refractive errors left uncorrected by ophthalmic lenses, including astigmatism, coma, focus error, and presbyopia, just as some harmful substances and drugs used in medicines to treat diseases can be delivered to the human body in a controlled manner in small enough amounts to be effective. These uncorrected refractive errors reduce the quality of vision correction in almost all eyes, causing poor visual acuity, distorted vision, and nighttime symptoms.

[0248] When these lenses with induced spherical aberration are placed in or on the eye, decentration of the lens from the visual axis of the eye is possible. The optical quality of the lens in the presence of decentration was simulated, and it was concluded that decentration of the lens within 0.5 mm has no or negligible effect on lens performance.

[0249] It should also be noted that excessive spherical aberration around the pupil of the eye can reduce night vision. Spherical aberration around the pupil can be treated in the same way as with conventional aspherical lenses. Wavefront lenses (single vision, progressive, trifocal, and QACIF lenses) offer several options for optical properties beyond the central aspherical zone around the pupil. These wavefront lenses can be configured to include: 1) a spherical zone outside the central aspherical zone; 2) a toric shape for the entire toric lens; or 3) an aspherical zone outside the central aspherical zone to modify the spherical aberration of corrective lenses with high refractive power and / or to correct the mean spherical aberration of normal eyes around the pupil.

[0250] Reference will now be made in detail to embodiments of the disclosed invention, one or more examples of which are illustrated in the accompanying drawings. Each example is provided to illustrate the present technology, not to limit it. Indeed, while the specification has described in detail certain embodiments of the present invention, those skilled in the art will understand that, upon gaining an understanding of the foregoing, they will be able to readily conceive of alterations, variations, and equivalents to these embodiments. For example, features illustrated or described as part of one embodiment can be used with another embodiment to yield still a further embodiment. Accordingly, the present subject matter is intended to cover all such modifications and variations within the scope of the appended claims and their equivalents. These and other modifications and variations to the present invention can be practiced by those skilled in the art without departing from the scope of the present invention, which is particularly set forth in the appended claims. Moreover, those skilled in the art will understand that the foregoing description is merely exemplary and is not intended to limit the present invention.

Claims

1. 1. A non-diffractive multifocal lens for an eye, comprising: an optical system having a front surface and a back surface, the optical system having a diameter D between 5 mm and 8 mm; ２ the optical zone comprises a plurality of optical subzones, the plurality of optical sub-zones include an outer annular optical sub-zone and a central optical sub-zone; (I) Inner diameter of 2.5 mm to 4.5 mm and outer diameter D of 5 mm to 8 mm ２ In the outer annular optical sub-region having The optical system has a baseline diopter power (essentially a single vision lens) or refractive spherical power Φ for baseline correction of the eye's hyperopic distance vision defect. ０ configured to have (II) Diameter D of 2.5 mm to 4.5 mm １ In the central optical sub-area having The central optical sub-zone has a first refractive spherical power Φ １ (Hereinafter, "first focus Φ １ "), and a second refractive spherical power Φ ２ (Hereafter, "second focus Φ ２ ") is configured as a non-diffractive multifocal lens, wherein: (a) the first focal point Φ １ has a refractive power and is configured to correct the distance vision error, and the first focus Φ １ is the baseline diopter power less than 0.4D, and the first focus Φ １ is the diameter D １ and configured to have an extended depth of focus (EDOF) compared to a single focal length lens having the same diameter as the lens; (b) the second focal point Φ ２ is the first focus Φ for correcting presbyopia １ and has a refractive power more positive than the refractive power of the following relation: F ２ =Φ １ +|δΦ| (Formula 1) (In formula 1, |δΦ| is in the range of 0.5D to 3.5D.) It is characterized in that The non-diffractive multifocal lens is achieved by the following (c) and (d): (c) the baseline diopter power or the refractive spherical power Φ ０ to induce a positive spherical aberration in a first area and a negative spherical aberration in a second area, the first and second areas being coaxial, and the first and second areas having a diameter D １ forming the central optical sub-area having (d) Diameter D within 2.5 mm ０ and the central optical zone has a refractive spherical power φ different from the refractive spherical power of the single vision lens of the outer annular optical sub-zone. ０ have A non-diffractive multifocal lens.

2. The central optical sub-zone has, in addition to the first focus Φ1 and the second focus Φ2, a third refractive spherical power Φ for near distance. ３ (Hereafter, "Third Focus Φ ３ ") The second focus is determined by the following relationship: Φ ２ = Φ １ + |δΦ １ | (Equation 2) (In formula 2, |δΦ １ | is in the range of 0.5D to 2.0D.) It is characterized in that The third focus Φ ３ is the following relation: Φ3 = Φ １ + |δΦ １ | + |δΦ ２ | (Equation 3) (In formula 3, |δΦ １ |+|δΦ ２ | is the power difference between the far and near focus, and |δΦ ２ | is greater than 0.5D to create three distinct focal points.) 2. The non-diffractive multifocal lens according to claim 1, wherein:

3. The diameter D of the central optical sub-zone １ 2. The non-diffractive multifocal lens of claim 1, wherein is 3 mm.

4. The diameter D ０ 2. The non-diffractive multifocal lens of claim 1, wherein the difference between the refractive spherical power of the central optical zone and the refractive spherical power of the single vision lens of the outer annular optical sub-zone is less than 3.0D.

5. The diameter D １ The non-diffractive multifocal lens of claim 1, characterized in that the EDOF compared to a single-focus lens having the same diameter can be quantified from the through-focus point spread function or the through-focus modulation transfer function (MTF).

6. The first focus φ １ 2. The non-diffractive multifocal lens of claim 1, wherein the contrast metric is greater than or equal to a threshold of 10% at a spatial frequency of 30 cycles / degree.

7. A non-diffractive multifocal lens as described in claim 1 or 2, wherein the first focus and the second focus, or the first focus, the second focus and the third focus of the non-diffractive multifocal lens in the central optical sub-zone, have a contrast that is greater than or equal to a threshold of 10% at a spatial frequency of 30 cycles per degree associated with a 20 / 20 vision metric.

8. 3. A non-diffractive multifocal lens as described in claim 1 or 2, wherein the first focus and the second focus, or the first focus, the second focus and the third focus of the non-diffractive multifocal lens of the central optical sub-zone are characterized by the through-focus point spread function.

9. The non-diffractive multifocal lens of claim 1, wherein the first focus and the second focus, or the first focus, the second focus and the third focus of the non-diffractive multifocal lens of the central optical sub-zone are characterized by the through-focus modulation transfer function (MTF).

10. The non-diffractive multifocal lens of claim 1 , wherein the central optical sub-zone has at least one aspheric surface.

11. 2. The non-diffractive multifocal lens of claim 1, wherein inducing positive spherical aberration in the first zone and negative spherical aberration in the second zone comprises a gradient index (GRIN) optic.

12. The non-diffractive multifocal lens of claim 1, further comprising a haptic area on the outside of the optical system, and configured as one of an intraocular lens (IOL), a phakic IOL, an implantable contact lens (ICL), or an accommodating intraocular lens (AIOL).

13. The non-diffractive multifocal lens of claim 1 further comprising a non-refractive zone outside the optical system and configured as a contact lens.

14. The induced positive spherical aberration in the first zone and the negative spherical aberration in the second zone are expressed in terms of optical path difference (OPD), or wavefront error, i.e., ρ≦r ０ In this case, OPD(ρ)=S １ ＊ (ρ / r ０ ) ４ r ０ <ρ≦r １ In this case, OPD(ρ) = (-S ２ ) ＊ (ρ / r １ ) ４ where ρ is the polar radius and S １ is positive and represents the positive spherical aberration of the first zone, and r ０ is the radius of the first region less than 1.2 mm and greater than 0.9 mm, and (-S ２ ) is negative and represents the negative spherical aberration of the second zone, and r １ 2. The non-diffractive multifocal lens of claim 1, wherein is an outer diameter smaller than 2.25 mm and larger than 1.25 mm.

15. The lens of the central optical sub-zone further comprises ρ ｎ 15. The non-diffractive multifocal lens of claim 14, which induces a generalized form of spherical aberration characterized as the sum of several terms:

16. The non-diffractive multifocal lens of claim 1 configured as a toric lens.

17. 2. The non-diffractive multifocal lens of claim 1, wherein the outer annular optical sub-zone is configured to include an aspheric surface to modify spherical aberration around the pupil of the human eye and to include correction of mean spherical aberration in the normal group.

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