Ophthalmic lens

Abstract

The invention relates to an ophthalmic lens 1 comprising a lens surface 2 having a lens profile that can be represented by a combination of a standard aspheric profile and an even order aspheric profile. The aspheric profiles are combined such that in a region immediately surrounding an apex 3 of the lens surface, the lens profile converges to the sum of the standard aspheric profile and the even order aspheric profile with decreasing radial distance from the apex, and in a peripheral region surrounding the apex, the lens profile converges to the standard aspheric profile with increasing radial distance from the apex.

Description

Technical Field

[0001] This invention relates to ophthalmic lenses and to a method for manufacturing ophthalmic lenses. Background Technology

[0002] Optical lenses with refractive lens profiles are known to be used in ophthalmology. Such refractive ophthalmic lenses are typically designed to provide sharp vision at essentially a specific distance. Therefore, the focal point of such lenses is usually quite localized, with a relatively narrow depth of focus, which can be understood as the distance at which clear vision is achieved on either side of the point of optimal focus. This narrow depth of focus leads to the problem that visual acuity at other distances remains unsatisfactory. For example, cataract patients whose natural lens has been removed during cataract surgery and replaced with an intraocular ophthalmic lens with a typical refractive surface profile typically regain sharp vision at only one of the far, intermediate, and near distances, while still requiring glasses for all other distances.

[0003] Recently, intraocular lenses that allow for extended focal depths have become available, with various optical concepts explored, including diffractive multifocality, refractive multifocality, and pinhole designs. While these approaches result in improvements in visual acuity at more than one distance, there remains the desire to extend the focal depth of ophthalmic lenses, particularly intraocular lenses, toward intermediate visual distances without sacrificing visual performance at far-sighted distances. Summary of the Invention

[0004] The purpose of this invention is to provide an ophthalmic lens with good farsightedness performance and improved intermediate vision performance.

[0005] In a first aspect of the invention, an ophthalmic lens includes a lens surface having a lens profile that can be represented by a combination of a standard aspherical profile and an even-order aspherical profile, wherein the aspherical profiles are combined such that in a region immediately surrounding a vertex of the lens surface, the lens profile converges to the sum of the standard aspherical profile and the even-order aspherical profile as the radial distance from the vertex decreases, and in a peripheral region surrounding the vertex, the lens profile converges to the standard aspherical profile as the radial distance from the vertex increases.

[0006] It has been found that a lens surface profile that induces an extended focal depth toward intermediate viewing distance can be achieved by combining a standard aspherical profile with an even-order aspherical profile, provided that the combination results in the lens profile converging to the sum of the standard aspherical profile and the even-order aspherical profile with decreasing radial distance from the vertex in the region immediately surrounding the vertex, and converging to the standard aspherical profile with increasing radial distance from the vertex in the peripheral region surrounding the vertex. In particular, ophthalmic lenses with such surface profiles can induce a focal depth extended toward higher optical power, and thus provide improved visual acuity at intermediate distances without sacrificing visual acuity at far distances. The proposed ophthalmic lens surface profile can also induce greater insensitivity to lens eccentricity.

[0007] The radial direction is perpendicular to the central axis of the ophthalmic lens, where the central axis can be an axis of symmetry (preferably rotational symmetry) of the lens surface. The vertex is the position where the central axis passes through the lens surface.

[0008] An aspherical profile is a non-spherical profile. Therefore, an aspherical profile is preferably a profile with a curvature that is not uniform in all places in the radial direction, resulting in a non-constant distribution of optical power across the lens surface. A standard aspherical profile preferably has the form of a conical section (especially a parabola). More specifically, a standard aspherical profile may correspond to a conical section as disclosed, for example, in W.S. Smith's (McGraw-Hill, 2000) textbook "Modern Optical Engineering" or in the user manual of the ray-tracing software Zemax OpticStudio, version 19.4 (Zemax LLC, 2019).

[0009] Even-order aspherical profiles are preferably given by a polynomial function of radial distance having only even-order terms. Thus, for example, the difference between a standard aspherical profile and an even-order aspherical profile is that the standard aspherical profile cannot be accurately described by a polynomial function (in particular, not even by a rational function).

[0010] The combination of aspherical profiles refers to a combination preferentially applied to the entire lens profile. That is, the lens profile is represented by a combination of a standard aspherical profile and an even-order aspherical profile. For example, the sag at each point of the lens profile can be represented as a combination of the sag at the corresponding point of the standard aspherical profile and the sag at the corresponding point of the even-order aspherical profile. In an embodiment, the lens profile can be represented by a function of the radial distance from the vertex, where the function depends on a first aspherical function describing the standard aspherical profile and a second aspherical function describing the even-order aspherical profile, such that the value of the function describing the lens profile at any radial distance is given by a linear combination of the values ​​of the first and second aspherical functions at that radial distance. For example, the function representing the lens profile could be a sag function.

[0011] Therefore, preferably, the lens profile of the lens surface of an ophthalmic lens can be understood as defining a single refractive zone, wherein the refractive power varies across the zone.

[0012] The convergence of the lens profile towards the sum of the standard aspherical profile and the even-order aspherical profile as the radial distance from the vertex decreases is preferably convergence in the inner region around the vertex, particularly in the vertex neighborhood. Therefore, the lens profile can be viewed as varying between a lens profile approximately described by the standard aspherical profile in the outer region around the vertex, and a lens profile approximately described by the sum of the standard aspherical profile and the even-order aspherical profile in the middle region around the vertex (particularly the vertex neighborhood). The outer region around the vertex is preferably the neighborhood of the outer boundary of the lens surface. The convergence of the lens profile can be tested, for example, with respect to a given function of radial distances representing the lens profile by expanding the function as a power series of radial distances at a) the vertex and b) the outer boundary of the lens surface, and comparing the terms in the power series with corresponding terms in the power series of the standard aspherical profile function (particularly at least the first two non-constant terms). Alternatively, the given function can be expressed as a standard aspherical profile function and terms of the remainder, where the constraints of the remainder can be determined with respect to the outer boundaries of a) the vertex and b) the lens surface.

[0013] In implementation, the combination of a standard aspherical profile and an even-order aspherical profile can be represented by a smoothing function of the radial position (i.e., the radial distance from the vertex). This can lead to a reduction in optical aberrations that may cause optical phenomena. The smoothing function is understood herein as a function whose second derivative does not contain any bends, or whose third derivative is continuous. In particular, the smoothing function can be understood as a function whose derivatives are all continuous, i.e., the smoothing function is infinitely differentiable.

[0014] In this implementation, the combination of the standard aspherical profile and the even-order aspherical profile can be represented by a function of radial position, which has a first derivative of zero at the vertices of the lens surface. This avoids undesirable optical effects caused by deflections at the vertices.

[0015] In implementation, the combination of standard aspherical profiles and even-order aspherical profiles can be represented by a function of radial position, which changes the sign of its second derivative as the radial position increases. Ophthalmic lenses can thus be particularly insensitive to eccentricity (i.e., the deviation of the central axis of the ophthalmic lens from the optical axis). Furthermore, insensitivity to lens tilt relative to the optical axis can also be achieved in this way. Insensitivity to eccentricity and tilt refers to insensitivity to the optical properties of the lens (such as, for example, the focal position and depth of focus). Optical properties can be measured based on modulation transfer functions (especially defocus module transfer functions).

[0016] Since the optical power associated with the lens profile is related to the second derivative of the function representing the phase of the light wave propagating through the lens, assuming the refractive index of the lens material is constant, the phase is entirely defined by the surface profile of the lens. It can be deduced that the change in the sign of the second derivative of the surface profile caused by the increase in radial position (i.e., the increase in radial distance from the vertex) leads to a corresponding change in the optical power along the radial position.

[0017] Preferably, the second derivative of the function representing the lens profile changes sign with increasing radial position, such that the optical power associated with the lens profile changes from positive to negative with increasing radial position, and then back to positive. Furthermore, the sign of the second derivative of the function representing the lens profile can change with increasing radial position, such that the optical power associated with the lens profile changes sign an odd number of times (e.g., 3 or 5 times). The optical power associated with the lens profile can be measured specifically relative to the value of the optical power at the apex.

[0018] Preferably, the second derivative of the function representing the lens profile changes sign only in the middle region of the lens surface, which extends from the vertex to a radial distance from the vertex that is less than or equal to two-thirds (preferably less than or equal to half) of the total radial extent of the lens surface. In the case of an intraocular lens, for example, the total radial extent of the lens surface can reach approximately 3 millimeters.

[0019] In a preferred embodiment, the sag function of a standard aspherical surface is defined by the following equation:

[0020]

[0021] Where r represents the radial distance from the vertex of the lens surface, c represents the curvature at the vertex of the lens surface, and k represents the conic constant. The conic constant k is preferably negative. The curvature c at the vertex of the lens surface is preferably positive. In an embodiment, the curvature c at the vertex of the lens surface is a) greater than or equal to 0.005 mm. -1 And b) is less than or equal to 0.25mm -1 In a preferred embodiment, the curvature c at the vertex of the lens surface is a) greater than or equal to 0.005 mm. -1 And b) is less than or equal to 0.08 mm -1 Furthermore, the conic constant k is preferably a) greater than or equal to -800 and b) less than or equal to 5. In a preferred embodiment, the conic constant k is a) greater than or equal to -800 and b) less than or equal to -5. It has been found that using such a standard aspherical profile allows for further improvements in the optical performance of ophthalmic lenses.

[0022] In this document, the sag function representing the lens profile is understood as a measurement of the depth of the lens profile relative to a constant height given by the axial position of the vertex of the lens surface that includes the lens profile. For example, the same lens profile can also be represented by a function measuring the height of the lens surface relative to a plane that virtually intersects the lens with respect to the lens's central axis and / or optical axis, where this alternative function can be given by, for example, the difference between a constant and the sag function of the lens profile.

[0023] In the implementation, the sag function of the even-order aspherical profile is defined by the following equation:

[0024]

[0025] Where r represents the radial distance from the vertex of the ophthalmic lens surface, and A 2n It is a constant. Preferably, the change in the sign of the second derivative of the function representing the lens profile caused by the increase in radial position is related to the constant A. 2n One or more ratios correspond between them. Constant A 2n The values ​​when expressed in mm -2n+1 When units are given, the range is preferably from -10. -2 The value at the order is up to 10 -2 The value at the order. It has been found that using such even-order aspherical profiles also allows for further improvements in the optical performance of ophthalmic lenses.

[0026] In a preferred embodiment, the combination of the standard aspherical profile and the even-order aspherical profile is defined by a combination function that depends on the radial distance from the vertex, such that at a certain radial distance from the vertex, the contributions of the standard aspherical profile and the even-order aspherical profile to the lens profile depend on the radial distance. Therefore, for example, the sag function of the standard aspherical profile and the sag function of the even-order aspherical profile are not simply proportional to each other, such that the function representing the lens profile is not simply a linear combination of the two sag functions.

[0027] In this implementation, the sag function of the lens profile is defined by the following equation:

[0028] S(r)=M(r)S1(r)+(1-M(r))(S1(r)+S2(r)), (3)

[0029] Where r represents the radial distance from the vertex of the lens surface, S1(r) represents the sag function of the standard aspherical profile, S2(r) represents the sag function of the even-order aspherical profile, and M(r) represents the combination function. Specifically, S1(r) and S2(r) can represent the sag functions given in equations (1) and (2) above. Equation (3) above can be equivalently expressed as:

[0030] S2(r)=S1(r)+(1-M(r))S2(r). (4)

[0031] The combination function preferably tends to 0 towards the vertex of the lens surface and preferably tends to 1 towards the outer boundary of the lens surface. It is also preferred that the combination function M(r) monotonically increases in the radial direction, i.e., it does not decrease anywhere in the radial direction. It has been found that using such a combination function also allows for further improvements in the optical performance of ophthalmic lenses.

[0032] In this implementation, the combination function is a smoothing function. Preferably, the combination function is defined by the following equation:

[0033]

[0034] Where A and ρ are constants. More generally, it is preferred that the combination function increases faster in the intermediate radial region than in the central and peripheral radial regions. In an embodiment, the constant A is greater than 2.0 mm. -1 And less than 10.0mm -1 And the constant ρ is greater than 0.3 mm and less than 2.5 mm. In a preferred embodiment, the constant A is greater than 4.0 mm. -1 And less than 7.0mm -1 Furthermore, the constant ρ is greater than 0.3 mm and less than 2.0 mm. These parameters also contribute to further improvements in the performance of ophthalmic lenses.

[0035] Preferably, the sag function S(r) of the lens profile is determined by the following set of parameter ranges: -800≤k≤5; 0.005mm -1 ≤c≤0.25mm -1 2.0mm -1 <A<10.0mm -1 ;0.3mm<ρ<2.5mm;-1.5×10 -2 mm -1 <A2<1.5×10 -2 mm -1 -1.5×10 -2 mm -3 <A4<1.5×10 -2 mm -3 -9.0×10 -3 mm -5 <A6<9.0×10 -3 mm -5 -2.9×10 -2 mm -7 <A8<2.9×10 -2 mm -7 -3.0×10 -2 mm -9 <A 10 <3.0×10 -2 mm -9 -1.2×10 -4 mm -11 <A 12 <1.2×10 -4 mm -11 -1.2×10 -4 mm -11 <A 14 <1.2×10 -4 mm -11 -1.2×10 -4 mm -11 <A 16 <1.2×10 -4 mm -11 In a particular embodiment, the sag function S(r) of the lens profile is determined by the following set of parameter ranges: -800 ≤ k ≤ -5; 0.005 mm -1 ≤c≤0.08mm -1 4.0mm -1 <A<7.0mm -1 ;0.3mm<ρ<2.0mm; 8.9×10 - 5 mm -1<A2<3.0×10 -4 mm -1 8.9×10 -3 mm -3 <A4<1.2×10 -4 mm -3 -9.0×10 -3 mm -5 <A6<4.0×10 -3 mm -5 -2.9×10 -2 mm -7 <A8<2.0×10 -2 mm -7 ; 2.0×10 -2 mm -9 <A 10 <2.8×10 -2 mm -9 -1.0×10 -4 mm -11 <A 12 <1.2×10 -4 mm -11 A 14 =0; A 16 =0.

[0036] In a preferred embodiment, the lens surface with the lens profile is a refractive lens surface. Therefore, the lens surface with the lens profile preferably does not include any diffractive elements. In this way, the monofocality of the ophthalmic lens can be improved.

[0037] In a preferred embodiment, the ophthalmic lens is an intraocular lens. As an intraocular lens, the ophthalmic lens is intended to be placed in the capsular bag of a patient's eye after the removal of an extracapsular cataract, serving as a refractive medium that replaces the eye's natural lens. However, the ophthalmic lens can also be another type of lens, such as a contact lens, or even a lens for eyeglasses, i.e., eyeglasses.

[0038] In another aspect of the invention, a method for manufacturing an ophthalmic lens is proposed, wherein the manufacturing method includes forming a lens profile of the lens surface of the ophthalmic lens, such that the lens profile can be represented by a combination of a standard aspherical profile and an even-order aspherical profile, wherein the aspherical profiles are combined such that in the region immediately surrounding the vertex of the lens surface, the lens profile converges to the sum of the standard aspherical profile and the even-order aspherical profile as the radial distance from the vertex decreases, and in the peripheral region surrounding the vertex, the lens profile converges to the standard aspherical profile as the radial distance from the vertex increases.

[0039] The lens profile can be formed, for example, using known forming processes or another technique commonly used to manufacture lenses. In particular, the lens profile can be formed by casting molding.

[0040] In another aspect of the invention, an ophthalmic lens is proposed that can be manufactured by a manufacturing method.

[0041] It should be understood that the ophthalmic lens of claim 1 and the manufacturing method of claim 15 have similar and / or identical preferred embodiments as defined in the dependent claims.

[0042] It should be understood that the preferred embodiments of the present invention may also be any combination of the dependent claims and the corresponding independent claims. Attached Figure Description

[0043] Figure 1 An embodiment of an ophthalmic lens is illustrated schematically and exemplary.

[0044] Figure 2 The sag function of a lens profile and the sag function of a standard aspherical profile are illustrated schematically and exemplary.

[0045] Figure 3 The sag function of an even-order aspherical profile is illustrated schematically and exemplary.

[0046] Figure 4 The combination function is illustrated schematically and exemplary.

[0047] Figure 5 The difference between the sag function of a lens profile and the sag function of a standard aspherical profile is illustrated schematically and exemplary.

[0048] Figure 6 The far modulation transfer function is illustrated schematically and exemplary.

[0049] Figure 7 The defocus modulation transfer function is illustrated schematically and exemplary.

[0050] Figure 8 The far modulation transfer function at a specific spatial frequency, which depends on the lens eccentricity, is illustrated schematically and exemplary.

[0051] Figure 9 The far modulation transfer function at another specific spatial frequency, which depends on the lens eccentricity, is illustrated schematically and exemplary.

[0052] Figure 10 An illustrative and exemplary illustration shows a device with... Figure 2 The sag functions shown are for different types of lens profiles and standard aspherical profiles.

[0053] Figure 11 An illustrative and exemplary illustration is shown with... Figure 6 The examples shown are remote modulation transfer functions of different types.

[0054] Figure 12 An illustrative and exemplary illustration is shown with... Figure 7 The defocus modulation transfer functions shown are of different types.

[0055] Figure 13 The optical power distribution on the surface of an ophthalmic lens is illustrated schematically and exemplary.

[0056] Figure 14 The sag function of a lens profile and the sag function of a standard aspherical profile in another embodiment are illustrated schematically and exemplary.

[0057] Figure 15 The sag function of an even-order aspherical profile is illustrated schematically and exemplaryly in another embodiment.

[0058] Figure 16 A combination function of another implementation is illustrated schematically and exemplary.

[0059] Figure 17 The difference between the sag function of a lens profile of another embodiment and the sag function of a standard aspherical profile is illustrated schematically and exemplary.

[0060] Figure 18 A remote modulation transfer function of another embodiment is illustrated schematically and exemplary.

[0061] Figure 19 The defocus modulation transfer function of another embodiment is illustrated schematically and exemplary.

[0062] Figure 20 The optical power distribution of an ophthalmic lens surface according to another embodiment is illustrated schematically and exemplary.

[0063] Figure 21 A flowchart illustrating an embodiment of a manufacturing method for producing ophthalmic lenses is provided as an example. Detailed Implementation

[0064] Figure 1 An embodiment of an ophthalmic lens 1 having a smooth lens surface 2 is schematically and exemplaryly illustrated. In this embodiment, the lens surface 2 is radially symmetrical, i.e., rotationally symmetrical about a central axis. The central axis virtually passes through the lens surface 2 at its center 3, wherein... Figure 1Center 3 is schematically indicated by a dot. Lens 1 is attached to a fixation element 4 for securing lens 1 in the eye, replacing the removed natural lens. Therefore, lens 1 is an intraocular lens.

[0065] Since lens surface 2 is radially symmetrical, its vertex is located at center 3. The curvature of lens surface 2 of lens 1 can be characterized by the lens profile, which corresponds to the intersection line of lens surface 2 and a virtual plane that includes the center of lens surface 2 and intersects with... Figure 1 The plan view is orthogonal. Because Figure 1 The lens surface 2 shown is radially symmetrical, therefore the obtained lens profile is independent of the angular orientation of the virtual plane. In other embodiments, the lens surface 2 may include different lens profiles in different radial directions.

[0066] Lens surface 2 is the front surface of lens 1, which has a diameter of 6 mm measured perpendicular to the central axis (i.e., in the radial direction). However, in other embodiments, the diameter may be smaller or larger. Front surface 2 is aspherically curved, i.e., an aspherical surface. Lens 1 also has Figure 1 The rear surface opposite to the front surface 2 is not shown in the diagram. The rear surface of lens 1 can also be an aspherical surface, or it can be a spherical surface.

[0067] Due to the curvature of the lens surface, the lens surface is a refractive surface, wherein two refractive surfaces together impart optical power to the ophthalmic lens 1. The material of lens 1 is a hydrophobic acrylic material comprising agents for absorbing ultraviolet light, such as benzotriazole, and chromophores for filtering blue light, such as monomethylimine, wherein the material is biocompatible and foldable. For further details regarding preferred lens materials, refer to US 8,647,383 B2 and US 9,265,603 B2. The refractive index of the lens material may be, for example, 1.544.

[0068] Figure 2 A graph of the sag function S(r) representing the lens profile of lens surface 2 is shown schematically and exemplary. Figure 2 The graph of the sag function S1(r) of a standard aspherical profile is also schematically and exemplaryly shown, and Figure 3 A schematic and exemplary graph of the sag function S2(r) of an even-order aspherical profile is shown, wherein its sag function S(r) is in Figure 2 The lens profile shown can be obtained from its sag function S1(r) in Figure 2 The standard aspherical profile and its sag function S2(r) shown in the figure are in Figure 3The combination representation of even-order aspherical profiles is shown in the figure. The combination of two aspherical profiles corresponding to the combination of the corresponding sag functions S1(r) and S2(r) can be represented by the combination function M(r). Figure 2 and Figure 3 The horizontal axis of the graph shown indicates the radial coordinate, which defines the radial distance r from the vertex to the corresponding position on the lens surface 2. This radial distance r is measured perpendicular to the central axis of the lens 1.

[0069] from Figure 2 As can be seen, the lens surface sag function S(r) is a smooth function of the radial position r. This smoothness of the radial position r means that, in particular, the first derivative of S(r) is continuous over the entire range of the radial position. The function S(r) extends from 0 at the lens center r = 0 to the radius r. B The value is positive within a range of approximately 0.175 mm at the outer boundary of the lens surface at r = 3 mm. At the vertex located at the center of the lens, r = 0, the lens surface sag function S(r) has a zero first derivative. In fact, in Figure 2 In the diagram shown, the difference between the lens surface sag function S(r) and the standard aspherical profile sag function S1(r) is almost invisible due to the resolution of the axes. The standard aspherical profile sag function S1(r) is defined by the above equation (1), where the curvature c at the vertex of the lens surface corresponds to the convex shape, and the conic constant k is negative, which means that the standard aspherical profile shown is a parabola.

[0070] The value of c can be regarded as a reference curvature corresponding to the reference optical power of lens 1, wherein the reference optical power can be selected based on the prescription in the clinical context.

[0071] A standard aspherical profile can also be considered a standard single-focal profile because a lens with such a profile will produce a essentially single, essentially localized focal point. Its sag function S(r) is... Figure 2 The reference optical power of lens 1 shown is approximately 20 diopters, appropriately chosen with a conic constant k. The reference optical power corresponds to the value c of the curvature at the vertex of lens surface 2.

[0072] Figure 3 The even-order aspherical profile sag function S2(r) shown in the curve is defined by the above equation (2), where the horizontal axis of the curve indicates the radial coordinate, the absolute value of which corresponds to the radial distance r from the vertex of the lens surface 2, and the constant A 2n They were appropriately selected. Because... Figure 3 The resolution of the vertical axis of the graph shown is... Figure 2The curves shown are quite different, thus appearing as if the even-order aspherical profile sag function S2(r) is essentially zero over half the radial extent of lens surface 2. However, only in this intermediate region of lens surface 2 is the even-order aspherical profile relative to its sag function S1(r)... Figure 2 The standard aspherical profile shown is not negligible.

[0073] exist Figure 4 The combination function M(r) corresponding to the exemplary lens 1 is shown below. The combination function M(r) corresponding to the exemplary lens 1 is defined by a smooth function of the radial position r, and its form is given in equation (5) above, where the constants A and ρ are appropriately chosen. Figure 2 The lens surface sag function of lens surface 2 shown is Figure 2 The standard aspherical profile sag function S1(r) and shown are... Figure 3 The combination of even-order aspherical profile sag functions S2(r) shown is given, where the combination of two sag functions is... Figure 4 The combined function M(r) shown is defined as follows. In this embodiment, the combined function M(r) depends on the radial distance from the vertex, such that the contribution of the standard aspherical profile sag function S1(r) to the lens profile sag function S(r) of lens 1 at a certain radial distance from the vertex and the contribution of the even-order aspherical profile sag function S2(r) to the lens profile sag function S(r) of lens 1 depend on the radial distance r. Therefore, the combined function M(r) can also be regarded as a masking function that masks the contributions from two different aspherical profiles, where the degree of masking depends on the radial position r.

[0074] The lens surface 2, described by the obtained lens profile sag function S(r), is configured such that in the region immediately surrounding the vertex of the lens surface 2, the lens profile converges to the sum of the standard aspherical profile described by S1(r) and the even-order aspherical profile described by S2(r) as the radial distance r from the vertex decreases, and in the outer region surrounding the vertex, the lens profile converges to the standard aspherical profile as the radial distance r from the vertex increases.

[0075] Since the standard aspherical profile sag function S1(r), the even-order aspherical profile sag function S2(r), and the combined function M(r) in this embodiment are all smooth functions, the combined sag function, i.e., the lens profile sag function S(r), is also smooth.

[0076] In this embodiment, the aspherical profile sag functions S1(r) and S2(r) that are combined to obtain the lens profile sag function S(r) are designed such that the second derivative of the lens profile sag function S(r) changes sign with increasing radial position, which is reflected by the intermediate radial region where the optical power associated with lens surface 2 becomes negative. This region is an annular region extending around a radial position of approximately 0.7 mm on lens surface 2. The lens profile sag function S(r) of lens 1 is defined by equation (3) above, which is equivalent to equation (4) above.

[0077] for Figures 1 to 4 The embodiment also shown in the figure, the second term of equation (4) corresponding to the difference (1-M(r))S2(r) between the lens profile sag function S(r) and the standard aspherical profile sag function S1(r) is in Figure 5 It is shown in the middle. According to, as Figure 5 The value of the difference function (1-M(r))S2(r) seen on the vertical axis of the graph shown is... Figure 2 The reason why the difference between the medium lens profile sag function S(r) and the standard aspherical profile sag function S1(r) is almost invisible is obvious.

[0078] As will be shown below, although by Figure 5 The difference function (1-M(r))S²(r) shown in the figure appears to have a small value, but the optical effect produced by this seemingly small deviation is unexpectedly large. Figure 5 The difference function (1-M(r))S2(r) shown in the diagram assumes a value corresponding to only a seemingly small deviation between lens surface 2 and the standard aspherical surface. In fact, the deviation between lens surface 2 and the standard aspherical surface can be designed to be only large enough and precisely positioned to widen the focal depth of lens 1 towards a smaller focal distance. Furthermore, the deviation can be designed to be small enough and precisely positioned to avoid undesirable optical phenomena generated by lens surface 2.

[0079] Figure 6 The modulation transfer function (MTF) calculated for a human eye in which an ophthalmic lens 1 has an aperture of 3.0 mm and 4.5 mm is schematically and exemplaryly illustrated, wherein the calculation is performed for a farsighted distance. Figure 6 As can be seen, regardless of the aperture, the modulation transfer function, which can be regarded as a measure of imaging quality, decreases only relatively slowly towards higher spatial frequencies.

[0080] Figure 7 The defocus modulation transfer function, calculated for a human eye with lens 1 placed therein, is illustrated schematically and exemplarily at a spatial frequency of 50 line pairs per millimeter. The defocus modulation transfer function can also be referred to as the defocus response curve. Figure 7 The focal modulation transfer function is shown for apertures of 3.0 mm and 4.5 mm. The horizontal axis indicates the movement of the focal point, i.e., the focal distance measured relative to the reference optical power of lens 1, where a negative focal movement corresponds to a higher optical power relative to the reference optical power. For Figure 7 The two aperture sizes shown have a wider peak at the primary, far focal point compared to the corresponding standard aspherical lens, particularly in the negative focal shift direction. Therefore, Figure 7 It shows that visual acuity of the human eye can be improved at intermediate visual distances.

[0081] Figure 8 The modulation transfer function corresponding to lens 1, which can be considered an enhanced aspherical lens, is schematically and exemplaryly shown at a spatial resolution of 50 line pairs per millimeter, for a distant viewing distance and with an aperture of 3 millimeters. Compared to the modulation transfer function of a standard aspherical lens, the modulation transfer function corresponding to lens 1, which can be considered an enhanced aspherical lens, depends on the lens's eccentricity (i.e., the deviation of the central axis of the lens surface from the optical axis). Figure 8 As can be seen, compared to a modulation transfer function corresponding to a standard aspherical lens, the value of the modulation transfer function decreases only slightly. This behavior is... Figure 9 It is also visible in the middle. Figure 9 and Figure 8 Correspondingly, the spatial resolution is chosen to be 100 line pairs per millimeter. For eccentricities exceeding approximately 0.6 millimeters, the modulation transfer function for lens 1 is even higher at both 50 line pairs per millimeter and 100 line pairs per millimeter compared to a standard aspherical lens.

[0082] Figure 10 This schematically and exemplary illustration shows an optical power of 6 diopter (i.e., a power greater than that provided by...). Figure 1 The lens surface 2 shown provides a small optical power, which can be obtained by... Figure 2 The sag function shown represents the lens profile sag function of the lens surface (optical power) and the corresponding standard aspherical profile sag function. Figure 10 As can be seen, the deviation between the sag function of the lens surface providing such a small optical power and the corresponding standard aspherical profile sag function is higher than the corresponding deviation of lens surface 2.

[0083] exist Figure 11 In the middle, for those that have been placed in people's eyes, as if by Figure 10 The modulation transfer function of the lens surface shown is schematically and exemplary, calculated for the far-seeing distance and for apertures of 3.0 mm and 4.5 mm, respectively. From Figure 11 It can be seen that, for something like... Figure 10For lens surfaces like the one shown, regardless of the aperture, the modulation transfer function decreases only relatively slowly toward higher spatial frequencies.

[0084] Figure 12 The illustration schematically and exemplaryly shows the spatial frequency at 50 line pairs per millimeter, for the surface where it has been placed. Figure 10 The defocus modulation transfer function of the lens, calculated by the human eye, is shown. Defocus modulation transfer functions for apertures of 3.0 mm and 4.5 mm are shown. The horizontal axis indicates focus movement, i.e., the focus distance measured relative to the reference optical power of the lens, where a negative focus movement corresponds to a higher optical power relative to the reference optical power. For Figure 12 The two aperture sizes shown indicate that the primary, far-focal peak is broadened relative to the corresponding standard aspherical lens, particularly in the negative focal shift direction. Therefore, Figure 12 It shows that it can also be used at medium sight distance. Figure 10 The lens on the surface shown improves the visual acuity of the human eye.

[0085] Figure 13 An illustrative and exemplary diagram is shown of an optical power distribution corresponding to a lens profile, which can be represented by a combination of a standard aspherical profile and an even-order aspherical profile. The illustrated power distribution includes local extrema corresponding to the poles of the second derivative of a function representing the corresponding lens profile (i.e., the lens's corresponding sag function), referring to the optical power measured relative to a reference optical power at the center of the lens. The optical power tends to a constant value towards the outer boundary of the lens surface. Figure 13 The optical power distribution shown illustrates the relative spherical power, and is consistent with that of the optical power distribution shown in the figure. Figures 2 to 5 The lens profile shown corresponds to the one depicted.

[0086] Figure 14 A graph illustrating, and exemplarily demonstrating, of another embodiment of the sag function S(r) that can represent the lens profile of lens surface 2 is shown. Additionally, like... Figure 2 Same Figure 14 It also schematically and exemplary shows a graph of the sag function S1(r) of a standard aspherical profile, and Figure 15 A schematic and exemplary graph of the sag function S2(r) of an even-order aspherical profile corresponding to another embodiment is shown. The sag function S(r) is... Figure 14 The lens profile shown can be obtained from its sag function S1(r) in Figure 14 The standard aspherical profile and its sag function S2(r) shown in the figure are in Figure 15The combination representation of even-order aspherical profiles is shown in the figure. The combination of two aspherical profiles corresponding to the combination of the corresponding sag functions S1(r) and S2(r) can be represented by the combination function M(r). Figure 14 and Figure 15 The horizontal axis of the graph shown indicates the radial coordinate, which defines the radial distance r from the vertex of the corresponding position on the lens surface 2. This radial distance r is measured perpendicular to the central axis of the lens 1.

[0087] from Figure 14 As can be seen, the lens surface sag function S(r) is a smooth function of the radial position r. This smoothness of the radial position r means that, in particular, the first derivative of S(r) is continuous over the entire range of the radial position. The function S(r) extends from 0 at the lens center r = 0 to the radius r. B The value is positive within a range of approximately 0.40 mm at the outer boundary of the lens surface at r = 3 mm. At the vertex located at the center of the lens (r = 0), the lens surface sag function S(r) has a zero first derivative. In fact, in Figure 14 In this embodiment, the difference between the lens surface sag function S(r) and the standard aspherical profile sag function S1(r) is almost invisible due to the resolution of the axes of the curve shown. The standard aspherical profile sag function S1(r) is defined by the above equation (1), where the curvature c at the vertex of the lens surface corresponds to convexity, and the conic constant k is negative, which means that the standard aspherical profile shown is parabolic. In this embodiment, the value of c can also be regarded as a reference curvature corresponding to the reference optical power of lens 1, where the reference optical power can be selected based on the prescription in the clinical context. Furthermore, in this embodiment, the standard aspherical profile can also be regarded as a standard single-focal profile, because a lens with such a standard aspherical profile essentially produces a single, essentially localized focal point. Its sag function S(r) is in Figure 14 The reference optical power of the lens 1 shown can be relatively high, and the conic constant k can be appropriately selected. In particular, in this embodiment, the conic constant k can be -6. The reference optical power corresponds to the value c of the curvature at the vertex of the lens surface 2.

[0088] Figure 15 The even-order aspherical profile sag function S2(r) shown in the curve is defined by the above equation (2), where the horizontal axis of the curve indicates the radial coordinate, the absolute value of which corresponds to the radial distance r to the vertex of the lens surface 2, and the constant A 2n It is appropriately selected. In particular, in this embodiment, the following constant is applied: A2 = 1.2 × 10 -3 mm -1 A4 = 1.3 × 10 -2mm -3 A6 = -6.0 × 10 -3 mm -5 A8 = -1.8 × 10 -2 mm -7 A 10 =2.2×10 -2 mm -9 A 12 =0, A 14 =0, A 16 =0.

[0089] because Figure 15 The resolution of the vertical axis of the graph shown is... Figure 14 The curves shown are quite different, and therefore in these graphs, it appears as if the even-order aspherical profile sag function S2(r) is essentially 0 over half the radial extent of lens surface 2. However, only in this intermediate region of lens surface 2 does the even-order aspherical profile exhibit sag function S1(r) relative to its sag function. Figure 14 The standard aspherical profile shown is not negligible.

[0090] Figure 16 Another embodiment of the combination function M(r) corresponding to exemplary lens 1 is shown. The combination function M(r) corresponding to exemplary lens 1 is defined by a smooth function of radial position r, and its form is given in equation (5) above, where constants A and ρ are appropriately chosen. In particular, in this embodiment, constant A is 4.0 mm. -1 And the constant ρ is 0.74 mm.

[0091] Figure 14 The lens surface sag function of lens surface 2 shown is Figure 14 The standard aspherical profile sag function S1(r) and shown are... Figure 15 The combination of even-order aspherical profile sag functions S2(r) shown is given, where the combination of two sag functions is... Figure 16 The combined function M(r) is defined as shown. In this embodiment, the combined function M(r) depends on the radial distance from the vertex, such that at a certain radial distance from the vertex, the contributions of the standard aspherical profile sag function S1(r) to the lens profile sag function S(r) of lens 1 and the contributions of the even-order aspherical profile sag function S2(r) to the lens profile sag function S(r) of lens 1 depend on the radial distance r. Therefore, the combined function M(r) can also be viewed as a masking function that masks the contributions from two different aspherical profiles, where the degree of masking depends on the radial position r.

[0092] In this embodiment, the lens surface 2, described by the obtained lens profile sag function S(r), is configured such that in the region immediately surrounding the vertex of the lens surface 2, the lens profile converges to the sum of the standard aspherical profile described by S1(r) and the even-order aspherical profile described by S2(r) as the radial distance r from the vertex decreases; and in the peripheral region surrounding the vertex, the lens profile converges to the standard aspherical profile as the radial distance r from the vertex increases. Furthermore, in this embodiment, since the standard aspherical profile sag function S1(r), the even-order aspherical profile sag function S2(r), and the combined function M(r) are all smooth functions, the combined sag function, i.e., the lens profile sag function S(r), is also smooth.

[0093] against Figures 14 to 16 The embodiments shown are in Figure 17 The second term of equation (4) is shown, which corresponds to the difference (1-M(r))S2(r) between the lens profile sag function S(r) and the standard aspherical profile sag function S1(r). According to... Figure 17 The value of the difference function (1-M(r))S2(r) shown on the vertical axis of the graph is... Figure 14 The reason why the difference between the medium lens profile sag function S(r) and the standard aspherical profile sag function S1(r) is almost invisible is obvious.

[0094] As will be shown below, although it corresponds only to the seemingly small deviation between lens surface 2 and the standard aspherical surface, Figure 17 The difference function (1-M(r))S2(r) shown in the figure seems to have a small value, but in this embodiment, the optical effect produced by the seemingly small deviation is surprisingly large.

[0095] Figure 18 The MTF calculated for a human eye in which an ophthalmic lens 1 has an aperture of 3.0 mm and 4.5 mm is illustrated schematically and exemplary, wherein the calculation is performed for a farsighted distance. Figure 18 As can be seen, regardless of the aperture, the modulation transfer function, which can be regarded as a measure of imaging quality, decreases only relatively slowly towards higher spatial frequencies.

[0096] Figure 19 The illustration schematically and exemplaryly shows the spatial frequency at 50 line pairs per millimeter, for which a [structure] has been placed. Figures 14 to 17 The defocus modulation transfer function of lens 1, as calculated by the human eye, is shown in another embodiment of the lens profile. Figure 19The diagram shows the defocus modulation transfer functions for apertures of 3.0 mm and 4.5 mm. The horizontal axis indicates focus movement, i.e., the focus distance measured relative to the reference optical power of lens 1, where a negative focus movement corresponds to a higher optical power relative to the reference optical power. For Figure 19 The two aperture sizes shown indicate that the width of the primary, far-focus peak is widened relative to the corresponding standard aspherical lens, particularly in the direction of negative focus movement. Therefore, Figure 19 This demonstrates that visual acuity of the human eye can be improved at intermediate visual distances.

[0097] Figure 20 The diagram schematically and exemplaryly illustrates an optical power distribution corresponding to a lens profile that can be represented by a combination of standard aspherical profiles and even-order aspherical profiles. The illustrated power distribution includes local extrema corresponding to the poles of the second derivative of a function representing the corresponding lens profile (i.e., the lens's corresponding sag function), referring to the optical power measured relative to a reference optical power at the center of the lens. The optical power tends to a constant value towards the outer boundary of the lens surface. Figure 20 The optical power distribution shown illustrates the relative spherical power, and is consistent with that of the optical power distribution shown in the figure. Figures 14 to 17 The lens profile shown corresponds to the one depicted.

[0098] In the following text, reference will be made to Figure 21 The flowchart shown exemplarily describes an implementation of a manufacturing method for producing ophthalmic lenses.

[0099] In step 101, a mathematical combination of a standard aspherical profile and an even-order aspherical profile is provided, wherein the aspherical profiles are combined such that in the region immediately surrounding the vertex of the lens surface, the lens profile converges to the sum of the standard aspherical profile and the even-order aspherical profile decreases with radial distance from the vertex, and in the peripheral region surrounding the vertex, the lens profile converges to the standard aspherical profile increases with radial distance from the vertex.

[0100] In step 102, the ophthalmic lens is formed such that the surface of the lens conforms to a combination of a standard aspherical profile and an even-order aspherical profile. For example, the lens can be formed using known molding processes and known lathe cutting processes, or another technique commonly used to manufacture lenses.

[0101] Although the lens is rotationally symmetric in the above embodiment, the lens may also have an annular lens surface. In this case, a first lens profile may be provided in a first radial direction of the lens surface, and a second lens profile may be provided with respect to a second radial direction of the lens surface, wherein the first and second radial directions may be perpendicular to each other.

[0102] Based on the study of the accompanying drawings, this disclosure, and the appended claims, those skilled in the art can understand and implement other variations of the disclosed embodiments in the practice of the protected invention.

[0103] In the claims, the word "comprising" does not exclude other elements or steps, and the indefinite articles "a" or "an" do not exclude multiple.

[0104] Any reference numerals in the claims should not be construed as limiting the scope.

Claims

1. An ophthalmic lens (1) comprising a lens surface (2) having a lens profile capable of being represented by a combination of a standard aspherical profile and an even-order aspherical profile, wherein, The aspherical profiles are combined such that, in the region immediately surrounding the vertex (3) of the lens surface, the lens profile converges to the sum of the standard aspherical profile and the even-order aspherical profile as the radial distance from the vertex (3) decreases, and in the peripheral region surrounding the vertex (3), the lens profile converges to the standard aspherical profile as the radial distance from the vertex (3) increases. The sag function of the standard aspherical profile is defined by the following equation: ， in, The radial distance from the vertex (3) of the lens surface (2) is indicated. The curvature at the vertex (3) of the lens surface (2) and Represents the conic constant. The sag function of the even-order aspherical profile is defined by the following equation: ， in, The radial distance from the vertex (3) of the ophthalmic lens surface (2) and It is a constant. The sag function of the lens profile is defined by the following equation: ， in, The radial distance from the vertex (3) of the lens surface (2) is indicated. The sag function represents the standard aspherical profile. The sag function representing the even-order aspherical profile, and This represents the combined function. The combination function is defined by the following equation: ， in, and It is a constant.

2. The ophthalmic lens (1) as defined in claim 1, wherein, The combination of the standard aspherical profile and the even-order aspherical profile can be represented by a smooth function of radial position.

3. The ophthalmic lens (1) as defined in any one of claims 1 and 2, wherein, The combination of the standard aspherical profile and the even-order aspherical profile can be represented by a function of radial position, which has a first derivative of zero at the vertex (3) of the lens surface.

4. The ophthalmic lens (1) as defined in any one of claims 1 and 2, wherein, The combination of the standard aspherical profile and the even-order aspherical profile is represented by a function of the radial position, the sign of the second derivative of which changes as the radial position increases.

5. The ophthalmic lens (1) as defined in any one of claims 1 and 2, wherein, The curvature at the vertex of the lens surface (2) Yes: a) Greater than or equal to 0.005 mm -1 And b) less than or equal to 0.25 mm -1 .

6. The ophthalmic lens (1) as defined in any one of claims 1 and 2, wherein, The conic constant Yes: a) greater than or equal to -800 and b) less than or equal to 5.

7. The ophthalmic lens (1) as defined in any one of claims 1 and 2, wherein, The curvature at the vertex of the lens surface (2) Yes: a) Greater than or equal to 0.005 mm -1 And b) less than or equal to 0.25 mm -1 , and therein, the conic constant Yes: a) greater than or equal to -800 and b) less than or equal to 5.

8. The ophthalmic lens (1) as defined in any one of claims 1 and 2, wherein, constant Greater than and less than and constants Greater than 0.3 mm and less than 2.5 mm.

9. The ophthalmic lens (1) as defined in claim 8, wherein, The curvature at the vertex of the lens surface (2) Yes: a) Greater than or equal to 0.005 mm -1 And b) less than or equal to 0.25 mm -1 .

10. The ophthalmic lens (1) as defined in claim 8, wherein, The conic constant Yes: a) greater than or equal to -800 and b) less than or equal to 5.

11. The ophthalmic lens (1) as defined in claim 8, wherein, The curvature at the vertex of the lens surface (2) Yes: a) Greater than or equal to 0.005 mm -1 And b) less than or equal to 0.25 mm -1 , and therein, the conic constant Yes: a) greater than or equal to -800 and b) less than or equal to 5.

12. The ophthalmic lens (1) as defined in any one of claims 1 and 2, wherein, The ophthalmic lens (1) is an intraocular lens.

13. A method for manufacturing an ophthalmic lens (1) as defined in any one of claims 1 to 12, wherein, The manufacturing method includes: forming (102) a lens profile of the lens surface (2) of an ophthalmic lens (1) such that the lens profile can be represented by a combination of a standard aspheric profile and an even-order aspheric profile, wherein the aspheric profiles are combined such that in the region immediately surrounding the vertex (3) of the lens surface (2), the lens profile converges to the sum of the standard aspheric profile and the even-order aspheric profile as the radial distance to the vertex (3) decreases, and in the peripheral region surrounding the vertex (3), the lens profile converges to the standard aspheric profile as the radial distance to the vertex (3) increases.

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