Abstract
The invention relates to an ophthalmic lens 1 comprising a lens surface 2 with a lens profile being representable 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 the vertex 3 of the lens surface, the lens profile converges to a sum of the standard aspheric profile and the even-order aspheric profile with decreasing radial distance to the vertex and, in an outer region surrounding the vertex, the lens profile converges to the standard aspheric profile with increasing radial distance to the vertex.
Claims
1. An ophthalmic lens comprising a lens surface with a lens profile being representable by a combination of a standard aspheric profile and an even-order aspheric profile, wherein the aspheric profiles are combined such that, in a region immediately surrounding the vertex of the lens surface, the lens profile converges to a sum of the standard aspheric profile and the even-order aspheric profile with decreasing radial distance to the vertex and, in an outer region surrounding the vertex, the lens profile converges to the standard aspheric profile with increasing radial distance to the vertex.
2. The ophthalmic lens as defined by claim 1, wherein the combination of the standard aspheric profile and the even-order aspheric profile is representable by a smooth function of the radial position.
3. The ophthalmic lens as defined by claim 1, wherein the combination of the standard aspheric profile and the even-order aspheric profile is representable by a function of the radial position, which has a first-order derivative of zero at the vertex of the lens surface.
4. The ophthalmic lens as defined by claim 1, wherein the combination of the standard aspheric profile and the even-order aspheric profile is representable by a function of the radial position, which changes the sign of the second-order derivative with increasing radial position.
5. The ophthalmic lens as defined by claim 1, wherein the sag function of the standard aspheric profile is defined by wherein r denotes the radial distance to the vertex of the lens surface, c denotes the curvature at the vertex of the lens surface and k denotes the conic constant.
6. The ophthalmic lens as defined by claim 5, wherein the curvature c at the vertex of the lens surface is a) larger than or equal to 0.005 mm.sup.−1 and b) smaller than or equal to 0.25 mm.sup.−1.
7. The ophthalmic lens as defined by claim 5, wherein the conic constant k is a) larger than or equal to −800 and b) smaller than or equal to 5.
8. The ophthalmic lens as defined by claim 1, wherein the sag function of the even-order aspheric profile is defined by wherein r denotes the radial distance to the vertex of the ophthalmic lens surface and the A.sub.2n are constants.
9. The ophthalmic lens as defined by claim 1, wherein the combination of the standard aspheric profile and the even-order aspheric profile is definable by a combination function which depends on the radial distance to the vertex such that the contribution of the standard aspheric profile and the contribution of the even-order aspheric profile to the lens profile at a certain radial distance to the vertex depends on the radial distance.
10. The ophthalmic lens as defined by claim 9, wherein a sag function of the lens profile is defined by
S(r)=M(r)S.sub.1(r)+(1−M(r))(S.sub.1(r)+S.sub.2(r)), wherein r denotes the radial distance to the vertex of the lens surface, S.sub.1(r) denotes a sag function of the standard aspheric profile, S.sub.2(r) denotes a sag function of the even-order aspheric profile and M(r) denotes the combination function.
11. The ophthalmic lens as defined by claim 9, wherein the combination function is a smooth function.
12. The ophthalmic lens as defined by claim 11, wherein the combination function is defined by
M(r)=½(1+tan h(A(r−ρ))), wherein A and ρ are constants.
13. The ophthalmic lens as defined by claim 12, wherein the constant A is larger than 2.0 mm.sup.−1 and smaller than 10.0 mm.sup.−1, and the constant p is larger than 0.3 mm and smaller than 2.5 mm.
14. The ophthalmic lens as defined by claim 1, wherein the ophthalmic lens is an intraocular lens.
15. A manufacturing method for manufacturing an ophthalmic lens as defined by claim 1, wherein the manufacturing method comprises forming a lens profile of a lens surface of the ophthalmic lens such that it is representable by a combination of a standard aspheric profile and an even-order aspheric profile, wherein the aspheric profiles are combined such that, in a region immediately surrounding the vertex of the lens surface, the lens profile converges to a sum of the standard aspheric profile and the even-order aspheric profile with decreasing radial distance to the vertex and, in an outer region surrounding the vertex, the lens profile converges to the standard aspheric profile with increasing radial distance to the vertex.
16. The ophthalmic lens as defined by claim 2, wherein the combination of the standard aspheric profile and the even-order aspheric profile is representable by a function of the radial position, which has a first-order derivative of zero at the vertex of the lens surface.
17. The ophthalmic lens as defined by claim 6, wherein the conic constant k is a) larger than or equal to −800 and b) smaller than or equal to 5.
18. The ophthalmic lens as defined by claim 10, wherein the combination function is a smooth function.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
[0034] FIG. 1 shows schematically and exemplarily an embodiment of an ophthalmic lens,
[0035] FIG. 2 shows schematically and exemplarily a sag function of the lens profile and a sag function of a standard aspheric profile,
[0036] FIG. 3 shows schematically and exemplarily a sag function of an even-order aspheric profile,
[0037] FIG. 4 shows schematically and exemplarily a combination function,
[0038] FIG. 5 shows schematically and exemplarily the difference between a sag function of a lens profile and a sag function of a standard aspheric profile,
[0039] FIG. 6 shows schematically and exemplarily a far modulation transfer function,
[0040] FIG. 7 shows schematically and exemplarily a through-focus modulation transfer function,
[0041] FIG. 8 shows schematically and exemplarily a far modulation transfer function at a particular spatial frequency depending on a lens decentration,
[0042] FIG. 9 shows schematically and exemplarily a far modulation transfer function at another particular spatial frequency depending on a lens decentration,
[0043] FIG. 10 shows schematically and exemplarily a sag function of a lens profile and a sag function of a standard aspheric profile which are of a different type than the sag functions shown in FIG. 2,
[0044] FIG. 11 shows schematically and exemplarily a far modulation transfer function of a different type than the one shown in FIG. 6,
[0045] FIG. 12 shows schematically and exemplarily a through-focus modulation transfer function of a different type than the one shown in FIG. 7,
[0046] FIG. 13 shows schematically and exemplarily an optical power profile of an ophthalmic lens surface,
[0047] FIG. 14 shows schematically and exemplarily a sag function of a lens profile and a sag function of a standard aspheric profile of a further embodiment,
[0048] FIG. 15 shows schematically and exemplarily a sag function of an even-order aspheric profile of the further embodiment,
[0049] FIG. 16 shows schematically and exemplarily a combination function of the further embodiment,
[0050] FIG. 17 shows schematically and exemplarily the difference between the sag function of the lens profile and the sag function of the standard aspheric profile of the further embodiment,
[0051] FIG. 18 shows schematically and exemplarily a far modulation transfer function for the further embodiment,
[0052] FIG. 19 shows schematically and exemplarily a through-focus modulation transfer function for the further embodiment,
[0053] FIG. 20 shows schematically and exemplarily an optical power profile of the ophthalmic lens surface of the further embodiment, and
[0054] FIG. 21 shows a flowchart exemplarily illustrating an embodiment of a manufacturing method for manufacturing an ophthalmic lens.
DETAILED DESCRIPTION OF EMBODIMENTS
[0055] FIG. 1 shows schematically and exemplarily an embodiment of an ophthalmic lens 1 having a smooth lens surface 2. The lens surface 2 is, in this embodiment, radially symmetric, i.e. symmetric against rotations about a central axis. The central axis virtually pierces through the lens surface 2 at a center 3 of the lens surface 2, wherein the center 3 is schematically indicated in FIG. 1 by a point. The lens 1 is attached to fixing elements 4 for fixing the lens 1 in an eye, in order to replace a natural lens, which has been removed, by the lens 1. Thus, the lens 1 is an intraocular lens.
[0056] Since the lens surface 2 is radially symmetric, the vertex of the lens surface 2 lies at the center 3. The curvature of the lens surface 2 of the lens 1 can be characterized by a lens profile, which corresponds to the line of intersection of the lens surface 2 with a virtual plane that includes the center of the lens surface 2 and is orthogonal to the plan view of FIG. 1. Since the lens surface 2 shown in FIG. 1 is radially symmetric, the so obtained lens profile is independent of the angular orientation of this virtual plane. In other embodiments, the lens surface 2 may comprise different lens profiles in different radial directions.
[0057] The lens surface 2 is an anterior surface of the lens 1 with a diameter, measured perpendicular to the central axis, i.e. in radial direction, of 6 mm. However, in other embodiments the diameter can also be smaller or larger. The anterior surface 2 is curved aspherically, i.e. is an aspheric surface. The lens 1 also has a posterior surface not shown in FIG. 1, which opposes the anterior surface 2. The posterior surface of the lens 1 can also be an aspheric surface, or it can be a spherical surface.
[0058] Due to their curvatures, the lens surfaces are refractive surfaces, wherein the two refractive surfaces jointly endow the ophthalmic lens 1 with an optical power. The material of the lens 1 is a hydrophobic acrylic material comprising an agent like benzotriazole for absorbing ultraviolet light and a blue-light filtering chromophore like monomethine, wherein the material is biocompatible and foldable. For more details regarding preferred lens materials, reference is made to U.S. Pat. Nos. 8,647,383 B2 and 9,265,603 B2. The refractive index of the lens material might be, for instance, 1.544.
[0059] FIG. 2 shows schematically and exemplarily a graph of the sag function S(r) representing the lens profile of the lens surface 2. FIG. 2 further shows schematically and exemplarily a graph of the sag function S.sub.1(r) of a standard aspheric profile, and FIG. 3 shows schematically and exemplarily a graph of the sag function S.sub.2(r) of an even-order aspheric profile, wherein the lens profile whose sag function S(r) is shown in FIG. 2 may be represented by a combination of the standard aspheric profile whose sag function S.sub.1(r) is shown in FIG. 2 and the even-order aspheric profile whose sag function S.sub.2(r) is shown in FIG. 3. The combination of the two aspheric profiles, which corresponds to a combination of the respective sag functions S.sub.1(r) and S.sub.2(r), can be represented by a combination function M(r). The horizontal axes of the graphs shown in FIGS. 2 and 3 indicate a radial coordinate, i.e. a coordinate defining the radial distance r of the respective position on the lens surface 2 to the vertex, as measured perpendicularly to the central axis of the lens 1.
[0060] As can be seen in FIG. 2, the lens surface sag function S(r) is a smooth function of the radial position r, meaning that particularly the first derivative of S(r) is continuous in the whole range of radial positions. The function S(r) takes positive values ranging from 0 at the lens center r=0 to about 0.175 mm at an outer boundary of the lens surface at a radius r.sub.B=3 mm. At the vertex, which is located at the lens center r=0, the lens surface sag function S(r) has a vanishing first order derivative. In fact, in FIG. 2, the difference between the lens surface sag function S(r) and the standard aspheric profile sag function S.sub.1(r) is hardly visible due to the resolution of the axes of the illustrated graph. The standard aspheric profile sag function S.sub.1(r) is defined by above equation (1), wherein the curvature c at the vertex of the lens surface corresponds to a convex shape and the conic constant k is negative, which means that the shown standard aspheric profile is parabolic.
[0061] The value of c may be regarded as a reference curvature corresponding to a reference optical power of the lens 1, wherein the reference optical power might be selected based on a prescription in a clinical context.
[0062] The standard aspheric profile may also be regarded as a standard monofocal profile, because the lens having a surface with such a standard aspheric profile would give rise to essentially a single, substantially localized focal point. The reference optical power of the lens 1 whose sag function S(r) is shown in FIG. 2 is approximately 20 diopter, and the conic constant k is chosen appropriately. The reference optical power corresponds to the value c of the curvature at the vertex of the lens surface 2.
[0063] The even-order aspheric profile sag function S.sub.2(r) shown in the graph of FIG. 3 is defined by above equation (2), wherein the horizontal axis of the shown graph indicates the radial coordinate whose absolute value corresponds to the radial distance r to the vertex of the lens surface 2, and the constants A.sub.2n are appropriately chosen. Due to the very different resolution of the vertical axis of the graph illustrated in FIG. 3 as compared to the graph illustrated in FIG. 2, it appears as if the even-order aspheric profile sag function S.sub.2(r) is substantially 0 over half the radial extent of the lens surface 2. However, already in this inner region of the lens surface 2, the even-order aspheric profile is not negligible with respect to the standard aspheric profile whose sag function S.sub.1(r) is shown in FIG. 2.
[0064] The combination function M(r) corresponding to the exemplary lens 1 is shown in FIG. 4. It is defined by a smooth function of the radial position r, and is of the form given in above equation (5), wherein the constants A and p are appropriately chosen. The lens surface sag function for the lens surface 2 shown in FIG. 2 is a combination of the standard aspheric profile sag function S.sub.1(r) shown in FIG. 2 and the even-order aspheric profile sag function S.sub.2(r) shown in FIG. 3, wherein the combination of the two sag functions is defined by the combination function M(r) shown in FIG. 4. In this embodiment, the combination function M(r) depends on the radial distance to the vertex such that the contribution of the standard aspheric profile sag function S.sub.1(r) and the contribution of the even-order aspheric profile sag function S.sub.2(r) to the lens profile sag function S(r) of the lens 1 at a certain radial distance to the vertex depends on the radial distance r. The combination function M(r) may therefore also be regarded as a mask function masking the contributions from the two different aspheric profiles, wherein the degree of masking depends on the radial position r.
[0065] The lens surface 2 described by the resulting lens profile sag function S(r) is shaped such that, in a region immediately surrounding the vertex of the lens surface 2, the lens profile converges to the sum of the standard aspheric profile, described by S.sub.1 (r), and the even-order aspheric profile, described by S.sub.2 (r), with decreasing radial distance r to the vertex and, in an outer region surrounding the vertex, the lens profile converges to the standard aspheric profile with increasing radial distance r to the vertex.
[0066] Since the standard aspheric profile sag function S.sub.1(r), the even-order aspheric profile sag function S.sub.2(r) and the combination function M(r) are all smooth functions in this embodiment, also the combined sag function, i.e. the lens profile sag function S(r), is smooth.
[0067] The aspheric profile sag functions S.sub.1(r) and S.sub.2(r) resulting in the lens profile sag function S(r) by combination are, in this embodiment, designed such that the second-order derivative of the lens profile sag function S(r) changes its sign with increasing radial position, which is reflected by an intermediate radial region in which the optical power associated with the lens surface 2 becomes negative. This region is an annular region of the lens surface 2 extending around a radial position of approximately 0.7 mm. The lens profile sag function S(r) of the lens 1 is defined by above equation (3), which is equivalent to above equation (4).
[0068] The second term of equation (4), which corresponds to the difference (1−M(r)) S.sub.2(r) between the lens profile sag function S(r) and the standard aspheric profile sag function S.sub.1(r), is shown in FIG. 5 for the embodiment also illustrated in FIGS. 1 to 4. From the values of this difference function (1−M(r)) S.sub.2(r) as seen on the vertical axis of the graph illustrated in FIG. 5, it is apparent why the difference between the lens profile sag function S(r) and the standard aspheric profile sag function S.sub.1(r) is hardly visible in FIG. 2.
[0069] As will be illustrated in the following, while the values assumed by the difference function (1−M(r)) S.sub.2(r) shown in FIG. 5 seem to be small, corresponding to only a seemingly small deviation of the lens surface 2 from a standard aspheric surface, the optical effects generated by the seemingly small deviation are surprisingly large. In fact, the deviation of the lens surface 2 from the standard aspheric surface may be designed to be just large enough and positioned just right such that the depth of focus of the lens 1 can be widened towards smaller focal distances. Moreover, the deviation can be designed to be still small enough and positioned just right such that undesired photic phenomena generated by the lens surface 2 can be avoided.
[0070] FIG. 6 shows schematically and exemplarily a modulation transfer function (MTF) calculated for a human eye into which the ophthalmic lens 1 has been placed, with an aperture of 3.0 mm and 4.5 mm, respectively, wherein the calculation was performed for far visual distances. It can be seen in FIG. 6 that the modulation transfer function, which may be regarded as a measure of imaging quality, falls off only relatively slowly towards higher spatial frequencies irrespective of the aperture.
[0071] FIG. 7 shows schematically and exemplarily a through-focus modulation transfer function calculated for a human eye into which the lens 1 has been placed, at a spatial frequency of 50 line pairs per millimeter. A through-focus modulation transfer function may also be referred to as a through-focus response curve. In FIG. 7, the through-focus modulation transfer function is shown for an aperture of 3.0 mm and for an aperture of 4.5 mm. The horizontal axis indicates a focal shift, i.e. a focal distance measured relative to the focal distance corresponding to the reference optical power of the lens 1, wherein negative focal shifts correspond to higher optical powers with respect to the reference optical power. For both aperture sizes shown in FIG. 7, the width of the main, far-focus peak is widened with respect to a corresponding standard aspheric lens, particularly in the negative focal shift direction. Thus, FIG. 7 illustrates that the visual acuity of the human eye can be improved at intermediate vision distances.
[0072] FIG. 8 schematically and exemplarily shows the modulation transfer function corresponding to the lens 1, which may be regarded as an enhanced aspheric lens, at a spatial resolution of 50 line pairs per millimeter, calculated for far vision distances and with an aperture of 3 mm, as compared to the one of a standard aspheric lens, in its dependence on the decentration of the lens, i.e. the deviation of the central axis of the lens surface from the optical axis. It can be seen in FIG. 8 that the value of the modulation transfer function decreases only relatively little as compared to the one corresponding to the standard aspheric lens. This behavior is also visible in FIG. 9, which corresponds to FIG. 8, except that the spatial resolution is chosen to be 100 line pairs per millimeter. For decentrations above approximately 0.6 mm, the modulation transfer function at both 50 line pairs per millimeter and 100 line pairs per millimeter is even higher for the lens 1 as compared to the standard aspheric lens.
[0073] FIG. 10 shows schematically and exemplarily a lens profile sag function and a corresponding standard aspheric profile sag function for a lens surface providing an optical power of 6 diopter, i.e. an optical power which is smaller than the one provided by the lens surface 2 shown in FIG. 1 and representable by the sag function shown in FIG. 2. It can be seen in FIG. 10 that the deviations of the lens surface sag function providing such a smaller optical power from the corresponding standard aspheric profile sag function are higher than the corresponding deviations for the lens surface 2.
[0074] In FIG. 11, a modulation transfer function calculated for far vision distances and with an aperture of 3.0 mm and 4.5 mm, respectively, is shown schematically and exemplarily for a lens having a lens surface as illustrated by FIG. 10 that has been placed in a human eye. From FIG. 11 it can be seen that, also for lens surfaces like the one illustrated by FIG. 10, the modulation transfer function falls off only relatively slowly towards higher spatial frequencies irrespective of the aperture.
[0075] FIG. 12 shows schematically and exemplarily a through-focus modulation transfer function calculated for a human eye into which the lens whose surface is illustrated in FIG. 10 has been placed, at a spatial frequency of 50 line pairs per millimeter. The through-focus modulation transfer function is shown for an aperture of 3.0 mm and for an aperture of 4.5 mm. The horizontal axis indicates a focal shift, i.e. a focal distance measured relative to the focal distance corresponding to the reference optical power of the lens, wherein negative focal shifts correspond to higher optical powers with respect to the reference optical power. For both aperture sizes shown in FIG. 12, the width of the main, far-focus peak is widened with respect to a corresponding standard aspheric lens, particularly in the negative focal shift direction. Thus, FIG. 12 illustrates that the visual acuity of the human eye can be improved at intermediate vision distances also with a lens having a surface as illustrated in FIG. 10.
[0076] FIG. 13 shows schematically and exemplarily an optical power profile corresponding to a lens profile that is representable by a combination of the standard aspheric profile and an even-order aspheric profile. The shown power profile, which refers to an optical power measured relative to a reference optical power at the lens center, comprises local extrema corresponding to extremal points of the second-order derivative of a function representing the corresponding lens profile, i.e., for instance, the corresponding sag function of the lens. Towards an outer boundary of the lens surface, the optical power tends to a constant value. The optical power profile shown in FIG. 13 illustrates the relative spherical power and corresponds to the lens profile illustrated by FIGS. 2 to 5.
[0077] FIG. 14 shows schematically and exemplarily a graph of a further embodiment of the sag function S(r) which might represent the lens profile of the lens surface 2. Also FIG. 14, like FIG. 2, further shows schematically and exemplarily a graph of the sag function S.sub.1(r) of a standard aspheric profile, and FIG. 15 shows schematically and exemplarily a graph of the sag function S.sub.2(r) of an even-order aspheric profile corresponding to the further embodiment, wherein the lens profile whose sag function S(r) is shown in FIG. 14 may be represented by a combination of the standard aspheric profile whose sag function S.sub.1(r) is shown in FIG. 14 and the even-order aspheric profile whose sag function S.sub.2(r) is shown in FIG. 15. The combination of the two aspheric profiles, which corresponds to a combination of the respective sag functions S.sub.1(r) and S.sub.2(r), can be represented by a combination function M(r). The horizontal axes of the graphs shown in FIGS. 14 and 15 indicate a radial coordinate, i.e. a coordinate defining the radial distance r of the respective position on the lens surface 2 to the vertex, as measured perpendicularly to the central axis of the lens 1.
[0078] As can be seen in FIG. 14, the lens surface sag function S(r) is a smooth function of the radial position r, meaning that particularly the first derivative of S(r) is continuous in the whole range of radial positions. The function S(r) takes positive values ranging from 0 at the lens center r=0 to about 0.40 mm at an outer boundary of the lens surface at a radius r.sub.B=3 mm. At the vertex, which is located at the lens center r=0, the lens surface sag function S(r) has a vanishing first order derivative. In fact, in FIG. 14, the difference between the lens surface sag function S(r) and the standard aspheric profile sag function S.sub.1(r) is hardly visible due to the resolution of the axes of the illustrated graph. The standard aspheric profile sag function S.sub.1(r) is defined by above equation (1), wherein the curvature c at the vertex of the lens surface corresponds to a convex shape and the conic constant k is negative, which means that the shown standard aspheric profile is parabolic. Also in this embodiment the value of c may be regarded as a reference curvature corresponding to a reference optical power of the lens 1, wherein the reference optical power might be selected based on a prescription in a clinical context. Moreover, also in this embodiment the standard aspheric profile may also be regarded as a standard monofocal profile, because the lens having a surface with such a standard aspheric profile would give rise to essentially a single, substantially localized focal point. The reference optical power of the lens 1 whose sag function S(r) is shown in FIG. 14 can be relatively high, and the conic constant k can be chosen appropriately. In particular, the conic constant k can −6 in this embodiment. The reference optical power corresponds to the value c of the curvature at the vertex of the lens surface 2.
[0079] The even-order aspheric profile sag function S.sub.2(r) shown in the graph of FIG. 15 is defined by above equation (2), wherein the horizontal axis of the shown graph indicates the radial coordinate whose absolute value corresponds to the radial distance r to the vertex of the lens surface 2, and the constants A.sub.2n are appropriately chosen. In particular, in this embodiment the following constants apply: A.sub.2=1.2×10.sup.−3 mm.sup.−1, A.sup.4=1.3×10.sup.−2 mm.sup.−3, A.sub.6=−6.0×10.sup.−3 mm.sup.−5, A.sub.8=1.8×10.sup.−2 mm.sup.−7, A.sub.10=2.2×10.sup.−2 mm.sup.−9; A.sub.12=0, A.sub.14=0, A.sub.16=0.
[0080] Due to the very different resolution of the vertical axis of the graph illustrated in FIG. 15 as compared to the graph illustrated in FIG. 14, also in these figures it appears as if the even-order aspheric profile sag function S.sub.2(r) is substantially 0 over half the radial extent of the lens surface 2. However, already in this inner region of the lens surface 2, the even-order aspheric profile is not negligible with respect to the standard aspheric profile whose sag function S.sub.1(r) is shown in FIG. 14.
[0081] A further embodiment of the combination function M(r) corresponding to the exemplary lens 1 is shown in FIG. 16. It is defined by a smooth function of the radial position r, and is of the form given in above equation (5), wherein the constants A and ρ are appropriately chosen. In particular, in this embodiment the constant A is 4.0 mm.sup.−1, and the constant ρ is 0.74 mm.
[0082] The lens surface sag function for the lens surface 2 shown in FIG. 14 is a combination of the standard aspheric profile sag function S.sub.1(r) shown in FIG. 14 and the even-order aspheric profile sag function S.sub.2(r) shown in FIG. 15, wherein the combination of the two sag functions is defined by the combination function M(r) shown in FIG. 16. Also in this embodiment, the combination function M(r) depends on the radial distance to the vertex such that the contribution of the standard aspheric profile sag function S.sub.1(r) and the contribution of the even-order aspheric profile sag function S.sub.2(r) to the lens profile sag function S(r) of the lens 1 at a certain radial distance to the vertex depends on the radial distance r. The combination function M(r) may therefore also be regarded as a mask function masking the contributions from the two different aspheric profiles, wherein the degree of masking depends on the radial position r.
[0083] Also in this embodiment, the lens surface 2 described by the resulting lens profile sag function S(r) is shaped such that, in a region immediately surrounding the vertex of the lens surface 2, the lens profile converges to the sum of the standard aspheric profile, described by S.sub.1(r), and the even-order aspheric profile, described by S.sub.2(r), with decreasing radial distance r to the vertex and, in an outer region surrounding the vertex, the lens profile converges to the standard aspheric profile with increasing radial distance r to the vertex. Moreover, also in this embodiment, since the standard aspheric profile sag function S.sub.1(r), the even-order aspheric profile sag function S.sub.2(r) and the combination function M(r) are all smooth functions in this embodiment, also the combined sag function, i.e. the lens profile sag function S(r), is smooth.
[0084] The second term of equation (4), which corresponds to the difference (1−M(r)) S.sub.2(r) between the lens profile sag function S(r) and the standard aspheric profile sag function S.sub.1(r), is shown in FIG. 17 for the embodiment illustrated in FIGS. 14 to 16. From the values of this difference function (1−M(r)) S.sub.2(r) as seen on the vertical axis of the graph illustrated in FIG. 17, it is apparent why the difference between the lens profile sag function S(r) and the standard aspheric profile sag function S.sub.1(r) is hardly visible in FIG. 14.
[0085] As will be illustrated in the following, while the values assumed by the difference function (1−M(r)) S.sub.2(r) shown in FIG. 17 seem to be small, corresponding to only a seemingly small deviation of the lens surface 2 from a standard aspheric surface, also in this embodiment the optical effects generated by the seemingly small deviation are surprisingly large.
[0086] FIG. 18 shows schematically and exemplarily an MTF calculated for a human eye into which the ophthalmic lens 1 has been placed, with an aperture of 3.0 mm and 4.5 mm, respectively, wherein the calculation was performed for far visual distances. It can be seen in FIG. 18 that the modulation transfer function, which may be regarded as a measure of imaging quality, falls off only relatively slowly towards higher spatial frequencies irrespective of the aperture.
[0087] FIG. 19 shows schematically and exemplarily a through-focus modulation transfer function calculated for a human eye into which the lens 1 with the lens profile of the further embodiment illustrated in FIGS. 14 to 17 has been placed, at a spatial frequency of 50 line pairs per millimeter. In FIG. 19, the through-focus modulation transfer function is shown for an aperture of 3.0 mm and for an aperture of 4.5 mm. The horizontal axis indicates a focal shift, i.e. a focal distance measured relative to the focal distance corresponding to the reference optical power of the lens 1, wherein negative focal shifts correspond to higher optical powers with respect to the reference optical power. For both aperture sizes shown in FIG. 19, the width of the main, far-focus peak is widened with respect to a corresponding standard aspheric lens, particularly in the negative focal shift direction. Thus, FIG. 19 illustrates that the visual acuity of the human eye can be improved at intermediate vision distances.
[0088] FIG. 20 shows schematically and exemplarily an optical power profile corresponding to a lens profile that is representable by a combination of the standard aspheric profile and an even-order aspheric profile. The shown power profile, which refers to an optical power measured relative to a reference optical power at the lens center, comprises local extrema corresponding to extremal points of the second-order derivative of a function representing the corresponding lens profile, i.e., for instance, the corresponding sag function of the lens. Towards an outer boundary of the lens surface, the optical power tends to a constant value. The optical power profile shown in FIG. 20 illustrates the relative spherical power and corresponds to the lens profile illustrated by FIGS. 14 to 17.
[0089] In the following, an embodiment of a manufacturing method for manufacturing an ophthalmic lens will exemplarily be described with reference to a flowchart shown in FIG. 21.
[0090] In step 101 a mathematical combination of a standard aspheric profile and an even-order aspheric profile is provided, wherein the aspheric profiles are combined such that, in a region immediately surrounding the vertex of a lens surface, the lens profile converges to a sum of the standard aspheric profile and the even-order aspheric profile with decreasing radial distance to the vertex and, in an outer region surrounding the vertex, the lens profile converges to the standard aspheric profile with increasing radial distance to the vertex.
[0091] In step 102 the ophthalmic lens is formed such that a surface of the lens is in accordance with the provided combination of the standard aspheric profile and the even-order aspheric profile. The lens might be formed, for instance, by using a known molding procedure and a known lathe cutting procedure, or by another technique generally used for manufacturing lenses.
[0092] Although in above described embodiments, the lenses are rotationally symmetric, the lenses could also have lens surfaces with a toric shape. In that case, a first lens profile could be provided in a first radial direction of the lens surface and a second lens profile could be provided for a second radial direction of the lens surface, wherein the first and the second radial direction may be perpendicular to each other.
[0093] Other variations to the disclosed embodiments can be understood and effected by those skilled in the art in practicing the claimed invention, from a study of the drawings, the disclosure, and the appended claims.
[0094] In the claims, the word “comprising” does not exclude other elements or steps, and the indefinite article “a” or “an” does not exclude a plurality.
[0095] Any reference signs in the claims should not be construed as limiting the scope.
