INTRAOCULAR LENS PROVIDING EXTENDED DEPTH OF FOCUS

Abstract

An intraocular lens providing an extended depth of focus, having a power profile that, in a first region, is increasing to an outer edge to achieve a lens power greater than base power and, in a second region is decreasing to achieve a minimum lens power that is less than the base power, and then increasing to achieve the base power, the second region maintaining the base power over at least 30% of the radial distance corresponding to a pupil of an eye for photopic vision conditions. An IOL using refractive features within a 1.4 mm radial distance of the optical axis to generate an MTF having a first peak with an absolute maximum MTF value of at least 0.35 and a region continuous with the first peak maintaining an MTF value of at least 0.15 to achieve a depth of focus of at least about 1.25 diopters.

Claims

1. An intraocular lens providing an extended depth of focus, the lens having an optical axis and a base power for achieving distance vision, the lens comprising: an optic having a surface with a sagittal surface profile defined in-part by EDOF features having a first region that is non-decreasing in curvature as a function of increasing radial position from the optical axis to an outer edge of the first region to achieve powers greater than the base power at the outer edge, and the sagittal surface profile having a second region extending radially outward from the outer edge that is non-increasing in curvature as a function of increasing radial position from the outer edge to achieve powers less than the base power thereby defining a non-increasing portion, the curvatures in the second region then non-decreasing to achieve the base power and then maintaining substantially the base power over at least 30% of the radial distance corresponding to a pupil of a user's eye for photopic vision conditions.

2. The lens of claim 1, wherein the first region is increasing in curvature as a function of increasing radial position from the optical axis to the outer edge of the first region, the second region is decreasing in curvature as a function of increasing radial position from the outer edge to achieve the powers less than the base power, and then increasing in curvature as a function of radial position to achieve the base power.

3. The lens of claim 1, wherein the sagittal surface profile can be specified by an equation z(r),
where z(r)=r.sup.2{R+√{square root over (R.sup.2−(1+c)r.sup.2)}}+∝m(r)*r.sup.m, and where m is 4 or higher.

4. The lens of claim 3, wherein m=4.

5. The lens of claim 1, wherein substantially the base power is maintained in the second region over a radial distance of at least 0.3 mm.

6. The lens of claim 1, wherein substantially the base power is maintained in the second region over a radial distance of at least 0.6 mm.

7. The lens of claim 3, where α(r) varies exponentially as a function of radial distance.

8. The lens of claim 7, wherein $\propto \left(r\right)=\{\begin{array}{cc}r\le r_{\lim };& {\propto }_1+2\left({\propto }_2-{\propto }_1\right)\left\{{\left(1+e^{-\mathrm{Ar}}\right)}^{-1}-0.5\right\}\\ r>r_{\lim };& \begin{array}{c}\mathrm{the}\mathrm{coefficeint}\propto \left(r\right)\mathrm{is}\mathrm{defined}\mathrm{to}\mathrm{attain}\\ a\mathrm{value}{\propto }_1\end{array}\end{array}$ r is the radial distance from the lens optical axis, R is the surface radius of curvature, c is the surface conic constant, α.sub.1, α.sub.2 and A are constants defining variation of the fourth order coefficient as a function of r, r.sub.lim is the location of the outer edge of the first region and defines a radial transition location for the fourth order coefficient (α (r)).

9. The lens of claim 8, wherein substantially the base power is maintained in the second region over a radial distance of at least 0.3 mm.

10. The lens of claim 8, wherein substantially the base power is maintained in the second region over a radial distance of at least 0.6 mm.

11. The lens of claim 8, wherein for r>r.sub.lim
∝(r)=∝.sub.1 whereby α(r) attains value α.sub.1 at r.sub.lim.

12. The lens of claim 8, wherein for r>r.sub.lim
∝(r)=∝.sub.2+2(∝.sub.1−∝.sub.2){(1+e.sup.−B(r−.sup.r.sub.lim)−0.5} where, B is a constant, whereby α(r) attains value α.sub.1 gradually for values of r greater than r.sub.lim.

13. The lens of claim 8, wherein z(r) further comprises a term z.sub.shift where $z_{\mathrm{shift}}=\{\begin{array}{cc}r\le r_{\lim };& 0\\ r>r_{\lim };& \left({\propto }_{\lim }{\left(r_{\lim }\right)}^4-{\propto }_1{\left(r_{l\mathrm{im}}\right)}^4\right)(2\left(\left(1+e^{-{B\left(r-r_{\lim }\right)}^{-1}}-0.5\right)\right)\end{array}$

14. The lens of claim 12, wherein substantially the base power is maintained in the second region over a radial distance of at least 0.3 mm.

15. The lens of claim 12, wherein substantially the base power is maintained in the second region over a radial distance of at least 0.6 mm.

16. The lens of claim 1, wherein the sagittal surface profile can be specified by an equation z(r), where
z(r)=r.sup.2{R+R.sup.2−(1+c)r.sup.2}.sup.−1+EDOF features sagittal profile term and, wherein the EDOF features sagittal profile term can be specified using a polynomial expression.

17. The lens of claim 16, wherein the polynomial expression approximates an exponential variation.

18. The lens of claim 16, wherein the polynomial expression is of a form Σ.sub.n=1.sup.mC.sub.2nr.sup.2n.

19. The lens of claim 18, wherein the polynomial expression is of 24.sup.th order or greater, whereby m ≥12.

20. The lens of claim 1, wherein the surface is an anterior surface or a posterior surface, and wherein the non-increasing curvature portion is characterized by a discontinuity located at the outer edge, such that the outer edge and the location of minimum lens power are substantially radially coincident.

21. The lens of claim 1, wherein the surface is an anterior surface or a posterior surface, and wherein the non-increasing curvature portion varies smoothly as a function of radius such that the distance from the outer edge of the first region to a radial location of a minimum lens power is less than 0.4 mm.

22. The lens of claim 1, wherein substantially the base power is maintained in the second region over a radial distance of at least 0.3 mm.

23. The lens of claim 1, wherein substantially the base power is maintained in the second region over a radial distance of at least 0.6 mm.

24. The lens of claim 1, wherein the lens is monofocal.

25. The lens of claim 1, wherein the sagittal surface profile is further defined by a diffractive profile superimposed on the surface.

26. The lens of claim 25, wherein the diffractive profile is configured to produce a depth of focus having a first peak in MTF and a second peak in MTF, and wherein the EDOF features increases the MTF between the first peak and the second peak, wherein the MTF is specified using the ISO 1 model eye, and wherein the MTF is specified for a spatial frequency of 50 lp/mm at the retina, at 546 nm light, for a 3 mm diameter pupil, and when the lens is immersed in aqueous humor having a refractive index of 1.336 at 546 nm.

27. The lens of claim 26, wherein the EDOF features increases the MTF only between the first peak and the second peak.

28. The lens of claim 26, wherein the diffractive profile is a bifocal diffractive profile.

29. The lens of claim 26, wherein the maximum MTF value is equal to or greater than 0.35.

30. The lens of claim 29, wherein the first peak in the MTF and the second peak are separated by about 2.5 diopters, and the EDOF features provides a depth of focus continuous with the first peak that maintains an MTF of 0.15 or greater for at least about 1.25 diopters, in the myopic direction from the first peak.

31. An intraocular lens providing an extended depth of focus, the lens having an optical axis and a base power for achieving distance vision, the lens comprising: an optic characterized by a power profile that, in a first region, is non-decreasing as a function of increasing radial position from the optical axis to an outer edge of the first region to achieve a lens power greater than the base power at the outer edge and, in a second region extending radially outward from the outer edge the power profile is non-increasing as a function of increasing radial position from the outer edge to achieve a minimum lens power that is less than the base power thereby defining a non-increasing portion, and then non-decreasing as a function of increasing radial position to achieve the base power, the second region then maintaining substantially the base power over at least 30% of the radial distance corresponding to a pupil of a user's eye for photopic vision conditions.

32. An intraocular lens having an optical axis and providing an extended depth of focus using refractive features within a 1.4 mm radial distance of the optical axis to generate a through-focus MTF characterized by a first peak having an absolute maximum MTF value in excess of 0.35 and a region continuous with the first peak maintaining an MTF value of greater than 0.15 to achieve a depth of focus of at least about 1.25 diopters extending in the myopic direction from the first peak, wherein the MTF is specified using the ISO 1 model eye, and wherein the MTF is specified for a spatial frequency of 50 lp/mm at the retina, at 546 nm light, for a 3 mm diameter pupil, when the lens is immersed in aqueous humor having a refractive index of 1.336 at 546 nm.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0068] FIG. 1A is a schematic plan view of an example of extended depth of focus (EDOF) intraocular lens (IOL) according to aspects of the present invention;

[0069] FIG. 1B is a schematic cross-sectional side view of the EDOF IOL of FIG. 1A taken along lines 1B-1B;

[0070] FIG. 2A is an example of a sagittal surface profile of a surface of an EDOF lens according to aspects of the invention;

[0071] FIG. 2B is a sagittal surface profile of the EDOF features of a surface of an EDOF lens of the lens as shown in FIG. 2A (i.e., aspects of the surface that are determined by the conventional conic term are omitted);

[0072] FIG. 3 is a graphical illustration of a power profile of a 20-diopter lens including the lens surface illustrated in FIG. 2A;

[0073] FIG. 4 is a graphical illustration of a through-focus MTF for the 20-diopter lens discussed with reference to FIG. 3;

[0074] FIG. 5 is second example of a sagittal surface profile of a surface of an EDOF lens according to aspects of the invention;

[0075] FIG. 6A is a sagittal surface profile of EDOF features of a surface of an EDOF lens (i.e., the conic term is omitted) in which the EDOF features are specified using a polynomial approximation of the EDOF features of the surface shown in FIG. 2B;

[0076] FIG. 6B is a graphical illustration of a through-focus MTF for a 20-diopter lens including the surface using a polynomial definition of the EDOF features as shown in FIG. 6A;

[0077] FIG. 7 illustrates an example of a sagittal surface profile of a surface of a refractive-diffractive EDOF lens according to aspects of the present invention; and

[0078] FIG. 8 a graphical illustration a through-focus MTF for a 20-diopter lens having a surface as shown in FIG. 7.

DETAILED DESCRIPTION

[0079] Aspects of the invention will be further discussed with reference to the following specific examples. It is understood that these examples are given by way of illustration and are not meant to limit the claimed inventions to any particular example.

[0080] FIGS. 1A and 1B are schematic plan and cross-sectional side view illustrations, respectively, of an example of an EDOF intraocular lens 100 having a base power for achieving distance vision and an extended depth of focus according to aspects of the present invention. As indicated below, IOL 100 has features that generate an extended depth of focus (EDOF) located within a radial perimeter corresponding to the pupil of the user's eye for photopic conditions.

[0081] IOL 100 comprises an optic 110 having an optical axis OA, and an anterior surface 112 and a posterior surface 114 both extending over an optical zone OZ. IOLs, such as IOL 100, typically have two or more haptics (not shown) to position the optic within an eye, although in some embodiments a single haptic may be present. Typically, lens 100 is rotationally symmetric, although, some embodiments may be rotationally asymmetric (e.g., toric).

[0082] FIG. 2A is an example of a sagittal surface profile of a surface 114 of EDOF lens 100 (shown in FIG. 1) according to aspects of the invention. In the illustrated embodiment, the posterior surface 114 has a sagittal surface profile 200 defined in-part by EDOF features having a first region R.sub.1 that is increasing in curvature as a function of increasing radial position from optical axis AO to an outer edge OE of the first region R.sub.1. The curvatures in the first region become greater than curvatures corresponding to a base-power sagittal surface profile as radial position is increased toward outer edge OE (i.e., the lens achieves a power greater than the base power in at least a portion of the first region). Although, in the illustrated embodiment, the first region has a monotonically increasing curvature, the first region may have one or more regions of uniform curvature and otherwise increase; that is, the first region may have a non-decreasing curvature. As set forth below, a sagittal surface profile may be further defined by a conventional conic term and/or a diffractive element.

[0083] The sagittal surface profile of posterior surface 114 has a second region R.sub.2 extending radially outward from outer edge OE, the sagittal surface profile in the second region is decreasing in curvature (as a function of radial position) from outer edge OE. The curvatures become less than curvatures corresponding to the base power profile (i.e., the lens achieves a power less than the base power in a portion of the second region). The curvatures in the second region are then non-decreasing (as a function of radial position) back to curvatures corresponding to the base power profile. Although, in the illustrated embodiment, the second region is decreasing in curvature and then increasing in curvature, the second region may have one or more regions of uniform curvature; that is, the second region may have a non-increasing curvature and then a non-decreasing curvature to achieve base power.

[0084] The curvature across outer edge OE (i.e., extending from a location within the first region to a location within the second region) may vary continuously, first increasing in first region R.sub.1 and then decreasing in second region R.sub.2; alternatively, there may be a discontinuity in curvature at outer edge OE. Additionally, the sagittal surface profile may be continuous across outer edge OE or may have a step in height.

[0085] For radial positions outward to where the base power is achieved (i.e., location BP shown in FIG. 3), second region R.sub.2 has a sagittal surface profile to maintain substantially the base power profile present over at least 30% of the radial distance corresponding to the pupil of the user's eye for photopic vision conditions. It will be appreciated that providing the base power over the outer portion of the photopic pupil (i.e., limiting the EDOF features to an inner portion of the photopic pupil) will decrease individual-to-individual variation in EDOF IOL performance and improve wearer satisfaction for a given population of wearers. For example, by locating the features of the lens that generate an extended depth of focus within a radial perimeter corresponding to the pupil of the user's eye for selected lighting conditions, the likelihood that a person in a target population will experience dysphotopsia (e.g., halos or ghosting) is also decreased. It will be appreciated that the optical zone extends further from the optical axis than a distance corresponding to the pupil of the user's eye for photopic vision conditions to accommodate vision during lower lighting conditions than photopic conditions. For example, the optical zone may extend to a radial distance from the optical axis to about 2.0 mm to 2.5 mm or about 3.0 mm. As stated above, according to aspects of the present invention, it is desirable that EDOF features not extend into a portion of a lens that is used for low light conditions (i.e., beyond the portion used for photopic vision).

[0086] For a given population, the pupil of a person's eye under photopic vision conditions, will typically be in the range 1.0-2.0 mm in radius. It will be appreciated that if, as set forth above, the base power profile is present over at least 30% of the radial distance corresponding to the pupil of the user's eye for photopic vision conditions (e.g., 0.3-0.6 mm), the EDOF features will be limited to 70% or less of the radial distance corresponding to the pupil of the user's eye for photopic vision conditions.

[0087] It is to be appreciated that, although the lens achieves the base power, the power is maintained at the base power or at substantially the base power (i.e., within about +/−10% of base power), for example, if compensation for spherical aberration of a user's eye is provided in the lens prescription.

[0088] Lenses having a surface as described above also comprise an opposing surface (i.e., as shown in FIG. 1i). The opposing surface may be convex or concave. The curvature of the opposing surface may be constant as a function of radial position. Alternatively, the curvature may be monotonically increasing or decreasing as function of radial position, from the optical axis to the edge of the lens. For example, to eliminate or reduce spherical aberration caused by the opposing surface or to compensate for spherical aberration of a user's eye, as is known in the art, (e.g., a convex surface may have a curvature that is monotonically decreasing as a function of radial location).

[0089] For the present example and all examples herein, the lens material is hydrophobic acrylic having a refractive index of 1.5332 at 546 nm. Although hydrophobic acrylic lenses are used in the examples, other materials may be used to achieve designs according to aspects of the present invention, such as hydrophilic acrylic, polymethyl-methacrylate (PMMA) or silicone. Lenses having EDOF features as described herein can be manufactured using any suitable technique, such as molding or machining.

[0090] FIG. 2B is graphical illustration of a sagittal surface profile of the EDOF features of a surface of an EDOF lens as shown in FIG. 2A with the sagittal surface profile contribution of the base lens subtracted out. In particular, the conventional component of the surface (i.e., as determined by the conic term of Equation 1(a), below, is omitted; and the aspects of the surface determined by fourth order term α(r)r.sup.4 are illustrated).

[0091] FIG. 3 is a graphical illustration of a power profile 300 of a 20-diopter lens including the lens surface 112 (shown in FIG. 1A) illustrated in FIG. 2A, in which the opposing surface has a uniform power or a substantially uniform power (i.e., within about +/−10%). In the illustrated example power profile, a first region R.sub.1 corresponds to the first region R.sub.1 in FIG. 2 (i.e., where the curvature of the lens is increasing). In first region R.sub.1, the power profile is increasing as a function of increasing radial distance across the entire first region, such that a lens power greater than the base power Φ.sub.base is achieved. First region R.sub.1 is disposed from optical axis OA to outer edge OE of the first region. Although surface 100 is illustrated as having increasing power across the entirety of first region R.sub.1, the first region may have one or more regions where the power is uniform as a function of radial distance. Accordingly, first region R.sub.1 may have a power profile that is non-decreasing as a function of radial distance.

[0092] Although, in the illustrated embodiment, the lens has a power corresponding to base power Φ.sub.base at the optical axis, such a configuration is not necessary. The purpose of first region R.sub.1 is to spread light along the optical axis and, when combined with light from the remainder of the lens, a focal spread along a depth of focus extending from distance vision toward intermediate vision is provided. The increase in power ΔD.sub.1 from the optical axis to outer edge OE is typically in the range 0.5 diopters to 5 diopters, where 0.5 diopters provides a relatively small depth of focus and 5 diopters provides a relatively large depth of focus.

[0093] The increase in the power that occurs within the first region is selected to be great enough to provide sufficient spread of light along the optical axis (i.e., to achieve a DOF of at least about 1 diopters to about 1.5 diopters) but not so great as to unreasonably increase the likelihood of dysphotopsia. A performance goal of lenses according to some aspects of the present invention is a single peak in perceived resolution (i.e., the lens is monofocal) with a depth of focus around the peak toward the myopic direction.

[0094] It is to be appreciated that variation in power ΔD.sub.1 in first region R.sub.1 is not equivalent to add power of the lens. Since each power (including the peak power) may occur only over an infinitesimally small radial extent, the add power perceived by a wearer is less than variation in power ΔD.sub.1.

[0095] As shown in FIG. 3, the power profile has a second region R.sub.2 (corresponding to the second region R.sub.2 in FIG. 1) that extends radially outward from outer edge OE. In second region R2, the power profile decreases from outer edge OE to a minimum lens power MP that is below the base power Φ.sub.base, and then increases to achieve the base power Φ.sub.base at location BP. As stated above, second region R2 has substantially the base power present over at least 30% of the radial distance corresponding to the pupil of the user's eye for photopic vision conditions.

[0096] The decrease in power (in the second region) to a power less than the base power Φ.sub.base may occur as a step in power (i.e., an abrupt change in curvature) at outer edge OE. It is to be appreciated that a step in power will result in the location of the outer edge and the location of minimum lens power being radially coincident or substantially radially coincident (i.e., as determined by manufacturing and measurement tolerances). Alternatively, the decrease in power may be achieved using a smoothly varying function. Typically, the decrease in power between the outer edge and minimum lens power MP happens relatively rapidly as a function of radial position (e.g., over a distance of less than 0.4 mm or less than 0.3 mm); for example, if the decrease does not occur as a step in power, a continuous function having a curvature that varies rapidly (and continuously) as function of radial position may be used. For example, a high-order polynomial (e.g., 24.sup.th order or greater) or another continuous function as described below, may be used.

[0097] In the illustrated embodiment, a power profile is achieved with the posterior surface having EDOF features (as described above) and the anterior surface having a substantially uniform power profile across the entire surface; however, either the anterior surface or the posterior surface can have EDOF features. In some embodiments, a curvature of at least one of the anterior surface and the posterior surface varies to achieve a power profile as described above; however, in some embodiments, an index of refraction of IOL 100 varies to achieve a power profile (i.e., the lens is a GRIN lens). The variation in index may provide the entire power of the lens (i.e., surfaces of the lens are planar); alternatively, one or both of the surfaces of a lens may be curved to provide some power.

[0098] One example of a set of equations suitable for generating a sagittal surface profile of a lens capable of providing an extended depth of focus as set forth above with reference to FIG. 2A and suitable for providing EDOF features limited to an inner portion of a photopic pupil as discussed above is given by Equations 1(a) and 1(b). These equations are also suitable for providing substantially the base power over at least 30% of the radial distance corresponding to the pupil of the user's eye for photopic vision conditions.

[00003]$\begin{array}{cc}Z\left(r\right)=r^2{\left\{R+\sqrt{R^2-\left(1+c\right)r^2}\right\}}^{-1}+\propto \left(r\right)*r^4& \mathrm{Equation}1\left(a\right)\end{array}$$\begin{array}{cc}\propto \left(r\right)=\{\begin{array}{cc}r\le r_{\lim };& {\propto }_1+2\left({\propto }_2-{\propto }_1\right)\left\{{\left(1+e^{-\mathrm{Ar}}\right)}^{-1}-0.5\right\}\\ r>r_{\lim };& r>r_{\lim };{\propto }_1\end{array}& \mathrm{Equation}1\left(b\right)\end{array}$ [0099] where r is the radial distance from the lens optical axis, [0100] R is the surface radius of curvature, [0101] c is the surface conic constant, [0102] α.sub.1, α.sub.2 and A are constants defining variation of the fourth order coefficient as a function of r, [0103] r.sub.lim is the location of the outer edge of the first region and defines a radial transition location for the fourth order coefficient (α (r)).

[0104] According to Equations 1(a) and 1(b), a surface is characterized by a SAG defining a curvature that increases from the optical axis OA to the outer edge of the first zone (r.sub.lim) using a fourth-order SAG term that increases from a value α.sub.1 (typically corresponding to base power) at the optical axis to a value α.sub.2 at the outer edge of the first zone. For values of r greater than r.sub.lim, the fourth order coefficient term is equal to a fixed value α.sub.1 and thus achieves base power for outer radial locations on the lens (i.e., over at least 30% of the radial distance corresponding to the pupil of the user's eye for photopic vision conditions). Although only a single term α(r)*r.sup.4 is shown, additional higher order terms (e.g., α.sub.6(r)*r.sup.6 and/or α.sub.8(r)*r.sup.8, etc.) may also be included.

[0105] Below is another set of equations 1(c)-1(d) capable of providing an extended depth of focus as set forth above and EDOF features limited to an inner portion of a photopic pupil.

[00004]$\begin{array}{cc}Z\left(r\right)=r^2{\left\{R+\sqrt{R^2-\left(1+c\right)r^2}\right\}}^{-1}+\propto \left(r\right)*r^4& \mathrm{Equation}1\left(c\right)\end{array}$$\begin{array}{cc}\propto \left(r\right)=\{\begin{array}{cc}r\le r_{\lim };& {\propto }_1+2\left({\propto }_2-{\propto }_1\right)\left\{{\left(1+e^{-\mathrm{Ar}}\right)}^{-1}-0.5\right\}\\ r>r_{\lim };& {\propto }_2+2\left({\propto }_1-{\propto }_2\right)\left\{(1+{e^{-B\left(r-r_{\lim }\right)}}^{-1}-0.5\right\}\end{array}& \mathrm{Equation}1\left(d\right)\end{array}$ [0106] where, B is a constant chosen for appropriate smoothening.

[0107] According to Equations 1(c) and 1(d), a surface is characterized by a SAG defining a curvature that increases from the optical axis OA to the outer edge of the first zone (r.sub.lim) using a fourth order SAG term having a coefficient that increases from a value α.sub.1 (corresponding to a base power) at the optical axis to a value α.sub.2 at the outer edge of the first zone. For values of r greater than r.sub.lim, the coefficient of the fourth order SAG term begins at a value α.sub.2 and returns to a value α.sub.1 and thus achieves substantially the base power for outer radial locations on the lens (i.e., over at least 30% of the radial distance corresponding to the pupil of the user's eye for photopic vision conditions).

[0108] According to Equations 1(c)-1(d), a surface has a radius of curvature that increases from the optical axis OA to an edge of the first zone r.sub.lim to achieve a curvature corresponding to a power greater than base power. For values of r greater than r.sub.lim, the radius of curvature of the surface begins at a curvature corresponding to a power greater than base power value, then the curvature decreases to curvatures corresponding to less than base power, and then returns to curvatures corresponding to substantially the base power for outer radial position on the lens. As discussed with equation 1(a) above, although equation 1(c) is shown having only a single term α(r)*r.sup.4, additional higher order terms (e.g., α.sub.6(r)*r.sup.6 and/or α.sub.8(r)*r.sup.8) may also be included.

[0109] In some instances, the surface z(r) is further smoothened at the radial position r.sub.lim to eliminate a step in the SAG profile that may occur at r.sub.lim for surfaces defined by equations 1(c)-1(d). Equations 1(e)-1(g) are capable of generating a sagittal surface profile having characteristics as discussed above with reference to FIG. 2A.

[00005]$\begin{array}{cc}Z\left(r\right)=r^2{\left\{R+\sqrt{R^2-\left(1+c\right)r^2}\right\}}^{-1}+\propto \left(r\right)*r^4+z_{\mathrm{shift}}& \mathrm{Equation}1\left(e\right)\end{array}$$\begin{array}{cc}\propto \left(r\right)=\{\begin{array}{cc}r\le r_{\lim };& {\propto }_1+2\left({\propto }_2-{\propto }_1\right)\left\{{\left(1+e^{-\mathrm{Ar}}\right)}^{-1}-0.5\right\}\\ r>r_{\lim };& {\propto }_2+2\left({\propto }_1-{\propto }_2\right)\left\{(1+{e^{-B\left(r-r_{\lim }\right)}}^{-1}-0.5\right\}\end{array}& \mathrm{Equation}1\left(f\right)\end{array}$$\begin{array}{cc}{z}_{\mathrm{shift}}=\left\{\begin{array}{cc}r\le r_{\lim };& 0\\ r>r_{\lim };& \begin{array}{c}\left({\propto }_{\lim }{\left(r_{\lim }\right)}^4-{\propto }_1{\left(r_{l\mathrm{im}}\right)}^4\right)\\ (2\left(\left(1+e^{-{B\left(r-r_{\lim }\right)}^{-1}}-0.5\right)\right)\end{array}\end{array}\right\}& \mathrm{Equation}1\left(g\right)\end{array}$

[0110] As discussed with equation 1(a) above, although equations 1(c) and 1(e) are shown having only a single term α(r)*r.sup.4, additional higher order terms (e.g., α.sub.6(r)*r.sup.6 and/or α.sub.8(r)*r.sup.8 etc.) may also be included.

[0111] Like Equations 1(c) and 1(d), Equations 1(e)-1(f) define a surface characterized by a SAG defining a curvatures that increase from the optical axis OA to the outer edge of the first zone (r.sub.lim) using a fourth order SAG coefficient term that increases from a value α.sub.1 (corresponding to base power) at the optical axis to a value α.sub.2 at the outer edge of the first zone. For values of r greater than r.sub.lim, the fourth order SAG coefficient term begins at a value α.sub.2 and returns to a value α.sub.1 and thus provides curvatures corresponding substantially to the base power for outer radial locations on the lens (i.e., over at least 30% of the radial distance corresponding to the pupil of the user's eye for photopic vision conditions). Additionally, Equation 1(g) provides an offset in the sag (z.sub.shift) to eliminate any step at r.sub.lim.

[0112] It is to be understood that a discontinuous change in curvature and a step in sagittal height as described above do not effect a lens's ability to provide an extended depth of focus; however, during examination of a lens prior to or after surgical implantation, a step may be readily apparent when illuminated with a light source. Accordingly, in some embodiments, it is advantageous that a surface is smoothened using Equations 1(c)-1(d) or Equations 1(e)-1(g).

[0113] The sagittal surface profile of lens 100 shown in FIG. 2A was generated from Equations 1(e)-1(g) using the following values:

R=21.722 mm

c=−1.2257

α.sub.1=−1.0×10.sup.−4

α.sub.2=24.0×10.sup.4, and

r.sub.lim=0.75 mm

A=−9.0

B=−9.0

[0114] Although in the above equations, Z(r), only a single term α(r)*r.sup.4 is shown, additional higher order terms (e.g., α.sub.6(r)*r.sup.6 and/or α.sub.8(r)*r.sup.8) may also be included.

[0115] FIG. 3 is a power profile, and FIG. 4 is a graphical illustration of a through-focus MTF, both, calculated using the above values to produce a posterior surface and having an anterior surface that is spherical and has a radius of curvature of 21.722 mm to form a 20-diopter lens. In particular, for the present example, and for all MTFs specified herein the MTF is calculated using the ISO 1 model eye, and the MTF is calculated for a 50 lp/mm image at the retina, for 546 nm light, and a 3 mm pupil. For all calculations made herein, lenses are assumed to be immersed in aqueous humor (refractive index of 1.336 at 546 nm).

[0116] As will be understood in the art, a power profile can be calculated, for example, using surface curvatures or can be measured using a suitable metrological instrument such as a wavefront measurement system.

[0117] EDOF features are present at locations radially inward of point BP (i.e., the location where base power is attained after minimum power MP). For example, the EDOF features may be located within a radius of 1.4 mm or 1.2 mm or 0.7 mm about the optical axis. It will be appreciated that the radial extent of the EDOF features is determined by constants α.sub.1, α.sub.2, A and r.sub.lim in the equations above.

[0118] In FIG. 4, the 0 diopter (D) location on the horizontal axis corresponds to distance vision and positive dioptric values correspond to amounts of myopic defocus. In some embodiments, an EDOF IOL is designed to have a best focus (i.e., an absolute MTF maximum) at far vision and a depth of focus extending toward near vision. It is apparent that acuity at far vision is relatively high MTF (0.5 or greater) and a depth of focus (i.e., locations continuous with the 0 diopter location and having an MTF greater than or equal to 0.15) of about 1.25 diopters is achieved. The lens has only a single peak in the MTF plot and is therefore monofocal.

[0119] As will be understood in the art, MTFs can be calculated in a straightforward numerical manner, using a raytracing program such as Oslo® from Sinclair Optics of Pittsford N.Y. or Zemax from Zemax, LLC of Kirkland, Wash. or by another existing simulation tool, or by self-written code, all of which provide equivalent results.

[0120] FIG. 5 illustrates a portion of a second example of a sagittal surface profile of a surface of an EDOF lens according to aspects of the invention. The illustrated portion of the sagittal surface profile shows a portion of the profile proximate r.sub.lim. The surface corresponds to a relatively low power lens (e.g., 6 diopters). The surface was generated using Equations 1(a)-1(b). The illustrated portion includes the discontinuous change in curvature and includes a step in the sagittal surface profile at r.sub.lim (at about 1.0 mm from the optical axis). A surface of a relatively low-power lens was chosen because the variation in sagittal height proximate r.sub.lim caused by changes in curvature specified by Equations 1(a) and 1(b) are most apparent. While the effects of the change in curvature is readily visible in FIG. 5, the step is relatively small as compared to the overall height variation of z(r) across the illustrated portion, and thus is not readily visible in FIG. 5.

[0121] The surface sagittal profile of the surface of FIG. 5 was generated using the following values:

R=45 mm

C=−1.2257

α.sub.1=−1.0×10.sup.−4

α.sub.22=7.0×10.sup.−4

A=−4, and

B=−20

[0122] The above sag equations (1(a)-1(b), 1(c)-1(d) and 1(e)-1(g)) illustrate that an aspheric SAG profile having a conic term and a fourth order term with an exponential coefficient (i.e., the SAG varies exponentially) is one technique to achieve a relatively rapid increase in a power profile to allow EDOF features to be maintained in the inner portion of the radius of the lens as set forth above, however, other mathematical equations can be used to achieve the desired rapid increase in power profile (and possibly a rapid decrease in power profile). For example, a surface can be described by a spline, a Bezier curve, or a SAG profile as shown in Equation 1(a) in which a sixth order or higher aspheric term is included (which may be in addition to a fourth order term or without a fourth order term; and terms lower than fourth order are not present), a high-order polynomial (e.g., 24.sup.th order or greater), or an empirically-derived SAG function which provides for variations in surface curvature as a function of r.

[0123] One example of another type of equations suitable for generating a SAG profile of a lens capable of limiting the EDOF features to an inner portion of the photopic pupil and providing substantially the base power profile over at least 30% of the radial distance corresponding to the pupil of the user's eye for photopic vision conditions is given by Equation 2. It will be appreciated that Equation 2 is an example of an equation suitable for specifying SAG using a high-order polynomial equations (e.g., 24.sup.th or greater order (m≥12)).

[00006]$\begin{array}{cc}z\left(r\right)=r^2{\left\{R+\sqrt{R^2-\left(1+c\right)r^2}\right\}}^{-1}+\underset{n=1}{\overset{m}{.Math.}}{C}_{2n}{r}^{2n}& \mathrm{Equation}2\end{array}$

[0124] FIG. 6A is a sagittal surface profile of an example of EDOF features of a surface of an EDOF lens (i.e., the conic term is omitted) in which the EDOF features are specified using a polynomial expression as shown in Equation 2. In particular, FIG. 6 illustrates the SAG of an EDOF features where

C.sub.2=2.2312345×10.sup.−04

C.sub.4=−8.6023283×10.sup.−04

C.sub.6=−1.9063097×10.sup.−02

C.sub.8=5.1027672×10.sup.−02

C.sub.10=−5.8342430×10.sup.−02

C.sub.12=3.8059413×10.sup.−02

C.sub.14=−1.5613206×10.sup.−02

C.sub.16=4.1760810×10.sup.−03

C.sub.18=−7.2856545×10.sup.−04

C.sub.20=8.0014765×10.sup.−05

C.sub.22=−5.0251952×10.sup.−06

C.sub.24=1.3766880×10.sup.−07

[0125] FIG. 6A also shows the sagittal surface profile of FIG. 2A for comparison. It will be appreciated that coefficients of a 24.sup.th order polynomial expression can be selected, for example, to provide a SAG that closely approximates the SAG generated using Equations 1(e)-1(g) from the optical axis to the edge of the lens. Although a surface generated using Equations 1(e)-1(g) was approximated for illustration, a surface generated using Equations 1(a)-1(b) or 1(c)-1(d) can be similarly approximated using a high-order polynomial expression.

[0126] For example, the EDOF features can be used to form a surface where R=21.722 mm and c=−1.2257 are used in the conic term of Equation 2 to form a posterior surface. Such a posterior surface may be used in combination with a spherical anterior surface having a radius of curvature of 21.722 mm to form a 20-diopter lens.

[0127] FIG. 6B is a graphical illustration showing that a through-focus MTF for the 20-diopter lens using the EDOF features defined by α.sub.24th order polynomial set forth with reference to FIG. 6A is very similar to the through-focus MTF of the surface generated using Equations 1(e)-1(g). Accordingly, given the similar SAG and MTF of the lens having a SAG specified using a polynomial and the lens specified using Equations 1(e)-1(g), it can be expected that a power profile of the lens specified using a polynomial will provide a similar power profile to that shown in FIG. 2B.

[0128] For example, the decrease in power extending outward from the outer edge of the first zone to a value less than the base power happens relatively rapidly as a function of radial position (e.g., over a distance of less than 0.4 mm or less than 0.3 mm).

[0129] In some embodiments, a diffractive profile is added to a lens surface configured to provide EDOF capabilities as described above to form a refractive-diffractive lens. For example, the diffractive profile may be superimposed on a surface containing a refractive EDOF design as set forth above (e.g., the diffractive profile provides add power to a surface specified using equations 1(a)-1(b) or equations 1(c)-1(d) or equations 1(e)-1(g)). FIG. 7 illustrates an example of a sagittal surface profile of a surface 800 of a refractive-diffractive EDOF lens according to aspects of the present invention. In the illustrated embodiment, the diffractive profile comprises four zones defined by zone edges 810a, 810b, 810c and 810D. The illustrated embodiment of a diffractive profile is of a bifocal configuration (having a zeroth order peak corresponding the base power of the lens and a second peak corresponding to an add power provided by the diffractive profile), however a diffractive profile may be of a multifocal configuration (having one or more additional peaks with corresponding add powers). While a diffractive profile may be of a multifocal design, the extended depth of focus which is provided by the refractive EDOF features will typically increase MTF values in a region of the depth of focus between a first peak (i.e., corresponding to far focus) generated by the diffractive profile and a second peak (i.e., a neighboring peak (the first peak in the myopic direction)) generated by the diffractive profile. In some embodiments, the increase in MTF only occurs between the first peak and second peak; however, in some embodiments, the increase in MTF occurs predominantly in the region between the first and second peaks, but extends beyond this region. Typically, it is desirable that the entire increase in MTF occurs in the myopic direction from the first peak rather than in the hyperopic direction.

[0130] The example refractive-diffractive sagittal surface profile illustrated in FIG. 7 is specified by equations 1(e)-1(g) where the following values were used:

R=21.722 mm

c=−1.2257

α.sub.1=−0.000197

α.sub.2=0.0005

A=−9,

B=−9, and

[0131] the diffractive profile is specified as follows: diffractive add power of 2.2 D, design wavelength of 546 nm, diffractive step height of 1.218 μm, and a central refractive zone of 0.4 mm radius. The diffractive profile, by itself, is of a conventional design for use in an IOL.

[0132] FIG. 8 is a graphical illustration of a through-focus MTF for a lens including the example surface as shown in FIG. 7. The lens used to generate the MTF is a 20 diopter lens in which the surface opposing surface 800 is a spherical surface having a radius of curvature of 18 mm. The bifocal diffractive profile directs light to peaks 820 and 830 and the refractive EDOF features direct light into region 850.

[0133] It is apparent that acuity at far vision (0 diopters) is relatively high (i.e., MTF in excess of 0.35) and a depth of focus (i.e., locations continuous with the 0 diopter location and having an MTF greater than 0.1) of about 1.3 diopters is achieved. The lens has two peaks in the MTF plot (using values greater than 0.1) and is therefore bifocal. It is to be appreciated that, while the depth of focus does not extend the full distance between the peaks 820 and 830, eye aberrations of selected wearers can be expected to cause the spread of light energy from the peaks to portions of the depth of focus between the peaks thus allowing continuous vision for a wearer, over about a 3 diopter depth of focus. To achieve the desired perceived depth of focus, in the some embodiments, the first peak in the MTF (corresponding to far vision) and the neighboring peak in MTF (in the myopic direction) are separated by about 2.5 diopters, and a depth of focus continuous with the first peak is at least about 1.25 diopters.

[0134] Various embodiments have been depicted and described in detail herein, it will be apparent to those skilled in the relevant art that various modifications, additions, substitutions, and the like can be made without departing from the spirit of the invention and these are therefore considered to be within the scope of the invention as defined in the claims which follow.