CA2697969A1 - Intraocular lens having extended depth of focus - Google Patents

Abstract

An intraocular lens is disclosed, which includes a diffractive element with a relatively low add power. The add power may be less than about 2 Diopters, may be less than about 1 Diopter, or may be in the ranges of 0.5 to 2.5 Diopters, or 1.0 lo 2.0 Diopters, or 1.5 to 2.0 Diopters, or 1.0 to 1.5 Diopters. The low-add-power diffractive element increases the depth of the focus of the intraocular lens, for example, compared to a similarly shaped intraocular lens without the diffractive element. In one embodiment, the depth of focus is defined in terms of a threshold MTF value at a particular spaiml frequency. The threshold may be an absolute threshold, such as 0.10, 0.15, 0.17, 0.20, 0.25 or 0.30, or may be a relative threshold, such as a particular percentage of the peak value. The spatial frequency may be 25 line pairs per mm. 50 line pairs per mm. 100 line pairs per mm, or any suitable value.

Description

INTRAOCULAR LENS HAVING EXTE' NDED DEPTH OF FOCUS
Related A iication The presei-it, application claims priority under 35 U.S.C 119(e) to provisional application No.
60/968,250, filed on August 27, 2007 under the same title, Full Paris Gozlvention priority is hereby expressly reserved.

fiacl~gl :ourad of the Invention Field of the I.xaveration This iz-ivention relates generally to intraocular lenses and associated systems and methods, aiid more specif-icaliy to intraocular lenses having aii extended depth of focus.

flescription of the Related Art There are maiiy medical conditions that degTade the vision of a patient's eye.
For instance, cataracts can cause the n.atura.i lens of an eye to become opaque.
Fortunately, in many of these cases, the natural lens of the eye may be remaved. surgically and replaced with an ixi.traocular lens, thereby restoring the vision of the eye.

An intraocular lens may be corrected for oaie or more particular object distances, so that objects at the particular object distance appear in focus, wlzile objects farther away froni the particular object distance appear increasingly blurred. The range of distances over which the blurring is acceptable small is kxzown as the depth of focus. There is ongoing effoi-t to improve the depth of focus of intraocular lenses, which can help reduce the dependence on spectacles, contact lenses, or other additional corrective opties.

Summary of the Invention The present invention is generally directed ophtkaalmic devices, systeins, and methods for extending the depth of focus of subject's vision. The ophtha.lmic device may be mi intraocular lens, a contact lens, a comeal inlay or oriiay, a pair of spectacles, or the like. Alternatively, tlle _l..

ophthalmic device may be a part of the natural eye, for exa.rnple, the resulting structure of a cornea.l surface after a refractive procedure sucb as a LASIK or PRK
procedure. One aspect of the present invention involves an ophthalmic devices comprising a first surface having a first shape azid an opposing second surface having a second shape, The first and second shapes provide a refractive power, A diffractive pattem is imposed oia at least one of the first shape aaid the second shape. The first and second surfaces together provide a base power, for exainple, to provide a subject witl'a distant vision for objects at aii optical infinit.y. TI-ie first and seconcl surfaces together also provide an add power that is less than a predetermined amount, for example, less than about two Dioplers. The add power is generally selected. to provide relatively high visual acuity foz=
1(1 objects at a distance that is closer than optical infinity. For example, the surfaces may be configured such that tlze visual acuity of objects at a predetermined distance from the eye of a subject is about the saine as objects at optical infinity. In one embodimezit, the ophthalmic device Iias an add power of about I Diopter and objects at about I meter from the subject have a relatively high visual acuity, for exainple, about the same visual acuity as objects at optical infiility.

In azaotlaer aspect of the present invention, an ophtltali-iiie device comprises a first surfa,ce having a first shape and an opposing second surface having a second shape, The first and second shapes provide a refractive power. A diffractive patter.a is im.posed on at least one of the first slZape and the second shape so that the iia.traocular lens has a base power arld all add power. The intraocular lens is optically described by a model lens, such that when the model lens is included.
in an intraocular lens p[ane of an eye model including a model corzxea, the modulation transfer function of the eye model exceeds about 4.17, at a spatial frequei-lcy of about 50 line pairs per millimeter, over a range of at least about 1.7 Diopters.

In yet another aspect of the preseiit invention, an plithalmic device comprises an optic comprisia-ig a first surface having a first shape and an opposii-ig second surface having a second shape. The first and second shapes provide a refractive power. A diffractive pattem is imposed on at least one of the shapes so that the optic laas a base power and an add power. When the optic is placed in an intraocular lens plane of a physical eye model including a model cornea, the modtzlatioii transfer function of the eye model exceeds about 0.17, at a spatial frequency of about 50 line pairs per millimeter, over a razige of at least about 1.7 Diopters.

-2-In still another aspect of the present invention, aii. ophthalmic device comprises a first surface having a first shape and an opposing second surface having a second shape. The first and second shapes provide a refractive power. A. diffractive pat:tern is imposed on at least one of the shapes so that tl-ie izitraocular lexis has a base power and an add power. In some embodiments, the diffractive pattem increases the depth of focus of the intraocular leiis when illuniinated at a predetermined wavelength by at least about 50 /a relative to a reference iiitraocula.r lens without the diffractive pattem and having substantially the sam.e refractive power and first and secoiad shapes. Alternatively or additionally, the diffractive pattern increa.ses the depth of focus of the intraocular lens wl-xen illuzninated by a palychromatic light source by at least about 30% relative to a reference intraocular lens without the diffractive pattern and having substantially the same refractive power and first and second shapes.

Brief Description of theDrawiiigs Embodiments of the present invention may be better understood from the following detailed. description when read. in conjunction with the accompanying drawiiigs. Such embcaclimerdts, which are for illusira.tive purposes only, depict the novel and tzon-obvious aspects of the invention. The drawings iiiclude the following figures, wzth like numerals indicating like parts:

FIG. I is a schezrÃatic drawing of a human eye aft-er implantation with an intraocular lens.
F1G, 2 is a schematic drawing of a thin lens model ilia.t approximates the human eye of FIG. 1.
FIG. 3 is a paraxial raytrace of a "typical" eye.

FIG. 4 is a plot of retiria-to-irnage separation versus recluired leiis power, for a variety of object distances, for the "typical eye" of FIG. 3.
FIG. 5 is a plot of tlle MTF for the "typical eye" of FIGS. 3 aaad 4, for various ailiouzats of defocus.

FIG. 6 is a plot of the MTF of the "typical eye" of FIGS. 3-5, versus defocus, at three representative spatial 'fi=equezicies.

FIG. 7 is a froilt-view schematic drawing of a diffractive element.
FIG. 8 is a radial cross-sectioixal drawing of the diffractive element of FIG.
7.

-3-FIG. 9 is a schematic drawing of the diffracted orders from a lens having both refractive and diffractive powers.
FIG, 10 is a cross-sectional slice of the phase imparted upon transmissioi-i through an exemplary diffractive element.
F1G. 31 is a through-focus plot of the.M'I'F of the diffractive element of FIG. 10, at tllree representative spatial frequencies.
F1G. 1.2 is a thzougli-focus plot of the MTF at 50 lp/mm of an exemplary diffi-active element, for a variety of central zone radii.
FIG. 13 is a cross-sectional slice of the phase imparted upoD transmission through an exemplary diffiactive element.
FIG. 14 is a tlirough-focus plot of the MTF of the diffractive element of FIG.
10; at three representative spatial frequencies.
FIG. 15 is a through-focus plot of the MTF at 50 lp/j-nm of an exemplary diffractive element, for a variety of central zone radii.
FIG. 16 is a cross-sectional slice of the phase imparted upon transmissioz-i through aai exemplazy difftctive eledrent.
F1G. 17 is a through-focus plot of the MTF of the diffractive elemeiit of F1G.
1.0, at three representative spatial frequencies.
F'iG. 18 is a through-focus plot of the MTF at 50 lp/mm of an exemplary rliffractive element, for two central zone radii.
FIG. 19 is a cross-sectional slice of the phase imparted upon transmission through an exemplary diffractive element.
FIG. 20 is a thraughWfocus plot of the MTF of the diffractive element of FIG.
10, at three representative spatial frequencies.
FIG. 21A, B are cross-sectioiia.i. drawings of aia exemplary intraocular lens, botti with and without a. diffractive elenient.
FIG. 22 is a surface-by-surface schematic drawing of a Liou-Brennan model eye with tl-ie intraocular iens of FIG. 21.
F1G. 23 is a through-focus plot of the calculated Modula.tion Transfer Function at 50 lp/mm for the intraocular lens ofFIG. 21 used in the Liou-Brei'man model eye oi'FIG. 22.

-4-FIG, 24 is a surface-by-surface schematic drawing of a Norrby model eye with the intraocular lens of FIG. 21.

FIG. 25 is a through-focus plot of tl-ze calculated Modulation Transfer Function at 50 lp/nim for the intraocular lens of FIG. 21 used in the Norrby model eye of FIG. 24.

Detailed f?escription FIG. I shows a human eye 10, after an intraocular lens 1 has been implanted.
Light eiiters from the left of FIG. 1, aiid passes through tlze cornea 12, the anterior chaniber 15, the iris 16, arad enters the capsular bag 17. Prior to surgery, the natural lens occupies essentially the entire interior of the capsular bag 17. After surgery, the capsular bag 17 may house the intraocular lens 1, in addition to a fluid that occupies the reinaining volume and equalizes tlle pressui-e in the eye 10.
The intraocular lens 1 is described in more detail below. After passing through the intraocular lens 1, light exits the posterior wall 18 of the capsular bag 17, passes tbrough the posterior cl-iamber 11, and strikes the retina 12, which detects the light and converts it to a signal transmitted through the optic nerve to the brain.

The intraocular lens 1 has a-i optic 1a that has a refractive index greater than the fluid that surrounds it. The optic 1 a has an anterior surface 2 facing away from the retina 12 and a posterior surface 3 facing toward the retina 12. The optic la is held in place by a haptic 19, which couples the optic la to the capsular ba.g 19. In the -ll ustrated ernbodzrnei-it, the optic la is suspeaided within the capsular bag 17, for exaa-nple, to allow accoinmodative movement of the optic la of the iiitraocular Ieixs I along the optical axis (a so called "accommodative intraocular lens").
Alternatively, the intraocular lens l. may be disposed adjacent to, and even pressed against, the posterior wall 18, for exanaple, to reduce cellular growth on the optic l. a.
The optic l a nlay be either a naorzofocal intraocular lens or a multifocal ii-itraocular 1ens.

A well-corrected eye forms an image at the retina 12. If the lens has too much or too little power, the image shifts axially along the optical axis away from the retina 12, toward or away from the lens. Note that the power required to focus oii a. close or near object is moze tliaii the power required to focus on a distant or far object. The difference in optical power between the farthest and nearest object than may be brought into focus by a paT-ticular lens or lens system is

-5-lcnown typically as the "add power" (e.g., in the case of a multifocal intraocular lens) or the "range of accommodation" or "accommodative range" (e.g., in the case of an accommodating intraocular lens that responds to ciliary muscle contraction to inove axially and./or deform so as to change the optical power of the optic). A normal rwige of add power or accommodation is about 4 DiapLers at the plane of the optic la of an intraocular leiis, although this number may be as low as 3 or fewer Diopters or as high as 6 or more Diopters, depending on the geometry of the patieiit's eye.
In many cases, the optical system of the eye may be well approximated by a tliira lens model, showax schematically in FIG. 2. Such a thin lons systei-n 20 may be used to predict the location of an image for a given object distance Z. in. addition, the tkzrn lens system 20 may also be used to predict the power required of a lens to bring objects at aii object distance Z into focus on the retina.

A margiiial light ray 29 originates at the base of an object 21, where it crosses the optical axis 28. The ray 29 passes through aii o,ptioizal spectacle 22 having a power Ospectade, arxd enters the eye. The eye itself is represented by a cornea 23 with a power Ocomea, an aperture stop (or pupil) 24, an intraocular lens 25 with a power and a retina 26. An image 27 is formed of the object 21 at the location w1here the marginal ray 29 intersects the optical axis 28. If tl-ie object 21 is "in focus", then the image 27 is formed at the retiz-ia 26. If the object is "out of focus", then the image is translated axially away frozn. the retiiia 26, either too close to the lens or too far from the Iens. The space between the object 21 and the cornea 23 is assumed to be filled with air, having a refractive index of na;r (typically 1). The space between the cornea 23 and.
the retina 26 is assumed to be filled with a fluid having a refractive index of ne.e.
Some specil"ic numbers are included in a paraxial raytrace of a"typicaf" eye, shown in FIG. 3. In addition to predicting where aii image will fall for a given object distance, such a raytrace may be used to generate one of a raumbei, of known formulas that predict t.lze required intraocular lens power for a particular patient's eye. Because the utility of sucli a raytrace may be great, it is beneficial to examine the raytrace methodology and some of its assumptions. The raytrace is described in detail in. the followiiig several paragraphs.

The calculations are performed using a paraxial. raytrace, with f-tve surfaces: (1) spectacles, (2) the comea; (3) the intraocular lens, (4) the iris (or aperture stop, or pupil), and (5) the retina.
For the purposes of this calculation, each of these five surfaces is assuined to be aii infinitely thin

-6-surface or thin lens having a particular power, which may be a value including zero. The nuinerical values used in the calcul.ations irxay vary depending on the preference of the practitioner, htit the tizin lens methodology rei-naiias essentially unchanged. Each of these surfaces is described in more detail below, Given the power 0 of each surface, the refractive index n between the surfacesa azid thickness t between the surfaces, one may use the well-knowM paraxial rei='racti.on and transfer equations to trace a ray througb the optical system of the eye.

The paraxial refraction equation predicts the "iting ray aiigle (relative to the optical axis) u', after refraction at a surface with power (D:
1.0 n'u'=nu --yO , where u is the incident ray angle, y is the incident aiid exiting ray height at the surface, and n and xa' are the iiicident and exiting ref'ractive iiidices, respectively.
The refractive indices are dimensionless, the ray angles are in radians, the ray heights are in mm [or, alternately, ml, and the surface powers are in rnrn"1 [or, alternately, Diopters].

The paraxial transfer equation predicts the ray height y' at a surface, after propagation by a distance t between a previous surface and the cilrre.nt surface:
y' = y -3- tu, where y is the ray height at the previous surface and u is tl-ie ray angle (relative to the optical axis) between the previous surface ajid the current surface. The ray angle is in radians and the ray heights and distances are both in mm [or, altemately, both in m].

The abov-, paraxial refraction and transfer equations are alteniately used to trace rays through a multi-surface optical system. The equations above trace rays from lei"t-to-rigllt, but may easily be inverted to trace rays from right-to-left.

There are two commonly used rays shown in the raytrace: (1) a marginal ray, which originates from the base of the object, passes through. the edge of the aperture stop, a.nd strikes the base of the image, and (2) a chief ray, which passes through the cerater of the aperture stop and extends to the edge of the field of view. Quaiitities that may be entered by the user are shown in thick-bordered cells; the remainiiig quantities are calculated. Note that several distances are calculated with respect to measurable or predictable quantities in the eye, sucli as Axial Length (AL) and Effective Lens Position (ELP). A Vertex Distance (VD) is the distance between the

-7-

8 PCT/EP2008/061235 spectacle and the cnrnea., and is talcen to be 14 rnm in this example. The object distance ("Z" in FIG. 2) may be infinite.

Once the rays are traced, one may use the ray-t.race results to derive a kiiown forinula for the required lens power 01,,15 for a giveii set of distances AL, ELP and VD, an infinite object distance, a given comea power ooornep, and a giveii (optional) spectacle power ~7Sp~~r~~ie power:

ny, ney-AL - .~.~P ELP

+ 0c001aa VD
~ specrarle For tla,e model, the cornea is then assumed to be a siiigle, infinitely-thin surface, with an optical power of (noor~,~~ - na;r) / RGqrõ... A typical measured value for the radius of curvature of the comea is about 7.704 mm, wlaich yields a. typical power of (1.3375 - 1) /
(7.704 mm) = 0.0438 rnrn"1, or 43.8 Diopters. For the model, the incident medium for the comea is air, with a refractive index of 1. The exiting medium of the coriiea is typically chosen to be the refractive index of the eye ~aeyQ, with a value of roughly 1.336. Note that the value of ncornea is used only to eaiculate the power of the cornea, aisd is not used a.t its exiting medium. In tracing rays beLvaeen the cornea at7d the lens, the refractive.index is takeli to be n~y,, or about 1.336.

ComanQ , ofF the-sbelf, intraocular- lenses are available froan powers of 5 Diopters to 30 Diopters, in increments of 0.5 Diopters. Some =n.anuf'acturers may eveii provide increments as small as 0.25 Diopters, or smaller. The above forxnula is cominonly used to estimate the required lens power, and the closest available off the-shelf lens power is typically chosen for implantation.
The numerical values themselves are for a so-called "typical" eye, although any suitable values inay be used. For typical values of axial length and effective lens position, 23.45 mm and 5.25 mm, respectively, a typical. separation between the intraocular lens aiid the retina is about 18.2 mm. The incident refractive index on the retina is neyej or about 1.336.
As a nuanerical example, coi-zsider the following typical values: n~,r 1, noornea - 1.3375, i7eye = 1.336s Rcornea = 7.704 mm, ~>cor:~ea =' 0.0438 r[ln1'1 (or 43.8 D), 0spectacies `0.0005 m1x1-1 (or -0.5 D), VD = 14 mm, ELP = 5.25 mm, and AL =23.45 mm. Iizserting these numerical values into the equation for the required power 4)ie,s of the intraocular lens gives a typical value of 0.4212 mm"1 (or 21.2 D).

_g_ The raytrace of FIG. 3 may also be used to predict the location of the image for a variety of object distances C"Z" in FIG. 2), and predict the power required of the intraocular letis to bring the objects into focus on the retina. FIG. 4 is a plot of retina-w-iÃnage separation versus required lens power, for a variety of object distances, for the "typical eye" of FIGS.
2 and 3, For an infiziitely distant object, located at a "far point," at or iiear optical infinity) the required lens power is 21.2 Diopters, and the image falls directly oii the retina. As the object moves closer to the eye, we see an increase in the power required of the lens to bring the object into focus at the retinaõ For an object located 250 mm away from the spectacle (ooznmozily denoted as the "izear point," althou.gli other "near point" definitions may be used), the required lens power is about 26.5 Diopters, for aii "accommodatioza. range" of about 5.3 Diopters. Note that if the lens is well-corrected for "far vision," then a "near" object will have its image displaced about 1.4 mm behind the retina in this model. These numerical values are for a"typical' eye;
individual eyes may vary frorn the "typical" values of FIG, 3. Although the numbers may vary, the trends are similar, with a higher lens power required at L`near'' focus than. at "far" focus.
Note that because of the generally linear shape of the cuive in FIG. 4, separations between the image arj,d the retina may be ex~pressed in terms of the equivalent power error.
For instance, if a lens is corrected for aia infinite far point, then an object I meter away will fon-n an image about 0.4 mna behind the retina. If the lens power were increased by 1.4 Diopters, then the object 1 meter away would be well-focused at the retiiia. The quantity typically used to describe this is "power error", wliich is usually expressed in Diopters. In otlaer words, 1.4 Diopters of extra power is sufficient to briiig a I meter-distant object into focus for a leiis that is well-corrected for infiniteiy distant objects. Equivalently, if the lens is designed for 1meter-distant objects, then decreasiiag the lens power by 1.4 Diopters is sufficient to bring infzniteJy-distant objects into focus.

Likewise, if a lens is corrected for the near point of 250 mm, then decreasing the lens power by 1.4 Diapters is sufficient to bring ob,jects iaito focus at a distance of 350 mm. In general, it is more convenient to describe object distailces by their corresporldilag power differences. For iiistaiice, without regard to sign, a"1..4 Diopter power error" may describe both a lens that is designed for infiizitely distant objects and used at 1imeter, and a lens tE-iat is designed for 250 mm and used at 350 mm; bot17 are "out of focus" by 1.4 Diopters. In inany cases, the effects of

-9-defocus may be symmetric through-focus, so that a-!-I.4 Diopter error may have roughly the same perfornxance as a-I.4 Diopter error, (Exceptions may include a non-zero spherical abeiTation, whicla is asymmetric through focus.) We may summarize the fjiidings of FIGS. 1 through 4 as follows: Defocus errors in the lens of an eye may be expressed in terms of equivalent power errors, in Diopters. A lens may be corrected for "fai=" objects, aiad may work su.f.'ficieiitly well in a+/-Diopter range around the "far poin.t." Likewise, a lens may be corrected for "near" objects, and. may vaork sufficiently well in a +1 Diopter range around "near." The term "work sufficiently well" is described in detail below.
One exeinplary figure of merit for tra.clcin.g tlie performance of visual systems is known as the "Modulation Transfer Function," or "MTF." MTF is particularly desirable as a figure of merit because it may be both predicted by simulation and approximately measured through the visual respanse of real patients.

The MTF is related to the apparent contrast of alternating briglzt aild dark bars of an image. If the MTF is I, then the briglit areas appear compietely bright, aiid tl-ie dark areas appear completely dark. If the MTF is 0, both areas appear as gray, with no distinction between bright and dark areas. Typically, MTjc values Iie bc;tweert 0 and 1, with szziie light bleeding intcs the clarlc areas and some darkness bleeding into the light areas.

The MTF has a dependence on spatial frequency, which is inversely related to the widtli of the alternating bright and dark bars in the image. Note that MTF is particularly well-suited for human vision testing, in that the spatial frequency may be controlled during a test by controlling the size of a letter `E" where the widths of the prongs in the "E' have a prescribed size.
Although MTF may be measured along two orEhogonal axes, we assume rotational symmetry in this document.

Spatial frequency is typically repoi? f:ed in units of line pairs per mm at the retina. At lo-vv spatial frequencies (wide bars), the MTF is generally higher than at high spatial frequencies (ziarrow bars). For frequencies higher than a particular cutoff spatial frequency, the MTF is exactly 0; this is a property governed by the physics of diffraction.
The cutoff spatial frequency SpFr,,taff may be calculated for a round pupil, and is given by S .~"7^ r = 21n,~~r1 ~ curo t x ., ~ ~..

where rj,,põj is the radius oftl-te exit pupil uf the lens, ?, is the wavelength, and F is the focal distance of the lens. For MTF calculations, we assume that the exit pupil of the lens and the principal planes of the lens are all coincider-it with the lens itsell: For the "typical eye" lelas of FIGS. 3 and 4, F is about 18.2 mm. We choose to evaluate the lens at a green wavelength of 550 nrn. We also choose a lens diai-neter of 3 mm for the lezis, so ru,tnjj = 1.5 mm. This yields a cutoff spatial frequency of about 300 line pairs per rnin. Note tlaa.t this value is for iizcoheren,i: light, as nearly everything seen with the eye is illuminated with incoherei-it l'zgixto Note that otlaer wavelengths, distances and pupil sizes may be used as well; these numbers are merely exemplary aiad should not be construed as limiting in ariy way.

MTF may be calculated in a straightforward numerical mani-icr, either by a raytracing program such as Oslo or Zemax, by anotl-ier existing sitnulation tool, or by self writlezi code, all of which provide generally equivalent results with varying degrees of sophistication. For the plots in this document, a self-written code was used, using a wavelength of 554 nm, a pupil radius of 1.5 nnni, axid a lens-to-retina separation of 18.2 inm. Note that other suitable values may be used for any or all of t:hese qu.azititzes, including multiple wavelengths.
FIG. 5 is a plot of the MTF for the "typical eye" of F1: GS. 3 and 4, _For various aFnouiits oi-defocus. The defocus is expressed. iaa terms of power error, as described above.
At a spatial frequency of zero, the MTF is 1. At increasing spatial frequencies, the MTF
decreases, not zaecessarily anonotonically, until it reaches a value of 0 at the cutoff frequeiicy of 300 line pairs per mm.

For no defocus, the MTF rolls off roughly linearly at low frequei7cies, then flattens out at high spatial frequeiicies. The value of this defocus-free MTF is known as the "diffraction limit,"
wlaich represents a maximum attainable MTF for a particular spatial frequency.
The actual values of the di1;'fraction-limited MTF are given by the following equation:
f I~fiIF~SpFq)=~ lcos- SpFq Sp rq 11 SPFq MpFq,u~,,ff 2SpFq,.ofr 2Sp.Fqf where SpFq is the spatial frequeza cy ai-id SpFqC,tQff is tlae (incoherent) spatial frequency cutoff, or about 300 lines pairs per mm (lp/mm, or miri i). This expression is valid only for a generally round pupil.

For non-zero defocus, the MTF decreases from tlle diffraction-limited. MTF.
For large enough dofocu.s (see the 0.36 Diopter curve), the MTF reaches zero arourad, 90 lp/miii, this results from the MTF being the magnitude of a complex quantity, the Optical Transfer Fuj'lction, or OTF, which passes through zero.

The five curves in FIG. 5 may be coinpared with Icnowaa MTF-versus-defocus plots for a round pupil. The curves for 0 D, 0.12 D, 0.24 D, 0.36 D and 0.48 D eacla correspond to wavefront errors (W020) of 0 waves, 0.25 waves, 0.5 waves, 0.75 waves ajid I wave, respectively.
The conversion from power in Diopters to wavefront error in waves may be accomplished as follows. Consider tl-ie power perturbation 0. The lens is assumed to have an unperturbed focal distance of 18.2 mm, aaid a perturbed focal distance of 1/(0 + 1/18.2 tnm).
Subtract the two, and rearrange to arrive at the axial distance Az:

AZ o (18.2tzam)2 The wavefront error WQ2p traay be related to the axial distance Az by pupu Wa20 Az.
2n.(I Ur?177Z)2 For many optical systems involving human vision, the MTF values are reported at one or more representative spatial frequezicies. For instance the perforniance of a systex-n may be reported using the MTF at 25 lp/mm, the MTF at 50 lp/mi-n and/or the MTF at 100 lp/mm. Azly or all of these may be used. as a figure of merit, with liigher values representing a"better" iinage.
FIG. 6 is a plot of the MTF of the "typical eye" of FIGS. 3-5, versus defocus, at three representative spatial frequencies. The peak of the MTF curves is at zero defocus, and the peak values correspond to the intersections of the diffraction-limited curve of FIG. 5 with the three dotted lines. Because there are no other aberrations present, the MTF curves are symmetric through focus.

We may define a depth of focus for a lens based on any number of criteria, such as full-width-half-max (FWHM) of any of the MTF curves, a pai-ticular increase in spot size or wavefror-it error, a particular decrease in Streh.l Ratio, or any other suitable criterion. For the illustrated embodiment, the depth of focus may be considered. to be the focal range over which the MTF at 50 lines pairs per mm is greater than 0.17. In FIG. 6, the depth of focus is about 0.8 5 Diopters.
As discussed in greater detail below herein, other criteria may be used to define a depth of focus.
Outside of the depth of focus, the MTF. curve at 50 line pairs per mm drops to an unacceptably low value, meaniaig that an object at this particular spatial frequency would appear unacceptably blurred.

In practical terms, this means that. if a single-focusintratacular lezis, such as the i.iitraocular lens 25 used in the "typical eye" of FIGS. 3-6, is designed for "far vision", it may not work for "near vision", which generally requires aii add or accommodative power of about 3-6 Diopters. A
patient with such a "far vision"-desia ed intraocular lens rnay see distant objects clearly, if the power er.ror corresponding to the distaAice is within the depth of focLis.
Such a patient would likely require additional reading glasses or contact lenses to focus on near objects, and. may require a second set of glasses for near or iiatermediate vision. This may be burdensome for the patient.

Fortunately, there exist multiple-focus intraocular lenses, which may fomi both a"near"
and a "far" image on the retina simultaneously. After implantation, the patient's brain leams to loracEntra.tg ori one image while ignoring the other. These lenses inay produce two foci, ea^l'x wit h its own depth of focus. The patient may be able to see "near" aiad "far"
objects clearly, but may still require glasses to provide interrnediate vision. This may be an improvement over a single-focus lens for the patierit, and less burdensome for the patient. There is an ongoing effort to increase the depth of focus of both single and multi-focus intraocular lenses, to further reduce the dependeace on spectacles for the patient.

Many of the multiple-focus intraocular lenses are constrtiicted as follows.
The anterior side and posterior side of the optic may each be convex, concave or planar.
The optical powers from the at3terior side and ti-ie posterior side add to form the refractive power of the lens.
Typically, the refractive power of an intraocular lens may be in the range of about 5 Diopters to about 30 Diopters. Eitl-ier or both of the anterior and posterior sides may have a. multifocal diffractive or refractive element oia it, for example in the fon-n of concentric rings or zones. In the case of a diffractive multi-focal intraocular lens, the diffractive zones may have a phase structure in the form of local thickness variations along the surface: of the diffractive elernent. For instance, "even"-nurnbered riixgs may be slightly more or less thick than "odd"-numbered rings, so that the transmitted optical path leiigth is greater or less in the even rings than in the odd rin.gs.
Alternatively, the zones rz-tay each include a curved profile that affects the relative d.iffraction efficiency of particular diffractioia. orders. As a further alternative, an an-iplitade structure may be used, in which certain, zones have a reduced or no ii-itensity transmission, although this is inherently less efficient than a phase structure. There are two gezieral classes of multifocal lenses, which may be similar in appearance and/or construction, but have sliglitly different characteristics.
Both contain phase o~jects on one or both sides of the optic, typically in concentric rings or zones.
For the purposes of this document, the phase object(s) may be referred to as a "diffractive elemerzt," for both classes discussed below.

The first class is k.nooai as "diffractive" inu.ltifocal, in which light transmitted through a radial zone may be rouglily 180 out of phase (or out of phase by any other suitable value) with light transmitted through adjacent zones. In diffractive anultifocal lenses, the radii that separate the zones are chosen for a particular desired power (or focal length), and are arranged in a prescribed rnaiu7er based on the radius of the central zoi-le. Light from a particular zone is not explicitly directed to one focus or the other; in otlier words, the diffractive elemei-it forins both foci by d'af-f'raction through the entire d.iffaactive elemen.t. As a result, a diffractive multifocal intraocular lens may be constructed to near and far vision perfort-nance that is substantially the same for vai}jing pupil sizes of the eye. Typically, diffractive multifocal lenses are bifocal in nature and, as a consequence, may not provide good intermediate visiozi. These "diffractive"
multifocal lenses are showr-i and described in further detail below.

The second class is known as "refractive" rn.ultifocal, in which light from a particular zone is explicitly directed to one of two foci. For instance, the central (or 0'h) zone may direct ligllt to the "iiear"' focus, the 151 zone may direct ligl-it to the "far" focus, the 2 d zozae may direct light to the "near" focus, and so forth. The redirection of light is accomplished by including a radial refractive profile withiii each zone; this is iD contrast witb the "diffractive" elements, which may Igave a generally flat radial pliase profile withita each zone. The zone radii in a "refractive"
element may be chosen arbitrarily, and may or may not coincide with those of a "diffractive"
element. These are described further below. In the case of refractive multifocal intraocular leiises, various zones or annular regions of the optic surface may be constructed to particular foci, For example, sorz-ie annular zones may be constructed to focus light onto the retina from a distant object or poitit source, while other zones are configured to focus light onto the retina froin ob~jects or point sources located at near or intermediate distances. As a result, refractive znultifocal intraocular lenses typically provide near and distai7t vision perforrnai3ee that varies witli pupil size of the eye. Because each zone in a refractive multifocal intraocular lens may be directed to a specific focus, refractive multit"ocal intraocular lenses may be designed to provide at: least some intermediate vision, in addition to near and distant vision.

The following text, as well as FIGS. 7 through 20, fiartl-zer describes "diffractive"
multifocal lenses. However, it vvzll. be appreciated that embodiments of the invention may also include the use of refractive multifocal iiitraocuiar lenses.

FIG. 7 is a front-view schematic drawiiig of a diffractive element 70.
Typically, the intraocular lens has refractive power from its two curved sides (or one curved side and c~ile fiat side), and additional diffractive power fronl the diffractive element 70. The diffractive element 70 may be located on one or both refractive sides of the optic; for the figures in this document, t1ie diffxactive element is shown as beinc, on only one side, although in practice there may be diffractive portions oii both sides.

r IG . 7 is a front-view plan drawino, of a diffractive element 70. The diffractlva element 70 includes a series of concentric rings or zoi-zes, with a central zone 71 and radially larger zones 71, 72, 73 and 74. Although four zones are pictured in FIG. 7, it wii.] be understood that more or fewer zones may be used.

In the diffractive elenieiit 70, light transmitted through "eveil " zoiies 72 and 74 inay be roughly 180 out of phase with Iight trazaasmitted tlirough "odd" zones 71 ajid 73. The tenns "odd"
and "even" are interchangeable 1lerein, becaiose there is no particular significance to the Ot" or lst zone. A numerical analysis of the zone radii follows below.

FIG. 8 is a radial cross-sectional drawing of the diffractive element 70 of FIG. 7. It will be understood that this diffractive element may be found along the curved surface of the optic, aild that only the diffractive portion is shown in F1G. S. The curved, refractive portioii of the surface is not shown in FIG. 8.

The zones 71-74 are separated by various radii, d.enoted ra through r3. The optical path lengths from these radii to a diffractive focus 75 are denoted as OPLa through OPL3, respectively.
Note tl-tat tl-ze separation between tl-ie diffractive eiemeiat 70 and the diffractive focus 75, dezioted as Fd;ffrattive, is the foaal length of the diffra.ctÃve elexnen.t if tiiere were no refi active elemelits ill the lens.

The relationships anioxag the optical path lengths C3PLi determine the i-adii ri, as follows.
To eiisure that adjaceilt zones are out of phase, we require that 0PL1+, - OPL, = A

where k is the wavelength. We assume the diffractive element is essetitially planar and write z 2 2 Fi+1 + Fdi~uine +FwJIaclive ~ -' We assume that the radii ri are much smaller than the diffractive focal length Fd,fft.tiw, and rewrite to obtain ~
~ iA z r=,= i~.Fd;ff,aGu>~ ~xa _ ~fo Od~ractive where tl-ie radius of the central zone ro may be chosen arbitrarily.
Note in the derivatiozi above that the path length difference between adjacent radii is set to be (7J2). To ensure fne conditioia tl-iat adjacent zones are out of phase, the optical patli difference may alternatively be set to (nJ2}, :L(3i,J2), (5V2), and so forth. These other path differeDces fon-n the various diffracted orders froin the diffractiozi element 70, witli effective diffractive focal lengths of Fdjffraetive, (Fdxffx.ctiv,,/a)g (Fdijrr.ctivel5), and so forth, ax-id corresponding diffractive powerS of :~:(Ddiffractive, 30dirrractive, zE50j;ffr=active, and so forth. It is interesting to note that these fonn only "odd" orders; there are iio "even" orders from. such a diffractive element.
FIG. 9 is a schematic dra.wiiig of the diffracted orders from a lens having both refractive (from the surface curvatures) aaad diffractive (from concentric zojies in the diffractive element) powers. The zeroth order of the diffractive element is located at tlae refractive focus of the lens, as if the diffractive element were absent. The positive and. negative orders may be evenly spaced, closer to and farther from the lens, respectively, it sbQuld, be noted that there may be no light directed into the non-zero even diffracted orders, as discussed above.
Before considering some specific examples of diffractive elernents, it is benei'acial to digress momentarily to discuss diffraction efficiency. For the purposes of this document, the diff.raction efficiency of each ciiffracted order is the percentage of incident power that is directed into each order. For a phase object, such as the diffraction eleznerats considered herein, the sum of the diffraction efficien.cies of all orders is generally 100 / .

We now present the calculated diffractioii efficiencies for a Iinear binary phase grating, which is similar in concept to the rotationally symiaeti-ic diffractive clernents considered herein, but is mathematically simpler. The diffraction efficieiicy may be calculated analytically, as a function of duty cycle "dc" (wlaicli cazi vary from 0, where the widtb. of the phase features is essentially zero, to 0.5, where the up/down phase features each have a width of half the pitch), peait-to-valley pbase depth "pd" (whicia can vary fropn 0 to 360 , but the diffraction elernents described berein have a peak-to-valley phase depth of 180 ), and order nuniber "n". The diffraction efficiency of the 0"T order is found to be 4(dc)2 cos~ (pd) The diffraction efficiency of the (non-zero) nth order is 4 sin2 dcxnx180 ) 2 pd 2 nZ sin (-2 For a duty cycle "dc-" of 0.5 and a plzase deptki "pd" of 180 , the diffractiozl effgcieracy of both the +1" aiid -1" order is (4/n2), or about 40.53%. The remaining 18.94%, of the light is divided ainong the rernainiiig odd orders. The diffraction efficiency of the even orders is zero, includijig the 0"' order.

Althougli the radiali), symmetric diffractioia elements ofF1GS. 7 through 9 do not llave the same calculated diffraction efficiencies as the linear biilary phase grating, some general trends may apply. First, the diffraction efficiency iiato the positive orders may be equal to the diffraction efficiency izito the negative orders. Specifically, for the diffractive elements considered herein, the a-I st and -1 St orders i-na.y have equal diffraction efficiencies.
Second, the diffraction efficiency of the Ot" order may be 0, unless at least one of two conditions occur: (I) The phase depth difference between adjacent zones is shifted away frorn. 180 , or (2) the duty cycle is shifted away from 50/50. In terms ofthe radially symmetric diffractive elements considered herein, the analogy to altering the duty cycle is varying the radius of the first ring. The aiialogous 50/50 condition is wliere the edge of the central zone is 184 out of phase with the center of the central zone.
Mathematically, this occurs wlien ~4 ~~~dlffracrltie +
- : ^j +~~'di~raclive =
V Otk,'ffiaaÃvs For a wavelei-igth of 550 nzn aiid a power expressed in Diopters, the radius of the central zone, expressed in mm, simplifies to sqrt (0.55 / Power). Some numerical examples follow: For a power of 1_5 Diopters, the radius of the ceiatral zone works out to 0.605 mm.
For 1.0 Diopters, the central radius is 0.742 mm. For 0.5 Diopters, the ceritral radius is 1049 mm.
Other powers may be used as well, such as 2 Diopters, 2.5 Diopters, 3 Diopters, and so 1'ortb..
Wbeia the central radius ro satisfies the above equation, the subsequezxt radii are calculated as described above, and the phase depth of adjacent zones is 180 , we expect that 3-zo liglit will be directed iaito the 0'~' order, that about 40% of the light will be direcfed into the -1" order, that anotber 40% of the liglxt will be directed into the +15` order, aid that the remaining 20 / of the light will be divided aanoi-ig the remairiing odd orders. Several diffractive elements that satisfy these criteria are considered below, as well as several diffractive elements that explicitly violate these criteria.

Note tiaat there may be some embodiments where more light is directed into one focus than into ibe other. For instance, rather than splztting the available ligiii.
(roughly 80% o1'the total incident light) equally (50150} ii-ito the near/far foci, the split may be 40/60, 60/40, 30/70, 70/30, or any other suitable ra,tio. In an extreme limit, the split may be 0/100 ixito tiie ilear/far, and the lens may be effectively moiiofocal.

FIGS. 10 through 20 describe various exemplary diffractive elements and their respective performaiices through-focus, when used as pai-t of the "le~xs" in. the "typical eye" described above.
In all cases, each lens iixay be adapted to or designed for iaiclusion in a real patient's eye; tlle "typical eye" is merely exemplary and should not be construed as lizniting in any way.
FIG. 10 is a cross-sectional slice of the phase imparted upon transmission through an exemplary dxffractive element. Here, as with all of the diffractive elements considered in FIGS.
] D through 20, the design wavelength is 550 nm. (in the green portion of the spectrum), and the pupil radius is 1.5 mm. These values are merely exemplary, and any suitable values for the design wavelengtli and pupil size may be used. Note that for the purposes of this document, the pupil size is the actual. size of the diffractive elei-neiit.

- I$-The diffractive power of the diffractive eIem.ent of FIG. 10 is 1.5 Diopters per order. For instance, if the refractive power of the lens is 21.2 Diopters, then the plus first diffracted order has a coinb'rned (refractive + diffractive) power of 22.7 Diopters, ibe rni.zaus first diffracted order has a combined power of 19.7 Diopters, and so forth.
The radius of the central zoiie is 0.61 mm, which satisfies the condition described above, wbere most of the light is directed into the +1 " and -1 " orders, witl'l very little in the O`h order. We therefore choose a"nears' focus to coincide with the --15t order and a "far"
focus to coincide with the +I.SF arder. In. this lens, "<nea.r" and "far" zoiies are separated by 3 Diopters, whic17 is a typical value fox dual-focus intraocular lenses. The radii of the otlier zone edges in FIG, 10 are 0.86 mm, 1.05 mrix, 1.21 mm, 1.35 mm and 1.48 mm..

The tbrougia. focus performance of this diffractive element is shown in FIG.
11. The MTF
cuives for 25 Ip/inm, 50 lp/mm and 100 1.plmrn are all shown tha=ough-focus.
(Recall that the horizontal axis is analogous to viewing objects at varying distances from the eye, with a"far'g object by the left edge of the plot aiid a"near ' ob~ject by the riglat edge of the plot.) As expected, there are peaks at 1.5 Dxopters, wizich correspoild to the 1"
orders, and no , peak at 0 Diopters, which correspoiids to the 0i'' order, For the definitio'-1 of deptl, of for1-1s ,rsed earlier, i.e., the region over which the MTF at 50 lp/mm is greater than 0.17, the depth of focus for each focus is about 0.6 Diopters.

In an attempt to increase the depth of focus beyoi-id the two discrete peaks of FIG. 1 I, we may adjust the radius of the central zone. As shown earlier in the linear grating analogy, if we shift the duty cycle away from 50/50, the diffraction efficiency of the Ou, order iilcreases from zero. For the diffraction elemeiit of FIG. 10, increasing the radius of the central zone beyond 0.61 mm has an aiaalogous effect, diverting liglat from the 1" orders back into the 4th order, tlaus potentially increasing the overall deptlr of focus (range over which the MTF
at 50 l.p/mm is greater than 0.17). The radii of other zones are calculated based oii the desired power of the lens and the radius of the central zone, as described above.

FIG. 12 is a through-focus plot of the MTF at 50 ip/mm, for a variety of ceiitra1 zoi7e radii.
We see that as the central zone radius increases from 0.6 mm to 1.5 mm, the 1 s` order peaks disappear, and the 0'h order peak grows. While the 0`" order grows to have a depth of focus of about 1.0 Diopter, we lose the effects of the 1S{ orders, each of which does not have a depth of focus substantially greater than the 0.6 Diopters shown in FIG. 11.

In particular, i-iote that as the central zone radius is varied over its range, the MTF plots form a"lmee, ' which may be thougl-it of as follows. For all the MTF curves in FIG. 12, we define a function as the maximum value of all the MTF curves, over the whole x-axis, The "knee" may be thought of as a local minimum of this I`ui7ction. We see a"lci3ee" at roughly 1.0 Diopters and an MTF value of around 0.08, and. a corresponding knee at -1.0 Diopters aiid an MTF of around 0.08. This knee falls belovv the depth of focus thresliolci. MTF value of 0.17. Thus, changing the size of the ceritral zone does not appear to provid.e a significai7t increase in overall deptl1 of focus.
Another parmneter that may be used in atteznlating to increase the depth of focus is reducing the diffractive power of the diffractive element so that the +1" axid -IS` orders are closer to each other. Referring to FIG. 13, a diffractivc lens is illustrated that, has a diffractive power of 1 Diopter per order. The central zone radius is chosen in accordance with the duty cycle colidition described above, and is 0.74 mm. The radii of the larger concentric zones are calculated as described above, and are 1.05 mm, 1.28 mm and 1.48 mm.
The performance 6i the diffractive e1enietit of FIG. 13 is sb.owzi in FIG. 14:
Compared with FIG. 13, the "near" and "far" foci are moved toward each other, but the depth of focus for each is still about 0.6 Diopters. This value may not be a sigiaifica.nt improvement over the depth of focus shown in the plots of FIG. 1.1. Simply moving the "iaear " and "far' foci closer together by reducing the power of the diffractive element, without doing anything else, does not seein to substantially increase the depth of focus.

If we then take the diffractive element of FIG. 13, and increase tlae central zone radius beyond 0.74 mm, and plot the through-focus MTF at 50 lp/mm, we arrive at the curves of FIG. 1. 5.
These curves also show a"lcnee" at about 0.6 Diopters and an MTF value of about 0.2, and a corresponding "knee' at -0.6 Diopters and ai-i MTF of 0.2. In contrast witla the curves of FIG. 12, it may be noted that this knee is above the MTF tbreshold of 0.17 that defines the depth of focus.
As the central zone radius is increased, the 1't order peaks shrink and the 0", order peak grows, but there is a range of cezitral zoi-ie radii at which the peaks all blend together, so that the overall depth of focus may be significwAy increased.

_20_ The curves of FIG. 15 show that adjusting the central zone radius (and therefore adjusting the diffractioii efficiency into the 0'h order) may have an effect on the depth affocu.s.
For a small central zone (r = 0o8 mm), most of the light is directed into the +X" and -l'Y
orders, with little remaining in the 0'~` order. As a result, we see two distinct peaks, separated by a region in which the MTF is lower than the threshold of 0.1.7. The dept$i of focus may not be signif-Icantly increased. due to these two separated peaks.

For a large central zoiie (r = 1.5 mm), most of the light is directed into the 0"' order, with little or iione reaching the -'-ls;: and -I" orders, Ti-iis is essentially the same case as a single-focus lens with no diffractive effects. The depth of focus, therefore, is not significantly increased beyond the single-focus case.

For a properly-sized central zone (r = 1.05 mm), the overall depth of focus may be increased by directing some light into all of the -1 ", 0"' and +15C orders.
The peak MTF is reduced from the single-focus case, however the width is increased over the single-focus case. This may be coiisidered aii extended depth focus. We examine the case of the properly-sized central zone in 35 more detail in FIGS. 16 and 17.

:A l-Diopter diffractive element; siinilar to FIG. 13 but having a ceiitral zone radius of 1.05 mm, is shown in FIG. 16. The subsequent zone radii are calculated as described above, and are 1.28 mm and 1.48 i-nzn. For a central zoi7e radius of 1.05 mm, tho edge of the central zone is 360 out of phase with the center of the central zone, compared to 180 for the elenlent of F1G. 13.
FIG. 17 shows the 1;hrough4oaus perforxnance of the element of FJ:G. 16. I-Iere, the depth of -1'ocus is about 1.8 Diopters, which is roughly three times the depth of focus of any single focus of FIGS. J 4-i.q-. In addition, the total range over which the MTF at 50 !p/mm is above a threshold value of 0. 17 is approxiznately 1.5 tinaes greater than that for both foai combined in FIGS. 1.0-14.
The MTFs at 25 lp/mi-n and 100 lp/nam are shown in FIG. 17 alojig witii the MTF at 50 lp/mm.
All three MTF curves are well-behaved within the +depth of focus, with none falling to zero in tiiis raiige.

FIG. 18 is a through-focus plot of MTF at 50 line pairs per mrri, for a diffractive element with. 0.5 Diopters per order, for a variety of ceiitral zone radii. The remaining zone radii are calculated as described. above. This plot is analogous to FIG. 15 (1 Diopter per order) and FIG. 12 (1.5 Diopters per order). The so-called "knee" of the curves in FIG. 18 occurs at about ~0.4 Diopters and an MTF of about 0.4. Here, the ]cnee is well above the MTF
threshold used to defiz-ie the depth of focus.

FIG. 19 illustrates a diffractive lens corresponding to tl-ze curve in. FIG.
18 in which the central zone lias a radius of 1.05 mm. The edge of the central zone is 180 out of phase with the center of the central zone; this is analogous in construction with the diffractive elements shown in 1~'IG. 13 (1 Diopter per order) and FIG. 10 (1.5 Diopters per order). The other zone radius is calculated as described above, mid is 1.48 mm. Note that because the pupil radius is 1.5 mm, that there is effectively oiily one additional zone beyond the cexitral zone.
FIGo 20 shows the throughWfocus perfozman.ce of the diffractive element of FIG. 19. The depth of focus, defined as the region over which the MTF at 50 lp/inm is greater thaii 0.17, is about 1.5 Diopters. However, the MTF at 100 lp/mral drops to zero near the center of this focus range, which 1nay be undesirable in soine circurnstarices. For instance, in some ernbodi7nents it may be a desirable characteristic that the MTF values be positive within the depth of focus, out to a particular spatial frequency, such as 100 lp/mm or any other suitable value.
However, in some cases, it may be acceptable to have an MTF drop to zero at a,parlicular spatial. frequency.
Note that tlierc may be other features present in the diffractive zones, in ;idd.itlon to or ir, place of a uniform ph ase object. For instance, there may be a radial phase feature known as a "blaze", analogous to the uniform "slarit" of the phase in a linear blazed grating, wl7ich can direct light prei'ererztia.l.ly iiito one or more diffracted orders. For ex.ainple, a blaze profile may have a dependence on r squared, where r is the distance from the optical axis. The blaze may extend over the entire diffractive element, or may be present in oialy select radial zones.
Much of the above aiialysis is applicable to such blazed diffractive lenses, only usiiig differezit diffracted orders from the +1" and -l" orders shown in FIGS. 10 through 20. For instance, the power inay be split between the 0"' and +1" orders, the +l'` and +2"d orders, the +2"d and +3`d orders, ox the +3a and +0 orders, and so forth. Using specific, predeterrnined orders othcr tban the +1't arid -1" orders may be beneficial in some embodiments, and may have advantages in eeiÃain circumstances. For instance, correction for chromatic a.berratioii may be possible and/or easier for certain combinations of orders. Examples of such designs aru found in.
U.S. Patent No.'s 5,144,483; 4,655,565; 5,748,282; or 5,229,797, all of wliich are herein incorporated by reference in their entirety.

Note also that tlae term "ad,jacexit " orders may refer to ccansecutive orders as defined above, so.ch as the 011 and +1" orders, the Ot" order and-l." orders, the +3rd aiid +0 orders, the -3Td and-4th orders, aaid so forth. Alternatively, the term "adjacent" orders may refer to consecutive orders that have a non-zero di~'raction efficiency or have a diffraction efficiency that is substantially greater than zero (e.g., greater thaia 2% or greater that1 5%) at a design wavelength or over a predetermined range of wavelengt:lis; recall above that in some cases the non-zero even diffracted orders may bave a diffraction efficiency of zero, or substantially zero, at a design wavelengtli or over a predeteri-nined range of wavelengths. lra these cases, the diffracted orders nlay be retaumbered so that boti-i even aDd odd orders may have non-zero diffraction efficiencies. Here, "adjacent" orders may refer to these renumbered orders.
In at least some of the above examples, axi exteiaded depth of focus was produced using diffractive lenses comprising zones of constant phase that produced sigraificari.f energy in at least two diffraction orders. As used herein, the tenn "extended depth of focus"
means a depth of focus that exceeds that of a sirnilar spherical intraocular lens comprising opposing spherical surfaces aiid having substantially the same optical power as an optical power of the lens witlli the extended deptn of ?:ocus_ in tho above Pxarr?pies, t:ne extended depth of focus was produced by us ng a coanbiriation of a relatively low add power (as compared to a traditional diffractive, multifocal intraocular lens) and predetermined radius for a central zone. Such extended depth of focus performance is illustrated at least in FIG. 15 (for a central zone radius of 1.05 mm), FIG. 17 (at least at a frequency of 50 lp/mm), FIG. 18 (for a ceiltral radius of 1.05 mm), and FIG. 20 (at least at afrequeiicy of 50 lp/mm).

Note also that intraocular lezises according to embodiments of the invention may use additional techniques to exteiid the depth of facus, in addition to those described above herein (e.g., the use of diffractive lenses with low add powers of about 2 Diopters (FIG. 16) or about 1 Diopter (FIU. 19)). For instance, in some embodiments, a refractive power aiadlor base curvature profile(s) of an intraocular leiis surface(s) may contain additioi-ial aspheric terms or an additional conic constant, wliich may generate a deliberate amoarri: of spherical aberratioii, rather thaii correct for spherical aberratian. In this manner, ligl-it from an object tl-iat passes through the cornea aiid the lens ina.y have a non-zero spherical aberratiozz. Because spherical aberration and defocus are related aberrations, having fourtli-order and second-order dependence on radial pupil coordinate, respectively, introduction of one may be used to affect the other. Such aspheric surface may be used to allow the separation between diffraction orders to be modified. as compared to wlieii only spherical refractive surfaces and/or spllerica.l diffractive base curvatures are used. An additional number of focus-extending techniques are described in detail in U.S. Patent No. 7,061,693, titled "Optical method and svstem for extended depth of focus," issued on 3un. 13, 2006 to Zalevslcy, and incorporated by reference in its eiitirety herein. In some embodiments, a refractive lens may include one or more surfaces having a patterti of surface deviations that are superimposed on a base curvature (either spberical or aspheric). Exa.mples of such lerzses, which may be adapted to provide lezases according to embodiments of the present invention, are disclosed in U.S. Pateizt No.'s 6,126,286 and 6,923,539 and U.S. Patent Application Number 2006/0116763, all of wb.iclz are herein incorporated by reference in tb.eir entirety.
Referring to FIGS. 21A and 21B, in ceitain ei-nbodiments of the presejit inveiition, alz oplatlialmic lens 200 comprises axi optic 210 that includes an anterior surface 220 baviz-ig a first shape 222 and a.i-i appasii-ig posterior surface 230 having a second. shape 232, the first and second shapes 222, 232 providing a refractive power. The optic 210 further comprises a diffractive element or patterya 240 imposed on, added to, or combined with tlic sec,ond sl^fape 232. The first aa-id second surfaces 220, 230 together provide a base power and aza add power; the add polver generally being less than or equal to about two Diopters or even less or equal to about one Diopter, depeiid.ing on the desired performance of the optic 210 (e.g., the range of the deptl-i of focus under certain conditions, the number of distinct foci desired under certain conditions, tl-te range of vision desired under certain conditions, and the like), The optic 21.0 l-ias a clear aperture thraugh wl-iich light from an object is trazismit-ted tlarough the anterior azad posterior surfaces 220, 230 to Form an image on the retitia of a subject or patient. As used herein the term "clear aperture" means the portion of an optic tl-zat limits the extent of the rays from an object that contribute to the corresponding or conjugate image. The "clear aperture" is generally express as a diaaneter of a circle.
In the illustrated embodiment, the diffractive pattem 240 includes a blazed radial profile.
Alternatively, a binary ptiase grating may be used, for example, as discussed above with regards to p'1GS. 14-20. It is instructive to compare aii exemplary lens having a diffTactive pattem (referred ..2q._ to below as "extended focus") with a similar intraocular 1eiis that Iaclcs such a diffractive pattern (referred to below as "refractive").

The surfaces 220 afidlor 230 of the optic 210 inay be purely refractive and have a shape or profile that is either spherical or aspheric. The shape of the surface may be represented by sag Z
given by the following equation:

Z(r ) y z I R + .4Dr ' + AEtA' l+ 1-r2(CC + 1)11Z z where r is a radial distance from the center or optical axis of the Ierzs, R
is the curvature at the center of the 1ens, CC is the so-cailed conic constant, aiid AD and AE are polynomial coefflcients additional to the caziic corzstant CC.
1n the illustrated embodiment, the diffractive pattern 240 has a relatively low add power and is imprased on second shape 232. The combination of the diffractive pattern 240 aald the second shape define the overall form of the posterior surface 230. The resulting optic 210, illustrated in FIG. 21B, provides an increased depth of focus when ii.lm-ainated at a predetersnined wavelength, or range of wavelengths, relative to a reference optic without the diffractive pattern 115 240 and uavissg a refrac;zvv power that is substantially equal to aba.se powex.
Note that the diffraction element or patterzt 240 may be imposed on, added to, or combined witb. the first shape 222 or diffractive patterns may be imposed on both shapes 222, 232. Note also that the optic inay be bi-canvex, as drawn in FIG. 21, or may optionally be plano-convex or meniscus. For the purposes of camparison between "spherical" ai-ad "extended focus'' Ienses, the exemplary optic 210 is assumed to be bi-convex and symmetric {having the saine radius of curvature), witii the diffractive pattern 240 being added to the second siaape 232 for provide the posterior surface 230 of a simulated "refractive" lens to form a simulated "extended focus" lens.
The simulations ii7ay be performed using, for example, ray tracing or Iei7s design software such as Oslo, Zemax, Code V, or aiay other suitable prograin.
The following two sectiozis provide two differeilt simulated comparisons of an "extended focus" lens with a"refractFve" lens. The first comparison uses aii atia.tomically accurate model of tiZe surfaces in the eye. The second uses an eye model that can also be used to measure a real lens in a physical laboratory instrument, in addition to being simulated. Both are described in greater detail below.

The first simu.lated comparisoxi uses a model eye based on an article by H..L.
Liou. and N.A. Brennan, "Anatomically accurate, finite model eye for optical modeling,"
J Opt Soc Am A, 14(8). 1684-1695, The Liou-Bxeiman model eye uses disfiaiices aiid curvatures that correspond to those in an average-shaped, averagePsized. eye.
RG. 22 is a surface-by-surface schematic drawing of the simulated eye systems for the Liou-Brennen naodel. The dotted lines in FIG. 22 represent rays from an infinitely distant object, passing througli the zeroth order of the diffractive element and forrnii-ig a "far" focus at the retina, There are six surfaces in the simulated Liou-Brennatt eye, with anuznber 0 surface located infinitely far away, Bach surface is described below.

Surface 0 may be considered to be the object of the system. Surface 0 is infinitely far away, or aDy suitable approximation of infinity, such as I e9 mm or 1 e20 mm.
The material aft-er surface zero is air, with a. refractive index of 1.

Surface 1 is the ai-iterior surface of the cornea, witli a radius of curvature of+7,7'7 mm and a conic constant (also kz-iown as "asphericity") of-p.1S.
1.5 The refractive index between surface I and surface 2 is the refractive index of the cornea, w gtb a value of about 1,3716 at a wavelength of 555 n.m. The separation between surface f and surface 2 is the thickness of ti-ie comea, 0.5 mm.

Surface 2 is the posterior surface of the cornea, with a radius of curvature of +6.4 mm aiid a coiiic constant of-ti.6.

The refractive index between surface 2 and surface s is the refractive index of the aqueous humor, with a value of about 1.336 at a wavelength of 555 zu-n. The separation between surface 2 and surface 3 is 3.16 mm, Surface 3 is the iris of the eye, and is the aperture stop of tlie simulated.
optical system. 1t lias a radius proportional to the pupif. diameter, and lias no power or curvature. The pupil diameter in the simulations is 3 mm.

The refractive iiidex between surface 3 and surface 4 is the refractive index of the aqueous humor, with a value of about 1.336 at a wavelength of 555 nrn. The separation between surface 3 and surface 4 is 0.5 mm.

Surface 4 is the anterior surface of the intraocular leiis, with a radius of curvature of +12.154 mm.

The refractive index between surface 4 and surface 5 is the refractive index of the intraocular lens. The lens is inade of a silicone material, witll a,value of about 1.459 at a wavelength of 555 1-im. The separation between surface 4 aiid surface 5 is the axial thicimess (or "center thickness") of the lens, 1mm.

Surface 5 is the posterior surface of the intraocular lens, with a radius of curvature of -12.154 mm. Note tliat the lens is bi-coiivex and symmetrical, witli a conic constant of 0 w-ld no aspheric terms. In other words, the shape of the anterior aiid posterior surfaces is spherical.
Alternatively, the anterior and/or posterior surfaces of the lexis may include a noii-zero conic constant or one or more aspheric terms.

For the "refractive" lens used as a benchmark in this comparison, the optic includes surfaces 4 aiid 5 as described above. For the "extended focus" lens, surface 5 also includes a parabolic, blazed diffractive profile, imposed on the shape of the surface.
The blazed profile may be described by equations equal to or similar to those described in the article by A.L. Cohen, "Practical design of a bifocal hcalogram. contact lens or intraocular lens," Applicd. Optics, 31(19), 375I1-3754 (1992). The diffractive element uses the V' and +l"
diffracted orders. The radius of the first ring in the diffra.c,tive profile is 0.95 mm, corresponding to a-i add power of 1.2 Diopters. The depth of the profile is 3.2 microns, which convelts to a phase imparted upon traismissxon of (3.2 microns times (1.459---1.336) divided by 0.555 .rnicrons), or abou.t 0.7 waveleiigf:hs, or about 255 degrees of phase. The parabolic profile cxtends across all.
zonas, with a step discoiatinuity at the edge of each zone. The step height may be varied from 3.2 microns, depending on the refractive index of ilae lens material or other design fa.ctors. The step height will generally be betweeii about l. micron and about 3 microns, preferably between about 1.5 microns aiid about 2.0 microns.

The refi-active index between surface 5 aiid surface 6 is the refractive index of the vitreous hurnor. in this inodel, the refractive index of the vitreous huinor is taken to be the same as the aqueous humor, or about 1.336 at a wavelength of 555 rain. The separation betweeii surface 5 and surface 6inay be set to a "solve" in a raytrace program., such as OSLO or ZENIP~.X, aild is about 18.7 mrn.

Surface 6 is the retina, and is the image plane far the simulated optical systern.

The eye model with the above intraocular lens was evaluated in polychromatic light, as described in the L'zoo-Brennan reference. Typically, the simulations may be perforined with a primary wavelength of 555 nrn, and a weighting for the other wavelengths in accord with the spectral response of the eye. In other einbodiments, the performaiice of the lens may be modeled and/or evaluated with other weighting factors, for example, to account for varying liglltinc conditions and/or to account for differences betweeii scotopic aiid photopic vision. Alternatively, the lens may be rnodeled and/or evaluated at a plurality of two or three waveleilgths representative of the visible range or a paa-ticular lighting coii.dition, or at a single wavelerigtli representative of the visible range or a particular lighting condition (e&, at a wavelength of 550 rlm).
F1G. 23 shows the performarzce of the "extended focus" lens of FIGS. 21, used in the systeni of FIG. 22, compared to the perfonnance of a similar "refractive" lens that does not have the 1.2 WDiopter-add-power dii"fractive element. FIG. 23 is a through-focus plot of the simulated Modulation Transfer Function at 50 liaae pairs per mm (or, equivalently, cycles per mm or c/mm) for the "spherical" and "extended focus" intraocular ]ei7ses described above.
The "extended focus" lens has a reduced peak MTF, but an increased width to the MTF
curve, compared to the "refractive" lens. The depth of focus may be defined in a nuinber of ways, and many definitions sliow this increased wid.tla. Two exemplary depth of focus definitions are considered below.

A first definition of depth of focns uses an absolute tb.resbold value of 0.17, wllere the depth of focus is the power range over which the MTF at 50 clrnrza exceeds 0.17, Using this definitiota, the "refractive" lens has a depth of focus of 1.36 Diopters, and the "extended focus"
lens has a depth of focus of 1.90 Diopters, which is about 39% larger than the "refractive" lens.
A second definition of depth of focus uses an absolute threshold value of 0.20, where tlle depth of focus is the power range over which the MTF at 50 clxnzn exceeds 0.20. Using this definition, the "refractive" lens has a depth of focus of 1..25 Diopters, and the "extended focus"
lens has a depth of focus of 1.72 Diopters, which is about 37% larger than the "refractive" lens.
Siniilarly, other definitions for depth of focus may be used, maliy of which also show the su.bstaz-itial increase in depth of focus of the "extended focus" lens (whi.ch includes a diffractive element with 1.2 Diopter add power) over the "refractive" lens (a similarly-shaped lens that does not include the diffractive element).

The sitnulated results for Liou-Brennen model may correspond to the surface spacings and shapes of an idealized real eye, but they are difficult to verify experimentally because the lens would be surgically izxa.planted inside the eye of a patient. Accordingly, there is a second eye model, the soWcalled "Norrby modified ISO rnodcl eye" or "Norrby model", whicll also may be simulated, but additionally allows for the measurement of a real lens on a physical testbed.
A second set of simulated results is presented below, whicb also confirins the increase in deptla of focus for the "extended focus" lens over the "refractive" ieiis.
This second simu.lation uses the "Norrby modified ISO model eye".
FIG. 24 is a surface-by-surface schematic drawing of the simulated eye systems for the Norrby model. The dotted lines in FIG. 24 represent rays from an infinitely distant o~ject, passing tixrough the zeroth order of the diffractive element and forniing a"far" focus at the retina. I'kaere are ten surfaces in the simulated Norrby eye, with a number 0 surface located infinitely far away.
Each surface is described below.

Surface 0 may be considered to be the object of the systen-1. Surface 0 is iz-ifinitely far away, or any suitable approximation of infinity, such as 1 e9 mm or 1 e20 mm.
The material aftet surface zerV is air, VYltli a rWfla6rtlvW index oi, 1.
Surfaces 1 and 2 are the anterior and posterior surfaces of a plano-cnnvex singlet tllat mimics the performa.nce of a typical comea. Surface I is the anterior surface of the plano-convex singlet, witli a radius of curvature of +19.24 mm and a conic constant (also lazown as "asphericity" or Q-value) of +0.226. The refractive index between surface 1 and surface 2 is the refractive index of the singlet, with a value of about 1.493 at a wavelengtll of 546 nm. The separation betweeii surface I and surface 2 is the thickness of the singlet,

10 mm. Surface 2 is essentially flat or planar. The singlet has a focal length in air of about 39 mm, or, equivalently, a power in air of about 25.6 Diopters.
The refractive index between surface 2 and surface 3 is 1. The separation between surface 2 arid surface 3 is 3rnm.
Surfaces 3 aiid 4 are the anterior and posterior surfaces of a vvindow. Both surfaces 3 and 4 are flat. The window is made of BK7 glass, which has a refractive index of about 1.517 at 546 nm. Alternativeiy, otiaer glasses may be used, su.cla as SF11, LaSFN9, BaK1, F2, fused silica, or any other suitable glass type. The separatioia between surfaces 3 and 4 is the window thickness, with a value of 6 mm.

The refractive index between surface 4 and surface 5 is roughly equal to that of the aqueous in an actual eye, wi1;b a value of about 1.336 at a wavelength of 546 nm. The separation between surface 4 and surface 5 is 6.25 mm.

Surface 5 is the iris of the eye, and is the aperture stop of the simulated optical system. It has a radius proportioiial to the pupil diameter, az-ici has gio power or curvature. The pupil diameter in the simulations is 3mm, The refractive index between surface 5 and surface 6 is about 1.336 at a waveleiigth of 546 nrn. The separation between surface 5 wid surface 6 is 0.

Surface 6 is the anterior surface of the intraocular lens, with a radius of curvature of +12.154 mm.

The refractive index between surface 6 ai-id surface 7 is tla.e refractive index of the intraocular lens. The lens is made of a silicpr-ie material, with a value of about 1.46 at a wavelength of 546 raan. The separatian between surface 6 and surface 7 is the axial thickness 4or ~.r`.LeI tE11C\
G 1r1ess ) of the lens, l min.

Surface 7 is the posterior surface of the intraocular lens, with a radius of curvature of -12.154 mni. Note that the lens is bi-convex and symmetrical, with a conic constant of 0 and no aspheric terms. In other words, the shape of the anterior and posterior sui-faccs is spherical.
Altematively, the anterior and/or posterior surfaces of the lens may include a non-zero conic constant or one or more aspheric terins, For the "refractive" lens used as a beiichmark in this comparison, the optic includes surfaces 6 and 7 as described above. For the "exteraded focus" lens, surface 7 also includes a parabolic, blazed diffractive profile, imposed oii the shape of tlle surface.
The blazed profile for the Norrby sirnulation. is similar to that described in the Liou-Brennan simulation, only with the radius of the first ring in the diffractive profile being l,.b mm, corresponding to an add power of 1. 1 Diopters, aiid a depth of the profile being 3.3 microns.
The refractive izic3ex between surface 7 and. surface 8 is about 1.336 at a wavelengtli of 546 nm. The separatioi-i between surface 7 and surface 8 is 9 mm.

Surfaces 8 and 9 are the anterior and posterior surfaces of a second window, similar in thiclmess (6 mm) and refractive index (1.517) to the window between surfaces 3 aild 4.
The refractive index between surface 9 and surface 10 is 1.
The thickness between surface 9 aiid surface 10 may be set to a "solve" in a raytrace prograirz, such as OSLO or ZEMAX, and. is about 3.4 mm.
Surface 10 is the retina, and is the image plane for the simulated optical systern, The Norrby eye model was evaluated in monochromatic light at a waveleiigth of 546 nm.
FIG. 25 shows the performance of the "exteDded -Cocus" lens of p'i;GS. 21, used in the system of FIG. 24, compared to the perforrnarice of a similar "refractive"
lens that does not have the l.l-Diopter-add-power diffractive element. p'iG, 25 is a through-focus plot of the simulated Modulation Trazisfer Function at 50 c/mm for the "spherical" and "extended focus" intraocular lenses described above.
The perfortriances of both leixses in the Norrby eye model (FIG. 25) are similar to those in the Liou.-Bremien eye model (FIG. 23). The "extended focus" lens has a reduced peak MTF, but an increased width to the MTF curve, compared to the "refractive" lens. As with the Liou-Brennan simulation, the Norrby slinalatiora considers two Lxex;kplar_y definitions for ctei)th of focus.
A first definition of depth of :Cocus uses an absolute threshold value of 0,17, where the dcptia of focus is the power raiige over which the MTF at 50 c/mrri exceeds 0.17. Using this definition, the "refractive" lens has a depth of focus of 1.18 Diopters, and the "extended focus"
lens .has a depth of focus of 1,80 Diopters, which is about 52% larger than the "re#'ractive" lens.
A second definition of depth of focus uses an absolute threshold value of 0.20, wlzere the depth of focus is the power rai-ige over wiiich the MTF at 50 c/mm exceeds 0.20, Using this definition, the "refractive" lens has a depth of focus of 1.04 Diopters, and the "extea-zd.ed focus"
lens has a depth off'ocus of 1.66 Diopters, wb.ich is about 59% larger than the "refractive" lens.
The Norrby model is conducive to testing real lenses in a physical testbed, wlaich is described in the following four paragraphs.
The lens under test is placed agairist the iris, so that the anterior surface of the lens becornes roughly coincident with the aperture stop of the test system. The lens under test is immersed in a fluid that mimics the fluids in the eye, and the lcias and flLiids are contained in. a chamber bounded by the first and second windows. The light comes to focus outside the chamber, in air. In practice, the separation between the secozid windovv (surface 9) and the image plane or detector (surface 10) rnay be adjusted, depending on the properties o.Cthe Iens under test, It should be noted that the refractive index of the fluid in the eye model has an influence on the measured MTF of dift:'i=active lenses. In order to simulate the iri vivo situation, the difference in refractive index between the lens material and the eye's aqueous humor (at 35 Celsius and in equilibrium with water) should be the same as under the test conditions in the cye n-iodel.
In the Norrby simulation, an aqueous fluid was used with a refractive index of 1.336. For otlier lens designs, other refractive indices may be more appropriate.
Specifically, using diffem-11t materials may require difl'erent refractive indice:s of the aqueous fluid. For example, consider a material "A", whicl7 has no water uptake, a refractive index of 1.5 at 546 nm and 22 C aa-id a decrease of refractive index of 0.0003/ C. As a result, the refractive index of "A" in vivo would be 1.496 (at 35 C) aiid the difference between the refractive indices of the eye and. the lens would be 1.496-1.336=0.160. In order to have the saine diff'erence under the test conditions at 22 C, tl-ie aqueous tluid sifould have a refractive index cs.i 1.5-0.1 6-1.34[l. A similar appxoach cai-i be applied in case that water uptake of the lens material influences the refractive index of the lens.
As an alternative for changing the refractive index of the fluid in the eye model, the measurernei-its can be perforna.ed at 35 C, with the lens in equilibrium with water and with the fluid having the standard refractive index of 1.336.
It is instructive to summarize the simulations perforirled with botb the I.,iou--Brennan and Norrby eye models. It is found that the addition of a diffractive elemeiit with a fairly low add power can increase tiZe depth of tl-ie focus of ati intraocular lens, compared to a similarly shaped intraocular leirs without the diffractive element. The add power of the diffractive element can be in the ranges of 0.5 to 2.5 Diopters, or 1.0 to 2.0 Diopters, or 1.5 to 2.0 Diopters, or 1.0 to 1..5 Diopters, In one embodiment, the depth of focus is defined in terms of a threshold MTF value at a particular spatial frequency. The threshold may be an absolute th.resliold, such as 0.10, 0.15, O.I 7, 0.20, 0.25 or 0.30, or may be a relative threshold, such as a particular percentage of the pealc value. The spatial frequency may be 25 liaae pairs per mm, 50 Iine pairs per mm, 100 Eiiie pairs per mm, or wiy suitable value.

_32..

The precediilg embodiments are merely for illustrative purposes, and should not be construed as limiting in any way. The above model parameters may be adjusted to suit a part.icular set of design objectives or to reflect a particular set ofineasurements for a particular set of eyes or an ii-idividual eye. For example, the parameters for the eye model may be selected based on statistical averages for a particular population, sucb as disclosed in U.S. 1'ateiit No.
6,705,729, which is herein incorporated by reference in its ei'ltirety. In addition, the design of the diffractive element may be adjusted to provide a pred.etermined visual response within the eye of a subject or patient. The add power between the diffractive orders of tl-ie iiitraocular lens is generally less than that of a substantially equivalent prior art r-nu.ltifocal, preferably less than about 3 Diopters, more preferably less than. 2.5 Diopter, less than 2 Diopters, or less tllai'i or equal to about 1 Diopter. In some embodiments, the add power may be selected to between about 0.5 Diopters and about 1.5 Diopters. Alternatively, even smaller add powers may be utilized, for example, less than about 0.5 Diopters.

In addition, the diffractive element may be configured to use other diffractive orders besides the zeroth and +1 diffractive orders, for example, the +1 and +2 diffractive orders or the -I aiid +1 dift'xactive orders. AlterratiyeFy, the diffractive element may be a combined grating or may comprise more than oiie physical grating surface, for example, as disclosed in U.S. Patent No.
5,117,306, which is herein ii-icorporated by reference in its entirety. In otl-ier enibodiinents, the diffractive element provides a lower add power over only a portion of the lens aperture, for example, similar to the configurations disclosed in U.S. Patent No. 7,1$8,949, which is also herein incorporated by referezice in its entirety.

For many of the examples provided in this document, we defined. the depth of focus as the region in a tllrough-focus plot over v+rliich the Modulatioii Transfer Function (MTF) at a spatial frequency of 50 line pairs per mm exceeded a cutoff value of 0.17. In some embadimeaits, the def~ziition of depth of focus may be based on a different cutoff (e.g., a cutoff value of about 0.1. 5, about 0.20, or about 0.25) or a different spatial frequency (e.g., a spatial frequ.ency of about 25 line pairs per mm or about 100 line pairs per mm). The depth of focus may be alternatively defined in terms of axial distance, or, equivalently, in terms of power, as shown in FIG.
4. There are ma.iiy possible alternative definitions of depth of focus tl-iat mai7y be used, as well as maiiy otlier figures of merit that may be used for the definitions.

_33_ The figures of merit, or alietrics, may be either purely optical in nature, or may incorporate some perception effects from the human eye.

For instance, aiiy or all of the following optical xnetrics may be uscd.: MTF
at a particular spatial frequency, MTF volume (integrated over a particular range of spatial frequencies, either in one dimension or in two dimensions), Strehl ratio, encircled energy, RMS spot size, peak-to-valley spot size, RMS ~njavefront error, peak-to-valley wavefront error, and edge transition width.
A.Itera-tatively, aiiy of the following psychophysical metrics may be used:
cozitrast sensitivity, visual acuity, and perceived blur. In addition, many more metrics may be found in the literature, such as those detailed in Marsack, J.1=3., Thibos, L.N. and.
Applegate, R.A., 2004, "Metrics of optical quality derived from wave aberrations predict visual performance," 3Vis, 4 (4), 322-8; and Villegas, E.A., Goiizalea, C., Bourdoncle, B., Bofinin, T. and Artal, P., 2002, "Correlation between optical and psychophysical parameters as a fui-ietion of defocus," Optom Vis Sci., 79 (1), 60-7. All of these references are herein incorporated by reference in their entirety.
Any or all of these metrics may be defined at a single wavelei7gth, such as 550 ran or aiiy other suitable wavele~igth, or over a larger spectral region, such as the visible spectrum from 400 riin to 700 The metrics may be weighted over a particular spectral regio,i, sucix as the weighting associated witli the spectral response of the human eye.
Given the many possible figures of merit, there are several ways to evaluate them to define a depth of focus.

One way is to define an absolute threshold, where the crossings of the figure of merit with the threshold define the depth of focus. For instance, the depth of focus may be defined as the regioxa over which the MTF at 50 lp/mrri exceeds a threshold of 0.17.
Alternativel.y, any suitable MTF absolute tliresbold may be used, such as 0.I, 0.15, 0.2, 0.25, 0.3 and so forth. Alternatively, the depth of focus may be defined as the region over wlaiclx the RMS spot size is less tllan a particular threshold value.
Another way is to define the depth of focus is based on a relative threshold, where the threshold is defiiaed based on a peak value of the figure of merit. For instalice, the depth of focus may be defined as the full width at half inax (PWI-iM) of t[-ie MTF at a particular spatial frequency. Other relative thresholds may be 95%, 90%, 80%, 70%, 60%, 50%, l/e, 1/e^2, or any suitable fraction of the peaic value oftb.e metric.

The descrilstion of the invention and its applications as set forth herein is illustrative and is iiot intended to limit the scope of the inveiition. Variations and modifications of the embodiments disclosed herein are possible, and practical alteniatives to and equivalents of the various elements of the embodiments would be understood to those of ordinary skill in. the art upon study of this patent docuinent. These and other variations and modifications of the embodiments disclosed herein may be made without departing from the scope and spirit of the invention.

Claims (20)

Claims

1. An intraocular lens, comprising:

a first surface having a first shape and an opposing second surface having a second shape, the first and second shapes providing a refractive power;

a diffractive pattern imposed on at least one of the first shape and the second shape;

the first and second surfaces providing a base power and an add power;

wherein the add power is less than or equal to about two Diopters.

2. The intraocular lens of claim 1, wherein the add power is either less than the difference between a near power and a far power or less than or equal to about one Diopter.

3. The intraocular lens of claim 1 or 2, wherein the diffractive pattern has a first diffracted order providing a first diffractive power, the base power being determined at least in part by the refractive power, the add power being determined at least in part by the first diffractive power.

4. The intraocular lens of claim 1 or 2, wherein the diffractive pattern has a nth diffracted order providing a first diffractive power and a(n+1)th diffracted order providing a second diffractive power, the base power being determined at least in part by the refractive power and the first diffractive power, the add power being determined at least in part by the difference between the second diffractive power and the first diffractive power.

5. The intraocular lens of any of claims 1 to 4, wherein at least one of the first and second shapes has an aspheric component.

6. The intraocular lens of any of claims 1 to 5, wherein the diffractive pattern has a plus first diffracted order providing a first diffractive power and a minus first diffracted order providing a second diffractive power, the base power being determined at least in part by the refractive power and the first diffractive power, the add power being determined at least in part by the difference between the second diffractive power and the first diffractive power.

7. The intraocular lens of any of claims 1 to 6, wherein the base power and the add power are formed from adjacent diffracted orders, respectively, from the diffractive pattern.

8. The intraocular lens of any of claims 1 to 6, wherein the base power and the add power result in a first focus and a second focus that have equal intensities.

9. The intraocular lens of any of claims 1 to 8, further comprising first and second foci formed from different diffracted orders.

10. An intraocular lens, comprising:

a first surface having a first shape and an opposing second surface having a second shape, the first and second shapes providing a refractive power;

a diffractive pattern imposed on at least one of the first shape and the second shape;

the first and second surfaces providing a base power and an add power;

the intraocular lens being optically described by a model lens, such that when the model lens is either included in, or placed in, an intraocular lens plane of an eye model including a model cornea, the modulation transfer function of the eye model exceeds about 0.17, at a spatial frequency of about 50 line pairs per millimeter, over a range of at least about 1.7 Diopters.

11. The intraocular lens of claim 10, wherein the lens comprises an optic, the optic comprising the first and second surfaces.

12. The intraocular lens of claim 10 or 11, wherein the eye model is a Liou-Brennan eye model or a Norrby Modified ISO eye model.

113. The intraocular lens of any of claims 10 to 12, wherein the eye model comprises a pupil disposed between the model lens and the model cornea, the pupil having a diameter of about 3 millimeter.

14. The intraocular lens of any of claims 10 to 13, wherein the modulation transfer function of the eye model exceeds about 0.20, at a spatial frequency of about 50 line pairs per millimeter, over a range of at least about 1.9 Diopters.

15. An intraocular lens, comprising a first surface having a first shape and an opposing second surface having a second shape, the first and second shapes providing a refractive power;

a diffractive pattern imposed on the first shape or the second shape;

the first and second surfaces providing a base power and an add power;

the intraocular lens having a depth of focus, when illuminated by a light source, that is at least about 30% greater than that of an intraocular reference lens without the diffractive pattern, the intraocular reference lens having a refractive power that is equal to the base power of the intraocular lens.

16. The intraocular lens of claim 15, wherein the light source is a polychromatic light source that is preferably described by a Liou-Brennan eye model.

17. The intraocular lens of claim 15, wherein the light source is at a predetermined wavelength and the intraocular lens has a depth of focus, when illuminated at the predetermined wavelength, that is at least about 50% greater than that of the intraocular reference lens.

18. The intraocular lens of claim 17, wherein the predetermined wavelength is about 546 nm.

19. The intraocular lens of any of claims 15 to 18, wherein, at a spatial frequency of about 50 line pairs per millimeter, the modulation transfer function of the lens exceeds 0.17 over a depth of focus that is greater than the depth of focus for the reference intraocular lens by at least about 0.5 Diopters.

20. The intraocular lens of any of claims 15 to 18, wherein the intraocular lens is optically described by a model lens, such that when the model lens is included in an intraocular lens plane of an eye model including a model cornea, the modulation transfer function of the eye model exceeds about 0.17, at a spatial frequency of about 50 line pairs per millimeter, over a range of at least about 1.7 Diopters.