U.S. patent application number 11/397305 was filed with the patent office on 2006-10-12 for optimal iol shape factors for human eyes.
Invention is credited to Xin Hong, Mutlu Karakelle, Michael J. Simpson, Dan Stanley, Stephen J. Van Noy, Jihong Xie, Xiaoxiao Zhang.
Application Number | 20060227286 11/397305 |
Document ID | / |
Family ID | 36930344 |
Filed Date | 2006-10-12 |
United States Patent
Application |
20060227286 |
Kind Code |
A1 |
Hong; Xin ; et al. |
October 12, 2006 |
Optimal IOL shape factors for human eyes
Abstract
The present invention provides an ophthalmic lens (e.g., an
intraocular lens) having an optic with an anterior surface and a
posterior surface, which exhibits a shape factor (defined as a
ratio of the sum of the anterior and posterior curvatures to the
difference of such curvatures) in a range of about -0.5 to about 4.
In a related aspect, the shape factor of the optic lies in a range
of about 0 to about 2. The above shape factors give rise to a
plurality of different lens shapes, such as concave-convex,
plano-convex and plano-concave.
Inventors: |
Hong; Xin; (Arlington,
TX) ; Van Noy; Stephen J.; (Fort Worth, TX) ;
Xie; Jihong; (Fort Worth, TX) ; Stanley; Dan;
(Midlothian, TX) ; Karakelle; Mutlu; (Fort Worth,
TX) ; Simpson; Michael J.; (Arlington, TX) ;
Zhang; Xiaoxiao; (Fort Worth, TX) |
Correspondence
Address: |
NUTTER MCCLENNEN & FISH LLP
WORLD TRADE CENTER WEST
155 SEAPORT BOULEVARD
BOSTON
MA
02210-2604
US
|
Family ID: |
36930344 |
Appl. No.: |
11/397305 |
Filed: |
April 4, 2006 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
60668520 |
Apr 5, 2005 |
|
|
|
Current U.S.
Class: |
351/159.01 |
Current CPC
Class: |
G02C 7/02 20130101; A61F
2/1613 20130101; A61F 2/1637 20130101 |
Class at
Publication: |
351/159 |
International
Class: |
G02C 7/02 20060101
G02C007/02 |
Claims
1. An ophthalmic lens, comprising an optic having an anterior
surface and a posterior surface, said optic exhibiting a shape
factor in a range of about -0.5 to about 4.
2. The ophthalmic lens of claim 1, wherein said optic exhibits a
shape factor in a range of about 0 to about 2.
3. The ophthalmic lens of claim 1, wherein said optic comprises a
biocompatible polymeric material.
4. The ophthalmic lens of claim 3, wherein the polymeric material
is selected from the group consisting of acrylic, silicone and
hydrogel materials.
5. The ophthalmic lens of claim 1, wherein both of said surfaces
have a generally convex profile.
6. The ophthalmic lens of claim 1, wherein one of said surfaces has
a generally convex profile and the other surface has a
substantially flat profile.
7. The ophthalmic lens of claim 1, wherein one of said surfaces has
a generally concave profile and the other surface has a
substantially flat profile.
8. The ophthalmic lens of claim 1, wherein one of said surfaces has
a generally concave profile and the other surface has a generally
convex profile.
9. The ophthalmic lens of claim 1, wherein at least one of said
surfaces is characterized by an aspherical base profile.
10. The ophthalmic lens of claim 9, wherein said aspheric base
profile is characterized by a conic constant (Q) in a range of
about -73 to about -27.
11. The ophthalmic lens of claim 1, wherein said lens comprises an
intraocular lens.
12. An ophthalmic lens, comprising an optic having an anterior
surface and a posterior surface, at least one of said surfaces
being characterized by an aspherical base profile defined by the
following relation: z = c .times. .times. r 2 1 + 1 - ( 1 + k )
.times. c 2 .times. r 2 ##EQU9## wherein, c denotes the curvature
of the surface at its apex (at its intersection with the optical
axis), r denotes the radial distance from the optical axis, and k
denotes the conic constant, wherein c is in a range of about 0.0152
mm.sup.-1 to about 0.0659 mm.sup.-1, r is in a range of about 0 to
about 5 mm, and k is in a range of about -73 to about -27, wherein
said optic exhibits a shape factor in a range of about -0.5 to
about 4.
13. The ophthalmic lens of claim 12, wherein said optic exhibits a
shape factor in a range of about 0 to about 2.
14. The ophthalmic lens of claim 12, wherein said lens comprises an
intraocular lens.
15. The ophthalmic lens of claim 12, wherein said surfaces
cooperatively provide a refractive optical power in a range of
about 16 D to about 25 D.
16. The ophthalmic lens of claim 12, wherein said optic is formed
of a biocompatible polymeric material.
17. An intraocular lens adapted for implantation in an eye having a
corneal radius equal to or less than about 7.1 mm, comprising an
optic having an anterior surface and a posterior surface, said
optic exhibiting a shape factor in a range of about -0.5 to about
4.
18. The intraocular lens of claim 17, wherein optic exhibits a
shape factor in a range of about +0.5 to about 4.
19. The intraocular lens of claim 17, wherein said optic exhibits a
shape factor in a range of about 1 to about 3.
20. An intraocular lens adapted for implantation in an eye having a
corneal radius in a range of about 7.1 to about 8.6 mm, comprising
an optic having an anterior surface and a posterior surface, said
optic exhibiting a shape factor in a range of about 0 to about
3.
21. The intraocular lens of claim 20, wherein said optic exhibits a
shape factor in a range of about +0.5 to about 3.
22. The intraocular lens of claim 20, wherein said optic exhibits a
shape factor in a range of about 1 to about 2.
23. An intraocular lens adapted for implantation in an eye having a
corneal radius equal to or greater than about 8.6 mm, comprising an
optic having an anterior surface and a posterior surface, said
optic exhibiting a shape factor in a range of about +0.5 to about
2.
24. The intraocular lens of claim 23, wherein said optic exhibits a
shape factor in a range of about 1 to about 2.
25. An intraocular lens adapted for implantation in an eye having
an axial length equal to or less than about 22 mm, comprising an
optic having an anterior surface and a posterior surface, said
optic having a shape factor in a range of about 0 to about 2.
26. The intraocular lens of claim 25, wherein the optic exhibits a
shape factor in a range of about 0.5 to about 2.
27. An ophthalmic lens, comprising an optic having an anterior
surface and a posterior surface, at least one of said surfaces
having an aspherical profile characterized by a conic constant in a
range of about -73 to about -27, wherein said optic exhibits a
shape factor in a range of about -0.5 to about 4.
28. The ophthalmic lens of claim 27, wherein said aspherical
profile is characterized by a conic constant in a range of about
-73 to about -27, and said optic exhibits a shape factor in a range
of about 0 to about 2.
29. A method of correcting vision, comprising selecting an IOL
comprising an optic exhibiting a shape factor in a range of about
-0.5 to about 4 for implantation in an eye having a corneal radius
equal or less than about 7.1 mm.
30. The method of claim 29, wherein the shape factor of the optic
is selected to be in a range of about +0.5 to about 4.
31. A method of correcting vision, comprising selecting an IOL
comprising an optic exhibiting a shape factor in a range of about 0
to about 3 for implantation in an eye having a corneal radius in a
range of about 7.1 mm to about 8.6 mm.
32. The method of claim 31, wherein the shape factor of the optic
is selected to be in a range of about +0.5 to about 3.
33. A method of correcting vision, comprising selecting an IOL
comprising an optic exhibiting a shape factor in a range of about
0.5 to about 2 for implantation in an eye having a corneal radius
equal to or greater than about 8.6 mm.
34. A method of correcting vision, comprising selecting an IOL
comprising an optic exhibiting a shape factor in a range of about 0
to about 2 for implantation in an eye having an axial length equal
to or less than about 22 mm.
35. The method of claim 34, wherein a shape factor of the optic is
selected to be in a range of about 0.5 to about 2.
36. A method of designing an ophthalmic lens, comprising defining
an error function indicative of variability in performance of a
lens in a patient population based on estimated variability in one
or more biometric parameters associated with that population, and
selecting a shape factor for the lens that reduces said error
function relative to a reference value.
37. The method of claim 36, wherein said error function further
incorporates an estimated error in optical power correction
provided by the lens.
38. The method of claim 37, wherein said error function further
incorporates an estimated aberration error.
39. The method of claim 38, wherein said error function (RxError)
is defined by the following relation: RxError = .DELTA. .times.
.times. Biometric 2 + .DELTA. .times. .times. IOLPower 2 + .DELTA.
.times. .times. Aberration 2 ##EQU10## wherein, .DELTA.Biometric
denotes variability due to biometric data errors, .DELTA.IOLPower
denotes variability due to optical power errors, and
.DELTA.Aberration denotes variability due to aberration
contributions.
40. The method of claim 39, wherein .DELTA.Biometric is defined by
the following relation: .DELTA.Biometric= {square root over
(.DELTA.k.sup.2+.DELTA.AL.sup.2+.DELTA.ACD.sup.2)} wherein,
.DELTA.k denotes error in keratometric measurements, .DELTA.AL
denotes error in axial length measurements, and .DELTA.ACD denotes
error in anterior chamber depth measurements.
41. The method of claim 39, wherein .DELTA.Aberration is defined by
the following relation: .DELTA.Aberration= {square root over
(.DELTA.Astig.sup.2+.DELTA.SA.sup.2+.DELTA.Other.sup.2)} wherein,
.DELTA.Astig represents variability due to astigmatic aberration,
.DELTA.SA represents variability due to spherical aberration, and
.DELTA.Other represents variability due to other aberrations.
42. The method of claim 39, wherein .DELTA.IOLPower is defined by
the following relation: .DELTA.IOLPower= {square root over
(.DELTA.IOLStep.sup.2+.DELTA.IOLTol.sup.2+.DELTA.ELP.sup.2)}
wherein, .DELTA.IOLStep represents variability caused by difference
between the lens power and a power need of a patient, .DELTA.IOLTol
represents manufacturing power tolerance, and .DELTA.ELP represents
variability in a shift of the lens effective position within the
eye.
Description
RELATED APPLICATION
[0001] The present application claims priority to U.S. Provisional
Patent Application Ser. No. 60/668,520 entitled "Intraocular Lens,"
filed on Apr. 5, 2005, which is herein incorporated by
reference.
[0002] A U.S. patent application entitled, "Intraocular Lens,"
assigned to the assignee of the present application, and filed
concurrently herewith, is herein also incorporated by
reference.
BACKGROUND
[0003] The present invention relates generally to ophthalmic
lenses, and more particularly, to intraocular lenses (IOLs) having
optimal shape factors.
[0004] Intraocular lenses are routinely implanted in patients' eyes
during cataract surgery to replace the clouded natural lens. The
post-operative performance of such IOLs, however, can be degraded
due to a variety of factors. For example, aberrations introduced as
a result of misalignment of the implanted IOL relative to the
cornea, and/or the inherent aberrations of the eye, can adversely
affect the lens's optical performance.
[0005] Accordingly, there is a need for improved IOLs that can
provide a more robust optical performance.
SUMMARY
[0006] In one aspect, the present invention provides an ophthalmic
lens (e.g., an intraocular lens) having an optic with an anterior
surface and a posterior surface. The optic exhibits a shape factor
in a range of about -0.5 to about 4. In a related aspect, the shape
factor of the optic lies in a range of about 0 to about 2. The
above shape factors give rise to a plurality of different lens
shapes, such as, bi-convex, plano-convex, plano-concave and
convex-concave.
[0007] In another aspect, the optic is formed of a biocompatible
polymeric material. By way of example, the optic can be formed of a
soft acrylic polymeric material. Other examples of suitable
materials include, without limitation, hydrogel and silicone
materials.
[0008] In another aspect, at least one surface of the optic can be
characterized by an aspheric base profile (i.e., a base profile
that exhibits deviations from sphericity). By way of example, the
base profile can be characterized by a conic constant in a range of
about -73 to about -27.
[0009] In a related aspect, the aspheric profile of the lens
surface can be defined in accordance with the following relation: z
= cr 2 1 + 1 - ( 1 + k ) .times. c 2 .times. r 2 ##EQU1##
wherein,
[0010] c denotes the curvature of the surface at its apex (at its
intersection with the optical axis),
[0011] r denotes the radial distance from the optical axis, and
[0012] k denotes the conic constant,
wherein
[0013] c can be, e.g., in a range of about 0.0152 mm.sup.-1 to
about 0.0659 mm.sup.-1,
[0014] r can be, e.g., in a range of about 0 to about 5, and
[0015] k can be, e.g., in a range of about -1162 to about -19
(e.g., in a range of about -73 to about -27).
[0016] In a related aspect, the optic of the above lens can have a
shape factor in a range of about 0 to about 2.
[0017] In some embodiments in which one or more surfaces of the
ophthalmic lens exhibit asphericity, the shape factor of the lens
(e.g., an IOL) can be selected as a function of that asphericity so
as to optimize the lens's optical performance. By way of example,
in one aspect, the invention provides an ophthalmic lens having an
optic with an anterior surface and a posterior surface, where at
least one of the surfaces exhibits an ashperical profile
characterized by a conic constant in a range of about -73 to about
-27. The optic exhibits a shape factor in a range of about -0.5 to
about 4.
[0018] In a related aspect, an ophthalmic lens having an optic with
a shape factor in a range of about 0 to about 2 includes at least
one aspherical surface characterized by a conic constant in a range
of about -73 to about -27.
[0019] In other aspects, an intraocular lens adapted for
implantation in an eye having a corneal radius equal to or less
than about 7.1 mm is disclosed, which includes an optic having an
anterior surface and a posterior surface. The optic exhibits a
shape factor in a range of about -0.5 to about 4. In a related
aspect, the optic exhibits a shape factor in a range of about +0.5
to about 4, or in a range of about 1 to about 3.
[0020] In another aspect, the invention provides an intraocular
lens adapted for implantation in an eye having a corneal radius in
a range of about 7.1 mm to about 8.6 mm, which includes an optic
having an anterior surface and a posterior surface. The optic
exhibits a shape factor in a range of about 0 to about 3. In a
related aspect, the optic exhibits a shape factor in a range of
about +0.5 to about 3, or in a range of about 1 to about 2.
[0021] In another aspect, an intraocular lens adapted for
implantation in an eye having a corneal radius equal to or greater
than about 8.6 is disclosed, which includes an optic having an
anterior surface and a posterior surface. The optic exhibits a
shape factor in a range of about 0.5 to about 2. In a related
aspect, the optic exhibits a shape factor in a range of about 1 to
about 2.
[0022] In another aspect, the invention provides an intraocular
lens adapted for implantation in an eye having an axial length
equal to or less than about 22 mm, which includes an optic having
an anterior surface and a posterior surface. The optic can have a
shape factor in a range of about 0 to about 2, or in a range of
about 0.5 to about 2.
[0023] In other aspects, the invention discloses methods for
selecting an ophthalmic lens for implantation in a patient's eye
based on one or more ocular biometric parameters of the patient.
For example, a method of correcting vision is disclosed that
includes selecting an IOL, which comprises an optic exhibiting a
shape factor in a range of about -0.5 to about 4 (or in a range of
about +0.5 to about 4), for implantation in an eye having a corneal
radius that is equal to or less than about 7.1 mm.
[0024] In another aspect, a method of correcting vision is
disclosed that includes selecting an IOL, which comprises an optic
exhibiting a shape factor in a range of about 0 to about 3 (or in a
range of about 0.5 to about 3), for implantation in an eye having a
corneal radius in a range of about 7.1 mm to about 8.6 mm.
[0025] In yet another aspect, a method of correcting vision is
disclosed that includes selecting an IOL, which comprises an optic
exhibiting a shape factor in a range of about 0.5 to about 2, for
implantation in an eye having a corneal radius that is equal to or
greater than about 8.6 mm.
[0026] In another aspect, a method of corrected vision is disclosed
that includes selecting an IOL, which comprises an optic exhibiting
a shape factor in a range of about 0 to about 2 (or in a range of
about 0.5 to about 2), for implantation in an eye having an axial
length equal to or less than about 22 mm.
[0027] In another aspect, a method of designing an ophthalmic lens
is disclosed that includes defining an error function, which is
indicative of variability in performance of a lens in a patient
population, based on estimated variability in one or more biometric
parameters associated with that population, and selecting a shape
factor for the lens that reduces the error function relative to a
reference value. In a related aspect, the error function can
further include an estimated error in optical power correction
provided by the lens and/or an estimated aberration error.
[0028] In a related aspect, the error function (RxError) can be
defined in accordance with the following relation: RxError =
.DELTA. .times. .times. Biometric 2 + .DELTA. .times. .times.
IOLPower 2 + .DELTA. .times. .times. Aberration 2 ##EQU2##
[0029] wherein,
[0030] .DELTA.Biometric denotes variability due to biometric data
errors,
[0031] .DELTA.IOLPower denotes variability due to optical power
correction errors, and
[0032] .DELTA.Aberration denotes variability due to aberration
contributions.
[0033] In another aspect, the .DELTA.Biometric can be defined in
accordance with the following relation: .DELTA.Biometric= {square
root over (.DELTA.k.sup.2+.DELTA.AL.sup.2+.DELTA.ACD.sup.2)}
[0034] wherein,
[0035] .DELTA.k denotes error in keratometric measurements,
[0036] .DELTA.AL denotes error in axial length measurements,
and
[0037] .DELTA.ACD denotes error in anterior chamber depth
measurements.
[0038] In another aspect, the .DELTA.Aberration can be defined in
accordance with the following relation: .DELTA.Aberration= {square
root over
(.DELTA.Astig.sup.2+.DELTA.SA.sup.2+.DELTA.Other.sup.2)}
[0039] wherein,
[0040] .DELTA.Astig represents variability due to astigmatic
aberration,
[0041] .DELTA.SA represents variability due to spherical
aberration, and
[0042] .DELTA.Other represents variability due to other
aberrations.
[0043] In a further aspect, the .DELTA.IOLPower can be defined in
accordance with the following relation: .DELTA.IOLPower= {square
root over
(.DELTA.IOLStep.sup.2+.DELTA.IOLTol.sup.2+.DELTA.ELP.sup.2)}
[0044] wherein, [0045] .DELTA.IOLStep represents variability caused
by difference between a power correction provided by the lens and a
power correction needed by a patient, [0046] .DELTA.IOLTol
represents manufacturing power tolerance, and [0047] .DELTA.ELP
represents variability in a shift of the lens effective position
within the eye.
[0048] Further understanding of the invention can be obtained by
reference to the following detailed description, in conjunction
with the associated drawings, which are discussed briefly
below.
BRIEF DESCRIPTION OF THE DRAWINGS
[0049] FIG. 1 is a schematic side view of an IOL in accordance with
one embodiment of the invention,
[0050] FIG. 2 presents simulated magnitude of different aberration
types (spherical, defocus, coma and astigmatic aberrations)
exhibited by an IOL as a function of its shape factor for a 1.5 mm
decentration,
[0051] FIG. 3 presents simulation results for aberrations exhibited
by an IOL due to tilt as a function of the IOL's shape factor,
[0052] FIG. 4A presents graphically calculated spherical aberration
exhibited by a model eye characterized by an average anterior
chamber depth in which an IOL is incorporated, as a function of the
IOL's shape factor,
[0053] FIG. 4B presents graphically calculated MTFs at 50 lp/mm and
100 lp/mm for a model eye characterized by an average anterior
chamber depth in which an IOL is incorporated, as a function of the
IOL's shape factor,
[0054] FIG. 5A depicts simulated MTFs at 50 lp/mm and 100 lp/mm for
a model eye characterized by a small anterior chamber depth in
which an IOL is incorporated, as a function of the IOL's shape
factor,
[0055] FIG. 5B depicts simulated spherical aberration exhibited by
a model eye characterized by a small anterior chamber depth in
which an IOL is incorporated, as a function of the IOL's shape
factor,
[0056] FIG. 6A depicts simulated spherical aberration exhibited by
a model eye characterized by a large anterior chamber depth in
which an IOL is incorporated, as a function of the IOL's shape
factor,
[0057] FIG. 6B depicts simulated MTFs at 50 lp/mm and 100 lp/mm for
a model eye characterized by a large anterior chamber depth in
which an IOL is incorporated, as a function of the IOL's shape
factor,
[0058] FIG. 7A depicts graphically simulated spherical aberrations
exhibited by a plurality of model eyes having different corneal
asphericities in which an IOL is incorporated, as a function of the
IOL's shape factor,
[0059] FIG. 7B depicts graphically simulated MTF as 50 lp/mm
obtained for model eyes having different corneal asphericities in
which an IOL is incorporated, as a function of the IOL's shape
factor,
[0060] FIG. 7C depicts graphically simulated MTF at 100 lp/mm
obtained for model eyes having different corneal asphericities in
which an IOL is incorporated, as a function of the IOL's shape
factor,
[0061] FIG. 8A depicts simulated spherical aberration exhibited by
two model eyes characterized by different corneal radii as a
function of the shape factor of an IOL incorporated in the
models,
[0062] FIG. 8B depicts simulated MTF at 50 lp/mm exhibited by two
model eyes characterized by different corneal radii as a function
of the shape factor of an IOL incorporated in the models,
[0063] FIG. 8C depicts simulated MTF at 100 lp/mm exhibited by two
model eyes characterized by different corneal radii as a function
of the shape factor of an IOL incorporated in the models,
[0064] FIG. 9A depicts simulated spherical aberration exhibited by
a plurality of model eyes having different axial lengths as a
function of the shape factor of an IOL incorporated in the
models,
[0065] FIG. 9B depicts simulated MTFs at 50 lp/mm exhibited by a
plurality of model eyes having different axial lengths as a
function of the shape factor of an IOL incorporated in the
models,
[0066] FIG. 9C depicts simulated MTFs at 100 lp/mm exhibited by a
plurality of model eyes having different axial lengths as a
function of the shape factor of an IOL incorporated in the
models,
[0067] FIG. 10 is a schematic side view of a lens according to one
embodiment of the invention having an aspheric anterior
surface,
[0068] FIG. 11 presents a plurality of graphs depicting the sag of
an aspheric surface of two lenses in accordance with the teachings
of the invention having different shape factors, and
[0069] FIG. 12 graphically presents Monte Carlo simulation results
for optical performance of a plurality of IOLs as a function of
manufacturing tolerances.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0070] FIG. 1 schematically depicts an IOL 10 in accordance with
one embodiment of the invention having an optic 12 that includes an
anterior surface 14 and a posterior surface 16. In this embodiment,
the anterior and posterior surfaces 14 and 16 are symmetrically
disposed about an optical axis 18, though in other embodiments one
or both of those surfaces can exhibit a degree of asymmetry
relative to the optical axis. The exemplary IOL 10 further includes
radially extending fixation members or haptics 20 that facilitate
its placement in the eye. In this embodiment, the optic is formed
of a soft acrylic polymer, commonly known as Acrysof, though in
other embodiments, it can be formed of other biocompatible
materials, such as silicone or hydrogel. The lens 10 provides a
refractive optical power in a range of about 6 to about 34 Diopters
(D), and preferably in a range of about 16 D to about 25 D.
[0071] In this exemplary embodiment, the lens 10 has a shape factor
in a range of about 0 to about 2. More generally, in many
embodiments, the shape factor of the lens 10 can range from about
-0.5 to about 4. As known in the art, the shape factor of the lens
10 can be defined in accordance with the following relation: Shape
.times. .times. Factor .function. ( X ) = C 1 + C 2 C 1 - C 2 Eq .
.times. ( 1 ) ##EQU3## wherein C.sub.1 and C.sub.2 denote,
respectively, the curvatures of the anterior and posterior
surfaces.
[0072] The shape factor of the IOL 10 can affect the aberrations
(e.g., spherical and/or astigmatic aberrations) that the lens can
introduce as a result of its tilt and decentration, e.g., when
implanted in the subject's eye or in a model eye. As discussed in
more detail below, aberrations caused by a plurality of IOLs with
different shape factors were theoretically studied as a function of
tilt and decentration by utilizing a model eye. Those studies
indicate that IOLs having a shape factor in a range of about 0 to
about 2 introduce much reduced aberrations as a result of tilt and
decentration.
[0073] More particularly, to study the effects of an IOL's shape
factor on aberrations induced by its tilt and decentration, a
hypothetical eye model having optical properties (e.g., corneal
shape) similar to those of an average human eye was employed. The
radii of optical surfaces and the separations between optical
components were chosen to correspond to mean values of those
parameters for the human population. The refractive indices of the
optical components were chosen to provide selected refractive power
and chromatic aberrations. Further, the anterior corneal surface of
the model was selected to have an ashperical shape. An IOL under
study replaced the natural lens in the model. Table 1 below lists
the various design parameters of the model eye: TABLE-US-00001
TABLE 1 Thick- Dia- Radius ness meter Conic Surface Type (mm) (mm)
Class (mm) Constant OBJ Standard Infinity Infinity 0.000 0.000 1
Standard Infinity 10.000 5.000 0.000 2 Standard 7.720 0.550 Cornea
14.800 -0.260 3 Standard 6.500 3.050 Aqueous 12.000 0.000 STO
Standard Infinity 0.000 Aqueous 10.000 0.000 5 Standard 10.200
4.000 Lens 11.200 -3.132 6 Standard -6.000 16.179 Vitreous 11.200
-1.000 IMA Standard -12.000 24.000 0.000
[0074] An optical design software marketed as Zemax.RTM. (version
Mar. 4, 2003, Zemax Development Corporation, San Diego, Calif.) was
utilized for the simulations of the optical properties of the model
eye. A merit function was defined based on the root-mean-square
(RMS) wavefront aberration, that is, the RMS wavefront deviation of
an optical system from a plane wave. In general, the larger the RMS
wavefront error, the poorer is the performance of the optical
system. An optical system with an RMS wavefront error that is less
than about 0.071 waves is typically considered as exhibiting a
diffraction-limited optical performance.
[0075] The effects of misalignment (tilt and/or decentration) of an
IOL on its optical performance for a number of different shape
factors was simulated by placing the IOLs in the above model eye
and utilizing the Zemax.RTM. software. For these simulations, the
IOL was assumed to have spherical surfaces so as to investigate the
effects of the shape factor alone (as opposed to that of the
combined shape factor and asphericity). To simulate the scotopic
viewing conditions for old patients, a 5 mm entrance pupil was
chosen. The following misalignment conditions were considered: 1.5
mm IOL decentration and a 10-degree IOL tilt. These two conditions
represent the extreme cases of IOL misalignments.
[0076] FIG. 2 presents the simulated magnitude of different
aberration types (spherical aberration, defocus, coma and
astigmatism) as a function of the shape factor for 1.5 mm
decentration of the IOL. These simulations indicate that IOLs with
a shape factor in a range of about 0 to about 2 exhibit much lower
aberrations as a result of the decentration. For example, an IOL
with a shape factor of about 1 introduces a defocus aberration of
0.07 D compared to a defocus aberration of 0.32 D introduced by an
IOL having a shape factor of -1.
[0077] FIG. 3 presents the simulation results for aberrations
introduced as a result of the IOL's tilt. These results indicate
that the defocus and astigmatic aberrations are not significantly
influenced by the IOL's shape factor while the coma and spherical
aberrations exhibit even stronger dependence on the shape factor
than their dependence in case of the IOL's decentration. Again, the
IOLs with shape factors in a range of about 0 to 2 exhibit a stable
performance.
[0078] In other aspects, it has been discovered that certain
biometric parameters of the eye (e.g., corneal radius and axial
length) can be considered while selecting the shape factor of an
IOL for implantation in the eye to provide enhanced performance of
the lens. As discussed in more detail below, in some embodiments,
optimal IOL shape factors are provided for different eye
populations, e.g., average human eye (eyes with average values for
certain biometric parameters), and other populations characterized
by extreme values for those parameters.
[0079] The biometric parameters of the above eye model were varied
to simulate the performance of a plurality of IOLs having different
shape factors for different eyes. For an average human eye, a
corneal radius (r) of 7.72 mm, a corneal asphericity (Q) of -0.26,
an anterior chamber depth (ACD) of 4.9 mm, and an axial length (AL)
of 24.4 mm were assumed. To investigate human eyes with extreme
large or small biometric values, the anterior chamber depth was
varied from 4.3 mm to 5.5 mm, the corneal asphericity was varied
from -0.50 to 0, the corneal radius was varied from 7.10 mm to 8.60
mm, and the axial length was varied from 22.0 mm to 26.0 mm. These
ranges are sufficiently broad to cover the values exhibited by the
majority of the population. The optical performance of the IOLs was
evaluated based on two criteria: calculated wave aberration and
modulation transfer function (MTF). As known to those having
ordinary skill in the art, the MTF provides a quantitative measure
of image contrast exhibited by an optical system, e.g., a system
formed of an IOL and the cornea. More specifically, the MTF of an
imaging system can be defined as a ratio of a contrast associated
with an image of an object formed by the optical system relative to
a contrast associated with the object.
[0080] Table 2 below presents the simulation results of the optical
performance of IOLs having shape factors in a range of about -2 to
about 4 for an eye having an average anterior chamber depth (ACD)
of 4.9 mm, a corneal radius of 7.72 mm, a corneal asphericity of
-0.26, and an axial length (AL) of 24.4 mm, at a pupil size of 5
mm. TABLE-US-00002 TABLE 2 Shape Spherical Factor (X) Aberration
(SA) MTF at 50 lp/mm MTF at 100 lp/mm -2 0.478 0.037 0.095 -1.5
0.386 0.117 0.051 -1 0.307 0.212 0.011 -0.5 0.244 0.331 0.016 0
0.195 0.455 0.128 0.5 0.162 0.555 0.250 1 0.142 0.615 0.334 1.5
0.134 0.637 0.366 2 0.138 0.625 0.348 3 0.174 0.516 0.199 4 0.239
0.340 0.021
[0081] For graphical presentation of the information in Table 2,
FIGS. 4A and 4B provide, respectively, the calculated spherical
aberration and MTF presented in Table 1 as a function of IOL's
shape factor.
[0082] Table 3 below presents the simulation results for the
optical performance of a plurality of IOLs having shape factors in
the above range of -2 to 4 at a pupil size of 5 mm for an eye
having a small anterior chamber depth (ACD) of 4.3 mm, but the same
corneal radius (7.72 mm) and asphericity (-0.26) as well as axial
length (24.4 mm) as that employed in the previous simulation. FIGS.
5A and 5B graphically depict, respectively, the calculated
spherical aberration (SA) and the MTF presented in Table 3 as a
function of the IOL's shape factor. TABLE-US-00003 TABLE 3 Shape
Sph. Aberration Factor (X) (waves) MTF at 50 lp/mm MTF at 100 lp/mm
-2 0.461 0.047 0.095 -1.5 0.374 0.125 0.042 -1 0.300 0.219 0.014
-0.5 0.240 0.337 0.021 0 0.194 0.457 0.130 0.5 0.161 0.553 0.249 1
0.141 0.613 0.331 1.5 0.133 0.636 0.365 2 0.136 0.627 0.353
[0083] Table 4 below presents the simulation results for the
optical performance of a plurality of IOLs having shape factors in
the above range of -2 to 4 at a pupil size of 5 mm for an eye
having a large anterior chamber depth (ACD) of 5.5 mm, a corneal
radius of 7.72 mm, a corneal asphericity of -0.26 and an axial
length of 24.4 mm. Further, FIGS. 6A and 6B graphically depict,
respectively, the calculated spherical aberration (SA) and the MTF
presented in Table 4 as a function of the IOL's shape factor.
TABLE-US-00004 TABLE 4 Shape Sph. Aberration Factor (X) (waves) MTF
at 50 lp/mm MTF at 100 lp/mm -2 0.498 0.026 0.093 -1.5 0.399 0.108
0.059 -1 0.316 0.204 0.008 -0.5 0.249 0.325 0.011 0 0.198 0.454
0.125 0.5 0.162 0.556 0.251 1 0.142 0.617 0.336 1.5 0.135 0.637
0.365 2 0.140 0.622 0.342
[0084] These simulations indicate that IOLs with shape factors in a
range of about -0.5 to about 4, and particularly those having shape
factors in a range of about 0 to about 2, provide enhanced optical
performance. The simulations, however, show that anterior chamber
depth does not significantly affect the performance of an IOL.
[0085] Although in the afore-mentioned simulations the spherical
aberrations were considered, in the IOL is misaligned relative to
the cornea, other aberrations (e.g., defocus, astigmatism and coma)
can also be present. The simulations of these aberrations for
average, small and large ACD confirm that the aberrations can be
minimized by utilizing shape factors in a range about 0 to about
2.
[0086] The impact of corneal asphericity (Q) on optimal IOL shape
factor was also investigated by utilizing the aforementioned eye
model and calculating spherical aberration and MTF for Q-=0
(spherical), Q=-0.26 and Q=-0.50. The more negative the Q value,
the flatter is the peripheral portion of the cornea. Q=-0.26
corresponds to the asphericity of the normal human cornea while
Q=-0.50 corresponds to the asphericity of an extremely flat cornea.
Table 5 below lists the results of these simulations, with FIGS.
7A, 7B and 7C graphically depicting, respectively, the simulated
spherical aberration, the MTF at 50 lp/mm and the MTF at 100 lp/mm
as a function of the IOL's shape factor. TABLE-US-00005 TABLE 5 SA
(micron) MTF@501 p/mm MTF@1001 p/mm X Q = 0 Q = -0.26 Q = -0.50 Q =
0 Q = -0.26 Q = -50 Q = 0 Q = -0.26 Q = -0.50 -2 0.609 0.478 0.364
0.000 0.037 0.143 0.036 0.095 0.027 -1.5 0.524 0.386 0.264 0.010
0.117 0.292 0.084 0.051 0.007 -1 0.451 0.307 0.180 0.058 0.212
0.503 0.091 0.011 0.182 -0.5 0.392 0.244 0.112 0.111 0.331 0.702
0.057 0.016 0.463 0 0.347 0.195 0.061 0.159 0.455 0.822 0.016 0.128
0.661 0.5 0.315 0.162 0.025 0.200 0.555 0.869 0.007 0.250 0.742 1
0.295 0.142 0.005 0.230 0.615 0.879 0.012 0.334 0.759 1.5 0.288
0.134 0.002 0.243 0.637 0.879 0.012 0.366 0.759 2 0.29 0.138 0.003
0.238 0.625 0.879 0.013 0.348 0.759 3 0.321 0.174 0.045 0.189 0.516
0.848 0.004 0.199 0.704 4 0.378 0.239 0.117 0.120 0.340 0.688 0.046
0.021 0.443
[0087] The spherical aberration exhibited by a spherical cornea
(Q=0) is significantly larger than those exhibited by the
aspherical corneas (Q=-0.26 and Q=-0.50), as expected. As a result,
the MTFs associated with Q=0 are lower than those for Q=-0.26 and
Q=-0.50. However, for each of the three cases, the above
simulations indicate that an optimal IOL shape factor lies in a
range of about -0.5 to about 4, and preferably in a range of about
0 to about 2.
[0088] In another set of simulations, the effect of corneal radius
on optimal shape factor was investigated. Table 6 below presents
the simulation results corresponding to spherical aberration as
well as MTFs at 50 lp/mm and 100 lp/mm obtained for a plurality of
IOLs having shape factors in a range of about -2 to about 8 by
utilizing the afore-mentioned eye model and varying the corneal
radius. More specifically, the ACD, Q and AL were fixed,
respectively, at 4.9 mm, -0.26, and 24.4 mm while the corneal
radius was varied. FIGS. 8A, 8B and 8C graphically depict,
respectively, variations of the spherical aberration, the MTF at 50
lp/mm and the MTF at 100 lp/mm in these simulations as a function
of the IOL's shape factor for two different radii. TABLE-US-00006
TABLE 6 r SA (waves) MTF@501 p/mm MTF@1001 p/mm r = 7.10 r = 7.72 r
= 8.60 r = 7.10 r = 7.72 r = 8.60 r = 7.10 r = 7.72 r = 8.60 X mm
mm mm mm mm mm mm mm mm -2 0.312 0.478 0.856 0.196 0.037 0.086
0.010 0.095 0.031 -1.5 0.282 0.386 0.635 0.245 0.117 0.00 0.015
0.051 0.032 -1 0.255 0.307 0.447 0.297 0.212 0.07 0.002 0.011 0.086
-0.5 0.233 0.244 0.300 0.347 0.331 0.234 0.029 0.016 0.011 0 0.215
0.195 0.195 0.393 0.455 0.468 0.067 0.128 0.139 0.5 0.201 0.162
0.133 0.432 0.555 0.65 0.105 0.250 0.382 1 0.190 0.142 0.111 0.463
0.615 0.711 0.139 0.334 0.476 1.5 0.182 0.134 0.127 0.485 0.637
0.667 0.165 0.366 0.408 2 0.177 0.138 0.174 0.499 0.625 0.528 0.182
0.348 0.210 3 0.175 0.174 0.344 0.503 0.516 0.173 0.188 0.199 0.008
4 0.182 0.239 0.579 0.483 0.340 0.008 0.163 0.021 0.062 5 0.195 --
-- 0.444 -- -- 0.118 -- -- 6 0.213 -- -- 0.394 -- -- 0.067 -- -- 7
0.234 -- -- 0.339 -- -- 0.022 -- -- 8 0.258 -- -- 0.285 -- -- 0.007
-- --
[0089] These simulations indicate that for a very steep cornea
(e.g., a corneal radius of 7.1 mm), the IOL's shape factor has a
relatively small impact on the spherical aberration and the MTF.
For example, in such a case, for shape factors in a wide range of
about -1 to about 8, good optical performance is observed, though
shape factors in a range of about 0.5 to about 4 are preferred.
However, for a cornea having a large radius, e.g., a radius larger
than about 8.6 mm, an optimal range of about 0 to about 2 (e.g.,
about 0.5 to about 2) for the IOL's shape factor is observed. The
peak of the IOL's optical performance as a function of the shape
factor also shifts as the corneal radius varies from a small value
to a large one. For example, the simulations indicate a peak
performance at a shape factor of about 3 for a cornea with a radius
of about 7.1 mm and at a shape factor of about 1 for a cornea with
a radius of about 8.6 mm.
[0090] Similar to corneal radius, it was discovered that an optimal
shape factor for an IOL can vary as a function of the eye's axial
length. By way of example, Table 7 below presents the results of
simulations for optical performance of a plurality of IOLs having
shape factors in a range of -2 to 8 for a plurality of different
axial lengths (ALs). The model eye utilized for these simulations
was characterized by an ACD=4.9 mm, a corneal radius (r)=7.72 mm,
and a corneal asphericity (Q)=-0.26. The graphical representation
of these simulations are provided in FIGS. 9A, 9B and 9C for
spherical aberration, MTF at 50 lp/mm and MTF at 100 lp/mm,
respectively. TABLE-US-00007 TABLE 7 SA (micron) MTF@501 p/mm
MTF@1001 p/mm AL = 22.0 AL = 24.4 AL = 26.0 AL = 22.0 AL = 24.4 AL
= 26.0 AL = 22.0 AL = 24.4 AL = 26.0 X mm mm mm mm mm mm mm mm mm
-2 -- 0.478 0.285 -- 0.037 0.209 -- 0.095 0.021 -1.5 -- 0.386 -- --
0.117 -- -- 0.051 -- -1 0.609 0.307 0.215 0.000 0.212 0.364 0.078
0.011 0.047 -0.5 -- 0.244 -- -- 0.331 -- -- 0.016 -- 0 0.281 0.195
0.166 0.322 0.455 0.507 0.015 0.128 0.200 0.5 -- 0.162 -- -- 0.555
-- -- 0.250 -- 1 0.168 0.142 0.138 0.591 0.615 0.596 0.284 0.334
0.318 1.5 -- 0.134 -- -- 0.637 -- -- 0.366 -- 2 0.240 0.138 0.127
0.407 0.625 0.629 0.070 0.348 -- 3 0.441 0.174 0.132 0.122 0.516
0.616 0.054 0.199 0.345 4 0.718 0.239 0.147 0.011 0.340 0.565 0.030
0.021 0.275 5 -- -- 0.171 -- -- 0.488 -- -- 0.176 6 -- -- 0.202 --
-- 0.395 -- -- 0.075 7 -- -- 0.237 -- -- 0.302 -- -- 0.001 8 -- --
0.274 -- -- 0.222 -- -- 0.024
[0091] The above simulations indicate that while for a long axial
length (e.g., an axial length of about 26 mm), IOLs having shape
factors over a wide range (e.g., in a range of about -1 to about 8)
provide substantially similar performance, for a short axial length
(e.g., an axial length of about 22 mm), an optimal IOL shape factor
lies in a range of about 0 to about 2 (preferably in a range of
about 0.5 to about 2). Further, the peak of optical performance
exhibits a shift as a function of axial length variation.
[0092] In some embodiments, an anterior or a posterior surface of
the IOL includes an aspherical base profile selected to compensate
for the corneal spherical aberration. Alternatively, both anterior
and posterior surfaces can be aspherical so as to collectively
provide a selected degree of compensation for the corneal spherical
aberration. By way of example, FIG. 10 shows an IOL 22 according to
one embodiment of the invention that includes an optic having a
spherical posterior surface 24 and an aspherical anterior surface
26. More specifically, the anterior surface 26 is characterized by
a base profile that is substantially coincident with a putative
spherical profile 26a (shown by dashed lines) for small radial
distances from an optical axis 28 but deviates from that spherical
profile as the radial distance from the optical axis increases. In
this embodiment, the aspherical anterior surface can be
characterized by the following relation: z = cr 2 1 + 1 - ( 1 + k )
.times. c 2 .times. r 2 Eq . .times. ( 2 ) ##EQU4## wherein,
[0093] c denotes the curvature of the surface at its apex (at its
intersection with the optical axis),
[0094] r denotes the radial distance from the optical axis, and
[0095] k denotes the conic constant.
[0096] In some embodiments, the conic constant k can range from
about -1162 to about -19 (e.g., from about -73 to about -27) and
the shape factor of the lens can range from about -0.5 to about 4,
and more preferably, from about 0 to about 2. To show the efficacy
of such aspherical IOLs in reducing the corneal spherical
aberrations, two aspherical IOLs were theoretically designed. The
IOLs were assumed to be formed of an acrylic polymer commonly known
as Acrysof. One of the IOLs was selected to have a shape factor of
zero (X=0) while the other was chosen to have a shape factor of 1
(X=1). The edge thickness for each IOL was fixed at 0.21 mm. For
the IOL with X=0, the anterior and posterior radii were set,
respectively, at 22.934 mm and -22.934 mm, the central thickness
was set at 0.577 mm and the anterior surface asphericity (i.e., the
conic constant) was selected to be -43.656. For the IOL with X=1,
the posterior surface was selected to be flat while the radius of
the anterior surface was set at 11.785 mm. The central thickness of
this lens was 0.577 mm and the anterior surface was assumed to have
an asphericity characterized by a conic constant of -3.594. FIG. 11
shows the sag of the anterior surfaces of these exemplary IOLs as a
function of radial distance from the optical axis.
[0097] The simulations of the optical performances of these two IOL
designs in the aforementioned eye model show a reduction of the
total RMS wavefront errors to about 0.000841 waves in case of the
IOL having a shape factor that approaches zero and to about
0.000046 in case of the IOL having a shape factor of unity.
[0098] Another factor that can affect the optical performance of an
IOL is its effective position. The effective lens position (e.g.,
defined here as the location of the principal plane relative to the
posterior surface) can vary as a function of the lens's shape. The
location of the second principal plane (PP.sub.2) relative to the
apex of the posterior surface can be defined by the following
relation: PP 2 = - n 1 .times. dF 1 n 2 .times. F L Eq . .times. (
3 ) ##EQU5## wherein n.sub.1 and n.sub.2 denote, respectively, the
refractive indices of the IOL and the surrounding medium, F.sub.1
represents the optical power of the anterior surface and F.sub.2
represents the optical power of the lens, and d is the lens's
central thickness. The haptics plane (the anchor plane for the
implanted IOL) located at the central-line of the lens edge can
have a distance from the apex of the posterior surface specified
as: HL = Sag 2 + ET 2 Eq . .times. ( 4 ) ##EQU6## wherein ET
denotes the lens's edge thickness and Sag.sub.2 denotes the sag
height of the posterior surface at the lens's edge. Utilizing the
above Equations (3) and (4), the location of the second principal
point relative to the haptics plane can be defined as follows:
.DELTA. .times. .times. PP 2 = Sag 2 + ET 2 - n 1 .times. dF 1 n 2
.times. F L Eq . .times. ( 5 ) ##EQU7## wherein .DELTA.PP.sub.2
denotes an offset shift of the principal plane, and the other
parameters are defined above.
[0099] By way of example, the 2.sup.nd principal plane shift for
the aforementioned IOL having a shape factor of zero (X=0) was
calculated (by utilizing the above equations) across a power range
of 0 to about 35 D as +/-0.03 mm, while the corresponding shift for
the IOL having a shape factor of unity (X=1) was calculated as
+/-0.15 mm.
[0100] To better appreciate the enhanced optical performance
provided by the IOLs of the invention, some of the major factors
contributing to the variability of post-operative refractive errors
can be considered. These factors are generally classified into
three categories: biometric data errors (.DELTA.Biometric), IOL
power errors (.DELTA.IOLPower) and high-order aberration
contributions (.DELTA.Aberration). An overall variability (Rx) can
be calculated based on these factors by utilizing, e.g., the
following relation: RxError = .DELTA. .times. .times. Biometric 2 +
.DELTA. .times. .times. IOLPower 2 + .DELTA. .times. .times.
Aberration 2 Eq . .times. ( 6 ) ##EQU8##
[0101] The .DELTA.Biometric can, in turn, be defined in accordance
with the following relation: .DELTA.Biometric= {square root over
(.DELTA.k.sup.2+.DELTA.AL.sup.2+.DELTA.ACD.sup.2)} Eq. (7) wherein
.DELTA.k denotes the error in keratometric measurement, .DELTA.AL
denotes the error in axial length measurement, and .DELTA.ACD
denotes the error in the anterior chamber depth measurement. The
.DELTA.IOLPower can be defined in accordance with the following
relation: .DELTA.IOLPower= {square root over
(.DELTA.IOLStep.sup.2+.DELTA.IOLTol.sup.2+.DELTA.ELP.sup.2)} Eq.
(8) wherein .DELTA.IOLStep denotes the variability caused by the
use of IOLs whose optical powers differ by finite steps for
correcting patients' refractive errors that vary over a continuous
range, .DELTA.IOLTol denotes manufacturing power tolerance, and
.DELTA.ELP denotes the variability in the shift of the IOL
effective position across the power range. Further,
.DELTA.Aberration can be defined in accordance with the following
relation: .DELTA.Aberration= {square root over
(.DELTA.Astig.sup.2+.DELTA.SA.sup.2+.DELTA.Other.sup.2)} Eq. (9)
wherein .DELTA.Astig, .DELTA.SA, .DELTA.Other denote, respectively,
astigmatic, spherical and other higher order aberrations.
[0102] The optical performance of the aforementioned exemplary IOL
designs having shape factors (X) of zero and unity were evaluated
based on estimated Rx variability for three conditions: (1)
uncorrected visual acuity (i.e., in the absence of corrective
spectacles) with IOL power step of 0.5 D (UCVA), (2) uncorrected
visual acuity with a refined IOL power step of 0.25 D (UCVA+) and
(3) best corrected visual acuity (i.e., utilizing optimal
corrective spectacles) (BCVA). The variability due to biometric
measurements was estimated from information available in the
literature. The focus of the analysis relates to estimating
contributions of the spherical aberration, errors due to IOL
misalignments, and the 2.sup.nd principal plane (PPL) shifts. For
comparison purposes, a baseline value of 0.65 D was assumed for
UCVA and UCVA+ and a baseline value of 0.33 D was assumed for BCVA,
for eyes with spherical IOLs. Table 8 below lists absolute and
percentage reductions in Rx relative to the baseline values for the
two IOLs: TABLE-US-00008 TABLE 8 IOL with X = 0 IOL with X = 1 UCVA
-0.03 D -4.39% 0.00 D 0.45% UCVA+ -0.05 D -7.13% -0.01 D -2.16%
BCVA -0.03 D -8.53% -0.05 D -13.87%
[0103] The information presented in Table 8 shows that reductions
in Rx variability are achieved for both IOLs (X=0, and X=1), thus
indicating improved optical performance of those lenses. For the
IOL with a vanishing shape factor (X=0), the visual benefits are
almost evenly distributed among UCVA, UCVA+ and BCVA while for the
other IOL (X=1), the visual benefit associated with BCVA is more
pronounced.
[0104] A variety of known manufacturing techniques can be employed
to fabricate the lenses of the invention. The manufacturing
tolerances can also affect the optical performance of an IOL. By
way of example, such tolerances can correspond to variations of,
e.g., surface radii, conic constant, surface decentration, surface
tilt, and surface irregularity, with tolerances associated with
surface asphericity (conic constant) generally playing a more
important role that others in affecting optical performance.
Simulations, however, indicate that the IOL's misalignments upon
implantation in the eye are typically more significant factors in
degrading optical performance than manufacturing tolerances (e.g.,
manufacturing errors can be nearly 10 times less than misalignment
errors). By way of further illustration, the optical performance of
the aforementioned aspherical lenses with X=0 and X=1, implanted in
the aforementioned eye model, was theoretically investigated by
employing Monte Carlo simulations. More specifically, 500
hypothetical lenses were generated under constraints of typical
manufacturing tolerances and were randomly oriented relative to the
cornea. For example, the tolerances associated with the surface
radii, surface irregularities, and surface decentration and tilt
were assumed to be, respectively, within +/-0.1 mm, 2 fringes, 0.05
mm and 0.5 degrees. The results of the Monte Carlo simulations are
summarized in FIG. 12. More than 50% of the simulated eyes exhibit
an RMS wavefront error that is less than about 0.2 waves (about
0.08 D equivalent defocus). For the lens having X=1, about 98% of
the simulated eyes show a wavefront error less than about 0.3 waves
(about 0.12 D).
[0105] Those having ordinary skill in the art will appreciate that
various changes can be made to the above embodiments without
departing from the scope of the invention.
* * * * *