Theoretical Optical Performance of Theoretical Optical Performance of an Equal Conic Intraocular Lens and an Equal Conic Intraocular Lens and Comparison to Spherical and Comparison to Spherical and Aspheric IOLsAspheric IOLs

Edwin J. Sarver, PhDEdwin J. Sarver, PhD

The author(s) acknowledge The author(s) acknowledge financial interest in the subject financial interest in the subject matter of this presentation.matter of this presentation.

Acknowledgement…Acknowledgement…

• Contributors on this project…Contributors on this project…– Don Sanders, MD, PhDDon Sanders, MD, PhD– John Clough, LensTecJohn Clough, LensTec– Hayden Beatty, LensTecHayden Beatty, LensTec– Jim Simms, LensTecJim Simms, LensTec

Background…Background…

• Recent studies have shown that aspheric IOLs can Recent studies have shown that aspheric IOLs can provide patients with significant optical benefits provide patients with significant optical benefits over traditional spherical surface IOLs.over traditional spherical surface IOLs.

1:  Altmann GE, Nichamin LD, Lane SS, Pepose JS. Optical performance of 3 intraocular lens designs in the presence of decentration. J Cataract Refract Surg. 2005 Mar;31(3):574-85.

2:  Bellucci R, Morselli S, Piers P. Comparison of wavefront aberrations and optical quality of eyes implanted with five different intraocular lenses. J Refract Surg. 2004 Jul-Aug;20(4):297-306.

3:  Packer M, Fine IH, Hoffman RS, Piers PA. Improved functional vision with a modified prolate intraocular lens. J Cataract Refract Surg. 2004 May;30(5):986-92.

4:  Kershner RM. Retinal image contrast and functional visual performance with aspheric, silicone, and acrylic intraocular lenses. Prospective evaluation. J Cataract Refract Surg. 2003 Sep;29(9):1684-94.

Optical benefits…Optical benefits…

• The optical benefits are due to a reduction in The optical benefits are due to a reduction in optical aberrations at the retina.optical aberrations at the retina.

• Primarily, Primarily, spherical aberrationspherical aberration is reduced. is reduced.

Spherical aberrationSpherical aberration

• Spherical aberration occurs when rays away Spherical aberration occurs when rays away from the paraxial region do not intersect at the from the paraxial region do not intersect at the paraxial focus.paraxial focus.

Paraxial ray…Paraxial ray…

Paraxial ray

A paraxial ray is an optical ray traced “near” the optical axis.

Paraxial focus…Paraxial focus…

Paraxial focus

Paraxial ray

The paraxial focus is where the paraxial ray crosses the optical axis after refraction by the lens.

Positive spherical aberration…Positive spherical aberration…

Paraxial focus

Paraxial ray

Off axis ray (positive sa)

When an off-axis ray is refracted by the lens and crosses the axis in FRONT of the paraxial focal point, the ray exhibits POSITIVE spherical aberration.

Paraxial focus

Paraxial ray

Off axis ray (positive sa)

Off axis ray (negative sa)

When an off-axis ray is refracted by the lens and crosses the axis in BACK of the paraxial focal point, the ray exhibits NEGATIVE spherical aberration.

Negative spherical aberration…Negative spherical aberration…

Corneal spherical Corneal spherical aberration…aberration…

• The mean corneal spherical aberration has been The mean corneal spherical aberration has been reported to be about +0.27 micronsreported to be about +0.27 microns11

• About 90% of the population has positive About 90% of the population has positive corneal spherical aberration corneal spherical aberration —— About 10% of About 10% of the population has negative corneal spherical the population has negative corneal spherical aberrationaberration22

1Holladay JT, et al, A new intraocular lens design to reduce spherical aberration of pseudophakic eyes. J Refract Surg., 2002 Nov-Dec;18(6):683-91.

2Krueger RR, et al, Wavefront Customized Visual Correction, Chapter 42, p. 368, 2004.

Approximate distribution of Approximate distribution of corneal spherical aberrationscorneal spherical aberrations

0.27 μm

10% negative 90% positive

Spherical IOLsSpherical IOLs

• A biconvex IOL with spherical surfaces exhibits A biconvex IOL with spherical surfaces exhibits positive spherical aberration.positive spherical aberration.

• Thus, usually, spherical IOLs ADD positive Thus, usually, spherical IOLs ADD positive spherical aberration to the already positive spherical aberration to the already positive corneal spherical aberrationcorneal spherical aberration

Aspheric IOLsAspheric IOLs• Aspheric IOLs attempt to improve pseudophakic Aspheric IOLs attempt to improve pseudophakic

vision by controlling spherical aberrationsvision by controlling spherical aberrations

• One strategy is to design a lens with negative One strategy is to design a lens with negative spherical aberrations to balance the normally spherical aberrations to balance the normally positive corneal spherical aberrationspositive corneal spherical aberrations

• Another strategy is to design a lens with Another strategy is to design a lens with minimum spherical aberrations so that no minimum spherical aberrations so that no additional spherical aberration is added to the additional spherical aberration is added to the corneal spherical aberrationscorneal spherical aberrations

– Could be an asymmetric designCould be an asymmetric design– Could be a symmetric designCould be a symmetric design

Comparison of IOLsComparison of IOLs

• Given these IOL design strategies we want to Given these IOL design strategies we want to investigate their potential strengths and investigate their potential strengths and weaknessesweaknesses

• First, we will describe the designs…First, we will describe the designs…

22 D IOL designs…22 D IOL designs…ParameterParameter Spherical Spherical

surface IOLsurface IOLNegative Negative spherical spherical aberrationsaberrations

Asymmetric Asymmetric zero spherical zero spherical aberrationsaberrations

Ref. indexRef. index 1.4271.427 1.4581.458 1.4271.427

R1R1 8.2348.234 11.04311.043 7.2857.285

K1K1 00 -1.03613-1.03613 -1.085667-1.085667

44thth & 6 & 6thth coef coef -0.000944, -0.000944,

-0.0000137-0.0000137

R2R2 -8.234-8.234 -11.043-11.043 -9.470-9.470

K2K2 00 00 -1.085667-1.085667

Altmann, et al, Optical performance of 3 intraocular lens designs in the presence of decentration, J Cataract Refract Surg. 2005;31(3):574-85.

22 D IOL design shapes…22 D IOL design shapes…

Spherical surface IOL

Sphere Sphere

Propagation of light

22 D IOL design shapes…22 D IOL design shapes…

Spherical surface IOL

Sphere Sphere

Propagation of light

Negative spherical aberrations IOL

6th order asphere Sphere

22 D IOL design shapes…22 D IOL design shapes…

Spherical surface IOL

Sphere Sphere

Propagation of light

Negative spherical aberrations IOL

6th order asphere Sphere

Asymmetric zero spherical aberrations IOL

Conic Conic

Equal conic, low spherical Equal conic, low spherical aberrations IOL…aberrations IOL…

• Want to use conic surface for both anterior and Want to use conic surface for both anterior and posteriorposterior

• Want both surfaces equalWant both surfaces equal

• Want low spherical aberrationsWant low spherical aberrations

Equal conic design strategy…Equal conic design strategy…

First, we find the apical radius for the front and back surfaces to give the desired power.

R -Rn0 = 1.336

F=1336 / PParaxial ray

Equal conic design strategy…Equal conic design strategy…

Next, we find the conic K parameter so that off axis rays intersect the paraxial focus.

K K

n0 = 1.336Off axis ray

Paraxial ray

22 D IOL designs…22 D IOL designs…ParameterParameter Sphere / Sphere /

SphereSphere66thth Order Order asphere / asphere / SphereSphere

Conic 1 / Conic 1 /

Conic 2Conic 2

Equal Equal conicconic

Ref. indexRef. index 1.4271.427 1.4581.458 1.4271.427 1.45851.4585

R1R1 8.2348.234 11.04311.043 7.2857.285 11.09311.093

K1K1 00 -1.03613-1.03613 -1.085667-1.085667 -1.23-1.23

44thth & 6 & 6thth coefcoef

-0.000944, -0.000944,

-0.0000137-0.0000137

R2R2 -8.234-8.234 -11.043-11.043 -9.470-9.470 -11.093-11.093

K2K2 00 00 -1.085667-1.085667 -1.23-1.23

Longitudinal aberrations…Longitudinal aberrations…

Negative sphericalaberration

Spherical

Note: spherical aberration in opposite directions.

Longitudinal aberrations…Longitudinal aberrations…

Negative sphericalaberration

Spherical

Negative spherical aberrations

Positive spherical aberrations

Equal conic

Unequal conic

Longitudinal aberrations…Longitudinal aberrations…

Note: scale is 1000 x smaller than previous slide.

More important…More important…

• Rather than just look at the performance of the Rather than just look at the performance of the IOL alone, it is more important to consider how IOL alone, it is more important to consider how it performs in the eye.it performs in the eye.

• To facilitate this analysis, we use a simple To facilitate this analysis, we use a simple aspheric eye model.aspheric eye model.

Choice of eye model…Choice of eye model…

• Negative spherical aberration IOL was Negative spherical aberration IOL was optimized for anterior cornea K = -0.1414optimized for anterior cornea K = -0.1414

• ““Zero” spherical aberration IOLs work best with Zero” spherical aberration IOLs work best with anterior cornea with K = -1/nanterior cornea with K = -1/n22 = -0.53 = -0.53

• Mean cornea has K = -0.26Mean cornea has K = -0.26

• KooijmanKooijman11 eye model has K = -0.25, (we use this eye model has K = -0.25, (we use this model)model)

1Atchison and Smith, Optics of the human eye, Butterworth-Heinemann, 2000, p.255.

Kooijman/optical modelKooijman/optical model

R1=7.8,K1=-0.25

ELP=4.5

n=1.336

AL adjusted to give best focus for 3 mm pupil.

R2=6.5,K2=-0.25

n=1.3771

Centered performance…Centered performance…

Centered – 3 mm PupilCentered – 3 mm Pupil

MTF -- Centered 3MM Pupil

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All IOLs work pretty well here – MTF is limited by diffraction.

Centered – 5 mm Pupil,Centered – 5 mm Pupil,K=-0.1414K=-0.1414

MTF -- Centered 5 mm Pupil

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This is where negative spherical aberration IOL works best.

Centered, 5 mm Pupil,Centered, 5 mm Pupil,K=-0.25K=-0.25

MTF -- Centered, 5 mm Pupil, Kooijman

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As the eye model is adjusted, note how dramatically the performance is modified.

Centered, 5 mm Pupil, Centered, 5 mm Pupil, K=-0.53K=-0.53

MTF -- Centered, 5 mm Pupil, K=-0.53

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When the cornea has spherical aberrations near zero, the “zero” spherical aberration IOLs perform best.

Centered IOL observations…Centered IOL observations…

• Over this range of K values, the spherical IOL is Over this range of K values, the spherical IOL is has lowest performancehas lowest performance

• The best performer in the group of conic surface The best performer in the group of conic surface IOLs depends upon the K valueIOLs depends upon the K value

• For the mean K of -0.25, the negative spherical For the mean K of -0.25, the negative spherical aberration IOL performs bestaberration IOL performs best

Tilt…Tilt…

10 deg tilt – 3 mm pupil,10 deg tilt – 3 mm pupil,K=-0.1414K=-0.1414

MTF -- 10 deg Tilt, 3 mm Pupil

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For this eye model, all IOLs perform about the same.

10 deg tilt, 3 mm pupil,10 deg tilt, 3 mm pupil,K=-0.25K=-0.25

MTF -- Tilt 10 deg, 3 mm Pupil, Kooijman

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For mean corneal shape, the negative spherical aberration IOL performance starts to fall off.

10 deg tilt, 5 mm pupil,10 deg tilt, 5 mm pupil,K=-0.1414K=-0.1414

MTF -- 10 deg Tilt, 5 mm Pupil

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Performance for all IOLs close again…

10 deg tilt, 5 mm pupil,10 deg tilt, 5 mm pupil,K=-0.25K=-0.25

MTF -- Tilt 10 deg, 5 mm Pupil, Kooijman

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“Zero” spherical aberration IOLs start to perform better for mean corneal shape.

Tilt observations…Tilt observations…

• Depending upon the corneal eccentricity:Depending upon the corneal eccentricity:– The performance of the IOL designs are comparableThe performance of the IOL designs are comparable– For some cases, the zero spherical aberration IOLs For some cases, the zero spherical aberration IOLs

out perform the spherical surface and negative out perform the spherical surface and negative spherical aberration IOLsspherical aberration IOLs

Decentration…Decentration…

Decentration 1 mm, Decentration 1 mm, 3 mm pupil, K=-0.14143 mm pupil, K=-0.1414

MTF -- 1 mm Decenter, 3 mm Pupil

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Clearly, the spherical surface and negative spherical aberrations IOLs have trouble with decentration.

Decentration 1 mm, Decentration 1 mm, 3 mm pupil, K=-0.253 mm pupil, K=-0.25

MTF -- Decenter 1mm, 3 mm Pupil, Kooijman

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This trend does not depend upon the corneal shape factor.

Decentration 1 mm – Decentration 1 mm – 5 mm pupil, K=-0.14145 mm pupil, K=-0.1414

MTF -- 1 mm Decenter, 5 mm Pupil

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The same optical behavior is seen for the 3 and 5 mm pupils.

Decentration 1 mm, Decentration 1 mm, 5 mm pupil, K=-0.255 mm pupil, K=-0.25

MTF -- Decenter 1mm, 5 mm Pupil, Kooijman

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Again, the same trend that does not depend upon corneal eccentricity.

Decentration observations…Decentration observations…

• For 1.0 mm decentration:For 1.0 mm decentration:– The spherical surface and negative spherical The spherical surface and negative spherical

aberration IOLs do not perform as well as zero aberration IOLs do not perform as well as zero aberration IOL designsaberration IOL designs

– The trends for decentration does not depend upon The trends for decentration does not depend upon pupil size or corneal eccentricitypupil size or corneal eccentricity

Defocus…Defocus…

Defocus 0.5D, 3 mm Pupil, Defocus 0.5D, 3 mm Pupil, K=-0.1414K=-0.1414

MTF -- Defocus 0.5D, 3 mm Pupil

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For a 3 mm pupil, the corneal eccentricity does not affect optical performance to a large degree – an seen in this and the next slide.

Defocus 0.5D, 3 mm Pupil, Defocus 0.5D, 3 mm Pupil, K=-0.25K=-0.25

MTF --Defocus 0.5D, 3 mm Pupil, Kooijman

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Defocus 0.5D, 5 mm Pupil, Defocus 0.5D, 5 mm Pupil, K=-0.1414K=-0.1414

MTF -- Defocus 0.5D, 5 mm Pupil

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The general performance of the IOLs for 0.5D of defocus and 5 mm pupil does not appear to depend upon corneal eccentricity.

Defocus 0.5D, 5 mm Pupil, Defocus 0.5D, 5 mm Pupil, K=-0.25K=-0.25

MTF --Defocus 0.5D, 5 mm Pupil, Kooijman

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As a side issue, the large ripples corresponding to the negative spherical aberration IOL indicate regions of contrast reversal.

Defocus observations…Defocus observations…

• For 0.5 D of defocus at 3.0 and 5.0 mm pupils, For 0.5 D of defocus at 3.0 and 5.0 mm pupils, the performance of all IOLs are about equal.the performance of all IOLs are about equal.

• The negative spherical aberration IOL shows The negative spherical aberration IOL shows more contrast for low frequency objects than the more contrast for low frequency objects than the other IOLsother IOLs

• The negative spherical aberration IOL showed The negative spherical aberration IOL showed significant regions of contrast reversal at 5.0 mm significant regions of contrast reversal at 5.0 mm pupilpupil

Closer look at EC & UCCloser look at EC & UC

• The equal conic IOLs and unequal conic IOL The equal conic IOLs and unequal conic IOL designs appear to perform about the samedesigns appear to perform about the same

• Want to consider variability in tangential and Want to consider variability in tangential and sagittal MTF components in more detailsagittal MTF components in more detail

Tilt of 10 deg, 5 mm pupilTilt of 10 deg, 5 mm pupil

MTF -- Tilt 10 deg, 5 mm pupil, Kooijman

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The tangential and sagittal MTF components indicate a greater variability for the unequal conic design compared to the equal conic design.

Tilt |T-S| graphTilt |T-S| graph

MTF -- Tilt 10 deg, 5 mm pupil, Kooijman, |T-S|

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The magnitude of the differences between the tangential and sagittal MTF components clearly show more variability for the unequal conic design.

DecentrationDecentration

MTF -- Decenter 1mm, 5 mm pupil, Kooijman

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It is more subtle which lens design is more variable.

Decentration |T-S| graphDecentration |T-S| graph

MTF -- Decenter 1mm, 5 mm pupil, Kooijman, |T-S|

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By comparison of the magnitude of the difference between tangential and sagittal MTF, we see that the equal conic design has less variability.

DiscussionDiscussion

• There are various conditions in which one IOL There are various conditions in which one IOL design will perform better than another, but design will perform better than another, but generally…generally…

– Aspheric IOLs perform better than spherical surface Aspheric IOLs perform better than spherical surface IOLsIOLs

– For the level of alignment errors investigated here, For the level of alignment errors investigated here, zero spherical aberration IOLs perform better than zero spherical aberration IOLs perform better than spherical surface IOLs and negative spherical spherical surface IOLs and negative spherical aberration IOLsaberration IOLs

Discussion…Discussion…

• Recognizing the variability in corneal Recognizing the variability in corneal eccentricity, it may be prudent to decide upon eccentricity, it may be prudent to decide upon the use of an aspheric IOL design as a function the use of an aspheric IOL design as a function of measured corneal aberrations (not ocular of measured corneal aberrations (not ocular aberrations)aberrations)

• This IOL selection strategy was suggested by This IOL selection strategy was suggested by Krueger et al.Krueger et al.

Krueger RR, et al, Wavefront Customized Visual Correction, Chapter 42, p. 368, 2004.

SummarySummary

• Aspheric IOLs have optical advantages over Aspheric IOLs have optical advantages over spherical IOLsspherical IOLs

• For small alignment errors and positive spherical For small alignment errors and positive spherical aberration corneas, negative spherical aberration aberration corneas, negative spherical aberration IOLs perform bestIOLs perform best

• For larger alignment errors, “zero” spherical For larger alignment errors, “zero” spherical aberration IOLs perform bestaberration IOLs perform best

SummarySummary• ““Zero” spherical aberration IOLs perform well Zero” spherical aberration IOLs perform well

over a wider range of corneal shapes and over a wider range of corneal shapes and alignment errors than negative spherical alignment errors than negative spherical aberration IOLsaberration IOLs

• The equal and unequal conic IOL designs The equal and unequal conic IOL designs perform are very similarperform are very similar

• The equal conic IOL design performs slightly The equal conic IOL design performs slightly better than the unequal conic IOL design in better than the unequal conic IOL design in terms of smaller variability in tangential and terms of smaller variability in tangential and sagittal MTF componentssagittal MTF components

Thank you!Thank you!