Optical design of poly(methyl methacrylate) intraocular lenses

Optical design of poly{methyl methacrylate) intraocular lenses David A. Atchison, Ph. D.

Ke Word

ntrati n. In' tilt. ph ri it)' intra ular In, I n modulation tran f, r fun tion, optic d ign. P' udophakia. ph rical ab rration p t diagram, w<\\ ab rration

Much attention has been given to the design of the intraocular lens (IOL) haptic to improve fixation stability and reduce complications . However, little attention has been given to the optical design parameters affecting retinal image quality. Many poly(methyl methacrylate) (PMMA) lenses are made in one of three simple forms: plano-convex (curved surface facing the cornea), plano-convex (curved surface facing the retina), and equi-convex. Other biconvex forms are also common. The form of the lens can be described by a shape factor

where C 1 and C2 are the front and back surface curvatures, respectively. The relationship between the form and the shape factor is

x<

X -1 < X X o< X X X

- 1 meniscus, more curved surface facing retin a 1 plano-convex , curved surface facing retina

=

-

=

+1

< 0 biconvex, more curved surface faCing retina = 0 equi-convex < + 1 hiconvex , more cu rved surface faCing cornea plano-convex, curved surface facing cornea

> + 1 m eniscus, more curved surface facin g cornea

Some lens forms are shown in Figure 1. The asphericity of the cornea should be conside red when designing IOLs. A simple aspheric surface is the

SlIllported by a gr(lnt from thc Australian ResC(lrch Counei/. Dr. .\1.]. Kir/ger prol'ider/ helpflll correspondence.

Th(, Kidl!.('/" Optics optical desil!.lI program . cersioll .3.5, W(lS IIsed for this illvestigation. Reprint rel(I/('~~ts to Da(:id A. Atchison , Ph. D ., Faculty of Health SCience, Queenslcmd Unillersity o'TechllOlog y GPO B ')434 B . b Q 4001, Allstralw . 'J , ox - ' , ns aile 178

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_

X=

-5

-2

-1

o

1

2

retina

5

Fig. 1.

(Atchison) Lens shape factor X.

X= conicoid, which can be expressed in an X, Y, Z rectangular coordinate system as

Z =

1 +v'1 -(1 + Q)c 2 p2

where the Z-axis is the optical axis, c is the vertex curvature, p2 = X2 + yz, Q is the asphericity factor. For Q < 0 the surface flattens away from its vertex, Q = 0 corresponds to a sphere, and for Q > 0 the surface steepens away from its vertex. Recent population studies of corneal topography have obtained mean and standard deviations of Q of -0.26±0 .18 1 and -0.IS±0.13. 2 With the conventional lens material poly(methyl methacrylate), the optimum lens shape for on-axis performance of a centered pseudophakic eye would seem to be approximately X = + 1.1:3 ,4 This shape minimizes spherical aberration for eyes with corneal asphericities Q ~ - 0.5 , which encompass most of the normal range. Wang and Pomerantzefi5 determined an optimum value of X = - 0.5 , but re latively few eyes would have negative asphericities greater than the equivalent conic asphericit y6 of - 0.66 in their modep ,2 Pomerantzeff and coauthors 4 also investigated offaxis performance out to ten-degree object angle with their model. They felt that the lens shape for best offaxis perform ance occurring at 7 .5. degrees gave the best overall performance. For this, the le ns shape was X = - 0.6 (biconvex, more curved surface facing retina). Atchison' investigated wave aberrations for ten-degree object angle using third order theory and thin lenses. He found that over a range of ocular parameters, spherical aberration and coma are the most rapidly changing aberrations with change in lens shape and hence should carry the greates t weight when determining optimum shapes. Spherical aberration was a minimum for X = + 1.1 and coma had minimums at X = -0.9 to X = -3.4. Hence, the optimum designs should lie within the range X = + 1.1 to ( - 0.9 to - 3.4). Intraocular lenses may not be always fitted correctly within pseudophakic eyes. Jalie R found refractive er-

rors in the presence of lens tilt were greatest for lens shapes X > + 1.0 (meniscus, more curved surface facing cornea). However, Atchison 9 found maximum refractive errors within the range X = + 0 .2 to X = + 0.7. The discrepancy was due to a difference in the position about which lenses were tilted. Atchison also found that refractive errors were much more affected by lens shape in the presence of decentration than in the presence of tilt. Minimum refractive errors with decentration occurred for the le ns shape X = + 0.5. Most suggestions for IOL shapes have been within the range X = - I to X = + 1, coinciding with the range in general use. Most studies ofIOL designs have been restricted in their mode l parameters. This study investigates which PMMA IOL forms perform optimally in pseudophakic eyes, and whether lens forms other than the conventional forms should be used. The following conditions were considered: (1) On-axis vision when lenses are correctly centered; (2) off-axis vision when lenses are correctly centered. The angle chosen is ten degrees in object space. This small angle was chosen because beyond a few degrees from the visual axis, resolution is limited more by neural than by optical factors . 10 (3) On-axis vision \-vhen lenses are displaced because of tilt or decentration. Tilting was assumed to take place at a po int midway between lens vertices. MATERIALS AND METHODS Methods have been discussed in detai1. 6 . 11 . 1Z The model used is similar to the Gullstrand number 1 schematic eye,13 except that the corneal anterior surface radius is 7.72 mm instead of 7.70 mm and its length is 24.40 mm instead of 24 .385 mm. The parameters of the model are given in Table 1. Three corneal asphericities have been used: Q = 0, - 0.26, and - 0.5 , which encompass most of the normal population. 1.2 There may be systematic postoperative changes in corneal asphericity, but no reasonable population data are available . Some variation was made to some of the parameters,l e.g., flatter/standard! steeper corneas combined with shortlstandardllonger

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179

Table 1. Model eye.

Component

Radius

Refrac-tive Index Distance to Next of Following Surface (mm) Medium (587.6 nm)

Anterior cornea

7.72

0.5

Posterior cornea

6.8

3.1

1.336

20.8

1.336

Aperture Retina

1.376

-12.0

axial lengths. Axial length was altered by varying posterior chamber depth. Sometimes eyes were undercorrected or overcorrected by IOLs, thus requiring additional spectacle lens correction. Unless stated, results refer to the standard model eye of Table 1. Two aperture diameters were considered, 3.550 mm and 1. 775 mm, corresponding approximately to entrance pupil sizes of 4.0 mm and 2.0 mm, respectively. Intraocular lenses had the refractive index of PMMA (1.492). The thickness of all lenses was 0.7 mm . A range of lens positions was considered. The anterior surfaces were placed 1.2 mm and 0.7 mm in front of the aperture, at the aperture, and 0.9 mm and 1.4 mm behind the aperture. The wavelength of light was .587.6 nm. A variety of image quality criteria were considered. These included (1) wave aberrations, which are the measure of the departure of the actual wavefront from an ideal spherical wavefront emanating from a point object, measured at the exit pupil (Figure 2); (2) spot diagrams, which are maps of transverse ray aberrations for a large number of rays traced through an optical system from the object point. A transverse ray aberration is the distance and direction of the intersection of a

ray, at the image surface, from the corresponding intersection of the pupil ray which passes through the center of the aperture; (3) longitudinal aberrations, in the form of the lens power at the anterior corneal plane required to change the direction of a ray so that it intercepts the pupil ray at the image surface; (4) modulation transfer function (MTF), which is the ratio of image and object contrasts of a sinusoidal luminance profile target, for a range of target spatial frequencies; (5) an optimization procedure , which minimizes a merit function 'l' = l (w j g)2 where Wj are weighting factors and gj are aberrations, by altering parameters of the system. The parameters allowed to vary are generally the surface curvatures of the IOL. For all meridian rays, the aberration selected is the transverse ray aberration. For pupil rays, the values of sagittal and tangential aberration and the distortion are selected. For skew rays, two aberrations are selected: the x and y components of transverse ray aberrations. For an on-axis object, three rays were traced for optimization. For an off-axis object, seven rays were traced. For optimization involving decentered or tilted surfaces, ravs were selected as for an off-axis object. More weighting was given to the on-axis position than to off-axis positions, rays at smaller apertures had larger weight than rays at larger apertures, and skew rays were given a larger weight than meridian rays. RESULTS On-Axis Vision Spherical aberration for pseudophakic eyes with IOLs fitted 1.4 mm behind the aperture is shown in Figures 3 and 4 for a 4.0 mm pupil. Figure 3 shows the primary wave aberrations of rays passing through the edge of the aperture, and Figure 4 shows the power of spectacle lenses that correct the aberrations of rays

Optical System

Image Pillne

"- .........

\o

O'

Fig. 2. \ Wauefront

1

,'waue Rberratlon Ideal

Wauerront 180

J CATARACT REFRACT

SURG-VOL 16. MARCH 1990

(Atchison) Wave aberration of a rav passing through an optical syste ll{.

10

o

en

~ c:

0 .-0 .5

~

~

0 . ·0.26

~

.!. ~

5

~

a:

0.0 0.·0.26 0.·0.5

w

CD


~

9: (f)

Z

UJ

-' (!!

Z

~

>a:

>=

U

0

UJ

a:

a:


::;;

0

u

~

Cl.

·8

. 5. '---'----'.2--""-------'-0--'----'2--""-------'4 4

·10 '---~-~~-~-~--~--L-~~~

·4

·2

o

2

4

SHAPE FACTOR X SHAPE FACTOR X

Fig. 3.

(Atchison) Primary wave spherical aberration at the edge of the aperture for eyes with IOLs 1.4 mm behind the aperture; 4.0 mm pupil size. Three corneal asphericities Q = 0, - 0.26, and - 0.5.

passing through the edge of the aperture. Minimum spherical aberration occurs for a lens shape X = + 1.2, similar to previous results. 3,4, 7 The effect of changing corneal asphericity is merely to alter the minimum spherical aberration value. Results for other fitting positions give similar magnitudes and positions of the plots. The optimum shape is fairly resistant to change in ocular parameters of axial length and corneal curvature, and also when additional spectacle corrections between - 3 D and + 3 D are required. Parameter

Fig. 4.

(Atchison) Power of lenses (D) placed at the anterior corneal plane to correct spherical aberration of rays passing through the edge of the aperture of pseudophakic eyes with IOLs 1.4 mm behind the aperture; 4 mm pupil size. Three corneal asphericities Q = 0, - 0.26, and -0.5.

combinations that require an appreciable shift in optimum lens shape do so in the positive X direction, but they produce small IOL powers for which spherical aberration is fairly insensitive to lens shape changes. 6 Figures 5 and 6 give some image quality assessments of pseudophakic eyes with conventional IOL shapes of 1.0

diffraction limit • 4mm pupil

~

Fitting +1.4mm

O.02mm -O.2 mm

-O.1mm

o

•

4mm pupil

+O.1mm

+O .2 mm

LL

~

•

0.5

X=+1

@

X-+ 1

@

X=·1

X.O ........

(@ X,.-1

..... OBJECT SPATIAL FREQUENCY (cycles/degree)

Fig. 5.

(Atchison) On-axis spot diagrams for pseudophakic eyes with IOLs fitted 1.4 mm behind the aperture. Lens shape factors X = -1, 0, - 1: 4 mm pupil size; corneal asphericity Q = -0.26.

Fig. 6.

(Atchison) On-axis monochromatic diffraction MTFs for pseudophakic eyes with IOLs fitted 1.4 mm behind the aperture. Lens shape factors X = - 1, 0, + 1; 4 mm pupil size; corneal asphericity Q = - 0.26.

J CATARACT REFRACT SURG- VOL 16, MARCH 1990

181

x = + 1, X = 0, and X = -1. Figure 5 contains spot diagrams when lenses are fitted 1.4 mm behind the aperture, pupil size is 4.0 mm, and corneal asphericity Q is - 0.26. Lens powers have been modified slightly to place the best image, as determined by optimization, at the retina. Central diagrams show the retinal image. Image quality at positions (- )0.2 mm and (- )0.1 mm in front of, and (+ )0.1 mm and (+ )0.2 mm behind the retina is also shown. The X = + 1 form is almost optimum but the image quality is much poorer for the X = - 1 form as shown by the increased spread of points. The lens of shape X = 0 gives intermediate performance. Figure 6 contains monochromatic MTFs for the same conditions. Lens powers have been modified to give the optimum modulation transfer for an object spatial frequency of 30 cycles/degrees. The X = + 1

form has nearly diffraction limited performance, but the performance of the X = - 1 form is much poorer. The lens of shape X = 0 gives intermediate performance. The differences in optical performance of the lens forms decrease as pupil size declines. For all pupil sizes, the optimum shape is approximately X = + 1.2.

O!fAxis Vision (Ten-Degree Object Angle) Wave aberration components for pseudophakic eyes are shown in Figures 7 to 9. Pupil size is 4.0 mm and corneal asphericity Q is - 0.26. Aberration components are oW40 (spherical aberration), W 31 (coma), W s (saggital aberration), W t (tangential aberration), and total transverse distortion. In Figure 7, the front surface of the IOL is at the aperture. Spherical aberration has a minimum at X = + 1.2 and is approximately a quadratic function oflens

10 10

oW 40(waves)

><..._-......-------;,....qli--

oW 40 (waves) Wj(waves)

W t (waves)

f-

r-='*==j"----===::==::::::=:::==

--:::2~~='ii;-'~==F==*,,==ili=== Distortion (%) Ws (waves)

·1

-2

-2

-3

-3

-4

-4

-S4L..-~--L_2-~--L-~~--''---~----'

_5L-_~_~_~_-L_~_-L_~_~

-4

-2

SHAPE FACTOR X

SHAPE FACTOR X

Fig. 7.

182

Distortion (%) Ws (waves)

-1

(Atchison) Aberrations at the edge ofthe aperture ft)r eyes as a function of lens shape factor X for IOLs at the aperture. The o\V~() wave aberration component was obtained for a zero degree field angle (on-axis), and the \V:31' \Vs and \V t wave aberration components and total transverse distortion were obtained for a ten-degree field angle. Corneal asphericity Q = -0.26; pupil size 4 mm.

J CATARACT REFRACT

Fig. 8.

(Atchison) Aberrations at the edge of the aperture for eyes as a function of lens shape factor X for IOLs 1.2 mm in front of the aperture. Other details as ft)r Figure 7.

SeRG- VOL 16, .'vlARCH 1990

10

W 31 (waves)

[]

0=0

x +

Q= -0.26 Q= -0.5

~­ - " - .

~-

-..."

~--...----- .... ~

WI (waves)

"

+-~-- __ -1::-::-.0 .....

OW40 (waves)

~-

--- ---_

Ws (waves)

1---::;:>-""----:-:=--==""--........- - - - Distortion (%)

- - -.c

.....

-1

-2

-3

---ON·AXIS .- - ON·/OFF-AXIS --OFF·AXIS

-4

-5L--~_~_~_~_~_~_~_~

-4

-2 -2~-~--L-~-~--~-~-~-~

-2

·1

SHAPE FACTOR X LENS POSITION (mm)

Fig. 9.

(Atchison) Aberrations at the edge of the aperture for eyes as a function of lens shape factor X for IOLs 1.4 mm behind the aperture. Other details as for Figure 7.

shape. Wave coma is approximately linearly related to lens shape and is zero for X = -1.8. Sagittal and tangential wave aberrations are less dependent on lens shape. Distortion is small across the shape range. The shapes of the aberration curves, except for spherical aberration and distortion, change when lenses are moved away from the aperture. For lenses fitted 1.2 mm in front of the aperture (Figure 8), the coma curve is quadratic in nature, and the sagittal and tangential aberration curves have negative slopes. For lenses fitted 1.4 mm behind the aperture (Figure 9), coma does not become zero but has a minimum at X = - 1. 7, and sagittal and tangential aberration curves now have positive slopes. Changing corneal asphericity alters the positions of the curves with greatest effect upon spherical aberration and coma, but has little effect upon curve shapes. 7 J CATARACT

Fig. 10.

(Atchison) Optimum lens shape factor X as a function of lens position relative to the aperture. Results are shown for the centered on-axis case, the off-axis case, and the combined on-/off-axis case. The three corneal asphericities are Q = 0, - 0.26, and - 0.5. Pupil size is 4mm.

Optimized lens shapes are plotted as a function of lens position relative to the stop for 4.0 mm pupils and three corneal asphericities in Figure 10. Negative lens position values correspond to the lens being in front of the aperture, Results are given for the on-axis case, the off-axis case, and a combined on- and off-axis case. For the on-axis case, all corneal asphericities and lens positions provide optimum shape factors of approximately X = + 1.2. For the off-axis case, the optimum shape factors are less positive, or even negative. As lens position moves farther away from the cornea, optimum shapes become less positive or more negative. As asphericity becomes more negative, the trend is also toward more negative shape factors. The on-/off-axis case has optimum shapes varying between X = + 1.1 and X = o. Using the ocular parameters of Pomerantzeff and coauthors 4 I obtained an optimized

REFRACT SURG-VOL 16, MARCH 1990

183

2 I------i 0.02 ....

-0.2,.,'" C

Q.()

x 0-.0 26 +

0-.0.5

~

)(

<

x.+ 1 -0. ' "'1ft

\.J

/"""\

0

'-i~1i~~(~~ .

~<.

Fitting + 1 .4mm 4mm pupil RETINA

+O . l",m

u

"'0 . 2m'"

....

. .. ~

(~

:::~~~1~~~:~'

..;;.:-:,:,

...:.;~:.::..:!:::: ..

...'"

<:I

z <

'b

." ,

....:

::~~~. ....

..

u •

.. . ... '

x

a:

~

~

u. W

o

Fig. 12.

Q.

c(

~

(Atchison) Spot diagrams for a pseudophakic eye with an IOL of shape X = + 1 fitted 1.4 mm behind the aperture. Pupil size 4 mm, corneal asphericity Q = - 0.26. On-axis and off-axis (ten-degree object angle) imagery shown. Central diagrams correspond to the best on-axis image, as determined by optimization, being placed at the retina.

·1

·2 .2L - - - - - ' - -..Ll--'---~O--"'-----:--........-~2

LENS POSITION (mm)

Fig. 11.

(Atchison) Optimum lens shape factor X as a function of lens position relative to the aperture. Details as for Figure 10, except pupil size is 2 mm.

off·axis shape of X = - 0.4, which is close to their result of - 0.6. Figure 11 shows optimized lens shapes for a 2.0 mm pupil. Optimnm shape factors for the on-axis case are similar to those obtained with a 4.0 mm pupil. However, off-axis there is a greater trend toward negative shape factors, with fitting positions behind the aperture requiring more negative shape factors than for fitting positions in front of the aperture. For the combined on-/off-axis case, optimum shape factors range from X = + 1.3 to X = -0.7. Optimization was performed with other combinations of axial length and corneal curvature. In general, the results follow the trends discussed, although some 184

optimum values are outside the relevant range for the standard model eye. Figure 12 gives an example of spot diagrams for offaxis vision using the conventional lens shape X = + 1 (lenses fitted 1.4 mm behind the aperture, pupil size 4.0 mm, corneal asphericity Q - 0.26). Off-axis image quality is inferior to on-axis image quality and the comet shape of coma is evident. This coma is less evident for X = 0 and X = - 1 shapes. Spot diagrams and monochromatic MTFs of pseudophakic eyes with conventional IOLs were analyzed for a range of corneal asphericities, pupil size and lens fitting position. Quality of the off-axis retinal image follows the same order as would be expected following an analysis of the optimization results (Figures 10 and ll).

On-Axis Vision in the Presence of Lens Displacement A lens tilt of ten degrees and a lens decentration of 1.5 mm are near the upper limits for these displacements. 13 ,14 Refractive errors for pseudophakic eyes when lenses are either tilted by ten degrees or decentered upward by 1..5 mm are shown in Figure 13. These results apply to lenses fitted 0.9 mm behind the aperture, but refractive errors are affected little by fitting position or corneal asphericity. It can be seen that refractive errors are more affected by lens shape when there is decentration than when there is tilt. For the former, minimum refractive errors occur at the lens shape X = + 0.5. In Figure 14, optimum lens shapes in the presence of tilt and decentration are shown for lens positions

J CATARACT REFRACT SURG-VOL 16, MARCH 1990

o Sphere, 10' tilt Sphere, 1.5mm decentration Cylinder, 10' tilt Cylinder, 1.5mm decentration

-1

Fig. 13. Lens fitting O.9mm behind stop

·2~--~---L--~~--~--~--~----~--~ -2 -1 o 2

(Atchison) Refractive errors (correcting spectacle lenses) of pseudophakic eyes due to ten-degree tilt and 1.5 mm transverse decentration of IOLs. Lenses 0.9 mm behind the aperture.

SHAPE FACTOR X

1.2 mm in front of and 0.9 mm behind the aperture for 4.0 mm pupils. Results are similar for a range of corneal asphericities. The optimum lens shapes are all meniscus with the more curved surface facing the cornea, but they are close to plano-convex (X = + 1). The use of 2.0 mm pupils makes the results even closer to plano-convex. Figures 15 to 18 give some image quality assessments of pseudophakic eyes with conventional IOL 1.5

1.Smm Decentration

x

10' tilt

a:

of-

~

W CL

-0:: I [/)

1.0

[/)

zW

-J

::;: ::;: f=

::J

4mm pupil

CL

o

0.5

L--__

-2

~

___L__ ___'__ _ _ _L -__- ' -___l..._ ___'__ __ _ l

-1

o

2

LENS POSITION (mm)

Fig. 14.

(Atchison) Optimum lens shape factor X as a function of lens fitting position relative to the aperture for ten-degree lens tilt and 1.5 mm lens decentration. Corneal asphericity Q = -0.26; 4 mm pupil size.

J CATARACT REFRACT

shapes. These apply for lenses fitted 0.9 mm behind the aperture. Pupil size is 4.0 mm and corneal asphericity Q is - 0.26. Figure 15 contains spot diagrams for a lens of shape X = + 1. This lens is close to the optimum shape for the on-axis centered case, with spherical aberration minimized (top row). In the presence of tendegree tilt, astigmatism is present (second row). Upon optimum spectacle correction, incorporating 0.40 D cylinder, image quality is near that occurring for the onaxis centered case (third row). Figure 16 contains spot diagrams with a lens of shape X = - 1. For the on-axis centered case, this lens has more spherical aberration than the previous lens (top row). With ten-degree lens tilt, a coma-like aberration and astigmatism are introduced, although a strong central core remains to the retinal spot diagram (second row). Retinal image quality is not much improved by optimum spectacle correction incorporating a 0.43 D cylinder (third row). Figure 17 contains spot diagrams for a pseudophakic eye with a lens of shape X = + 1. Performance is only slightly affected by 1.5 mm decentration (second row) and cannot be much improved by a spectacle correction incorporating 0.12 D cylinder (third row). Figure 18 contains spot diagrams with the lens of shape X = -1. With decentration, coma-like aberration is introduced, but a strong central core remains to the retinal spot diagram (second row). Upon optimum spectacle correction incorporating 0.76 D cylinder, retinal image quality does not appear to be much improved (third row). For both tilt and decentration, monochromatic MTFs show the same trends as for the spot diagrams; similar results are found when IOLs are fitted 1.2 mm

SURG-vOL 16, MARCH 1990

185

X=+1 -O.2mm

o

-O . 1mm

Fitting +O.9mm RETINA

+0 . 1mm

4mm pupil

............. 0 . 04",m -0.2mm

o

+0 .2m'"

a:

•

OJ

0-

Z

W

o

0~

0-

Z

•

a: w

•

0-

Z

W

o

t

~

!: ....

...

•

W

~o:

in front of the aperture~ pseudophakic eyes with lenses of shape X = 0 are intermediate in performance between eyes with lenses of shapes X = + 1 and X = -1.

DISCUSSION For corneal asphericities Q :? - 0.5, which occur in most of the population, optimum on-axis performance of centered IOLs is obtained with IOLs of shapes near

~ o.o

.. m," X=+ 1

-0.2mm

~ ~

-0.1mm

•

Z

w

0

Flttln9 +O.9mm RETINA

... O.lmm

Fig. 16.

'to . 2M'"

X=-1 o

-0.2mm

a:

IU

~ W o

Z

0-

Z

OJ

0

W

oz 0

~-=

i=~
0: a:

0-0

ZO

w% 0w_ ....

•

o

•

11>6

'-:':"

"':':.: : .:

Fitting +O.9mm +0 . 1 mm

RETINA

• "

>o

......

~~

: : ...... "

zi=

2~
•

.~ ~.~

>-a:

.

.

+0 . 2m'"

.':

t>

··>. J1

z

IU

4mm pupil

...... ....

",

.::~,.:':

< a:

......

. " .. "

0:0

~O lUr

0>-

:!li

O;t

Fig. 17.

-0.1 mm

;:

•

..

X = + 1 (plano-convex, curved surface facing the cornea). This optimum shape is fairly resistant to variation in ocular parameters. Lenses of shape X = + 1 give considerably better performance than the reverse form (X = -1). Lens displacement by tilt or decentration adversely affects on-axis retinal image quality. With conventional lens shapes and reasonable levels of displacement, the deterioration is either small or retinal image quality can be nearly restored to predisplacement levels by spectacle correction. Optimum lens shapes are still close to X = + 1. The optimum lens shape for an off-axis position varies with lens fitting position, corneal asphericity, and pupil size. Optimum lens shapes for a ten-degree

IU

•

....

(Atchison) Spot diagrams for pseudophakic eyes with an IOL of shape X = - 1. Other details as for Figure 15.

4mm pupil

0

< a:

::: -....i:..~.

o

(Atchison) Spot diagrams for pseudophakic eyes with an IOL of shape X = + 1 fitted 0.9 mm behind the aperture. Pupil size 4 mm, corneal asphericity Q = - 0.26. The central diagram in top row corresponds to the best image for the on-axis centered case, as determined by optimization, being placed at the retina. The top row shows the on-axis centered case, the second row shows the case for a ten-degree tilt, and the third row shows the tilted case after optimum spectacle correction.

'

:.

~o

Fig. 15.

z ;:

...

~~ ~ ~ a: 'llf

o

0

....

Z

~o

+0 , 2,..

RETINA

:,:.~~:

0-

%0

;to

-O.lmm

4mm pupil

....

f

%0

0-0:

Flttln9 +O.9mm

•

OJ

OJ

X=-1

(Atchison) Spot diagrams for pseudophakic eyes with an IOL of shape X = + 1. The second row shows the case for a 1.5 mm decentration and the third row shows the decentered case after optimum spectacle correction. Other details as for Figure 15.

J CATARACT REFRACT

Fig. 18.

(Atchison) Spot diagrams for pseudophakic eyes with an IOL of shape X = - 1. Other details as for Figure 17.

SURG- VOL 16, MARCH 1990

off-axis object position range from near the X = + 1 shape to near the reverse form (X = -1). As on-axis imagery should be weighted more heavily than the off-axis imagery, and conditions favoring the reverse form include small pupils for which image quality is relatively insensitive to lens shape variation, a reasonable compromise between the demands of good on-axis and off-axis visual quality would be provided by lenses with shapes between X = + 1 and X = O. Thus, these two conventional lens shapes and shapes between them are recommended for IOLs, but the X = - 1 lens shape is not. This work has assumed that lenses are made of transparent homogeneous PMMA with perfectly spherical surfaces. The results and conclusions do not apply if lenses have aspherical surfaces and might not be appropriate for lenses made of materials with different refractive indexes (e.g., polyHEMA, refractive index 1.43).

REFERENCES 1. KielyPM, Smith G, Carney LG: The mean shape of the human

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