aberrations associated with rigid contact lenses

David A. Atchison Vol. 12, No. 10 /October 1995 /J. Opt. Soc. Am. A 2267

Aberrations associated with rigid contact lenses

David A. Atchison

Centre for Eye Research, School of Optometry, Queensland University of Technology,Locked Bag No. 2, Red Hill, Q 4059, Australia

Received September 12, 1994; revised manuscript received December 16, 1994; accepted January 17, 1995

A rigid contact lens on an eye can produce levels of spherical aberration very different from those produced bya spectacle lens in front of the eye. These levels are considerably affected by contact lens surface asphericity.Change in longitudinal spherical aberration associated with aspherizing a contact lens surface is well predictedby a simple equation for change in sagittal power of the surface. Displacing an aspheric contact lens on theeye can produce considerable defocus, which is well predicted by simple equations for change in sagittal andtangential surface powers. The best refractive correction with contact lenses can be determined only byoverrefraction with a patient wearing a contact lens of power and characteristics similar to that which will beprescribed. An aspheric contact lens that moves to a considerable extent on the eye will cause more unstablevision than will a spherical lens that moves to the same extent.

Key words: aberrations, asphericity, contact lens, spherical aberration.

1. INTRODUCTION

Aberrations reduce image quality of optical systems.They prevent the image from being a perfect replica,apart from size and luminance differences, of an object.They are important in the optical systems with whichoptometrists deal, namely, the eye by itself or in combi-nation with spectacle lenses, contact lenses, or intraocularlenses. For different ophthalmic appliances, because oftheir power and the different ways that they move rela-tive to the eye, different aberrations are important.

In designing spectacle lenses, the important aberra-tions are transverse chromatic aberration, field curvature,astigmatism, and distortion corresponding to foveal visionwhen the eye rotates about its center of rotation to viewobjects that are not on the lens optical axis. Sphericalaberration and coma are negligible because of the rela-tively low surface curvatures of spectacle lenses. Longi-tudinal chromatic aberration is also ignored because thatintroduced by spectacle lenses is small compared withthat of the eye and because there is evidence that cor-rection of the eye’s chromatic aberration does not havemuch effect on visual performance.1 In designing spec-tacle lenses, one can consider spectacle lenses largely inisolation from the eye, with the eye providing only its cen-ter of rotation as the stop of the lens.2

Because contact lenses move with the rotating eye,off-axis aberrations are important only when lenses aredecentered. In designing contact lenses, spherical aber-ration is important because of the high surface curvaturesof contact lenses. To this aberration must be added comaand comalike aberrations and defocus that are due to fieldcurvature and astigmatism when the lenses are decen-tered. Longitudinal chromatic aberration is ignored forthe same reason as for spectacle lenses.

Unlike in the case of spectacle lenses, contact lensescannot be considered in isolation from the eye. The ma-jor aberration of a contact lens is spherical aberration,which also afflicts the eye. A contact lens can undercor-rect, correct, or overcorrect the spherical aberration of the

0740-3232/95/102267-07$06.00

eye. Because the eye is not a true rotationally symmet-ric system, it also suffers from comalike aberrations on itsvisual axis.3 – 5 The fit of a contact lens on the eye canalso affect these aberrations.

The two major design variables of spectacle lens designare lens bending and surface asphericity. The formeris severely limited in contact lens design because thecurvature of the posterior lens surface must closely followthat of the anterior cornea. However, the latter can beemployed for three main purposes:

1. To improve fit and comfort on the eye (asphericityon the posterior surface),

2. To correct aberrations of the eye (asphericity oneither surface),

3. To be used as a progressive-addition lens (aspheric-ity on either surface).

Note that purposes 2 and 3 can interact.Claims are often made in the contact lens promotional

literature about particular aspheric contact lens typesperforming well because they improve comfort or reduceaberrations. Few, if any, of these claims have any basis,as corneal shapes and overall ocular aberration levelsvary considerably among people,3 – 7 so that lenses wouldneed to be individually designed yield these benefits.

Westheimer8 was possibly the first to consider the aber-rations of contact lenses. He calculated the sphericalaberration of some rigid spherical contact lenses in air.This method will mimic the on-eye situation well only ifthe anterior cornea surface and the posterior lens sur-face have the same radius of curvature and if the formeris also spherical. Westheimer wrote, “This is an impor-tant preliminary step in the evaluation of the influence ofcontact lens aberration on vision in a given eye” and ac-knowledged that the effect of the contact lens on retinalimagery depends on the corneal configuration.

Bauer9 did theoretical ray tracing through both flexible(soft) and rigid (hard) contact lenses. He determinedsurface asphericities to correct spherical aberration but

1995 Optical Society of America

2268 J. Opt. Soc. Am. A/Vol. 12, No. 10 /October 1995 David A. Atchison

Fig. 1. Parameters needed for determining the change inspherical aberration with contact lenses on an eye relative tothe change obtained with spectacle lenses in front of the eye.Not to scale.

considered the lenses in air, that is, in isolation fromthe eye.

Campbell10 determined the change in angular sphericalaberration produced by placement of contact lenses on theeye relative to that produced by spectacle correction. Helimited his investigation to contact lenses and corneaswith spherical anterior surfaces. He converted thechange in angular aberration to change in longitudinalaberration. The change in longitudinal spherical aber-ration (LSA) for 5-mm-diameter stops was found to varybetween 10.40 diopters (D; 115-D power) and 20.19 D(29-D power). Campbell concluded that the sphericalaberration added to the optical system through the useof contact lenses is small. However, the small valuesof the changes are due to a systematic error in calcu-lating the angular spherical aberration with spectaclelenses11; when this error is corrected, the changes arefound to be approximately four times greater than theabove values.

Cox12 also calculated the change in spherical aberra-tion produced by placement of a contact lens on the eye.The anterior cornea was given a range of curvatures andconicoid asphericities. He used both flexible and hardcontact lenses. For flexible contact lenses he theoreti-cally determined the change in surface shapes producedby their placement on the eye. One of his calculationsof spherical aberration included the tear film and theanterior cornea. Like Campbell, he intended to showthe change in spherical aberration resulting from place-ment of contact lenses on the eye. Unfortunately thecomparison he made was with the anterior cornea fora distant object rather than the anterior cornea withcorrecting spectacle lenses (or, as the spherical aberra-tion of spectacle lenses is negligible, the anterior corneawith an object at the eye’s far point). Assuming that theeye would usually be corrected, this is the only reason-able comparison.

Hammer and Holden13 extended the research of Cox toconsider the effect of aspherizing lens surfaces on spheri-cal aberrations for a few examples of 13- and 23-D rigidcontact lenses.

Charman and Walsh14,15 did ray tracing throughprogressive-addition contact lenses and an optically per-

fect reduced eye. They determined spot diagrams andmodulation transfer functions when lenses were correctlycentered and were then displaced by as much as 2 mm onthe eye. In general, displacement made image qualityconsiderably worse. Charman and Walsh emphasizedthe importance of good centration of aspheric contactlenses.

As first mentioned by Westheimer,8 it is difficult todetermine the exact effect of a contact lens on an eye,as this presupposes a considerable understanding of theoptics of the eye. However, it is possible to determinethe likely change in aberrations produced by a contactlens relative to that produced by a spectacle lens. Oneway to do this is to ray trace through all the elementsthat a contact lens adds to the eye. These are the con-tact lens and the tear film. Air is placed behind thetear film, but the posterior tear film must match theshape of the anterior cornea (Fig. 1). This air–lens–tears–air model has already been adopted by Hammerand Holden.13

In this paper I present theoretical results about howrigid, single-vision contact lenses, when worn on the eye,change aberrations (particularly spherical aberration ofthe eye) and how this change is affected by surface as-phericity. Flexible lenses are not discussed because it isnot easy to predict how the shape of the flexible contactlens will be altered when the lens is fitted onto an indi-vidual cornea.

2. METHODSUsing the Kidger Optics optical design program SIGMA, Iperformed finite ray tracing through contact lenses com-bined with the anterior cornea and through spectaclelenses combined with the anterior cornea. The limita-tions to this procedure are obvious: it does not take intoaccount nonrotationally symmetric irregularities in theanterior corneal surface and ignores the contribution ofthe eye’s lens to image quality. The purpose here is toshow how contact lens wear is likely to alter the aberra-tions of the eye compared with spectacle lens wear. Thechanges to the aberration of the eye can be approximatelyequated with changes in the aberration of the correctingdevice and anterior cornea because these represent themajority of the power of the eye and are close to the prin-cipal planes of the eye.

The spectacle lenses were taken to be thin with planeback surfaces, of refractive index 1.5, and were placedagainst the eye. All corneas were taken to have a radiusof curvature of 7.7 mm and a refractive index of 1.376.Anterior cornea asphericities used were 0 and 20.26, thelatter being a good estimate of mean asphericity.6 Theposterior surfaces of contact lenses were also taken to be7.7 mm. Rigid gas-permeable lenses of refractive index1.479 were used. Thicknesses were taken to be 0.18 mmfor back vertex powers of 210 to 16 D, 0.30 mm for18-D back vertex power, and 0.40 mm for 110-D backvertex power. The tear film was assigned a thickness of0.007 mm and a refractive index of 1.336.

The stop was placed at the corneal plane. Its diam-eter was 5 mm, which corresponds to an iris aperture ofapproximately 4.5 mm (Gullstrand No. 1 eye). There areslight errors associated with this choice, as the entrance


pupil size of eyes corresponding to a particular iris aper-ture will depend on the power of the correcting lens. Thevariation will be small and of the order of 7% when oneis comparing 210- and 110-D contact lenses.

The LSA associated with the ray passing through theedge of the stop for the centered system was calculatedby comparison of where the ray intersects the optical axiswith the Gaussian image position, according to

LSA n0ylf0 2 n0lg

0 ,

where n0 is the refractive index in image space (cornea)and lf

0 and lg0 are the distances from the anterior corneal

surface vertex to the finite ray intersection position andthe Gaussian image plane, respectively.16

For displacement of contact lenses on the eye, in theray-tracing program used here they were decentered andwere tilted the required amounts for 1- and 1.5-mm down-ward displacements of the posterior surface, which slidaround the anterior cornea. Tilts were 7.46± and 11.22±,respectively. Because, in modeling, the tilt and the de-centration would leave the contact lens well in front ofthe cornea, the lenses had to be moved toward the corneaby distances of 0.065 and 0.147 mm. Rays were tracedclose to the pupil (chief or principal) ray in both the tan-gential and the sagittal planes to calculate the tangentialand the sagittal image positions relative to the Gaussianimage plane. Sagittal and tangential power errors werecalculated in a manner similar to the calculation of LSA.

Apart from determinations of LSA and introduceddefocus (power) errors, spot diagrams were used forimage quality assessment (again by means of the KidgerOptics program SIGMA). Ten rings of rays were tracedthrough systems, and ray intersections were determinedfor several planes near and including the Gaussian im-age plane.

Our discussion now turns to conicoids and third-ordertheory. A conicoid surface that has its vertex at thepoint (0, 0, 0) in a Cartesian x, y, z system and that isrotationally symmetric about the z axis (optical axis) canbe expressed in the form

z csx2 1 y2d

1 1 f1 2 c2s1 1 Qdsx2 1 y2dg0.5,

where z is the sag of the surface and c is the vertex curva-ture. The inverse of c is the vertex radius of curvaturer. If Q is negative, the surface flattens away from thevertex; if Q is positive, the surface steepens away from itsvertex; and if Q is zero, the surface is spherical. Someauthors use the term p, where

s1 1 Qd p ,

and others use the eccentricity e, where

Q 2e2 ,

for hyperboloids, paraboloids, and oblate ellipses.17 Qand p are not related to e for prolate ellipses.

From an analysis of third-order theory, the change inSeidel spherical aberration sS1d produced by aspherizinga surface as a conicoid is18

DS1 c3h4Qsn0 2 nd , (1)

where h is the height of the ray at the surface and n andn0 are the refractive indices on the object and the imagesides, respectively, of the surface. It can be shown thatthe third-order LSA is given approximately by19

LSA 2S1yD2 , (2)

where D is the diameter of the entrance pupil of theoptical system.

A contact lens is close to the entrance pupil of the eye,so that

h ø Dy2 , (3)

and thus the change in LSA by means of relations (1)–(3)is

DLSA c3h2Qsn0 2 ndy2 . (4)

Now the sagittal (circumferential) radius of curvature rs

of a conicoid is given by20

rs sr2 2 Qh2d0.5 .

In curvature terms this equation is

cs cys1 2 Qc2h2d0.5 ø cs1 1 Qc2h2y2d .

The change in sagittal curvature Dcs that is due to as-pherizing is thus

Dcs ø c3h2Qy2 .

The corresponding change in sagittal surface power DFs

is given by

DFs Dcssn0 2 nd

ø c3h2Qsn0 2 ndy2 . (5)

The right-hand sides of relations (4) and (5) are identical,so that

DLSA ø DFs ;

that is, the change in LSA produced by aspherizing thesurface of a contact lens is approximately the same as thechange in sagittal surface power. Note that the aberra-tion is proportional to the asphericity, the third power ofthe surface curvature, and the second power of the rayheight.

The tangential (radial) radius of curvature rt of a coni-coid is given by20

rt rs3yr2 .

In curvature terms this equation is

ct cs3yc2 ,

from which

ct cys1 2 Qc2h2d1.5 ø cs1 1 3Qc2h2y2d .

The change in tangential curvature Dct that is due toaspherizing is thus

Dct ø 3c3h2Qy2 ,


and the change in tangential surface power DFt is givenby

DFt Dctsn0 2 nd

ø 3c3h2Qsn0 2 ndy2

3DFs . (6)

3. RESULTSFigure 2 shows the longitudinal aberrations of anteriorcorneal surfaces combined with either spectacle lenses orspherical contact lenses for a distant object. With spec-tacle lens correction the slope is negative. The anteriorcorneal asphericity has a considerable effect on the aber-ration, as using Q 20.26 makes the aberration lesspositive by approximately 0.7 D for all lens powers. Withcontact lens correction the slope is positive. The anteriorcorneal sphericity now has little effect on the aberration,as approximately 90% of it is neutralized by the tear film(this neutralization would not occur for flexible contactlenses because of the wrapping of the contact lens aroundthe eye). The change in aberration that is due to cornealasphericity is only 20.08 D.

Figure 2 also shows the LSA’s of a spherical anteriorcorneal surface combined with either spectacle lenses orspherical contact lenses for a near object (200 mm). Thechange from distance object to near object causes only asmall increase of 10.2 to 10.3 D with both spectacles andcontact lenses. The reason for this result is that the ob-ject vergence change (5 D) is small relative to the com-bined power of lens and anterior cornea (139 to 159 D).

Figure 3 uses the data of Fig. 2 to show differences inLSA for spherical contact lens wear and spectacle lenswear. This information is provided for the three condi-tions of distance object with spherical cornea, distance ob-ject with aspheric cornea, and near object with sphericalcornea. The differences in LSA between contact lensesand spectacle lenses change at a rate of approximately0.13 D per diopter of lens power and can be quite large,

Fig. 2. LSA for contact lenses and spectacle lenses of variouslens powers in combination with the anterior cornea. ≤: Dis-tance object, spherical cornea (Q 0.0); j: distance object,aspheric cornea sQ 20.26d; s: near object (200-mm distance),spherical cornea. Stop diameter, 5.0 mm. Other details aregiven in the text.

Fig. 3. Differences in LSA between contact lens and spec-tacle lens wear for various lens powers in combination with aspherical anterior cornea. ≤: Distance object, spherical cornea(Q 0.0); j: distance object, aspheric cornea sQ 20.26d; s:near object (200-mm distance), spherical cornea. Stop diameter,5.0 mm. Other details are given in the text.

Fig. 4. LSA of contact lenses combined with an anterior cornealsurface, as a function of anterior lens surface asphericity, for dis-tance vision. m: 16-D power, n: 26-D power. Third-orderpredictions of changes in LSA are also shown. Distance object;stop diameter, 5.0 mm. Note the different vertical scale fromthat of Figs. 2 and 3. Other details are given in the text.

e.g., 21.27 D at 210-D power and 10.45 D at 110-Dpower (distance object with spherical cornea). When thecornea is aspherized for a distance object, the differenceschange by 20.7 D because most of the cornea asphericityis neutralized by the tear film during contact lens wear,as discussed above. When the object is moved from dis-tance to near, the differences are affected little.

Figure 4 shows the LSA of 26- and 16-D contactlenses, with varying degrees of anterior surface aspheric-ity, combined with a spherical anterior corneal surface, fordistance vision. The third-order changes in sphericalaberration predicted according to Eq. (4) are also shown.For 26-D lenses these changes give a reasonable predic-tion of the finite values, being better for negative thanfor positive asphericity values. The change in spheri-


cal aberration is approximately DLSA 12.4Q. For16-D lenses the third-order changes also give a rea-sonable prediction of the finite values and again arebetter for negative than for positive asphericity values.The change in spherical aberration is approximatelyDLSA 14.2Q. The constant here is higher than for26-D lenses because of the greater front surface curva-ture [see Eq. (4)].

In Eq. (4) and with the selected parameters, sn0 2 ndis 0.479 at the front surface and 20.143 at the back sur-face of a contact lens. It can thus be appreciated that, atthe same curvature, a change in back surface asphericity

will have approximately 230% of the effect of a changein front surface asphericity on LSA. For example, if a11-D change in LSA occurs for a change in front surfaceasphericity, a change in LSA of approximately 20.30 Doccurs for the same change in back surface aspheric-ity. This relationship is evident from examination of theHammer–Holden Figs. 2B, 3, and 4.13

Figure 5(a) shows spot diagrams for a 16-D contactlens with spherical surfaces combined with a spheri-cal anterior cornea. Lens displacements of 0 mm (toprow), 1 mm (middle row), and 1.5 mm (bottom row) areused. Spot diagrams corresponding to various image

(a)

(b)Fig. 5. Spot diagrams for a 16-D contact lens combined with a spherical cornea. (a) Spherical contact lens, (b) aspherical frontsurface (Q 20.4) contact lens. Lens displacements of 0 mm (top row), 1 mm (middle row), and 1.5 mm (bottom row) are shown.Results are for the Gaussian image plane and for the planes in front of it (20.6, 20.4, 20.2 mm) and behind it (10.2 mm). Distanceobject; stop diameter, 5.0 mm. Other details are given in the text.


planes relative to the Gaussian image plane are shown.Negative values correspond to movement of the imageplane toward the cornea. The centered, spherical lenshas a 12.0-D LSA associated with the edge of the stop,and best image quality occurs at approximately 0.4 mmin front of the Gaussian image plane. Neither 1- nor1.5-mm displacements cause much further deteriorationin image quality or much change in the shape and thesize of the spot diagrams. They introduce negligibleastigmatism (,0.02 D).

Figure 5(b) shows spot diagrams for a 16-D contactlens with an aspheric front surface when combined witha spherical anterior cornea. Again, lens displacements of0, 1, and 1.5 mm are used. The asphericity of Q 20.4was chosen for near elimination of spherical aberration,with less than 10.15 D at the edge of the stop (see alsoFig. 2). Lens displacement causes considerable reduc-tion in image quality, with 1.5-mm displacement (thirdrow) producing image quality similar to that for thespherical lens. Considerable coma is introduced, andthere is also appreciable defocus of 20.30 DSy20.56 DCfor 1-mm displacement and 20.66 DSy21.25 DC for1.5-mm displacement (DS, diopters sphere; DC, diopterscylinder). These coincide closely with approximatechanges in sagittal and tangential powers obtained ac-cording to relations (5) and (6) of 20.27 DSy20.54 DC for1-mm and 20.61 DSy21.21 DC for 1.5-mm displacement.

Spot diagrams for smaller pupils (e.g., 3 mm) wouldshow a smaller spread of points at the image plane.The loss in image quality produced by displacement ofthe aspheric contact lens would be greater relative to theloss in image quality produced by the spherical aberrationwith the spherical lens than is the case for a 5-mm stop.This is because the transverse spherical aberration is ap-proximately a cubic function of ray height at the stop,transverse coma is a second-order function, and trans-verse defocus is a linear function.

The analysis given above was repeated for an asphericcornea with Q 20.26, but the corneal asphericity hadlittle effect. The analysis was also done for 26-D con-tact lenses in conjunction with the anterior cornea. Aspherical contact lens produces a LSA of 11.0 D at a5-mm aperture, which is slightly overcompensated by ap-plication of an anterior surface asphericity of Q 20.5.The imagery with the spherical 26-D contact lens isslightly better than for that presented above for a spheri-cal 16-D contact lens. The same is true for the aspheric26-D contact lens when compared with the 16-D asphericcontact lens, with the shapes of spot diagrams appearingvery similar.

4. DISCUSSIONIn this study the difference in LSA produced by con-tact lenses and spectacles was considerable (Fig. 3), beingsimilar to the data obtained by Cambell at a similar stopsize after an error in his calculations is corrected.10,11

The change in LSA associated with aspherizing a surfaceof a contact lens can also be considerable and is well pre-dicted by the simple relation (5) for the change in sagit-tal power of the aspheric surface (Fig. 4). This relationworks well because the aberration is mainly primary aber-ration at 5-mm pupil size, but it would be less accurate

at large pupil sizes for which higher-order aberrationsare expected.

Displacing an aspheric contact lens on the eye can pro-duce considerable levels of defocus [Fig. 5(b)] as wellas some coma. The former is well predicted by thesimple relations (5) and (6) for the change in sagittaland tangential power associated with the displacement.The results shown in Fig. 5 indicate that an aspheric con-tact lens that moves to a considerable extent on the eyemay cause more unstable vision than would a sphericalcontact lens that moves to the same extent. Hammerand Holden13 pointed out that “rigid contact lenses arerarely exactly centered on the cornea, and they move withevery blink.”

This paper deals with rigid contact lenses. However,the findings of large differences in LSA produced by con-tact lenses and spectacle lenses and the considerablechange in LSA associated with aspherizing a contact lenssurface are also applicable for flexible contact lenses. Itis less easy to predict aberration levels with flexible con-tact lenses than with rigid contact lenses because of alack of understanding about how the shape of the flex-ible contact lens will be altered when fitted onto an in-dividual cornea. Mention has already been made of thefact that the tear film neutralization of corneal aspheric-ity does not occur with flexible contact lenses, so that theaberrations with centered flexible contact lenses will beconsiderably influenced by corneal asphericity, unlike inthe case of rigid lenses. The defocus and other aberra-tions arising from decentering contact lenses are less ofan issue with flexible than with rigid lenses because theformer decenter less and move less on blinking than dothe latter.

Two things should be noted about the aberration levelsas presented in this paper. First, the Stiles–Crawfordeffect21,22 may reduce the effective aberration in photopiclighting levels. However, when this effect is modeled asan apodization in the pupil, it seems to have little effect onoptical image quality.23 – 25 Second, the spherical aberra-tion results have been presented as the aberration asso-ciated with the marginal ray passing through the opticalsystem. This approach inflates the apparent importanceof the aberration. In a system with primary sphericalaberration, the mean level of LSA across the whole pupilis half the value associated with the marginal ray.

5. CONCLUSIONThis paper has presented results in terms of aberrationsand spot diagrams but not in terms of visual performance.There is little information in the literature on the effectsof spherical aberration on visual performance.16,26 Basedon the observations of the previous paragraph, if we takea simplistic approach that a level of longitudinal sphericalaberration associated with a marginal ray is equivalent tohalf that level of longitudinal defocus, levels and changesof 1.0-D spherical aberration and higher can certainly beconsidered significant because, for example, changes of0.50-D defocus can alter visual acuity by more than 0.1 logunit for a range of pupil sizes.27

When performing a refraction, the ophthalmic practi-tioner is actually obtaining a balance between defocus andaberrations to obtain the best visual performance, usually


measured by visual acuity. As contact lenses will pro-duce a very different level of aberrations at appreciablepowers relative to those produced by spectacle lenses, itis most likely that the refraction will be strongly depen-dent on the nature of the contact lens to be worn. Henceoverrefractions should be determined when the patient iswearing a contact lens of power and characteristics simi-lar to that which will be prescribed.

There has been some controversy about which powershould be considered important in specifying the addi-tion of progressive-addition contact lenses: the sagittalpower or the tangential power.28 Neither forms a dis-tinct image in the normal wearing of contact lenses, andboth are revealed only when apertures are placed in thepathway of a focimeter. The tangential power is revealedby small round apertures placed off center. The sagit-tal power can also be revealed in this manner or byuse of annular apertures. The sagittal power has sig-nificance in that it can show the approximate spheri-cal aberration (or addition) of a contact lens associatedwith a particular diameter of a lens, but the tangen-tial power has no significance here. The most appro-priate addition to use for a progressive-power contactlens will be somewhat less than the additional introducedsagittal power associated with the peripheral ray. Onemay ascertain this addition theoretically by ray tracingto obtain spot diagrams and modulation transfer func-tions, but clinically this determination is more likely tobe by trial and error. Both the sagittal and the tan-gential values are of importance in the additional re-fractive error induced by displacement of the lens onthe eye.

The introduction of asphericity to produce aprogressive-addition contact lens will interact with theexisting aberrations of the eye involved. This inter-action may give particularly good imagery for somedistances and much poorer imagery for other distances.For successful wear it may be important to know muchmore about the underlying aberrations of the eye.

The author’s e-mail address is [email protected].

REFERENCES1. L. N. Thibos, A. Bradley, and X. Zhang, “Effect of ocular chro-

matic aberration on monocular visual performance,” Optom.Vis. Sci. 68, 599–607 (1991).

2. D. A. Atchison, “Modern optical design assessment and spec-tacle lenses,” Opt. Acta 32, 607–634 (1984).

3. H. C. Howland and B. Howland, “A subjective method forthe measurement of monochromatic aberrations of the eye,”J. Opt. Soc. Am. 67, 1508–1518 (1977).

4. G. Walsh, W. N. Charman, and H. Howland, “Objective tech-nique for the determination of monochromatic aberrations ofthe human eye,” J. Opt. Soc. Am. A 1, 987–992 (1984).

5. G. Walsh and W. N. Charman, “Measurement of the axialwavefront of the human eye,” Ophth. Physiol. Opt. 5, 23–31(1985).

6. P. Kiely, G. Smith, and L. G. Carney, “The mean shape ofthe human cornea,” Opt. Acta 29, 1027–1040 (1982).

7. M. Guillon, D. P. M. Lydon, and C. Wilson, “Corneal topogra-phy: a clinical model,” Ophthalmic Physiol. Opt. 6, 47–56(1986).

8. G. Westheimer, “Aberrations of contact lenses,” Am. J.Optom. Arch. Am. Acad. Optom. 38, 445–448 (1961).

9. G. L. Bauer, “Longitudinal spherical aberration of modernophthalmic lenses and its effect on visual acuity,” Appl. Opt.19, 2226–2234 (1980).

10. C. E. Campbell, “The effect of spherical aberration of con-tact lenses to the wearer,” Am. J. Optom. Physiol. Opt. 58,212–217 (1981).

11. C. E. Campbell, Humphrey Instruments, Inc., San Leandro,Calif. 94577-0700 (personal communication, 1994).

12. I. Cox, “Theoretical calculation of the longitudinal sphericalaberration of rigid and soft contact lenses,” Optom. Vis. Sci.67, 277–282 (1990).

13. R. M. Hammer and B. A. Holden, “Spherical aberrationof aspheric contact lenses on eye,” Optom. Vis. Sci. 71,522–528 (1994).

14. W. N. Charman and G. Walsh, “Properties of conicoidalsurfaces and the Bausch and Lomb PA1 Soflens bifocal,”Optom. Today 26(17), 573–574, 576–578, 580 (1986).

15. W. N. Charman and G. Walsh, “Retinal images with differ-ent designs of bifocal contact lenses,” in Transactions of theBritish Contact Lens Association. Annual Clinical Confer-ence 1986 (British Contact Lens Association, London, 1986),pp. 13–19.

16. M. J. Collins, B. Brown, D. A. Atchison, and S. D. Newman,“Tolerance to spherical aberration induced by rigid contactlenses,” Ophth. Physiol. Opt. 12, 24–28 (1992).

17. A. G. Bennett, “Aspherical and continuous curve contactlenses. Part one,” Optom. Today 28(1), 11–14 (1988).

18. H. H. Hopkins, The Wave Theory of Aberrations (Clarendon,Oxford, 1950).

19. G. Smith and C-W Lu, “The spherical aberration of intra-ocular lenses,” Ophth. Physiol. Opt. 8, 287–294 (1988).

20. A. G. Bennett, “Aspherical contact lens surfaces. Part two,”Ophth. Optician 8, 1297–1300, 1311 (1968).

21. W. S. Stiles and B. H. Crawford, “The luminous efficiency ofrays entering the eye pupil at different points,” Proc. R. Soc.London Ser. B 112, 428–450 (1933).

22. R. A. Applegate and V. Lakshminarayanan, “Parametric rep-resentation of Stiles–Crawford functions: normal variationof peak location and directionality,” J. Opt. Soc. Am. A 10,1611–1623 (1993).

23. J. P. Carroll, “Apodization model of the Stiles–Crawfordeffect,” J. Opt. Soc. Am. 70, 1155–1156 (1980).

24. A. van Meeteren, “Calculation on the optical modulationtransfer function of the human eye for white light,” Opt.Acta 21, 395–412 (1974).

25. D. A. Atchison, “Visual optics in man,” Aust. J. Optom. 67,141–150 (1984).

26. G. Smith, “The spherical aberration of aphakic eyes cor-rected with intraocular lenses,” Clin. Exp. Optom. 75, 27–34(1992).

27. D. A. Atchison, G. Smith, and N. Efron, “The effect of pupilsize on visual acuity in uncorrected and corrected myopia,”Am. J. Optom. Physiol. Opt. 56, 315–323 (1979).

28. T. D. Winkler, “A new model for determining add power,”Contact Lens Spectrum 7(12), 23, 25, 28 (1992).

aberrations associated with rigid contact lenses

Documents