Correcting ocular spherical aberration with soft contact lenses

H. H. Dietze and M. J. Cox

Vol. 21, No. 4 / April 2004 / J. Opt. Soc. Am. A

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Correcting ocular spherical aberration with soft contact lenses Holger H. Dietze and Michael J. Cox Department of Optometry, University of Bradford, Richmond Road, Bradford, BD7 1DP, UK Received April 8, 2003; revised manuscript received November 5, 2003; accepted December 5, 2003 Following aberroscopy, aspheric front surface soft contact lenses (SCLs) were custom-made to correct spherical refractive error and ocular spherical aberration (SA) of 18 myopic and five hypermetropic subjects (age, 20.5 ⫾ 5 yr). On-eye residual aberrations, logMAR visual acuity, and contrast sensitivity were compared with the best-correcting spectacle lens, an equally powered standard SCL, and an SCL designed to be aberration free in air. Custom-made and spherical SCLs reduced SA ( p ⬍ 0.001; p ⬍ 0.05) but did not change total root-meansquare (rms) wave-front aberration (WFA). Aberration-free SCLs increased SA ( p ⬍ 0.05), coma ( p ⬍ 0.05), and total rms WFA. Visual acuity remained unchanged with any of the SCL types compared with the spectacle lens correction. Contrast sensitivity at 6 cycles/degree improved with the custom-made SCLs ( p ⬍ 0.05). Increased coma with aspheric lens designs and uncorrected astigmatism limit the small possible visual benefit from correcting ocular SA with SCLs. © 2004 Optical Society of America OCIS codes: 330.0330, 330.1070, 330.1800, 330.4460, 220.0220, 220.1000.

1. INTRODUCTION Higher-order ocular aberrations are refractive errors beyond defocus and astigmatism traditionally corrected by spectacle lenses, contact lenses, or intraocular lenses. Their correction improves visual performance in theory1,2 and in practice.3–5 Fourth-order wave-front aberrations (WFAs), of which spherical aberration (SA) is the most important component, account for 20%–40% of higherorder ocular aberrations when the pupil is large.6–9 It has been argued that correcting fourth-order aberration might have a greater effect on the quality of the retinal image than correcting third-order (coma-like) aberrations.2 Adaptive optics correction of monochromatic ocular aberrations is the province of research laboratories.5,10,11 Wave-front guided LASIK, intraocular lenses, and contact lenses are the potential means for correcting monochromatic higher-order aberrations in a clinical environment. Little is known about the ability of soft contact lenses (SCLs) to correct for individual levels of ocular aberrations. SCLs have been used to induce predetermined levels of SA and investigate the visual effect.12,13 The visual effect of SCLs designed to be aberration free in air has also been investigated.14 More recently, it has been shown that asymmetrical surfaces generating spherical and coma-like aberrations in SCLs can predictably manipulate the ocular aberrations within the limitations of lens movement and flexure.15 All higher-order aberrations vary with orientation except for SA.16 Contact lenses, however, rotate on eye after each blink unless special stabilization elements at the cost of increased thickness and decreased comfort are provided. The application of rotationally symmetrical contact lenses for correcting higher-order aberrations is therefore restricted to SA. A contact lens on eye will correct ocular SA if it pro1084-7529/2004/040473-13$15.00

duces equal levels of SA of opposite sign. Modifying the asphericity of an ellipsoidal SCL front surface can generate individual levels of SA. Depending on lens power, curvature, and surface shape, higher-order aberrations produced by the SCL itself are significant12,17,18 and cannot be neglected when aberration-correcting contact lenses are designed. For thin SCLs, the aberrations are similar on eye and off eye,15,18,19 although the effects of lens flexure on the on-eye lens power and hence on the aberrations are hard to predict.20 The aim of this work is to investigate the feasibility and the possible visual benefit of correcting individual levels of ocular SA by using SCLs with aspheric front surfaces. Basing our approach on Hartmann–Shack aberrometer measurements of individual ocular aberrations and a model predicting the SA produced by the lens on eye, we designed aspheric SCLs correcting the ocular SA. To investigate the effect on visual performance, we compare visual acuity and contrast sensitivity measurements obtained with three different SCLs of equal power on eye: a lens designed to correct individual levels of ocular SA, a standard spherically surfaced lens, and a lens designed to be aberration free in air. The latter lens type was examined as it is sometimes marketed as a device that gives significant visual benefits and is suitable for a wide range of individuals. To confirm or refute the subjective results, we utilize aberrometer measurements of each of the three contact lenses on eye.

2. METHODS A. Subjects and Materials Eighteen myopic (Rx ⭐ ⫺2.00 D) and five hypermetropic (Rx ⭓ ⫹ 2.00 D) subjects participated in the study (refractive error range, ⫺9.00 to ⫹7.50; mean age, 20.5 ⫾ 5 yr). Only subjects with healthy eyes, no media opacities, and astigmatism less than or equal to 1.25 D © 2004 Optical Society of America

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J. Opt. Soc. Am. A / Vol. 21, No. 4 / April 2004


were included. The tenets of the Declaration of Helsinki were followed, and informed consent was obtained from all subjects before the study. The research was approved by the institutional ethics committee. All SCLs used in the study were made of Biogel 60– Filcon 4 (60% water content) with a spherical back optic zone radius of 8.7 mm, a refractive index of 1.404 (hydrated), and a center thickness of 0.1 mm for a back vertex power of ⫺3.00 D. All subjects were measured wearing three equally powered SCLs in random order on their dominant eye: one designed to correct the individual ocular SA (the ‘‘custom-made lens’’), one spherical standard SCL (the ‘‘standard lens’’), and one designed to be aberration free in air (the ‘‘aberration-free lens’’). The lens power was determined as the best mean sphere at a 0.00-mm vertex distance, following subjective refraction at a 4-m testing distance (the working distance for which our logMAR chart was designed). All lenses were produced on a high-precision CNC lathe machine (Hecht Contactlinsen GmbH, Freiburg, Germany). B. Optical Quality Measurements The ocular WFA, the contact-lens-induced WFA, and the WFA of the respective eye–SCL system were measured with a Hartmann–Shack aberrometer as first described by Liang et al.21 This used a wave-front sensor with a focal length of 34.0 mm and a lenslet diameter of 0.3125 mm. For each condition, we averaged the first- to sixthorder Zernike coefficients from at least three measurements. A detailed description of the apparatus and the method is given elsewhere,22 with the only changes being the use of an illuminating wavelength of 632.8 nm and 0 D of ocular accommodation stimulus for the subject throughout the measurements. The optimum spherical correction was determined by subjective (over)refraction and applied by using a Badallens system in the aberrometer. In air, rotationally symmetrical lenses with ellipsoidal surfaces mainly produce or correct third-order SA, well described by the fourthorder Zernike coefficient C 40 . The SA added by an SCL on eye was found as C 40 共 SCL兲 ⫽ C 40 共 Eye⫹SCL兲 ⫺ C 40 共 Eye兲 ,

(1)

where C 40 ( SCL) is the SA induced by the SCL, C 40 ( Eye⫹SCL) is the SA of the eye–SCL system, and C 40 ( Eye) is the ocular SA. The aberrometer was calibrated by measuring the C 40 coefficient of 18 polymethyl methacrylate (PMMA) buttons with precisely known spherical aberration, ranging from C 40 ⫽ ⫺0.30 ␮ m to C 40 ⫽ 0.60 ␮ m for a 6-mm pupil, expressed in the orthonormal standard double-index format.23 Optical quality was summarized with derived values of root-mean-square (rms) WFA and the Strehl ratio, given the appropriate pupil size for the condition being tested. The Strehl ratio was radially averaged for comparison against logMAR measurements but was limited to the horizontal and vertical meridians for comparison with contrast sensitivity to horizontal and vertical sinusoidal gratings.

C. Visual Performance To assess the visual performance, we measured highcontrast logMAR visual acuity and contrast sensitivity with each SCL in place and with the best-correcting spectacle lens. The visual acuity for each condition was measured monocularly by using two Bailey–Lovie charts with different letter sequences to keep intrasubject variability24 and training effect25 at a minimum. The charts were presented in random order and revealed only immediately before the measurement to avoid memorization of any letters. Each letter seen was scored as 0.01 log unit. The charts were externally illuminated by room light giving an average luminance of L ⫽ 100 cd m⫺2 . Natural pupils were used, and an adaptation time of at least 5 min was allowed before any results were taken. The testing distance was 4 m. We measured the monocular contrast sensitivity at spatial frequencies of 6, 12, and 24 cycles/degree under low-photopic viewing conditions (L ⫽ 17 cd m⫺2 ) at a testing distance of 4 m. Sinusoidal gratings were generated by an RGB framestore, which was part of a purposebuilt display controller, the Cambridge Research System VSG 2/3. Gamma correction prevented any of the CRTmonitor-based nonlinearities from introducing spurious spatial frequencies into the gratings, and a passive resistor network gave high accuracy in control of the sinusoidal luminance.26 A chromatically narrowband sinusoidal grating stimulus (only the green gun on the CRT monitor was driven by the display controller) was presented with random phase within a Gaussian spatial envelope. The spatial envelope had a standard deviation of 2 grating cycles and was truncated at a radius of 4 grating cycles to limit the spread of contrast energy into a narrow band of spatial frequencies centered on the required spatial frequency. The three spatial frequencies were presented with two orientations (horizontal and vertical). The minimum possible Michelson contrast that could be presented by the system was close to 0.1%, which is well below the minimum sinusoidal grating contrast detectable by the human visual system at the spatial frequencies at which we were testing. The threshold was determined by using a method of ascending limits with contrast increments of 2 dB. Following 5 min of luminance adaptation, the six stimuli were presented in a random order. For each stimulus, the subject was shown the grating at a level above the contrast threshold before the threshold determination. This procedure was used to ensure that the subject was responding to the correct stimulus waveform. For each stimulus, five repetitions of the contrast threshold measurement were made and averaged to give an estimate of the average threshold contrast from which the log contrast sensitivity for each stimulus was calculated. As we wanted to investigate the effects of higher-order aberrations only, we performed a subjective refraction over each contact lens (at a 4-m testing distance) and used spectacle lenses to correct any residual refractive error. If measurements of visual acuity and contrast sensitivity are taken for different conditions, any effects of spectacle lens magnification must be taken into account. This principally affects the measurements made under the spectacle lens correction condition. For the SCL con-



ditions, the overrefraction was so small that the magnification effect was minimal. Using a standard formula, we calculated the magnification of the best mean sphere for the spectacle lens condition. The scaled logMAR visual acuity, log MARS , was found as log MARS ⫽ log共 MAR ⫻ m 兲 ,

(2)

where m is the spectacle magnification and MAR is the minimum angle of resolution, given as 10log MAR, where log MAR is the measured logMAR acuity. To scale contrast sensitivity, we found the ocular spatial frequencies of the gratings seen under the spectacle lens condition by dividing the nominal spatial frequency of the gratings by the spectacle lens magnification factor. The contrast sensitivity for 6, 12, and 24 cycles/degree was estimated for each subject by using the linear regression line fitted through their contrast sensitivity versus ocular spatial frequency data. As higher-order aberrations strongly depend on the aperture diameter, we measured the pupil size of each subject in both luminance conditions with an open field-ofview autorefractor, Shin-Nippon SRW 5000.27 Images of the pupil were taken with the internal infrared camera of the autorefractor and relayed onto an external television screen while the subject was viewing the test chart (L ⫽ 100 cd cm⫺2 ) and the gratings (L ⫽ 17 cd m⫺2 ), respectively. A scale was imaged simultaneously to determine the magnification factor of the instrument. D. Modeling To calculate the SA produced by the SCL on eye, we assumed that the thickness change over each point of the lens in the pupil plane remains negligibly small as the lens flexes. If this and the assumption that the back surface of the SCL closely aligns with the corneal front surface20 are true, then the optical path difference for each ray traveling through the lens, and hence the wavefront aberration across the pupil, remains unchanged. Consequently, the on-eye aberration of an SCL will be equivalent to that predicted in air.18 However, if the back surface of the contact lens does not align closely with the corneal front surface, then this constancy does not occur and in the case of aberration-free negatively powered contact lenses results in a contact lens that may increase the amount of eye–lens SA when placed on the eye. This can occur when the front surface of the contact lens takes on an asphericity designed to produce positive spherical aberration that offsets the negative spherical aberration of its spherical rear surface. As the rear contact lens surface refraction is substantially neutralized by the tear lens, and the rear surface of the tear lens (which has the same asphericity as that of the corneal front surface) has less negative SA than the spherical rear surface of the contact lens, the compensating positive SA of the contact lens front surface becomes too large, adding to the usually positive ocular SA. The magnitude of the required SA produced by the aberration-free lenses is 0. The magnitude of the required SA produced by the custom-made lens must be equal to the ocular SA but of opposite sign:

C 40 共 custom兲 ⫽ ⫺C 40 共 eye兲 ,

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(3)

where C 40 ( custom) is the SA of the custom-made lens. Using our simple assumptions and the required SA C 40 coefficient, we calculated the required classical thirdorder Seidel SA and subsequently computed the required transverse aberrations in the focal plane for a number of rays. The required classical Seidel SA will correct both the fourth-order rotationally symmetrical WFA and the balancing second-order (dioptric) rotationally symmetrical aberration for any given pupil diameter. A raytracing program (BEAM3, Stellar Software, Berkeley, Calif.) optimized the p value of the ellipsoidal front surface of the SCL by using a least-squared-error routine to produce a set of rays with the desired transverse aberrations. E. Verification of Soft Contact Lenses To verify the SCLs used in the study, we positioned a lens holder and a mirror in the ray path of the Hartmann– Shack aberroscope. We mounted a plano-convex PMMA button (front surface vertex radius ⫽ 8.20 mm, eccentricity e ⫽ 0.3, center thickness t ⫽ 4.7 mm, C 40 ⫽ 0.045 ␮ m) in the lens holder so that its optical axis was vertical. The soft lens under investigation was placed on this button. One drop of saline solution ensured good physical and optical coupling of the lens to the button. The state of lens hydration and the shape and the power of the button (⬃60 D) were chosen to resemble the conditions on a real eye as closely as possible within the limitations of an absent blink mechanism to smooth the lens on the button surface (hence a flatter vertex radius was used to better match the contact lens back surface) and the desire to produce only a small amount of SA from the button itself. An image plane was mounted on a micrometer thread and positioned at the paraxial focal plane of the lens–button system, approximately 12 mm behind the back surface of the button. Third-order SA of the contact lens is given by C 40 共 SCL兲 ⫽ C 40 共 system兲 ⫺ C 40 共 button兲 ,

(4)

where each C 40 is the average of at least three independent aberrometer measurements.

3. RESULTS A. Optical Quality Measurements Figures 1 (measurements at the photopic luminance used for visual acuity testing) and 2 (measurements at the lowphotopic luminance used for contrast sensitivity measurement) show averaged and individual Zernike C 40 coefficients for the eye–SCL system and the eye alone with the different lenses used. The average pupil diameter was 4.06 ⫾ 0.31 mm for the visual acuity measurements (L ⫽ 100 cd m⫺2 ) and 5.36 ⫾ 0.4 mm for the contrast sensitivity measurements (L ⫽ 17 cd m⫺2 ). The magnitude of the ocular SA is positive except for one subject. It shows considerable variation across our sample [photopic mean ⫾ standard deviation (SD) ⫽ 0.034 ⫾ 0.023 ␮ m, low-photopic mean ⫾ SD ⫽ 0.106 ⫾ 0.50 ␮ m]. There is no relationship between the SA and the refractive error in our data, even when restricted to only the myopic subjects

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Fig. 1. Orthonormal C 40 Zernike coefficients representing third-order SA. Pupil diameter is that measured when viewing a logMAR visual acuity chart at a luminance of 100 cd m⫺2. (a) Mean C 40 for each condition tested: Open, ocular SA; diagonal lines, standard SCL; crossed diagonal lines, custom-made SCL; horizontal lines, aberration-free SCL. The error bars represent 1 standard error. (b)– (d) C 40 for each subject plotted against contact lens power. For each contact lens design [standard SCL (b), custom-made SCL (c), aberration-free SCL (d)], the unticked end of the line represents the ocular SA and the ticked end of the line represents the eye ⫹ SCL SA.

(r ⫽ 0.23, p ⬎ 0.05, Pearson product moment correlation coefficient for a constant pupil diameter of 6 mm). A one-way repeated-measures analysis of variance (ANOVA) showed that the correction method significantly affected the measured SA (photopic pupils, F ⫽ 20.62, df ⫽ 3, 66, p ⬍ 0.001; low-photopic pupils, F ⫽ 27.64, df ⫽ 3, 66, p ⬍ 0.001). The standard contact lens reduced the C 40 coefficient compared with the ocular condition. The reduction was significant for photopic pupils (post hoc Tukey honest significant difference (HSD) test p ⬍ 0.05, mean ⫾ SD ⫽ 0.01 ⫾ 0.03 ␮ m) and approached significance for the low-photopic pupils (post hoc Tukey HSD test p ⫽ 0.06, mean ⫾ SD ⫽ 0.06 ⫾ 0.08 ␮ m). As most subjects were myopic (18), their standard lenses were expected to produce negative SA, at least partly canceling the positive ocular SA. In fact, for

three of our myopic subjects our model predicted a complete correction of SA by the standard lens. The custom-made contact lens also reduced the C 40 coefficient significantly compared with the ocular condition (post hoc Tukey HSD test p ⬍ 0.001 for both pupil sizes, mean ⫾ SD photopic pupils ⫽ ⫺0.01 ⫾ 0.04, mean ⫾ SD low-photopic pupils ⫽ 0.016 ⫾ 0.07). For the SCLs designed to be free of SA in air, our model predicts a residual aberration of magnitude equal to that of the ocular SA. For both pupil size groups, the mean C 40 coefficient with the aberration-free lens on eye was more positive than the mean ocular C 40 coefficient (mean ⫾ SD photopic pupils ⫽ 0.06 ⫾ 0.03, mean ⫾ SD lowphotopic pupils ⫽ 0.16 ⫾ 0.06), statistically significant for the low-photopic pupil condition (post hoc Tukey HSD test p ⬍ 0.01). The mean C 40 was significantly more positive than the mean C 40 for both the custom-made and


the standard SCLs, for both pupil size groups (post hoc Tukey HSD test p ⬍ 0.001 for both conditions). Of the nonrotationally symmetrical higher-order Zernike coefficients, only the C 31 coefficient, representing horizontal third-order coma, varied significantly with the correction method (photopic pupils, F ⫽ 7.1, df ⫽ 3, 66, p ⬍ 0.001; low-photopic pupils, F ⫽ 6.7, df ⫽ 3, 66, p ⬍ 0.001). When compared with the ocular condition, C 31 increased with both aspheric lens designs, reaching statistical significance with the aberration-free design for both the photopic and low-photopic luminance conditions (post hoc Tukey HSD test p ⬍ 0.001). With the aberration-free lens on eye, the mean value of C 31 was 0.17 ␮m, almost three times as large as the mean ocular C 31 coefficient for the low-photopic condition (0.06 ␮m). The Pearson product moment correlation coefficient showed a significant dependency of C 31 on SCL front surface eccentricity (r ⫽ 0.29, n ⫽ 72, p ⬍ 0.05). Figure 3(a) shows the Strehl intensity ratio for the eye–SCL system and the eye alone with the different


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lenses used, calculated for the two pupil conditions and a constant 6-mm-diameter pupil for comparison. Figures 3(b)–3(d) show the rms WFA for individual Zernike orders up to sixth order and their sum, for each contact lens type, at the same two pupil conditions and the constant 6-mm-diameter pupil. Corresponding optical quality metrics produced by pure spherical defocus of 0.25 D are presented for comparison. One-way repeated-measures ANOVAs showed that the correction method significantly affected both the Strehl ratio and the total rms WFA for all pupil size groups (Strehl photopic pupils, F ⫽ 8.44, df ⫽ 3, 66, p ⬍ 0.001; Strehl low-photopic pupils, F ⫽ 13.54, df ⫽ 3, 66, p ⬍ 0.001; Strehl 6-mm pupils, F ⫽ 14.30, df ⫽ 3, 66, p ⬍ 0.001; rms WFA photopic pupils, F ⫽ 5.53, df ⫽ 3, 66, p ⬍ 0.01; rms WFA low-photopic pupils, F ⫽ 7.51, df ⫽ 3, 66, p ⬍ 0.01; rms WFA 6-mm pupils, F ⫽ 9.65, df ⫽ 3, 66, p ⬍ 0.001). The correction method also affected the third-order terms (photopic pupils, F ⫽ 3.01, df ⫽ 3, 66, p ⬍ 0.05; low-photopic pupils,

Fig. 2. Same as Fig. 1, but with pupil diameters measured when viewing a 17-cd m⫺2 mean luminance sinusoidal grating and background.

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Fig. 3. Strehl intensity ratios and rms WFA produced under the different correction conditions: open, ocular SA; diagonal lines, standard SCL; crossed diagonal lines, custom-made SCL; horizontal lines, aberration-free SCL; vertical lines, 0.25-D spherical defocus. (a) Strehl intensity ratios based on all higher-order aberrations, grouped by pupil size. (b)–(d) rms WFA, grouped by orders: (b) for pupils corresponding to logMAR measurement conditions (photopic), (c) for pupils corresponding to contrast sensitivity measurement conditions (low photopic), (d) for pupil diameters standardized at 6 mm. Astigmatism and defocus are set to 0 and do not contribute to any of the optical quality metrics shown in the figure. The error bars represent 1 positive standard error.

F ⫽ 3.09, df ⫽ 3, 66, p ⬍ 0.05; 6-mm pupils, F ⫽ 3.34, df ⫽ 3, 66, p ⬍ 0.05), the fourth-order terms (photopic pupils, F ⫽ 5.17, df ⫽ 3, 66, p ⬍ 0.01; low-photopic pupils, F ⫽ 16.47, df ⫽ 3, 66, p ⬍ 0.001; 6-mm pupils, F ⫽ 15.15, df ⫽ 3, 66, p ⬍ 0.001), and the sixth-order terms (photopic pupils, F ⫽ 3.70, df ⫽ 3, 66, p ⬍ 0.05; low-photopic pupils, F ⫽ 3.44, df ⫽ 3, 66, p ⬍ 0.05; 6-mm pupils, F ⫽ 1.65, df ⫽ 3, 66, p ⬎ 0.05). Thirdorder rms WFA increased with the aberration-free lens for both the low-photopic and 6-mm pupil size groups (post hoc Tukey HSD test p ⬍ 0.05). Fourth-order rms WFA increased with the aberration-free lens design in all pupil size groups (post hoc Tukey HSD test p ⬍ 0.05), while it decreased for both the low-photopic and 6-mm pupil size groups with the custom-made design (post hoc Tukey HSD test p ⬍ 0.05). Sixth-order rms WFA increased with the standard design for both the low-photopic and

6-mm pupil size groups (post hoc Tukey HSD test p ⬍ 0.05). Comparing the ocular condition with the custom-made SCL condition, we found a significant reduction of the WFA for the fourth-order terms only (lowphotopic pupils, p ⬍ 0.05; 6-mm pupils, p ⬍ 0.01). In the low-photopic pupil size group, the custom-made lens corrected 30% of the ocular fourth-order aberration, and in the 6-mm pupil size group it corrected 38% of the ocular fourth-order aberration. From inspection of Fig. 3, the ocular WFA produced by fourth-order terms, of which roughly 80% are produced by third-order SA, accounts for less than the rms WFA produced by a residual spherical refractive error of 0.25 DS. All aberrations increase with pupil size, higher-order aberrations faster than lower-order ones. At the photopic pupil diameters present for our visual acuity measurements, the rms WFA produced by ocular SA is only 31% of


that produced by 0.25-D defocus. This proportion increases to 48% for low-photopic pupil diameters, as found for our contrast sensitivity measurements, and is 75% for 6-mm pupil diameters. However, the SA found by Thibos et al.9 as more representative of the general population SA would degrade the retinal image only 15% as much as 0.25-D defocus over our average photopic pupil and one third as much as 0.25-D defocus when the pupil is as large as 6 mm. At a pupil diameter of 6 mm, the rms WFA produced by all higher-order aberrations found in our study is approximately equivalent to that produced by 0.25-D defocus. B. Visual Performance Figure 4 shows the mean logMAR visual acuity measured with the different forms of correction [panel (a)] and how


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it changes for each subject with each of the three contact lens designs [panels (b)–(d)]. Figure 5 shows the relationship between the change in the absolute level of SA due to the SCL [panel (a)] or the change in the Strehl ratio [panel (b)] and the resulting change in visual acuity. Over each contact lens on eye, the optimum overrefraction was worn to minimize the effect of any residual lower-order aberrations, such as defocus and astigmatism. The photopic pupil size was used for calculating the SA and the Strehl ratio. The average visual acuity with the best-correcting spectacle lens was ⫺0.151; with the standard lens on eye, ⫺0.139; with the custom-made lens, ⫺0.149, and with the aberration-free lens, ⫺0.155 (standard error ⬃0.016 for all conditions). The maximum gain or loss for individual measurements in visual acuity compared with the best-correcting spectacle lens

Fig. 4. Visual acuity (logMAR). (a) Average visual acuity for all conditions tested: open, ocular SA; diagonal lines, standard SCL; crossed diagonal lines, custom-made SCL; horizontal lines, aberration-free SCL. Error bars represent 1 negative standard error. (b)– (d) Individual visual acuity for each subject plotted against contact lens power. For each contact lens design [standard SCL (b), custommade SCL (c), aberration-free SCL (d)], the unticked end of the line represents the visual acuity with a spectacle lens correction only and the ticked end of the line represents the visual acuity with an SCL correction. For all contact lenses on eye, the visual acuity was measured with the optimum overcorrection.

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Fig. 5. Effect of optical quality changes on visual acuity. (a) Change (from the spectacle correction condition) in logMAR visual acuity versus change in absolute value of C 40 for the three SCL types [standard SCL (䊐), custom-made SCL (䊊), aberration-free SCL (䉭)]. (b) Change in logMAR visual acuity versus change in Strehl ratio for the three SCL types. Pupil sizes used for the optical metrics were those measured under visual acuity measurement conditions. The solid lines are the regression lines fitted through the combined data.

was ⫾0.1 log unit, which corresponds to one line on the logMAR chart. No statistically significant difference was found between any of the four test conditions (one-way ANOVA for repeated measurements, F ⫽ 1.00, df ⫽ 3, p ⬎ 0.05). A Pearson product moment correlation test did not show any statistically significant dependence of the differences in visual acuity on the change in the absolute level of SA (r ⫽ 0.07, p ⬎ 0.05) or Strehl ratio (r ⫽ ⫺0.09, p ⬎ 0.05) with any of the lens designs ( p ⬎ 0.05), although the combined data do show regression lines where a larger amount of SA or a smaller Strehl ratio is associated with a larger logMAR, as would be expected. Figure 6 shows results for horizontal grating contrast sensitivity in the left panels [(a), (c), (e)] and for vertical gratings in the right panels [(b), (d), (f)]. The mean log contrast sensitivities for 6, 12, and 24 cycles/degree for each of the lens types is shown in the upper panels [(a), (b)]. The change in log contrast sensitivity and the associated change in the C 40 coefficient for the different lenses is shown in the middle panels [(c), (d)]. The change in log contrast sensitivity and the associated change in the Strehl ratio for the different lenses is shown in the lower panels [(e), (f)]. All optical quality measurements were made with the low-photopic pupil sizes measured with the same luminances as those used for contrast sensitivity. A three-factor ANOVA showed that the orientation by correction method by spatial-frequency interaction was significant (F ⫽ 2.9, df ⫽ 6,132, p ⬍ 0.05), so individual one-way ANOVAs were used for each orientation and spatial frequency, with correction method as the factor. The correction method had a significant effect only on the contrast sensitivity to 6-cycle/degree gratings oriented horizontally (F ⫽ 5.33, df ⫽ 3, 66, p ⬍ 0.05). Wearing the custom-made lens improved the mean log contrast sensitivity for horizontal gratings of 6 cycles/degree (post hoc Tukey HSD test p ⬍ 0.05) by 0.1 log unit compared with

the best-correcting spectacle lens. Significant differences in the log contrast sensitivity between the custom-made and aberration-free lenses were found for horizontal gratings of 6 cycles/degree (post hoc Tukey HSD test p ⬍ 0.01). Differences in the log contrast sensitivity to vertical gratings of 6 and 12 cycles/degree for the same comparison approached, but did not reach, significance ( p ⫽ 0.052 for 6 cycles/degree and p ⫽ 0.08 for 12 cycles/ degree). No other log contrast sensitivity differences were found for any other contact lens design or test condition. A Pearson product moment correlation test did not show any statistically significant dependence of the differences in contrast sensitivity results on the change of SA with any of the three SCL designs on eye ( p ⬎ 0.05), although there is a tendency for decreased contrast sensitivity for gratings of 6 cycles/degree with increased levels of SA (horizontal, r ⫽ ⫺0.16, p ⬎ 0.05; vertical, r ⫽ ⫺0.13, p ⬎ 0.05). The change in Strehl ratio shows a statistically significant correlation with the change in contrast sensitivity to vertical gratings of 6 cycles/degree for the combined data (r ⫽ 0.3, p ⬍ 0.05) but not for horizontal gratings (r ⫽ 0.06, p ⬍ 0.05).

C. Verification of Soft Contact Lenses Figure 7 shows the correlation between the Zernike C 40 coefficient over a 6-mm pupil measured on eye and on the custom-made lens holder for each of the three lens types. For the standard lens [Fig. 7(a)], the correlation is weakest (r ⫽ 0.46). For the custom-made lens, our verification method agrees well with the levels of C 40 found for the SCLs on eye (r ⫽ 0.75). There is slightly less agreement between the two measurement methods for the aberration-free design (r ⫽ 0.65). The correlations between the C 40 value found on the lens holder and that predicted from the design were higher at r ⫽ 0.76 for the standard lens and r ⫽ 0.70 for the aberration-free design.



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Fig. 6. Effect of optical quality changes on contrast sensitivity. Horizontal grating contrast sensitivity is shown in the left panels [(a), (c), (e)], and vertical sensitivity in the right panels [(b), (d), (f)]. The mean log contrast sensitivities for 6, 12, and 24 cycles/degree for each of the lens types is shown in the upper panels [(a), (b)]: open, ocular SA; diagonal lines, standard SCL; crossed diagonal lines, custom-made SCL; horizontal lines, aberration-free SCL. Error bars represent 1 standard error. The change in log contrast sensitivity and the associated change in the C 40 coefficient for the different lenses is shown in the middle panels [(c), (d)]. The change in log contrast sensitivity and the associated change in Strehl ratio for the different lenses is shown in the lower panels [(e), (f)]: standard SCL (䊐), custom-made SCL (䊊), aberration-free SCL (䉭). Pupil sizes used for the optical metrics were those measured under contrast sensitivity measurement conditions. The solid lines are the regression lines fitted through the combined data.

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Fig. 7. Correlation data between C 40 coefficients measured on a lens holder versus those found on the eye for (a) standard, (b) custommade, and (c) aberration-free SCLs. Pupil diameter is fixed at 6 mm.

Compared with predicted levels of SA over a 6-mm pupildiameter, a tendency for an increasingly too positive C 40 with increasingly negative SCL power was observed for all lens designs (average difference holder measured C 40 ⫺ predicted C 40 ⫽ 0.083 ␮ m for the standard lenses, 0.086 ␮m for the custom-made lenses, and 0.14 ␮m for the aberration-free lenses; SD holder measured C 40 ⫺ predicted C 40 ⫽ 0.1 ␮ m for each lens design).

4. DISCUSSION A. Optical Quality Measurements Our results suggest that ocular SA can be successfully corrected with customized front aspherical SCLs. The negative SA produced by negatively powered standard SCLs partly cancels the on-average positive ocular SA in myopes. SCLs designed to be free of SA in air (‘‘aberration-free contact lenses’’) increase the SA of the eye–contact lens system. Our simple in-air model predicts that negative standard SCLs, depending on lens power, cancel rather large proportions of the on-average positive ocular SA of myopic eyes, whereas positively powered standard lenses add to the positive ocular SA of hypermetropes. Custom-made lenses should cancel all SA present in the eye–contact lens system, whereas aberration-free lenses should not alter the level of ocular SA. The data, however, do not agree with our predictions and the findings of previous research.15,18,19 The SA induced by any of our SCLs designs on eye is more positive than predicted. We believe that the source of this extra positive SA could lie in the manufacturing process of the lenses rather than in any effects of lens flexure on eye, even though lens flexure effects have been assumed to alter the SA of a lens on eye.28 This is discussed further in Subsection 4.C. The average change in SA produced by each contact lens series is also reflected by the change in fourth-order rms WFA (see Fig. 3), of which the C 40 coefficient describing SA is the major contributor. However, the percentage change in the total of all fourth-order aberrations combined is significantly less than the change in SA alone, as other fourth-order coefficients describe aberrations lacking rotational symmetry. Consequently, they cannot be modified by rotationally symmetrical contact lenses.

Uncorrected nonrotationally symmetrical fourth-order aberrations as well as increased third-order aberrations contribute to the failure of the custom-made lens to significantly decrease the total rms WFA. Both increased fourth-order and increased third-order aberration result in the significant increase in the total rms WFA with the aberration-free lens design on eye. A possible explanation for the increased horizontal coma with the aspheric lenses lies in the alignment of the corneal axis with the fixation axis of the eye. With respect to the line of sight, the human cornea is temporally tilted,29 and its apex is likely to be temporally displaced,30 although studies investigating the cornea apex location are not uniform.31 A contact lens centered on the tilted and translated cornea will produce nonrotationally symmetrical (coma-like) aberrations influencing measurements relying on the line of sight, such as aberroscopy, visual acuity, and contrast sensitivity measurements. Comatic aberrations increase with tilt angle,32 translation, and asphericity of the refracting surface.33 For example, a ⫺6.00-D front aspheric SCL in air with a p value of 0.5, horizontally tilted by a physiological angle of 3°29 and translated by 0.5 mm in the same direction,30 more than doubles horizontal coma produced by an equally tilted and displaced spherical contact lens over a 6-mm diameter pupil (C 31 ⫽ 0.31 ␮ m instead of 0.13 ␮m). The increase in coma with the custom-made and aberrationfree lenses also accounts for the increase in third-order rms WFA with both designs. In addition, small physiological displacements of our SCLs on eye, which have been reported to be up to 0.6 mm,34 may have contributed to the increased third-order aberrations found with both aspheric designs. Studies investigating the correlation between ametropia and the magnitude of higher-order ocular aberrations are not common, and their conclusions are far from uniform. In accordance with recent findings,35 our results suggest that levels of ametropia and ocular SA are uncorrelated. The magnitude of the average C 40 (0.21 ␮m for a 6-mm pupil diameter) in our predominantly myopic cohort, however, is slightly more positive than that reported for larger samples representing the more general population.2,6,7,9 This indicates an increase in fourthorder aberrations with myopia as described elsewhere.36 Our small sample size (n ⫽ 23) and the large SD, which


is generally reported for individual aberration coefficients,6,7,9 can equally explain the higher SA found in our study (mean C 40 ⫽ 0.21 ␮ m, standard error ⫽ 0.025 ␮ m). Increased fourth-order aberrations, of which SA is the most prominent contributor, also explain the low ratio of asymmetrical (third-order) to symmetrical (fourth-order) aberration of nearly 1:1 for pupil diameters of 6 mm (see Fig. 3). Other recent studies report higher proportions of asymmetrical aberrations for a 6-mm pupil diameter, with ratios of 5:4,7 3:2,2 5:3,37 and even 2:1.8 B. Visual Performance Considering the small changes in the total higher-order rms WFA (see Fig. 2) with the lenses on eye and our correction of lower-order errors using overrefraction, it is unsurprising that we were not able to identify any changes in visual acuity. For photopic pupil diameters, the rms WFA produced by all higher-order aberrations together is less than that produced by 0.25-D defocus. Even if the pupil size increases to a diameter of 6 mm, the higherorder WFA hardly exceeds that generated by 0.25-D defocus, in agreement with other research.2,9 When considering the potential for correcting the higher-order aberrations, we can straightforwardly modify only the C 40 coefficient. At photopic pupil sizes, our average ocular SA produces only 31% of the rms WFA resulting from 0.25-D defocus for a 4.1-mm pupil, the average pupil diameter for our visual acuity measurements. Hence our ability to measure the effect of the contact lens design for an individual is likely to be critically limited by the precision of our overrefraction and the 95% limits of agreement for visual acuity measurement24,38 (0.1 log unit for our methods and conditions). Nevertheless, a change in the mean logMAR visual acuity of a population wearing a particular design of SCL of nearly as small as 0.02 log unit (⫽2 standard errors) would have been detected by our method. In all cases during our measurements of visual function, we corrected the sphero-cylindrical error of the subjects. The effective power of the eye–contact lens system depends on the level of aberrations present in the system.2 More precisely, this power is made up of paraxial lens power, which is independent of pupil size, and the effect of aberrations, which is dependent on pupil size. Choosing the best-correcting spherical trial lens for a given pupil diameter minimizes the effect of SA and other aberrations. Expressed in more familiar raytracing terms, optimizing the spherical prescription at a given pupil diameter shifts the circle of least confusion onto the retina. A spherically surfaced ⫺7.00-D contact lens on a 6-mm-diameter pupil, for example, generates enough SA for a ⫺0.50-D power shift to occur.18 Consequently, all methods utilizing the optimum spherocylindrical correction for a given pupil diameter investigate the minimum effect of aberrations only. If this balancing of the dioptric effects of the SA had not been performed, then the effects of changing the spherical aberration at larger pupil diameters would have been larger. For example, a C 40 coefficient of 0.2 ␮m requires ⫺0.32 D of correction for a 4.1-mm pupil diameter but ⫺0.55 D for a 5.4-mm pupil diameter and ⫺0.68 D for a 6-mm pupil. Only one of these levels of dioptric correcting power could


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be prescribed in an SCL. An SCL that corrects not the induced dioptric defocus for a given pupil size but the SA inducing this defocus at such a level will benefit wearers not only by correcting their C 40 coefficients but also by providing a better dioptric focus over a range of pupil diameters. The use of sphero-cylindrical corrections over the contact lenses, and the consequent setting of lower-order aberration coefficients to 0 when computing the Strehl ratio, explains the generally high levels of Strehl ratios obtained from our data. This is reinforced by the measurement method of aberrometry, which takes no account of any light scatter that may occur in the eye and affect the retinal image quality. When one is dealing with rotationally symmetrical SCLs without the use of supplementary lenses, any residual astigmatism remains uncorrected. For prescriptions up to ⫾1.00-D astigmatism, it is common contactlens-fitting practice to correct the best-mean-sphere refractive error only. In our sample (exclusion criteria astigmatism ⬎⫾1.25 D), the mean residual astigmatism, measured and corrected with trial lenses, was 0.50 DC. This indicates that, when SCLs are worn, more retinal image degradation than that caused by all higher-order aberrations together is commonly accepted in the form of uncorrected astigmatism (rms WFA produced by a residual cylinder of ⫺0.25/⫹0.50 ⫻ 90 ⫽ 0.46 ␮ m as opposed to an average of 0.36 ␮m for all higher-order aberrations combined, across our population, for a 6-mm pupil diameter). Optical aberrations depend on pupil size, the dependency increasing with the order number of their mathematical descriptor. Hence correcting higher-order aberrations will be more effective when the pupil is large. Under natural viewing conditions, however, the pupil is largest when the sensitivity to small details is lowest, under scotopic viewing conditions. It is therefore questionable whether high-contrast visual acuity testing under natural viewing conditions is a sensitive enough method to detect the small effects that higher-order aberrations have on retinal image quality. Visual acuity measurements performed under mydriasis, on the other hand, do not represent viewing conditions likely to be experienced by the subjects (bright targets, large pupils). Compared with visual acuity measurements, larger pupils under low-photopic testing conditions, and hence larger effects of modifying the SA, are the likely reason for the improved contrast sensitivity found with the custom-made lens on eye as well as the differences found between the custom-made lens and the aberration-free lens. Compared with theoretical predictions2,4,5 and findings using more sophisticated techniques,3,5 the gain in contrast sensitivity is small but statistically significant. Increased third-order aberrations with the custommade lenses, while not reaching statistical significance, had a small effect in canceling some of the positive effect of reducing the SA. The statistically significant correlation between the change in Strehl ratio and the change in log contrast sensitivity for vertically oriented 6-cycle/degree gratings (Fig. 6) is consistent with the concept that increased coma with displaced aspheric surfaces adversely affects visual performance. The increased horizontal coma will have affected the visual performance with both aspheric lens de-

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signs on eye. In combination with the reduction in SA, this is demonstrated by the lack of any improvement in the log contrast sensitivity to vertical gratings when the custom-made SCL is used. In contrast, the custom-made SCL did produce a significant increase in log contrast sensitivity to horizontal gratings, albeit only at 6 cycles/ degree. For the aberration-free SCLs, where both coma and SA increased when compared with the standard SCLs, the log contrast sensitivity for moderate spatial frequencies of 6 and 12 cycles/degree was reduced for both horizontal and vertical gratings. Once again, the 95% limits of agreement for logcontrast-sensitivity measurement, at ⫾3.3 dB for our methods and conditions, limits the application of logcontrast-sensitivity improvements for individual subjects, but our error of measurement is typical.38,39 C. Verification of Soft Contact Lenses The lenses used in this study were manufactured on a lathe machine, whereas previously used lenses18 were manufactured by using spin casting. All lens specifications such as back optic zone radius, back vertex power, center thickness, and water content of the material were very similar. To provide better wearing comfort, the transition between the peripheral zone and the 7-mm optic zone of the lathed unhydrated lenses was blended with a polishing tool. Polishing in the peripheral optic zone removes material and steepens the peripheral curvature of any lens relative to its nominal shape, which leads to a reduction in negative SA or an increase in positive SA. As the lens power increases, the transition between the zones becomes more pronounced and hence requires more material to be removed through blending. This might explain the observed tendency that the discrepancy between predicted and measured SA increases with lens power. We believe that our verification method, which gave too positive a SA that was very similar in mean magnitude to the excess on-eye SA found for each of the three lens designs (based on a 6-mm pupil diameter), is evidence for this assumption, even though the correlation between oneye and on-lens-holder measurements of SA (Fig. 7) is limited. Measuring an SCL on a model eye gives poorer aberroscope images and makes data analysis more difficult, as the smoothness of the tear film found after a blink on a soft lens on eye cannot be provided.

5. CONCLUSION Individually designed front aspheric SCLs can reduce the level of SA of the eye–contact lens system. The negative SA produced by negatively powered standard SCLs partly cancels the on-average positive ocular SA in myopes. Aberration-free SCLs can increase the SA compared with standard lenses in a population containing a high proportion of myopes. Physiological corneal tilt and/or imperfect lens centration can produce levels of coma-like aberration, reducing the visual benefits of correcting SA with contact lenses using aspheric surfaces. A number of natural and technical limitations restrict the predicted visual benefit of correcting SA. However, making a contact lens completely stable on the cornea and then measuring its position, orientation, azimuth, and elevation would al-


low for the fabrication of a lens design offering correction of both rotationally symmetrical and nonrotationally symmetrical aberrations. Such a stable lens fitting would present a considerable challenge in the use of such a lens for ocular physiological safety and comfort. Factors limiting the possible benefits of conventional aberration-correcting SCLs are chromatic aberrations,5 manufacturing problems also reported elsewhere,15 dynamics of the contact lens34 and the tear film,40 lens flexure,20 the state of lens hydration, and changes of the ocular aberrations with accommodation,41,42 time,43 and age.44,45 This study shows that coma-like aberrations arising from small tilt and/or displacements of aspheric contact lenses can be a limiting factor. The common acceptance of residual astigmatism and the comparatively small contribution of higher-order aberrations on image formation, as well as the risk of adding coma with an only slightly decentered and/or tilted aspheric contact lens, make the benefit of SA-correcting contact lenses questionable.

ACKNOWLEDGMENTS W. A. Douthwaite and S. Tripathy (both of the University of Bradford) are thanked for their help and valuable advice. D. Muckenhirn and O. Roming (both of the Hecht Contactlinsen GmbH) provided valuable support for this project. The corresponding author is Michael J. Cox, Department of Optometry, University of Bradford, Richmond Road, Bradford BD7 1DP, UK; e-mail, M.Cox @bradford.ac.uk.

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