On-eye Evaluation of Optical Performance of Rigid and Soft Contact Lenses

On-eye Evaluation of Optical Performance of Rigid and Soft Contact Lenses

On-eye Evaluation of Optical Performance of Rigid and Soft Contact Lenses

On-eye Evaluation of Optical Performance of Rigid and Soft Contact Lenses Xin Hong, Nikole Himebaugh, Larry Thibos, Arthur Bradley and Carolyn Begley School of Optometry, Indiana University Abstract A Shack-Hartmann aberrometer was used to assess the optical performances of eyes corrected with rigid or soft contact lenses compared to spectacles. Metrics of optical quality derived from the measured wave aberrations were consistent with the subjective rating by subjects of visual clarity. Further aberration analysis illustrated the differences in aberration structures of eyes wearing different optical corrections.

These observations can be explained by theoretical calculations of the aberrations of the eye + lens optical system. We conclude that aberrometry provides a better understanding of the optical effects of contact lenses in situ and could be useful for optimizing future designs of contact lens. Introduction The purpose of contact lenses is to correct refractive errors of an eye in order to improve the optical quality of the retinal image, thereby improving vision [Bennett, 1999]. However, the degree of success in achieving this goal varies with the method of correction. Several studies have demonstrated that visual performance can vary substantially depending on whether the contact lens is a rigid, gas-permeable (RGP) lens or a soft hydrogel (SH) lens [Johnson, 1991; Timberlake, 1992; Fonn, 1995].

The general consensus of these studies is that RGP contact lenses provide the patient with superior vision compared to SH lenses, and even compared to spectacle lenses in many instances. However, the reason for this variation of optical performance is unclear. Perhaps RGP lenses minimize the amount of residual, uncorrected astigmatism and spherical refractive errors. Alternatively, perhaps the higher-order aberrations (e.g. coma, spherical aberration, etc.) are minimized when the eye is fitted with RGP lenses. Below we review the results of previous attempts to answer this question by a variety of empirical and theoretical methods.

Unfortunately, these studies share one important limitation: they all used indirect methods to assess the effect of contact lenses on the optical performance of the eye. The purpose of our study was to overcome this limitation by directly measuring the residual refractive errors and higher-order aberrations of the eye while wearing the contact lens. We did this with a Shack-Hartmann aberrometer, a relatively new diagnostic

On-eye Evaluation of Optical Performance of Rigid and Soft Contact Lenses

instrument which employs wavefront sensing technology to measure the aberration structure of the eye with or without the contact lens in place [ref: Thibos, Principles of SH aberrometer]. Several early studies have suggested that contact lenses have inherently large aberrations, especially spherical aberration [Westheimer, 1961; Bauer, 1980; Cox, 1990]. Thus we might expect the optical aberrations of an eye to increase when viewing through a contact lens. Paradoxically, visual performance was found to be slightly worse when viewing through an aberrated contact lens compared to an aberration-free lens Brabander, [Brabander, 1998].

One possible resolution of this paradox is the realization that an analysis of the contact lens in air is not sufficient to predict its performance when placed on the eye. Instead, one needs to consider the lens in situ, taking account of the entire optical system of contact lens, eye, and the tear film interface.

Theoretical modeling of the optical effect of contact lenses have often simplified the problem by considering the interaction of contact lens with the cornea in isolation, thereby ignoring the aberrations of the crystalline lens. For example, Cox [Cox, 1990] calculated the on-eye spherical aberration (SA) of contact lens as the difference of SA between contact lens + cornea combination and the cornea alone. These on-eye aberrations of the contact lenses were found to be quite different from the in-air aberrations. Based on these calculations, Cox and Holden [Cox & Holden, 1990] suggested that visual performance could be optimized by an aspheric contact lenses which minimized spherical aberration of the cornea + lens system.

Later, Atchison rightly pointed out that the proper comparison for an ametropic eye corrected by a contact lens is when the eye is corrected by a spectacle lens [Atchison, 1995]. This is important because spectacle lenses alter the angle of incidence of rays onto the cornea and therefore have the potential to have a large impact on the spherical aberration of the cornea even if the spectacle lens by itself has little aberration. Using Atchison's approach, Collins et al. [Collins, 1992] demonstrated that by manipulating the amount of spherical aberration of the corneal surface by a RBP contact lens, significant changes in visual performance could be obtained.

However, the lens which minimized the spherical aberration of the cornea did not necessarily yield the vest visual performance, presumably because of additional spherical aberration contributed by the crystalline lens. Previous omission of the crystalline lens in the computational model made the optical performance of the contact lens/eye combination virtually unpredictable, indicating that the role of crystalline lenses cannot usually be ignored [El Hage, 1972; Artal, 1998]. Thus, the ideal solution is to use a contact lens which neutralizes the aberrations of the whole eye, not just the cornea [Cox and Williams, 2000].

Additional uncertainties about the interactions between contact lenses and human eyes continues to hamper theoretical optical modeling of the differences between soft and hard contact lenses. The two uncertainties most frequently mentioned in the literature are movement and conformity of the contact lens to the natural corneal shape. Estimated movement of contact lens on the human cornea is about 1-2mm for rigid contact lens and 0.5-1mm for soft contact lens. Such movement would be expected to decenter the eye and lens, thus affecting the overall aberration structure. Nevertheless, computer simulations indicate that

On-eye Evaluation of Optical Performance of Rigid and Soft Contact Lenses

induced asymmetric aberrations caused by lens movement is probably small for spherical RGP lenses [Atchison, 1995] and even less for soft lenses. The issue of conformity takes different forms for hard and soft lenses. The rigid anterior surface of RGP lens replaces the irregular surface of the natural cornea with a smooth anterior interface that should reduce the amount of higher- order aberrations of the eye. To the contrary, soft contact lens would be expected to preserve at least some of these higher-order aberrations depending on the degree of conformity . In a recent study, the degree of conformity was quantified for different types of soft contact lenses based on the power of the tear lens which lies between the eye and lens [Plainis & Charman, 1998].

The resulting predictions of performances of soft lens on the eye varied considerably, depending on the nature of flexure and the degree of conformity assumed. Given the limitations faced by the studies reviewed above, we decided to employ a Shack-Hartmann aberrometer to measure the aberration structure of the whole eye with contact lens in place. By this strategy we aimed to take account of the aberrations of the crystalline lens, the tear lens, the change in aberrations of the cornea resulting from the contact lens, and to gain control over the uncertainties associated with decentration and conformity.

In order to assess the visual impact of these optical aberrations, we also measured visual performance by patients while wearing the lens and compared the results with theoretical predictions based on optical modeling.

Methods Subjects All 4 subjects enrolled in this experiment have healthy and normal eyes. Only right eyes (OD) were used in this experiment. Subjects wore a variety of hard (MiniconE, Boston Equalens, Polycon II) and soft (Biomedic, Softlens Toric, Optima) lens designs. The prescriptions of spectacles, RGP, and SH contact lenses for each subject is shown in Table 1. Fitting by experienced optometrists following the standard clinical procedure based on keratometry (“on-K” for RGP, flatter for SH with fitting factor about 1.2). All of the RGP lenses used in this experiment had spherical surfaces.

Visual acuity was measured in a dark room with the natural pupil. Patients were also asked to describe the clarity of vision for each optical correction in comparative way, i.e. rating the best vision as 3 and the worst vision as 1. These measures of visual performance are tabulated in Table 1 for each prescription.

Table 1. The prescriptions and visual performances of spectacles, RGP, and SH contact lenses for all subjects. Subject Eye (OD) Spectacle Soft RGP Prescription -1.25,-0.50x085 -1.50 -1.50 Visual acuity 20/15 20/15 20/15 CB Rating 2 1 3 Prescription -5.75,-0.75x164 -5.50 -5.50

On-eye Evaluation of Optical Performance of Rigid and Soft Contact Lenses

Visual acuity 20/15 20/20 20/15 KF Rating 2 1 3 Prescription -6.75,-1.00x167 -6.00,-1.00x180 -6.25 Visual acuity 20/15-20/20 20/20 20/15 NH Rating 2 1 3 Prescription -2.50,-0.50x070 -2.75 -2.50 Visual acuity 20/20 20/15 20/15 PP Rating 1 3 2 Apparatus A Shack-Hartmann (SH) aberrometer described elsewhere [Liang, et al, 1994; Thibos & Hong, 1999] was used to measure the optical aberrations of eye when corrected by spectacle, SH, or RGP contact lens.

The SH aberrometer provides a brief (200ms) flash of collimated light from a He-Ne laser beam (633 nm) which the corrected eye focuses to a point image on the retina. This image then becomes a source of reflected light that exits the eye and then is subdivided by a two-dimensional array of lenslets placed optically conjugate to the eye’s entrance pupil plane. The result is an array of images of the common retinal source point captured by a CCD video camera. The local slope of the wavefront over each lenslet is estimated from the lateral shift in the image spot relative to the optical axis of the corresponding lenslet.

These measures of slope are then integrated to reconstruct the wave aberration.

The sampling density of the lenslet array in the pupil plane was 0.4mm/lenslet. Light energy at the cornea was 0.01mW, which is about 1% of the maximum exposure recommended by ANSI. The wave aberrations were measured along the line-of-sight which is the axis connecting the fixation point, the pupil center, and the fovea. Previous studies have shown that the Shack- Hartmann aberrometer has good repeatability and high accuracy in measuring the optical aberrations of normal human eyes [Liang, et al, 1994; Liang, Williams, 1997; Salmon, Thibos, 1998] as well as clinically abnormal eyes of patients with dry eyes [Hong & Thibos, 1997], keratoconus [Thibos & Hong, 1999], and refractive surgery [Thibos & Hong, 1999, Hong, Thibos, 2000].

Procedures Each patient’s eye was corrected for distant vision by each of three methods, as illustrated in Fig. 1. Spectacle correction represents the control condition in which the aberration structure of the naked eye is preserved. (A spectacle lens contributes negligible aberration due to the large radii of its two surfaces.) Retention of corneal aberrations would be expected also for soft lenses if the contact lens conformed fully to the cornea, as shown by Figure 1(b) because the cornea irregularity would be transferred to the front surface of the contact lens. Partial conformity would presumably preserve corneal aberrations partially.

On the other hand, a hard contact lens retains its own surface shape (Fig. 1c) which has the potential to neutralize aberrations of the cornea as the

tears fill the gap between the contact lens and the cornea. We assume that the aberrations of the rest of the eye (crystalline lens and intraocular medium) remain the same for all three optical correction methods since rays follow the same path inside the eye. Figure 1. Schematic diagram of the eye with (a) spectacle, (b) soft hydrogel (SH) contact lens and (c) rigid gas-permeable (RGP) contact lens. The shaded regions indicate the tear layer. Corneal distortions are exaggerated to illustrate the differences between different optical corrections.

In order to avoid any possible influence on ocular aberrations, no drugs were used to dilate the pupil or paralyze accommodation.

Head movement was stabilized with a bite-bar and fixation was maintained by a distant point source. Shack-Hartmann measurements were always taken three seconds after blinking to avoid variability of tear film thickness and movement of the contact lens. Measurements of optical aberrations were conducted in a darkened room. The pupil sizes of all our subjects were about 6.0mm under this lighting condition. The measurements were repeated 5 times for each method of optical correction of the eye.

Data analysis Wavefront aberrations were fit with Zernike polynomials up to the tenth order for a 6.0mm pupil using the method of Liang et al. [Liang, et al, 1994]. The magnification effects of spectacle lenses on the eye’s entrance pupil size was compensated in software. Mean Zernike coefficients were determined for 5 repeated measurements. Since accommodation was not paralyzed, the defocus term in wave aberrations were omitted in subsequent analysis to eliminate possible influence of accommodation fluctuations of focus. The 1st order aberrations were also omitted from calculations of wavefront error since these prismatic terms have no effect on monochromatic image quality.

Thus the included terms were astigmatism (2nd -order Zernike modes) and all terms of order 3 to 10.

In order to quantify the differences in optical performance of the eye provided by various corrective lenses, four different measures of optical quality were calculated from the wave aberration function. We adopted this approach because different optical measures emphasize different aspects of optical performance, and because we have little prior knowledge to guide our choice of the best optical measure. Thus an ancillary aim of our study was to correlate the

different measures of optical quality with visual performance so as to discover the best measure for comparison of contact lenses.

The most direct measure of optical quality is wavefront variance, which quantifies the average deviation between an aberrated wavefront and the ideal reference wavefront from a non-aberrated system. Larger wavefront variance indicates poorer optical quality. The other three measures of optical quality, as illustrated in Fig. 2, are indirect in the sense that they are derived from the retinal image rather than from the optical system which forms that image. Enveloped area Cutoff SF Neural Threshold rMTF (a) Iab Idf SR=Iab/Idf Position (b) Figure 2. The optical measures used in this study, (a) the intersection of rMTF and neural threshold indicates the cutoff spatial frequency of the visual system and the enveloped area under these two curves shows the contrasts of retinal images.

(b) the Strehl ratio is defined as the ratio between peak intensities of point spread functions of aberrated and ideal optical systems.

Performance of an optical system in the frequency domain is characterized by a radial-averaged (average across the same radial spatial frequencies) modulation transfer function (rMTF) which defines the maximum possible contrast on the retinal contrast for different spatial frequencies. The minimum amount of contrast needed for visual detection is set by the neural threshold. From these two curves we derive two metrics of image quality, as shown in Fig. 2a. The first is “enveloped area”, which defines those combinations of spatial frequency and contrast which can be achieved by the optical system (below rMTF) and are visible (above neural threshold).

The second is “cutoff spatial frequency”, which is the highest visible spatial frequency (intersection of rMTF and neural threshold). Qualitatively, larger cutoff frequency and enveloped area indicates better optical quality.

Optical performance in the spatial domain is characterized by the point spread function (PSF), which is simply the image of a distant point source as shown by Fig. 2b. A variety of methods are available for comparing an aberrated PSF with the ideal PSF of a non-aberrated system. We chose to use Strehl ratio (SR), which is the ratio of peak intensity of the aberrated PSF to the peak of the non-aberrated PSF.

Results Example of aberration analysis Figure 3 shows examples of the wave aberration of subject KF when wearing a spectacle lens, a soft contact lens, or a rigid contact lens.

The sign convention for these contour maps is that white means phase advance and black means phase retardation for the reflected wavefront coming out of the eye. In general, more contour lines in a wavefront map indicates a more aberrated optical system. For this subject , the control condition (spectacles, Fig. 3a) indicates the presence of large, irregular aberrations of the eye. Note especially the bulging out of the inferior part of the wavefront which is indicative of coma. This asymmetric feature is clearly present also when the eye was corrected with the SH lens (Fig. 3b), as expected if the lens conforms closely to the cornea.

Overall, the SH correction leaves the eye with much larger aberrations due to the uncorrected astigmatism (-0.75D, axis 164°) left by this non-toric lens. This uncorrected astigmatism is responsible for the saddle shape which dominates the wavefront map. Zernike analysis of this wavefront confirmed the presence of uncorrected astigmatism (–0.79D, axis 173°), which is almost identical to the astigmatism determined by subjective refraction.

(c) 0.0 0.5 (b) 0.0 1.0 2.0 1.0 2.0 3.0 -1.0 -2.0 -1.0 -2.0 (a) 0.0 1.0 1.0 2.0 -1.0 Spectacle Soft RGP Figure 3. Wavefront aberrations of the right eye (OD) of subject KF displayed as iso- aberration contour maps. Correction method was (a) spectacle, (b) soft hydrogel contact lens and (c) rigid gas-permeable contact lens. The wavefront is displayed to match clinicians’ view of the pupil: Left (Temporal), Right (Nasal), Top (Superior) and Bottom (Inferior). Iinterval between contour lines is 0.5λ = 0.316µm). Contour labels have units of µm. White is the peak of wave aberrations and black is the valley.

By comparison, the wavefront error for the RGP correction (Fig. 3c) was greatly reduced, as expected if the lens replaced the irregular corneal surface with a smooth spherical surface that reduced corneal astigmatism and high-order irregularities. Zernike analysis indicates little residual astigmatism, which is consistent with clinical experience for RGP lenses. The magnitude of aberrations of the eye with RGP lens is reduced dramatically (4-fold reduction in terms of peak-valley value) compared to the spectacle condition. A similar reductions of corneal aberrations was observed for all subjects in our study.

Spatial Frequency (cpd) Subject: KF RGP Soft Spex 10 arcmin (a) (b) Figure 4. Monochromatic (a) radial-averaged modulation transfer functions (rMTF’s) and (b) point spread functions (PSF’s) calculated from the wave aberrations of Figure 3. The intersection of rMTF’s and neural threshold are the cutoff spatial frequency and the areas between rMTF’s and neural threshold are enveloped areas of perceivable contrasts. (b) The intensity of point spread functions are γ-corrected to show the low- intensity tails. The sizes of images of PSF’s are 10 arcminutes. Measures of retinal image quality derived from the aberration functions in Fig.

3 are shown in Fig. 4. The RGP lens provided the best MTF and the most compact PSF, while the SH lens has the worst MTF and the widest PSF. These qualitative observations were reflected in quantitative measures of cutoff spatial frequency, enveloped area, and Strehl ratio reported in Table 2. A similar analysis for the other subjects is reported next.

Correlation of optical quality and visual performance A summary of the objective measures of optical quality determined for each lens on each eye results is shown in Table 2. The lens which provided best image quality by each metric is shown in bold-face type. In nearly every case these objective results agreed with the subjective rating of visual clarity reported in Table 1. The only exception was for the Strehl-Ratio metric for subject CB. Likewise, in most cases the lens given the worst rating for visual clarity also gave the worst optical performance.

Table 2. The derived optical measures (wave variance, cutoff spatial frequency, enveloped area and Strehl ratio) for different optical corrections of different subjects.

Bold-face type indicates the correcting lens which provided superior optical quality. Subject Eye (OD) Spectacle Soft RGP Wave variance (µm2) 0.358 0.230 0.105 Cutoff SF (cpd) 39.8 39.2 46.9 CB Enveloped area 8.83 8.69 14.2

Strehl ratio 0.0223 0.0182 0.0413 Wave variance (µm2 ) 0.345 0.7158 0.0604 Cutoff SF (cpd) 36.1 34.0 40.7 Enveloped area 7.26 5.61 12.1 KF Strehl ratio 0.0142 0.0118 0.0365 Wave variance (µm2) 0.629 0.759 0.278 Cutoff SF (cpd) 36.6 31.3 39.7 Enveloped area 7.68 4.90 8.76 NH Strehl ratio 0.0169 0.0084* 0.0124 Wave variance (µm2) 0.587 0.235 0.359 Cutoff SF (cpd) 36.5 43.9 43.1 Enveloped area 7.16 11.6 9.09 PP Strehl ratio 0.0136 0.0300 0.0259 A quantitative analysis of the correlation between the 4 metrics of optical quality and 2 metrics of visual performance is presented in Fig. 5. These results indicate high correlation between different optical measures which can be understood qualitatively.

Smaller wave variance should give a better MTF and a sharper PSF, therefore resulting in a higher cutoff spatial frequency, a larger enveloped area, and a higher Strehl ratio. The metrics with highest correlation are enveloped area with Strehl ratio (r2 =0.9), and enveloped area with cutoff spatial frequency (r2 =0.86). Such high correlation values indicates a high level of redundancy in the description of optical quality with multiple optical measures. To find the metric of optical quality that correlates best with visual performance, we created the matrix of scatter plots and linear regressions shown in Fig.

5. Every optical measure used in this study correlates well with the subjective rating for visual clarity and subjective measurements of visual acuity. The minimum correlation coefficient (0.61) was for Strehl Ratio vs. MAR and the maximum correlation (0.88) was for wavefront variance vs. MAR. These strong correlations indicate that any of these four optical measures could be used to quantify visual performance but wave variance is the best and Strehl ratio the worst for our group of subjects. Some caution is required for interpreting these results, however, since visual clarity is not necessarily a linear scale, and both performance measures are quantized whereas the optical metrics are all continuous variables.

Figure 5. The correlation between optical measures and visual performances. The correlation scatter plots are organized into triangular matrix. Each data point is for a single subject wearing a particular optical correction (N=4 subjects X 3 lenses = 12 points per scatter plot). Given the above results, we selected wavefront variance as the optical measure of choice to compare the different types of correcting lens. The results, averaged across subjects, is presented in Fig. 6. Clearly that the RGP lens had significant better optical quality than the other two lenses. The SH lens gave almost the same visual performance as spectacle.

The variability of performances was greatest in SH lenses, possibly because of variability in conformity to the cornea.

Figure 6. The average performances of three different optical corrections (spectacle and soft, RGP contact lenses). The optical measure chosen for comparison here is the wave variance. The error bars indicate ± 1 standard error of the mean. Role of high-order aberrations a Asymmetric aberrations The asymmetric aberrations normally refer to those Zernike modes which are rotationally anti-symmetric. Under this notation, the asymmetric aberrations include odd-order (1st , 3rd , 5th , 7th and 9th ) Zernike aberrations. We show, in Figure 7, the wave variances of asymmetric aberrations (including 3rd , 5th , 7th and 9th order aberrations) of different type of optical corrections for all subjects.

Our data on asymmetric aberrations is consistent with the previous studies [Howland, 1978; Williams, 1994] that the 3rd order aberrations (comas and trefoils) were the dominating asymmetric aberrations. the previous conclusions.

Figure 7. The wave variances of asymmetric aberrations of spectacles and soft, RGP contact lenses for 4 different subjects CB, KF, NH and PP. The standard errors of means are too small to show up in this graph. The human eye usually has considerable amounts of asymmetric aberrations, which is confirmed by the measured asymmetric aberrations when subjects were wearing spectacles. Since the irregular corneal anterior surface contributes significantly to the asymmetric aberrations [Artal, 1998; Hong, 2001], the eye with soft lens would be expected to have similar amounts of asymmetric aberrations as the eye with spectacle if the soft lens conform and align perfectly to the cornea.

However, our data shows that the asymmetric aberrations of the eye with soft lens are quite different from those of the eye with spectacle. For the toric cornea, the soft lens didn’t conform to the cornea well and thus has quite different asymmetrical aberrations, as shown by subject KF (see Figure 3 and Figure 7) and subject NH (see Figure 8 and Figure 7). The bad-fitting of soft toric contact lens (subject NH) can be problematic. For subject NH, the soft contact lens was habitually sitting on the temporal superior part of the cornea, which generate the asymmetric wavefront as shown by Figure 8.

These large asymmetric aberrations explained why subject NH prefers the RGP lens and the spectacle much better than the soft contact lens.

0.0 -1.0 -2.0 1.0 0.0 -1.0 Figure 8. The wave aberration map for subject NH when wearing soft contact lens. The interval between contour lines is 0.5λ. Left (Temporal), Right (Nasal), Upper (Superior) and Lower (Inferior). The wavefront is centered at the superior temporal part of pupil. The asymmetric aberrations of eyes with RGP lenses are much smaller than those with other two optical corrections. Our data confirms Atchison’s theoretical prediction that the decentration of spherical RGP lens induced only small amounts of asymmetric aberrations. More importantly, the RGP lens provides the smooth spherical surface and neutralizes the asymmetric aberrations of the cornea by filling in corneal irregularity with tears.

The reduced amounts of asymmetric aberrations contribute to the superior visual performances of RGP lenses.

b Longitudinal spherical aberration (LSA) Longitudinal spherical aberration is usually defined as the difference between axial dioptric powers for paraxial and marginal rays. Positive spherical aberration means that the power is greater for marginal rays than for paraxial rays. Using these conventions we use the wavefront aberration function to calculate the amount of spherical aberrations of eyes wearing different optical corrections and the results are shown in Figure 9. Both types of contact lenses

changed the amount of spherical aberrations in the negative direction when compared to the spectacle control condition.

This resulted in less positive spherical aberration for those subjects (CB, NH, PP) who had positive aberration in the control condition and more negative aberration for the subject (KF) who had negative aberration in the control condition. These results may help explain why correcting myopia with a contact lens sometimes gives better vision than for spectacles since the amount of positive spherical aberration can evidently be reduced by the lens.

Figure 9. The spherical aberrations of spectacle and soft, RGP lenses for subject CB, KF, NH and PP. The positive value of the spherical aberration means stronger power at the pupil margin. Discussion Relative performance of hard and soft contact lenses For our 4 subjects, the reduced corneal aberrations produced by RGP lenses resulted in better optical performance of the eye. However, this is not necessarily a general rule because in some individuals the aberrations of the cornea compensate for the aberrations of the crystalline lens, resulting in an eye with little net aberration. If the corneal aberrations of such an eye were to be neutralized by an RGP lens, the balance between cornea and crystalline lens would be upset and the net aberrations of the whole eye would increase.

Thus we understand an otherwise paradoxical situation in which the reduction of corneal aberrations with an RGP lens could increase the aberrations of the whole eye.

Asymmetric aberrations

Optical modeling suggests that asymmetric aberrations introduced by decentration of RGP lens are small [Atchison, 1995]. Nevertheless, we attempted to avoid any such aberrations by waiting for the contact lens to settle on the eye for 3 seconds after a blink before taking aberration measurements. Thus, the amount of asymmetric aberrations of the eye when corrected by the RGP lens may have been greater immediately after a blink. Further experimentation would be required to answer this question. Present results support the hypothesis that the irregularity and asphericity of the anterior cornea was more or less transferred to the flexible anterior surface of the SH lens and was eliminated by the rigid surface of the RGP contact lens.

This suggests that the quantitative aberration analysis described in this report may prove useful in the future to measure the conformity of soft lenses. Longitudinal spherical aberration (LSA) Our finding that spherical aberration changes in the negative direction when myopia is corrected by contact lenses is consistent with previous theoretical predictions [Cox, 1990; Atchison, 1995]. There are two apparent reasons for the change. First, the anterior surface of a contact lenses with negative power has larger radius of curvature than does the natural cornea, which therefore reduces the amount of positive spherical aberration contributed by the anterior corneal surface.

Second, correcting myopia with spectacles changes spherical aberration of the eye in a positive direction because a negative spectacle diverges rays (see Figure 1), thereby increasing the angle of incidence of rays compared to an emmetropic eye with the same corneal shape. Thus the control condition of spectacle correction is biased in the direction of positive spherical aberration. By switching to a contact lens, this bias is removed and, at the same time, the shape of the anterior refracting surface is altered, again in a direction which reduces the amount of positive spherical aberration of the eye.

Thus both factors work in concert to reduce the eye’s positive spherical aberration.

The reduction of spherical aberration was found to be much less for RGP lenses than for SH lenses. This difference can be explained by the different asphericity values of the lenses on the eye. Soft contact lenses conform to the cornea, at least to some extent, thus preserving the relatively small amounts of spherical aberration of the natural cornea. To the contrary, a hard lens with spherical surfaces will replace the natural cornea with a surface that has a large amount of positive spherical aberration. Thus the net change in the negative direction produced by the two mechanisms described above will be less for RGP lenses compared to SH lenses.

Comparison with optical models Cox’s optical model of a soft lens on the cornea can be used to account for the measured differences of longitudinal spherical aberrations between SH lenses and spectacles [Cox, 1990]. According to Table 4B in Cox’s paper, the combined cornea + SH lens of subject KF (Rx=-5.50D, r=7.365mm and p=0.6329) should have 0.33D of spherical aberration and subject NH (Rx=-6.50D, r=7.739 and p=0.8956) should have 0.95D of aberration for a 6mm pupil. By comparison, the

spherical aberration for the spectacle + cornea combination can be calculated by ray tracing method if the corneal topography is known.

We therefore gathered toptography information for two subjects (KF, NH) using the EyeSys, Inc. corneal topographer. The spherical aberrations for spectacle/cornea combination was computed to be 1.769D for KF and 2.303D for NH. Therefore the difference between soft lens and spectacle conditions should be -1.47D for KF and -1.35D for NH, which is very close to the experimental results of -1.54D for KF and - 1.56D for NH reported in Fig. 9.

The small remaining discrepancy may be due to (a) the slightly different fitting factor (about 1.16) for subject KF and NH compared to the fitting factor (1.10) in theoretical calculation and (b) the mechanism and the degree of conformity. A previous study [Plainis & Charman, 1998] indicated that the power of the tear lens could vary in the range from –0.48D to 0.38D. The same source can also contribute to the aberrations of the soft lens + eye system. The test of the existing flexure hypotheses by the differences of back vertex powers between on-eye and in vitro narrowed down the candidates of good flexure hypotheses, but still can’t determine which one actually represented the reality of conformity [Plainis & Charman, 1998].

Perhaps by using aberration analysis associated with the conformity, we may come to understand how the soft lens conforms to the cornea.

The differences of spherical aberrations between RGP lens and spectacle reported in Fig. 9 were also in agreement with theoretical prediction. The spherical aberrations are 1.39D for KF and 1.30D for NH for RGP lens + cornea combination for a 6mm pupil (see Table 4A in Cox’s paper). Therefore the predicted difference should be –0.38D for KF and –1.00D for NH, which is consistent with the experimental difference –0.214D for KF and –1.33D for NH. The remaining discrepancy might be attributed to parameter changes in RGP lens caused by cleaning and handling which is well-documented in the literature [O’Donnell, 1994].

Acknowledgement This study was supported by NEI grant R01-EY05109 from the National Institutes of Health. X. Hong is supported by the SOLA Graduate Fellowship in Ophthalmic Optics. References 1. P. Artal and A. Guirao, "Contributions of the cornea and the lens to the aberrations of the human eye", Opt. Lett., Vol. 23, 1713-1715, 1998. 2. D. A. Atchison, "Aberrations associated with rigid contact lens", J. Opt. Soc. Am. A, Vol. 12, No. 10, 2267-2273, 1995. 3. G. L. Bauer, "Longitudinal spherical aberration of modern opthalmic lenses and its effect on visual acuity", Appl. Opt. 19, 2226-2234, 1980.

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