The paraxial power of a thin lens is proportional to the difference in curvature of its front and back surfaces, with a constant of proportionality equal to the difference in refractive index between the lens and the surrounding material: *P* = (Δ*n*)/(1/*r*_{1} − 1/*r*_{2}). Likewise, a thin conforming soft contact lens (SCL) will change the refracting power of an eye by changing the curvature of the air/eye interface by the difference in curvature of its front and back surfaces. Because of this, the power of a thin SCL in air will approximate its refractive effect on the eye.^{1,2} These two values may not be identical, however, for a combination of several reasons. First, a SCL may fail to conform to the cornea, creating an effective “tear lens” between the lens and cornea, as occurs with gas-permeable lens fittings.^{1,3,4} Second, the lens may change shape and relative thickness while on the eye.^{5} This latter scenario is often termed “lens flexure” and is thought to be the primary source of undercorrection by high plus-powered SCLs,^{5,6} with increasingly plus-powered lenses losing more power (e.g., 0.50 undercorrection with +5.00D lenses,^{5, 6} and around 1.00D undercorrection with +10.00D lenses^{6}). It is possible that these two hypotheses can occur simultaneously. The term “supplemental power effect” has been used to describe this scenario, where a lens shape and/or thickness change may occur in combination with an optically powered nonuniform thickness tear layer or “lens.”^{3,4}

To confirm that some on-eye interaction effect (e.g., flexure) is responsible for the observed differences between expected and observed refractive effects of SCLs requires that the optical characteristics of SCLs be measured off-eye. However, the same physical characteristics of SCLs (e.g., edge and center thicknesses of <0.07 mm, elastic modulus as low as 0.4 MPa for silicone hydrogel lenses, and water content as high as ≥60%), which make them ideal for on-eye comfort and biocompatibility, make them difficult to measure in air. In this case, the SCLs will dry out quickly^{7–9} and deform under their own weight.^{10} An alternate strategy is to measure the lenses in a wet cell and scale the observed optical effects by the ratio of refractive index differences.^{1,11,12} In water, a SCL is approximately neutrally buoyant, fully hydrated, and surrounded by a uniform refractive index. To use this scaling strategy, however, an accurate estimate of lens refractive index is required.

In addition to designing SCLs with controlled amounts of sphere power, there are now numerous designs that include controlled levels of spherical aberration (SA).^{13–16} Also, the level of SA varies approximately linearly with sphere power in spherically surfaced SCLs^{2,11} as predicted by geometric optics.^{17} In this study, we used two types of Shack-Hartmann wavefront aberrometers to measure the sphere power and SA of several common SCLs on the eye and in a wet cell. We specifically examine the hypothesis that lenses *with* flexure-induced changes in sphere power will also exhibit changes in higher order aberrations.

#### METHODS

We used two Shack-Hartmann wavefront aberrometers (AMO-Wavefront Sciences, Albuquerque, NM) to measure the optics of SCLs on and off of the eye. A COAS-HD clinical aberrometer was used to quantify the monochromatic aberrations of the naked eye and the eyes wearing various contact lenses. A single-pass ClearWave contact lens aberrometer was used to measure contact lenses off of the eye while the SCLs rested in a saline-filled wet cell.^{11}

Assuming conformity of the lens to the corneal anterior surface, and a uniformly thin tear layer, the change in the eye’s optical path length (OPL) produced by an SCL when on the eye should be equal to the OPL of the contact lens in air. This issue is most commonly described in terms of SCL lower order aberration (i.e., power),^{18} but the concept holds true for all optical aberrations. Both when in air and when on the eye, the contact lens replaces air in the optical path with the contact lens material. Consequently, lens optical measurements taken in air require no special conversion to the on-eye optical impact of the lens. However, measurements taken in the saline-filled wet cell require conversion to in-air equivalent power and thus on-eye refractive impact. The expected paraxial power (*D*) of the contact lens in air, *P*_{air}, can be determined from the measured power in water, *P*_{wet}, with knowledge of the lens base curve radius (*r*_{2}, in meters), the refractive index of the lens (*n*_{lens}), the refractive index of the solution (*n*_{sol}), and center thickness of the lens (meters, *d*) using Equation 1,

where *c*_{1} is determined by Equation 2,

and *P*_{wet} is the measured power of the lens in the wet cell (in diopters).^{19,20} (For additional details on the derivation of the exact wet-to-in-air conversion equation, see Kollbaum et al).^{11}

The equation used to convert wet cell to in-air equivalent values for higher-order aberration is a simplified version of Equation 1 and is shown in Equation 3,

where *Z* is any given Zernike term or series of terms.^{11,20,21} This approximation, which assumes a lens center thickness of zero, ignores the minor effects of wavefront propagation between the two surfaces, which is appropriate given the lens thicknesses of less than0.1 mm and the low levels of higher-order aberrations typically encountered in contact lenses.

To calculate the expected on-eye or in-air performance of lenses from data collected in the wet cell (see Equations 1 to 3), an accurate estimate of the lens refractive index at the ClearWave measurement wavelength of 540 nm is required. However, these refractive index data may not be available for all lenses. ANSI ISO 9342 specifies two wavelengths at which index values can be reported for contact lenses: 546 and 587 nm.^{22} However, many of the instruments commercially available and used by manufacturers to measure refractive index, such as the CLR 12-70 (Index Instruments, Cambridge, UK) and Arias 500/600/700 (Reichert, Depew, NY) report refractive index at 589 nm. Furthermore, there have been reports of difficulties in measuring the index of some silicone hydrogel materials^{23} (Vogt A, personal communication, 2011).

The impact of small errors in refractive index can be seen in an example shown in Fig. 1. Using the manufacturer-provided refractive index of 1.426 for the PureVision silicone hydrogel sphere lens to convert wet cell measurements to in-air powers, the data are best fit by a line with a slope of 0.91, indicating too little plus and too little minus power (black line). However, when we alter the refractive index estimate instead to 1.416, the data are well fit by a line with a slope of 1.00 (95% confidence interval [CI], 0.99 to 1.01) (gray line). Therefore, using this lower refractive index, the off-eye data more closely agree with the nominally labeled power. This highlights the importance of an accurate estimation of lens refractive index when using a single-pass lens-only aberrometer like the ClearWave to predict the on-eye or in-air power.

Given the potential inaccuracies in determining the refractive index of contact lens materials, and the lack of understanding of what the refractive index of the lens truly is at the time of measurement, if the off-eye data for a given lens seemed to have a power that was a scaled version of the expected power (observed versus expected slope not equal to 1, but a correlation coefficient of >0.99), we assumed that our initial estimate of the refractive index was in error, and we used a revised index estimate that produced a slope closest to 1 (i.e., 95% CI included 1). This adjustment was only required for the two silicone hydrogel lenses evaluated, which indicates that the reported refractive index estimates of silicone hydrogel materials are not sufficiently accurate, consistent with reports indicating that they are more difficult to obtain^{23} (Vogt A, personal communication, 2011).

The COAS-HD aberrometer uses an infrared (850 nm) super-luminescent diode as the light source, and uses a Shack-Hartmann lenslet array to sample 1541 spots over a 7-mm-diameter pupil (spatial resolution at the pupil plane of 158 μm) to measure the lower- and higher-order aberrations of an eye. We computed the optical impact of the contact lens on the eye using the method of Dietze and Cox^{2} where the wavefront error (WFE) of the SCL (WFE_{SCL}) = the WFE_{(eye plus SCL)} − WFE_{(eye alone)}. Off-eye measurements of SCLs used a single-pass ClearWave aberrometer in which a collimated 540-nm visible light source and a 101 × 101 lenslet array with a 10.4 × 10.4-mm field of view, providing a spatial resolution of 104 μm.^{11}

To compare the two methods, differences in source wavelength and plane of measurement had to be compensated for. First, the ClearWave aberrometer measures the lens optics using 540 nm wavelength visible light, whereas the COAS aberrometer uses a 840-nm wavelength infrared light. Although expected to cause a very small difference, all COAS aberrometer-measured coefficient values were converted to their 540-nm reference equivalent values to match the wavelength used by the ClearWave aberrometer, using a method in which a reduced eye model is constructed by adjusting the length of the Indiana Eye model to make the model emmetropic for the original wavelength. Then, an aberration-free Cartesian oval was perturbed to account for the measured wave aberration. From this the optical path difference between the aberrated wavefront and the Cartesian oval of a field of marginal rays and a central ray were found at 540 nm by changing the refractive index of the model.^{24–26} This approach is described in detail in the study of Ravikumar et al.^{27}

Second, the ClearWave instrument is designed to provide a detailed description of the lens optics relative to the contact lens back vertex, whereas the COAS aberrometer quantifies the eye/lens optics at the entrance pupil plane. We corrected for the wavefront propagation distance between the pupil plane and lens back vertex, assuming this distance to be 3 mm (based on the estimated difference between the cornea and entrance pupil plane). The method used was identical to that commonly used in the clinical setting to “vertex” a spectacle prescription to a contact lens prescription (Equation 4), where *F*_{PP} is the power of the lens at the pupil plane and *F*_{BV} is the power of the lens at the lens back vertex.

Because the higher-order Zernike coefficients are typically small (e.g., ≪1 μm), and the difference in distance between these two measurement planes is also small (e.g., 3 mm), this propagation effect was ignored in our analysis of higher-order aberrations. In addition, we have previously shown experimentally that axial misalignments of higher-order aberrometry measurements of this magnitude have little impact.^{28}

Paraxial sphere powers were obtained by first converting the Zernike coefficients into the power vector components *J*_{0}, *M*, and *J*_{45}.^{29} We found the paraxial spherical equivalent, *M*, by Equation 5,^{30} which effectively sums the *r*^{2} components of both *C*_{2}^{0} and *C*_{4}^{0}.^{29}

Astigmatism (first order) was included in the determination of the final clinical paraxial sphere power, using the methods of Thibos et al.^{29} Zernike SA was converted to the clinically relevant units of peak-to-valley longitudinal spherical aberration (LSA) at the pupil margin by Equation 6,

where LSA is the longitudinal spherical aberration in diopters, *C*_{4}^{0} is the OSA-normalized Zernike SA coefficient value in micrometers, and *r*^{2} is the pupil radius in millimeter squared.^{11} For the current study, the analysis radius was always 3 mm.

Both eyes of the subject were pharmacologically dilated with 1% tropicamide and 2.5% phenylephrine to ensure a large pupil size and to help minimize accommodation. Repeated instillations of both medications occurred halfway through the 2-hour testing period to ensure a sustained effect. All lenses were fit according to the manufacturer’s fitting guides and were allowed to stabilize for 15 minutes after insertion before taking a measurement. To minimize the effect of any local tear film changes, blink-induced lens movements, and any residual accommodation five repeated measurements were taken, and the Zernike coefficients over a 6-mm analysis diameter corresponding to each single measurement were averaged to represent the result for that “trial.” Each individual acquisition was taken immediately after the investigator-observed (through the instrument alignment camera) approximate stabilization of the lens on the eye after a blink (i.e., 1 to 2 seconds after a blink). Subjects wore lenses of different types in the two eyes during testing (e.g., a series of lenses ranging from high minus to high plus power ACUVUE 2 lenses on the right eye and a series of lenses ranging from high minus to high plus power Frequency 55 sphere on the left eye). Not all lens type-power combinations were tested on all eyes/subjects, and several combinations were tested on many eyes. The range of overcorrection provided by the Badal refraction system inherent to the COAS instrument to measure and compensate for the sphere power of the eye limited the contact lens power testing range possible, so the lens testing range for each eye was tailored to each individual eye based on each baseline sphere equivalent refraction. Lens type-power combinations and testing order were randomized for each eye of each subject. Naked eye data were collected at the beginning and end of each lens measurement session, and the Zernike coefficients were averaged to yield a baseline level of eye-alone aberration to use in the analysis.

The parameters of the contact lenses (as reported by the manufacturers in the respective product inserts) used in the series of experiments described below are shown in Table 1. In the current study, we refer to the powers reported on the lens labels (as determined by the manufacturers) as the “expected power.”

The optical effects of lens flexure are minimized when the refracting medium at the anterior surface closely matches that at the posterior surface (e.g., if lens deformations are mirrored on the front and back surfaces, their optical impact will approximate zero when *n*_{1} = *n*_{2}),^{11} as is the case in the ClearWave, where the contact lens is sitting entirely in a wet cell. Previously, comparisons of rigid and soft CLs measured with the ClearWave found flexure effects within the saline-filled cell to be quite small (<0.1D LSA for lenses ±10D).^{11} On the eye, however, any flexure effects at the front surface of the lens will only be partially cancelled at the posterior surface because of the difference in refractive index of the tears and air. In addition, with any lens flexures, a corresponding tear lens could be formed (e.g., as in GP lens).^{1,12}

A range of dioptric powers (e.g., −12.00 to +8.00 in 1.00D steps) for several different types of spherical hydrogel lenses (Focus Dailies [ALCON Vision Care, Duluth, GA], ACUVUE 2 [Vistakon, Jacksonville, FL], and Frequency 55 [CooperVision, Fairport, NY]) and spherical silicone hydrogel lenses (Air Optix Night and Day [ALCON Vision Care, Duluth, GA] and PureVision [Bausch + Lomb, Rochester, NY]) lenses were measured in the ClearWave and using the on-eye method on 30 eyes of 15 subjects over a 6-mm analysis diameter (for both instruments). In all, 104 different lens type/power combinations were evaluated. Each subject wore an average of six lenses on each eye. The paraxial sphere and LSA powers obtained (calculated using Equations 5 and 6 above, respectively) using these two methods were compared. This study followed the Declaration of Helsinki conventions and was approved by the Indiana University Institutional Review Board. Subjects were informed of the study purpose, procedures, and consequences, and written consent was obtained.

#### RESULTS

##### Paraxial Sphere Power

The first part of this study compared the measured sphere power to the manufacturer’s specified sphere power for spherical SCLs ranging in power from −12.00 diopters to +8.00 diopters. We present these data in observed versus expected plots (Figs. 2A–C), and of course, if the measured sphere power equals the observed, data should be well fit by a straight line with slope of 1.00 and intercept of 0.00. We also quantify any discrepancies between the observed and expected values using a Bland-Altman type of plot,^{31} in which the differences between observed and expected are plotted as a function of the expected (Figs. 2D–F). This type of plot provides insight into any systematic errors (mean slope and intercept of the difference data) as well as evidence of nonsystematic errors (95% CI for best fitting line).

The off-eye ClearWave-measured (observed) versus manufacturer-labeled (expected) lens paraxial sphere power for a series of ALCON Vision Care Focus Dailies sphere lenses is shown in Fig. 2A. The best-fit line of these data approximates the *y* = *x* line with a slope of 1.01, which is not significantly different from 1 (95% CI, 0.99 to 1.02), and an intercept of −0.03, which is not significantly different from 0 (95% CI, −0.10 to 0.04). These results indicate that the manufacturer’s lens specifications accurately represent the SCL power in air, as shown previously.^{11} The paraxial sphere results of the on-eye measurement method are best fit with a line with a slope of 0.95 and an intercept of −0.34, which are significantly different from 1 (95% CI, 0.94 to 0.96) and 0 (95% CI, −0.38 to −0.26), respectively. For negative lens powers, the data fall close to the *y* = *x* line, but on-eye positive lens powers are less than expected. Similar off- and on-eye data are shown for two other hydrogel spherical lenses, (Vistakon ACUVUE 2 shown in Fig. 2B and CooperVision Frequency 55 sphere shown in Fig. 2C). In both cases, the off-eye measurements are as predicted by the manufacturer, whereas the on-eye measurements show reduced plus power with increasing positive lens powers.

These subtle deviations in the on-eye paraxial sphere power from that expected can be seen more clearly in Figs. 2D to F, which plot the difference between the observed and expected powers on the *y* axis against the expected lens power on the *x* axis. In this graphical format, negative values indicate that the observed values were less positive or more negative than expected. The solid line marks the regression of the data and indicates the pattern of systematic errors; the solid ellipse, the 95% confidence estimate of the mean (plus sign); and the dashed ellipse, the 95% CI of the data. The slope of the off-eye Focus Dailies data (Fig. 2D) approximates the *y* = 0 line (*m* = 0.01; 95% CI, −0.01 to 0.02; *b* = −0.03; 95% CI, −0.10 to 0.04), indicating that the off-eye results show no systematic difference from expected. In this case, the 95% CI of the difference scores spans about +/−0.25D, indicating significant between-lens variability, which is significantly higher than the ±0.10D test-retest measurement variability of lenses previously found.^{11} When on the eye, negative-powered Focus Dailies lenses have effective lens powers close to expected; however, positive powered lenses are significantly underpowered, becoming between 0.50D and 1.00D underpowered at +6.00D labeled power. This negative slope seen in these on-eye data (*m* = −0.05; 95% CI, −0.06 to −0.04) has an *x* intercept at about −5.00D, indicating that both low-powered negative lenses and positive-powered lenses generally are more negative or less positive than expected (*b* = −0.32; 95% CI, −0.38 to −0.26). These differences are probably clinically insignificant, except for the highly positive lenses.

The results for the ACUVUE 2 (Fig. 2E) and Frequency 55 (Fig. 2F) lens show similar trends. Off of the eye, neither of the slopes were significantly different from 0, indicating no trend in the difference from expected as a function of lens power. However, the Frequency 55 lenses had an intercept that was very slightly but significantly greater than 0 (*b* = 0.08; 95% CI, 0.01 to 0.14), indicating that the measured lenses typically were of higher plus/less minus power than expected. On the eye, the ACUVUE 2 lens again demonstrated trends similar to the Focus Dailies lens (slopes and intercepts significantly different from 0), with both low-powered negative lenses and higher positive-powered lenses generally having more negative or less positive than expected. However, the Frequency 55 lenses were more variable on the eye, and more negative/less positive power was found across the full power range of lenses (mean observed − predicted power = −0.33D). Because off-eye measurements for the Frequency 55 were not more variable than other lenses, yet the on-eye measurements were, the observed variability reflects between-subject variability in how the lenses combine optically with these eyes.

##### Importance of Precise Knowledge of Contact Lens Refractive Index

Using the same graphical approaches as Fig. 2, Fig. 3 shows the observed versus expected (Figs. 3A and B) results for the silicone hydrogel PureVision and Air Optix Night and Day lenses, respectively. As expected from our index optimization of these lenses, for both lenses, the slopes of the off-eye observed versus expected data were not significantly different from 1. In addition, the intercepts did not differ significantly from 0. The on-eye data for the PureVision lens show reduced plus power with increasing positive lens powers (Fig. 3A). The positive- and negative-powered Night and Day lenses (Fig. 3B) appear quite similar to the expected and to the off-eye data. The difference (observed − expected) plots (Figs. 3C and D) show that, when on the eye, the PureVision lenses tended to have less minus and less plus power than observed off-eye (*m* = −0.10; 95% CI, −0.14 to −0.06) with on-eye effective lens power of the high plus and high minus lenses differing by greater than 0.50D from expected. The observed − expected on-eye data for the Night and Day lenses did not show this pattern, but interestingly, the wet cell measurement of these lenses revealed a small but consistent minus bias of about −0.20D.

##### Longitudinal Spherical Aberration

Generally, spherically surfaced negative lenses generate negative SA, while spherically surfaced positive lenses generate positive SA in direct proportion to their sphere power.^{17} Mahajan^{17} described a nonlinear equation (Equation 7) to calculate the expected SA of a thin lens (*a*_{s}) (in micrometers at the edge of the pupil of radius (*r*)) based on the front (*R*_{1}) and back surface (*R*_{2}) radii, pupil radius in meters (*r*), and refractive index (*n*) of the lens material.

Redistributing this equation to eliminate unknown terms, assuming a position factor (*p*) of −1 for a distant object and substituting in a shape factor (*q*) = (*R*_{2} + *R*_{1})/(*R*_{2} − *R*_{1}), and 1/*f* ′= (*n* − 1)(*R*_{2} − *R*_{1})/(*R*_{1}*R*_{2}), we arrive at Equation 8.

This result (LSA at pupil margin) is then divided by to get the *Z*_{4}^{0} coefficient, which can be converted to LSA in diopters using Equation 6. Using this equation, *n* of 1.39 and *R*_{2} of 8.7 mm, we predict 0.0259 μm of *C*_{4}^{0} per diopter of power for a distant target.

This theoretical expectation of Mahajan was confirmed by Dietze and Cox^{2} who used ray tracing to evaluate the expected SA of SofLens 66 lenses (Bausch + Lomb) as a function of lens power. They also used an on-eye technique to measure the SA of these same lenses on the eye. In general, their modeled and on-eye results were quite close (slopes of best-fitting straight lines of 0.0277 and 0.0267 μm Zernike SA/D power and intercepts of 0.0088 and 0.0363 μm, for the modeled and on-eye results, respectively). However, as evidenced by the intercept differences in the best-fitting regression lines, they observed slightly more positive SA in the on-eye case than predicted by ray tracing.

A direct comparison between the theoretical prediction of Mahajan^{17} (calculated based on the manufacturer-reported refractive index and base curve) and our on- and off-eye experimental results for a series of Focus Dailies lenses is plotted in Fig. 4. The Mahajan^{17} predictions have been converted from micrometers to a more clinically relevant unit of measured longitudinal SA (LSA) (dioptric difference between the focus of a paraxial and a marginal ray at a radius of 3 mm; see Equation 6). In this case, the Mahajan prediction for an unflexed lens (solid line in Fig. 4) is 0.155D of LSA per D of spherical power. We also include a second prediction from Mahajan with slightly different parameters, with a flexed base curve radius (*R*_{2} = 7.3 mm), which generates more SA (slope = 0.18D of LSA per D of power; dot-dashed line in Fig. 4). This result shows how sensitive SA is to the lens base curve. Both the on- and off-eye measures of LSA were generally close to the predictions of Mahajan^{17} in the maximum flexure case, which used the steeper base curve radius, but were always greater than the minimum flexure prediction of Mahajan in which the manufacturer-specified lens base curve radius was used. These measured results were similar to the results reported by Dietze and Cox,^{2} who found slopes of 0.17D and 0.16D of LSA per D of sphere, respectively, with the SofLens 66 lens.

Similar trends in LSA are shown for the ACUVUE 2 (Fig. 5A) and Frequency 55 (Fig. 5B) lenses, both revealing similar on- and off-eye levels of SA that do not follow the minimum flexure predictions of Majahan (solid lines) but generally follow the predictions of Mahajan if the base curve were maximally flexed (dot-dashed lines). In all cases, the prediction was based on the parameters for each specific lens type (linear fits to off-eye data each have slopes of 0.20D of LSA per D of sphere). A somewhat different pattern of LSA is seen with the PureVision (Fig. 5C) and Night and Day (Fig. 5D) silicone hydrogel lenses. The approximately linear relationship between LSA and sphere power is only seen in the off-eye LSA data of the PureVision lenses (Fig. 5C); the observed on-eye LSA with higher-powered negative lenses deviates significantly from this pattern, indicating some significant on-eye flexure, specifically a flattening of the lens radius or tear lens. Interestingly, the negative-powered Night and Day silicone hydrogel lenses (Fig. 5D) follow the trend observed with the hydrogel lenses and that expected from geometric optics. In the positive-powered Night and Day lenses, however, LSA is generally unaffected by sphere power both on and off-eye, indicating a potential asphericity inherent or designed into these lenses.

Knowledge of the actual intended level of LSA within a lens design is not readily available (e.g., cannot read off of the packaging as with sphere power) and generally not specified for typical spherical lens designs. Therefore, it is generally not possible to compare our observed measures of lens LSA to those intended by the manufacturer. We were, however, fortunate to obtain the manufacturer-designed and expected level of LSA for the Focus Dailies lens design (ALCON Vision Care, technical communication). The observed versus expected LSA for the series of Focus Dailies sphere lenses is shown in Fig. 6. The regression line fit to the off-eye data (Fig. 6A, black line) approximates the *y* = *x* line with a slope of 1.00, with a slightly positive *y* intercept (intercept = 0.14D, 95% CI, 0.02 to 0.27). The on-eye measured LSA (gray symbols and line) of the lenses appear close to the expected values for minus lenses (minus lenses predict minus LSA), but there is a negative bias over most of the power range, resulting in a slope and intercept that differ significantly from 1 and 0, respectively (slope = 0.77; 95% CI, 0.66 to 0.87; intercept = −0.31; 95% CI, −0.46 to −0.17). The difference between these two data sets indicates a significant change in lens optics when on the eye.

Again, these subtle differences in LSA from expected can be seen more easily in plotting the differences from the expected (*y* axis) against the expected lens power (Fig. 6B). As stated previously, in this graphical format, negative values indicate that the observed values were lower than expected. The solid line marks the regression of the data; the solid ellipse, the 95% confidence estimate of the mean (plus sign); and the dashed ellipse, the 95% CI of the data. In this example, the off-eye data (black circles) approximate a line with a slope not significantly different from 0 (−0.00; 95% CI, −0.02 to 0.02), but with the *y* intercept significantly different from 0 (0.15; 95% CI, 0.03 to 0.27). The on-eye data (gray squares) reflect a slope (−0.06; 95% CI, −0.08 to −0.03) and intercept (−0.31; 95% CI, −0.46 to −0.17) significantly different from 0.

#### DISCUSSION

This study has used two methods for assessing the optical performance of SCLs, one in a saline-filled wet cell and one with the lens on the eye. Both approaches generate accurate and precise measurements of lower- and higher-order monochromatic aberrations,^{11,28,32} and we used both to compare the on- and off-eye aberrations of defocus and SA observed over a wide dioptric range of three hydrogel and two silicone hydrogel contact lenses. The wet cell provides neutral buoyancy and stable hydration and thus largely avoids the mechanical forces and hydration fluctuations that might be present when on the eye. Differences between the two datasets, therefore, provide a direct experimental method for separating lens-specific (e.g., manufacturing process) from on-eye flexure and/or tear lens contributions to the optical imperfections of SCLs. To make these comparisons, however, accurate refractive index data are required to convert in-water measurements to expected in-air and thus on-eye performance. Our observations indicate that the specified refractive index of silicone hydrogel lenses may not be precisely correct. For example, in order for the off-eye data to match the on-eye performance, the effective refractive index estimate at 540 nm had to be modified from 1.426 to 1.416 for PureVision and Night and Day lenses, respectively. These minor alterations in the refractive indices of silicone hydrogel lenses were all within error estimates previously reported^{23} (Vogt A, personal communication, 2011), which may also be significantly affected by minor temperature changes (e.g., wet cell solution temperature was typically around 78°F, whereas corneal temperatures may typically approach upward of 95°F).^{1} The refractive index values obtained for the hydrogel lenses provided off-eye power measures that were indistinguishable from the manufacturer’s reported powers, indicating that these refractive index estimates (Table 1) were correct.

Measuring the optical properties of SCLs on the eye does not require knowledge of refractive index. However, the on-eye optics of SCLs include two additional components. First, any failure of the SCL posterior surface to conform to the cornea will generate a “tear lens” between the two, which increases the OPL or product of the physical distance and the refractive index of the medium. In the case of a tear layer filling the space between the posterior contact lens and anterior cornea, the OPL would be increased by an amount that varies across the diameter of the lens. This change in OPL can introduce changes in power and higher-order aberrations. Alternatively, the very process of conforming can alter the relative thickness of an SCL, called “lens flexure.” Similarly, in this second case, these regional changes in OPL within the lens can also change the power and higher-order aberrations. Conformation and failure to conform are known to influence the optical effects of SCLs. Indeed, there is a long history of studies attributing unexpected refractive effects of gas-permeable^{1,12} and soft-contact^{3–6,33–52} lenses to their failure to conform to the anterior corneal surface and/or lens flexure. Our measurement methodology generated similar differences between observed and expected sphere power as some of the earlier studies. Fig. 7 plots the difference data from two hydrogel lenses (circles, black line) of the current study and best-fit lines representing data from the previous results of Holden et al,^{6} Weissman,^{50} the equal percentage change hypothesis,^{40} equal-change hypothesis,^{3} and Plainis and Charman.^{5}

On the basis of the hypothesis that the SCL completely conforms to the corneal surface., the optical effect of the contact lens on the eye can be determined as the difference between the optics of the eye wearing the contact lens and the eye alone,^{1,2} in which case subtracting the off-eye or expected power of the contact lens from this total would yield 0. However, the current study found that this is not always the case and that there are residual or supplemental optical effects due to a combination of on-eye lens thickness or shape changes and/or the creation of an optically powered tear layer between the contact lens and cornea (Fig. 8).

If we make the simplifying assumption that the on-/off-eye differences are due entirely to the formation of a tear layer, we can divide the *WF* differences observed on-eye from those observed off-eye by the difference between the index of refraction of air and that of tears to estimate the change in thickness of the this tear film across the pupil (*Dt*) (Equation 9).

Equation 9 could also be used to determine lens thickness changes caused by lens flexure by substituting the index of refraction of the lens (*n*_{lens}) instead of that of the tears (*n*_{tear}) (e.g., OPL changed by adding more lens material for light to pass through). This analysis is shown schematically in the top row of Fig. 8, which shows sample data from ACUVUE 2 lenses, with corresponding sample wavefronts shown in the bottom row for each component of the numerator of Equation 9 in the bottom row. The current analysis presents results assuming that the differences in OPL are entirely due to tears, but these differences could also be due to lens flexure thickness changes, in which case they are merely approximately 83% (*n*_{tear}/*n*_{lens}) lower than what we report below.

Previous measures of postcontact lens tear film thickness have ranged from a minimum of 2.3 μm^{53} to around 4.5 μm^{54} to a maximum of 11.5 μm^{55} but have been restricted to one location on the cornea and to one or two low minus lens powers. We provide an estimate for tear thickness across the entire central 6 mm of the cornea for a range of lens powers. For low-powered lenses, the current results are quite similar to the results of Nichols and King-Smith.^{53} Because the WFE method for estimating tear lens thickness (Fig. 8) only documents changes in tear lens thickness, it will not include any uniform thickness component of the tear lens, and thus, methods that measure the actual tear lens thickness (e.g., OCT, interferometry) would always report a thicker tear lens than what we observe. Because optical imaging is unaffected by any constant (piston) term (at the visible and infrared wavelengths used in the current study),^{56} it is typically ignored when computing image quality.

In reality, this difference between on- and off-eye lens measurements will also contain the impact of any on-eye lens decentrations as well as these tear lens and lens flexure optical differences. For example, Guirao et al^{57} predicted the induction of prism and coma from the decentration of lenses containing sphere and SA. Presumably, on-eye flexures and/or tear lenses could be asymmetric in nature and, therefore, accordingly contain levels of prism and coma. However, in the current analysis, we make the assumption that any extra coma introduced when the SCL is on the eye is a result of lens decentrations, and thus, we did not include these in our calculations of lens flexure/tear lens.^{11}

The top row in Fig. 9 shows the results of using Equation 9 to quantify the thickness (μm) of the tear layer under the entire lens surface necessary to fully account for the differences observed on- and off-eye for a +1D, +4D, and +8D Vistakon ACUVUE 2 lens. As predicted by the very similar on- and off-eye performance of low-powered plus lenses, low-powered lenses generate virtually no tear lens, whereas higher-plus lenses have a very thin central tear thickness but an increasingly thick periphery. This is the classic negative-powered “tear lens” encountered with gas-permeable lens fitting.^{1} For example, a +1D lens has a maximum tear thickness under the entire lens surface of only 2.32 μm (mean [SD], 0.89 [0.14] μm), whereas a +8D lens has a max tear thickness of 15.91 μm (mean [SD], 12.15 [1.17] μm). It is plausible that the thicker high plus power lenses will act more like a rigid gas-permeable contact lens conforming less to the cornea. Therefore, in these high plus lenses, it is likely that the differences between on- and off-eye performance with these lenses are due to a tear lens. Alternatively, because negative power SCLs can have very thin centers (e.g., 50 to 60 μm), it is likely that they conform well to the cornea^{2} and on-/off-eye differences reflect lens flexure not a tear lens.

The differences between on- and off-eye WFE data observed in the current study may in fact not be just a tear or lens thickness change but a combination of tear lens and lens flexure, which has been referred to as a “supplemental power effect.”^{4}

The reduced plus power of the SCL on the eye predicts a reduction in positive SA. Also, because the lens is, presumably, conforming to some unknown combination of the cornea and tears, there is added potential for changes in SA as well as changes in lens paraxial power. Indeed, our on-eye measurements of SA fail to mirror those of the same lenses in the wet cell, indicating that the lens-eye interaction can alter SA as well as spherical power. This issue becomes significant when we consider that many modern lenses are designed to introduce controlled levels of SA, such as aspheric lenses (e.g., CooperVision Biofinity, Bausch + Lomb PureVision), multifocal lenses (e.g., Bausch + Lomb PureVision Multifocal, ALCON Vision Care AirOptix Multifocal), or custom aberration-correcting lenses.

It is important to note that the calculations of flexure effects reported here may contain variability from several sources. Off-eye measurements show that variability (e.g., Fig. 2D, black symbols) of roughly ±0.25D exists due to either the off-eye measurement or the manufacturing process. This amount of variability is significantly higher than the test-retest variability previously reported^{11} and is believed to be largely due to manufacturing. The more variable on-eye results (e.g., Fig. 2F, gray symbols) clearly identify that lenses will conform differently on different eyes, resulting in a slightly different amount of flexure-induced optical change depending on the eye on which the lens is placed. However, when evaluating these trends across the sample population (as a function of lens power), the current results approximate previous reports in the literature using different techniques.^{5,6}

#### CONCLUSIONS

The results of the current study indicate that if lens refractive index is known precisely, off-eye measures of lens power and SA are mostly as expected, but on-eye measurements indicate lenses often have less power and SA. These optical differences can be accounted for by on-eye changes in lens flexure resulting in local lens thickness and/or post-lens tear thickness changes. To achieve predictable and optimized performance with a lens design, knowledge of the optical impact of how the SCL conforms to the eye may be essential.

Pete S. Kollbaum

Indiana University, School of Optometry

800 E Atwater Ave

Bloomington, IN 47405

e-mail: kollbaum@indiana.edu