purpose. To evaluate the stability of clinical monochromatic aberrometry measurements over a wide range of time scales.

methods. Monochromatic aberrations in four normal eyes were measured with a clinical Shack-Hartmann aberrometer. A chin rest or a supplemental bite bar attachment was used to stabilize head and eye position. Five repeated measurements were taken within one test (5 frames, *t* < 1 second) without realignment. With realignment between each measurement, aberration measurements were repeated five times (*t* < 1 hour) on each day, at the same time of day on five consecutive days, and again on 5 days at monthly intervals. A control experiment studied the effect of systematically misaligning the eye to determine whether fixation errors can account for the variation in the repeated measurements.

results. Variability of wavefront root mean square (RMS) error (excluding defocus and astigmatism) was tracked across repeated measurements. Variances for different time scales were: 8.10 × 10^{−5} μm^{2} (*t* < 1 second), 3.24 × 10^{−4} μm^{2} (*t* < 1 hour), 4.41 × 10^{−4} μm^{2} (*t* < 1 week), 9.73 × 10^{−4} μm^{2} (*t* < 1 year). Bite bar and chin rest data were almost identical. Rotational fixation error up to 3° accounts for only part of the variability.

conclusions. Increased variability in aberration maps between days and months indicates biological fluctuations that are large enough to prevent achievement of “perfect vision,” even in the unlikely event that spherical and astigmatic refractive errors are corrected perfectly. However, lack of stability does not justify withholding treatment. A lasting benefit of aberration correction is expected despite temporal variability.

^{ 1 }

^{ 2 }

^{ 3 }

^{ 4 }or wavefront-guided corneal ablation.

^{ 5 }

^{ 6 }

^{ 7 }

^{ 8 }

^{ 9 }

^{ 10 }The success of these new technologies depends on the stability of the eye’s higher-order aberrations. By analogy with the example just given, correcting an eye with positive spherical aberration would be of little value and indeed would be detrimental, if the next day the eye had negative spherical aberration.

^{ 11 }Even in eyes that are changing due to progression of myopia, the rate of change is low (e.g., mean change up to approximately −0.50 D per year,

^{ 12 }

^{ 13 }with an SD of 0.25 D

^{ 14 }

^{ 15 }). In contrast to this picture of longitudinal stability, test–retest studies of refractive error indicate a substantial degree of variability in the measurement of refractive error.

^{ 16 }

^{ 17 }

^{ 18 }

^{ 19 }

^{ 20 }For example, repeated measures of spherical equivalent on the same eye by different clinicians can differ by up to ±0.75 D (95% limit of agreement).

^{ 16 }

^{ 17 }A similar degree of variability is found in repeated measures of astigmatism (e.g., 95% limit of agreement for cylinder power = ±0.80 D

^{ 17 }). Repeated subjective refractions by the same clinician can also vary by almost the same amount.

^{ 16 }Objective refractions with autorefractors tend to be less variable,

^{ 16 }

^{ 17 }but there is some question regarding their accuracy.

^{ 20 }This variability in the measured sphere and astigmatism is thought to reflect measurement error, rather than variability in the eye’s refraction, because stabilizing accommodation, which is the largest potential source of variability in spherical refractive error, increases test–retest variance.

^{ 16 }

^{ 21 }

^{ 22 }

^{ 23 }

^{ 24 }For example, for small and large pupil sizes, the wavefront variance (WFV) generated by higher-order monochromatic aberrations (third order up to seventh order) is less than would be generated by 0.25 D of defocus.

^{ 24 }Consequently, effective correction of higher-order aberrations requires a higher level of measurement accuracy and repeatability than the current standard of care for lower-order aberrations. Efficacy also requires that biological variability in the eye’s higher-order aberrations be significantly smaller than the mean level of aberration, which is already very small. In short, the eye must be stable and measurements must be reliable to assure the success of higher-order corrections.

^{ 25 }we examined the accuracy and stability of a clinical aberrometer based on a Shack-Hartmann wavefront sensor for measuring higher-order monochromatic aberrations of a series of model eyes. We found that measurement accuracy exceeded the manufacturing tolerances of the model eyes we used to perform the tests. Furthermore, test–retest variance was extremely small (e.g., the 95% probability range of five repeated measurements of higher-order aberrations for a single alignment was ±0.002 D and ±0.005 D for multiple alignments). Using this same instrument, we examined test–retest variability of higher-order aberrations in human eyes. The purpose of this report is to describe the stability of these higher-order aberrations over time scales of seconds, minutes, days, and months.

^{ 26 }

^{ 27 }We have confirmed, in a series of single-surface aspherical model eyes, that the COAS provides extremely accurate measures of lower- and higher-order aberrations over a larger range than we encountered in the present study.

^{ 25 }All the measurements were taken in a temperature- and humidity-controlled environment at the Borish Center for Ophthalmic Research at the Indiana University School of Optometry.

^{ 27 }

^{7}seconds in 1 year, this experimental design allowed us to study temporal variability of individual eyes over seven orders of magnitude of time. Initial concerns about the effects of head movements prompted us to supplement some of the measurements made using the manufacturer’s head and chin rest with a second set of data obtained with a rigid bite bar for head restraint.

^{ 25 }

*P*< 0.05 significance level) was used to compare the variances of aberration measurements for each subject at different time scales, and to establish whether variability increased over time. We also used ANOVA to compare aberrations measured with the two restraint methods (bite bar and chin rest). The overall variances at each time scale were calculated across subjects as follows. On the time scale of seconds, the between-frame variance was calculated for the five measurements taken within 1 second for each subject. We then averaged these variances across the four subjects and across the five repetitions made over 1 hour. On the hour time scale, the between-trial variance was calculated for five individual frames, one from each of five consecutive trials (e.g., the first frame in each trial). We then averaged these variances across the four subjects and across the five frames on each trial. On the week time scale, the between-day variances were calculated for individual trials across the 5 days for each subject (e.g., first trial on each day). We then averaged these variances across the four subjects and across the five trials on each day. On the year time scale, the between-month variance was calculated for individual trials across the 5 months for each subject (e.g., first trial in each month). We then averaged these variances across the three subjects and across the five trials in each month.

*M*e) is calculated with the following equation:

*M*e = 4√3·RMS/

*r*

^{2}, in which

*r*is the pupil radius in millimeters.

^{ 24 }As with RMS wavefront error, equivalent defocus quantifies only the amount of aberration in the eye and not its visual impact (Cheng X, et al.

*IOVS*2003;44:ARVO E-Abstract 2123; Applegate RA, et al.

*IOVS*2003;44:ARVO E-Abstract 2124).

^{ 28 }

^{ 29 }

^{ 16 }

^{ 17 }

*r*= 0.799,

*P*< 0.05) and one showed a decreasing trend (subject CT,

*r*= 0.473,

*P*< 0.05) in the levels of higher-order aberrations.

_{n}

^{m}).

^{ 26 }

^{ 27 }Each of these aberration coefficients may be examined separately for test–retest stability in a manner analogous to the tests on RMS error described earlier. A summary of this analysis is shown in Figure 5 for one subject (LT). A pyramid of box-and-whisker plots show how the mean amplitude of each Zernike coefficient varies with time scale (each graph shows data for all four time scales: S, second; H, hour; W, week; Y, year). Each row in the pyramid represents a different radial order (

*n*= 2–4), and the horizontal position in the pyramid indicates meridional frequency (

*m*= −4 to +4). A short horizontal line indicates the mean coefficient amplitude, the confidence interval for this mean (±2 SEM) is a box centered on the mean, and the 95% probability range (±2 SD) is shown by the error bars (i.e., whiskers). Visual inspection of these graphs reveals whether the mean values of individual aberrations modes are significantly different from zero (i.e., the box crosses zero). Had additional data been collected, we would predict that 95% of all new data would lie within the range denoted by the whiskers.

_{2}

^{0}, Z

_{2}

^{±2}, Z

_{3}

^{±1}, Z

_{3}

^{+3}, Z

_{4}

^{0}, and Z

_{4}

^{±2}) were statistically significantly different from zero at all four time scales. However, some modes were significantly different from zero only on some time scales (e.g., Z

_{3}

^{−3}, Z

_{4}

^{±4}, and so forth). As we saw in the total RMS data (Fig. 4) , the variability of repeated measurements of each aberration mode generally increased with longer time scales. Even in cases in which the mean aberration level is significant, the 95% probability range sometimes crosses zero, indicating that some of the significant aberration coefficients changed sign from one measurement to the next.

_{4}

^{−4}, a significant decrease in Z

_{4}

^{0}, and no significant change in Z

_{4}

^{−2}. These results demonstrate that using the overall RMS to determine the stability of aberrations can mask changes in individual Zernike coefficients.

*P*< 0.05) in each of the other two eyes. Although statistically significant, these six coefficients measured with the bite bar and chin rest were similar (mean absolute difference = 0.01 μm). We found no evidence of reduced variability in the bite bar data. In fact, the standard deviation of the measurements for each mode differed on average by only 0.0003 μm (slightly larger with the chin-rest than with the bite bar). These results clearly show that the increased head stability provided by the bite bar did not significantly reduce the variability in our data, and thus the increased variability in eye position observed with the chin rest

^{ 30 }

^{ 31 }is not a significant source of variability in our higher-order aberration data. However, we observed significantly more variability in the lower-order prism terms (Z

_{1}

^{±1}) with the chin rest than with the bite bar.

_{1}

^{+1}), horizontal coma (Z

_{3}

^{+1}), and horizontal–vertical astigmatism (Z

_{2}

^{+2}). Regression analysis of such data (e.g., horizontal coma, as shown in Fig. 8 ) allowed us to estimate the variability in eye rotation necessary to create the variability in these terms that occurs under normal fixation. In the case of horizontal coma, for example, to generate the 95% probability range in Z

_{3}

^{+1}of 0.0612 μm, the 95% probability fixation range would have to be 3.5°. Because fixation variability is approximately one order of magnitude smaller than this (95% probability range = ±0.2°

^{ 30 }), we conclude that fixational noise is not a significant contributor to the variability in measured aberrations.

^{ 25 }that used the COAS aberrometer to measure aberrations of model eyes, we found that repeated measures within a second produced almost identical aberration measurements (between frame variance of higher-order RMS = 1 × 10

^{−6}μm

^{2}). Over this same time scale, variance of RMS in the human eye data (variance = 81 × 10

^{−6}μm

^{2}) was 80 times larger (Fig. 9) . This comparison shows that the short-term variability in the human eye data does not reflect instrument noise, but most likely reflects changes in the eye’s optics, such as microfluctuation of accommodation, instability of the tear film, or small fixational eye movements, all occurring over a very short time scale. Second, although both eye position and rotation vary during any series of measurements, our control experiments indicate that these two factors have little impact on measure variability in aberrations. Third, our previous measurements in model eyes show that operator realignment between measurements introduces a significant but still small amount of variability into the data (between realignment variance of higher-order RMS = 92 × 10

^{−6}μm

^{2}in the model eye), which is approximately 3.5 times smaller than the between-trial variability (variance = 324 × 10

^{−6}μm

^{2}) in human eyes. Therefore, we conclude that 72% of the trial-to-trial variance of higher-order RMS can be attributed to the eye (again, due to accommodation fluctuation, tear film instability, and eye movements), and not instrument alignment. Finally, we note that the variability in the higher-order RMS wavefront error over multiple days and multiple months is even larger (e.g., 441 and 973 × 10

^{−6}μm

^{2}, respectively) than within a day. It indicates that the optical fluctuations of the eye are larger over longer time scales, which includes not only all the fluctuations that exist in shorter time scales, but also fluctuations that may reflect the genuine long-term changes in the eye’s optics.

*IOVS*2003;44:ARVO E-Abstract 2123; Applegate RA, et al.

*IOVS*2003;44:ARVO E-Abstract 2124). Therefore, any fluctuation in OTFs or other image-quality metrics may not directly translate to variation in quality of vision. For example, radial-averaged modulation transfer functions (rMTFs) computed for 2 days in the week for which the wavefronts were least similar are shown in Figure 10 (line 1–4) for two eyes (AB and CT). Lines 1 and 2 show rMTFs calculated from aberration maps that included the second-order as well as the higher-order aberrations on the 2 days. Lines 3 and 4 show rMTFs on the same 2 days calculated from just the higher-order aberrations by setting the second-order aberrations (defocus and astigmatism) to zero, which assumes perfect correction and zero fluctuations of spherical and astigmatic defocus. In both cases, and for both eyes, we can see that the rMTFs were virtually identical, even though the aberrations differed on the 2 days. This stability in rMTF is not surprising for subject AB, who had a very stable RMS (higher-order RMS differed by only 6% between these 2 days). Small differences can be seen in the higher-order rMTFs of subject CT (lines 3 and 4), in whom the higher-order RMS varied by approximately 20% between the two least similar days of the week. These two examples emphasize that the observed fluctuations in monochromatic aberrations do not translate into significant fluctuations in rMTF, even when the second-order aberrations are corrected perfectly.

^{ 10 }We therefore considered the potential impact of optical variability on image quality of an eye with full correction of higher and lower-order aberrations. For example, if we fully correct AB’s and CT’s monochromatic aberrations measured on a given day, we would expect the monochromatic rMTF to be diffraction limited on that day (Fig. 10 , line 7). However, as we have shown, these eyes had different aberrations on other days. Thus, the correction applied to eliminate aberrations on 1 day of the week is an inappropriate correction for the other days. The postcorrection level of aberration jumps from zero on the day of correction (assuming correction is perfect) to a small level of aberration on another day. This emerging low level of aberration is the difference of the aberrations measured on these 2 days. For the 2 days used in Figure 10 , higher-order RMS differs by 0.058 μm (0.04 D, AB) and 0.073 μm (0.06 D, CT). The postcorrection rMTFs on the day of the week with optics most different from the day of correction are shown in Figure 10 as line 6. In both eyes, rMTF has been reduced significantly below that of the perfect, diffraction-limited eye because of day-to-day variability. As expected, when only considering the anticipated higher-order aberrations, AB still has very high rMTF because this eye had very small day-to-day fluctuations in higher-order RMS (Fig. 4) . However, lower-order aberrations also varied throughout the week, and when we calculate postcorrection image quality for residual aberrations including higher- and lower-order aberrations, the resultant rMTFs are much poorer (Fig. 10 , line 5).

*IOVS*2003;44:ARVO E-Abstract 2123; Applegate RA, et al.

*IOVS*2003;44:ARVO E-Abstract 2124) for subject AB. Open symbols show the mean VSR computed for the uncorrected eye. Closed symbols show the mean VSR assuming the eye is corrected with a prescription based on the mean of five measurements on day 1. The shaded regions show the 95% probability range (computed as ±2 SD) for the VSR before and after correction. Had more measurements been made on the same eye, we would have expected 95% of those measurements to fall within the shaded areas. The graph on the left shows the improvement in VSR created by correcting higher-order aberrations, assuming perfect correction of the lower-order aberrations at all times, and thus it is only fluctuations in higher-order aberrations that degrade image quality. The graph on the right shows VSR improvement when fluctuations in astigmatism also degrade image quality. The main conclusion to be drawn from the data in Figure 11 is that the improvement in image quality (in terms of VSR) created by correcting higher-order aberrations is substantial over the long-term provided there is zero variation in the lower-order Zernike modes. The improvement of VSR is more modest, but still very significant, if astigmatism also fluctuates after correction.

**Figure 1.**

**Figure 1.**

**Figure 2.**

**Figure 2.**

**Figure 3.**

**Figure 3.**

**Figure 4.**

**Figure 4.**

**Figure 5.**

**Figure 5.**

**Figure 6.**

**Figure 6.**

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**Figure 7.**

**Figure 8.**

**Figure 8.**

**Figure 9.**

**Figure 9.**

**Figure 10.**

**Figure 10.**

**Figure 11.**

**Figure 11.**

**Figure 12.**

**Figure 12.**

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