purpose. It is assumed that wavefront error data arising from aberrometry are adequately described by a Zernike polynomial function, although this assumption has not been extensively tested. Inaccuracies in wavefront error may compromise clinical testing and refractive correction procedures. The current retrospective study correlates visual acuity with corneal wavefront error and with the residual surface elevation error after fitting with the Zernike method.

methods. Corneal topography maps were obtained from 32 keratoconus cases, 27 postoperative penetrating keratoplasty cases, and 29 postoperative conductive keratoplasty cases (88 total). The best spectacle-corrected visual acuity (BSCVA) for each case ranged from −0.2 to 1.3 logarithm of the minimum angle of resolution (logMAR) units (20/12.5–20/400). Topography was analyzed to determine wavefront error and the elevation fit error for a 4-mm optical zone. The 4th and 10th expansion series were analyzed with the 0th-order (piston) and 1st order (tip and tilt) removed. Linear regression analysis was performed. The difference in root mean square (RMS) error between the 4th- and 10th-order analyses was assessed for both wavefront and elevation fit error.

results. The correlation of BSCVA to wavefront error for 4th-order terms was moderately strong and significant (*R* ^{2} = 0.581; *P* < 0.001). The 10th-order correlation for wavefront error had a similar result (*R* ^{2} = 0.565; *P* < 0.001), but the regression was not significantly different from the 4th-order result. The correlation of BSCVA to the elevation fit error was strong and significant for the 4th order (*R* ^{2} = 0.658; *P* < 0.001). The 10th-order data had a similar result (*R* ^{2} = 0.509; *P* < 0.001), and there was no significant difference between the two regressions. Only 72% of the cases showed a shift toward increased wavefront error with the 10th-order series, whereas 18% lost wavefront error. All cases showed a shift toward improved elevation fit with the 10th-order expansion.

conclusions. The wavefront error correlation to acuity was moderately strong, but the corneal elevation fit error also strongly correlated with visual acuity, indicating that Zernike polynomials do not fully characterize the surface shape features that influence vision and that exist in postsurgical or pathologic eyes. In addition, the change in wavefront error when using a larger expansion series was found to increase or diminish somewhat unpredictably. The authors conclude that Zernike polynomials fail to model all the information that influences visual acuity, which may confound clinical diagnosis and treatment.

^{ 1 }

^{ 2 }

^{ 3 }

^{ 4 }

^{ 5 }A variety of wavefront-sensing or aberrometry devices now exist,

^{ 6 }

^{ 7 }

^{ 8 }

^{ 9 }

^{ 10 }

^{ 11 }and they all record in some manner the difference between the aberrant wavefront of light reaching the retina and the theoretical, ideally focused wavefront. This difference is called the wavefront error of the eye, and it is typically defined within the area delimited by the pupil.

^{ 12 }

^{ 13 }

^{ 14 }Each Zernike term has a coefficient with a magnitude and sign that indicate the relative strength and direction of the aberration contributed by that term. The wavefront error is often expressed as the sum of the root mean square (RMS) error to avoid sign discrepancies for certain terms, particularly when combining left and right eyes into a single cohort.

^{ 15 }

^{ 12 }

^{ 16 }

^{ 17 }(Smolek MK, et al.

*IOVS*2002;43:ARVO E-Abstract 3943).

^{ 18 }Several thousand topographic data points are necessary for adequate detection of corneal surface irregularities that can decrease vision; however, the number of data points measured with wavefront-sensing instruments varies from the low hundreds to several thousand.

*R*

^{2}) of each correlation from the Pearson product moment correlation coefficient (

*R*). If it had been possible to determine the patient’s precise pupil diameter for the BSCVA measurement, the correlations we obtained would have been more significant, but the correlation coefficient would not necessarily have changed. A

*t*-test on regressions was performed to assess whether the correlations were significant among the different test conditions.

*R*= 0.762;

*R*

^{2}= 0.581;

*P*< 0.001). When BSCVA was correlated with the 4th-order elevation fit error (i.e., the difference error between the original corneal topography and the 4th-order Zernike estimate of the topography), the correlation was stronger (Fig. 2 ;

*R*= 0.811;

*R*

^{2}= 0.658;

*P*< 0.001). A comparison of the difference of the two 4th-order regressions (0.762 and 0.811) indicated a significant difference (

*P*< 0.001). The strong correlation of the elevation fit error result to BSCVA indicates that there remained a significant amount of topographic information that was not described by the Zernike fit model, but which still had a strong influence on visual acuity.

^{ 19 }it was important to test whether using higher order Zernike expansion fits would leave behind less residual surface information of visual consequence. Using a 10th-order Zernike expansion, the correlation coefficient for BSCVA as a function of wavefront error (

*R*= 0.751;

*R*

^{2}= 0.565;

*P*< 0.001; Fig. 3 ) did not show any significant improvement over the 4th-order fit (

*P*> 0.01). Likewise, the correlation coefficient for BSCVA as a function of a 10th-order Zernike expansion for the elevation fit (

*R*= 0.713;

*R*

^{2}= 0.509;

*P*< 0.001; Fig. 4 ) did not show a significant improvement over that of the 4th-order elevation fit (

*P*< 0.01). A comparison of the 10th-order regressions for wavefront error (0.751) and elevation fit (0.713) was significant (

*P*> 0.001).

*R*

^{2}value).

*IOVS*2002;43:ARVO E-Abstract 3943). On the contrary, there are physical limitations on the current diameter of the laser beam that also play a major role in determining the resolution of correction that can be achieved, irrespective of the number of Zernike terms used for fitting.

^{ 19 }

**Figure 1.**

**Figure 1.**

**Figure 2.**

**Figure 2.**

**Figure 3.**

**Figure 3.**

**Figure 4.**

**Figure 4.**

**Figure 5.**

**Figure 5.**

**Figure 6.**

**Figure 6.**

**Figure 7.**

**Figure 7.**

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