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MK Smolek, SD Klyce; Reliability Of Zernike Polynomials In Corneal and Wavefront Analysis . Invest. Ophthalmol. Vis. Sci. 2002;43(13):3943.
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Purpose: This study measures the goodness-of-fit between Zernike-reconstructed and actual corneal surfaces as a function of Zernike order (number of terms) for a variety of conditions. Accuracy in representing the cornea by Zernike terms is critical for assessing refractive surgery and optical modeling tasks. Methods: TMS corneal topography maps (n=253) were obtained from the LSU Eye Center. Conditions included normal sphere; astigmatism (AST); LASIK, PRK, and RK postoperative maps (myopic spherical correction); keratoconus suspect (KCS); mild, moderate, and severe keratoconus (KC); pellucid marginal degeneration (PMD); contact lens-induced corneal warpage (CLW); and penetrating keratoplasty. CTView (v.3.20; Sarver & Assoc) extracted the goodness-of-fit (RMS error) of the Zernike representation of surface elevation. Zernike radial orders were varied from 3 to 14 (10 to 120 terms) during analysis of each map. The mean SEM of the RMS error was computed for each condition and plotted as a function of Zernike term order. Results: The greater the irregularity of the cornea or the lower the order of Zernike terms used for fitting, the higher was the RMS error, as expected. The relationship was nonlinear. The normal spherical cornea group achieved the lowest RMS error and did not require terms above the 4th order (15 terms) to achieve <1 µm RMS error. KCS and AST met the 1 µm threshold at the 5th order (21 terms). LASIK, PRK, RK, mild and moderate KC, PMD, and CLW were grouped similarly, with approximately 3 times the error of the normal spherical group. For these conditions, at least 8 orders (45 terms) are needed to reduce error to <1 µm RMS. Keratoplasty and advanced KC had RMS errors 8 to 16 times that of normal corneas and never met the 1 µm threshold. Conclusion: Corneal shape is a major influence on refraction, particularly in abnormal corneas. Consequently, Zernike fits to whole eye wavefront data may contain significant error if the cornea is abnormal. Many Zernike terms are needed to accurately estimate abnormal corneal shapes; too few terms results in an overly smooth surface estimation. For example, a normal cornea that has undergone LASIK surgery requires approximately 3 times more Zernike terms to accurately represent its new shape with an RMS error <1 µm. Thus, surgical laser algorithms using Zernike terms only up to the 4th order will be inaccurate for retreatment procedures. In general, surgical algorithms must take into account the level of abnormality of the preoperative wavefront in order to produce the most effective treatment. Extremely irregular corneas may not be candidates for customized corneal ablations because of inadequate description by Zernike polynomials.
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