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S.M. Pantanelli, G. Yoon; Can The Zernike Polynomials Reliably Represent The Aberration In Normal And Abnormal Eyes? . Invest. Ophthalmol. Vis. Sci. 2006;47(13):1204.
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© ARVO (1962-2015); The Authors (2016-present)
Recently, there has been a discussion regarding the accuracy with which the Zernike polynomials can represent the wavefront aberration. The goal of this study was to investigate whether the Zernike reconstruction algorithm can provide a reliable description of the aberration in normal and abnormal eyes.
As a reference ocular aberration, the corneal topography of 87 normal and 56 abnormal (27 keratoconic (KC), 9 penetrating keratoplasty (PK), and 20 post–LASIK complaint) eyes was measured over a 6.0 mm pupil using a Bausch & Lomb Orbscan corneal topographer. Using a computer algorithm, the raw elevation map was converted into local wavefront slopes. To simulate sampling by a lenslet array with 0.3 mm spacing, the local wavefront slopes were averaged over a 0.3 x 0.3 mm area. This resulted in 277 sampling points for a 6.0 mm pupil. Finally, a conventional Zernike reconstruction algorithm was used to generate up to 130 Zernike coefficients. For each eye, a map was reconstructed using an increasing number of Zernike modes. Each map was compared to the raw elevation map and the RMS difference between the two maps was calculated. This was done until the RMS difference was less than one–tenth of a diopter, or 0.13 microns for a 6 mm pupil. This determined the minimum number of Zernike modes needed to achieve an acceptable representation of the aberration. The condition number of a matrix, which indicates the accuracy of matrix conversion, was used to evaluate reconstruction stability and reliability.
The cornea aberration of normal, KC, PK, and post–LASIK complaint eyes can be described using 30 ± 11, 40 ± 14, 47 ± 24, 42 ± 12 (mean ± standard deviation) Zernike modes, respectively. The average eye’s aberration could be described using 9th order Zernike polynomials or less. With this number of modes, the stability of the condition number indicated that the coefficients can be accurately determined, given that the lenslet spacing remained smaller than 0.5 mm. Therefore, with the appropriate number of lenslets, enough Zernike modes can be calculated to describe the wavefront aberration of both normal and abnormal eyes.
Zernike polynomials have been proven reliable for representation of the wavefront aberration in both normal and abnormal eyes. The design parameters of the Shack–Hartmann aberrometer can be optimized to facilitate determination of these Zernike modes in excess of what is required.
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