In the past few years considerable effort has been made to extract basic surface aberrations, such as mean surface power and surface astigmatism, from corneal surface-height data, e.g., as measured by videokeratoscopes. Two applications are corneal surgery and contact lens adjustment. Another primary application is the derivation of the mean power and astigmatism of a wave front, e.g., in interferometers and other wave-front sensors. Both surface and wave-front quantities can be computed by means of Zernike polynominals. One advantage of this computation is that Zernike polynominal expansion provides all the coefficients at once for calculating Seidel aberrations. We present accurate analytical formulas for computing the mean power and astigmatism of both surface and wave front from Zernike coefficients. Therefore, in general, those quantities are not a function of quadratic-order terms alone, as stated in M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1975), Sec. 9.2, but include linear-order terms as well.
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