A new method for describing the aberrations of the eye using Zernike polynomials

The standard Zernike polynomial functions are reformulated in a way so that the number of functions (or terms) needed to describe an arbitrary wavefront surface to a given Zernike radial order is reduced by a factor of approximately two, and the terms are described in a fashion quite similar to that used to describe common sphero-cylindrical errors of the eye. A wavefront is represented using these terms by assigning a pair of values, a magnitude and an axis, to all terms that are radially symmetric so that the individual aberrations are presented in a way similar to the way common astigmatism is currently given in terms of cylinder power and axis. The root mean square of these magnitudes gives the root mean square wavefront error just as does the root mean square of the standard Zernike coefficients. Formulas are given to convert standard Zernike coefficients to the magnitude and axis values.