The Wavefront and its Representation with Zernike Polynomials

Abstract

This paper is a review of the wavefront concept based on Fermat’s principle, first in general terms and then for the exit pupil of an optical system that creates images. The reference wavefront and the real wavefrontare defined in the exit pupil and the difference between them determines the wavefront aberrations. The wavefront and the wavefront aberration are then represented mathematically. The Cartesian coordinate system is used as at the beginning to describe the aberration polynomial in general termsand discuss the meaning of the first terms (primary aberrations), and then the polar coordinate system is used.The aberration terms in this representation have a simpler mathematical form and it is ideal to describe the wavefront of a circular pupil. Finally, after adding a few compensation terms to the mathematical expressions in the polar representation in order to minimize the effect of the aberrations in the final image, we reach the Zernike polynomials. The use of Zernike coefficients is explained, and an example is presented of the wavefront obtained with an experimental Hartmann-shack aberrometer when using a physical model of the human eye.