The circle polynomials of Zernike and their application in optics
Abstract
The Zernike polynomials are orthogonal functions defined on the unit circle, which have been used primarily in the diffraction theory of optical aberrations. A summary of their principal properties is given. It is shown that the polynomials, which are closely related to the general spherical harmonics, are especially useful in numerical calculations. In particular, by using the polynomials as a basis to represent the commonly encountered functions of optical theory, it is often possible to avoid numerical quadrature and computations are reduced to the simple manipulation of expansion coefficients.
 Publication:

Applied Physics
 Pub Date:
 August 1977
 DOI:
 10.1007/BF00882606
 Bibcode:
 1977ApPhy..13..327T
 Keywords:

 PACS Codes 02  42.30;
 02;
 42.30