Orthonormal vector polynomials in a unit circle, Part II : Completing the basis set.
Zernike polynomials provide a well known, orthogonal set of scalar functions over a circular domain, and are commonly used to represent wavefront phase or surface irregularity. A related set of orthogonal functions is given here which represent vector quantities, such as mapping distortion or wavefront gradient. Previously, we have developed a basis of functions generated from gradients of Zernike polynomials. Here, we complete the basis by adding a complementary set of functions with zero divergence--those which are defined locally as a rotation or curl.
College of Optical Sciences, the University of Arizona, 1630 E. University Blvd, Tucson, AZ 85721, USA. czhao@optics.arizona.edu
Chunyu
C
Zhao
James H
JH
Burge
D015233:Models, Statistical; D055095:Optics and Photonics