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Circular and Annular Zernike Polynomials

Dr Brett Patterson
Organization: UK Astronomy Technology Centre
URL: http://www.roe.ac.uk
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lenses This package defines functions Zernike[i, r, theta] and Zernike[i, r, theta, e] that give, respectively, the circular and annular Zernike polynomials, as described by Noll (JOSA 66, 207, 1976) and Mahajan (JOSA 71, 75, 1981).

These polynomials form complete orthonormal sets over the unit disk r < 1, and the annular domain e < r < 1.

For convenience, the functions return zero for r > 1, or r < e.

The functions are defined so as to be efficient and practical for numerical work.

The annular Zernikes are particularly useful for analysing the abberations of telescopes with annular pupils (e.g. Cassegrain telescopes).

Zernike polynomials are commonly used in the analysis of Adaptive Optics systems.

*Mathematics > Calculus and Analysis > Special Functions
*Science > Physics > Optics

Circular Zernike Polynomials, Annular Zernike Polynomials, Least-Squares fitting basis functions to data, Adaptive Optics, Telescope Abberations
Downloads Download Wolfram CDF Player

SimpleFit.m (760 B) - Mathematica Package
Zernike.m (3.6 KB) - Mathematica Package
Zernike.nb (885.4 KB) - Mathematica Notebook