Abstract

A set of orthogonal functions, convenient for the aberration analysis of the quasi-gaussian beams such as the laser TEM₀₀ mode is derived. It is a set of hypergeometric functions. We can expand the aberration function of a quasi-gaussian beam in terms of it, and can calculate the diffraction patterns of aberrations. This set of functions has some characteristics of orthogonality to each other and relations to the Bessel functions. It bears a resemblance to the Zernike’s circle polynomials, but has some different characteristics. It is useful in holography, optical communications, and optical measurement.

© 1974 Optical Society of America

Aberration balancing in rotationally symmetric lenses*

Berge Tatian
J. Opt. Soc. Am. 64(8) 1083-1091 (1974)

Method to evaluate beam quality of Gaussian beams with aberrations

Yuntao Qiu, Lei Huang, Mali Gong, Liu Qiang, Ping Yan, and Haitao Zhang
Appl. Opt. 51(27) 6539-6543 (2012)

Zernike annular polynomials for imaging systems with annular pupils

Virendra N. Mahajan
J. Opt. Soc. Am. 71(1) 75-85 (1981)

Aberration-balancing technique for radially symmetric amplitude distributions: a generalization of the Maréchal approach

Stanisław Szapiel
J. Opt. Soc. Am. 72(7) 947-956 (1982)

Least-squares fitting of orthogonal polynomials to the wave-aberration function

J. L. Rayces
Appl. Opt. 31(13) 2223-2228 (1992)