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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 13, Iss. 3 — Mar. 1, 1996
  • pp: 517–522

Zernike expansions for non-Kolmogorov turbulence

Glenn D. Boreman and Christopher Dainty  »View Author Affiliations


JOSA A, Vol. 13, Issue 3, pp. 517-522 (1996)
http://dx.doi.org/10.1364/JOSAA.13.000517


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Abstract

We investigate the expression of non-Kolmogorov turbulence in terms of Zernike polynomials. Increasing the power-law exponent of the three-dimensional phase power spectrum from 2 to 4 results in a higher proportion of wave-front energy being contained in the tilt components. Closed-form expressions are given for the variances of the Zernike coefficients in this range. For exponents greater than 4 a von Kármán spectrum is used to compute the variances numerically as a function of exponent for different outer-scale lengths. We find in this range that the Zernike-coefficient variances depend more strongly on outer scale than on exponent and that longer outer-scale lengths lead to more energy in the tilt terms. The scaling of Zernike-coefficient variances with pupil diameter is an explicit function of the exponent.

© 1996 Optical Society of America

History
Original Manuscript: June 19, 1995
Revised Manuscript: August 21, 1995
Manuscript Accepted: September 12, 1995
Published: March 1, 1996

Citation
Glenn D. Boreman and Christopher Dainty, "Zernike expansions for non-Kolmogorov turbulence," J. Opt. Soc. Am. A 13, 517-522 (1996)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-13-3-517

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