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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 49, Iss. 31 — Nov. 1, 2010
  • pp: G47–G52

Numerical modeling of atmospherically perturbed phase screens: new solutions for classical fast Fourier transform and Zernike methods

Marcel Carbillet and Armando Riccardi  »View Author Affiliations

Applied Optics, Vol. 49, Issue 31, pp. G47-G52 (2010)

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We describe new solutions permitting us to overcome the well-known problems encountered when employing the two main classical methods for numerical modeling of atmospherically perturbed phase screens. The first method, the fast-Fourier-transform-based numerical method, suffers from a lack of low frequencies. Subharmonics adding is an already-known solution to this problem, but no criterion has been defined up to now in order to precisely determine how many subharmonics are necessary for each given case of physical and numerical characteristics. We define two criteria and show their practical efficiency. The second, Zernike-based, method suffers, a contrario, from bad behavior of the phase screens at high spatial frequencies. To overcome this problem, due to numerical instability, we developed an algorithm based on an alternative definition of the Zernike polynomials, involving the recurrence definition of the Jacobi polynomials, as well as the relationship between the Zernike and the Jacobi polynomials. The methods described and used in this paper have been implemented within the freely distributed software package CAOS.

© 2010 Optical Society of America

OCIS Codes
(010.1300) Atmospheric and oceanic optics : Atmospheric propagation
(010.1330) Atmospheric and oceanic optics : Atmospheric turbulence
(350.1260) Other areas of optics : Astronomical optics
(070.7345) Fourier optics and signal processing : Wave propagation

ToC Category:
Turbulence Modeling

Original Manuscript: January 20, 2010
Manuscript Accepted: May 14, 2010
Published: June 25, 2010

Marcel Carbillet and Armando Riccardi, "Numerical modeling of atmospherically perturbed phase screens: new solutions for classical fast Fourier transform and Zernike methods," Appl. Opt. 49, G47-G52 (2010)

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