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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

  • Editor: Stephen A. Burns
  • Vol. 24, Iss. 1 — Jan. 1, 2007
  • pp: 139–155

Zernike annular polynomials and atmospheric turbulence

Guang-ming Dai and Virendra N. Mahajan  »View Author Affiliations


JOSA A, Vol. 24, Issue 1, pp. 139-155 (2007)
http://dx.doi.org/10.1364/JOSAA.24.000139


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Abstract

Imaging through atmospheric turbulence by systems with annular pupils is discussed using the Zernike annular polynomials. Fourier transforms of these polynomials are derived analytically to facilitate the calculation of variance and covariance of the aberration coefficients. Zernike annular shape functions are derived and used to calculate the Strehl ratio and the residual phase structure and mutual coherence functions when a certain number of modes are corrected using, say, a deformable mirror. Special cases of long- and short-exposure images are also considered. The results for systems with a circular pupil are obtained as a special case of the annular pupil.

© 2006 Optical Society of America

OCIS Codes
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(010.1330) Atmospheric and oceanic optics : Atmospheric turbulence
(220.1000) Optical design and fabrication : Aberration compensation
(220.1010) Optical design and fabrication : Aberrations (global)

ToC Category:
Atmospheric and Oceanic Optics

History
Original Manuscript: June 7, 2006
Manuscript Accepted: July 28, 2006

Citation
Guang-ming Dai and Virendra N. Mahajan, "Zernike annular polynomials and atmospheric turbulence," J. Opt. Soc. Am. A 24, 139-155 (2007)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-24-1-139

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