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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 30, Iss. 12 — Dec. 1, 2013
  • pp: 2455–2465

Statistics of the sparse spectrum turbulent phase

Mikhail Charnotskii  »View Author Affiliations

JOSA A, Vol. 30, Issue 12, pp. 2455-2465 (2013)

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A recently published sparse spectrum (SS) model of the phase front perturbations by atmospheric turbulence [J. Opt. Soc. Am. A 30, 479 (2013)] is based on the trigonometric series with discrete random support. The SS model enables fewer computational efforts, while preserving the wide range of scales typically associated with turbulence perturbations. We present an improved version of the SS model that accurately reproduces the power-law spectral density of the phase fluctuations in the arbitrary wide spectral band. We examine the higher-order statistics of the SS phase samples for four versions of the SS model. We also present the calculations of the long-exposure Strehl numbers and scintillation index for the different versions of the SS model. A nonoverlapping SS model with a log-uniform partition emerges as the most appropriate for the atmospheric turbulence representation.

© 2013 Optical Society of America

OCIS Codes
(010.0010) Atmospheric and oceanic optics : Atmospheric and oceanic optics
(010.1330) Atmospheric and oceanic optics : Atmospheric turbulence
(030.6600) Coherence and statistical optics : Statistical optics
(110.0115) Imaging systems : Imaging through turbulent media

ToC Category:
Atmospheric and Oceanic Optics

Original Manuscript: September 5, 2013
Revised Manuscript: October 8, 2013
Manuscript Accepted: October 10, 2013
Published: November 5, 2013

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Vol. 9, Iss. 2 Virtual Journal for Biomedical Optics

Mikhail Charnotskii, "Statistics of the sparse spectrum turbulent phase," J. Opt. Soc. Am. A 30, 2455-2465 (2013)

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  1. M. I. Charnotskii, “Sparse spectrum model for a turbulent phase,” J. Opt. Soc. Am. A 30, 479–488 (2013). [CrossRef]
  2. V. I. Tatarskii, Wave Propagation in a Turbulent Medium (McGraw-Hill, 1961).
  3. M. Charnotskii, “Sparse spectrum model for the turbulent phase simulations,” Proc. SPIE 8732, 873208 (2013). [CrossRef]
  4. R. J. Hill, “Models of the scalar spectrum for turbulent advection,” J. Fluid Mech. 88, 541–662 (1978). [CrossRef]
  5. L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).
  6. M. Charnotskii, “Sparse spectrum model of the sea surface,” Proceedings of the 30th International Conference on Ocean, Offshore and Arctic Engineering, Rotterdam, The Netherlands, 2011, paper 49958.
  7. M. Charnotskii, “Sparse spectrum model of the sea surface elevations,” Proceedings of the 22nd International Offshore and Polar Engineering Conference, Rhodes, Greece, 2012, pp. 655–659.
  8. M. I. Charnotskii, “Statistical modeling of the point spread function for imaging through turbulence,” Opt. Eng. 51, 101706 (2012). [CrossRef]
  9. K. S. Gochelashvili and V. I. Shishov, “Focused irradiance beyond a layer of turbulent atmosphere,” Opt. Acta 19, 327–332 (1972). [CrossRef]

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