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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 53, Iss. 7 — Mar. 1, 2014
  • pp: 1442–1448

Estimating the atmospheric correlation length with stochastic parallel gradient descent algorithm

R. Yazdani, M. Hajimahmoodzadeh, and H. R. Fallah  »View Author Affiliations

Applied Optics, Vol. 53, Issue 7, pp. 1442-1448 (2014)

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The atmospheric turbulence measurement has received much attention in various fields due to its effects on wave propagation. One of the interesting parameters for characterization of the atmospheric turbulence is the Fried parameter or the atmospheric correlation length. We numerically investigate the feasibility of estimating the Fried parameter using a simple and low-cost system based on the stochastic parallel gradient descent (SPGD) algorithm without the need for wavefront sensing. We simulate the atmospheric turbulence using Zernike polynomials and employ a wavefront sensor-less adaptive optics system based on the SPGD algorithm and report the estimated Fried parameter after compensating for atmospheric-turbulence-induced phase distortions. Several simulations for different atmospheric turbulence strengths are presented to validate the proposed method.

© 2014 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
(010.1285) Atmospheric and oceanic optics : Atmospheric correction
(110.1080) Imaging systems : Active or adaptive optics

ToC Category:
Atmospheric and Oceanic Optics

Original Manuscript: November 20, 2013
Revised Manuscript: January 12, 2014
Manuscript Accepted: January 23, 2014
Published: February 27, 2014

R. Yazdani, M. Hajimahmoodzadeh, and H. R. Fallah, "Estimating the atmospheric correlation length with stochastic parallel gradient descent algorithm," Appl. Opt. 53, 1442-1448 (2014)

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  1. L. C. Andrews, Field Guide to Atmospheric Optics (SPIE, 2004).
  2. H. W. Babcock, “The possibility of compensating astronomical seeing,” Astron. Soc. Pac. 65, 229–236 (1953). [CrossRef]
  3. T. Weyrauch and M. A. Vorontsov, “Free-space laser communications with adaptive optics: atmospheric compensation experiments,” J. Opt. Fiber. Commun. Rep. 1, 355–379 (2004). [CrossRef]
  4. P. Yang, X. Lei, R. Yang, M. Ao, L. Dong, and B. Xu, “Fast and stable enhancement of the far-field peak power by use of an intracavity deformable mirror,” Appl. Phys. B 100, 591–595 (2010). [CrossRef]
  5. R. A. Muller and A. Buffington, “Real-time correction of atmospherically degraded telescope images through image sharpening,” J. Opt. Soc. Am. 64, 1200–1210 (1974). [CrossRef]
  6. C. A. Primmerman, T. R. Price, R. A. Humphreys, B. G. Zollars, H. T. Barclay, and J. Herrmann, “Atmospheric-compensation experiments in strong-scintillation conditions,” Appl. Opt. 34, 2081–2088 (1995). [CrossRef]
  7. V. P. Lukin and B. V. Fortes, “Phase correction of an image turbulence broading under condition of strong intensity fluctuations,” Proc. SPIE 3763, 61–72 (1999). [CrossRef]
  8. H. Ma, C. Fan, P. Zhang, J. Zhang, C. Qiao, and H. Wang, “Adaptive optics correction based on stochastic parallel gradient descent technique under various atmospheric scintillation conditions: numerical simulation,” Appl. Phys. B 106, 939–944 (2012). [CrossRef]
  9. D. L. Fried, “Statistics of a geometric representation of wavefront distortion,” J. Opt. Soc. Am. 55, 1427–1435 (1965). [CrossRef]
  10. N. Anugu and J. P. Lancelot, “Study of atmospheric turbulence with Shack-Hartmann wavefront sensor,” J. Opt. 42, 128–140 (2013). [CrossRef]
  11. M. A. Vorontsov, G. W. Carhart, and J. C. Ricklin, “Adaptive phase-distortion correction based on parallel gradient descent optimization,” Opt. Lett. 22, 907–909 (1997). [CrossRef]
  12. A. N. Kolmogorov, “The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers,” Proc. R. Soc. A 434, 9–13 (1991). [CrossRef]
  13. R. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66, 207–211 (1976). [CrossRef]
  14. V. Lakshminarayanan and A. Fleck, “Zernike polynomials: a guide,” J. Mod. Opt. 58, 545–561 (2011). [CrossRef]
  15. M. A. Vorontsov, G. W. Carhart, M. Cohen, and G. Cauwenberghs, “Adaptive optics based on analog parallel stochastic optimization: analysis and experimental demonstration,” J. Opt. Soc. Am. A 17, 1440–1453 (2000). [CrossRef]
  16. B. L. McGlamery, “Restoration of turbulence-degraded images,” J. Opt. Soc. Am. 57, 293–297 (1967). [CrossRef]
  17. B. J. Herman and L. A. Strugala, “Method for inclusion of low-frequency contributions in numerical representation of atmospheric turbulence,” Proc. SPIE 1221, 183–192 (1990). [CrossRef]
  18. N. A. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. 29, 1174–1180 (1990). [CrossRef]
  19. W. H. Jiang, N. Ling, X. J. Rao, and F. Shi, “Fitting capability of deformable mirror,” Proc. SPIE 1542, 130–137 (1991). [CrossRef]
  20. M. Born and E. Wolf, Principles of Optics (Pergamon, 1986), p. 768.
  21. H. Song, G. Vdovin, R. Fraanje, G. Schitter, and M. Verhaegen, “Extracting hysteresis from nonlinear measurement of wavefront-sensorless adaptive optics system,” Opt. Lett. 34, 61–63 (2009). [CrossRef]
  22. A. Dubra, J. S. Massa, and C. Paterson, “Preisach classical and nonlinear modeling of hysteresis in piezoceramic deformable mirrors,” Opt. Express 13, 9062–9070 (2005). [CrossRef]
  23. H. Janocha and K. Kuhnen, “Real-time compensation of hysteresis and creep in piezoelectric actuators,” Sens. Actuators A 79, 83–89 (2000). [CrossRef]
  24. Q. Yang, C. Ftaclas, M. Chun, and D. Toomey, “Hysteresis correction in the curvature adaptive optics system,” J. Opt. Soc. Am. A 22, 142–147 (2005). [CrossRef]
  25. T. Weyrauch, M. A. Vorontsov, T. G. Bifano, J. A. Hammer, M. Cohen, and G. Cauwenberghs, “Microscale adaptive optics: wave-front control with a μ-mirror array and a VLSI stochastic gradient descent controller,” Appl. Opt. 40, 4243–4253 (2001). [CrossRef]

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