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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 6 — Mar. 16, 2009
  • pp: 4540–4552

Alternative Phase-Diverse Phase Retrieval algorithm based on Levenberg-Marquardt nonlinear optimization

Heng Mao and Dazun Zhao  »View Author Affiliations

Optics Express, Vol. 17, Issue 6, pp. 4540-4552 (2009)

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A modified Levenberg-Marquardt (MLM) algorithm is proposed to substitute for modified G-S (MGS) algorithm in some situations of phase-diverse phase retrieval wavefront sensing (WFS), such as the obstructed pupil, in which the second derivative information is specifically employed to eliminate the local minimum stagnation. Experiments have been performed to validate MLM algorithm in WFS accuracy (less than λ/30 RMS) referring to ZYGO interferometer results and in WFS repeatability (less than λ/200 RMS), even the dynamic range is more than 7λ PV. Moreover, experiments have shown the MLM algorithm is superior to the MGS algorithm both in WFS accuracy and repeatability.

© 2009 Optical Society of America

OCIS Codes
(010.7350) Atmospheric and oceanic optics : Wave-front sensing
(100.5070) Image processing : Phase retrieval
(120.3940) Instrumentation, measurement, and metrology : Metrology

ToC Category:
Image Processing

Original Manuscript: November 3, 2008
Revised Manuscript: December 14, 2008
Manuscript Accepted: January 2, 2009
Published: March 6, 2009

Heng Mao and Dazun Zhao, "Alternative phase-diverse phase retrieval algorithm based on Levenberg-Marquardt nonlinear optimization," Opt. Express 17, 4540-4552 (2009)

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  1. R. W. Gerchberg and W. O. Saxton, " A Practical Algorithm for the Determination of Phase from Image and Diffraction Plane Pictures, " OPTIK 35, 237-246 (1972).
  2. B. H. Dean, D. L. Aronstein, J. S. Smith, R. Shiri, and D. S. Acton, "Phase Retrieval Algorithm for JWST Flight and Testbed Telescope," Proc. SPIE 6265, 626511-1 (2006). [CrossRef]
  3. R. A. Gonsalves, "Phase Retrieval from Modulus Data," J. Opt. Soc. Am. 66, 961-964 (1976). [CrossRef]
  4. R. A. Gonsalves, "Phase Retrieval and Diversity in Adaptive Optics," Opt. Eng. 21, 829-832 (1982).
  5. C. Roddier and F. Roddier, "Combined Approach to the Hubble Space Telescope Wave-Front Distortion Analysis," Appl. Opt. 32, 2992-3008 (1993). [CrossRef] [PubMed]
  6. J. R. Fienup, "Phase-retrieval algorithms for a complicated optical system," Appl. Opt. 32, 1737-1746 (1993). [CrossRef] [PubMed]
  7. D. C. Redding, P. Dumont, and J. Yu, "Hubble Space Telescope prescription retrieval," Appl. Opt. 32, 1728-1736 (1993). [CrossRef] [PubMed]
  8. D. C. Redding, S. Basinger, A. Lowman, A. Kissil, P. Bely, R. Burg, R. Lyon, G. Mosier, M. Femiano, M. Wilson, G. Schunk, L. Craig, D. Jacobson, J. Rakoczy, and J. Hadaway, "Wavefront Sensing and Control for a Next Generation Space Telescope," Proc. SPIE 3356, 758-772 (1998). [CrossRef]
  9. D. C. Ghiglia and M. D. Pritt, "Minimum-norm methods," in Two-Dimensional Phase Unwrapping (Wiley Press, 1998), pp. 178-278.
  10. D. Cohen and D. C. Redding, "NGST High Dynamic Range Unwrapped Phase Estimation," Proc. SPIE 4850, 336-344 (2003). [CrossRef]
  11. D. S. Acton, P. Atcheson, M. Cermak, L. Kingsbury, F. Shi, and D. C. Redding, "James Webb Space Telescope Wavefront Sensing and Control Algorithms," Proc. SPIE 5487, 887-896 (2004). [CrossRef]
  12. C. M. Ohara, D. C. Redding, F. Shi, and J. J. Green, "PSF monitoring and in-focus wavefront control for NGST," Proc. SPIE 4850, 416-427 (2003). [CrossRef]
  13. D. Malacara and S. DeVore, "Interferogram evaluation and wavefront fitting," in Optical Shop Testing 2nd Ed. (Wiley Press, 1992), pp. 455-487.
  14. G. R. Brady and J. R. Fienup, "Nonlinear optimization algorithm for retrieving the full complex pupil function," Opt. Express 14, 474-486 (2006). [CrossRef] [PubMed]
  15. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, "Nonlinear models," in Numerical Recipes in C++: The Art of Scientific Computing 2nd Ed. (Cambridge University Press, 2002), pp. 686-694.
  16. J. J. Green, D. C. Redding, S. Shaklan, and S. A. Basinger, "Extreme wavefront sensing accuracy for the Eclipse Coronagraphic Space Telescope," Proc. SPIE 4860, 266-276 (2003). [CrossRef]
  17. Heng Mao, Xiao Wang, and Dazun Zhao, "Application of phase-diverse phase retrieval to wavefront sensing in non-connected complicated pupil optics", Chinese Opt. Lett. 5, 397-399 (2007).
  18. J. J. Green, D. C. Redding, Y. Beregovski, A. E. Lowman, and C. M. Ohara, "Interferometric validation of image-based wavefront sensing for NGST," Proc. SPIE 4850, 345-352 (2003). [CrossRef]

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