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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 14 — Jul. 2, 2012
  • pp: 15928–15944

Maximum-likelihood estimation of parameterized wavefronts from multifocal data

Julia A. Sakamoto and Harrison H. Barrett  »View Author Affiliations


Optics Express, Vol. 20, Issue 14, pp. 15928-15944 (2012)
http://dx.doi.org/10.1364/OE.20.015928


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Abstract

A method for determining the pupil phase distribution of an optical system is demonstrated. Coefficients in a wavefront expansion were estimated using likelihood methods, where the data consisted of multiple irradiance patterns near focus. Proof-of-principle results were obtained in both simulation and experiment. Large-aberration wavefronts were handled in the numerical study. Experimentally, we discuss the handling of nuisance parameters. Fisher information matrices, Cramér-Rao bounds, and likelihood surfaces are examined. ML estimates were obtained by simulated annealing to deal with numerous local extrema in the likelihood function. Rapid processing techniques were employed to reduce the computational time.

© 2012 OSA

OCIS Codes
(100.5070) Image processing : Phase retrieval
(120.3940) Instrumentation, measurement, and metrology : Metrology
(120.5050) Instrumentation, measurement, and metrology : Phase measurement

ToC Category:
Image Processing

History
Original Manuscript: February 22, 2012
Revised Manuscript: May 30, 2012
Manuscript Accepted: June 6, 2012
Published: June 28, 2012

Citation
Julia A. Sakamoto and Harrison H. Barrett, "Maximum-likelihood estimation of parameterized wavefronts from multifocal data," Opt. Express 20, 15928-15944 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-14-15928


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References

  1. I. S. Stefanescu, “On the phase retrieval problem in two dimensions,” J. Math. Phys.26(9), 2141–2160 (1985). [CrossRef]
  2. J. H. Seldin and J. R. Fienup, “Numerical investigation of the uniqueness of phase retrieval,” J. Opt. Soc. Am. A7(3), 412–427 (1990). [CrossRef]
  3. M. R. Teague, “Deterministic phase retrieval: a Green’s function solution,” J. Opt. Soc. Am.73(11), 1434–1441 (1983). [CrossRef]
  4. G. R. Brady and J. R. Fienup, “Improved optical metrology using phase retrieval,” 2004 Optical Fabrication & Testing Topical Meeting, OSA, Rochester, NY, paper OTuB3 (2004).
  5. G. R. Brady and J. Fienup, “Phase retrieval as an optical metrology tool,” Optifab: Technical Digest, SPIE Technical DigestTD03, 139–141 (2005).
  6. G. R. Brady, M. Guizar-Sicairos, and J. R. Fienup, “Optical wavefront measurement using phase retrieval with transverse translation diversity,” Opt. Express17(2), 624–639 (2009). [CrossRef] [PubMed]
  7. H. H. Barrett and K. J. Myers, Foundations of Image Science (Wiley, 2004).
  8. J. W. Goodman, Introduction to Fourier Optics (Roberts & Company Publishers, 2005).
  9. A. Corana, M. Marchesi, C. Martini, and S. Ridella, “Minimizing multimodal functions of continuous variable with the ‘simulated annealing’ algorithm,” ACM Trans. Math. Softw.13(3), 262–280 (1987). [CrossRef]
  10. H. H. Barrett, C. Dainty, and D. Lara, “Maximum-likelihood methods in wavefront sensing: stochastic models and likelihood functions,” J. Opt. Soc. Am. A24(2), 391–414 (2007). [CrossRef] [PubMed]
  11. C. R. Rao, “Information and accuracy attainable in the estimation of statistical parameters,” Bull. Calcutta Math. Soc.37, 81–91 (1945).
  12. H. Cramér, Mathematical Methods of Statistics (Princeton University Press, 1946).

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