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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 27, Iss. 5 — May. 1, 2010
  • pp: 1185–1193

Joint estimation of Stokes images and aberrations from phase-diverse polarimetric measurements

John R. Valenzuela, Jeffrey A. Fessler, and Richard G. Paxman  »View Author Affiliations

JOSA A, Vol. 27, Issue 5, pp. 1185-1193 (2010)

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The technique of phase diversity has been used in traditional incoherent imaging systems to jointly estimate an object and optical system aberrations. This paper extends the technique of phase diversity to polarimetric imaging systems. Specifically, we describe penalized-likelihood methods for jointly estimating Stokes images and optical system aberrations from measurements that contain phase diversity. Jointly estimating Stokes images and optical system aberrations involves a large parameter space. A closed-form expression for the estimate of the Stokes images in terms of the aberration parameters is derived and used in a formulation that reduces the dimensionality of the search space to the number of aberration parameters only. We compare the performance of the joint estimator under both quadratic and edge-preserving regularization; we also compare the performance of the reduced parameter search strategy to the full parameter search strategy under quadratic regularization. The joint estimator with edge-preserving regularization yields higher fidelity polarization estimates than with quadratic regularization. With the reduced parameter search strategy, accurate aberration estimates can be obtained without recourse to regularization “tuning.”

© 2010 Optical Society of America

OCIS Codes
(100.3010) Image processing : Image reconstruction techniques
(100.3020) Image processing : Image reconstruction-restoration
(100.3190) Image processing : Inverse problems

ToC Category:
Image Processing

Original Manuscript: November 24, 2009
Revised Manuscript: March 22, 2010
Manuscript Accepted: March 23, 2010
Published: April 30, 2010

John R. Valenzuela, Jeffrey A. Fessler, and Richard G. Paxman, "Joint estimation of Stokes images and aberrations from phase-diverse polarimetric measurements," J. Opt. Soc. Am. A 27, 1185-1193 (2010)

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  1. J. S. Tyo, D. L. Goldstein, D. B. Chenault, and J. A. Shaw, “Review of passive imaging polarimetry for remote sensing applications,” Appl. Opt. 45, 5453–5469 (2006). [CrossRef] [PubMed]
  2. H. Barrett and K. J. Myers, Foundations of Image Science (Wiley, 2004).
  3. W. G. Egan, “Polarization and surface roughness,” Proc. SPIE 3426, 144–152 (1998). [CrossRef]
  4. G. C. Giakos, “Multifusion, multispectral, optical polarimetric imaging sensing principles,” IEEE Trans. Instrum. Meas. 55, 1628–1633 (2006). [CrossRef]
  5. R. A. Chipman, “Polarimetry,” in Handbook of Optics, 2nd ed., M.Bass, ed. (McGraw-Hill, 1995), Vol. 2, Chap. 22.
  6. E. Hecht, Optics, 3rd ed. (Addison-Wesley, 1998).
  7. J. R. Valenzuela and J. A. Fessler, “Joint reconstruction of Stokes images from polarimetric measurements,” J. Opt. Soc. Am. A 26, 962–968 (2009). [CrossRef]
  8. R. Paxman, T. Schulz, and J. Fienup, “Joint estimation of object and aberrations by using phase diversity,” J. Opt. Soc. Am. A 9, 1072–1085 (1992). [CrossRef]
  9. D. J. Lee, M. C. Roggemann, and B. M. Welsh, “Cramer–Rao analysis of phase-diverse wave-front sensing,” J. Opt. Soc. Am. A 16, 1005–1015 (1999). [CrossRef]
  10. J. W. Goodman, Fourier Optics, 3rd ed. (Roberts, 2005).
  11. R. J. Knoll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66, 207–211 (1976). [CrossRef]
  12. H. W. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems (Kluwer Academic, 1996). [CrossRef]
  13. R. A. Gonsalves and R. Chidlaw, “Wavefront sensing by phase retrieval,” Proc. SPIE 207, 32–39 (1979).
  14. J. A. Nelder and R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).
  15. D. Liu and J. Nocedal, “On the limited memory BFGS method for large scale optimization,” Math. Program. 45, 503–528 (1989). [CrossRef]
  16. J. Fessler, Department of Electrical and Computer Engineering, University of Michigan, 1301 Beal Avenue, Ann Arbor, Michigan 48109–2122, USA, is preparing a book to be called Image Reconstruction: Algorithms and Analysis.

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