OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 18 — Sep. 1, 2008
  • pp: 14274–14287

Estimation of physically realizable Mueller matrices from experiments using global constrained optimization

Jawad Elsayed Ahmad and Yoshitate Takakura  »View Author Affiliations


Optics Express, Vol. 16, Issue 18, pp. 14274-14287 (2008)
http://dx.doi.org/10.1364/OE.16.014274


View Full Text Article

Enhanced HTML    Acrobat PDF (3297 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

One can explicitly retrieve physically realizable Mueller matrices from quantified intensity data even in the presence of noise. This is done by integrating the physical realizability criterion obtained by Givens and Kostinski, [J. Mod. Opt. 40, 471 (1993)], as an active constraint in a global optimization process. Among different global optimization techniques, two of them have been tested and their robustness analyzed: a deterministic approach based on sequential quadratic programming and a stochastic approach based on constrained simulated annealing algorithms are implemented for this purpose. We illustrate the validity of both methods on experimental data and on the inadmissible Mueller matrix given by Howell, [Appl. Opt. 18, No. 6, 808-812 (1979)]. In comparison, the constrained simulated annealing method produced higher accuracy with similar computing time.

© 2008 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(120.4820) Instrumentation, measurement, and metrology : Optical systems
(120.5410) Instrumentation, measurement, and metrology : Polarimetry
(230.5440) Optical devices : Polarization-selective devices

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: July 9, 2008
Revised Manuscript: August 15, 2008
Manuscript Accepted: August 16, 2008
Published: August 28, 2008

Citation
Jawad Elsayed Ahmad and Yoshitate Takakura, "Estimation of physically realizable Mueller matrices from experiments using global constrained optimization," Opt. Express 16, 14274-14287 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-18-14274


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  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. J. M. Bueno and M. C. W. Campbell, "Confocal scanning laser ophthalmoscopy improvement by use of Muellermatrix polarimetry," Opt. Lett. 27, 830-832 (2002). [CrossRef]
  3. A. Weber, M. Cheney, Q. Smithwick, and A. Elsner, "Polarimetric imaging and blood vessel quantification," Opt. Express 12, 5178-5190 (2004). [CrossRef] [PubMed]
  4. D. Miyazaki, K. Kagesawa, and K. Ikeuchi, "Transparent Surface Modeling from a Pair of Polarization Images," IEEE Trans. Pattern Anal. Mach. Intell. 26, 72-83 (2004).
  5. J. L. Pezzaniti and R. A. Chipman, "Mueller matrix imaging polarimetry," Opt. Eng. 34, 1558-1568 (1995). [CrossRef]
  6. B. J. Howell, " Measurements of the polarization effects of an instrument using partially polarized light," Appl. Opt. 18, 808-812 (1979). [CrossRef]
  7. J. W. Hovenier, H. C. van de Hulst, and C. V. M. van der Mee, "Conditions for the elements of the scattering matrix," Astron. Astrophys. 157, 301-310 (1986).
  8. J. W. Hovenier and C. V. M. van der Mee, "Testing scattering matrices: A compendium of recipes," J. Quant. Spectrosc. Radiat. Transfer 55, 649-661 (1996). [CrossRef]
  9. J. -F. Xing, "On the Deterministic and Non-deterministic Mueller Matrix," J. Mod. Opt. 39, 461-484 (1992). [CrossRef]
  10. E. Landi Degl�??Innocenti and J. C. del Toro Iniesta, "Physical significance of experimental Mueller matrices," J. Opt. Soc. Am. A 15, 533-537 (1998). [CrossRef]
  11. C. R. Givens and A. B. Kostinski, "A simple necessary and sufficient condition on physically realizable Mueller matrices," J. Mod. Opt. 40, 471-481 (1993). [CrossRef]
  12. S. R. Cloude and E. Pottier, "A Review of Target Decomposition Theorems in Radar Polarimetry," IEEE Trans. Geosci. Remote Sens. 34, 498-518 (1996). [CrossRef]
  13. F. Le Roy-Brehonnet, B. Le Jeune, P. Eliès, J. Cariou, and J. Lotrian, "Optical media characterization by Mueller matrix decomposition," J. Phys. D: Appl. Phys. 29, 34-38 (1996). [CrossRef]
  14. A. Aiello, G. Puentes, D. Voigt, and J. P. Woerdman, "Maximum-likelihood estimation of Mueller matrices," Opt. Lett. 31, 817-819 (2006). [CrossRef] [PubMed]
  15. A. V. Gopala Rao,K. S. Mallesh, and Sudha, "On the algebraic characterization of a Mueller matrix in polarization optics," J. Mod. Opt. 45, 955-987 (1998).
  16. M. Reimer and D. Yevick, "Least-squares analysis of the Mueller matrix," Opt. Lett. 31, 2399-2401 (2006). [CrossRef] [PubMed]
  17. R. M. Azzam, "Photopolarimetric measurement of the Mueller matrix by Fourier analysis of a single detected signal," Opt. Lett. 2, 148-150 (1978). [CrossRef] [PubMed]
  18. R. A. Horn and C. R. Johnson, Matrix Analysis (Cambridge U. Press, 1985).
  19. D. Anderson and R. Barakat, "Necessary and sufficient conditions for a Mueller matrix to be derivable from a Jones matrix," J. Opt. Soc. Am. A. 11, 2305-2319 (1994). [CrossRef]
  20. R. Barakat, "Bilinear constraints between elements of the 4�?4 Mueller-Jones transfer matrix of polarization theory," Opt. Commun. 38, 159-161 (1981). [CrossRef]
  21. J. R. Huynen, Phenomenological Theory of Radar Targets, PhD. thesis, University of Technology, The Netherlands (1970).
  22. P. Spellucci, "A SQP method for general nonlinear programs using only equality constrained subproblems," Math. Program 82, 413-448 (1998). [CrossRef]
  23. R. Fletcher, Practical Methods of Optimization (Wiley, 1987).
  24. B. W. Wah and T. Wang, in Principles and Practice of Constraint Programming, (Springer, Heidelberg, 1999) Vol. 461.
  25. R. A. Chipman, Handbook of Optics, 2nd ed., M. Bass ed., (McGraw-Hill, 1995) Vol. II.
  26. P. J. M. Laarhoven and E. H. L. Aarts, Simulated annealing: theory and applications (Kluwer Academic Publishers, 1987).
  27. M. Lundy and A. Mees, in Mathematical Programming (Springer, 1986).
  28. B. DeBoo, J. Sasian, and R. Chipman, "Degree of polarization surfaces and maps for analysis of depolarization," Opt. Express 12, 4941-4958 (2004). [CrossRef] [PubMed]
  29. Y. Takakura and J. Elsayed Ahmad, "Noise distribution of Mueller matrices retrieved with active rotating polarimeters," Appl. Opt. 46, 7354-7364 (2007). [CrossRef] [PubMed]
  30. D. S. Sabatke, M. R. Descour, E. Dereniak, W. C. Sweatt, S. A. Kemme, and G. S. Phipps, " Optimization of retardance for complete Stokes polarimeter," Opt. Lett. 25, 802-804 (2000). [CrossRef]
  31. S. R. Cloude, "Conditions for the realisability of matrix operators in polarimetry," Proc. SPIE 1166, 177-185 (1989).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited