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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Stephen A. Burns
  • Vol. 22, Iss. 11 — Nov. 1, 2005
  • pp: 2532–2541

Cramer–Rao lower bounds on the estimation of the degree of polarization in coherent imaging systems

Nicolas Roux, François Goudail, and Philippe Réfrégier  »View Author Affiliations


JOSA A, Vol. 22, Issue 11, pp. 2532-2541 (2005)
http://dx.doi.org/10.1364/JOSAA.22.002532


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Abstract

We analyze the estimation precision of the parameter of the orthogonal state contrast image (OSCI) under coherent illumination. This parameter represents the degree of polarization of the light if the materials that compose the scene are purely depolarizing. Two different estimation modes are considered, depending on the uniformity of the illumination of the scene. We first determine lower bounds on the estimation precision in both cases by computing the Cramer–Rao lower bounds (CRLBs) for unbiased estimation. This allows us to compare the potential precision that can be reached in each mode. We then consider the estimators based on empirical averaging of the data, and we show that there are cases where they are strongly biased. We thus propose and characterize another estimator based on the natural representation of the OSCI, which is asymptotically unbiased and whose variance is close to the unbiased CRLB.

© 2005 Optical Society of America

OCIS Codes
(110.0110) Imaging systems : Imaging systems
(260.5430) Physical optics : Polarization
(280.0280) Remote sensing and sensors : Remote sensing and sensors

ToC Category:
Physical Optics

History
Original Manuscript: January 19, 2005
Revised Manuscript: April 26, 2005
Manuscript Accepted: April 26, 2005
Published: November 1, 2005

Citation
Nicolas Roux, François Goudail, and Philippe Réfrégier, "Cramer–Rao lower bounds on the estimation of the degree of polarization in coherent imaging systems," J. Opt. Soc. Am. A 22, 2532-2541 (2005)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-22-11-2532


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References

  1. R. B. Holmes, “Applications of lasers to imaging of distant objects,” in Intense Laser Beams and Applications, W. E. McDermott, ed., Proc. SPIE1871, 306–315 (1993).
  2. G. R. Osche, D. S. Young, “Imaging laser radar in the near and far infrared,” Proc. IEEE 84, 103–125 (1996). [CrossRef]
  3. D. G. Laurin, J. A. Beraldin, F. Blais, M. Rioux, L. Cournoyer, “Three-dimensional tracking and imaging laser scanner for space operations,” in Laser Radar Technology and Applications, G. W. Kamerman and Ch. Werner, eds., Proc. SPIE3707, 278–289 (1999).
  4. R. C. Hardie, M. Vadyanathan, P. F. McManamon, “Spectral band selection and classifier design for a multispectral imaging laser radar,” Opt. Eng. 37, 752–762 (1998). [CrossRef]
  5. L. B. Wolff, “Polarization-based material classification from specular reflection,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 1059–1071 (1990). [CrossRef]
  6. B. Johnson, R. Joseph, M. L. Nischan, A. Newbury, J. P. Kerekes, H. T. Barclay, B. C. Willard, J. J. Zayhowski, “Compact active hyperspectral imaging system for the detection of concealed targets,” in Detection and Remediation Technologies for Mines and Minelike Targets IV, A. C. Dubey, J. F. Harvey, J. T. Broach, and R. E. Dugan, eds., Proc. SPIE3710, 144–153 (1999).
  7. J. L. Pezzaniti, R. A. Chipman, “Mueller matrix imaging polarimetry,” Opt. Eng. 34, 1558–1568 (1995). [CrossRef]
  8. R. A. Chipman, “Polarization diversity active imaging,” in Image Reconstruction and Restoration II, T. J. Schulz, ed., Proc. SPIE3170, 68–73 (1997).
  9. S. Breugnot, Ph. Clémenceau, “Modeling and performances of a polarization active imager at lambda=806nm,” in Laser Radar Technology and Applications IV, G. W. Kamerman and C. Werner, eds., Proc. SPIE3707, 449–460 (1999).
  10. P. Terrier, V. DeVlaminck, “Robust and accurate estimate of the orientation of partially polarized light from a camera sensor,” Appl. Opt. 40, 5233–5239 (2001). [CrossRef]
  11. P. Gerligand, M. H. Smith, R. A. Chipman, “Polarimetric images of a cone,” Opt. Express 4, 420–430 (1999). [CrossRef] [PubMed]
  12. S. Breugnot, P. Clémenceau, “Modeling and performances of a polarization active imager at λ=806nm,” Opt. Eng. 39, 2681–2688 (2000). [CrossRef]
  13. J. W. Goodman, “Laser speckle and related phenomena,” in Statistical Properties of Laser Speckle Patterns, Vol. 9 of Topics in Applied Physics (Springer-Verlag, 1975), pp. 9–75.
  14. W. G. Egan, W. R. Johnson, V. S. Whitehead, “Terrestrial polarization imagery obtained from the Space Shuttle: characterization and interpretation,” Appl. Opt. 30, 435–442 (1991). [CrossRef] [PubMed]
  15. F. Goudail, Ph. Réfrégier, “Statistical techniques for target detection in polarisation diversity images,” Opt. Lett. 26, 644–646 (2001). [CrossRef]
  16. F. Goudail, Ph. Réfrégier, “Statistical algorithms for target detection in coherent active polarimetric images,” J. Opt. Soc. Am. A 18, 3049–3060 (2001). [CrossRef]
  17. F. Goudail, Ph. Réfrégier, “Target segmentation in active polarimetric images by use of statistical active contours,” Appl. Opt. 41, 874–883 (2002). [CrossRef] [PubMed]
  18. S. L. Jacques, J. C. Ramella-Roman, K. Lee, “Imaging skin pathology with polarized light,” J. Biomed. Opt. 7, 329–340 (2002). [CrossRef] [PubMed]
  19. T. S. Ferguson, “Exponential families of distributions,” in Mathematical Statistics, a Decision Theoretic Approach (Academic, 1967), pp. 125–132.
  20. J. W. Goodman, “Some problems involving high-order coherence,” in Statistical Optics (Wiley, 1985), pp. 237–285.
  21. J. W. Goodman, “The speckle effect in coherent imaging,” in Statistical Optics (Wiley, 1985), pp. 347–356.
  22. H. L. Van Trees, Detection, Estimation and Modulation Theory. Part I: Detection, Estimation and Linear Modulation Theory (Wiley, 1968).
  23. Ph. Réfrégier, F. Goudail, N. Roux, “Estimation of the degree of polarization in active coherent imagery using the natural representation,” J. Opt. Soc. Am. A 21, 2292–2300 (2004). [CrossRef]
  24. Ph. Réfrégier, Noise Theory and Application to Physics: From Fluctuations to Information (Springer, 2004). [CrossRef]
  25. A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill, 1991).

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