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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Joseph N. Mait
  • Vol. 49, Iss. 4 — Feb. 1, 2010
  • pp: 683–693

Estimation precision of the degree of linear polarization and of the angle of polarization in the presence of different sources of noise

François Goudail and Arnaud Bénière  »View Author Affiliations


Applied Optics, Vol. 49, Issue 4, pp. 683-693 (2010)
http://dx.doi.org/10.1364/AO.49.000683


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Abstract

We consider imaging systems that measure the three first elements of the Stokes vector and deduce from them the degree of linear polarization and the angle of polarization. They require the acquisition of at least three intensity measurements, but performing more measurements is often thought to improve the estimation precision. We show that if the total acquisition time is fixed, the optimal number of measurements depends on the type of noise that affects the image: the estimation variance increases with the number of measurements N when the noise is additive; it is independent of N in the presence of Poisson shot noise and decreases with N when the angles of the analyzers fluctuate. In general, the optimal number of measurements results from a compromise on the robustness of these different types of perturbations.

© 2010 Optical Society of America

OCIS Codes
(030.4280) Coherence and statistical optics : Noise in imaging systems
(260.5430) Physical optics : Polarization

ToC Category:
Polarization

History
Original Manuscript: October 13, 2009
Manuscript Accepted: November 17, 2009
Published: January 27, 2010

Citation
François Goudail and Arnaud Bénière, "Estimation precision of the degree of linear polarization and of the angle of polarization in the presence of different sources of noise," Appl. Opt. 49, 683-693 (2010)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-49-4-683


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References

  1. S. Huard, “Polarized optical wave,” in Polarization of Light (Wiley, 1997), pp. 1-35.
  2. L. B. Wolff and T. E. Boult, “Constraining object features using a polarization reflectance model,” IEEE Trans. Pattern Anal. Machine Intell. 13, 635-657 (1991). [CrossRef]
  3. D. Miyazaki, M. Kagesawa, and K. Ikeuchi, “Transparent surface modeling from a pair of polarization images,” IEEE Trans. Pattern Anal. Machine Intell. 26, 73-82 (2004). [CrossRef]
  4. O. Morel, C. Stolz, F. Meriaudeau, and P. Gorria, “Active lighting applied to 3D reconstruction of specular metallic surfaces by polarization imaging,” Appl. Opt. 45, 4062-4068 (2006). [CrossRef] [PubMed]
  5. I. J. Vaughn and B. G. Hoover, “Noise reduction in laser polarimeter based on discrete waveplate rotations,” Opt. Express 16, 2091-2108 (2008). [CrossRef] [PubMed]
  6. D. H. Goldstein and R. A. Chipman, “Error analysis of a Mueller matrix polarimeter,” J. Opt. Soc. Am. A 7, 693-700 (1990). [CrossRef]
  7. A. Ambirajan and D. C. Look, “Optimum angles for a polarimeter: part I,” Opt. Eng. 34, 1651-1658 (1995). [CrossRef]
  8. D. S. Sabatke, M. R. Descour, E. L. Dereniak, W. C. Sweatt, S. A. Kemme, and G. S. Phipps, “Optimization of retardance for a complete Stokes polarimeter,” Opt. Lett. 25, 802-804 (2000). [CrossRef]
  9. M. H. Smith, “Optimization of a dual-rotating-retarder Mueller matrix polarimeter,” Appl. Opt. 41, 2488-2493 (2002). [CrossRef] [PubMed]
  10. J. S. Tyo, “Design of optimal polarimeters: maximization of the signal-to-noise ratio and minimization of systematic error,” Appl. Opt. 41, 619-630 (2002). [CrossRef] [PubMed]
  11. J. Zallat, S. Ainouz, and M. P. Stoll, “Optimal configurations for imaging polarimeters: impact of image noise and systematic errors,” J. Opt. A Pure Appl. Opt. 8, 807-814 (2006). [CrossRef]
  12. Y. Takakura and J. Elsayed Ahmad, “Noise distribution of Mueller matrices retrieved with active rotating polarimeters,” Appl. Opt. 46, 7354-7364 (2007). [CrossRef] [PubMed]
  13. A. Ramos and M. Collados, “Error propagation in polarimetric demodulation,” Appl. Opt. 47, 2541-2549 (2008). [CrossRef]
  14. 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]
  15. S. M. Kay, Fundamentals of Statistical Signal Processing--Volume I: Estimation Theory (Prentice-Hall, 1993).
  16. J. S. Tyo, “Optimum linear combination strategy for an N-channel polarization sensitive imaging or vision system,” J. Opt. Soc. Am. A 15, 359-366 (1998). [CrossRef]
  17. G. C. Holst, CCD Arrays, Cameras, and Displays, 2nd ed. (JCD, 1998).
  18. A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill, 1991).
  19. V. L. Gamiz and J. F. Belsher, “Performance limitations of a four channel polarimeter in the presence of detection noise,” Opt. Eng. 41, 973-980 (2002). [CrossRef]
  20. F. Goudail, “Noise minimization and equalization for Stokes polarimeters in the presence of signal-dependent Poisson shot noise,” Opt. Lett. 34, 647-649 (2009). [CrossRef] [PubMed]
  21. M. Unser and M. Eden, “Maximum likelihood estimation of linear signal parameters for Poisson processes,” IEEE Trans. Acoust. Speech Signal Processing 36, 942-945 (1988). [CrossRef]
  22. K. M. Twietmeyer and R. Chipman, “Optimization of Mueller matrix polarimeters in the presence of error sources,” Opt. Express 16, 11589-11603 (2008). [CrossRef] [PubMed]
  23. A. G. Andreau and Z. K. Kalyjian, “Polarization imaging: principles and integrated polarimeters,” IEEE Sens. J. 2, 566-576 (2002). [CrossRef]
  24. D. L. Bowers, J. K. Boger, L. D. Wellems, S. E. Ortega, M. P. Fetrow, J. E. Hubbs, B. M. Black, B. M. Ratliff, and J. S. Tyo, “Unpolarized calibration and nonuniformity correction for LWIR microgrid imaging polarimeters,” Opt. Eng. 47, 046403 (2008). [CrossRef]
  25. J. Hough, “Polarimetry: a powerful diagnostic tool in astronomy,” Astron. Geophys. 47, 3.31-3.35 (2006). [CrossRef]

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