## Invariant polarimetric contrast parameters of light with Gaussian fluctuations in three dimensions

JOSA A, Vol. 23, Issue 1, pp. 124-133 (2006)

http://dx.doi.org/10.1364/JOSAA.23.000124

Enhanced HTML Acrobat PDF (142 KB)

### Abstract

We propose a rigorous definition of the minimal set of parameters that characterize the difference between two partially polarized states of light whose electric fields vary in three dimensions with Gaussian fluctuations. Although two such states are *a priori* defined by eighteen parameters, we demonstrate that the performance of processing tasks such as detection, localization, or segmentation of spatial or temporal polarization variations is uniquely determined by three scalar functions of these parameters. These functions define a “polarimetric contrast” that simplifies the analysis and the specification of processing techniques on polarimetric signals and images. This result can also be used to analyze the definition of the degree of polarization of a three-dimensional state of light with Gaussian fluctuations in comparison, with respect to its polarimetric contrast parameters, with a totally depolarized light. We show that these contrast parameters are a simple function of the degrees of polarization previously proposed by
Barakat [Opt. Acta
30, 1171 (1983)
] and
Setälä et al. [Phys. Rev. Lett.
88, 123902 (2002)
]. Finally, we analyze the dimension of the set of contrast parameters in different particular situations.

© 2006 Optical Society of America

**OCIS Codes**

(030.0030) Coherence and statistical optics : Coherence and statistical optics

(030.4280) Coherence and statistical optics : Noise in imaging systems

(260.5430) Physical optics : Polarization

**ToC Category:**

Physical Optics

**Citation**

Philippe Réfrégier, Muriel Roche, and François Goudail, "Invariant polarimetric contrast parameters of light with Gaussian fluctuations in three dimensions," J. Opt. Soc. Am. A **23**, 124-133 (2006)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-23-1-124

Sort: Year | Journal | Reset

### References

- R. S. Cloude and E. Pottier, "Concept of polarization entropy in optical scattering," Opt. Eng. (Bellingham) 34, 1599-1610 (1995). [CrossRef]
- M. Floc'h, G. Le Brun, C. Kieleck, J. Cariou, and J. Lotrian, "Polarimetric considerations to optimize lidar detection of immersed targets," Pure Appl. Opt. 7, 1327-1340 (1998). [CrossRef]
- S. Breugnot and 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.H.Werner, eds., Proc. SPIE 3707, 449-460 (1999).
- A. Gleckler and A. Gelbart, "Multiple-slit steak tube imaging lidar MS-STIL applications," in Laser Radar Technology and Applications V, G.W.Kamerman, U.N.Singh, C.H.Werner, and V.V.Molebny, eds., Proc. SPIE 4035, 266-278 (2000).
- L. B. Wolff, "Polarization camera for computer vision with a beam splitter," J. Opt. Soc. Am. A 11, 2935-2945 (1994). [CrossRef]
- J. S. Tyo, M. P. Rowe, E. N. Pugh, and N. Engheta, "Target detection in optical scattering media by polarization-difference imaging," Appl. Opt. 35, 1855-1870 (1996). [CrossRef] [PubMed]
- J. E. Solomon, "Polarization imaging," Appl. Opt. 20, 1537-1544 (1981). [CrossRef] [PubMed]
- W. G. Egan, W. R. Johnson, and V. S. Whitehead, "Terrestrial polarization imagery obtained from the Space Shuttle: characterization and interpretation," Appl. Opt. 30, 435-442 (1991). [CrossRef] [PubMed]
- J. L. Pezzaniti and R. A. Chipman, "Mueller matrix imaging polarimetry," Opt. Eng. (Bellingham) 34, 1558-1568 (1995). [CrossRef]
- Ph. Réfrégier and F. Goudail, "Invariant polarimetric contrast parameters for coherent light," J. Opt. Soc. Am. A 19, 1223-1233 (2002). [CrossRef]
- Ph. Réfrégier, F. Goudail, P. Chavel, and A. Friberg, "Entropy of partially polarized light and application to statistical processing techniques," J. Opt. Soc. Am. A 21, 2124-2134 (2004). [CrossRef]
- R. Barakat, "N-fold polarization measures and associated thermodynamic entropy of N partially coherent pencils of radiation," Opt. Acta 30, 1171-1182 (1983). [CrossRef]
- P. Pellat-Finet, "Geometrical approach to polarization optics-II: Quaternionic representation of polarized light," Optik (Stuttgart) 87, 68-76 (1991).
- T. Setälä, M. Kaivola, and A. T. Friberg, "Degree of polarization in near fields of thermal sources: effects of surface waves," Phys. Rev. Lett. 88, 123902 (2002). [CrossRef] [PubMed]
- J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, "Degree of polarization of statistically stationary electromagnetic fields," Opt. Commun. 248, 333-337 (2005). [CrossRef]
- G. S. Agarwal, "Utility of 3×3 polarization matrix for partially polarized transverse electromagnetic fields," J. Mod. Opt. 32, 651-654 (2005). [CrossRef]
- T. S. Ferguson, "Invariant statistical decision problems," in Mathematical Statistics, a Decision Theoretic Approach, (Academic Press, 1967), pp. 143-197.
- J. W. Goodman, "Some first-order properties of light waves," in Statistical Optics (Wiley, 1985), pp. 116-156.
- C. Brosseau, "Stokes parameters and coherency matrix formalism," in Fundamentals of Polarized Light--A Statistical Approach (Wiley, 1998), pp. 105-109.
- J. W. Goodman, "The speckle effect in coherent imaging," in Statistical Optics (Wiley, 1985), pp. 347-356.
- T. M. Cover and J. A. Thomas, "Information theory and statistics," in Elements of Information Theory (Wiley, 1991), pp. 279-335. [CrossRef]
- F. Goudail, N. Roux, and Ph. Réfrégier, "Performance parameters for detection in low-flux coherent images," Opt. Lett. 28, 81-83 (2003). [CrossRef] [PubMed]
- F. Goudail, Ph. Réfrégier, and G. Delyon, "Bhattacharyya distance as a contrast parameter for statistical processing of noisy optical images," J. Opt. Soc. Am. A 21, 1231-1240 (2004). [CrossRef]
- F. Goudail and Ph. Réfrégier, "Contrast definition for optical coherent polarimetric images," IEEE Trans. Pattern Anal. Mach. Intell. 26, 947-951 (2004). [CrossRef]
- J. C. Samson, "Descriptions of the polarization states of vector processes: applications to ULF magnetic fields," Geophys. J. R. Astron. Soc. 34, 403-419 (1973).
- B. R. Frieden, "Continuous random variables," in Probability, Statistical Optics and Data Testing (Springer-Verlag, 2001), p. 71.

## 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.