OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 27, Iss. 9 — Sep. 1, 2010
  • pp: 1999–2003

Statistics of spatial derivatives of Stokes parameters for isotropic random polarization field

Shun Zhang, Mitsuo Takeda, and Wei Wang  »View Author Affiliations


JOSA A, Vol. 27, Issue 9, pp. 1999-2003 (2010)
http://dx.doi.org/10.1364/JOSAA.27.001999


View Full Text Article

Enhanced HTML    Acrobat PDF (289 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The statistical properties of the spatial derivatives of the Stokes parameters for a random polarization field are studied. Based on the Gaussian assumption for the electric fields, the six-dimensional joint probability density function for the derivatives of the Stokes parameters is obtained from the statistics of the derivatives of the random polarization field. Subsequently, three two-dimensional probability density functions of derivatives of each Stokes parameter and the corresponding six marginal probability density functions are given. Finally, the joint and marginal density functions of the magnitude of the gradient of Stokes parameters are also derived for the first time, to our knowledge.

© 2010 Optical Society of America

OCIS Codes
(000.5490) General : Probability theory, stochastic processes, and statistics
(030.6140) Coherence and statistical optics : Speckle
(030.6600) Coherence and statistical optics : Statistical optics
(260.5430) Physical optics : Polarization
(290.0290) Scattering : Scattering

ToC Category:
Coherence and Statistical Optics

History
Original Manuscript: April 16, 2010
Revised Manuscript: July 3, 2010
Manuscript Accepted: July 9, 2010
Published: August 13, 2010

Citation
Shun Zhang, Mitsuo Takeda, and Wei Wang, "Statistics of spatial derivatives of Stokes parameters for isotropic random polarization field," J. Opt. Soc. Am. A 27, 1999-2003 (2010)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-27-9-1999


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J.C.Dainty, ed. (Springer-Verlag, 1975). [CrossRef]
  2. J. W. Goodman, Speckle Phenomena in Optics: Theory and Application (Roberts and Company, 2006).
  3. J. W. Goodman, Statistical Optics (Wiley, 2000).
  4. A. F. Fercher and P. F. Steeger, “First-order statistics of Stokes parameters in speckle fields,” Opt. Acta 28, 443–448 (1981). [CrossRef]
  5. D. Eliyahu, “Vector statistics of correlated Gaussian fields,” Phys. Rev. E 47, 2881–2892 (1993). [CrossRef]
  6. P. F. Steeger, T. Asakura, K. Zocha, and A. F. Fercher, “Statistics of the Stokes parameters in speckle fields,” J. Opt. Soc. Am. A 1, 677–682 (1984). [CrossRef]
  7. P. F. Steeger, “Probability density function of the intensity in partially polarized speckle fields,” Opt. Lett. 8, 528–530 (1983). [CrossRef] [PubMed]
  8. R. Barakat, “Statistics of the Stokes parameters,” J. Opt. Soc. Am. A 4, 1256–1263 (1987). [CrossRef]
  9. M. V. Berry and M. R. Dennis, “Polarization singularities in isotropic random vector waves,” Proc. R. Soc. London, Ser. A 457, 141–155 (2001). [CrossRef]
  10. M. R. Dennis, “Polarization singularities in paraxial vector fields: morphology and statistics,” Opt. Commun. 213, 201–221 (2002). [CrossRef]
  11. G. V. Bogatyryova, K. V. Felde, P. V. Polyanskii, and M. S. Soskin, “Nongeneric polarization singularities in combined vortex beams,” Opt. Spectrosc. 97, 782–789 (2004). [CrossRef]
  12. J. F. Nye, “Local solutions for the interaction of wave dislocations,” J. Opt. A, Pure Appl. Opt. 6, S251–S254 (2004). [CrossRef]
  13. J. F. Nye, “Lines of circular polarization in electromagnetic wave fields,” Proc. R. Soc. London, Ser. A 389, 279–290 (1983). [CrossRef]
  14. J. F. Nye and J. V. Hajnal, “The wave structure of monochromatic electromagnetic radiation,” Proc. R. Soc. London, Ser. A 409, 21–36 (1987). [CrossRef]
  15. J. F. Nye, Natural Focusing and the Fine Structure of Light (IOP, 1999).
  16. Y. Ohtsuka and K. Oka, “Contour mapping of the spatiotemporal state of polarization of light,” Appl. Opt. 33, 2633–2636 (1994). [CrossRef] [PubMed]
  17. K. J. Ebeling, “Statistical properties of spatial derivatives of the amplitude and intensity of monochromatic speckle patterns,” Opt. Acta 26, 1505–1521 (1979). [CrossRef]
  18. R. Barakat, “Zero-crossing rate of differentiated speckle intensity,” J. Opt. Soc. Am. A 11, 671–673 (1994). [CrossRef]
  19. D. A. Kessler and I. Freund, “Level-crossing densities in random wave fields,” J. Opt. Soc. Am. A 15, 1608–1618 (1998). [CrossRef]
  20. J. Ohtsubo, “Exact solution of the zero crossing rate of a differentiated speckle pattern,” Opt. Commun. 42, 13–18 (1982). [CrossRef]
  21. M. S. Longuet-Higgins, “The statistical analysis of a random moving surface,” Philos. Trans. R. Soc. London, Ser. A 249, 321–387 (1957). [CrossRef]
  22. E. Ochoa and J. W. Goodman, “Statistical properties of ray directions in a monochromatic speckle pattern,” J. Opt. Soc. Am. 73, 943–949 (1983). [CrossRef]
  23. M. Born and E. Wolf, Principle of Optics, 7th ed. (Cambridge Univ. Press, 1999).
  24. A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, 1960).
  25. I. I. Gradshteyn and I. M. Ryzhik, Table of Integrals Series and Products (Academic, 1965).
  26. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, 1965).

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.

Figures

Fig. 1 Fig. 2
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited