OSA's Digital Library

Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 12, Iss. 20 — Oct. 4, 2004
  • pp: 4941–4958

Degree of polarization surfaces and maps for analysis of depolarization

B. DeBoo, J. Sasian, and R. Chipman  »View Author Affiliations


Optics Express, Vol. 12, Issue 20, pp. 4941-4958 (2004)
http://dx.doi.org/10.1364/OPEX.12.004941


View Full Text Article

Enhanced HTML    Acrobat PDF (1938 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The concept of degree of polarization surfaces is introduced as an aid to classifying the depolarization properties of Mueller matrices. Degree of polarization surfaces provide a visualization of the dependence of depolarization on incident polarization state. The surfaces result from a non-uniform contraction of the Poincaré sphere corresponding to the depolarization properties encoded in a Mueller matrix. For a given Mueller matrix, the degree of polarization surface is defined by moving each point on the unit Poincaré sphere radially inward until its distance from the origin equals the output state degree of polarization for the corresponding input state. Of the sixteen elements in a Mueller matrix, twelve contribute to the shape of the degree of polarization surface, yielding a complex family of surfaces. The surface shapes associated with the numerator and denominator of the degree of polarization function are analyzed separately. Protrusion of the numerator surface through the denominator surface at any point indicates non-physical Mueller matrices. Degree of polarization maps are plots of the degree of polarization on flat projections of the sphere. These maps reveal depolarization patterns in a manner well suited for quantifying the degree of polarization variations, making degree of polarization surfaces and maps valuable tools for categorizing and classifying the depolarization properties of Mueller matrices.

© 2004 Optical Society of America

OCIS Codes
(120.5410) Instrumentation, measurement, and metrology : Polarimetry
(230.5440) Optical devices : Polarization-selective devices
(260.5430) Physical optics : Polarization

ToC Category:
Research Papers

History
Original Manuscript: August 20, 2004
Revised Manuscript: September 24, 2004
Published: October 4, 2004

Citation
Brian DeBoo, J. Sasian, and R. Chipman, "Degree of polarization surfaces and maps for analysis of depolarization," Opt. Express 12, 4941-4958 (2004)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-20-4941


Sort:  Journal  |  Reset  

References

  1. R.C. Jones, �??A new calculus for the treatment of optical systems: I. Description and discussion of the calculus,�?? J. Opt. Soc. Am. 31, 488-493 (1941). [CrossRef]
  2. R.C. Jones, �??New calculus for the treatment of optical systems: VIII. Electromagnetic theory,�?? J. Opt. Soc. Am. 46, 126-131 (1956). [CrossRef]
  3. M. Izdebski, W. Kucharczyk, and R.E. Raab, �??Application of the Jones calculus for a modulated doublerefracted light beam propagating in a homogeneous and nondepolarizing electro-optic uniaxial crystal,�?? J. Opt. Soc. Am. A 21, 132-139 (2004). [CrossRef]
  4. K.D. Abhyankar and A.L. Fymat, �??Relations between the elements of the phase matrix for scattering,�?? J. Math Phys. 10, 1935-1938 (1969). [CrossRef]
  5. E.S. Fry and G.W. Kattawar, �??Relationships between elements of the Stokes matrix,�?? Appl. Opt. 20, 2811-2814 (1981). [CrossRef] [PubMed]
  6. W. Swindell, ed., Benchmark Papers in Optics: Polarized Light, (Hutchinson and Ross, Stroudsburg, 1975).
  7. R.A. Chipman, �??Polarimetry,�?? in Handbook of Optics, Vol. II, (McGraw Hill, New York, 1995).
  8. J.L. Pezzaniti, S.C. McClain, R.A. Chipman, and S.Y. Lu, �??Depolarization in liquid crystal TV�??s,�?? Opt. Lett. 18, 2071-2073 (1993). [CrossRef] [PubMed]
  9. S.-M.F. Nee and T.-W. Nee, �??Principal Mueller matrix of reflection and scattering for a one-dimensional rough surface,�?? Opt. Eng. 41, 994-1001 (2002). [CrossRef]
  10. M.W. Williams, �??Depolarization and cross polarization in ellipsometry of rough surfaces.�?? Appl. Opt. 25, 3616-3621 (1986). [CrossRef] [PubMed]
  11. B. Laude-Boulesteix, A. DeMartino, B. Drévilon, and L. Schwartz, �??Mueller polarimetric imaging system with liquid crystals,�?? Appl. Opt. 43, 2824-2832 (2004). [CrossRef] [PubMed]
  12. N. Ghosh, H.S. Patel, and P.K. Gupta, �??Depolarization of light in tissue phantoms�??effect of a distribution in the size of scatterers,�?? Opt. Express 11, 2198-2205 (2003). [CrossRef] [PubMed]
  13. K. Sassen, �??Cirrus cloud iridescence: a rare case study,�?? Appl. Opt. 42, 486-491 (2003). [CrossRef] [PubMed]
  14. G.E. Jellison, C.O. Griffiths, D.E. Holcomb, and C.M. Rouleau, �??Transmission two-modulator generalized ellipsometry measurements,�?? Appl. Opt. 41, 6555-6566 (2002). [CrossRef] [PubMed]
  15. W.-N. Chen, C.-W. Chiang, J.-B. Nee, �??Lidar ratio and depolarization ratio for cirrus clouds,�?? Appl. Opt. 41, 6470-6476 (2002). [CrossRef] [PubMed]
  16. V.A. Ruiz-Cortés, and J.C. Dainty, �??Experimental light-scattering measurements from large-scale composite randomly rough surfaces,�?? J. Opt. Soc. Am. A 19, 2043-2052 (2002). [CrossRef]
  17. I. Shoji, Y. Sato, S. Kurimura, V. Lupei, T. Taira, A. Ikesue, and K. Yoshida, �??Thermal-birefringenceinduced depolarization in NdYAG ceramics,�?? Opt. Lett. 27, 234-236 (2002). [CrossRef]
  18. S.-M. F. Nee, �??Depolarization and principal Mueller matrix measured by null ellipsometry,�?? Appl. Opt. 40, 4933-4939 (2001). [CrossRef]
  19. M. Moscoso, J.B. Keller, and G. Papanicolaou, �??Depolarization and blurring of optical images by biological tissue,�?? J. Opt. Soc. Am. A 18, 948-960 (2001). [CrossRef]
  20. S.-M.F. Nee, �??Depolarization and retardation of a birefringent slab,�?? J. Opt. Soc. Am. A 17, 2067-2073 (2000). [CrossRef]
  21. J.J. Gil and E. Bernabeau, �??Depolarization and polarization indices of an optical system,�?? Opt. Acta 33, 185-189 (1986). [CrossRef]
  22. B. DeBoo, �??Investigation of polarization scatter properties using active imaging polarimetry,�?? PhD dissertation, Optical Sciences Center, University of Arizona (2004).
  23. D. Goldstein, Polarized Light, Second Ed., Revised and Expanded, (Marcel Dekker, New York, 2003). [CrossRef]
  24. R.C. Yates, A Handbook on Curves and Their Properties, (J. W. Edwards, Ann Arbor, 1952).
  25. G.B. Arfken, and H.J. Weber, Mathematical Methods for Physicists, (Academic Press, San Diego, 2001).
  26. S.-Y. Lu, �??An interpretation of polarization matrices,�?? PhD dissertation, Dept. of Physics, University of Alabama at Huntsville (1995).
  27. S.-Y. Lu and R.A. Chipman, �??Interpretation of Mueller matrices based on polar decomposition,�?? J. Opt. Soc. Am. A 13, 1106-1113 (1996). [CrossRef]
  28. C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach, (John Wiley and Sons, Inc., New York, 1998).
  29. C.R. Givens and A.B. Kostinski, �??A simple necessary and sufficient condition on physically realizable Mueller matrices,�?? J. Mod. Opt. 41, 471-481 (1994).
  30. J. Cariou, B. Le Jeune, J. Lotrian, and Y. Guern, �??Polarization effects of seawater and underwater targets,�?? Appl. Opt. 29, 1689- (1990) [CrossRef] [PubMed]

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.

Supplementary Material


» Media 1: MPG (1330 KB)     
» Media 2: MPG (1328 KB)     
» Media 3: MPG (967 KB)     
» Media 4: MPG (1457 KB)     

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited