OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 40, Iss. 1 — Jan. 1, 2001
  • pp: 34–44

Real-time measurement of the polarization transfer function

Mircea Mujat and Aristide Dogariu  »View Author Affiliations

Applied Optics, Vol. 40, Issue 1, pp. 34-44 (2001)

View Full Text Article

Enhanced HTML    Acrobat PDF (171 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We present a simple method for measuring the Mueller matrix associated with a scattering medium. Without involving moving parts, four input states of polarization are generated sequentially, and for each of them all four Stokes vector parameters are simultaneously measured for the complete determination of the Mueller matrix. Two liquid-crystal variable retarders are used for controlling the input state of polarization, whereas the measurement of the state of polarization involves phase modulation with a single-pass photoelastic modulator, and Fourier analysis in two polarization channels. The setup is controlled by a computer, allowing for real-time measurement of the Mueller matrix. The method is tested on standard elements such as polarizers and quarter-wave plates, as well as on inhomogeneous particulate systems.

© 2001 Optical Society of America

OCIS Codes
(120.5410) Instrumentation, measurement, and metrology : Polarimetry
(260.5430) Physical optics : Polarization
(290.5850) Scattering : Scattering, particles
(290.7050) Scattering : Turbid media

Original Manuscript: June 6, 2000
Revised Manuscript: October 1, 2000
Published: January 1, 2001

Mircea Mujat and Aristide Dogariu, "Real-time measurement of the polarization transfer function," Appl. Opt. 40, 34-44 (2001)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
  2. C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (Wiley, New York, 1998).
  3. W. A. Shurcliff, Polarized Light (Harvard University, Cambridge, Mass., 1966).
  4. H. Mueller, “The foundations of optics (abstract),” J. Opt. Soc. Am. 38, 661 (1948).
  5. E. Collett, “Measurement of the four Stokes polarization parameters with a single circular polarizer,” Opt. Commun. 52, 77–80 (1996). [CrossRef]
  6. A. Ambirajan, D. C. Look, “Experimental investigation of the multiple scattering of a polarized laser beam,” J. Thermophys. Heat Transfer 12, 153–163 (1998). [CrossRef]
  7. J. Cariou, B. L. Jeune, J. Lotrian, Y. Guern, “Polarization effects of seawater and underwater targets,” Appl. Opt. 29, 1689–1695 (1990). [CrossRef] [PubMed]
  8. W. S. Bickel, W. M. Bailey, “Stokes vectors, Mueller matrices, and polarized scattered light,” Am. J. Phys. 53, 468–478 (1985). [CrossRef]
  9. W. M. McClain, W. Jeng, B. Pati, Y. Shi, D. Tian, “Measurement of the Mueller scattering matrix by use of optical beats from a Zeeman laser,” Appl. Opt. 33, 1230–1241 (1994). [CrossRef] [PubMed]
  10. R. M. A. Azzam, “Photopolarimetric measurement of the Mueller matrix by Fourier analysis of a single detected signal,” Opt. Lett. 2, 148–150 (1978). [CrossRef] [PubMed]
  11. D. H. Goldstein, “Infrared laser polarimeter,” U.S. patent5,247,176 (21September1993).
  12. R. M. A. Azzam, “Polarimeter,” U.S. patent4,306,809 (22December1981).
  13. Z. Sekera, “Light scattering in the atmosphere and the polarization of sky light,” J. Opt. Soc. Am. 47, 484–490 (1957). [CrossRef]
  14. G. D. Lewis, D. L. Jordan, “Backscattering Mueller matrices from bead-blasted aluminum surfaces,” in Polarization: Measurement, Analysis, and Remote Sensing, D. H. Goldstein, R. A. Chipman, eds., Proc. SPIE3121, 434–443 (1997).
  15. G. D. Lewis, D. L. Jordan, E. Jakeman, “Backscatter linear and circular polarization analysis of roughened aluminum,” Appl. Opt. 37, 5985–5992 (1998). [CrossRef]
  16. R. M. A. Azzam, “Division-of-amplitude photopolarimeter (DOAP) for the simultaneous measurement of all four Stokes parameters of light,” Opt. Acta 29, 685–689 (1982). [CrossRef]
  17. R. M. A. Azzam, “Photodetector arrangement for measuring the state of polarization of light,” U.S. patent4,681,450 (21July1987).
  18. A. M. El-Saba, R. M. A. Azzam, M. A. G. Abushagur, “Performance optimization and light-beam-deviation analysis of the parallel-slab division-of-amplitude photopolarimeter,” Appl. Opt. 38, 2829–2836 (1999). [CrossRef]
  19. S. Krishnan, P. C. Nordine, “Mueller matrix ellipsometry using the division-of-amplitude photopolarimeter: a study of depolarization effects,” Appl. Opt. 33, 4184–4192 (1994). [CrossRef] [PubMed]
  20. S. Krishnan, P. C. Nordine, “Fast ellipsometry and Mueller-matrix ellipsometry using the division-of-amplitude photopolarimeter,” in Polarization Analysis and Applications to Device Technology, T. Yoshizawa, H. Yokota, eds., Proc. SPIE2173, 152–156 (1996). [CrossRef]
  21. J. E. Bille, “Ellipsometer,” U.S. patent5,822,035 (13October1998).
  22. S. Jasperson, S. E. Schnatterly, “An improved method for high reflectivity ellipsometry based on a new modulation technique,” Rev. Sci. Instrum. 40, 761–767 (1969). [CrossRef]
  23. A. J. Hunt, D. R. Huffman, “A new polarization-modulated light scattering instrument,” Rev. Sci. Instrum. 44, 1753–1762 (1973). [CrossRef]
  24. B. W. Bell, “Mueller matrix: an experimental and analytical tool for magneto-optics,” Opt. Eng. 28, 114–119 (1989).
  25. G. C. Salzman, C. T. Gregg, W. K. Grace, R. D. Hiebert, “Biological particle identification apparatus,” U.S. patent4,884,886 (5December1989).
  26. R. Anderson, “Measurement of Mueller matrices,” Appl. Opt. 31, 11–13 (1992). [CrossRef] [PubMed]
  27. G. E. Jellison, F. A. Modine, “Two modulator generalized ellipsometer for complete Mueller matrix measurement,” U.S. patent5,956,147 (21September1999).
  28. B. DeVolk, F. Allen, C. D. Newman, R. J. Frastz, “Particle identifying apparatus,” U.S. patent4,953,980 (4September1990).
  29. R. C. Thompson, J. R. Bottiger, E. S. Fry, “Measurement of polarized light interactions via the Mueller matrix,” Appl. Opt. 19, 1323–1332 (1980). [CrossRef] [PubMed]
  30. E. Compain, B. Drevillon, “Complete high-frequency measurement of Mueller matrices based on a new coupled-phase modulator,” Rev. Sci. Instrum. 68, 2671–2680 (1997). [CrossRef]
  31. E. Compain, B. Drevillon, J. Huc, J. Y. Parey, J. E. Bouree, “Complete Mueller matrix measurement with a single high frequency modulation,” Thin Solid Films 313–314, 47–52 (1998).
  32. E. Compain, B. Drevillon, “High-frequency modulation of the four states of polarization of light with a single phase modulator,” Rev. Sci. Instrum. 69, 1574–1580 (1998). [CrossRef]
  33. E. Compain, B. Drevillon, “Broadband division-of-amplitude polarimeter based on uncoated prisms,” Appl. Opt. 37, 5938–5944 (1998). [CrossRef]
  34. B. Kaplan, E. Compain, B. Drevillon, “Phase-modulated Mueller ellipsometry characterization of scattering by latex sphere suspensions,” Appl. Opt. 39, 629–636 (2000). [CrossRef]
  35. Z. Zhuang, S. W. Suh, J. S. Patel, “Polarization controller using nematic liquid crystals,” Opt. Lett. 24, 694–696 (1999). [CrossRef]
  36. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland Publishing, Amsterdam, 1997).
  37. J. M. Schmitt, A. H. Gandjakhche, R. F. Bonner, “Use of polarized light to discriminate short-path photons in a multiply scattering medium,” Appl. Opt. 31, 6535–6546 (1992). [CrossRef] [PubMed]
  38. M. Mujat, A. Dogariu, “Real-time Mueller matrix measurement for particulate systems,” in Laser Radar Technology and Applications V, G. W. Kamerman, U. N. Singh, C. Werner, V. V. Molebny, eds., Proc. SPIE4035, 390–400 (2000). [CrossRef]
  39. D. Bicout, C. Brosseau, A. S. Martinez, J. M. Schmitt, “Depolarization of multiply scattered waves by spherical diffusers: influence of the size parameter,” Phys. Rev. E 49, 1767–1770 (1994). [CrossRef]

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.

CrossCheck Deposited