OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 31, Iss. 3 — Mar. 1, 2014
  • pp: 610–615

Measuring the Mueller matrix of an arbitrary optical element with a universal SU(2) polarization gadget

Salla Gangi Reddy, Shashi Prabhakar, A. Aadhi, Ashok Kumar, Megh Shah, R. P. Singh, and R. Simon  »View Author Affiliations

JOSA A, Vol. 31, Issue 3, pp. 610-615 (2014)

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



We propose a new method for determining the Mueller matrix of an arbitrary optical element and verify it with three known optical elements. This method makes use of two universal SU(2) polarization gadgets to obtain the projection matrix directly from the experiment. It allows us to determine the Mueller matrix without precalibration of the setup, since the generated polarization states are fully determined by the azimuths of the wave plates. We calculate errors in determining the Mueller matrix and compare with other techniques.

© 2014 Optical Society of America

OCIS Codes
(120.2130) Instrumentation, measurement, and metrology : Ellipsometry and polarimetry
(260.5430) Physical optics : Polarization

ToC Category:

Original Manuscript: October 30, 2013
Revised Manuscript: January 11, 2014
Manuscript Accepted: January 15, 2014
Published: February 20, 2014

Salla Gangi Reddy, Shashi Prabhakar, A. Aadhi, Ashok Kumar, Megh Shah, R. P. Singh, and R. Simon, "Measuring the Mueller matrix of an arbitrary optical element with a universal SU(2) polarization gadget," J. Opt. Soc. Am. A 31, 610-615 (2014)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. 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]
  2. S. Manhas, M. K. Swami, P. Buddhiwant, N. Ghosh, P. K. Gupta, and K. Singh, “Mueller matrix approach for determination of optical rotation in chiral turbid media in backscattering geometry,” Opt. Express 14, 190–202 (2006). [CrossRef]
  3. W. C. Kuo, N. K. Chou, C. Chou, C. M. Lai, H. J. Huang, S. S. Wang, and J. J. Shyu, “Polarization-sensitive optical coherence tomography for imaging human atherosclerosis,” Appl. Opt. 46, 2520–2527 (2007). [CrossRef]
  4. C. K. Hitzenberger, E. Götzinger, M. Sticker, M. Pircher, and A. F. Fercher, “Measurement and imaging of birefringence and optic axis orientation by phase resolved polarization sensitive optical coherence tomography,” Opt. Express 9, 780–790 (2001). [CrossRef]
  5. V. K. Jaiswal, R. P. Singh, and R. Simon, “Producing optical vortices through forked holographic grating: study of polarization,” J. Mod. Opt. 57, 2031–2038 (2010). [CrossRef]
  6. I. Moreno, A. Lizana, J. Campos, A. Márquez, C. Iemmi, and M. J. Yzuel, “Combined Mueller and Jones matrix method for the evaluation of the complex modulation in a liquid-crystal-on-silicon display,” Opt. Lett. 33, 627–629 (2008). [CrossRef]
  7. T. Novikova, A. De Martino, S. B. Hatit, and B. Drévillon, “Application of Mueller polarimetry in conical diffraction for critical dimension measurements in microelectronics,” Appl. Opt. 45, 3688–3697 (2006). [CrossRef]
  8. J. Tinbergen, Astronomical Polarimetry (Cambridge University, 1996).
  9. K. J. Voss and E. S. Fry, “Measurement of the Mueller matrix for ocean water,” Appl. Opt. 23, 4427–4439 (1984). [CrossRef]
  10. R. Simon and N. Mukunda, “Minimal three-component SU(2) gadget for polarization optics,” Phys. Lett. A 143, 165–169 (1990). [CrossRef]
  11. V. Bagini, R. Borghi, F. Gori, M. Santarsiero, F. Frezza, G. Schettini, and G. Schirripa Spagnolo, “The Simon–Mukunda polarization gadget,” Eur. J. Phys. 17, 279–284 (1996). [CrossRef]
  12. B. Neethi Simon, C. M. Chandrashekar, and S. Simon, “Hamilton’s turns as visual tool-kit for designing of single qubit unitary gates,” Phys. Rev. A 85, 022323 (2012). [CrossRef]
  13. M. Hayman and J. P. Thayer, “Lidar polarization measurements of PMCs,” J. Atmos. Sol. Terr. Phys. 73, 2110–2117 (2011). [CrossRef]
  14. M. Hayman and J. P. Thayer, “General description of polarization in lidar using Stokes vectors and polar decomposition of Mueller matrices,” J. Opt. Soc. Am. A 29, 400–409 (2012). [CrossRef]
  15. U. Schilling, J. V. Zanthier, and G. S. Agarwal, “Measuring arbitrary-order coherences: tomography of single-mode multiphoton polarization-entangled states,” Phys. Rev. A 81, 013826 (2010). [CrossRef]
  16. J. C. Loredo, O. Ortz, R. Weingärtner, and F. De Zela, “Measurement of Pancharatnam phase by robust interferometric and polarimetric methods,” Phys. Rev. A 80, 012113 (2009). [CrossRef]
  17. D. Layden, M. F. G. Wood, and I. A. Vitkin, “Optimum selection of input polarization states in determining the sample Mueller matrix: a dual photoelastic polarimeter approach,” Opt. Express 20, 20466–20481 (2012). [CrossRef]
  18. W. S. Bicke and W. M. Bailey, “Stokes vectors, Mueller matrices and polarized light scattering,” Am. J. Phys. 53, 468–478 (1985). [CrossRef]
  19. 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]
  20. D. Goldstein, Polarized Light (Marcel Dekker, 2003).
  21. R. Simon, “The connection between Mueller and Jones matrices of polarization optics,” Opt. Commun. 42, 293–297 (1982). [CrossRef]
  22. E. S. Fry and G. W. Kattawar, “Relationships between elements of the Stokes matrix,” Appl. Opt. 20, 2811–2814 (1981). [CrossRef]
  23. H. H. Ku, “Notes on the use of propagation of error formulas,” J. Res. Natl. Bur. Standards C 70C, 263–273 (1966).
  24. A. C. Melissinos, Experiments in Modern Physics (Academic, 1966), Sec. 10.4, pp. 467–479.
  25. D. F. V. James, P. G. Kwait, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001). [CrossRef]
  26. D. H. Goldstein, “Mueller matrix dual-rotating retarder polarimeter,” Appl. Opt. 31, 6676–6683 (1992). [CrossRef]
  27. K. Dev and A. Asundi, “Mueller Stokes polarimetric characterization of transmissive liquid crystal spatial light modulator,” Opt. Lasers Eng. 50, 599–607 (2012). [CrossRef]
  28. J. M. Bueno, “Polarimetry using liquid-crystal variable retarders: theory and calibration,” J. Opt. A 2, 216–222 (2000). [CrossRef]
  29. J. S. Baba, J. R. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Cote, “Development and calibration of an automated Mueller matrix polarization imaging system,” J. Biomed. Opt. 7, 341–349 (2002). [CrossRef]
  30. A. Ling, K. P. Soh, A. L. Linares, and C. Kurtsiefer, “Experimental polarization state tomography using optimal polarimeters,” Phys. Rev. A 74, 022309 (2006). [CrossRef]
  31. M. W. Mitchell, C. W. Ellenor, S. Schneider, and A. M. Steinberg, “Diagnosis, prescription, and prognosis of a Bell-state filter by quantum process tomography,” Phys. Rev. Lett. 91, 120402 (2003). [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.


Fig. 1. Fig. 2.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited