OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 47, Iss. 14 — May. 10, 2008
  • pp: 2541–2549

Error propagation in polarimetric demodulation

A. Asensio Ramos and M. Collados  »View Author Affiliations

Applied Optics, Vol. 47, Issue 14, pp. 2541-2549 (2008)

View Full Text Article

Enhanced HTML    Acrobat PDF (459 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The polarization analysis of light is typically carried out using modulation schemes. The light of an unknown polarization state is passed through a set of known modulation optics, and a detector is used to measure the total intensity passing the system. The modulation optics is modified several times, and, with the aid of several such measurements, the unknown polarization state of the light can be inferred. How to find the optimal demodulation process has been investigated in the past. However, since the modulation matrix has to be measured for a given instrument and the optical elements can present problems of repeatability, some uncertainty is present in the elements of the modulation matrix or covariances between these elements. We analyze in detail this issue, presenting analytical formulas for calculating the covariance matrix produced by the propagation of such uncertainties on the demodulation matrix, on the inferred Stokes parameters, and on the efficiency of the modulation process. We demonstrate that even if the covariance matrix of the modulation matrix is diagonal, the covariance matrix of the demodulation matrix is in general nondiagonal because matrix inversion is a nonlinear operation. This propagates through the demodulation process and induces correlations on the inferred Stokes parameters.

© 2008 Optical Society of America

OCIS Codes
(120.2130) Instrumentation, measurement, and metrology : Ellipsometry and polarimetry
(120.4570) Instrumentation, measurement, and metrology : Optical design of instruments

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: December 14, 2007
Revised Manuscript: April 10, 2008
Manuscript Accepted: April 10, 2008
Published: May 1, 2008

A. Asensio Ramos and M. Collados, "Error propagation in polarimetric demodulation," Appl. Opt. 47, 2541-2549 (2008)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. C. R. Givens and A. Kostinski, “Physical significance of experimental Mueller matrices,” J. Mod. Opt. 40, 471-481 (1993). [CrossRef]
  2. E. Landi Degl'Innocenti and J. C. del Toro Iniesta, “Physical significance of experimental Mueller matrices,” J. Opt. Soc. Am. A 15, 533-537 (1998). [CrossRef]
  3. H. P. Povel, H. Aebersold, and J. O. Stenflo, “Charge-coupled-device image sensor as a demodulator in a 2-D polarimeter with a piezoelastic modulator,” Appl. Opt. 29, 1186-1190 (1990).
  4. H. P. Povel, “Imaging Stokes polarimetry with modulators and charge coupled-device image sensors,” Opt. Eng. 34, 1870-1878 (1995).
  5. M. Semel, J.-F. Donati, and D. E. Rees, “Zeeman-Doppler imaging of active stars. III. Instrumental and technical considerations,” Astron. Astrophys. 278, 231-237 (1993).
  6. J.-F. Donati, M. Semel, B. D. Carter, D. E. Rees, and A. Collier Cameron, “Spectropolarimetric observations of active stars,” Mon. Not. R. Astron. Soc. 291, 658-682 (1997).
  7. V. Martínez Pillet, M. Collados, J. Sánchez Almeida, V. González, A. Cruz-Lopez, A. Manescau, E. Joven, E. Paez, J. Diaz, O. Feeney, V. Sánchez, G. Scharmer, and D. Soltau, “LPSP & TIP: full Stokes polarimeters for the Canary Islands Observatories,” in High Resolution Solar Physics: Theory, Observations, and Techniques, Vol. 183 of Astronomical Society of the Pacific Conference Series, T.R.Rimmele, K.S.Balasubramaniam, and R.R.Radick, eds. (Astronomical Society of the Pacific, 1999), p. 264.
  8. A. López Ariste, J. Rayrole, and M. Semel, “First results from THEMIS spectropolarimetric mode,” Astron. Astrophys. Suppl. Ser. 142, 137-148 (2000). [CrossRef]
  9. J. C. del Toro Iniesta and M. Collados, “Optimum modulation and demodulation matrices for solar polarimetry,” Appl. Opt. 39, 1637-1642 (2000).
  10. M. Collados, “High resolution spectropolarimetry and magnetography, in Third Advances in Solar Physics Euroconference: Magnetic Fields and Oscillations, Vol. 184 of Astronomical Society of the Pacific Conference Series, B. Schmieder, A. Hofmann, and J. Staude, eds. (Astronomical Society of the Pacific, 1999), p. 3.
  11. E. H. Moore, “On the reciprocal of the general algebraic matrix,” Bull. Am. Math. Soc. 26, 394-395 (1920).
  12. R. Penrose, “A generalized inverse for matrices,” Proc. Cambridge Philos. Soc. 51, 406-413 (1955).
  13. D. S. Sabatke, M. R. Descour, E. L. Dereniak, W. C. Sweatt, S. A. Kemme, and G. S. Phipps, “Optimization of retardance for a complete Stokes polarimeter,” Opt. Lett. 25, 802-804(2000). [CrossRef]
  14. Y. Takakura and J. E. Ahmad, “Noise distribution of Mueller matrices retrieved with active rotating polarimeters,” Appl. Opt. 46, 7354-7364 (2007). [CrossRef]
  15. P. S. Hauge, “Mueller matrix ellipsometry with imperfect compensators,” J. Opt. Soc. Am. 68, 1519-1528 (1978).
  16. J. Zallat, S. Aïnouz, and M. P. Stoll, “Optimal configurations for imaging polarimeters: impact of image noise and systematic errors,” J. Opt. A Pure Appl. Opt. 8, 807-814 (2006). [CrossRef]
  17. S.-M. F. Nee, “Error analysis for Mueller matrix measurement,” J. Opt. Soc. Am. A 20, 1651-1657 (2003). [CrossRef]
  18. S.-M. F. Nee, “Errors of Mueller matrix measurements with a partially polarized light source,” Appl. Opt. 45, 6497-6506(2006). [CrossRef]
  19. J. S. Tyo, “Noise equalization in Stokes parameter images obtained by use of variable-retardance polarimeters,” Opt. Lett. 25, 1198-1200 (2000). [CrossRef]
  20. J. S. Tyo, “Design of optimal polarimeters: maximization of signal-to-noise and minimization of systematic error,” Appl. Opt. 41, 619-630 (2002). [CrossRef]
  21. M. H. Smith, “Optimization of a dual-rotating-retarder Mueller matrix polarimeter,” Appl. Opt. 41, 2488-2493 (2002). [CrossRef]
  22. D. H. Goldstein and R. A. Chipman, “Error analysis of a Mueller matrix polarimeter,” J. Opt. Soc. Am. A 6, 693-700 (1990).
  23. G. J. Hahn and S. S. Shapiro, Statistical Models in Engineering (Wiley, 1967).
  24. M. Lefebvre, R. K. Keeler, R. Sobie, and J. White, “Propagation of errors for matrix inversion,” Nucl. Instrum. Methods Phys. Res. A 451, 520 (2000).
  25. E. L. Dereniak, D. S. Sabatke, M. R. Locke, M. R. Descour, W. C. Sweatt, J. P. García, D. Sass, T. Hamilton, S. A. Kemme, and G. S. Phipps, “Design and optimization of a complete Stokes polarimeter for the MWIR,” (Office of Scientific & Technical Information, 2000).
  26. A. Ambirajan and D. C. Look, “Optimum angles for a polarimeter: part I,” Opt. Eng. 34, 1651-1655 (1995).
  27. V. Martínez Pillet, M. Collados, L. R. Bellot Rubio, I. Rodríguez Hidalgo, B. Ruiz Cobo, and D. Soltau, “The Tenerife Infrared Polarimeter,” Astron. Gess. Abstract Ser. 15, 141 (1999).
  28. D. F. Elmore, B. W. Lites, S. Tomczyk, A. P. Skumanich, R. B. Dunn, J. A. Schuenke, K. V. Streander, T. W. Leach, C. W. Chambellan, and H. K. Hull, “The advanced Stokes polarimeter: a new instrument for solar magnetic field research,” in Polarization Analysis and Measurement, D. H. Goldstein and R. A. Chipman, eds., Proc. SPIE 1746, 22-24 (1992).

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 Fig. 3

Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited