OSA's Digital Library

Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics


  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 6, Iss. 8 — Aug. 26, 2011

Polar decomposition of the Mueller matrix: a polarimetric rule of thumb for square-profile surface structure recognition

J. M. Sanz, J. M. Saiz, F. González, and F. Moreno  »View Author Affiliations

Applied Optics, Vol. 50, Issue 21, pp. 3781-3788 (2011)

View Full Text Article

Enhanced HTML    Acrobat PDF (1136 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



In this research, the polar decomposition (PD) method is applied to experimental Mueller matrices (MMs) measured on two-dimensional microstructured surfaces. Polarization information is expressed through a set of parameters of easier physical interpretation. It is shown that evaluating the first derivative of the retardation parameter, δ, a clear indication of the presence of defects either built on or dug in the scattering flat surface (a silicon wafer in our case) can be obtained. Although the rule of thumb thus obtained is established through PD, it can be easily implemented on conventional surface polarimetry. These results constitute an example of the capabilities of the PD approach to MM analysis, and show a direct application in surface characterization.

© 2011 Optical Society of America

OCIS Codes
(050.0050) Diffraction and gratings : Diffraction and gratings
(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology
(120.2130) Instrumentation, measurement, and metrology : Ellipsometry and polarimetry
(120.5410) Instrumentation, measurement, and metrology : Polarimetry
(120.5820) Instrumentation, measurement, and metrology : Scattering measurements
(290.0290) Scattering : Scattering

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: February 15, 2011
Revised Manuscript: May 3, 2011
Manuscript Accepted: May 24, 2011
Published: July 11, 2011

Virtual Issues
Vol. 6, Iss. 8 Virtual Journal for Biomedical Optics

J. M. Sanz, J. M. Saiz, F. González, and F. Moreno, "Polar decomposition of the Mueller matrix: a polarimetric rule of thumb for square-profile surface structure recognition," Appl. Opt. 50, 3781-3788 (2011)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. G. Videen and W. S. Bickel, “Light-scattering mueller matrix for a rough fiber,” Appl. Opt. 31, 3488–3492 (1992). [CrossRef] [PubMed]
  2. S. N. Savenkov, L. T. Mishchenko, R. S. Muttiah, Y. A. Oberemok, and I. A. Mishchenko, “Mueller polarimetry of virus-infected and healthy wheat under field and microgravity conditions,” J. Quant. Spectrosc. Radiat. Transfer 88, 327–343 (2004). [CrossRef]
  3. Y. Cui and R. M. A. Azzam, “Applications of the normal-incidence rotating-sample ellipsometer to high- and low-spatial-frequency gratings,” Appl. Opt. 35, 2235–2238 (1996). [CrossRef] [PubMed]
  4. J. J. Gil and E. Bernabeu, “Obtainment of the polarizing and retardation parameters of a non-depolarizing optical system from the polar decomposition of its mueller matrix,” Optik 76, 67–71 (1987).
  5. 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]
  6. J. Chung, W. Jung, M. J. Hammer-Wilson, P. Wilder-Smith, and Z. Chen, “Use of polar decomposition for the diagnosis of oral precancer,” Appl. Opt. 46, 3038–3045 (2007). [CrossRef] [PubMed]
  7. M. K. Swami, S. Manhas, P. Buddhiwant, N. Ghosh, A. Uppal, and P. K. Gupta, “Polar decomposition of 3×3 mueller matrix: a tool for quantitative tissue polarimetry,” Opt. Express 14, 9324–9337 (2006). [CrossRef] [PubMed]
  8. C. Collet, J. Zallat, and Y. Takakura, “Clustering of mueller matrix images for skeletonized structure detection,” Opt. Express 12, 1271–1280 (2004). [CrossRef] [PubMed]
  9. M. Foldyna, A. De Martino, R. Ossikovski, E. Garcia-Caurel, and C. Licitra, “Characterization of grating structures by Mueller polarimetry in presence of strong depolarization due to finite spot size,” Opt. Commun. 282, 735–741 (2009). [CrossRef]
  10. M. H. Smith, “Optimization of a dual-rotating-retarder Mueller matrix polarimeter,” Appl. Opt. 41, 2488–2493(2002). [CrossRef] [PubMed]
  11. 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]
  12. S. R. Cloude, “Group theory and polarization algebra,” Optik 75, 26–36 (1986).
  13. J. M. Sanz, P. Albella, F. Moreno, J. M. Saiz, and F. González, “Application of the polar decomposition to light scattering particle systems,” J. Quant. Spectrosc. Radiat. Transfer 110, 1369–1374 (2009). [CrossRef]
  14. J. J. Gil, “Polarimetric characterization of light and media,” Eur. Phys. J. Appl. Phys. 40, 1–47 (2007). [CrossRef]
  15. M. Foldyna, E. García-Caurel, R. Ossikovski, A. D. Martino, and J. Gil, “Retrieval of a non-depolarizing component of experimentally determined depolarizing mueller matrices,” Opt. Express 17, 12794–12806 (2009). [CrossRef] [PubMed]
  16. J. de la Peña, J. Saiz, P. Valle, F. González, and F. Moreno, “Tracking scattering minima to size metallic particles on flat substrates,” Part. Part. Syst. Charact. 16, 113–118 (1999). [CrossRef]
  17. H. Hulst, Light Scattering by Small Particles (Dover, 1981).
  18. J. L. de la Peña, F. González, J. M. Saiz, F. Moreno, and P. J. Valle, “Sizing particles on substrates. a general method for oblique incidence,” J. Appl. Phys. 85, 432–438(1999). [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