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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics


  • Editor: Gregory W. Faris
  • Vol. 1, Iss. 11 — Nov. 13, 2006

Polar decomposition of 3×3 Mueller matrix: a tool for quantitative tissue polarimetry

M. K. Swami, S. Manhas, P. Buddhiwant, N. Ghosh, A. Uppal, and P. K. Gupta  »View Author Affiliations

Optics Express, Vol. 14, Issue 20, pp. 9324-9337 (2006)

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The polarization properties of any medium are completely described by the sixteen element Mueller matrix that relates the polarization parameters of the light incident on the medium to that emerging from it. Measurement of all the elements of the matrix requires a minimum of sixteen measurements involving both linear and circularly polarized light. However, for many diagnostic applications, it would be useful if the polarization parameters can be quantified with linear polarization measurements alone. In this paper, we present a method based on polar decomposition of Mueller matrix for quantification of the polarization parameters of a scattering medium using the nine element (3×3) Mueller matrix that requires linear polarization measurements only. The methodology for decomposition of the 3×3 Mueller matrix is based on the previously developed decomposition process for sixteen element (4×4) Mueller matrix but with an assumption that the depolarization of linearly polarized light due to scattering is independent of the orientation angle of the incident linear polarization vector. Studies conducted on various scattering samples demonstrated that this assumption is valid for a turbid medium like biological tissue where the depolarization of linearly polarized light primarily arises due to the randomization of the field vector’s direction as a result of multiple scattering. For such medium, polar decomposition of 3×3 Mueller matrix can be used to quantify the four independent polarization parameters namely, the linear retardance (δ), the circular retardance (ψ), the linear depolarization coefficient (Δ) and the linear diattenuation (d) with reasonable accuracy. Since this approach requires measurements using linear polarizers only, it considerably simplifies measurement procedure and might find useful applications in tissue diagnosis using the retrieved polarization parameters.

© 2006 Optical Society of America

OCIS Codes
(110.7050) Imaging systems : Turbid media
(120.5410) Instrumentation, measurement, and metrology : Polarimetry
(170.0170) Medical optics and biotechnology : Medical optics and biotechnology
(170.4580) Medical optics and biotechnology : Optical diagnostics for medicine
(290.4210) Scattering : Multiple scattering

ToC Category:
Medical Optics and Biotechnology

Original Manuscript: July 7, 2006
Revised Manuscript: September 7, 2006
Manuscript Accepted: September 12, 2006
Published: October 2, 2006

Virtual Issues
Vol. 1, Iss. 11 Virtual Journal for Biomedical Optics

M. K. Swami, S. Manhas, P. Buddhiwant, N. Ghosh, A. Uppal, and P. K. Gupta, "Polar decomposition of 3 x 3 Mueller matrix: a tool for quantitative tissue polarimetry," Opt. Express 14, 9324-9337 (2006)

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  1. D. Bicout, C. Brosseau, A.S. Martinez, and J.M. Schmitt, "Depolarization of multiply scattered waves by spherical diffusers: Influence of the size parameter," Phys. Rev. E 49, 1767-1770 (1994). [CrossRef]
  2. A.D. Kim and M. Moscoso, "Influence of the refractive index on the depolarization of multiply scattered waves," Phys. Rev. E 64, 026612, 1-4 (2001). [CrossRef]
  3. V. Sankaran, J.T. Walsh, Jr., and D.J. Maitland, "Comparative study of polarized light propagation in biological tissues," J. Biomed. Opt. 7, 300-306 (2002). [CrossRef] [PubMed]
  4. N. Ghosh, P.K. Gupta, H.S. Patel, B. Jain, and B.N. Singh, "Depolarization of light in tissue phantoms - effect of collection geometry," Opt. Commun. 222, 93-100 (2003). [CrossRef]
  5. 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]
  6. N. Ghosh, A. Pradhan, P.K. Gupta, S. Gupta, V. Jaiswal, and R.P. Singh, "Depolarization of light in a multiply scattering medium: effect of refractive index of scatterer," Phys. Rev. E 70, 066607 (2004). [CrossRef]
  7. J.F. de Boer, T.E. Milner, M.J.C. van Gemert, and J.S. Nelson, "Two-dimensional birefringence imaging in biological tissue by polarization-sensitive optical coherence Tomography," Opt. Lett. 22, 934-936 (1997). [CrossRef] [PubMed]
  8. D.J. Maitland and J.T. WalshJr., "Quantitative measurement of linear birefringence during heating of native collagen," Lasers Surg. Med. 20, 310-318 (1997). [CrossRef] [PubMed]
  9. M.H. Smith, "Interpreting Mueller matrix images of tissues," Proceedings SPIE 4257, 82 - 89 (2001). [CrossRef]
  10. G.L. Liu, Y. Li, and B.D. Cameron, "Polarization based optical imaging and processing techniques with application to the cancer diagnostics," Proceedings SPIE 4617, 208 - 220 (2002). [CrossRef]
  11. C.W. Sun, L.S. Lu, C.C. Yang, Y.W. Kiang, and M.J. Su, "Myocardial tissue characterization based on the time-resolved Stokes-Mueller formalism," Opt. Express 10, 1347 - 1353 (2002). [PubMed]
  12. J. Zhang, S. Guo, W. Jung, J.S. Nelson, and Z. Chen, " Determination of birefringence and absolute optic axis orientation using polarization-sensitive optical coherence tomography with PM fibers," Opt. Express 11, 3262 - 3270 (2003). [CrossRef] [PubMed]
  13. O. Kostyuk and R.A. Brown, "Novel Spectroscopic Technique for In Situ Monitoring of Collagen Fibril Alignment in Gels," Biophys. J. 87, 648-655 (2004). [CrossRef] [PubMed]
  14. F. Boulvert, B. Boulbry, G Le Brun, S. Rivet, and J. Cariou, "Analysis of the depolarization properties of irradiated pig skin," J. Opt. A: Pure Appl. Opt. 7, 21 - 28 (2005). [CrossRef]
  15. R.J. McNichols and G.L. Cote, "Optical glucose sensing in biological fluids: an overview," J. Biomed. Opt. 5, 5 - 16 (2000). [CrossRef] [PubMed]
  16. B.D. Cameron and G.L. Cote, "Noninvasive glucose sensing utilizing a digital closed loop polarimetric approach," IEEE Trans. Biomed. Eng. 44, 1221-227 (1997). [CrossRef] [PubMed]
  17. I.A. Vitkin and R.C.N Studinski, "Polarization preservation in diffusive scattering from in-vivo turbid biological media: Effects of tissue optical absorption in the exact backscattering direction," Opt. Commun. 190, 37-43 (2001). [CrossRef]
  18. K.C. Hadley and I.A. Vitkin, "Optical rotation and linear and circular depolarization rates in diffusively scattered light from chiral, racimic and achiral turbid media," J. Biomed. Opt. 7, 291-299 (2002). [CrossRef] [PubMed]
  19. I. Vitkin, R.D. Laszlo, and C.L. Whyman, "Effects of molecular asymmetry of optically active molecules on the polarization properties of multiply scattered light," Opt. Express 10, 222 - 229 (2002). [PubMed]
  20. X. Wang, G. Yao, and L.V. Yang, "Monte Carlo model and single scattering approx. Of the propagation of polarized light in turbid media containing glucose," Appl. Opt. 41, 792 - 801, (2002). [CrossRef] [PubMed]
  21. D. Cote and I. Vitkin, "Robust concentration determination of optically active molecule in turbid media with validated three dimensional polarization sensitive Monte Carlo calculation," Opt. Express 13, 148-163 (2005). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-148 [CrossRef] [PubMed]
  22. 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] [PubMed]
  23. S. Yau Lu and R.A. Chipman, "Interpretation of Mueller matrices based on polar decomposition," J. Opt. Soc. Am. A 13, 1106-1113 (1996). [CrossRef]
  24. R.A. Chipman, "Hand book of optics (polarimetry)," OSA/McGraw-Hill, 22.1-22.35, (1994).
  25. B.L. Boulesteix, A. De Martino, B. Dre villon, and L. Schwartz, "Mueller polarimetric imaging system with liquid crystal," Appl. Opt. 43, 2824-2832 (2004). [CrossRef]
  26. E. Collett and V. Gazerro, "Polarization measurements in a spectrofluorophotometer," Opt. Commun. 129, 229-236 (1996). [CrossRef]
  27. E . Gar cia-Caurel, A. De Martino, and B. Drevillon, "Spectroscopic Mueller polarimeter based on liquid crystal devices," Thin Solid Films 455-456, 120-123 (2004). [CrossRef]
  28. <jrn>. J. Morio and F. Goudail, "Influence of the order of diattenuator, retarder, and polarizer in polar decomposition of Mueller matrices," Opt. Lett. 29, 2234-2236 (2004).</jrn> [CrossRef] [PubMed]
  29. M. Wong, M.J. Hendrix, K. Von der Mark, C. Little and R. Stern, "Collagen in the egg shell membranes of the hen," Dev. Biol. 104 (1), 28-36 (1984). [CrossRef]
  30. C.F. Bohren and D.R. Huffman, "Absorption and scattering of light by small particles," Wiley, New York (1983).

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