Comparative study of differential matrix and extended polar decomposition formalisms for polarimetric characterization of complex tissue-like turbid media

Abstract. Development of methodologies for quantification/unique interpretation of the intrinsic polarimetry characteristics of biological tissues are important for various applications involving tissue characterization/diagnosis. A detailed comparative evaluation of the polar decomposition and the differential matrix decomposition of Mueller matrices for extraction/quantification of the intrinsic polarimetry characteristics (with special emphasis on linear retardance δ, optical rotation Ψ and depolarization Δ parameters was performed, because these are the most prominent tissue polarimetry effects) from complex tissue-like turbid media exhibiting simultaneous scattering and polarization effects. The results suggest that for media exhibiting simultaneous linear retardance and optical rotation polarization events, the use of retarder polar decomposition with its associated analysis which assumes sequential occurrence of these effects, results in systematic underestimation of δ and overestimation of Ψ parameters. Analytical relationships between the polarization parameters (δ, Ψ) extracted from both the retarder polar decomposition and the differential matrix decomposition for either simultaneous or sequential occurrence of the linear retardance and optical rotation effects were derived. The self-consistency of both decompositions is validated on experimental Mueller matrices recorded from tissue-simulating phantoms (whose polarization properties are controlled, known a-priori, and exhibited simultaneously) of increasing biological complexity. Additional theoretical validation tests were performed on Monte Carlo-generated Mueller matrices from analogous turbid media exhibiting simultaneous depolarization (Δ), linear retardance (δ) and optical rotation (Ψ) effects. After successful evaluation, the potential advantage of the differential matrix decomposition over the polar decomposition formalism was explored for monitoring of myocardial tissue regeneration following stem cell therapy.

[1]  Noé Ortega-Quijano,et al.  Experimental validation of Mueller matrix differential decomposition. , 2012, Optics express.

[2]  William S. Bickel,et al.  Stokes vectors, Mueller matrices, and polarized scattered light , 1985 .

[3]  Xinxin Guo,et al.  Polarized light propagation in multiply scattering media exhibiting both linear birefringence and optical activity: Monte Carlo model and experimental methodology. , 2007, Journal of biomedical optics.

[4]  Rasheed M. A. Azzam,et al.  Propagation of partially polarized light through anisotropic media with or without depolarization: A differential 4 × 4 matrix calculus , 1978 .

[5]  M. K. Swami,et al.  Muller matrix approach for determination of optical rotation in chiral turbid media in backscattering geometry , 2006, Saratov Fall Meeting.

[6]  R. Chipman,et al.  Interpretation of Mueller matrices based on polar decomposition , 1996 .

[7]  R. Azzam,et al.  Polarized light in optics and spectroscopy , 1990 .

[8]  Valery V. Tuchin,et al.  Optical polarization in biomedical applications , 2006 .

[9]  Nirmalya Ghosh,et al.  Polarimetry in turbid, birefringent, optically active media: A Monte Carlo study of Mueller matrix decomposition in the backscattering geometry , 2009 .

[10]  Nirmalya Ghosh,et al.  Toward Noninvasive Glucose Sensing Using Polarization Analysis of Multiply Scattered Light , 2008 .

[11]  J. M. de Bougrenet de la Tocnaye,et al.  Complex amplitude modulation by use of liquid-crystal spatial light modulators. , 1997, Applied optics.

[12]  Paul J. Wu,et al.  Stokes polarimetry imaging of rat tail tissue in a turbid medium: degree of linear polarization image maps using incident linearly polarized light. , 2006, Journal of biomedical optics.

[13]  A. de Martino,et al.  Forward and reverse product decompositions of depolarizing Mueller matrices. , 2007, Optics letters.

[14]  Razvigor Ossikovski,et al.  Differential matrix formalism for depolarizing anisotropic media. , 2011, Optics letters.

[15]  Nirmalya Ghosh,et al.  Influence of the order of the constituent basis matrices on the Mueller matrix decomposition-derived polarization parameters in complex turbid media such as biological tissues , 2010 .

[16]  R. Clark Jones,et al.  A New Calculus for the Treatment of Optical Systems. VII. Properties of the N-Matrices , 1948 .

[17]  E Tajahuerce,et al.  Phase-only modulation with a twisted nematic liquid crystal display by means of equi-azimuth polarization states. , 2006, Optics express.

[18]  J. L. Arce-Diego,et al.  Mueller matrix differential decomposition. , 2011, Optics letters.

[19]  Nirmalya Ghosh,et al.  Tissue polarimetry: concepts, challenges, applications, and outlook. , 2011, Journal of biomedical optics.

[20]  Nirmalya Ghosh,et al.  Polarized Light Assessment of Complex Turbid Media Such as Biological Tissues Using Mueller Matrix Decomposition , 2010 .

[21]  Oriol Arteaga,et al.  Pseudopolar decomposition of the Jones and Mueller-Jones exponential polarization matrices. , 2009, Journal of the Optical Society of America. A, Optics, image science, and vision.

[22]  M. E. Cox.  Handbook of Optics , 1980 .

[23]  Razvigor Ossikovski,et al.  Analysis of depolarizing Mueller matrices through a symmetric decomposition. , 2009, Journal of the Optical Society of America. A, Optics, image science, and vision.

[24]  Nirmalya Ghosh,et al.  Mueller matrix decomposition for extraction of individual polarization parameters from complex turbid media exhibiting multiple scattering, optical activity, and linear birefringence. , 2008, Journal of biomedical optics.

[25]  R. Chipman,et al.  Mueller matrix roots algorithm and computational considerations. , 2012, Optics express.

[26]  Nirmalya Ghosh,et al.  Mueller matrix decomposition for polarized light assessment of biological tissues , 2009, Journal of biophotonics.

[27]  R. Jones.  A New Calculus for the Treatment of Optical Systems. IV. , 1942 .

[28]  Razvigor Ossikovski,et al.  Differential and product Mueller matrix decompositions: a formal comparison. , 2012, Optics letters.

[29]  E. García-Caurel,et al.  Depolarizing Mueller matrices: how to decompose them? , 2008 .

[30]  M. K. Swami,et al.  Mueller matrix approach for determination of optical rotation in chiral turbid media in backscattering geometry. , 2006, Optics express.