Monte Carlo modeling of polarized light propagation: Stokes vs. Jones. Part I.

This bipartite comparative study aims at inspecting the similarities and differences between the Jones and Stokes-Mueller formalisms when modeling polarized light propagation with numerical simulations of the Monte Carlo type. In this first part, we review the theoretical concepts that concern light propagation and detection with both pure and partially/totally unpolarized states. The latter case involving fluctuations, or "depolarizing effects," is of special interest here: Jones and Stokes-Mueller are equally apt to model such effects and are expected to yield identical results. In a second, ensuing paper, empirical evidence is provided by means of numerical experiments, using both formalisms.

[1]  Scott A Prahl,et al.  Three Monte Carlo programs of polarized light transport into scattering media: part II. , 2005, Optics express.

[2]  Tsu-Wei Nee,et al.  Scattering depolarization by a bio-medium with anisotropic bio-molecules , 2008, Optical Engineering + Applications.

[3]  Rolf H. Muller,et al.  Definitions and conventions in ellipsometry , 1969 .

[4]  Min Xu,et al.  Electric field Monte Carlo simulation of polarized light propagation in turbid media. , 2004, Optics express.

[5]  Paul,et al.  Unpolarized light: Classical and quantum states. , 1996, Physical review. A, Atomic, molecular, and optical physics.

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

[7]  Maynard,et al.  Faraday effect and multiple scattering of light. , 1994, Physical review. B, Condensed matter.

[8]  Igor Meglinski,et al.  Coherent Backscattering of Circularly Polarized Light from a Disperse Random Medium , 2011 .

[9]  A. Luis Degree of polarization in quantum optics , 2002 .

[10]  Michael S. Feld,et al.  Imaging human epithelial properties with polarized light-scattering spectroscopy , 2001, Nature Medicine.

[11]  L V Wang,et al.  Light backscattering polarization patterns from turbid media: theory and experiment. , 1999, Applied optics.

[12]  T. Booth,et al.  MCNP variance reduction overview , 1985 .

[13]  A. Dogariu,et al.  Probing Random Media with Singular Beams , 2005 .

[14]  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.

[15]  Jessica C Ramella-Roman,et al.  Imaging skin pathology with polarized light. , 2002, Journal of biomedical optics.

[16]  Emil Wolf,et al.  CHAPTER VIII – ELEMENTS OF THE THEORY OF DIFFRACTION , 1980 .

[17]  Ralf Lenke,et al.  Magnetic field effects on coherent backscattering of light , 2000 .

[18]  A H Hielscher,et al.  Influence of particle size and concentration on the diffuse backscattering of polarized light from tissue phantoms and biological cell suspensions. , 1997, Applied optics.

[19]  Ashleyj . Welch,et al.  Optical-Thermal Response of Laser-Irradiated Tissue , 1995 .

[20]  H. V. Hulst Light Scattering by Small Particles , 1957 .

[21]  I. L. Maksimova,et al.  The effect of multiple scattering in disperse media on polarization characteristics of scattered light , 2002 .

[22]  V. Maxia Light polarization problems. , 1976, Applied optics.

[23]  H. Hurwitz The Statistical Properties of Unpolarized Light , 1945 .

[24]  L V Wang,et al.  Measurement and calculation of the two-dimensional backscattering Mueller matrix of a turbid medium. , 1998, Optics letters.

[25]  George Gabriel Stokes,et al.  On the Composition and Resolution of Streams of Polarized Light from different Sources , 2009 .

[26]  F. Perrin Polarization of Light Scattered by Isotropic Opalescent Media , 1942 .

[27]  R. Simon Nondepolarizing systems and degree of polarization , 1990 .

[28]  Alwin Kienle,et al.  Multiple scattering of polarized light: comparison of Maxwell theory and radiative transfer theory. , 2012, Journal of biomedical optics.

[29]  Masato Shibuya,et al.  Incoming inclination factor for scalar imaging theory , 2010 .

[30]  J. Rička,et al.  Polarized Light: Electrodynamic Fundamentals , 2010 .

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

[32]  D. Côté,et al.  Robust concentration determination of optically active molecules in turbid media with validated three-dimensional polarization sensitive Monte Carlo calculations. , 2005, Optics express.

[33]  G. Plass,et al.  Radiance and polarization of multiple scattered light from haze and clouds. , 1968, Applied optics.

[34]  D. James,et al.  Definitions of the degree of polarization of a light beam. , 2007 .

[35]  George W. Kattawar,et al.  A Search for Circular Polarization in Nature , 1994 .

[36]  J. Goodman Statistical Optics , 1985 .

[37]  A H Hielscher,et al.  Monte Carlo simulations of the diffuse backscattering mueller matrix for highly scattering media. , 2000, Applied optics.

[38]  P. Soleillet Sur les paramètres caractérisant la polarisation partielle de la lumière dans les phénomènes de fluorescence , 1929 .

[39]  Hidayet Günhan Akarçay,et al.  Simulating light propagation: Towards realistic tissue models , 2011 .

[40]  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 .

[41]  Hervé Saint-Jalmes,et al.  Description and time reduction of a Monte Carlo code to simulate propagation of polarized light through scattering media. , 2003, Applied optics.

[42]  Schmitt,et al.  Depolarization of multiply scattered waves by spherical diffusers: Influence of the size parameter. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[43]  W. H. McMaster,et al.  MATRIX REPRESENTATION OF POLARIZATION , 1961 .

[44]  E. Bernabeu,et al.  A Depolarization Criterion in Mueller Matrices , 1985 .

[45]  Martin Frenz,et al.  From Electrodynamics to Monte Carlo Simulations , 2010 .

[46]  Zhu,et al.  Polarization memory of multiply scattered light. , 1989, Physical review. B, Condensed matter.

[47]  Stephen J. Matcher,et al.  Monte Carlo modeling of polarized light propagation in biological tissues , 2004 .

[48]  A Hielscher,et al.  Diffuse backscattering Mueller matricesof highly scattering media. , 1997, Optics express.

[49]  Ping Sun,et al.  Spatial pattern characterization of linear polarization-sensitive backscattering Mueller matrix elements of human serum albumin sphere suspension , 2013, Journal of Biological Physics.

[50]  Tsu-Wei Nee,et al.  Polarization of dipole scattering by isotropic medium , 2008, Optical Engineering + Applications.

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

[52]  Steven L. Jacques,et al.  Monte Carlo Modeling of Light Transport in Tissue (Steady State and Time of Flight) , 2010 .

[53]  E. Collett Mueller-Stokes Matrix Formulation of Fresnel's Equations , 1971 .

[54]  R. Azzam A perspective on ellipsometry , 1976 .

[55]  L. Mandel,et al.  Relationship between Jones and Mueller matrices for random media , 1987 .

[56]  Matthew H. Smith,et al.  Interpreting Mueller matrix images of tissues , 2001, SPIE BiOS.

[57]  Angelo Pierangelo,et al.  Mueller matrix imaging of human colon tissue for cancer diagnostics: how Monte Carlo modeling can help in the interpretation of experimental data. , 2010, Optics express.

[58]  L. Wang,et al.  Propagation of polarized light in birefringent turbid media: time-resolved simulations. , 2001, Optics express.