Equivalence relations and symmetries for laboratory, LIDAR, and planetary Müeller matrix scattering geometries.

Symmetry relationships for optical observations of matter generally fall into several common scattering geometries. The "planetary" configuration is preferred by observers of extraterrestrial planets, "laboratory" observations are performed in the biomedical research field, and the LIDAR configuration is preferred by those using lasers to probe optical properties of horizontal surfaces with mirror or axial symmetry. This paper begins with the Stokes matrix formalism and uses symmetries of Müller matrix scattering to establish links among the mathematical symmetries of each geometric configuration. We finish the paper by identifying and correcting an influential misapplication of rotational scattering matrices in the literature. The corrected equation should find wide application in models of the LIDAR scattering process.

[1]  He Yonghong,et al.  Linear polarization difference imaging and its potential applications. , 2009, Applied optics.

[2]  Ping Yang,et al.  Polarization and effective Mueller matrix for multiple scattering of light by nonspherical ice crystals. , 2006, Optics express.

[3]  Donald W. Mueller,et al.  Analytical expressions for the radiation emergent from a scattering medium exposed to a polarized laser beam , 2000 .

[4]  M. van der Mee,et al.  Transfer of Polarized Light in Planetary Atmospheres: Basic Concepts and Practical Methods , 2005 .

[5]  B. Cameron,et al.  Determination of optical scattering properties in turbid media using Mueller matrix imaging. , 2006, Journal of biomedical optics.

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

[7]  Ignacio San José,et al.  Explicit algebraic characterization of Mueller matrices. , 2014, Optics letters.

[8]  Dwight C. Look,et al.  A backward Monte Carlo study of the multiple scattering of a polarized laser beam , 1997 .

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

[10]  Gang Yao,et al.  Monte Carlo model and single-scattering approximation of the propagation of polarized light in turbid media containing glucose. , 2002, Applied optics.

[11]  Yinqi Feng.  Revisit to the symmetry relations in diffusely backscattered polarization patterns of turbid media , 2006 .

[12]  S. Dunagan,et al.  The MARTE VNIR imaging spectrometer experiment: design and analysis. , 2008, Astrobiology.

[13]  Ayan Banerjee,et al.  Turbid medium polarimetry in biomedical imaging and diagnosis , 2011 .

[14]  A. Brown.  Spectral bluing induced by small particles under the Mie and Rayleigh regimes , 2014 .

[15]  Lihong V. Wang,et al.  Propagation of polarized light in birefringent turbid media: a Monte Carlo study. , 2002, Journal of biomedical optics.

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

[17]  Adrian J. Brown.  Spectral curve fitting for automatic hyperspectral data analysis , 2006, IEEE Transactions on Geoscience and Remote Sensing.

[18]  J. Conway,et al.  The Symmetries of Things , 2008 .

[19]  Nan Zeng,et al.  Probing microstructural information of anisotropic scattering media using rotation-independent polarization parameters. , 2014, Applied optics.

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

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

[22]  Anthony Colaprete,et al.  The case for a modern multiwavelength, polarization-sensitive LIDAR in orbit around Mars , 2015 .

[23]  Adrian J. Brown,et al.  Symmetry relations revealed in Mueller matrix hemispherical maps , 2012 .

[24]  Igor Meglinski,et al.  Online object oriented Monte Carlo computational tool for the needs of biomedical optics , 2011, Biomedical optics express.

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

[26]  Jérôme Dillet,et al.  Size determination by use of two-dimensional Mueller matrices backscattered by optically thick random media. , 2006, Applied optics.

[27]  M. Yurkin.  Symmetry relations for the Mueller scattering matrix integrated over the azimuthal angle , 2013 .

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

[29]  L. Rayleigh,et al.  The theory of sound , 1894 .

[30]  C. Baravian,et al.  Fast optical sizing without dilution , 2007 .

[31]  Jessica Ramella-Roman,et al.  Three Monte Carlo programs of polarized light transport into scattering media: part I. , 2005, Optics express.

[32]  D. Batens,et al.  Theory and Experiment , 1988 .

[33]  Edouard Berrocal,et al.  Laser light scattering in turbid media Part I: Experimental and simulated results for the spatial intensity distribution. , 2007, Optics express.

[34]  R. S. Krishnan.  The reciprocity theorem in colloid optics and its generalisation , 1938 .

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

[36]  Razvigor Ossikovski,et al.  Alternative depolarization criteria for Mueller matrices. , 2010, Journal of the Optical Society of America. A, Optics, image science, and vision.

[37]  S. Pal,et al.  Polarization properties of lidar backscattering from clouds. , 1973, Applied optics.

[38]  I. Alex Vitkin,et al.  Detecting axial heterogeneity of birefringence in layered turbid media using polarized light imaging , 2012, Biomedical optics express.

[39]  Joop W. Hovenier,et al.  Polarized light in planetary atmospheres for perpendicular directions , 1985 .

[40]  Adrian J. Brown,et al.  The MARTE VNIR imaging spectrometer experiment: design and analysis. , 2008, Astrobiology.

[41]  Nan Zeng,et al.  Linear polarization different imaging and its potential applications , 2008, 2008 Asia Optical Fiber Communication & Optoelectronic Exposition & Conference.