Experimental validation of Mueller matrix differential decomposition

Abstract

Mueller matrix differential decomposition is a novel method for retrieving the polarimetric properties of general depolarizing anisotropic media [N. Ortega-Quijano and J. L. Arce-Diego, Opt. Lett. 36, 1942 (2011), R. Ossikovski, Opt. Lett. 36, 2330 (2011)]. The method has been verified for Mueller matrices available in the literature. We experimentally validate the decomposition for five different experimental setups with different commutation properties and controlled optical parameters, comparing the differential decomposition with the forward and reverse polar decompositions. The results enable to verify the method and to highlight its advantages for certain experimental applications of high interest.

Mueller polarimetric imaging for surgical and diagnostic applications: a review

“…A number of methods including Lu-Chipman's polar decomposition [31], reverse polar decomposition [116], symmetric decomposition [117], differential decomposition [118][119][120][121][122][123] and root decomposition [37,124], Mueller matrix transformation techniques [125][126][127][128][129][130][131], Cloude's sum decomposition [132], serial parallel decomposition [133], etc. have been developed.…”

“…Differential decomposition has been validated in simulations as well as phantom and tissue experiments and has demonstrated advantages for quantifying fundamental polarization properties of many homogeneous samples. [118,[121][122][123]142] For a light beam propagating along the z axis, the Mueller matrix M(z + dz) can be written in the form of an iterated differential function as [118] MðzþdzÞ ¼UðdzÞMðzÞ ¼Iþmdz ð25Þ…”

“…The solution can be then given by [118] M¼ expðbmÞ m / L¼ lnðMÞ ð27Þ b can be regarded as a scalar parameter that does not interfere with the interpretation of m in terms of depolarization, retardance and diattenuation. m can be derived from the matrix logarithm of the Mueller matrix L. The fundamental polarization properties can be determined by constructing the Lorentz antisymmetric and symmetric components L m and L u [118,119,122],…”

Physical model of differential Mueller matrix for depolarizing uniform media

“…[4], Ossikovski provides a physical interpretation of this symmetry breaking in the matrix m. He proposes to consider the d 0-6 parameters as mean values of the non-depolarizing properties (m ND part) and d [7][8][9][10][11][12][13][14][15] as their respective uncertainties resulting from the depolarization (m D part). The elementary optical non-depolarizing properties are [1] the amplitude or isotropic absorption (d 0-), the linear dichroism along the x-y laboratory axes (d 1 ), the linear dichroism along the 45° axes (d 2 ), the circular dichroism (d 3 ), the linear birefringence along the x-y axes (d 4 ) , the linear birefringence along the 45° axes (d 5 ) and the circular birefringence (d 6 ).…”

“…The elementary optical non-depolarizing properties are [1] the amplitude or isotropic absorption (d 0-), the linear dichroism along the x-y laboratory axes (d 1 ), the linear dichroism along the 45° axes (d 2 ), the circular dichroism (d 3 ), the linear birefringence along the x-y axes (d 4 ) , the linear birefringence along the 45° axes (d 5 ) and the circular birefringence (d 6 ). d [13][14][15] are the anisotropic absorptions coefficients along the x-y, 45° and circular axes respectively.…”