From a nondepolarizing Mueller matrix to a depolarizing Mueller matrix

Abstract

The depolarizing properties of a generic Mueller matrix are synthesized from a corresponding nondepolarizing reference Mueller matrix, which is appropriately factorized and transformed by sequentially adjusting the values of three indices of polarimetric purity (IPP) [Opt. Commun.284, 38 (2011)OPCOB80030-4018]. This procedure allows generating type-I and type-II arbitrary Mueller matrices from an adequate choice of the reference Mueller matrix and, by reducing, in a consistent way, the starting 1-valued IPP. This synthesis procedure also provides better understanding of the sources and structure of depolarization.

On optimal filtering of measured Mueller matrices

“…[32], 0 C M is the identity matrix when f M is type-I, and it corresponds to a diattenuator when f M is type-II. It is remarkable that, since the number  of 1-valued IPP of  M is equal to that of f M [32], it turns out that the so-called reference pure Mueller matrix…”

“…constitutes an useful representation of the sample in the sense that the characteristic component U 0 f M (which coincides with the reference pure Mueller matrix of f M [32]) is associated with the maximal relative weight Funding Information. Ministerio de Economía y Competitividad (FIS2014-58303-P); Gobierno de Aragón (E99).…”

Invariant quantities of a nondepolarizing Mueller matrix

“…To simplify, and to make easier the interpretation of certain operations with Mueller matrices, when appropriate we will use the following partitioned block expression of a Mueller matrix M, which reflects important features of the structure of the information contained in M [17]     00 11 12 13 21 22 23 00 31 32 33 01 02 03 10 20 30 00 00 1 1 1 1 , , , ,…”

“…Nondepolarizing (or pure) Mueller matrices, being a particular class of Mueller matrices, play a very important role in polarimetry because 1) they represent the more basic linear polarimetric interactions, 2) any Mueller matrix can be considered as an ensemble average of nondepolarizing Mueller matrices [13][14][15], 3) many media behave, at least in the first-order approximation, like nondepolarizing, so that nondepolarizing Mueller matrices represent, by themselves, a wide range of polarimetric behaviors [16] and 4) any depolarizing Mueller matrix has an associated reference pure Mueller matrix [17].…”

Universal Synthesizer of Mueller Matrices Based on the Symmetry Properties of the Enpolarizing Ellipsoid

“…Furthermore, a general algebraic synthesizer of Mueller matrices has been developed [13] by using the normal form of a Mueller matrix [14][15][16][17][18][19][20] and tuning the indices of polarimetric purity (P 1 , P 2 , P 3 ) [21] of the central canonical type-I and type-II depolarizers [19,20], which start with their maximal values P 1 = P 2 = P 3 = 1 (nondepolarizing, or pure, Mueller matrix) and decrease, in a consistent manner (0 ≤ P 1 ≤ P 2 ≤ P 3 ≤ 1), so that any Mueller matrix can be constructed through this procedure. The problem of the synthesis of a general depolarizing Mueller matrix has also been studied by Cloude [22], who developed a parameterization that allows for modeling any depolarizing Mueller matrix from a pure one by considering all possible ways in which that the system can depolarize light.…”