Ossikovski Razvigor, Gil José J, San José Ignacio
J Opt Soc Am A Opt Image Sci Vis. 2013 Nov 1;30(11):2291-305. doi: 10.1364/JOSAA.30.002291.
By using the symmetric serial decomposition of a normalized Mueller matrix M [J. Opt. Soc. Am. A 26, 1109 (2009)] as a starting point and by considering the reciprocity property of Mueller matrices, the geometrical features of the Poincaré sphere mapping by M are analyzed in order to obtain a new parameterization of M in which the 15 representative parameters have straightforward geometrical interpretations. This approach provides a new geometry-based framework, whereby any normalized Mueller matrix M is completely described by a set of three associated ellipsoids whose geometrical and topological properties are characteristic of M. The mapping analysis considers the cases of type-I and type-II, as well as singular and nonsingular Mueller matrices. The novel parameterization is applied to several illustrative examples of experimental Mueller matrices taken from the literature.
以归一化穆勒矩阵(M)的对称序列分解[《美国光学学会志A》26, 1109 (2009)]为起点，并考虑穆勒矩阵的互易特性，分析了由(M)进行的庞加莱球映射的几何特征，以获得(M)的一种新参数化，其中15个代表性参数具有直接的几何解释。这种方法提供了一个基于几何的新框架，据此任何归一化穆勒矩阵(M)都由一组三个相关椭球体完全描述，其几何和拓扑特性是(M)的特征。映射分析考虑了I型和II型情况，以及奇异和非奇异穆勒矩阵。这种新颖的参数化应用于从文献中选取的几个实验穆勒矩阵的示例。
