Sheppard Colin J R, Bendandi Artemi, Le Gratiet Aymeric, Diaspro Alberto
J Opt Soc Am A Opt Image Sci Vis. 2018 Dec 1;35(12):2058-2069. doi: 10.1364/JOSAA.35.002058.
The elements of the coherency matrix give the strength of the components of a Mueller matrix in the coherency basis. The Z-matrix (called the polarization-coupling matrix or state-generating matrix) represents a partial sum of the coherency expansion. For transmission through a deterministic medium, the coherency elements can be used directly as generators to calculate the development of polarization upon propagation. The commutation properties of the coherency elements are investigated. New matrices that we call the W-matrix and the X-matrix, both different representations of the Z-matrix in a Jones basis, are introduced. The W-matrix controls the transformation of the Jones vector and also the covariance matrix. The product of the X-matrix with its complex conjugate gives the matrix representation of the Mueller matrix in the Jones basis. The development of Mueller matrix and coherency matrix elements upon propagation through some examples of a uniform medium is investigated. It is shown that the coherency matrix is more easily interpreted than the Mueller matrix. Analytic expressions are presented to calculate the elementary polarization properties from coherency matrix elements or Mueller matrix parameters.
相干矩阵的元素给出了在相干基下穆勒矩阵各分量的强度。Z矩阵（称为偏振耦合矩阵或状态生成矩阵）表示相干展开的部分和。对于通过确定性介质的传输，相干元素可直接用作生成器，以计算传播过程中偏振的演变。研究了相干元素的对易性质。引入了我们称为W矩阵和X矩阵的新矩阵，它们都是Z矩阵在琼斯基下的不同表示形式。W矩阵控制琼斯矢量以及协方差矩阵的变换。X矩阵与其复共轭的乘积给出了琼斯基下穆勒矩阵的矩阵表示。通过均匀介质的一些示例研究了传播过程中穆勒矩阵和相干矩阵元素的演变。结果表明，相干矩阵比穆勒矩阵更容易解释。给出了从相干矩阵元素或穆勒矩阵参数计算基本偏振特性的解析表达式。
