LPICM, Ecole Polytechnique, CNRS, 91128 Palaiseau, France.
Opt Lett. 2012 Jan 15;37(2):220-2. doi: 10.1364/OL.37.000220.
It is shown that the Mueller matrix logarithm and the Mueller matrix roots decompositions used for the extraction of the elementary polarization properties of a depolarizing medium, although being computationally different, are formally equivalent, being both based upon the differential representation of a continuously depolarizing medium. The common set of six elementary polarization properties provided by these two decompositions is generally different from that obtained from the various product decompositions summarized by the G-polar decomposition whereby the depolarization phenomenon is treated as being concentrated, and not uniformly distributed, within the medium. However, if the medium is weakly depolarizing, the two sets of elementary properties coincide to the first order in the depolarization and tend to the set of properties of the nondepolarizing estimate of the measured Mueller matrix obtained from its Cloude sum decomposition.
研究表明，尽管用于提取退偏介质基本偏振特性的 Mueller 矩阵对数分解和 Mueller 矩阵根分解在计算上有所不同，但它们在形式上是等效的，因为它们都基于连续退偏介质的微分表示。这两种分解提供的共同的六组基本偏振特性通常与由 G 偏振分解总结的各种乘积分解获得的特性不同，其中退偏现象被视为集中而不是均匀分布在介质中。然而，如果介质是弱退偏的，那么两组基本特性在退偏的一阶近似中是一致的，并且趋向于从其 Cloude 求和分解获得的测量 Mueller 矩阵的非退偏估计的一组特性。
