Unlike optical elements, medium such as tissue usually has several polarization properties simultaneously. So it is desirable to identify the existence of types of optical behaviors and determine their values from measured Mueller matrices. In this work, we will review the methods of decomposing the macroscopic Mueller matrix and differential Mueller matrix in order to quantify polarization properties of media and correctly interpret information about anisotropic structures contained in the measured Mueller matrices. The review is divided into three parts, macroscopic Mueller matrix decomposition, differential Mueller matrix decomposition and quantifying anisotropic tissue structures.

In the first part of this review, first of all, the development of the concepts and mathematical models for characterizing the polarimetric properties of optically anisotropic media is briefly described. The content in this part is essential for understanding the capability of the Mueller matrix concept. Second, the important properties of Mueller matrix and their potential applications are summarized. These properties are the starting points for many applications for Mueller matrix methods. Third, methods for decomposing a measured macroscopic Mueller matrix are described and the related Mueller matrix theorems used are pointed out. In addition to point out the success and limitations of each decomposition method, we try to summarize the practical methods of calculating the desired polarization effects from the decomposition processes. Fourth, the properties of the Mueller matrix of random medium are discussed. The determination of the forms of the Mueller matrix of random media is one of the most challenging problems in Mueller matrix analysis. Finally, the potential applications of macroscopic polarization parameters are considered.

In the second part of this review, we consider the differential Mueller matrix decomposition methods. First, the definition of a differential Mueller matrix and its relation with the macroscopic Mueller matrix of the same medium are briefly described. This definition formula can be used to determine the forms of the differential Mueller matrix of nondepolarizing (or deterministic) media directly from the measured Mueller matrices. Second, the facts about both the differential and macroscopic Mueller matrices are analyzed that have been used to find the forms of the differential Mueller of depolarizing media. The decomposition methods based on differential Mueller matrix are analyzed. Third, a simple comparison between differential decomposition methods is presented. Fourth, the important relationships between differential and macroscopic Mueller matrices are summarized. These relations are very useful in practical applications and can be used to calculate the differential matrix from measured macroscopic Mueller matrix (for example). Finally, the future development of quantifying anisotropic structures of tissue with parameters derived from a measured macroscopic Mueller matrix is pointed out.

In the third part, we will focus on the applications of Mueller matrix for quantifying anisotropic structures of cells and tissues. First of all, forms of Mueller matrices for different types of tissues are reviewed. Second, techniques based on polarization properties of anisotropic media are discussed. Methods for measuring Mueller matrices are then described. The polarization parameters that have been used to quantify anisotropic tissue structures are discussed in details. The diseases that have been correlated to one or a combination of polarization parameters are then summarized. Finally, the challenging problems we are facing and possible solutions are considered.

与光学元件不同，组织等介质通常同时具有多种偏振特性。因此，需要识别光学行为类型的存在并从测量的穆勒矩阵中确定它们的值。在这项工作中，我们将回顾分解宏观穆勒矩阵和微分穆勒矩阵的方法，以量化介质的极化特性并正确解释测量的穆勒矩阵中包含的各向异性结构的信息。综述分为三个部分，宏观穆勒矩阵分解、微分穆勒矩阵分解和量化各向异性组织结构。

在这篇综述的第一部分，首先简要描述了表征光学各向异性介质偏振特性的概念和数学模型的发展。这部分的内容对于理解穆勒矩阵概念的能力至关重要。其次，总结了穆勒矩阵的重要性质及其潜在应用。这些属性是 Mueller 矩阵方法许多应用的起点。第三，描述了分解被测宏观穆勒矩阵的方法，并指出了所使用的相关穆勒矩阵定理。除了指出每种分解方法的成功和局限性外，我们还尝试总结从分解过程计算所需极化效应的实用方法。第四，讨论了随机介质的Mueller矩阵的性质。确定随机介质的穆勒矩阵的形式是穆勒矩阵分析中最具挑战性的问题之一。最后，考虑了宏观偏振参数的潜在应用。

在本综述的第二部分，我们考虑微分 Mueller 矩阵分解方法。首先简要说明微分穆勒矩阵的定义及其与同一介质宏观穆勒矩阵的关系。该定义公式可用于直接从测量的穆勒矩阵确定非去极化（或确定性）介质的微分穆勒矩阵的形式。其次，分析了关于微分和宏观穆勒矩阵的事实，这些事实已被用于发现去极化介质的微分穆勒的形式。分析了基于微分Mueller矩阵的分解方法。第三，给出了微分分解方法之间的简单比较。第四，总结了微分和宏观穆勒矩阵之间的重要关系。这些关系在实际应用中非常有用，可用于从测量的宏观穆勒矩阵（例如）计算微分矩阵。最后，指出了使用来自测量的宏观穆勒矩阵的参数量化组织各向异性结构的未来发展。

在第三部分，我们将重点介绍穆勒矩阵在量化细胞和组织的各向异性结构中的应用。首先，回顾了不同类型组织的穆勒矩阵形式。其次，讨论了基于各向异性介质极化特性的技术。然后描述了测量穆勒矩阵的方法。详细讨论了用于量化各向异性组织结构的极化参数。然后汇总与一个或多个极化参数相关的疾病。最后，考虑了我们面临的具有挑战性的问题和可能的解决方案。