Mueller matrix decomposition methods for tissue polarization tomography

Abstract

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.