Mueller matrix polarization parameter tomographic imaging method in the backscattering configuration

Highlights

• To the best of our knowledge, for the first time a mueller matrix polarization parameter tomographic imaging (MMPPTI) in backscattering configuration for generating the depth-resolved cross sectional images of the polarization parameters of biological tissue is described. The general expressions of the optically anisotropic properties of medium have been derived that can be employed to calculate the related polarization parameters directly from the measured macroscopic mueller matrix without decomposition.

• In our model a thin layer at a depth within the medium is represented by a depolarization mueller matrix. It is shown that the model is valid in cases in which the depolarizing effect occurs continuously in the forward-pass and the backward-pass of the light beam through the medium. It is also demonstrated that the model provides the underlying physical basis of the symmetrical decomposition of the mueller matrix of the depolarizing anisotropic medium.

• The tomographic images of the polarization properties of tissues in vivo and ex vivo are presented to demonstrate the capability of our method.

• The model for MMPPTI in backscattering case can be modified to find the explicit expressions for the polarization parameters of media with some specific anisotropic structures or being imaged in transmitted mode.

Abstract

A Mueller matrix polarization parameter tomographic imaging (MMPPTI) in backscattering configuration for generating the depth-resolved cross sectional images of the polarization parameters of biological tissue is described. First, a theoretical model is proposed, which can be used to directly determine the polarization properties of anisotropic medium from the measured Mueller matrix. Several polarization parameters such as diattenuation of the medium can be expressed in terms of the elements of the measured Mueller matrix. The model proposed can be regarded as a physical interpretation of the symmetric decomposition of a Mueller matrix. To calibrate the new method for generating depth-resolved Mueller matrix images of the media with several polarization effects simultaneously, it is proposed in this work to use porcine liver as a mostly isotropic standard sample. The depth-resolved cross sectional images of 16 elements of the Mueller matrix, and the polarization properties of tissues in vivo and ex vivo are presented to demonstrate the capability of our method. Our MMPPTI method has the potential for being able to image all the polarization parameters of any depolarizing anisotropic medium. The model for MMPPTI in backscattering case can be modified to find the explicit expressions for the polarization parameters of media with some specific anisotropic structures or being imaged in transmitted mode.

Introduction

The effects of an anisotropic medium on the changes in polarization state of a light beam can be represented by a Jones matrix when the medium is non-depolarizing [1] or by a Mueller matrix when the medium is polarizing or depolarizing [2]. Due to the fact that Mueller matrix can completely describes the polarization properties of both the deterministic and the random medium, many methods have been proposed to interpret the measured Mueller matrix. Among them, three methods are the most frequently used. The first is the polar decomposition in which a Mueller matrix is decomposed into three component matrices representing depolarization, retardance, and diattenuation [3]. The second is the symmetric decomposition in which a diagonal matrix representing the depolarization properties is sandwiched between and multiplied by two pure Mueller matrices. When investigating the medium with obvious depolarization properties, the parameters are obtained by the complete diagonalization of the auxiliary matrices [4]. The third is differential decomposition that is introduced to describe the local action of homogeneous medium, in which parameters can be calculated by the eigenvalues and eigenvectors of the macroscopic Mueller matrix [5], [6]. One common limitation of above mentioned methods is that the extraction of polarization and depolarization parameters requires the decomposition or the transformation of the measured macroscopic Mueller matrix, which leads to the complexity when extracting parameters from the experimental data.

Note that when many effects simultaneously occur in medium, the elements of Mueller matrix are affected by polarization effects in a complex way [7], [8]. It is still desirable to derive the information about the polarization properties of the medium directly from some combinations of the elements of its Mueller matrix. In a recent work, it is demonstrated by both the experimental data and Monte-Carlo simulated results that some polarization properties can really be expressed approximately in terms of the elements of the macroscopic Mueller matrices measured with a dual rotating retarder configuration [9], [10]. However, no theoretical analysis of this result has been published up to now.

Polarization properties of human tissue, including birefringence, optics axis orientation, and depolarization, arise from its optically asymmetric structure. For example, clinically relevant features and disease that are related to the heterogeneity like retinal pigment epithelium (RPE) [11] and cervical cancer [12] can be revealed by the images of depolarization. Airway smooth muscle (ASM) can be investigated by optic axis orientation imaging [13]. The disease of ophthalmology, burning skin and scars, atherosclerotic lesions and muscle fiber can be diagnosed and assessed by retardance imaging [14]. Recently, studies have shown that diattenuation imaging in certain diseased or damaged tissues, including cancerous tissue [15,16], burned and injured tissues [17, 18] and ocular disease tissues [19, 20] can be used as an important indicator for diagnosis, analyzing tissue thickness [20] and distinguishing different parts of the tissue [21]. Therefore, changes in polarization properties can thus be exploited to diagnose the existence and development of the diseases. It is thus desirable to directly determine the parameter representing the changes of the characteristic from the macroscopic Mueller matrix.

In this work, we proposed a new Mueller matrix polarization parameter tomographic imaging (MMPPTI) method in backscattering configuration for generating depth-resolved images of the polarization properties of the medium directly from the measured macroscopic Mueller matrix. Our method is based on a theoretical model in which a thin scattering layer within the medium is represented by a depolarization Mueller matrix and the effects of medium on the forward-pass and the backward-pass propagation of light through it are represented by two non-depolarizing matrices. With the help of this model, for the first time the explicit expressions are then derived for the elements of the macroscopic Mueller matrix from the formulas for calculating some polarization properties of medium that are expressed in terms of these elements. The depth-resolved cross sectional images of the magnitude of 16 elements of the Mueller matrix, and the corresponding images of polarization parameters of retardance, diattenuation, depolarization and orientation of optic axis in biological tissues in backscattering configuration are presented. It is shown that our results are in good agreement with the experimental data obtained in some literatures. Finally, our model can be regarded as a physical interpretation of the symmetrical decomposition. Therefore, the outperformance of the method can be direct calculation and physical situation related.