Significance Polarization imaging technology has the advantages of non-invasive detection, rich information, sensitivity to the microstructure of the sample, and compatibility with traditional optical imaging technology, which makes it suitable for combining with microscopy techonology based on staining methods to distinguish the characteristics of different microstructures of pathological tissues. By adding the polarization state analyzer (PSA) and polarization state generator (PSG) modules to the commercial transmission and colinear reflection optical microscopes, the Mueller matrix microscopic imaging can be performed. The Mueller matrix can realize the complete characterization of the polarization properties of the sample.

Progress We have established the upright transmission Mueller matrix microscope ( Fig. 1, DRR-UTMMM) and collinear reflection Mueller matrix microscope ( Fig. 2, DRR-CRMMM) based on dual rotating retarders in which PSA and PSG modules consist of a fixed linear polarizer and a rotatable quarter-wave plate, respectively. The working principles are based on Fourier coefficient analysis. During each measurement process, two quarter-wave plates rotate with a fixed step angle ratio, and 30 images with different polarization states are collected to reconstruct the Mueller matrix of the sample. In order to eliminate the possible systematic errors and improve the measurement accuracy, the calibration of the Mueller matrix measurement system is necessary. For the transmission system, the analytic calibration method (ACM) is adopted. The systematic errors can be accurately solved by establishing the error model between each systematic error and the measurement signal. For the collinear reflection system, due to the complex relationship between the measurement signal and errors, it is difficult to derive the expression directly, so the numerical calibration method (NCM) is used to calculate the systematic errors and rebuild the system instrument matrix, which has a higher applicable scope and flexibility. In order to perform the fast Mueller matrix imaging, linear polarization CCD based on division of focal plane (DoFP) is used, which is capable of measuring the linear polarization states of light by equipping micro-polarizer array in front of the ordinary imaging sensor. We designed and implemented the upright transmission Mueller matrix microscope based on dual DoFP linear polarization CCDs ( Fig. 4, DoFPs-UTMMM). Two linear polarization CCDs are fixed in the transmission and reflection ends of a non-polarized beam splitter, respectively, one of which is equipped with a fixed angle quarter-wave plate. The real-time polarization state analyzer is realized by combining the multi-channel polarization data from two linear polarization CCDs. In order to eliminate the parasitic polarization artifacts introduced by the beam splitter, the Mueller matrix of the beam splitter is considered in PSA instrument matrix after calibration. Two different schemes of PSG are also discussed. The performance of DoFPs-UTMMM is validated by conducting Mueller matrix imaging on standard polarization samples with different azimuths. The results show that DoFPs-UTMMM has a higher measurement accuracy and faster measurement speed compared to DRR-UTMMM, which make it suitable for monitoring dynamic processes or living tissues.

In this article, we also introduce some biomedical applications of the Mueller matrix microscope. By perfoming Mueller matrix imaging of cancerous liver tissues in different stages and calculating polarization parameters, it can realize the characterization of the degree of liver fibrosis in the cancerous liver tissue (Figs. 5--7). By combining with data technologies including machine learning, new polarization parameters used to quantitatively characterize the microstructure of biological tissues can be derived, which can accurately distinguish specific pathological structures (Fig. 8). Through the fast and accurate polarization measurement of blood cells (Fig. 9), it can be tested that the system has the potential for real time and accurate polarization monitoring of the dynamic process of living cells in the future.

Conclusions and Prospects In this article, we summarize several modular polarization microscopes implemented in our previous studies, including the transmission Mueller matrix microscope and the collinear reflection Mueller matrix microscope based on dual rotating retarders, as well as the transmission Mueller matrix microscope based on dual linear polarization CCDs. Then we introduce some applications of modular polarization microscope in the biomedicine field. With the combination of microscopy and polarization imaging technology, Mueller matrix microscope can be directly upgraded from ordinary optical microscopy methods. It has the following advantages: suitable for the studies of biological living systems, capable of obtaining cross-scale image information, and easy to be combined with data science technologies. Besides biomedicine, the Mueller matrix microscope can be also applied to many fields including material science, defect detection, etc. There also exsit some aspects that need to be improved: relatively small imaging area, and high requirement for system stability and residual polarization artifacts of the optics inside the system. This article puts forward specific suggestions for the above problems. In the future, the development tread of Mueller matrix microscope is faster measurement speed and higher measurement accuracy. With the improvements of polarization modulation and measurement technology, the Mueller matrix microscope is expected to perform real-time and accurate full-polarization measurement of living cells and in-vivo tissues, and becomes an important tool to promote biomedical applications.