# Error Analysis and Calibration Improvement of the Imaging Section in a Mueller Matrix Microscope
## 1 Introduction  
The technique of polarized light imaging can provide microstructural information on samples, and the Mueller matrix offers a comprehensive description of the polarization properties of samples. Therefore, when the polarized light imaging technique is combined with the Mueller matrix measurement technique, microstructural information can be obtained with great effectiveness [1]. A Mueller matrix microscope is usually designed by adding both the polarization state generator and analyzer (polarizing section) to a microscope (imaging section) and has the ability to measure the Mueller matrix of samples via imaging, which enhances the contrast ratio of the anisotropic structures and has been reported to be extremely helpful in biomedical diagnosis, especially for cancer detection [2; 3]. The elements of the Mueller matrix contain all the polarization information necessary for clear and physically meaningful characterization of the measured samples; these elements, either singly or in combination, include diattenuation, retardation, and depolarization. Mueller matrix polar decomposition [4], Mueller matrix transformation [5], and other similar techniques based on transforming polarization parameters are useful and proven tools in biomedicine [6; 7], material testing [8], and other fields. Unfortunately, fabrication imperfections and/or assembly misalignment ofthe polarizing components in the optical path can lead to errors in the measurement of the Mueller matrix elements. To ensure accurate measurements, the Mueller instrument must be calibrated. One method of doing this is to establish a stabilized optical layout by using a liquid crystal wave plate instead of rotating the mechanical parts for the rotation of the fast axis of the wave plate in the path, thereby improving the stability of the instrument [9]. However, when using a liquid crystal wave plate, the spectral range of the measuring equipment is restricted to the visible spectrum. Under these considerations, the dual-rotating-retarder configuration [10] is applied owing to its relative simplicity. By using a wave plate made of quartz, the spectral range can be expanded from ultraviolet to near-infrared [11]; however, this requires a rotating mechanical part and thereby introduces measurement errors, which presents the need for further calibration. Several improvements in the mathematical model have been suggested to calibrate the systematic error in a dual-rotating-retarder polarimeter. [PERSON] treated the characteristics of the wave plate to include diattenuation [12]. [PERSON] introduced a system model containing not only the retardance error of the wave plates but also the misalignment of the polarizing elements [13]. [PERSON] introduced the characteristics of depolarization in the wave plate [14], and [PERSON] et al. discussed the first- and second-order differential forms of the systematic error and presented a scheme of four-zone averaging measurement to obtain stable results [15; 16]. [PERSON] and [PERSON] [17; 18] developed a polarimeter possessing the optimal initial position for a rotating wave plate. [PERSON] [19] further optimized the Mueller matrix polarimeter with respect to the condition number parameter and proved that an overspecified polarimeter with more than 16 states could significantly improve the measurement stability, thus introducing the concept of \"instrument matrix\" into the polarimeter design. Specifically speaking, there are mainly two different types of methods used to calibrate the systematic error of a Mueller matrix measurement system. The first is the eigenvalue calibration method, which uses a variety of standard Mueller measurement samples to realize complete modeling and calibration of the optical system without calculating the model of each specific device of the polarization state generator and analyzer [20]. The other type of calibration method, in contrast, requires high accuracy of calculation of the misalignments and imperfections of the polarizing elements.