## 1 Introduction  
As a non-invasive, non-contact and label-free tool, Mueller matrix polarimetry is widely used in biomedical studies and clinical applications, for it can provide abundant microstructural information about tissues and cells [1, 2, 3, 4]. Specifically, the Mueller matrix measurement system can be used for abnormal tissue detection for both backward imaging of bulk tissue samples and forward imaging of thin tissue slices [5, 6, 7]. However, although a Mueller matrix contains a comprehensive description of the polarization-related structural and optical properties of the medium, it is often difficult to obtain intrinsic polarimetric characteristics such as diattenuation, retardance and depolarization encoded in the Muellermatrix elements directly. To solve this problem, in the past decades several methods have been proposed to decompose the Mueller matrix into groups of parameters related to specific optical properties which can be used to reveal the microstructural information of tissue samples more clearly and quantitatively [8; 9; 10; 11; 12; 13; 14].  
Until now, the Mueller matrix polar decomposition (MMPD) and Mueller matrix transformation (MMT) are two popular methods in tissue polarimetry studies and applications. Nevertheless, unlike the MMPD method, which decomposes the Mueller matrix into three sub-matrices with clear physical meanings of depolarization, retardance, and diattenuation [12; 13], the MMT method directly combines groups of Mueller matrix elements to derive parameters related to certain characteristics of tissue-like media with an advantage of fast calculation speed [14]. Both the MMPD and MMT methods have demonstrated the diagnostic potential in various cancerous tissue detection, including breast cancer, liver cancer, inflammatory bowel diseases and cervical cancer [15; 16; 17; 18; 19; 20]. However, it is worth noting that the parameters derived from the MMPD and MMT methods are based on specific deduction models and calculation assumptions. Therefore, for accurate diagnostic purposes, their applicability and interpretability regarding different types of samples requires further discussion and analysis. Recently, some efforts have been made in this area, and some useful conclusions have been drawn by [PERSON] and us [21; 22; 23; 24].  
In this study, to compare the difference among the parameters derived from the MMPD and MMT methods more comprehensively while applying them on different types of tissue samples measured by both backscattering and transmission imaging setups, we prepare seven kinds of thin tissue samples for forward measurement and five kinds of bulk tissue samples for backward measurement. Based on the Mueller matrix data obtained using the setups, we carry out thoroughly comparative analysis of the parameters derived from both methods representing the same polarization properties, namely depolarization, retardance, fast axis orientation and diattenuation. Specifically, according to tissue structures, we further proposed several modified MMT parameters, whose abilities were also analyzed for revealing information with regard to specific types of tissue samples. We discuss the applicability of the original and modified MMT parameters based on the comparisons, and then give suggestions for appropriate parameter selection in tissue polarimetry.