## 2 Materials and Methods  
### Experimental Setup and Tendon Tissue Samples  
In this work, a polarized camera-based (Dofp PHX050S-P, Lucid Vision Labs, Richmond, BC, Canada) backscattering measurement device was used to obtain the 3 \(\times\) 3 Mueller matrix images of the samples. Each pixel of the polarization camera is covered with four miniature polarizers along 0, 45, 90 and 135 deg to detect four SOPs at the same time. Thus, the raw image acquired by the polarization camera can be divided into four images, recording the light intensity data of 0, 45, 90 and 135 deg of linearly polarized light, respectively. Then the first three components of the Stokes vector S1, S2 and S3 can be calculated accordingly [13]. To obtain the complete 3 \(\times\) 3 Mueller matrix, incident light with three states of polarization (SOP) of 0 deg, 45 deg and 90 deg were used.  
As shown in Figure 1a, the incident light emitted from an LED (3 W, 633 nm, Daheng Optic, Beijing, China) passes through the lens L1(LBTEK Optic, Changsha, China), and the rotatable polarizer (P1, extinction ratio >1000:1, LBTEK Optic, Changsha, China) becomes linearly polarized light with different SOPs. The photons scattered from the sample are detected by the polarization camera (Dofp PHX050S-P, Lucid Vision Labs, Vancouver, Canada) after passing through the lens L2 (LBTEK Optic, Changsha, China). To avoid the influence of sample surface reflection, there is an oblique incident angle (8) of 7 deg between the incident light arm and the detection arm. Before the measurements, the Mueller matrix imaging system was calibrated using several standard samples, including air, polarizers, fibrous scatterers and retarders in both transmission and backscattering modes. The results showed that the maximum error of the individual Mueller matrix elements is about 0.8%. More details of the calibration process can be found in Ref. [14].  
Tendon tissues are highly anisotropic, resulting from both optical birefringence and scattering of fibrous structures [15]. There are abundant collagen fibers in tendon tissues, and most of them are arranged in the same direction [16]. Previously, it has been demonstrated that information on fibrous structures in tendon tissues, such as their density and orientation, can be obtained from the Mueller matrix [17]. However, applying an external force on tendon tissues will lead to changes in their mechanical features and anisotropic properties [18]. Here, to study the ability of Mueller matrix derived parameters to evaluate the mechanical properties of tendon tissues when stretched by external forces at different orientations, we measure fresh bovine tendon tissue samples sequentially at different physiological states as Figure 1b shows: without stretching (origin), transverse stretching (TDO), longitudinal stretching (MDO) and 45 deg stretching (ODO). Bovine tendon tissue with no external force is called the origin state sample, whose length and width are both 4.5  cm and the thickness is 0.5 cm. We stretched the tendon tissue 1 cm perpendicular to the alignment direction of the original collagen fibers, and this tissue is called the transverse stretching (TDO) state sample. Then, the restored tendon tissue was stretched 1 cm along the alignment direction of the original collagen fibers, and this tissue is called the longitudinal stretching (MDO) state sample. Last, we stretched the restored tendon tissue 1  cm along the 45 deg direction with the alignment of the original collagen fibers, and this tissue is called the 45 deg stretching (ODO) state sample. For each sample, a total of four 3 \(\times\) 3 Mueller matrix images in different states are recorded for further analysis.