## 1 Introduction  
Due to the advantages of non-invasive, high-resolution, and real-time imaging, optical coherence tomography has demonstrated its application in biomedical and clinical medicine. Since its introduction in 1991, OCT technology has been developed for over 30 years [1]. Various functional OCT technologies have been developed to cater to a wide range of practical applications [2]. For example, endoscopic OCT, which is OCT together with a well-designed catheter, has already shown the advantages of in vivo imaging for the human body cavity [3, 4]; Doppler OCT, which combines OCT and the optical Doppler effect, provides information on both the internal structure of blood in vessels and the direction of blood flow velocity [5, 6]; OCT Angiography (OCTA) is another method, used to visualize vascular distribution in cardiology [7] by analyzing consecutive images to find the changes caused by the movement of blood components [8]; Optical Coherence Elastography (OCE), which shows the availability of measuring tissue's elastic properties, through the visualization of the propagation of shear waves and calculation of Young's modulus [9]; and polarization sensitive optical coherence tomography (PSOCT), which was designed for biological tissues with birefringence, such as teeth, fiber textures and nerves. For skin burn assessment in surgery, birefringent properties enable differentiation between distinct tissues and the determination of the degree of injury, providing valuable information for medical diagnosis [10, 11, 12]. In ophthalmology, PSOCT can be used to diagnose ophthalmic diseases due to the birefringent properties of the cornea [13, 14]. From the point of view of practical application, polarization sensitive imaging relies on the birefringence effect in specific tissues. When incident with circularly polarized light, the propagation of light through these tissues will be divided into two parts. One part propagates along the long axis, and the other part travels along the short axis. Polarization sensitive imaging is achieved by measuring the optical path difference, or the so-called phase difference, between two propagation paths. Compared with reflectivity or refractive index imaging, polarization sensitive imaging provides richer details and structural information. In 1992, [PERSON] et al. introduced the first PSOCT system, which measured the phase delay map of chicken myocardial tissue [15]. This map revealed the color changes caused by birefringence, offering a clearer depiction of the fibrous structure of muscle tissue than intensity maps. During this period, PSOCT systems were typically built in free space, determining the propagation of polarization states through Jones matrices. Since then, PSOCT systems have undergone numerous updates and iterations, with continuous attempts to integrate them with medical imaging technologies for clinical diagnostics. PSOCT systems gradually transitioned toward fiber optics due to clinical constraints. To ensure the stable transmission of polarization states, bias-preserving optical fibers have been commonly used [16; 17]. Hardware- and software-based methods have been proposed to correct the phase shift situation in optical fibers, which is caused by the bias-preserving fibers [18; 19]. PSOCT can be divided into two types based on the imaging principle: PSOCT with a single circularly input state and PSOCT based on multiple input states. Single-input-state PSOCT systems use only one input state and one detected intensity signal [20]. The incident light is circularly polarized to obtain richer polarization information and compensate for the limitations associated with a single incident state. On the other hand, multiple-input-state PSOCT uses cross-polarization imaging and variable reference imaging to alter the reference polarization [21; 22]. PSOCT systems with multiple input states take into account the circular birefringence and attenuation of the sample but require two or more polarization states of incident light [23; 24].