## 1 Introduction  
Since the 1980s, Fourier transform imaging spectroscopy (FTIS) has gained attention internationally for its high accuracy and robustness, which can be classified into three types: tempo-modulated, spatio-modulated, and spatio-tempo hybrid modulated. The tempo-modulated type involves moving a mirror to acquire a time series of optical path differences (OPD). The spatio-modulated type includes a slit in the front telescope system to limit the imaging range, enabling the acquisition of complete interferogram information for ground elements along the slit direction with a single exposure. The spatio-tempo hybrid modulated type eliminates the need for slit and moving parts, allowing for the acquisition of a complete image with a single exposure. The spectral component of tempo-modulated type mostly employs Michelson interferometers, which require high-precision mirror drive systems and exhibit poor real-time performance, rendering them unsuitable for fast-changing spectral measurements. The latter two types are, generally, Sagnac interferometers [1; 2; 3; 4], Mach-Zehnder interferometers [5; 6], or birefringent crystal interferometers. Of these, the static birefringent Fourier transform imaging spectrometer (SBFTIS) [7; 8; 9; 10; 11; 12; 13; 14; 15] has gained attention for its compact size, low cost, superior stability, and high energy utilization. However, traditional SBFTIS has slit-limited luminous flux and a fixed spectral resolution, which restricts its applicability. Compared to the spatio-modulated type, the spatio-tempo hybrid modulated type is slit-free, which leads to a relatively higher light flux. In our previous work [16; 17], a novel spatio-tempo hybrid modulated SBFTIS with an adjustable spectral resolution based on the dual Wollaston prism (DWP) group with an adjustable air gap has been proposed, which greatly reduces the size of spectral image data [18; 19], while improving the luminous flux. However, the luminous flux is still affected by the clear aperture [20], which greatly limits the system's applicability. The clear aperture is a crucial parameter of an SBFTIS, as it directly corresponds to the selection of the aperture stop, which is a significant parameter in determining the system's maximum field of view (FOV), the range of spectral resolution zooming, and the size of the CMOS (Complementary Metal-Oxide-Semiconductor) camera chip. The exit aperture plane plays a crucial role in determining a clear aperture. When only one of the two linearly polarized lights is emitted from the DWP correctly, which is separated by the beam splitter DWP, it is impossible to form neither an interferogram nor a high-quality imaging on the detector. Despite its importance, there are few reports on the research of the clear aperture of DWP, with approximate processing methods being predominantly employed, which ignore the impact of crystal birefringence on a clear aperture. This is mainly due to the complexity of the laws of light propagation in wedge-shaped birefringent crystals. Therefore, it is necessary to analyze the relationship between the system's aperture and light flux. In this paper, based on a brief introduction to SBFTIS, we focus on the theoretical derivation and simulation analysis of the change in the clear aperture and the luminous flux utilization caused by the birefringence phenomenon of the DWP. The wave normal tracing method [21; 22; 23] is employed to accurately calculate the light displacement and offset of DWP under any incident direction, validating the effectiveness of the calculation by comparing it with experimental results. The problems of the aperture and luminous flux are not systematically studied and analyzed in the SBFTIS with a zoomable spectral resolution. The maximum aperture is analyzed, and the relationship of luminous flux utilization with FOV and air gap thickness is obtained.