## 4 Analysis  
### Restricted Conditions of Luminous Flux  
Due to the existence of displacement, the light incidents from the front surface may not all exit from the rear surface. Although this part can be correctly imaged, the interference pattern cannot be generated correctly, resulting in the limitation of the luminous flux of the system. Figure 12 is the captured incorrect interferogram, and the interference fringes are evidently missing at the edge.  
The maximum incident range that allows light to exit completely from the rear surface is the aperture stop of the system. Taking the prism used in the prototype as an example, its size can be expressed as:  
\[S_{\text{max}}=[(10-\text{max}(\Delta_{ze}))-(-10-\text{min}(\Delta_{ze}))] \times[(10-\text{max}(\Delta_{ye}))-(-10-\text{min}(\Delta_{ye}))], \tag{13}\]  
The luminous flux of SBFTIS is determined by the size of its aperture stop. Therefore, aperture utilization can be used in order to measure the luminous flux utilization. The  
Figure 11: Variation in \(d^{\prime}\) with \(s\).  
Figure 12: A typical incorrect interferogram.  
aperture utilization rate is the ratio of the aperture stop to the surface area \(S_{0}\) of the Wollaston prism, denoted as \(\eta\). When the prism parameters have been determined, a higher value of \(\eta\) indicates higher luminous flux.  
According to the calculation, the luminous flux utilization is related to the direction of the incident light, which is determined by two parameters: the angle \(\omega\) between the incident surface and the main section of the crystal and the incident angle \(i\). When \(s=0\) mm, in the case of constant \(\omega\), taking light propagating in the main section as an example within the range of \(i=\pm 5^{\circ}\), the continuous variation in \(\eta\) with \(i\) is shown in Figure 13:  
Due to the geometric relationship between the relative positions of the two lights, \(\eta\) changes linearly with \(i\) in a three-stage manner: firstly, an increase from 90.96% to 94.20%, followed by a slight increase to 94.52%, and, finally, a decrease to 91.86%, and the minimum area of the clear aperture of the DWP \(S_{min}=363.84\) mm\({}^{2}\). This is due to the change in the relative position of the oeeo wave and the eooe wave: when the incident angle is large and positive, the eooe light limits the aperture; when the incident angle is large and negative, the oeeo light limits the prism aperture; and when the incident angle is small, the two beams of light jointly limit the prism aperture.  
Similarly, when keeping the incident angle constant at \(i=\pm 5^{\circ}\), in the range of \(\omega=\pm 90^{\circ}\), the continuous variation relationship of \(\eta\) with \(\omega\) is shown in Figure 14, respectively.  
As shown in Figure 14, \(\eta\) varies from 96.99% to 89.72%. In order to ensure that the light always propagates in the crystal during the rotation of \(\omega\) and exits from the rear surface, and when the incident plane angle \(\omega=\pm 45^{\circ}\) and \(i\) is less than \(0^{\circ}\), the luminous  
Figure 14: Luminous flux utilization as a function of \(\omega\) when \(i=\pm 5^{\circ}\).  
Figure 13: Luminous flux utilization as a function of \(i\) when \(\omega=0^{\circ}\).  
flux utilization rate of the prism group is the smallest, and the minimum area of the clear aperture of the DWP \(S_{min}\) = 358.88 mm\({}^{2}\).