# A Convenient Way to Determine the Optimum Angle of Incidence of Fizeau Interferometer
## 4 Intensity Optimization  
According to expression \(\frac{dE}{d\theta}\), when the value of reflectivity or wedge angle is relatively low, the variation trend of the sum of the amplitude vector is insensitive to the change of \(\theta\) near the optimum incidence angle. Only when R is relatively large (e.g., R is greater than 0.9) or wedge angle is relatively large (e.g., \(\alpha\) is greater than 0.5 mrad), the difference of the sum of amplitude vector between oblique incidence and normal incidence can be clearly seen. In order to verify the effectiveness of the formula proposed in this paper, Figure 8 is the comparison diagram of the interference intensity before and after correction when the focal plane array is at \(\mathrm{z}=0\) and the focal plane array is within 10 mm from the wedge apex. Compared with the direct normal incidence of the beam into the wedge cavity, the intensity of the sub-peak is significantly reduced, and the intensity of the main peak is improved when the beam is incident at the optimum incidence angle.  
However, when the selected position of y is relatively large, only under the condition of a slight wedge angle or low value of reflectivity, the beam incident at the optimum incident angle will have a good correction effect on the interference intensity. Like in the case of \(\alpha\) = 0.1 mrad, a better correction can be obtained at the peak of y = 5007 mm. However, in the case of high reflectivity (such as R = 0.9 or R = 0.95), when \(\alpha\) > 0.5 mrad, the interference intensity has not been well corrected. Especially when the reflectivity is greater than 0.9, and the wedge angle is greater than 0.5 mrad, the interference intensity has lost the characteristics of the periodic distribution. These features can be easily seen in Figure 9. The reason for the fringe distortion is that the structural instability makes the interference beam move in the direction of increasing the plate spacing so that the beam gradually dephases. This dephasing is mainly related to two parameters. High reflectivity and large wedge angle will aggravate the dephasing of interference intensity in the y-direction. This dephasing phenomenon is caused by the structure of the Fizeau interferometer itself and can't be corrected by changing the incident angle of the beam.  
Figure 7: Comparison of the optimum incident angles obtained by different methods with the condition of (**a**) \(\alpha\ =\ 0.1\) mrad; (**b**) \(\alpha\ =\ 0.5\) mrad; (**c**) \(\alpha\ =\ 1\) mrad.  
At present, the design angle of the wedge-shaped cavity is 0.1 mrad, and the thickness of the parallel plate constituting the wedge-shaped cavity is 10 mm, so it is necessary to  
Figure 8: When the focal plane array is at the position of Z = 0 and the focal plane array is within 10 mm from the apex of the wedge, the interference intensity curve is corrected by using the formula derived in this paper. The blue line represents the state before correction, and the red line represents the state after correction.  
Figure 9: When the selected position of y is relatively large, only under the condition of a small wedge angle or low value of reflectivity, the beam incident at the optimum incident angle will have a good correction effect on the interference intensity. In the case of higher reflectivity or larger wedge angle, the interference intensity has not been well corrected. The blue line represents the state before correction, and the red line represents the state after correction (\(\lambda~{}=~{}1610\) nm).  
analyze the fringe correction effect under the specific structure. Here we simulate the comparison of light intensity before and after correction when the thickness of the parallel plate is d = 10 mm, as shown in Figure 10. It is found that when the reflectivity is 0.5, 0.7, 0.9, and 0.95, respectively, the optimum incidence angle obtained by the formula still has a good correction effect on the intensity distribution.