## 4 Experiment  
A prototype was built to demonstrate the omnidirectional receiving ability. The light received by the receiving sub module converges on the filter through a short focal lens. When the incident light angle is moved, the relationship between the light intensity received by the detector and the departure angle is described as:  
\[\mathrm{P_{1}}=\mathrm{P_{0}}\cos(\theta-15^{\circ})0^{\circ}\leq\theta\leq 30 ^{\circ} \tag{13}\]  
Figure 5: System model of omnidirectional reception. where \(\rm P_{0}\) is the intensity of the normal incident light, and \(\rm\theta\) is the angle between the incident light and the normal incident light when the incident light is moved. When the light moves, the spot received by the detector will first move from the edge to the center of the detector, and then gradually move out of the detector. Therefore, the ratio of the spot area on the detector to the whole spot area \(\rm S/S_{0}\) will first increase, then remain unchanged, and finally decrease. The light intensity received by the detector is:  
\[\rm P=P_{1}\times\frac{S}{S_{0}} \tag{14}\]  
The output electrical signal of the module is proportional to the intensity of the incident light. When the incident light is moved, the relationship between the output voltage of the receiving sub module and the departure angle can be denoted as:  
\[\rm U=U_{0}\cos(\theta-15^{\circ})\times\frac{S}{S_{0}}0^{\circ}\leq\theta \leq 30^{\circ} \tag{15}\]  
where \(\rm U_{0}\) is the output voltage at normal incidence. In Figure 6, the relationship between the departure angle and the output voltage theoretically is represented by the blue line. At the same time, the output voltage of a receiving sub module at different departure angles from \(0^{\circ}\) to \(30^{\circ}\) is actually tested as shown by the orange line in Figure 6. It can be seen from Figure 6 that when the signal light is obliquely incident at \(0^{\circ}\) to \(8^{\circ}\) and \(22^{\circ}\) to \(30^{\circ}\), the theoretical data are in good agreement with the measured results. When the signal light is approximately normal incidence at \(8^{\circ}\) to \(22^{\circ}\) the theoretical data have a little deviation from the measured results, and the closer the signal light is to normal incidence, the greater the deviation is. This is because the filter will affect the oblique incident signal light. With the increase of the incident angle, the central wavelength and passband of the filter will move to the short wave direction [26]. Therefore, in order to ensure the signal quality of oblique incidence, the window wavelength of the filter of the receiving sub module is slightly biased to the short wave direction. In this way, the wavelength of the signal light and the window wavelength of the filter cannot be completely matched in normal incidence. This will make the filter have some attenuation to the signal and make the measured result lower than the signal strength of the theoretical data. However, because the light intensity of normal incidence is stronger than that of oblique incidence, the receiving sub module can still receive good signal even the filter has attenuation effect. Figure 6: Relationship between the output voltage of the receiving sub module and the departure angle. Then, the loss in the switching process of the combined optical system is analyzed. Since the window angle of each receiving sub module is 30\({}^{\circ}\), 12 modules are used to achieve \(360^{\circ}\times 30^{\circ}\left(\theta_{\parallel}\times\theta_{\perp}\right)\) circular reception. Consequently, when the direction of the incident light moves on the annular band, the relationship between the output voltage and the offset angle of the combined optical system changes periodically with a period of 30\({}^{\circ}\). The image of each cycle is the same as that of a single receiving sub module. In Figure 7, theoretically, the relationship between the departure angle and the output voltage is represented by the blue line.