## 4 Experiment and Results
### Comparison with Direct Detection  
The experimental system of the heterodyne coherent angle measurement was adjusted to construct a direct detection angle measurement experimental system, and the block diagram of the experimental system is shown in Figure 12. The FSM was employed to deflect the initial angle of the transmitting laser beam, and the two laser beams, shifted by the AOM frequency, were coupled by the optical fiber to generate a Sin signal of 1 MHz and transmitted to the QD photosensitive surface. The received optical power \(P_{1}\), \(P_{2}\), \(P_{3}\), and \(P_{4}\) in each quadrant, in conjunction with the spot center position detection algorithm, facilitated the determination of the spot center in the azimuth and pitch axis of the offset. Subsequent trigonometric function calculations further resolved the angular deflection amount. The FSM angular deflection amount was then integrated into the calculation of the standard deviation. Consequently, the direct detection angle measurement was achieved.  
A direct detection angle measurement accuracy experiment was carried out. The power of the transmitting laser beam directed toward the QD photosensitive surface was adjusted to \(-16\) dBm, and the deflection of the FSM azimuth and pitch angle was set to 0. The results of the direct detection angle measurement accuracy at this time are presented in Figure 13. The experimental results indicate that the angular measurement accuracy was \(13.54\)\(\upmu\)rad for the azimuth axis and \(12.51\)\(\upmu\)rad for the pitch axis. The heterodyne  
Figure 11: Results of the heterodyne coherent angle measurement accuracy under different loop bandwidths.  
Figure 12: Block diagram of the direct detection angle measurement experiment.  
coherent angular measurement demonstrated a higher angular measurement accuracy compared with direct detection under the same power condition. This is particularly advantageous for the high accuracy demanded in the scenario of inter-satellite long-distance beam measurement.  
In response to the high detection sensitivity requirement for long-distance beam measurement between satellites, further detection sensitivity comparison experiments were carried out. The power of the local oscillator laser beam was adjusted to \(-7\) DBM and the loop bandwidth to \(10\) Hz. Firstly, the signal laser beam power was set to \(-15\) dBm, and the angular measurement accuracy was evaluated based on heterodyne coherence and direct detection mode, respectively. Secondly, the signal laser beam power was systematically reduced in \(1\) dB steps to assess the angle measurement accuracy of heterodyne coherence and direct detection under varying optical powers. Finally, the angle measurement accuracy threshold was set to \(20\)\(\upmu\)rad, and the minimum signal optical power of the heterodyne coherence and direct detection methods under this threshold was compared and analyzed. The ensuing test results are presented in Figure 14. The experimental results demonstrated that for an angular measurement accuracy threshold of \(20\)\(\upmu\)rad, the phase measurement method exhibited a sensitivity of \(-50\) dBm, while it was \(-20\) dBm in the direct detection method. This observation indicates that the phase measurement method can maintain the same angular measurement accuracy under lower signal optical power, making it more suitable for high detection sensitivity requirements in inter-satellite long-distance beam measurement scenarios.  
Figure 14: Zero detection sensitivity comparison of the test results.  
Figure 13: Zero direct detection angle measurement accuracy results. **(a)** Azimuth axis. **(b)** Pitch axis.