## 4 Experiment and Results  
### System Setup  
The experimental system for heterodyne coherent angle measurement was constructed based on the theoretical model and the results of the simulation system. The schematic block diagram of the experimental system is presented in Figure 6a. Figure 6b provides a detailed depiction of the fast-steering mirror (FSM) calibration process. Figure 7a showcases the  
Figure 4: Results of the phase-locked loop operation in each quadrant. (**a**) Loop locked state. (**b**) NCO indexed calculated phase. Figure 5: Heterodyne coherent angle measurement accuracy. (**a**) Azimuth axis. (**b**) Pitch axis. physical diagram of the experimental system, while Figure 7b offers a visual representation of the laser beam spot inside the charge-coupled device (CCD). In this figure, the signal and local oscillation laser beams are depicted as being in an overlapping state. Among them, red represents the signal laser beam and green represents the local oscillation laser beam. A dual-channel parallel acousto-optic modulator (AOM) was adopted to offset the frequency of the signal and the local oscillator laser beam, simulating the heterodyne beat frequency signal generated by the frequency difference between the two laser beams in the actual system. After completing the angular calibration, FSM was utilized to deflect the signal laser beam by a known angle, thus simulating the angular shift of the laser beam incidence due to the relative rotation or motion of the terminals in the actual system. Four parallel Costas phase-locked loops were adopted to track and detect the phase of the beat frequency signal, accurately measuring the phase differences between the received signals in each quadrant of the QD. The DWS algorithm was adopted to further convert the phase difference into the angular deflection amount, and the standard deviation was calculated in combination with the FSM angular deflection amount, thereby achieving high-precision angular measurements. The key parameters of the desktop experimental system for the heterodyne coherent angle measurements are shown in Table 1.  
Figure 6: Block diagram of the heterodyne coherent angle measurement experimental system. (**a**) General block diagram. (**b**) FSM calibration. Figure 7: Physical diagram of the heterodyne coherent angle measurement experimental system. (**a**) Total system. (**b**) CCD laser beam spots. The experimental system for the heterodyne coherent angle measurements consisted of two subsystems: the coherent optical front-end and the angle accuracy measurement. The coherent optical front-end is responsible for simulating the signal and local oscillation laser beams within the actual system and for coherently mixing them in the QD photosensitive surface. This configuration is predicated on a beaconless space laser communication scenario. The system laser source is a 1550 nm narrow linewidth laser. The outgoing laser beam signal undergoes 50:50 beam splitting and enters the dual parallel AOM for frequency shifting. Following this process, the frequency of the local oscillation laser beam is 193 THz + 100 MHz, while the frequency of the signal laser beam is 193 THz + 101 MHz. The frequency-shifted fiber signal subsequently generates a spatial laser beam through a collimator, in which the signal laser beam is deflected at a known angle through the FSM. The two laser beams are then reflected and transmitted at the 50:50 spatial beam splitter, and transmitted together to the QD photosensitive surface for coherent mixing to produce a 1 MHz beat frequency signal. The function of the angle precision measurement subsystem is to perform phase tracking and angle calculation on the beat frequency signal. After the QD front-end circuit converts the beat frequency signal into a digital signal, it enters the Costas phase-locked loop. The phase-locked loop is composed of a field programmable gate array (FPGA) and an advanced RISC machine (ARM).