## 2 Principle  
The block diagram illustrating the principle flow of the heterodyne coherent angle measurement is shown in Figure 1a. At the optical front end, as shown in Figure 1b, the signal laser beam (red beam) and the local oscillation laser beam (green beam) propagate to the QD photosensitive surface through the 50:50 beam splitter, and there is an initial frequency difference between the two laser beams, which generates a beat frequency signal corresponding to the frequency difference. As shown in Figure 1c, at the QD photosensitive surface, the local oscillation laser beam is collimated into the incident beam, and the relative rotation or motion between the terminals causes the signal laser beam to have an incident angular deviation \(\alpha_{AZI}\) and \(\alpha_{PIT}\) along the azimuth and pitch axes, respectively. According to the principle of the angular phase conversion of DWS, the angular deviation of the signal laser beam makes the phase of the beat frequency signal in each quadrant of the QD differ from that of \(\psi_{1}\), \(\psi_{2}\), \(\psi_{3}\), and \(\psi_{4}\). Each quadrant of the beat frequency signal is then entered into the phase tracking and detection module for high accuracy measurement of the phase, as shown in Figure 1d. The signal is first processed by a signal conditioning circuit, followed by amplification through a transimpedance amplifier (TIA), and then converted from analog to digital using an analog-to-digital converter (ADC). Thereafter, the signal enters the Costas phase-locked loop, a specialized circuit dedicated to phase tracking and detection. This loop comprises a phase discriminator (multiplier), an integrator (INT), a loop filter (LPF), and a numerically controlled oscillator (NCO). By adjusting the output frequency of the NCO signal, the NCO tracks the phase of the beat frequency signal, obtains the phase \(\psi_{1}\), \(\psi_{2}\), \(\psi_{3}\), and \(\psi_{4}\) of the beat frequency signal in each quadrant at the same moment, and solves for the phase difference \(\Delta\psi_{AZI}\) and \(\Delta\psi_{PIT}\). Finally, through the DWS phase-angle conversion process, the phase difference is converted to angle \(\alpha^{\prime}{}_{AZI}\), \(\alpha^{\prime}{}_{PIT}\), thus realizing the measurement and compensation of the initial incidence angle deviation \(\alpha_{AZI}\), \(\alpha_{PIT}\) of the signal laser beam. First, the spatially coherent mixing process of the optical front-end was analyzed, as showed in Figure 1b. In accordance with the coherence condition, the signal and the local oscillation laser beam were configured to be linearly polarized laser beams with parallel polarization vectors. It was observed that there was a certain degree of deviation in the wavefront phase of the signal laser beam. The two laser beams were then subjected to a process of coherent mixing at the QD photosensitive plane, with the vector \(\mathbf{r}\) representing the QD plane. The signal and the local oscillation laser beam light fields \(E_{S}\) (\(\mathbf{r}\), \(t\)) and \(E_{LO}\left(\mathbf{r},t\right)\) can be expressed as Equation (1), where the variables \(\mid\!E_{S}(\mathbf{r})\!\mid\) and \(\mid\!E_{LO}(\mathbf{r})\!\mid\) represent the light intensity, \(\psi_{S}(\mathbf{r})\) and \(\psi_{LO}(\mathbf{r})\) represent the wavefront phase generated by the incident angular deviation, \(\omega_{S}\) and \(\omega_{LO}\) represent the angular frequency, \(\varphi_{S}\) and \(\varphi_{LO}\) represent the initial optical phase, and \(t\) represents the time [6]. \[ \begin{array}{l}E_{S}(\mathbf{r},t)=|E_{S}(\mathbf{r})|\times\exp(iy_{S}(\mathbf{r})) \times\exp(i[\omega_{S}t+\varphi_{S}])\\ E_{LO}(\mathbf{r},t)=|E_{LO}(\mathbf{r})|\times\exp(i\psi_{LO}(\mathbf{r}))\times\exp(i[ \omega_{LO}t+\varphi_{LO}])\end{array}