## 1 Introduction  
In gravitational wave measurement systems, the relative rotation between test masses introduces angular deviations that have an impact on the accuracy of optical range difference measurements. This field has numerous mature systems [1, 2]. In 2016, American scientists successfully detected for the first time the gravitational wave signals generated by the merger of cosmic double black holes through the ground-based gravitational wave observation system LIGO (Laser Interferometer Gravitational-Wave Observatory) [3]. Concurrently, the National Aeronautics and Space Administration (NASA) and the European Space Agency (ESA) have announced their joint undertaking of the Laser Interferometer Space Antenna program, LISA (Laser Interferometer Space Antenna) [4, 5]. The distance between the test masses is 5,000,000 km, and the angular measurement accuracy is better than 20 \(\mathrm{nrad}/\mathrm{Hz}^{1/2}\) in the low frequency band of 0.1 mHz\(\sim\)100 mHz [6]. NASA and the German Aerospace Center (DLR) have announced the GRACE Follow-On satellite mission, which utilizes an interstellar distance of 220 km and an angular pointing measurement accuracy of better than 1 \(\mathrm{\SIUnitSymbolMicro rad}/\mathrm{Hz}^{1/2}\) at the 0.1 Hz frequency [7; 8; 9]. The Taiji program, which is overseen by the Chinese Academy of Sciences, with a distance of 3,000,000 km between satellites, has developed interferometers in the 0.1 Hz\(\sim\)1 Hz band that can limit noise to 10 \(\mathrm{pm}/\mathrm{Hz}^{1/2}\)[10; 11]. The integration of communication and tracking in space laser communication systems represents a prevailing trend in future development. The system employs a beaconless design, eschewing the 800 nm beacon laser beam and utilizing a 1550 nm communication laser beam for concurrent high-rate data transmission, high-accuracy beam angle detection, and tracking. The distance between satellites in a laser communication link can span thousands of kilometers, and the relative motion between satellites and other factors can introduce angular deviations to the signal beam at the receiving end. This can compromise the performance of the system. To ensure the stability of the laser link, high-sensitivity detection and the high-accuracy measurement and compensation of the angular deviation of the weak signal are essential. In addition, the reconfigurability of laser communication terminals has emerged as a pivotal area of research in programs such as the U.S. Space-Based Adaptive Communication Node (Space-BACN) [12]. The aim of this study was to realize multiple wavelength switching and repeatable configurations in the range of 1530-1565 nm. When the communication wavelength changes by 0.01 nm, the corresponding amount of optical frequency change is 1.25 GHz. The frequency of beat note signals in the laser heterodyne interferometric angular measurement system is up to 20 MHz. The isolation of different communication wavelengths is realized by adjustment of the optical frequency of the local oscillation laser beam, which can be better applied to the multi-node laser communication network system. Therefore, it is of great significance to develop an angle measurement scheme with high detection sensitivity and high accuracy for future laser communication terminal design work. A four-quadrant detector (QD) was compared with a conventional charge-coupled device (CCD) and a position sensitive detector (PSD). QDs have a MHz bandwidth, simpler signal processing circuits, and higher measurement accuracy and sensitivity, which make them capable of correctly receiving complete waveforms and accurately solving phase information for MHz-scale beat-frequency continuous wave signals. Therefore, a QD was chosen as the photodetector of the heterodyne coherent angle measurement system. The traditional QD angle measurement system adopts the direct detection technology, which is based on the received signal amplitude information for the spot center position solution and is converted to the angle through the trigonometric function.