Objective Gravitational waves are ripples of the curvature of space and time in the universe. They dominate the evolution and operation of the universe in the form of waves. Gravitational wave detection has been widely used by many scholars at home and abroad and has achieved breakthrough results. Gravitational wave detection is one of the most concerned frontiers of scientific research in the history of contemporary physics. Space laser heterodyne interferometer is a key component of gravitational wave detection system. The four -quadrant detector is an important part of the laser interference gravitational wave detector, which can be used for spot position detection, laser angle measurement, data transmission and reception, etc. The performance of the four -quadrant detector will directly affect the accuracy of the gravitational wave detector. Influenced by noise factors, the system signal-to-noise ratio (SNR) of laser interference gravitational wave detector and other parameters will be affected, thus affecting the detection accuracy and performance of the system. Therefore, it is necessary to establish a complete mathematical model for the position detection process of the four -quadrant detector and verify it through the simulation system, so as to analyze the factors affecting the position detection accuracy and improve the detection method. Methods In order to analyze the factors that affect the position detection accuracy of the four -quadrant detector, in this paper, firstly, the noise factors in the laser heterodyne interferometer and the relationship between the local oscillator power and the system SNR are analyzed. The mathematical theoretical model of the four -quadrant detector position detection is established, and the main factors affecting the position detection accuracy are theoretically derived. Then the position detection simulation system is established by using Monte Carlo random simulation method, and the Monte Carlo random points are used to characterize the receiving and solving process of the four -quadrant detector spot. Finally, the simulation results are compared with the theoretical results of the mathematical model, and the correctness and accuracy of the simulation results are verified. Results and Discussions The simulation system of four -quadrant detector position detection model based on Monte Carlo method is established. The simulation system is based on the Monte Carlo idea and consists of three parts: the Gaussian spot generation process, the spot center position calculation process, and the error evaluation process (Fig. 4). The estimated spot center position is compared with the true value to judge the accuracy of the Monte Carlo simulation method (Fig. 5). The simulation results show that due to the correlation of beat frequency signal noise among the four quadrants, the position detection accuracy is not affected by beat frequency signal noise (Fig. 6). Due to the independence of detector noise in the four quadrants, when the system SNR caused by detector noise rises from 30 dB to 44 dB, the position detection accuracy is improved (Fig. 7). The smaller the Gaussian spot radius is, the more concentrated the spot energy is, and the higher the position detection accuracy is (Fig. 8). The closer the spot center position is to the center of the four -quadrant detector photosensitive surface, the higher the position detection accuracy is (Fig. 9). Conclusions In this paper, the mathematical model of the position detection accuracy of the four -quadrant detector is studied theoretically and verified by the Monte Carlo simulation system. The key parameters that affect the position detection accuracy are obtained: system SNR, Gaussian spot radius and spot center position. The simulation system data show that the position detection accuracy can be improved by improving the system SNR, selecting small light spot for detection and using light spot incident near the origin of the detector photosensitive surface. In addition, the estimated value of the Monte Carlo simulation system is in good agreement with the solution of the mathematical model, which proves that the precision of the Monte Carlo method is high. This research has certain guiding significance for engineering applications.
