In laser communication systems, target acquisition, aiming, and tracking are critical tasks. Central to these tasks is the precise detection of spot positions, which is essential for determining the target’s spatial location and motion trajectory, thus facilitating accurate communication signal guidance. Consequently, precise tracking detectors are indispensable for ensuring the stability and reliability of the system. Among these, quadrant detector positioning algorithms are widely employed in optical measurement and tracking systems, offering notable accuracy. However, traditional algorithms encounter inherent limitations when applied to models of Gaussian spots, primarily due to systematic errors and computational constraints. To address these challenges, we propose an enhanced positioning method based on the finite element method (FEM). By discretizing the detector model into a finite set of mesh elements and aggregating the signals within these elements, the proposed approach aims to optimize the computational process, thus improving both positioning accuracy and efficiency. Experimental results substantiate the effectiveness of the proposed method, emphasizing its significant potential for practical engineering applications.

In this paper, we employ an improved algorithm based on FEM to enhance the modeling and analysis of the quadrature detector’s response to Gaussian spots. The system is divided into two independent components: the detector model and the spot model, each of which is formulated within the FEM framework (Fig. 5). First, the detector model is discretized using FEM while accounting for the effects of the dead zone and boundary conditions (Eqs. 5?9). Subsequently, the spot model is discretized, incorporating the influences of lens distortion and external light interference during optical transmission (Eq. 10). Finally, the detector and spot models are coupled, and the response of each finite element is computed using FEM (Eq. 11). Based on this improved FEM-based algorithm, the relationship between the coordinate offset of the Gaussian spot and its center position on the quadrature detector is further analyzed, thus improving measurement accuracy.

The simulation results demonstrate that the proposed improved algorithm based on FEM significantly outperforms other algorithms in terms of positioning error. Specifically, when compared to traditional positioning algorithms, the maximum reduction in error can reach 87% when the spot center displacement is 0.7824 mm (Fig. 7). To further validate the effectiveness of the proposed modeling method, a spot experimental detection device is constructed, and the results are compared with experimental data (Fig. 8). The number of mesh elements in the FEM is determined by the value of n. Multiple sets of n values are selected, and the results are compared with experimental measurement data. The experimental results show that the mathematical models established for multiple n values exhibit a good match with the experimental data (Fig. 9). As n increases from 500 to 2000, the root mean square error (RMSE) between model predictions and experimental results decreases significantly. When n reaches 2000, the rate of decrease in RMSE continues but stabilizes (Table 1). The proposed method achieves RMSE with mm-level precision, further validating the high accuracy of spot positioning.

In this paper, we propose an enhanced positioning method based on FEM to overcome the limitations of traditional algorithms in accurately solving Gaussian spot models. The proposed approach divides the illumination of the spot on the detector into two independent components: the detector model and the spot model. These two models are mathematically formulated under the FEM framework. The detector model incorporates the effects of dead zones and boundary conditions, while the spot model accounts for lens distortion and external light interference during optical transmission. By separating the two models, the proposed method optimizes the computational process, leading to improved positioning accuracy and computational efficiency. Simulation results demonstrate that the proposed method significantly outperforms other positioning algorithms in terms of coordinate offset error. Specifically, when compared to traditional positioning algorithms, at the spot center displacement of 0.7824 mm, the maximum error reduction reaches 87%. Experimental validation further confirms the effectiveness of the proposed method. An experimental setup for spot detection is developed, and the results are compared with experimental data. The experimental findings indicate that the mathematical models established using FEM exhibit good agreement with the experimental data and show excellent performance under varying mesh resolutions. As the number of mesh elements increases, RMSE decreases significantly, achieving millimeter-level precision. These results validate the high accuracy of spot positioning and emphasize the method’s significant potential for practical engineering applications. The proposed approach provides a promising solution for enhancing positioning accuracy in laser communication systems and holds substantial potential for future applications in the field.