Enhanced Neural-Network-Based Quadrant Detector Array Calibration Method for Vortex Beams

This study proposes a comprehensive method for positioning Laguerre-Gaussian (LG) beams using a quadrant detector (QD) array combined with an optimized backpropagation (BP) neural network. By addressing the limitations of traditional techniques, such as infinite integration and polynomial fitting, the BP neural network demonstrates superior performance in terms of root mean square error ( $\delta _{\text {RMSE}}$ ) and classification accuracy. Experimental results confirm that the proposed model achieves precise predictions for angular quantum indices (p and l) and beam radii (R), with classification accuracy exceeding 99%. In addition, $\delta _{\text {RMSE}}$ in both 1-D and 2-D measurements is as low as the order of $10^{-3}$ mm. These findings underscore the robustness and scalability of the model, positioning it as a promising solution for real-time beam position detection in orbital angular momentum (OAM)-based wireless optical communication systems.