面 向 深 度 学 习 的 光 纤 阵 列 激 光 系 统 误 差 自 校 准 方 法

Objective Deep learning, with its powerful high-dimensional nonlinear fitting capabilities, can learn the mapping relationship between the far-field intensity distribution and near-field phase of fiber laser array systems from labeled data sets, thereby enabling efficient and accurate phase prediction and control. This approach simplifies system complexity, reduces hardware dependency, and offers advantages such as fast response speed and no need for iteration. However, obtaining real data with phase labels is challenging and costly. Researchers often rely on numerical simulations to generate training data. However, the physical model parameters in simulations (such as beam spatial position) may deviate from actual systems, leading to significant performance degradation of models trained on simulation data when applied to real systems. Therefore, to eliminate the differences between simulation and actual systems, this paper proposes a self-calibration method for fiber laser array systems and conducts simulation experiments to validate beam position calibration. Resolving these discrepancies can effectively improve phase prediction accuracy and coherent beam combining (CBC) efficiency. Methods First, a 19-channel fiber laser CBC system is constructed and its key parameters are defined. The beam propagation model is derived, and the corresponding near-field and far-field intensity distributions are numerically generated. Subsequently, based on the automatic differentiation (AD) algorithm, the beam position is inversely estimated from the input far-field speckle patterns. The effectiveness of the AD-based calibration is validated by analyzing the loss function convergence curve and the residuals of the optimized positions. We generate 2×10⁴ training samples for predicting an 18-dimensional phase vector. Combining the calibrated beam positions with the beam propagation model, a“pattern-phase”dataset is constructed. Model_ori is trained using the design position data, whereas model_calib is trained using the calibrated position data. The prediction accuracies of the two models are compared in terms of phase error, and their coherent beam combining performance is evaluated using the normalized power in the bucket (PIB). Results and Discussions After approximately 300 iterations of the AD algorithm, the loss function decreases and stabilizes at the magnitude of 10⁻¹⁰, with the entire iterative process converging within 4.68 s. The optimized beam center position closely matches the real position, with a maximum residual of 1.02×10⁻⁷ mm in the x-direction and 1.31×10⁻⁷ mm in the y-direction. Compared with the initial (design) positions, the deviations are significantly reduced, which demonstrates that the AD algorithm can accurately obtain the real beam positions. The normalized phase Circular-mean squared error (Circular-MSE) predicted by the model decreased from 2.72× 10⁻² to 9.08×10⁻⁴, with an accuracy improvement of approximately 96.7%. Additionally, the Circular-MSE loss function accelerates model convergence by a factor of 3.6, with the final loss decreasing to below 0.002, achieving more precise phase prediction. After calibration, the mean normalized PIB value of beam combining efficiency increases from 0.816 to 0.988 (an improvement of 21.1%), and the far-field intensity distribution after compensation is basically consistent with the ideal coherent state, proving that the calibrated method can effectively improve the performance of CBC. Conclusions We present a deep learning-oriented self-calibration method for fiber laser arrays. Using the AD algorithm, the method accurately obtains the center coordinates of each individual beam in the array. The deep learning model trained using the calibrated parameters reduces the phase prediction Circular-MSE from 2.72×10⁻² to 9.08×10⁻⁴ and improves the mean normalized PIB of CBC from 0.816 to 0.988, fully demonstrating the necessity of calibrating the beam position in practical applications.It should be noted that this study only focuses on single-parameter calibration of beam position, assuming that other parameters such as phase and tip/tilt are in an ideal state, which has certain limitations. In the future, a self-calibration framework for multi-parameter joint optimization will be further developed to facilitate the practical deployment of deep learning in laser array systems.