In optical fiber communication, the collimator is a fundamental component with substantial market demand. However, its manufacturing process has long been mired in manual or semiautomatic stages, resulting in low efficiency, high costs, and poor product consistency. Existing semiautomatic systems employ closed-loop feedback control based on the deviation of production data from predefined targets for global optimization, which leads to issues such as high computational burden, lengthy processing time, and sensitivity to production parameters. This study proposes a methodology that combines classical Gaussian beam propagation theory with nonlinear fitting, to swiftly achieve the target spot diameter during collimator fabrication.

Classical Gaussian beam propagation theory was employed to perform nonlinear fitting on production process data. The independent variable was the distance between the optical fiber and lens, and the dependent variable was the detected collimator output spot diameter at the measurement position. Parameters such as lens length (L), fiber mode field radius (ω₀), lens curvature radius (R), and lens refractive index (n) of the collimator were determined through fitting, deriving the distance between the optical fiber and lens corresponding to the target spot diameter in a single step. The nonlinear fitting of production data utilized the Levenberg?Marquardt algorithm. Considering the adaptability issues of different collimator models and the difficulty of obtaining ideal target values in practice, this study incorporates the actual measured spot diameters into subsequent rounds of nonlinear fitting to progressively approach the target, thereby enhancing the adaptability and efficiency of the algorithm.

Classical Gaussian beam propagation theory was employed for the nonlinear fitting of the production process data. Comparative testing with commercial systems, as depicted in Fig. 3, shows that the rolling fitting LM system optimizes within 1?2 steps on average to achieve the target spot diameter size, except for the fixed search points, thereby reducing the number of optimization steps by an average of 57% compared to commercial systems. As shown in Fig. 4, when faced with different collimator parameters, the rolling fitting LM system stabilizes the production of fiber collimators at an average of 18.3 s after switching the fiber parameters, with a standard error of 1.2 s, reducing the production time by 43.7% compared to commercial systems. The average spot diameter error is -0.14%, for a spot diameter reduction error of 1.0%. As illustrated in Fig. 5, even with changes in detection distance z, the algorithm maintains stable production time of 18?19 s, with the average accuracy of optimized spot diameter fluctuating within ±0.3% and the overall error fluctuation not exceeding ±2%. These results demonstrate the robustness and high consistency of the algorithm, indicating its strong resilience and minimal error susceptibility to product nonuniformity.

In this study, a system of nonlinear equations was established based on classical Gaussian beam formulas and actual measurement data, thereby formulating an objective function using the least-squares method and introducing a rolling optimization feedback mechanism to enhance the traditional LM algorithm. This allows the system to rapidly converge while intelligently searching for the target spot diameter, which differs significantly from traditional methods in imparting clear physical significance rather than a simple point-by-point search or abstract mathematical polynomial approximations, thereby significantly reducing the production time of the fiber collimators. The rolling fitting LM system required an average of five optimization steps with an average production time of 18.3 s per collimator. The average accuracy of optimized spot diameter was -0.2%, with an error fluctuation of ±1.1%. Compared to commercial systems, the spot diameter error range was reduced by 1.0%, ensuring higher quality assurance for fiber collimators. More importantly, the rolling fitting LM system reduced the production time for fiber collimators by over 43.7% compared to commercial systems, significantly enhancing automation efficiency. The system demonstrated robustness in consistently optimizing the steps, optimization time, and spot diameter error rates across different parameter configurations of fiber collimators, providing a method of significant reference value for optimization in fiber collimator industry.