Efficiency comparison of stochastic and gradient descent algorithms for laser beam focusing into a single-mode fiber

This study investigates the performance of stochastic and gradient descent algorithms within an active optical system for free-space optical communication applications. The primary function of the adaptive optical system in this context is to dynamically focus a laser beam through a diaphragm emulating a single-mode optical fiber input, utilizing the specified control algorithms. The efficiency of the focusing process is quantified by the proportion of total laser energy transmitted through the diaphragm. The selected algorithms offer a comparative advantage in implementation simplicity over more common alternatives such as stochastic parallel gradient descent (SPGD) or genetic algorithms.
The core objective of the study is to increase the integrated photodiode signal, which serves as the system's merit function, and to iteratively enhance this signal by applying wavefront correction. This correction aims to reshape the laser beam's wavefront to minimize transmission losses through the target aperture. A feedback control loop was established between a piezoelectric deformable mirror and the photodiode, using stochastic and gradient descent algorithms to optimize the aperture's phase profile. The fundamental goal of these optimization routines is to maximize the energy density in the far-field focal spot. This is achieved by minimizing the spot diameter toward the diffraction limit while concurrently increasing its peak intensity.
Empirical findings indicate that the stochastic algorithm, by its nature, progresses rapidly and converges in fewer iterations, albeit with lower final precision. In contrast, the gradient descent algorithm converges more slowly but yields a superior final value for the merit function. Experimental results demonstrated that a 45 mm piezoelectric mirror with 32 control channels was capable of focusing approximately 90% of the initial beam energy through diaphragms of 19 μm and 9 μm diameter, using either optimization strategy.