Wavefront Sensing using GMM Clustering for Initialization of L-BFGS Optimization

Phase diversity wavefront sensing (PDWS) is a model-based wavefront estimation technique that avoids additional optical components, making it suitable for resource-constrained environments. However, conventional optimization-based PDWS methods often suffer from high computational costs and sensitivity to initial values. To address these challenges, this paper proposes a hybrid PDWS method that integrates deep learning with nonlinear optimization to improve efficiency and accuracy. The deep learning model provides an initial estimate of wavefront aberrations, which is further refined by the L-BFGS optimization algorithm to achieve high-precision reconstruction. Simulation and experimental results indicate that the proposed method achieves an RMS wavefront error below 0.05λ within [−0.5λ, 0.5λ] and exhibits a certain level of generalization up to [−0.7λ, 0.7λ]. Compared with conventional PDWS approaches, the proposed method reduces computational time by approximately 89% while maintaining a reliable reconstruction accuracy under moderate aberration conditions. These findings indicate that the hybrid approach achieves a trade-off between computational efficiency and estimation accuracy, suggesting its potential applicability in wavefront sensing tasks.