Deep learning phase inversion technique for single frame image based on Walsh function modulation

The far-field wavefront inversion exhibits degeneracy states, leading to the problem of encountering multiple solutions when recovering the wavefront. In comparison to traditional iterative algorithms, the combination of phase modulation and deep learning in the phase inversion method not only significantly reduces computational complexity but also effectively solves multi-solution problems. This method possesses strong real-time capabilities and a simple structure, showcasing its unique advantages. In this paper, different Walsh functions are used to modulate the phase, and a deep learning approach is taken to train a convolutional neural network to obtain the 4th-30th order Zernike coefficients from the modulated single-frame far-field intensity maps so as to recover the original wavefront, which solves the problem of multiple solutions of phase inversion. For the residual wavefront of the turbulent aberration of 3-15 cm atmospheric coherence length, the ratio of its RMS to the RMS of the original wavefront can reach 7.8%. In addition, this paper also deeply investigates the effects of various factors such as Zernike order, random noise, occlusion, and intensity map resolution on the wavefront recovery accuracy. The results show that this deep learning-based phase inversion method exhibits good robustness in complex environments.