Nondeterministic wavefront estimation based on deep learning for multi-band synchronous high-resolution reconstruction technology

To enhance the quality of the images observed by the ground telescopes, image post- processing technology is usually required. Multi-band synchronous high-resolution reconstruction technology utilizes a phase retrieval algorithm to estimate the instantaneous wavefront based on the deconvolved focal plane point spread function (PSF) in high signal-to-noise ratio (SNR) bands, then it uses the estimated wavefront to calculate the PSF of other bands to achieve the fast and high-resolution reconstruction of multi-band images. However, due to a single-frame focal plane PSF corresponding to a pair of complex conjugate wavefronts, this ambiguity makes existing phase retrieval algorithms difficult to converge, seriously affecting their accuracy of wavefront estimation, and further affecting the estimation accuracy of multi-band PSFs. Therefore, existing phase retrieval algorithms are difficult to meet the requirements of multi-band synchronous high-resolution reconstruction technology and need to be further optimized. In response to the shortcomings of the existing methods, this research proposes a nondeterministic estimation (ND-Estimation) method that modifies the datasets and loss function during the training process to enable the network to update and learn toward one direction of a pair of complex conjugate wavefronts based on the network initial state. These improvements enable the network to accurately estimate the nondeterministic wavefront corresponding to a single-frame focal plane deconvolved PSF, thereby achieving precise estimation of multi-band PSFs. We also built an effective lightweight single-frame focal-plane residual network (SF-ResNet). Simulation and experimental results show that the SF-ResNet combined with the ND-Estimation method can achieve high-precision wavefront estimation under different turbulence intensities, and further realize subsequent high-precision estimation of multi-band PSFs. Its inference time is 2.7566 ms, reaching the millisecond level. This approach significantly improves the accuracy of wavefront estimation compared to existing phase retrieval algorithms based on single-frame focal plane information. This study provided a feasible method for multi-band synchronous high-resolution reconstruction technology. (c) 2025 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement