Reliable wavefront reconstruction from a single lateral shearing interferogram using Bayesian convolutional neural network

Abstract

The reconstruction of the original wavefront from its sheared information is an ill-posed inverse problem in the sense of Hadamard. In this paper, we present a new technique for reconstructing the wavefront from a single lateral shearing interferogram using a Bayesian convolutional neural network. With the synthesized data, the trained network can robustly invert the physical model, recover the spectral leakage problem caused by the shear operation, and reconstruct the desired phase distribution. In addition, a quantitative pixel-level uncertainty measure of the reconstruction results is provided simultaneously, which can be used as an indicator to judge the validity of reconstruction accuracy in the absence of ground truth. Numerical experiments are carried out to investigate the robustness and accuracy of the method, in which the effects of different noise levels and shear distances on reconstruction accuracy are evaluated. We further show that the uncertainty maps are highly indicative of the true error and properly calibrated. Finally, optical tests on reconstructing the topology of object deformation have confirmed that our method can considerably increase the accuracy of wavefront reconstruction as compared with the two baseline methods.