Learning-based fringe analysis with uncertainty quantification

Abstract

Recently, the deep learning technology has been successfully applied to many applications of optical metrology, e.g., fringe-pattern analysis, fringe denoising, digital holography, and three-dimensional shape measurements. However, deep neural networks (DNNs) cannot always produce a provably correct solution, and the prediction error cannot be easily detected and evaluated unless the ground truth is available. This issue is critical for optical metrology, as the reliability and repeatability of the measurement are of major importance for high-stakes scenarios. As most deep neural networks are driven by data completely and work without considering any physical principles, how to believe the prediction of the DNN in optical metrology is a big challenge. Inspired by recent successful Bayesian deep learning approaches, we demonstrate that a Bayesian convolutional neural network (BNN) can be trained to not only retrieve the phase from a single fringe pattern but also produce uncertainty maps depicting the pixel-wise confidence measure of the estimated phase. Experimental results show that the proposed BNN can quantify the reliability of phase predictions under conditions of various training dataset sizes and never-before-experienced inputs. We believe that a DNN that can provide confidence measure of the estimated phase is crucial to fringe-pattern analysis and it has great potentials for inspiring novel and reliable learning-based optical metrology approaches.