Physics-informed deep learning for fringe pattern analysis

Recently,deep learning has yielded transformative success across optics and photonics,especially in optical metrology.Deep neural networks (DNNs) with a fully convolutional architecture (e.g.,U-Net and its derivatives) have been widely implemented in an end-to-end manner to accomplish various optical metrology tasks,such as fringe denoising,phase unwrapping,and fringe analysis.However,the task of training a DNN to accurately identify an image-to-image transform from massive input and output data pairs seems at best naive,as the physical laws governing the image formation or other domain expertise pertaining to the measurement have not yet been fully exploited in current deep learning practice.To this end,we introduce a physics-informed deep learning method for fringe pattern analysis (PI-FPA) to overcome this limit by integrating a lightweight DNN with a learning-enhanced Fourier transform profilometry (Le FTP) module.By parameterizing conventional phase retrieval methods,the Le FTP module embeds the prior knowledge in the network structure and the loss function to directly provide reliable phase results for new types of samples,while circumventing the requirement of collecting a large amount of high-quality data in supervised learning methods.Guided by the initial phase from Le FTP,the phase recovery ability of the lightweight DNN is enhanced to further improve the phase accuracy at a low computational cost compared with existing end-to-end networks.Experimental results demonstrate that PI-FPA enables more accurate and computationally efficient single-shot phase retrieval,exhibiting its excellent generalization to various unseen objects during training.The proposed PI-FPA presents that challenging issues in optical metrology can be potentially overcome through the synergy of physics-priors-based traditional tools and data-driven learning approaches,opening new avenues to achieve fast and accurate single-shot 3D imaging.

Fringe pattern analysis using deep learning

In many optical metrology techniques,fringe pattern analysis is the central algorithm for recovering the underlying phase distribution from the recorded fringe patterns.Despite extensive research efforts for decades,how to extract the desired phase information,with the highest possible accuracy,from the minimum number of fringe patterns remains one of the most challenging open problems.Inspired by recent successes of deep learning techniques for computer vision and other applications,we demonstrate for the first time,to our knowledge,that the deep neural networks can be trained to perform fringe analysis,which substantially enhances the accuracy of phase demodulation from a single fringe pattern.The effectiveness of the proposed method is experimentally verified using carrier fringe patterns under the scenario of fringe projection profilometry.Experimental results demonstrate its superior performance,in terms of high accuracy and edge-preserving,over two representative single-frame techniques:Fourier transform profilometry and windowed Fourier transform profilometry.

A Mean Curvature Regularized Based Model for Demodulating Phase Maps from Fringe Patterns

We introduce a variationalmethod for demodulating phasemaps fromfringe patterns.This newmethod is based on themean curvature of the level sets of the phase surface that is used for regularization.The performance of the method is illustrated with both synthetic and real data.