DeepQuadrature: universal convolutional neural network enlarging space–bandwidth product in single-shot fringe pattern optical metrology

Abstract One representative of state-of-the-art full-field optical metrology techniques is fringe-pattern-based methods, where the measurand is encoded in the phase distribution of the recorded spatially-periodic intensity pattern. The phase demodulation process comprises a crucial part of a measurement defining the overall achieved accuracy, and its algorithm imposes one of the main information throughput limitations of the entire experimental unit. In this paper, we propose a novel solution that increases the phase space–bandwidth product (SBP) of the optical system in a purely numerical way. It is based on deep learning and a convolutional neural network called DeepQuadrature. It takes two images as the input data: the prefiltered fringe pattern (denoised and detrended by variational image decomposition, for example) and the local orientation map (modulo 2 π ). The network’s output is the quadrature function (input fringe pattern shifted in phase by π /2). The phase distribution is finally calculated via the arctangent function of input and output fringe patterns. The working principle is somewhat motivated by the state of the art in high SBP classical phase estimation, called Hilbert spiral transform, however, with novel adaptive spectral features promoting DeepQuadrature as a versatile and universally applicable method. Phase decoding results for widespread simulated and experimental (testing technical and biological objects) fringe data compare favorably with classical algorithms: learning-free variational Hilbert quantitative phase imaging and the reference multi-frame method. DeepQuadrature thus opens new possibilities in fringe-based high-content optical metrology and is poised to advance biomedical and technical label-free microscopy.