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Quantitative phase imaging is the representative of state-of-the-art marker-free full-field optical metrology techniques based on principles of interferometry, holography, microscopy and numerical processing. The measurand is encoded in the phase distribution (optical path delay) of the recorded fringe pattern. To retrieve the measured information the phase demodulation process needs to be performed. Considering the analysis of biomedical samples, the development of very accurate single-frame interferogram/hologram demodulation method is especially important because of the changing nature of the studied phenomenon. In that case the whole process of information recovery can be divided into two steps: (1) interferogram/hologram preprocessing and (2) phase demodulation. We are proposing the “black-box” algorithmic solution called Deep Variational Hilbert Quantitative Phase Imaging (Deep-VHQPI), where convolutional neural networks were used for automation, facilitation and acceleration of the previously complicated and arduous multi-step fringe pattern filtration and orientation estimation processes. It is worth to mention that convolutional neural networks in this work were used for the support of mathematically rigorous quantitative phase imaging algorithm (Hilbert transformation), not with aim to supersede it. For the sake of metrological figure of merit deep learning based solutions were employed to accelerate powerful and well-established VHQPI approach, not to bypass it completely. Deep-VHQPI algorithm enables analysis of variety of biological samples and constitutes an important step towards simplifying optical measurement of complicated and fragile biological samples. Phase decoding results are compared with reference algorithms, i.e., classical VHQPI, the Hilbert-Huang and Fourier transforms. Versatility of the proposed method and its potentially ubiquitous applications in full-field optical metrology are highlighted.
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