Phase Extraction from Single Interferogram Including Closed-Fringe Using Deep Learning

In an optical measurement system using an interferometer, a phase extracting technique from interferogram is the key issue. When the object is varying in time, the Fourier-transform method is commonly used since this method can extract a phase image from a single interferogram. However, there is a limitation, that an interferogram including closed-fringes cannot be applied. The closed-fringes appear when intervals of the background fringes are long. In some experimental setups, which need to change the alignments of optical components such as a 3-D optical tomographic system, the interval of the fringes cannot be controlled. To extract the phase from the interferogram including the closed-fringes we propose the use of deep learning. A large amount of the pairs of the interferograms and phase-shift images are prepared, and the trained network, the input for which is an interferogram and the output a corresponding phase-shift image, is obtained using supervised learning. From comparisons of the extracted phase, we can demonstrate that the accuracy of the trained network is superior to that of the Fourier-transform method. Furthermore, the trained network can be applicable to the interferogram including the closed-fringes, which is impossible with the Fourier transform method.