Skeleton extraction and phase interpolation for single ESPI fringe pattern based on the partial differential equations

A novel phase extraction method for single electronic speckle pattern interferometry (ESPI) fringes is proposed. The partial differential equations (PDEs) are used to extract the skeletons of the gray-scale fringe and to interpolate the whole-field phase values based on skeleton map. Firstly, the gradient vector field (GVF) of the initial fringe is adjusted by an anisotropic PDE. Secondly, the skeletons of the fringe are extracted combining the divergence property of the adjusted GVF. After assigning skeleton orders, the whole-field phase information is interpolated by the heat conduction equation. The validity of the proposed method is verified by computer-simulated and experimentally obtained poor-quality ESPI fringe patterns.