Digital carrier superposition by Hilbert–Huang transform for optical phase recovery in speckle shearing interferometry

Industrial production constraints often require technical tests and controls. Optical metrology methods allow a non destructive test of wide range of parameters, such as defects and displacements, with very good accuracy. The phase retrieval is an effective way that allows three-dimensional profile reconstruction from intensity shearograms. This research work focuses on the extraction of the phase from one uncarrier shearogram using the Hilbert–Huang transform. An algorithm for the phase calculation based on the bidimensional empirical mode decomposition, Hilbert transform (HT), and Fourier transform (FT) is presented. A spatial digital carrier has been superimposed before the application of the FT or HT which uses two π2 shifted shearograms, to get access to the phase map via a global analysis of intensity images. An evaluation was made through a numerical simulation to validate and confirm the performance of the proposed algorithm. The main advantage of this technique is its ability to provide a metrological solution for fast dynamic analysis.