Similarity study between speckle shearing phase and speckle correlation phase derivative using Riesz transform

Speckle metrology techniques utilize the phenomenon of speckle patterns for various measurement applications. Speckle pattern interferometry and speckle shearography are the widely used speckle metrological techniques in diverse fields. In speckle interferometry, the phase map embedded in the speckle pattern fringes is directly proportional to the displacement; however, in speckle shearography, it is related directly to displacement derivative. We aim to explore the relationship between the extracted phase derivative from speckle fringe pattern and the phase from their corresponding shearing fringes along the x and y directions. A speckle fringe pattern and the sheared fringes along the x and y directions are numerically generated. From speckle fringe pattern, the phase derivatives along the x and y directions are extracted by using the Riesz transform algorithm, whereas from the shearing fringes, the phase distribution is extracted by using monogenic signal. The similarity between the phase derivate distribution from speckle fringe pattern and phase distribution from sheared fringe is quantitatively evaluated by using image quality index. Furthermore, application experimental data are also presented.