Riesz transform for fringes pattern analysis: advantages and limitations - Tounsi, Yassine; Kumar, Manoj; Siari, Ahmed; Mendoza Santoyo, Fernando; Matoba, Osamu; Nassim, Abdelkrim (SPIE, 2020)
Fringe pattern analysis is an essential step in optical techniques including the digital speckle pattern interferometry (DSPI), digital speckle shearing interferometry (DSPSI), digital holographic interferometry (DHI), moiré interferometry, and others. This step enables to evaluate the coded phase distribution related to a physical magnitude of the material under study such as deformation, displacement, refractive index, strain, temperature. Several methods have been proposed for the extraction of phase distribution such as phase-shifting techniques and other transform-based methods like Fourier, Hilbert, and wavelet transforms. In phase-shifting techniques, the intensity is sampled spatially or temporally, and the object should be stable during the acquisition of at least three frames. So, this technique is not suitable for the analysis of dynamic events. Recently, Riesz transform, two-dimensional extension of the Hilbert transform, has been exploited in several works including the phase evaluation. In this work, we present a variety of methods based on the Riesz transform for fringe pattern analysis. The analysis concerns the extraction of the encoded phase distribution from the recorded/processes fringe patterns obtained from the interferometric techniques and their horizontal and vertical phase derivatives. Using numerical simulation, we study the performance of these Riesz transform-based methods with a quantitative appraisal, and finally, the experimental application will be presented. The advantages and limitations of the Riesz transform-based methods will be discussed.