Multidirectional wavelet-based fringe analysis for surface diagnosis by optical profilometry

Fringe Phase-Shifting Field Based Fuzzy Quotient Space-Oriented Partial Differential Equations Filtering Method for Gaussian Noise-Induced Phase Error

“…The PSNR and the standard deviation of phase error that are caused by Gaussian noise (STD) are used as indicators for filtering evaluation. The proposed FOPDEs method is compared with the commonly used methods, such as Gaussian filtering [16,17,18,21], mean filtering [16,17,18], wavelet transform [17], TV [19,20], and OPDEs [24], as shown in Table 1. Table 1 reflects the results of adding uniform noise to phase-shifting images and adding different noise to different phase-shifting images.…”

“…However, the edges of binary patterns are often difficult to precisely distinguish, which reduces the measurement accuracy. The filtering method [16,17,18,19,20,21,22,23,24] is to reduce noise by means of filtering algorithms. Image filtering is a process of restoring noise-free image from noise image, in which the difficulty is how to protect details while reducing noise.…”

“…Therefore, how to filter the Gaussian noise effectively is very important in accurately extracting the phase information. Traditional filtering methods [16,17,18,19,20], such as Gaussian filtering, median filtering, and wavelet transform, were proposed to reduce the noise. Villa [21] proposed a fringe pattern denoising method based on Gaussian convolution to improve the performance of low-frequency fringes.…”

Hilbert transform for modulation of interference fringes of liquid substances

“…However, the instruments and methodology reported so far require high stability and are also limited by the experimental set-up [3][4], this problem has been solved with the use of interferometers that provide the stability and measurement range that is not achieved with conventional refractometers and holographic techniques, among them the Jamin, Mach Zehnder and Michelson interferometers [4,[10][11]. Despite the reliability that interferometers provide to the measurement, the problem of a later demodulation of the fringe pattern obtained arises, this pattern shows the changes before and after the deformation to later obtain the optical phase, commonly, by means of techniques based on Fourier Transform [12], Wavelet [13][14][15][16][17][18] and Hilbert [19][20][21][22][23], the problem increases if the interferograms obtained have a circular configuration, their carrier frequency is very low, and they also present several reflections caused by the arrangement of the instruments and the analysed material, requiring more computational work and the implementation of new spectral and temporal analysis techniques [24][25][26][27][28][29][30][31][32].…”