Strain analysis for moiré interferometry using the two-dimensional continuous wavelet transform

A Procedure for Accurate One-Dimensional Strain Measurement Using the Grid Method

“…It must be emphasized that stronger changes in the frequency of the carrier due to deformation that would appear using other techniques such as interferometric moiré could also be analyzed using a similar approach. Wavelets would be used in this case because they enable us to detect the local frequency from the ridge of the scalogram, as shown in several studies dealing with fringe processing [19][20][21][22][23][24]. This more general framework is however not necessary for the grid method.…”

On window size selection in the windowed Fourier ridges algorithm

“…This difficulty was cleverly overcome by using a 2D directional wavelet basis that is scaled by a total frequency [2][3][4]. The 2D DWR can be similarly expressed as [3,4] ½Aðu; vÞ; Yðu; vÞ ¼ arg max a;y jf ðu; vÞ z a;y ðu; vÞj,…”

Wavelet selection in two-dimensional continuous wavelet transform technique for optical fringe pattern analysis

“…In optical fringe pattern or interferogram analysis, the two-dimensional continuous wavelet transform (2D-CWT) technique has recently drawn considerable attention because of its superior advantages over the conventional techniques, such as insensitivity to noise and the capability of corrupted data recovery. For instance, the technique has been successfully applied to the analysis of a variety of optical fringe patterns, such as moiré pattern [1,2], projection fringe pattern [3,4], laser interferogram [5,6], speckle fringe pattern [7], digital hologram [8] and so on.…”

“…The mother wavelet is an essential component in the wavelet transform, and many mother wavelets have been employed in the 2D-CWT fringe pattern analysis. A typical one is the well-known Gabor wavelet, which was initially used for processing the moiré interferogram [1] and later developed to analyze the speckle fringe pattern [7] as well as the digital hologram [8]. Another commonly used mother wavelet is the Morlet wavelet and it has been successfully applied to practical optical measurements [2,3,5,9].…”