Why Use Wavelet Transform Profilometry (WTP)?
It is well known in the digital signal processing theory that the Fourier transform is more suitable for analysing stationary signals than non-stationary signals. A stationary signal is a signal whose frequency contents do not change in time, whereas a non-stationary signal is a signal whose frequency contents do change in time. Figure 1(a) shows a stationary signal, whereas Figure 1(b) shows a non-stationary signal. Figure 1(c) shows a real fringe pattern and Figure 1(d) shows a row taken from the fringe pattern image. The red line shown in Figure 1(c) indicates the position of this row. Figure 1(d) indicates that the fringe pattern contains non-stationery signals.
As mentioned earlier, the wavelet transform is very suitable for the analysis of non-stationary signals. Consequently it can be used for fringe pattern analysis. The complex continuous wavelet transform has been found to be very useful for the analysis of fringe patterns.
The WTP technique has a number of advantages over Fourier transform profilometry (FTP). Firstly, the WTP is much less affected by the leakage distortion that is associated with Fourier method and which results in distortions at the borders of the extracted phase map. Additionally, the background illumination of a fringe pattern is removed automatically by the WTP algorithm. Conversely, the automation of background removal using the FTP method is one of the obstacles involved in using this method. Since there is no substitute for experimental work, we advise that you analyse your fringe patterns using the WTP method utilising the code given here, and see for yourself.
