Discuss the structure condition and sampling condition of wavelet transform profilometry

The structure condition and sampling condition of a wavelet transform profilometry are deduced in this paper and an exhaustive discussion is accomplished. As we all know, by the wavelet transform profilometry, the shape of an object can be obtained by a correlation operation, which provides an approach to retrieve the phase when to some extent there is frequency overlapping between the fundamental spectrum and other spectra. However, it is impossible to obtain the correct phase if the wavelet coefficient at the 'ridge' position is not correct. Therefore, it is necessary to discuss the measurement range of the wavelet transform profilometry. Here, from the point of view of the frequency analysis, the discussions, including the structure condition of the measurement system and the sampling condition introduced by digitizing the deformed fringe, have to be done. The conclusion shows that as long as both of the two conditions are met, the correct phase included in the deformed fringe pattern can be retrieved by this method. The computer simulations and experiments verify our analysis.