Discuss the measuring range of dual-frequency wavelet transform profilometry

We discuss the structure condition and sampling condition of wavelet transform profilometry (WTP) based on dual-frequency fringe pattern in this work. In the mentioned method a grating fringe with dual-frequency components is projected onto an object. And two wavelet ridge lines can be extracted by means of wavelet analysis, from which we can calculate two groups of wrapped phase information. Afterwards the retrieved phase with higher precision can be obtained through phase unwrapping process. However, it should be noted that the spectral aliasing of the deformed fringe pattern must be avoided in order to restore the correct phase information. And the two fringe carrier frequencies have to obey some rules as well. In this paper, the structure condition and sampling condition of the proposed method is deduced from the point of view of frequency analysis. It is proven that there would be no frequency overlapping in the deformed fringe pattern only when both of the two conditions mentioned previously are fulfilled. The results of computer simulations and experiments verify the validity of our theory.