Error caused by sampling in Fourier transform profilometry

The phase error caused by sampling the fringe patterns in practical Fourier transform profilometry is discussed. In the FTP method, a grating pattern is projected onto an object surface and the deformed fringe is Fourier-transformed and processed in its spatial frequency domain as well as in its space-signal domain. It has been stated that the fundamental spectrum must separate from zero and higher order spectra, because only the fundamental component is needed for phase retrieval. Here we discuss another kind of spectrum overlapping that is caused by the discrete Fourier transform (DFT). The DFT of a digitized fringe pattern results in periodically equi-spaced frequency islands in the spectrum domain. The higher order spectra from adjacent islands may overlap the fundamental spectrum that is filtered out for phase reconstruction. This kind of overlapping also introduces noise into the reconstructed phase. The conclusion is that to obtain a correct reconstruction of the measured object, the fundamental spectrum does not alias with zero order or higher order spectra in the same frequency island nor with the higher order spectra from adjacent frequency islands. Theoretical analysis is given and the criteria of selecting sampling frequency are discussed. Computer simulations and experiments verified our theories. (C) 1999 Society of Photo-Optical Instrumentation Engineers. [S0091-3286(99)02206-0].