Eliminating zero spectra in Fourier transform profilometry by application of Hilbert transform

Hilbert transform has the features of inducing a phase shifting of 90 degree and removing the DC component. We propose a novel method based on the piecewise Hilbert transform to suppress the background intensity of the deformed fringe pattern using only one fringe pattern in Fourier transform profilometry according to the approximation that the background of the fringe is a slowly varying function and its distribution in each half period of the fringe can be regarded as a constant. In the method, Hilbert transform deals with each segmented fringe section to remove the DC component and then forms a result fringe whose background intensity is suppressed well by putting the fringe pieces together. The proposed method can enlarge the measurement range and reduce the measurement error of FTP. The theoretical analysis is given. Computer simulations and experimental results demonstrate the effectiveness of the proposed method.