Fourier transform profilometry employing novel orthogonal elliptic band-pass filtering for accurate 3-D surface reconstruction

The article proposes a novel orthogonal elliptic band-pass filtering methodology in Fourier Transform Profilometry (FTP) for significant improvement of accurate 3-D measurement surface reconstruction with arbitrary object colors. Compared with phase shifting profilometry (PSP), FTP using fringe projection can achieve a general 3-D surface profilometry more efficiently by employing one-shot imaging. However, a challenging problem commonly encountered by FTP using fringe projection is its unreliable extraction of precise spectral information from the spectral domain especially when the spectral domain is complicated to process. Various filtering methods previously proposed in FTP have been proved unsuccessful or nonrobust. Thus, a new band-pass filter is developed from an adaptive orthogonal elliptic region to achieve higher accuracy of 3-D surface reconstruction. A comprehensive theoretical analysis is performed to investigate the physical measurement limits of the proposed method. The experimental results obtained confirm that the measurement accuracy of dimension and sphericity can be greatly enhanced when compared with that achieved by the traditional circular band-pass filter. The proposed method is proved to outperform all the other existing FTP band-pass filtering approaches. The maximum dimensional error measured can be controlled within 1.25% of the overall measuring height with various surface colors. However, it is also verified that the traditional three-step PSP can achieve slightly better measuring repeatability than the proposed method.