Selection of optimal frequencies in multiple-frequency fringe projection profilometry

Abstract

The selection of frequencies which are in some sense optimal is an open research problem in phase shifting profilometry. We propose a novel method for selecting multiple frequencies for phase shifting profilometry. The frequencies are selected to provide the best possible resistance to phase unwrapping errors when temporal unwrapping is used. The proposed frequency selection method is based on the maximization of the minimal distance between lines of the line-constellation in the wrapped phase space. It is realized as an exhaustive search over the fringe counts, which is more efficient than searching over the frequencies or over the wavelengths. We also propose an efficient and effective method for filtering points for which the phase may be incorrectly unwrapped. The proposed filtering method is based on limiting the distance between the wrapped phase measurement and the line of the line-constellation. We demonstrate the applicability of the proposed frequency selection method through the construction and the experimental validation of several frequency designs which contain only high frequencies, and which are insensitive to large errors in wrapped phase. We also demonstrate the effectiveness of the proposed filtering.