<title>New error-compensating seven-sample phase-shifting algorithm and application in 3D fringe projection profilometry</title>

Abstract

In this paper, a new 7-sample algorithm is derived based on the Surrel 6-sample algorithm by using the averaging technique. The Surrel 6-sample algorithm and the new 7- sample algorithm are analyzed using the Fourier description method and it is shown that the new 7-sample is more insensitive to linear phase-shift miscalibration than the Surrel 6-sample algorithm. By computer simulation, it is found that the linear phase-shift miscalibration produces the periodic phase error at three times the fringe frequency when the fringe signal contains a second-harmonic component. P-V phase error plots show that the new 7-sample algorithm is the least sensitive to the linear phase-shift miscalibration of the five phase-shifting algorithms considered in this paper when the fringe signal contains the second-harmonic component. A 3D fringe projection phase- shifting profilometry is constructed using a white light source and projecting a quasi-sinusoidal grating. The fringe pattern is captured by a CCD camera connected to a frame grabber in a PC computer. The new 7-sample algorithm is used and the experimental results are presented.