Determination of optimal binary defocusing based on digital correlation for fringe projection profilometry

Abstract

In fringe projection profilometry (FPP), non-sinusoidal projected fringes due to the gamma effect of a projector will cause phase measurement errors. To solve this problem, a binary defocusing technique has been introduced in recent years, while it is difficult to determine an appropriate amount of defocus quantitatively with high sensitivity and high accuracy. In this paper, a novel approach based on digital correlation is proposed to determine an optimal amount of defocus, aiming to get sinusoidal fringes from a binary-structured fringe pattern with projector defocusing. Firstly, a window containing multiple fringes is selected from the captured binary defocusing fringe pattern projected onto a calibration plate or a flat part of the surface of the object being measured. Then calculate the correlation coefficient between the selected window and its second-order differential in the direction perpendicular to the fringe. Since the second-order differential of a sinusoidal wave remains still sinusoidal, the maximum correlation coefficient should correspond to the optimal sinusoidality of the binary defocusing fringe. Therefore, by finding the maximum correlation coefficient while defocusing the projector, the optimal binary defocusing level can be determined accordingly. One of the characteristics of the proposed method is that only one fringe window is required to judge the defocus level in practical measurement, which may speed up 3D measurement. In addition, the proposed method has no requirements for fringe pitch and is applicable to fringes of any spatial frequency. Both numerical simulations and experimental results have been demonstrated to exhibit the validity and high accuracy of the proposed method.