Phase error correction for fringe projection profilometry by using constrained cubic spline

In fringe projection profilometry, the nonlinear intensity response caused by the γ effect of a digital projector results in periodic phase error and therefore measurement error. Previous error correction methods are largely based on the calibration of single γ value. However, in practice, it is difficult to accurately model the full range of the intensity response with a one-parameter γ function. In this paper, a compensated intensity response curve is generated and fitted with the constrained cubic spline. With the compensated curve, the full range of the nonlinear intensity response can be corrected and the periodic phase errors can be removed significantly. Experimental results on a flat board confirm the average root mean square (RMS) of the phase error which can be reduced to at least 0.0049 rad.