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

Abstract

In fringe projection profilometry, the nonlinear intensity response caused by the c 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 c value. However, in practice, it is difficult to accurately model the full range of the intensity response with a one-parameter c 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.

Phase accuracy evaluation for phase-shifting fringe projection profilometry based on uniform-phase coded image

“…Although the phase error distributions are similar to a sinusoidal curve when N = 3, 4, 6, 8, and 10, the initial phases of these sinusoidal curves are not consistent as the phase shift number changes. Note that the detected gamma phase error in figure 5 does not strictly coincide with that in PSFPP because the gamma phase error partly depends on the fringe period [39]. Experiments show that the larger the fringe period, the larger the gamma phase error becomes.…”

“…However, most of them accomplish this task by virtue of a large-step phase-shifting algorithm; they assume the phase calculated with a large-step phase-shifting algorithm is free from the gamma phase error. Indeed, there is no standard on how large the phase shift number should be (the phase shift numbers are selected as 48 and 16 in [13,39], respectively). The proposed method is capable of uncovering the answer, and hence is a beneficial supplement to the existing methods.…”

The optimal algorithm for eliminating nonlinear error in phase measurement profilometry based on global statistical phase feature function

“…The other method does not require complicated advance calibration, and the corresponding system parameters can be obtained during the measurement process. Among them, Peng et al [9] proposed a method using a constrained cubic spline method to compute the compensated input gray values. Zhang et al [10] proposed to actively superimpose specific harmonics on the initial fringe patterns instead of compensating for the phase error in the retrieved 3D contour.…”

Full-field phase error detection and compensation method for digital phase-shifting fringe projection profilometry

“…Many methods have been proposed to reduce the adverse influence of gamma in the last decade [4][5][6][7][8][9][10][11][12][13][14]. Some methods pre-calibrate the gamma curve, and then pre-distort the intensity of projected fringe patterns based on it [4][5][6]14]; some methods detect the phase error distribution caused by gamma to compensate the calculated phase [7][8][9]13]; some methods analyse the gamma of the measurement system, and meanwhile work out a more accurate phase based on some statistical characteristics [10,11]; increasing the phase shift number is also an effective way to suppress the phase error caused by gamma [12]. All of these methods contribute to decreasing the phase error caused by gamma.…”