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.
Jun-Zheng Peng Hang-Kong Ouyang Quan Yu Ying-Jie Yu Ke-Sheng Wang
. Phase error correction for fringe projection profilometry by using
constrained cubic spline[J]. Advances in Manufacturing, 2014
, 2(1)
: 39
-47
.
DOI: 10.1007/s40436-014-0058-1
1. Gorthi SS, Rastogi P (2010) Fringe projection techniques: whither
we are? Opt Lasers Eng 48:133–140
2. Zhang S, Yau S-T (2007) Generic nonsinusoidal phase error
correction for three-dimensional shape measurement using a
digital video projector. Appl Opt 46:36–43
3. Pan B, Kemao Q, Huang L et al (2009) Phase error analysis and
compensation for nonsinusoidal waveforms in phase-shifting
digital fringe projection profilometry. Opt Lett 34:416–418
4. Guo H, He H, Chen M (2004) Gamma correction for digital
fringe projection profilometry. Appl Opt 43:2906–2914
5. Hoang T, Pan B, Nguyen D et al (2010) Generic gamma correction
for accuracy enhancement in fringe-projection profilometry.
Opt Lett 35:1992–1994
6. Liu K, Wang Y, Lau DL et al (2010) Gamma model and its
analysis for phase measuring profilometry. J Opt Soc Am A
27:553–562
7. Huang PS, Zhang C, Chiang F-P (2003) High-speed 3-D shape
measurement based on digital fringe projection. Opt Eng 42:
163–168
8. Zuo C, Chen Q, Gu G et al (2013) High-speed three-dimensional
shape measurement for dynamic scenes using bi-frequency tripolar
pulse-width-modulation fringe projection. Opt Lasers Eng
51:953–960
9. Kokes J, Nghien NB (2011) Using constrained cubic spline
instead of natural cubic spline to eliminate overshoot and
undershoot in HTT. Ann Fac Eng Hunedoara-Int J Eng 9:23–28
10. Zhang X, Zhu L, Li Y et al (2012) Generic nonsinusoidal fringe
model and gamma calibration in phase measuring profilometry.
J Opt Soc Am A 29:1047–1058
11. Zhang S (2009) Phase unwrapping error reduction framework for
a multiple-wavelength phase-shifting algorithm. Opt Eng 48:
105601–105601-8
12. Li Z, Li Y (2011) Gamma-distorted fringe image modeling and
accurate gamma correction for fast phase measuring profilometry.
Opt Lett 36:154–156
