Gamma model and its analysis for phase measuring profilometry

Li, Kai; Wang, Yongchang; Lau, Daniel L.; Hao, Qi; Hassebrook, Laurence G.

doi:10.1364/josaa.27.000553

Cited by 171 publications

(87 citation statements)

References 24 publications

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“…6 Liu et al developed a method based on their model of the harmonic coefficients of the gamma value. 10 The method works well for their purpose. However, it is time consuming to calibrate the gamma value.…”

Section: Introductionmentioning

confidence: 99%

Phase error elimination considering gamma nonlinearity, system vibration, and noise for fringe projection profilometry

et al. 2014

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Abstract. Fringe projection profilometry (FPP) using a digital video projector is widely used for three-dimensional shape measurement. However, the gamma nonlinearity, system vibration, and noise cause the captured fringe patterns to be nonsinusoidal waveforms and have a grayscale deflection from their true value. This leads to an additional phase measurement error for a general phase-shifting algorithm. Based on the theoretical analysis, we propose a method to eliminate the phase error considering two factors. In this method, four-step phaseshifting is done four times with an initial phase offset of 22.5 deg and the average of these four phase maps precisely results in the real phase. As a result, phase error caused by gamma nonlinearity can be effectively suppressed. In addition, every image in phase shifting is replaced by the average of 20 fringe images continuously captured at the same state to avoid the phase error caused by system vibration and noise. Experimental results show that this method is effective in eliminating the phase error in practical phase-shifting FPP. In general, more than 90% of the phase error can be reduced.

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Section: Introductionmentioning

confidence: 99%

Phase error elimination considering gamma nonlinearity, system vibration, and noise for fringe projection profilometry

et al. 2014

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“…Guo et al [4] proposed a c correction method by statistically analyzing the captured fringe images. Hoang et al [5] and Liu et al [6] developed algorithms to establish the relationship between the c value and the correct phase value. However, the gamma value is estimated based on the projected patterns with specific pitch.…”

Section: Introductionmentioning

confidence: 99%

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

Peng

Ouyang

et al. 2014

Adv. Manuf.

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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.

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“…And then gamma calibration is required. Numerous methods [4][5][6][7][8][9] have been proposed to reduce the measurement errors caused by the nonlinear gamma. Though successful, the residual errors are usually nonnegligible for high-precision measurement applications.…”

Section: Introductionmentioning

confidence: 99%

Comparison of the squared binary, sinusoidal pulse width modulation, and optimal pulse width modulation methods for three-dimensional shape measurement with projector defocusing

Wang

Zhang

2012

Appl. Opt.

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This paper presents a comparative study on three sinusoidal fringe pattern generation techniques with projector defocusing: the squared binary defocusing method (SBM), the sinusoidal pulse width modulation (SPWM) technique, and the optimal pulse width modulation (OPWM) technique. Because the phase error will directly affect the measurement accuracy, the comparisons are all performed in the phase domain. We found that the OPWM almost always performs the best, and SPWM outperforms SBM to a great extent, while these three methods generate similar results under certain conditions. We will briefly explain the principle of each technique, describe the optimization procedures for each technique, and finally compare their performances through simulations and experiments. Disciplines Computer-Aided Engineering and Design | Mechanical Engineering CommentsThis article is from Applied Optics 51 (2012) This paper presents a comparative study on three sinusoidal fringe pattern generation techniques with projector defocusing: the squared binary defocusing method (SBM), the sinusoidal pulse width modulation (SPWM) technique, and the optimal pulse width modulation (OPWM) technique. Because the phase error will directly affect the measurement accuracy, the comparisons are all performed in the phase domain. We found that the OPWM almost always performs the best, and SPWM outperforms SBM to a great extent, while these three methods generate similar results under certain conditions. We will briefly explain the principle of each technique, describe the optimization procedures for each technique, and finally compare their performances through simulations and experiments.

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Gamma model and its analysis for phase measuring profilometry

Cited by 171 publications

References 24 publications

Phase error elimination considering gamma nonlinearity, system vibration, and noise for fringe projection profilometry

Phase error elimination considering gamma nonlinearity, system vibration, and noise for fringe projection profilometry

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

Comparison of the squared binary, sinusoidal pulse width modulation, and optimal pulse width modulation methods for three-dimensional shape measurement with projector defocusing

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