Abstract

The recently proposed binary defocusing technique has brought speed breakthroughs for three-dimensional (3D) shape measurement with a digital fringe projection system. Despite this, motion-induced phase error is still inevitable due to the multi-shot nature of the phase-shifting algorithm. To alleviate this problem, this paper proposes a motion-induced error reduction method by taking advantage of additional temporal sampling. Particularly, each illuminated fringe pattern will be captured twice in one projection cycle, resulting in two sets of phase shifted fringe images being obtained. Due to the mechanism of binary defocusing projection, the motion-induced phase error could be effectively separated from the fixed phase shift value by evaluating the difference between the two phase maps. Based on this, an iterative compensation strategy is further applied to compensate the phase error until high-quality phase maps are generated. Meanwhile, different synchronization schemes are also proposed and tested to evaluate the error compensation effects. Both simulation and experiments demonstrated that the proposed methods can substantially reduce motion-introduced measurement errors. Since defocused 1-bit binary patterns are utilized to bypass rigid camera-projector synchronization, this method has potential for high-speed applications.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (2)

S. Feng, C. Zuo, T. Tao, Y. Hu, M. Zhang, Q. Chen, and G. Gu, “Robust dynamic 3-d measurements with motion-compensated phase-shifting profilometry,” Opt. Laser. Eng. 103, 127–138 (2018).
[Crossref]

Z. Liu, P. C. Zibley, and S. Zhang, “Motion-induced error compensation for phase shifting profilometry,” Opt. Express 26, 12632–12637 (2018).
[Crossref] [PubMed]

2016 (2)

2015 (1)

P. Cong, Z. Xiong, Y. Zhang, S. Zhao, and F. Wu, “Accurate dynamic 3d sensing with fourier-assisted phase shifting,” IEEE J. Sel. Top. Signal Process. 9, 396–408 (2015).
[Crossref]

2014 (3)

2013 (1)

2012 (1)

2011 (1)

2010 (3)

S. Gorthi and P. Rastogi, “Fringe projection techniques: Whither we are?” Opt. Laser. Eng. 48, 133–140 (2010).
[Crossref]

S. Zhang, “Recent progresses on real-time 3-d shape measurement using digital fringe projection techniques,” Opt. Laser Eng. 48, 149–158 (2010).
[Crossref]

X. Su and Q. Zhang, “Dynamic 3-d shape measurement method: A review,” Opt. Laser. Eng 48, 191–204 (2010).
[Crossref]

2009 (1)

2004 (1)

Chen, Q.

S. Feng, C. Zuo, T. Tao, Y. Hu, M. Zhang, Q. Chen, and G. Gu, “Robust dynamic 3-d measurements with motion-compensated phase-shifting profilometry,” Opt. Laser. Eng. 103, 127–138 (2018).
[Crossref]

C. Zuo, Q. Chen, S. Feng, F. Feng, G. Gu, and X. Sui, “Optimized pulse width modulation pattern strategy for three-dimensional profilometry with projector defocusing,” Appl. Opt. 51, 4477–4490 (2012).
[Crossref] [PubMed]

Cong, P.

P. Cong, Z. Xiong, Y. Zhang, S. Zhao, and F. Wu, “Accurate dynamic 3d sensing with fourier-assisted phase shifting,” IEEE J. Sel. Top. Signal Process. 9, 396–408 (2015).
[Crossref]

Dai, J.

B. Li, Y. Wang, J. Dai, W. Lohry, and S. Zhang, “Some recent advances on superfast 3d shape measurement with digital binary defocusing techniques,” Opt. Laser Eng. 54, 236–246 (2014).
[Crossref]

Feng, F.

Feng, S.

S. Feng, C. Zuo, T. Tao, Y. Hu, M. Zhang, Q. Chen, and G. Gu, “Robust dynamic 3-d measurements with motion-compensated phase-shifting profilometry,” Opt. Laser. Eng. 103, 127–138 (2018).
[Crossref]

C. Zuo, Q. Chen, S. Feng, F. Feng, G. Gu, and X. Sui, “Optimized pulse width modulation pattern strategy for three-dimensional profilometry with projector defocusing,” Appl. Opt. 51, 4477–4490 (2012).
[Crossref] [PubMed]

Gorthi, S.

S. Gorthi and P. Rastogi, “Fringe projection techniques: Whither we are?” Opt. Laser. Eng. 48, 133–140 (2010).
[Crossref]

Gu, G.

S. Feng, C. Zuo, T. Tao, Y. Hu, M. Zhang, Q. Chen, and G. Gu, “Robust dynamic 3-d measurements with motion-compensated phase-shifting profilometry,” Opt. Laser. Eng. 103, 127–138 (2018).
[Crossref]

C. Zuo, Q. Chen, S. Feng, F. Feng, G. Gu, and X. Sui, “Optimized pulse width modulation pattern strategy for three-dimensional profilometry with projector defocusing,” Appl. Opt. 51, 4477–4490 (2012).
[Crossref] [PubMed]

Guo, Q.

Han, B.

Hu, Y.

S. Feng, C. Zuo, T. Tao, Y. Hu, M. Zhang, Q. Chen, and G. Gu, “Robust dynamic 3-d measurements with motion-compensated phase-shifting profilometry,” Opt. Laser. Eng. 103, 127–138 (2018).
[Crossref]

Hyun, J.-S.

Karpinsky, N.

Lei, S.

Li, B.

B. Li, N. Karpinsky, and S. Zhang, “Novel calibration method for structured light system with an out-of-focus projector,” Appl. Opt. 53, 3415–3426 (2014).
[Crossref] [PubMed]

B. Li, Y. Wang, J. Dai, W. Lohry, and S. Zhang, “Some recent advances on superfast 3d shape measurement with digital binary defocusing techniques,” Opt. Laser Eng. 54, 236–246 (2014).
[Crossref]

Liu, Z.

Lohry, W.

B. Li, Y. Wang, J. Dai, W. Lohry, and S. Zhang, “Some recent advances on superfast 3d shape measurement with digital binary defocusing techniques,” Opt. Laser Eng. 54, 236–246 (2014).
[Crossref]

Lu, L.

Rastogi, P.

S. Gorthi and P. Rastogi, “Fringe projection techniques: Whither we are?” Opt. Laser. Eng. 48, 133–140 (2010).
[Crossref]

Su, X.

Sui, X.

Tao, T.

S. Feng, C. Zuo, T. Tao, Y. Hu, M. Zhang, Q. Chen, and G. Gu, “Robust dynamic 3-d measurements with motion-compensated phase-shifting profilometry,” Opt. Laser. Eng. 103, 127–138 (2018).
[Crossref]

Wang, Y.

B. Li, Y. Wang, J. Dai, W. Lohry, and S. Zhang, “Some recent advances on superfast 3d shape measurement with digital binary defocusing techniques,” Opt. Laser Eng. 54, 236–246 (2014).
[Crossref]

Y. Wang and S. Zhang, “Superfast multifrequency phase-shifting technique with optimal pulse width modulation,” Opt. Express 19, 5143–5148 (2011).

Wang, Z.

Wu, F.

P. Cong, Z. Xiong, Y. Zhang, S. Zhao, and F. Wu, “Accurate dynamic 3d sensing with fourier-assisted phase shifting,” IEEE J. Sel. Top. Signal Process. 9, 396–408 (2015).
[Crossref]

Xi, J.

Xiong, Z.

P. Cong, Z. Xiong, Y. Zhang, S. Zhao, and F. Wu, “Accurate dynamic 3d sensing with fourier-assisted phase shifting,” IEEE J. Sel. Top. Signal Process. 9, 396–408 (2015).
[Crossref]

You, Z.

Yu, Y.

Zhang, M.

S. Feng, C. Zuo, T. Tao, Y. Hu, M. Zhang, Q. Chen, and G. Gu, “Robust dynamic 3-d measurements with motion-compensated phase-shifting profilometry,” Opt. Laser. Eng. 103, 127–138 (2018).
[Crossref]

Zhang, Q.

X. Su and Q. Zhang, “Dynamic 3-d shape measurement method: A review,” Opt. Laser. Eng 48, 191–204 (2010).
[Crossref]

Zhang, S.

Zhang, Y.

P. Cong, Z. Xiong, Y. Zhang, S. Zhao, and F. Wu, “Accurate dynamic 3d sensing with fourier-assisted phase shifting,” IEEE J. Sel. Top. Signal Process. 9, 396–408 (2015).
[Crossref]

Zhao, S.

P. Cong, Z. Xiong, Y. Zhang, S. Zhao, and F. Wu, “Accurate dynamic 3d sensing with fourier-assisted phase shifting,” IEEE J. Sel. Top. Signal Process. 9, 396–408 (2015).
[Crossref]

Zhou, P.

Zhu, J.

Zibley, P. C.

Zuo, C.

S. Feng, C. Zuo, T. Tao, Y. Hu, M. Zhang, Q. Chen, and G. Gu, “Robust dynamic 3-d measurements with motion-compensated phase-shifting profilometry,” Opt. Laser. Eng. 103, 127–138 (2018).
[Crossref]

C. Zuo, Q. Chen, S. Feng, F. Feng, G. Gu, and X. Sui, “Optimized pulse width modulation pattern strategy for three-dimensional profilometry with projector defocusing,” Appl. Opt. 51, 4477–4490 (2012).
[Crossref] [PubMed]

Appl. Opt. (3)

IEEE J. Sel. Top. Signal Process. (1)

P. Cong, Z. Xiong, Y. Zhang, S. Zhao, and F. Wu, “Accurate dynamic 3d sensing with fourier-assisted phase shifting,” IEEE J. Sel. Top. Signal Process. 9, 396–408 (2015).
[Crossref]

Opt. Express (4)

Opt. Laser Eng. (2)

B. Li, Y. Wang, J. Dai, W. Lohry, and S. Zhang, “Some recent advances on superfast 3d shape measurement with digital binary defocusing techniques,” Opt. Laser Eng. 54, 236–246 (2014).
[Crossref]

S. Zhang, “Recent progresses on real-time 3-d shape measurement using digital fringe projection techniques,” Opt. Laser Eng. 48, 149–158 (2010).
[Crossref]

Opt. Laser. Eng (1)

X. Su and Q. Zhang, “Dynamic 3-d shape measurement method: A review,” Opt. Laser. Eng 48, 191–204 (2010).
[Crossref]

Opt. Laser. Eng. (2)

S. Gorthi and P. Rastogi, “Fringe projection techniques: Whither we are?” Opt. Laser. Eng. 48, 133–140 (2010).
[Crossref]

S. Feng, C. Zuo, T. Tao, Y. Hu, M. Zhang, Q. Chen, and G. Gu, “Robust dynamic 3-d measurements with motion-compensated phase-shifting profilometry,” Opt. Laser. Eng. 103, 127–138 (2018).
[Crossref]

Opt. Lett. (3)

Supplementary Material (5)

NameDescription
» Visualization 1       Experimental results of measuring a moving spherical object using double-shot-in-single-illumination
» Visualization 2       Experimental results of measuring a moving spherical object using repeated fringe projection
» Visualization 3       Experimental data for measuring a moving object with mainly planar x-y motions.
» Visualization 4       Experimental data for measuring a moving object with mainly rotational motions.
» Visualization 5       Experimental data for measuring a complex moving object.

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Figures (9)

Fig. 1
Fig. 1 A schematic demonstration of the binary deofucsing technique which generates sinusoidal profile via projector defocusing.
Fig. 2
Fig. 2 The timing control of proposed double-shot-in-single-illumination technique.
Fig. 3
Fig. 3 Proposed computational framework for motion-induced phase error reduction.
Fig. 4
Fig. 4 The modified timing control scheme.
Fig. 5
Fig. 5 Simulation results for three-step phase-shifting algorithm. (a) Phase error reduction effect for different iteration times when δ = 0.1 rad; (b) the phase error plots for different phase-shift errors δ ∈ [−0.1, 0.1] rad after applying the conventional three-step phase shifting, the double-speed three-step phase shifting and the proposed method.
Fig. 6
Fig. 6 Simulation results for three-step phase-shifting algorithm with non-uniform motion. (a) Phase error reduction for different iterations; (b) The phase error plots before and after applying the proposed compensation method.
Fig. 7
Fig. 7 Experimental results of measuring a moving spherical object using the timing control illustrated in Fig. 2 (associated Visualization 1). (a)–(b) A sample reconstructed 3D frame using the standard three-step phase-shifting method and the proposed error compensation method; (c) cross-section plots of Fig. 7(a), Fig. 7(b) and an ideal sphere; (d) cross-section plots of errors of Figs. 7(a)–7(b). The mean and root-mean-square (RMS) errors are 0.5356 mm and 0.8482 mm for the standard three-step phase-shifting method; and 0.056 mm and 0.4130 mm for the proposed error compensation method.
Fig. 8
Fig. 8 Experimental results of measuring a moving spherical object using the timing control illustrated in Fig. 4 (associated Visualization 2). (a)–(b) A sample reconstructed 3D frame using the standard three-step phase-shifting method and the proposed error compensation method; (c) cross-section plots of Fig. 8(a), Fig. 8(b) and an ideal sphere; (d) cross-section plots of errors of Figs. 8(a)–8(b). The mean and RMS errors are 0.4116 mm and 0.6154 mm for the standard three-step phase-shifting method; and 0.0643 mm and 0.3731 mm for the proposed error compensation method.
Fig. 9
Fig. 9 Additional experimental results to test the robustness of the algorithm. (a) – (c) Results of a sphere moving mainly planar xy movement (associated Visualization 3); (d) – (f) corresponding result of a bottle with rotational movement (associated Visualization 4); (g) – (i) corresponding result of a complex object (associated Visualization 5).

Equations (10)

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I k ( x , y ) = I ( x , y ) + I ( x , y ) cos [ Φ ( x , y ) δ k ] ,
[ a 0 ( x , y ) a 1 ( x , y ) a 2 ( x , y ) ] = [ N cos δ k sin δ k cos δ k cos 2 δ k cos δ k sin δ k sin δ k cos δ k sin δ k sin 2 δ k ] 1 [ I k I k cos δ k I k sin δ k ] .
φ ( x , y ) = tan 1 [ a 2 ( x , y ) a 1 ( x , y ) ] .
Φ ( x , y ) = φ ( x , y ) + k ( x , y ) × 2 π .
I 11 ( x , y ) = I ( x , y ) + I ( x , y ) cos [ Φ ( x , y ) 2 π / 3 ] ,
I 21 ( x , y ) = I ( x , y ) + I ( x , y ) cos [ Φ ( x , y ) + δ ] ,
I 31 ( x , y ) = I ( x , y ) + I ( x , y ) cos [ Φ ( x , y ) + 2 π / 3 + 2 δ ] .
I 12 ( x , y ) = I ( x , y ) + I ( x , y ) cos [ Φ ( x , y ) 2 π / 3 + δ / 2 ] ,
I 22 ( x , y ) = I ( x , y ) + I ( x , y ) cos [ Φ ( x , y ) + δ + δ / 2 ] ,
I 32 ( x , y ) = I ( x , y ) + I ( x , y ) cos [ Φ ( x , y ) + 2 π / 3 + 2 δ + δ / 2 ] .

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