Abstract

Object motion can introduce phase error and thus measurement error for phase-shifting profilometry. This paper proposes a generic motion error compensation method based on our finding that the dominant motion-introduced phase error doubles the frequency of the projected fringe frequency, and the Hilbert transform shifts the phase of a fringe pattern by π/2. We apply a Hilbert transform to phase-shifted fringe patterns to generate another set of fringe patterns, calculate one phase map using the original fringe patterns and another phase map using Hilbert transformed fringe patterns, and then use the average of these two phase maps for three-dimensional reconstruction. Both simulation and experiments demonstrated that the proposed method can substantially reduce motion-introduced measurement error.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref] [PubMed]
  6. 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]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
  15. D. Malacara, ed., Optical Shop Testing, 3rd ed. (John Wiley and Sons, New York, 2007).
    [Crossref]
  16. 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]

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 (1)

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]

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. (2)

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)

Other (1)

D. Malacara, ed., Optical Shop Testing, 3rd ed. (John Wiley and Sons, New York, 2007).
[Crossref]

Supplementary Material (2)

NameDescription
» Visualization 1       Visualization 1
» Visualization 2       Visualization 2

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Figures (10)

Fig. 1
Fig. 1 Illustration of non-homogeneous phase-shift error introduced by the motion of a deformable object.
Fig. 2
Fig. 2 Simulation results of the motion-introduced phase error for three-step phase-shifting algorithm. (a) Uniform motion; (b) non-uniform motion.
Fig. 3
Fig. 3 Simulation results of the motion-introduced phase error for four-step phase-shifting algorithm. (a) Uniform motion; (b) non-uniform motion.
Fig. 4
Fig. 4 Simulation results of phase error compensation for three-step phase-shifting algorithm. (a) Phase error plots when 1 = 0.1 rad and 2 = 0.2 rad; (b) Phase error plots when 1 = 0.1 rad and 2 = 0.3 rad; (c) phase rms error with uniform motion; (d) phase rms error with nonuniform motion.
Fig. 5
Fig. 5 Phase error compensation for four-step phase-shifting algorithm. (a) Phase error plots when 1 = 0.1 rad, 2 = 0.2 rad, and 3 = 0.3 rad; (b) Phase error plots when 1 = 0.1 rad, 2 = 0.3 rad, and 3 = 0.6 rad; (c)phase rms error with uniform motion; (d) phase rms error with nonuniform motion.
Fig. 6
Fig. 6 Measurement result of a moving sphere using three-step phase-shifting algorithm (associated Visualization 1). (a) 3D result from original phase-shifted fringe patterns; (b) 3D result from Hilbert transformed fringe patterns; (c) 3D result using our proposed method; (d) error map of the result in (a) (mean: 0.172 mm, standard deviation: 0.124 mm); (e) error map of (b) (mean: 0.160 mm, standard deviation: 0.116 mm); (f) error map of (c) (mean: 0.038 mm, standard deviation: 0.032 mm).
Fig. 7
Fig. 7 Measurement result of a moving sphere for four-step phase-shifting algorithm. (a) 3D result from original phase-shifted fringe patterns; (b) 3D result from Hilbert transformed fringe patterns; (c) 3D result using our proposed method; (d) error map of the result in (a) (mean: 0.118 mm, standard deviation: 0.099 mm); (e) error map of (b) (mean: 0.104 mm, standard deviation: 0.090 mm); (f) error map of (c) (mean: 0.031 mm, standard deviation: 0.027 mm).
Fig. 8
Fig. 8 Measurement result of a moving vase with complex surface structures. (a) Photograph; (b) raw 3D result; (c) 3D result using our proposed method.
Fig. 9
Fig. 9 Measurement result of a dynamically deformable facial expressions (associated Visualization 2). (a) 3D result from original fringe patterns; (b) 3D result from Hilbert transformed fringe patterns; (c) 3D result using our proposed method.
Fig. 10
Fig. 10 Experimental results of texture image generation. (a) Texture image from original fringe patterns; (b) texture image using corrected phase.

Equations (31)

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I n ( x , y ) = A ( x , y ) + B ( x , y ) cos ( Φ + δ n ) ,
ϕ ( x , y ) = tan 1 [ n = 0 N 1 I n ( x , y ) sin δ n n = 0 N 1 I n ( x , y ) cos δ n ] ,
Φ ( x , y ) = ϕ ( x , y ) + k ( x , y ) × 2 π .
δ n ( x , y ) = δ n + n ( x , y ) ,
I n ( x , y ) = A ( x , y ) + B ( x , y ) cos ( ϕ ( x , y ) + δ n ) ,
ϕ ( x , y ) = tan 1 [ n = 0 N 1 I n ( x , y ) sin δ n n = 0 N 1 I n ( x , y ) cos δ n ] .
Δ ϕ ( x , y ) = ϕ ( x , y ) ϕ ( x , y )
= tan 1 [ cos ϕ n = 0 N 1 I n ( x , y ) sin δ n + sin ϕ n = 0 N 1 I n cos δ n sin ϕ n = 0 N 1 I n sin δ n cos ϕ n = 0 N 1 I n cos δ n ] ,
= tan 1 [ cos ϕ n = 0 N 1 cos ( ϕ + δ n ) sin δ n + sin ϕ n = 0 N 1 cos ( ϕ + δ n ) cos δ n sin ϕ n = 0 N 1 cos ( ϕ + δ n ) sin δ n cos ϕ n = 0 N 1 cos ( ϕ + δ n ) cos δ n ] ,
= tan 1 [ cos 2 ϕ n = 0 N 1 sin α n + sin 2 ϕ n = 0 N 1 cos α n n = 0 N 1 sin n sin 2 ϕ n = 0 N 1 sin α n cos 2 ϕ n = 0 N 1 cos α n n = 0 N 1 sin n ] ,
I n ( x , y ) = A + B cos [ ϕ ( x , y ) + ( n 1 ) * ( 2 π / 3 + ) ] , n = 0 , 1 , 2 ,
ϕ ( x , y ) = tan 1 [ 3 ( I 0 I 2 ) 2 I 1 I 0 I 2 ] ,
Δ ϕ ( x , y ) = tan 1 { sin 2 ϕ [ cos ( + π / 3 ) 1 / 2 ] ( cos + 1 / 2 ) cos 2 ϕ [ cos ( + π / 3 ) 1 / 2 ] } .
cos ( + π / 3 ) 1 / 2 = cos ( ) cos ( π / 3 ) sin ( ) sin ( π / 3 ) 1 / 2 3 / 2 ,
cos + 1 / 2 3 / 2 .
Δ ϕ ( x , y ) tan 1 [ 3 sin 2 ϕ 3 + 3 cos 2 ϕ ] ,
tan 1 [ 3 sin 2 ϕ 3 ] ,
( 3 3 ) sin 2 ϕ .
I n ( x , y ) = A + B cos [ ϕ ( x , y ) + ( 2 n 3 ) * ( π / 4 + ) ] , n = 0 , 1 , 2 , 3 ,
ϕ ( x , y ) = tan 1 [ I 3 I 1 I 0 I 2 ] + 3 π / 4 ,
Δ ϕ ( x , y ) = tan 1 [ ( I 3 I 1 ) cos ( ϕ 3 π / 4 ) ( I 0 I 2 ) sin ( ϕ 3 π / 4 ) ( I 3 I 1 ) sin ( ϕ 3 π / 4 ) + ( I 0 I 2 ) cos ( ϕ 3 π / 4 ) ] ,
= tan 1 [ γ 0 cos 2 ( ϕ 3 π / 4 ) γ 0 sin 2 ( ϕ 3 π / 4 ) + γ 1 ] ,
γ 0 = 2 [ sin ( 3 ) sin ] 2 [ 3 ] = 4 ,
γ 1 = 2 [ cos ( 3 ) + cos ] 4 .
Δ ϕ ( x , y ) tan 1 [ cos 2 ( ϕ 3 π / 4 ) ] , ( ) sin 2 ϕ .
H ( μ ) ( t ) = 1 π μ ( τ ) t τ d τ .
( H ( μ ) ( ω ) ) = δ H ( ω ) × ( μ ) ( ω ) ,
δ H ( ω ) = { i = e i π / 2 , if ω < 0 0 , if ω = 0 i = e i π / 2 , if ω > 0
I n H ( x , y ) = H [ I n ( x , y ) ] = A ( x , y ) + B ( x , y ) sin [ ϕ ( x , y ) + δ n ] .
ϕ H ( x , y ) = tan 1 [ n = 1 N I n H ( x , y ) cos δ n n = 1 N I n H ( x , y ) sin δ n ] .
ϕ f ( x , y ) = [ ϕ ( x , y ) + ϕ H ( x , y ) ] / 2 .

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