Abstract

Using 1-bit binary patterns for three-dimensional (3D) shape measurement has been demonstrated as being advantageous over using 8-bit sinusoidal patterns in terms of achievable speeds. However, the phase quality generated by binary pattern(s) typically are not high if only a small number of phase-shifted patterns are used. This paper proposes a method to improve the phase quality by representing each pattern with the difference of two binary patterns: the first binary pattern is generated by triangular pulse width modulation (TPWM) technique, and the second being π shifted from the first pattern that is also generated by TPWM technique. The phase is retrieved by applying a three-step phase-shifting algorithm to the difference patterns. Through optimizing the modulation frequency of the triangular carrier signal, we demonstrate that a high-quality phase can be generated for a wide range of fringe periods (e.g., from 18 to 1140 pixels) with only six binary patterns. Since only 1-bit binary patterns are required for 3D shape measurement, this paper will present a real-time 3D shape measurement system that can achieve 30 Hz.

© 2017 Optical Society of America

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References

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    [Crossref] [PubMed]
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2017 (1)

2016 (2)

2014 (2)

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]

2013 (1)

C. Zuo, Q. Chen, G. Feng, S. Feng, F. Feng, R. Li, and G. Shen, “High-speed three-dimensional shape measurement for dynamic scenes using bi-frequency tripolar pulse-width-modulation fringe projection,” Opt. Laser Eng. 51, 953–960 (2013).
[Crossref]

2012 (2)

2011 (3)

2010 (5)

G. A. Ayubi, J. A. Ayubi, J. M. D. Martino, and J. A. Ferrari, “Pulse-width modulation in defocused 3-d fringe projection,” Opt. Lett. 35, 3682–3684 (2010).
[Crossref] [PubMed]

Y. Wang and S. Zhang, “Optimal pulse width modulation for sinusoidal fringe generation with projector defocusing,” Opt. Lett. 35, 4121–4123 (2010).
[Crossref] [PubMed]

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]

2001 (1)

1992 (1)

X. Y. Su, W. S. Zhou, G. Von Bally, and D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94, 561–573 (1992).
[Crossref]

Ajubi, G. A.

Ayubi, G. A.

Ayubi, J. A.

Chen, Q.

C. Zuo, Q. Chen, G. Feng, S. Feng, F. Feng, R. Li, and G. Shen, “High-speed three-dimensional shape measurement for dynamic scenes using bi-frequency tripolar pulse-width-modulation fringe projection,” Opt. Laser Eng. 51, 953–960 (2013).
[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]

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]

Ekstrand, L.

Feng, F.

C. Zuo, Q. Chen, G. Feng, S. Feng, F. Feng, R. Li, and G. Shen, “High-speed three-dimensional shape measurement for dynamic scenes using bi-frequency tripolar pulse-width-modulation fringe projection,” Opt. Laser Eng. 51, 953–960 (2013).
[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]

Feng, G.

C. Zuo, Q. Chen, G. Feng, S. Feng, F. Feng, R. Li, and G. Shen, “High-speed three-dimensional shape measurement for dynamic scenes using bi-frequency tripolar pulse-width-modulation fringe projection,” Opt. Laser Eng. 51, 953–960 (2013).
[Crossref]

Feng, S.

C. Zuo, Q. Chen, G. Feng, S. Feng, F. Feng, R. Li, and G. Shen, “High-speed three-dimensional shape measurement for dynamic scenes using bi-frequency tripolar pulse-width-modulation fringe projection,” Opt. Laser Eng. 51, 953–960 (2013).
[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]

Ferrari, J. A.

Flores, J. L.

Gorthi, S.

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

Gu, G.

Hyun, J.-S.

Karpinsky, N.

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]

Li, R.

C. Zuo, Q. Chen, G. Feng, S. Feng, F. Feng, R. Li, and G. Shen, “High-speed three-dimensional shape measurement for dynamic scenes using bi-frequency tripolar pulse-width-modulation fringe projection,” Opt. Laser Eng. 51, 953–960 (2013).
[Crossref]

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]

Martino, J. M. D.

Munoz, A.

Rastogi, P.

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

Shen, G.

C. Zuo, Q. Chen, G. Feng, S. Feng, F. Feng, R. Li, and G. Shen, “High-speed three-dimensional shape measurement for dynamic scenes using bi-frequency tripolar pulse-width-modulation fringe projection,” Opt. Laser Eng. 51, 953–960 (2013).
[Crossref]

Silva, A.

Su, X.

Su, X. Y.

X. Y. Su, W. S. Zhou, G. Von Bally, and D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94, 561–573 (1992).
[Crossref]

Sui, X.

Sun, J.

J. Sun, Pulse Width Modulation (Springer, NY, 2012), chap. 2, pp. 25–61.

Von Bally, G.

X. Y. Su, W. S. Zhou, G. Von Bally, and D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94, 561–573 (1992).
[Crossref]

Vukicevic, D.

X. Y. Su, W. S. Zhou, G. Von Bally, and D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94, 561–573 (1992).
[Crossref]

Wang, Y.

Xian, T.

You, Z.

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.

Zhou, P.

Zhou, W. S.

X. Y. Su, W. S. Zhou, G. Von Bally, and D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94, 561–573 (1992).
[Crossref]

Zhu, J.

Zuo, C.

C. Zuo, Q. Chen, G. Feng, S. Feng, F. Feng, R. Li, and G. Shen, “High-speed three-dimensional shape measurement for dynamic scenes using bi-frequency tripolar pulse-width-modulation fringe projection,” Opt. Laser Eng. 51, 953–960 (2013).
[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. (7)

Opt. Commun. (1)

X. Y. Su, W. S. Zhou, G. Von Bally, and D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94, 561–573 (1992).
[Crossref]

Opt. Express (1)

Opt. Laser Eng. (3)

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

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]

C. Zuo, Q. Chen, G. Feng, S. Feng, F. Feng, R. Li, and G. Shen, “High-speed three-dimensional shape measurement for dynamic scenes using bi-frequency tripolar pulse-width-modulation fringe projection,” Opt. Laser Eng. 51, 953–960 (2013).
[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. (1)

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

Opt. Lett. (4)

Other (2)

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

J. Sun, Pulse Width Modulation (Springer, NY, 2012), chap. 2, pp. 25–61.

Supplementary Material (4)

NameDescription
» Visualization 1       Visualization 1
» Visualization 2       Visualization 2
» Visualization 3       Visualization 3
» Visualization 4       Visualization 4

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Figures (10)

Fig. 1
Fig. 1 Principle of triangular pulse width modulation with different initial phase values. (a) Cosine function with initial phase θ0 = 0; (b) cosine function with initial phase θ0 = π.
Fig. 2
Fig. 2 Proposed difference signal by taking the difference between the TPWM signal with the initial phase θ0 = 0 and that with the initial phase θ0 = π. The left two signals show the originally PWM signals and the right shows the difference signal.
Fig. 3
Fig. 3 Representative candidates of the difference patterns and the corresponding phase rms error with different modulation frequencies and different filter sizes. fc = 22 f0 is considered to be the “best” candidate. (a)–(d) One of the resultant three phase-shifted difference patterns with modulation frequency fc = 11 f0, fc = 14 f0, fc = 22 f0, fc = 25 f0, respectively; (e)–(h) corresponding phase rms error.
Fig. 4
Fig. 4 Frequency spectrum of the pwm patterns. (a) Regular pwm pattern; (b) π phase-shifted pwm pattern; (c) difference pattern; (d) – (f) frequency spectrum of the above pattern shown in (a)–(c) respectively.
Fig. 5
Fig. 5 Resultant fringe patterns with different amount of defocusing for fringe period of T = 60 pixels. (a) Gaussian filter size 3 × 3; (b) Gaussian filter size 9 × 9; (c) Gaussian filter size 15 × 15; (d) Gaussian filter size 21 × 21.
Fig. 6
Fig. 6 Phase rms error of the best modulation frequency for various fringe periods. (a) Results from ideal modulated patterns for various filter sizes; (b) experimental data for seven different amounts of defocusing.
Fig. 7
Fig. 7 Measurement result of a complex 3D statue. (a) Photograph of the statue; (b) – (e) one of fringe patterns for fringe period 36, 120, 360, and 1140 pixels, respectively; (f) one of the difference fringe patterns for fringe period 36 pixels; (g)–(j) wrapped phase for fringe period 36, 120, 360, and 1140 pixels, respectively.
Fig. 8
Fig. 8 Resultant 3D shapes of the complex 3D statue with different temporal phase unwrapping algorithms. (a) 3D from the unwrapped phase obtained by using the phase of fringe period T = 1140 pixels; (b) 3D from the unwrapped phase obtained by using the phase of fringe periods T = 1140 and 360 pixels; (c) 3D from the unwrapped phase obtained by using the phase of fringe period T = 1140 and 120 pixels; (d) 3D from the unwrapped phase obtained by using the phase of fringe period T = 1140, 360, and 120 pixels; (e)–(h) zoom-in view of the bottom left corner of the above 3D geometry.
Fig. 9
Fig. 9 Typical frames of real-time 3D shape measurement using standard two-frequency phase unwrapping method (associated Visualization 1 and Visualization 2). Top row shows different hands gestures, and bottom row shows different facial expressions.
Fig. 10
Fig. 10 Typical frames of real-time 3D shape measurement using the enhanced two-frequency phase unwrapping method (associated Visualization 3 and Visualization 4). Top row shows different hands gestures, and bottom row shows different facial expressions.

Tables (1)

Tables Icon

Table 1 “best” modulation frequencies for a large range of fringe periods.

Equations (10)

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I 1 ( x , y ) = I ( x , y ) + I ( x , y ) cos ( ϕ 2 π / 3 ) ,
I 2 ( x , y ) = I ( x , y ) + I ( x , y ) cos ( ϕ ) ,
I 3 ( x , y ) = I ( x , y ) + I ( x , y ) cos ( ϕ + 2 π / 3 ) ,
ϕ ( x , y ) = tan 1 [ 3 ( I 1 I 3 ) / ( 2 I 2 I 1 I 3 ) ] .
pwm g ( x ) = M 2 cos ( 2 π f 0 x + θ 0 ) + m = 1 { 2 m π sin [ m π 2 ] J 0 ( m π M 2 ) cos [ m ( 2 π f c x + θ c ) ] } + m = 1 n = ± 1 ± { 2 m π sin [ ( m + n ) π 2 ] J n ( m π M 2 ) cos [ m ( 2 π f c x + θ c ) + n ( 2 π f 0 x + θ 0 ) ] } ,
J n ( z ) = j n π 0 2 π e j z cos θ e j n θ d θ
pwm 1 ( x ) = M 2 cos ( 2 π f 0 x ) + m = 1 { 2 m π sin [ m π 2 ] J 0 ( m π M 2 ) cos [ m ( 2 π f c x ) ] } + m = 1 n = ± 1 ± { 2 m π sin [ ( m + n ) π 2 ] J n ( m π M 2 ) cos [ ( 2 m π f c + 2 n π f 0 ) x ] } .
pwm 2 ( x ) = M 2 cos ( 2 π f 0 x π ) + m = 1 { 2 m π sin [ m π 2 ] J 0 ( m π M 2 ) cos [ m ( 2 π f c x ) ] } + m = 1 n = ± 1 ± { 2 m π sin [ ( m + n ) π 2 ] J n ( m π M 2 ) cos [ ( 2 m π f c + 2 n π f 0 ) x n π ] } .
pwm ( x ) = pwm 1 ( x ) pwm 2 ( x ) = M cos ( 2 π f 0 x ) + m = 1 n = + { 2 m π cos [ ( m + n ) π ] J 2 n 1 ( m π M ) cos [ 4 π m f c + ( 4 n 2 ) π f 0 ] x } .
Δ Φ = Φ Φ r × T / 18 .

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