Abstract

Recent advancements in 3D measurement technologies have increased the urgency of requiring high-speed 3D measurement in many fields. This study presents a novel four-step triangular pattern phase-shifting 3D measurement using the motion blur method, which combines the advantages of phase-shifting methods. To comply with the high speed requirement, binary coded triangular patterns are projected and could dither vertically. Therefore, the image captured by the camera is blurred into grayscale-intensity triangular patterns, which can be used for phase unwrapping and 3D reconstruction. The proposed method decreased the projection time compared with sinusoidal patterns using a DMD (digital micromirror device) projector. Furthermore, this study presents a four-step triangular phase-shifting unwrapping algorithm. The experiments indicate that the proposed method can achieve high-speed 3D measurement and reconstruction.

© 2017 Optical Society of America

Full Article  |  PDF Article
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References

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2016 (2)

C. Zuo, L. Huang, M. Zhang, Q. Chen, and A. Asundi, “Temporal phase unwrapping algorithms for fringe projection profilometry: a comparative review,” Opt. Lasers Eng. 85, 84–103 (2016).

S. Heist, P. Lutzke, I. Schmidt, P. Dietrich, P. Kühmstedt, A. Tünnermann, and G. Notni, “High-speed three-dimensional shape measurement using GOBO projection,” Opt. Lasers Eng. 87, 90–96 (2016).

2015 (2)

2014 (8)

S. Heist, A. Mann, P. Kühmstedt, P. Schreiber, and G. Notni, “Array projection of aperiodic sinusoidal fringes for high-speed three-dimensional shape measurement,” Opt. Eng. 53, 139–152 (2014).

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. Lasers Eng. 54, 236–246 (2014).

G. Yang, C. Sun, P. Wang, and Y. Xu, “High-speed scanning stroboscopic fringe-pattern projection technology for three-dimensional shape precision measurement,” Appl. Opt. 53(2), 174–183 (2014).
[PubMed]

S. Feng, Q. Chen, C. Zuo, J. Sun, and S. L. Yu, “High-speed real-time 3-D coordinates measurement based on fringe projection profilometry considering camera lens distortion,” Opt. Commun. 329, 44–56 (2014).

J. Dai, B. Li, and S. Zhang, “Intensity-optimized dithering technique for three-dimensional shape measurement with projector defocusing,” Opt. Lasers Eng. 53, 79–85 (2014).

P. Cao, J. Xi, Y. Yu, Q. Guo, and L. Song, “3D shape measurement based on projection of triangular patterns of two selected frequencies,” Opt. Express 22(23), 29234–29248 (2014).
[PubMed]

Z. Yang, K. Wu, J. Xi, and Y. Yu, “Intensity ratio approach for 3D profile measurement based on projection of triangular patterns,” Appl. Opt. 53(2), 200–207 (2014).
[PubMed]

W. Lohry and S. Zhang, “High-speed absolute three-dimensional shape measurement using three binary dithered patterns,” Opt. Express 22(22), 26752–26762 (2014).
[PubMed]

2013 (2)

Y. Wang, J. I. Laughner, I. R. Efimov, and S. Zhang, “3D absolute shape measurement of live rabbit hearts with a superfast two-frequency phase-shifting technique,” Opt. Express 21(5), 5822–5832 (2013).
[PubMed]

C. Zuo, Q. Chen, G. Gu, 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. Lasers Eng. 51(8), 953–960 (2013).

2012 (2)

2010 (5)

2009 (1)

2007 (1)

P. Jia, J. Kofman, and C. English, “Two-step triangular-pattern phase-shifting method for three-dimensional object-shape measurement,” Opt. Eng. 46, 0832018 (2007).

Ahn, S.

Aoyama, T.

Y. Liu, H. Gao, Q. Gu, T. Aoyama, T. Takaki, and I. Ishii, “A fast 3-D shape measurement method for moving object,” in 2014 International Conference on Progress in Informatics and Computing (PIC, 2014), pp. 219–223.

Asundi, A.

C. Zuo, L. Huang, M. Zhang, Q. Chen, and A. Asundi, “Temporal phase unwrapping algorithms for fringe projection profilometry: a comparative review,” Opt. Lasers Eng. 85, 84–103 (2016).

Cao, P.

Chen, Q.

C. Zuo, L. Huang, M. Zhang, Q. Chen, and A. Asundi, “Temporal phase unwrapping algorithms for fringe projection profilometry: a comparative review,” Opt. Lasers Eng. 85, 84–103 (2016).

S. Feng, Q. Chen, C. Zuo, J. Sun, and S. L. Yu, “High-speed real-time 3-D coordinates measurement based on fringe projection profilometry considering camera lens distortion,” Opt. Commun. 329, 44–56 (2014).

C. Zuo, Q. Chen, G. Gu, 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. Lasers Eng. 51(8), 953–960 (2013).

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(19), 4477–4490 (2012).
[PubMed]

C. Zuo, Q. Chen, G. Gu, S. Feng, and F. Feng, “High-speed three-dimensional profilometry for multiple objects with complex shapes,” Opt. Express 20(17), 19493–19510 (2012).
[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. Lasers Eng. 54, 236–246 (2014).

J. Dai, B. Li, and S. Zhang, “Intensity-optimized dithering technique for three-dimensional shape measurement with projector defocusing,” Opt. Lasers Eng. 53, 79–85 (2014).

Dietrich, P.

S. Heist, P. Lutzke, I. Schmidt, P. Dietrich, P. Kühmstedt, A. Tünnermann, and G. Notni, “High-speed three-dimensional shape measurement using GOBO projection,” Opt. Lasers Eng. 87, 90–96 (2016).

Efimov, I. R.

English, C.

P. Jia, J. Kofman, and C. English, “Two-step triangular-pattern phase-shifting method for three-dimensional object-shape measurement,” Opt. Eng. 46, 0832018 (2007).

Feng, F.

Feng, S.

S. Feng, Q. Chen, C. Zuo, J. Sun, and S. L. Yu, “High-speed real-time 3-D coordinates measurement based on fringe projection profilometry considering camera lens distortion,” Opt. Commun. 329, 44–56 (2014).

C. Zuo, Q. Chen, G. Gu, 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. Lasers Eng. 51(8), 953–960 (2013).

C. Zuo, Q. Chen, G. Gu, S. Feng, and F. Feng, “High-speed three-dimensional profilometry for multiple objects with complex shapes,” Opt. Express 20(17), 19493–19510 (2012).
[PubMed]

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(19), 4477–4490 (2012).
[PubMed]

Gao, H.

Y. Liu, H. Gao, Q. Gu, T. Aoyama, T. Takaki, and I. Ishii, “A fast 3-D shape measurement method for moving object,” in 2014 International Conference on Progress in Informatics and Computing (PIC, 2014), pp. 219–223.

Gorthi, S. S.

S. S. Gorthi and P. Rastogi, “Fringe projection techniques: Whither we are?” Opt. Lasers Eng. 48, 133–149 (2010).

Grosse, M.

Gu, G.

Gu, Q.

Y. Liu, H. Gao, Q. Gu, T. Aoyama, T. Takaki, and I. Ishii, “A fast 3-D shape measurement method for moving object,” in 2014 International Conference on Progress in Informatics and Computing (PIC, 2014), pp. 219–223.

Guo, Q.

Hao, Q.

Hassebrook, L. G.

Heist, S.

S. Heist, P. Lutzke, I. Schmidt, P. Dietrich, P. Kühmstedt, A. Tünnermann, and G. Notni, “High-speed three-dimensional shape measurement using GOBO projection,” Opt. Lasers Eng. 87, 90–96 (2016).

S. Heist, P. Kühmstedt, A. Tünnermann, and G. Notni, “Theoretical considerations on aperiodic sinusoidal fringes in comparison to phase-shifted sinusoidal fringes for high-speed three-dimensional shape measurement,” Appl. Opt. 54(35), 10541–10551 (2015).
[PubMed]

S. Heist, A. Mann, P. Kühmstedt, P. Schreiber, and G. Notni, “Array projection of aperiodic sinusoidal fringes for high-speed three-dimensional shape measurement,” Opt. Eng. 53, 139–152 (2014).

Huang, L.

C. Zuo, L. Huang, M. Zhang, Q. Chen, and A. Asundi, “Temporal phase unwrapping algorithms for fringe projection profilometry: a comparative review,” Opt. Lasers Eng. 85, 84–103 (2016).

Ishii, I.

Y. Liu, H. Gao, Q. Gu, T. Aoyama, T. Takaki, and I. Ishii, “A fast 3-D shape measurement method for moving object,” in 2014 International Conference on Progress in Informatics and Computing (PIC, 2014), pp. 219–223.

Ishikawa, M.

S. Tabata, S. Noguchi, Y. Watanabe, and M. Ishikawa, “High-speed 3D sensing with three-view geometry using a segmented pattern,” in 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS, 2015), pp. 3900–3907.

Jia, P.

P. Jia, J. Kofman, and C. English, “Two-step triangular-pattern phase-shifting method for three-dimensional object-shape measurement,” Opt. Eng. 46, 0832018 (2007).

Justusson, B.

Kang, M.

Kieu, H.

Kofman, J.

P. Jia, J. Kofman, and C. English, “Two-step triangular-pattern phase-shifting method for three-dimensional object-shape measurement,” Opt. Eng. 46, 0832018 (2007).

Kowarschik, R.

Kühmstedt, P.

S. Heist, P. Lutzke, I. Schmidt, P. Dietrich, P. Kühmstedt, A. Tünnermann, and G. Notni, “High-speed three-dimensional shape measurement using GOBO projection,” Opt. Lasers Eng. 87, 90–96 (2016).

S. Heist, P. Kühmstedt, A. Tünnermann, and G. Notni, “Theoretical considerations on aperiodic sinusoidal fringes in comparison to phase-shifted sinusoidal fringes for high-speed three-dimensional shape measurement,” Appl. Opt. 54(35), 10541–10551 (2015).
[PubMed]

S. Heist, A. Mann, P. Kühmstedt, P. Schreiber, and G. Notni, “Array projection of aperiodic sinusoidal fringes for high-speed three-dimensional shape measurement,” Opt. Eng. 53, 139–152 (2014).

Kwon, Y.

Lau, D. L.

Laughner, J. I.

Le, M.

Li, B.

J. Dai, B. Li, and S. Zhang, “Intensity-optimized dithering technique for three-dimensional shape measurement with projector defocusing,” Opt. Lasers Eng. 53, 79–85 (2014).

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. Lasers Eng. 54, 236–246 (2014).

Li, R.

C. Zuo, Q. Chen, G. Gu, 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. Lasers Eng. 51(8), 953–960 (2013).

Liu, K.

Liu, Y.

Y. Liu, H. Gao, Q. Gu, T. Aoyama, T. Takaki, and I. Ishii, “A fast 3-D shape measurement method for moving object,” in 2014 International Conference on Progress in Informatics and Computing (PIC, 2014), pp. 219–223.

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. Lasers Eng. 54, 236–246 (2014).

W. Lohry and S. Zhang, “High-speed absolute three-dimensional shape measurement using three binary dithered patterns,” Opt. Express 22(22), 26752–26762 (2014).
[PubMed]

Lutzke, P.

S. Heist, P. Lutzke, I. Schmidt, P. Dietrich, P. Kühmstedt, A. Tünnermann, and G. Notni, “High-speed three-dimensional shape measurement using GOBO projection,” Opt. Lasers Eng. 87, 90–96 (2016).

Mann, A.

S. Heist, A. Mann, P. Kühmstedt, P. Schreiber, and G. Notni, “Array projection of aperiodic sinusoidal fringes for high-speed three-dimensional shape measurement,” Opt. Eng. 53, 139–152 (2014).

Nguyen, D.

Nguyen, H.

Noguchi, S.

S. Tabata, S. Noguchi, Y. Watanabe, and M. Ishikawa, “High-speed 3D sensing with three-view geometry using a segmented pattern,” in 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS, 2015), pp. 3900–3907.

Notni, G.

S. Heist, P. Lutzke, I. Schmidt, P. Dietrich, P. Kühmstedt, A. Tünnermann, and G. Notni, “High-speed three-dimensional shape measurement using GOBO projection,” Opt. Lasers Eng. 87, 90–96 (2016).

S. Heist, P. Kühmstedt, A. Tünnermann, and G. Notni, “Theoretical considerations on aperiodic sinusoidal fringes in comparison to phase-shifted sinusoidal fringes for high-speed three-dimensional shape measurement,” Appl. Opt. 54(35), 10541–10551 (2015).
[PubMed]

S. Heist, A. Mann, P. Kühmstedt, P. Schreiber, and G. Notni, “Array projection of aperiodic sinusoidal fringes for high-speed three-dimensional shape measurement,” Opt. Eng. 53, 139–152 (2014).

Pankow, M.

Park, Y.

Rastogi, P.

S. S. Gorthi and P. Rastogi, “Fringe projection techniques: Whither we are?” Opt. Lasers Eng. 48, 133–149 (2010).

Schaffer, M.

Schmidt, I.

S. Heist, P. Lutzke, I. Schmidt, P. Dietrich, P. Kühmstedt, A. Tünnermann, and G. Notni, “High-speed three-dimensional shape measurement using GOBO projection,” Opt. Lasers Eng. 87, 90–96 (2016).

Schreiber, P.

S. Heist, A. Mann, P. Kühmstedt, P. Schreiber, and G. Notni, “Array projection of aperiodic sinusoidal fringes for high-speed three-dimensional shape measurement,” Opt. Eng. 53, 139–152 (2014).

Shen, G.

C. Zuo, Q. Chen, G. Gu, 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. Lasers Eng. 51(8), 953–960 (2013).

Song, L.

Sui, X.

Sun, C.

Sun, J.

S. Feng, Q. Chen, C. Zuo, J. Sun, and S. L. Yu, “High-speed real-time 3-D coordinates measurement based on fringe projection profilometry considering camera lens distortion,” Opt. Commun. 329, 44–56 (2014).

Tabata, S.

S. Tabata, S. Noguchi, Y. Watanabe, and M. Ishikawa, “High-speed 3D sensing with three-view geometry using a segmented pattern,” in 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS, 2015), pp. 3900–3907.

Takaki, T.

Y. Liu, H. Gao, Q. Gu, T. Aoyama, T. Takaki, and I. Ishii, “A fast 3-D shape measurement method for moving object,” in 2014 International Conference on Progress in Informatics and Computing (PIC, 2014), pp. 219–223.

Tünnermann, A.

S. Heist, P. Lutzke, I. Schmidt, P. Dietrich, P. Kühmstedt, A. Tünnermann, and G. Notni, “High-speed three-dimensional shape measurement using GOBO projection,” Opt. Lasers Eng. 87, 90–96 (2016).

S. Heist, P. Kühmstedt, A. Tünnermann, and G. Notni, “Theoretical considerations on aperiodic sinusoidal fringes in comparison to phase-shifted sinusoidal fringes for high-speed three-dimensional shape measurement,” Appl. Opt. 54(35), 10541–10551 (2015).
[PubMed]

Waas, A. M.

Wang, P.

Wang, Y.

Wang, Z.

Watanabe, Y.

S. Tabata, S. Noguchi, Y. Watanabe, and M. Ishikawa, “High-speed 3D sensing with three-view geometry using a segmented pattern,” in 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS, 2015), pp. 3900–3907.

Wu, K.

Xi, J.

Xu, Y.

Yang, G.

Yang, Z.

Yu, S. L.

S. Feng, Q. Chen, C. Zuo, J. Sun, and S. L. Yu, “High-speed real-time 3-D coordinates measurement based on fringe projection profilometry considering camera lens distortion,” Opt. Commun. 329, 44–56 (2014).

Yu, Y.

Zhang, M.

C. Zuo, L. Huang, M. Zhang, Q. Chen, and A. Asundi, “Temporal phase unwrapping algorithms for fringe projection profilometry: a comparative review,” Opt. Lasers Eng. 85, 84–103 (2016).

Zhang, S.

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. Lasers Eng. 54, 236–246 (2014).

J. Dai, B. Li, and S. Zhang, “Intensity-optimized dithering technique for three-dimensional shape measurement with projector defocusing,” Opt. Lasers Eng. 53, 79–85 (2014).

W. Lohry and S. Zhang, “High-speed absolute three-dimensional shape measurement using three binary dithered patterns,” Opt. Express 22(22), 26752–26762 (2014).
[PubMed]

Y. Wang, J. I. Laughner, I. R. Efimov, and S. Zhang, “3D absolute shape measurement of live rabbit hearts with a superfast two-frequency phase-shifting technique,” Opt. Express 21(5), 5822–5832 (2013).
[PubMed]

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

Zuo, C.

C. Zuo, L. Huang, M. Zhang, Q. Chen, and A. Asundi, “Temporal phase unwrapping algorithms for fringe projection profilometry: a comparative review,” Opt. Lasers Eng. 85, 84–103 (2016).

S. Feng, Q. Chen, C. Zuo, J. Sun, and S. L. Yu, “High-speed real-time 3-D coordinates measurement based on fringe projection profilometry considering camera lens distortion,” Opt. Commun. 329, 44–56 (2014).

C. Zuo, Q. Chen, G. Gu, 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. Lasers Eng. 51(8), 953–960 (2013).

C. Zuo, Q. Chen, G. Gu, S. Feng, and F. Feng, “High-speed three-dimensional profilometry for multiple objects with complex shapes,” Opt. Express 20(17), 19493–19510 (2012).
[PubMed]

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(19), 4477–4490 (2012).
[PubMed]

Appl. Opt. (7)

J. Opt. Soc. Korea (1)

Opt. Commun. (1)

S. Feng, Q. Chen, C. Zuo, J. Sun, and S. L. Yu, “High-speed real-time 3-D coordinates measurement based on fringe projection profilometry considering camera lens distortion,” Opt. Commun. 329, 44–56 (2014).

Opt. Eng. (2)

S. Heist, A. Mann, P. Kühmstedt, P. Schreiber, and G. Notni, “Array projection of aperiodic sinusoidal fringes for high-speed three-dimensional shape measurement,” Opt. Eng. 53, 139–152 (2014).

P. Jia, J. Kofman, and C. English, “Two-step triangular-pattern phase-shifting method for three-dimensional object-shape measurement,” Opt. Eng. 46, 0832018 (2007).

Opt. Express (5)

Opt. Lasers Eng. (7)

S. Heist, P. Lutzke, I. Schmidt, P. Dietrich, P. Kühmstedt, A. Tünnermann, and G. Notni, “High-speed three-dimensional shape measurement using GOBO projection,” Opt. Lasers Eng. 87, 90–96 (2016).

C. Zuo, Q. Chen, G. Gu, 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. Lasers Eng. 51(8), 953–960 (2013).

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

S. S. Gorthi and P. Rastogi, “Fringe projection techniques: Whither we are?” Opt. Lasers Eng. 48, 133–149 (2010).

C. Zuo, L. Huang, M. Zhang, Q. Chen, and A. Asundi, “Temporal phase unwrapping algorithms for fringe projection profilometry: a comparative review,” Opt. Lasers Eng. 85, 84–103 (2016).

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. Lasers Eng. 54, 236–246 (2014).

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Y. Liu, H. Gao, Q. Gu, T. Aoyama, T. Takaki, and I. Ishii, “A fast 3-D shape measurement method for moving object,” in 2014 International Conference on Progress in Informatics and Computing (PIC, 2014), pp. 219–223.

Supplementary Material (1)

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» Visualization 1: AVI (2911 KB)      dynamic-measurement-results

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Figures (16)

Fig. 1
Fig. 1

Binary block, blurred patterns, and wave form of (a) saw tooth wave, (b) half-circle wave, (c) half-sinusoidal wave, (d) sinusoidal wave, (e) triangular wave with triangular block, and (f) triangular wave with diamond-like block.

Fig. 2
Fig. 2

The process of conventional DMD 8-bit grayscale projection method. The grayscale of projected point is 174 (10101100 in binary).

Fig. 3
Fig. 3

The 16 dithering steps of diamond-like binary blocks and the grayscale pattern comprised by these 16 binary blocks. The width of fringe pattern is 16 pixels.

Fig. 4
Fig. 4

Basic block based on the binary triangular pattern. The width and height of each block are 2a and 2b, respectively.

Fig. 5
Fig. 5

Relationship between Tcos(x) and cos(x): Tcos(x) is in period 4, where cos(x) is in period 2π. Only one period of these two functions is shown in the graph.

Fig. 6
Fig. 6

Simulation result of the proposed phase unwrapping method: (a) four-step phase shifting pattern images and their phase unwrapping result, (b) waveform of a pattern image (80 points in a row), and (c) waveform of the phase unwrapping result (80 points in a row).

Fig. 7
Fig. 7

Captured images in different exposure times: (a) single static binary pattern with 4000 us exposure, (b)–(g) dithering patterns with exposures at 200, 800, 1600, 2400, 3200, and 4000 us.

Fig. 8
Fig. 8

Measurement system using one DMD projector and two cameras.

Fig. 9
Fig. 9

Results of the proposed triangular pattern phase unwrapping method for the experiment involving a plaster jaw: (a) Projected binary patterns, (b) one fringe pattern image, and (c) phase calculating result for the fringe width of 20; (d) Projected binary patterns, (e) one fringe pattern image, and (f) phase calculating result for the fringe width of 24; (g) Projected binary patterns, (h) one fringe pattern image, and (i) phase calculating result for the fringe width of 28; (j) Phase unwrapping result using (c), (f), and (i).

Fig. 10
Fig. 10

Experiment involving the plaster jaw using the unwrapping images of the triangular pattern phase unwrapping method and two calibrated cameras: (a) plaster jaw; (b) one fringe pattern image, (c) local parts of the fringe pattern image, and (d) phase unwrapping results of the left camera; (e) one fringe pattern image, (f) local parts of the fringe pattern image, and (g) phase unwrapping results of the right camera.

Fig. 11
Fig. 11

Experiment involving the rubber bottle using the unwrapping images of the triangular pattern phase unwrapping method and two calibrated cameras: (a) rubber bottle; (b) one fringe pattern image, (c) local parts of the fringe pattern image, and (d) phase unwrapping results of the left camera; (e) one fringe pattern image, (f) local parts of the fringe pattern image, and (g) phase unwrapping results of the right camera.

Fig. 12
Fig. 12

3D reconstruction result using the unwrapping images of the triangular pattern phase unwrapping method: (a) polygonized point cloud result of the plaster jaw; (b) polygonized point cloud result of the rubber bottle; (c) color representation of the plaster jaw image that shows depth (Z) values of the measured points; and (d) color representation of the rubber bottle image that shows depth (Z) values of the measured points.

Fig. 13
Fig. 13

High-speed measurement of dynamic object: (a) on shot of triangular fringe pattern image acquired by left camera. (b) 4 frames selected from 31continuous frames of 3D data. See Visualization 1.

Fig. 14
Fig. 14

Measurement deviation estimation: measuring a standard plane board using the proposed method; The absolute mean error is 0.054 mm, and standard deviation of errors is 0.072 mm.

Fig. 15
Fig. 15

Measurement results of our proposed method and SPWM method: (a) the five results of 3D reconstruction of our proposed method whose measurement distances are 706 mm, 758 mm, 819 mm, 876 mm and 917 mm respectively. (b) the five results of 3D reconstruction of SPWM method whose measurement distances are 702 mm, 751 mm, 821 mm, 895 mm and 930 mm respectively. (c) 3D reconstruction of plane using our proposed method in measurement distance of 819 mm. (d) 3D reconstruction of plane using SPWM method in measurement distance of 821 mm. (e) 3D reconstruction of plane using our proposed method in measurement distance of 706 mm. (f) 3D reconstruction of plane using SPWM method in measurement distance of 702 mm.

Fig. 16
Fig. 16

The standard deviations of plane measurements using our proposed method and SPWM method in different measurement distances.

Equations (15)

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F block (x)= 0 w f block (x,y)dx ,
F block (x)= 0 h f block (x,y)dy ,
f block (x,y)={ 1 1 b | yb |+ 1 a | xa |<1 0 1 b | yb |+ 1 a | xa |1 , x[ 0,2a ) y[ 0,2b )
F block (x)= 0 2b f block (x,y)dy ={ 2b a x+2b x[ 0,a ] 2b a x2b x( a,2a ] . x[ 0,2a )
F block (x)={ x+1 x[ 0,2 ] x3 x( 2,4 ] .
I i ( x,y )= F block [(4/N)×mod(x,N)+i],
g i (x,y)=A(x,y)+B(x,y)cos[Φ(x,y)+iπ/2], i=0,1,2,3
Φ(x,y)=arctan( g 3 g 1 g 2 g 0 ).
T cos (x)= F block (x)={ x+1 x[ i,2+i ] x3 x( 2+i,4+i ] iZ
T sin (x)= T cos (x2).
g i (x,y)=A(x,y)+B(x,y) T cos [Φ(x,y)+i], i=0,1,2,3
G(x,y)= g 3 g 1 g 2 g 0 = T cos [Φ(x,y)] T sin [Φ(x,y)] = T tan [Φ(x,y)].
T tan (x)={ x 1x x[ 1,0 ] x 1+x x( 0,1 ] .
T arctan (x)={ x 1+x x( ,0 ] x 1x x( 0,+ ) ,
Φ(x,y)= T arctan ( g 3 g 1 g 2 g 0 ).