Abstract

Three-dimensional (3D) acquisition of an object with modest accuracy and speed is of particular concern in practice. The performance of digital sinusoidal fringe pattern projection using an off-the-shelf digital video projector is generally discounted by the nonlinearity and low switch rate. In this paper, a binary encoding method to encode one computer-generated standard sinusoidal fringe pattern is presented for circumventing such deficiencies. In previous work [Opt. Eng. 54, 054108 (2015) [CrossRef]  ], we have developed a 3D system based on this encoding tactic and showed its prospective application. Here, we first build a physical model to explain the mechanism of how to generate good sinusoidality. The phase accuracy with respect to the conventional spatial binary encoding method and sinusoidal fringe pattern is also comparatively evaluated through simulation and experiments. We also adopt two phase-height mapping relationships to experimentally compare the measurement accuracy among them. The results indicate that the proposed binary encoding strategy has a comparable performance to that of sinusoidal fringe pattern projection and enjoys advantages over the spatial binary method under the same conditions.

© 2017 Optical Society of America

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References

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  1. S. S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are?” Opt. Lasers Eng. 48, 133–140 (2010).
    [Crossref]
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    [Crossref]
  4. Y. Xu, L. Ekstrand, J. Dai, and S. Zhang, “Phase error compensation for three dimensional shape measurement with projector defocusing,” Appl. Opt. 50, 2572–2581 (2011).
    [Crossref]
  5. B. W. Li, Y. J. Wang, J. F. 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).
    [Crossref]
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    [Crossref]
  7. Y. Wang and S. Zhang, “Optimal pulse width modulation for sinusoidal fringe generation with projector defocusing,” Opt. Lett. 35, 4121–4123 (2010).
    [Crossref]
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    [Crossref]
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    [Crossref]
  10. W. Lohry and S. Zhang, “3D shape measurement with 2D area modulated binary patterns,” Opt. Lasers Eng. 50, 917–921 (2012).
    [Crossref]
  11. Y. Wang and S. Zhang, “Three-dimensional shape measurement with binary dithered patterns,” Appl. Opt. 51, 6631–6636 (2012).
    [Crossref]
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    [Crossref]
  13. W. Lohry and S. Zhang, “Genetic method to optimize binary dithering technique for high-quality fringe generation,” Opt. Lett. 38, 540–542 (2013).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  24. X. Y. Su, W. Song, Y. Cao, and L. Q. Xiang, “Phase-height mapping and coordinate calibration simultaneously in phase-measuring profilometry,” Opt. Eng. 43, 708–712 (2004).
    [Crossref]

2017 (2)

2016 (3)

S. Heist, P. Kühmstedt, A. Tünnermann, and G. Notni, “Experimental comparison of aperiodic sinusoidal fringes and phase-shifted sinusoidal fringes for high speed three-dimensional shape measurement,” Opt. Eng. 55, 024105 (2016).
[Crossref]

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).
[Crossref]

J. P. Zhu, P. Zhou, X. Y. Su, and Z. S. You, “Accurate and fast 3D surface measurement with temporal-spatial binary encoding structured illumination,” Opt. Express 24, 28549–28560 (2016).
[Crossref]

2015 (3)

J. P. Zhu, X. Y. Su, Z. S. You, and Y. K. Liu, “Temporal-spatial encoding binary fringes toward three-dimensional shape measurement without projector nonlinearity,” Opt. Eng. 54, 054108 (2015).
[Crossref]

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, 10541–10551 (2015).
[Crossref]

M. Liu, S. B. Yin, S. R. Yang, and Z. H. Zhang, “An accurate projector gamma correction method for phase-measuring profilometry based on direct optical power detection,” Proc. SPIE 9677, 96771D (2015).
[Crossref]

2014 (1)

B. W. Li, Y. J. Wang, J. F. 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).
[Crossref]

2013 (3)

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

J. Dai and S. Zhang, “Phase-optimized dithering technique for high-quality 3D shape measurement,” Opt. Laser Eng. 51, 790–795 (2013).
[Crossref]

W. Lohry and S. Zhang, “Genetic method to optimize binary dithering technique for high-quality fringe generation,” Opt. Lett. 38, 540–542 (2013).
[Crossref]

2012 (3)

2011 (4)

2010 (4)

2004 (1)

X. Y. Su, W. Song, Y. Cao, and L. Q. Xiang, “Phase-height mapping and coordinate calibration simultaneously in phase-measuring profilometry,” Opt. Eng. 43, 708–712 (2004).
[Crossref]

Alonso, J. R.

Asundi, A.

Ayubi, G. A.

Ayubi, J. A.

Cao, Y.

X. Y. Su, W. Song, Y. Cao, and L. Q. Xiang, “Phase-height mapping and coordinate calibration simultaneously in phase-measuring profilometry,” Opt. Eng. 43, 708–712 (2004).
[Crossref]

Chen, Q.

Chua, P. S. K.

Dai, J.

J. Dai and S. Zhang, “Phase-optimized dithering technique for high-quality 3D shape measurement,” Opt. Laser Eng. 51, 790–795 (2013).
[Crossref]

Y. Xu, L. Ekstrand, J. Dai, and S. Zhang, “Phase error compensation for three dimensional shape measurement with projector defocusing,” Appl. Opt. 50, 2572–2581 (2011).
[Crossref]

Dai, J. F.

B. W. Li, Y. J. Wang, J. F. 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).
[Crossref]

Di Martino, J. M.

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).
[Crossref]

Ekstrand, L.

Feng, F. X.

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

Feng, S.

Feng, S. J.

S. J. Feng, Q. Chen, C. Zuo, T. Y. Tao, Y. Hu, and A. Asundi, “Motion-oriented high speed 3-D measurements by binocular fringe projection using binary aperiodic patterns,” Opt. Express 25, 540–559 (2017).
[Crossref]

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

Fernández, A.

Ferrari, J. A.

Forster, F.

Gorthi, S. S.

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

Gu, G. H.

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

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).
[Crossref]

S. Heist, P. Kühmstedt, A. Tünnermann, and G. Notni, “Experimental comparison of aperiodic sinusoidal fringes and phase-shifted sinusoidal fringes for high speed three-dimensional shape measurement,” Opt. Eng. 55, 024105 (2016).
[Crossref]

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, 10541–10551 (2015).
[Crossref]

Hu, Y.

Huang, L.

Hyun, J. S.

J. S. Hyun and S. Zhang, “Superfast 3D absolute shape measurement using five binary patterns,” Opt. Lasers Eng. 90, 217–224 (2017).
[Crossref]

Kühmstedt, P.

S. Heist, P. Kühmstedt, A. Tünnermann, and G. Notni, “Experimental comparison of aperiodic sinusoidal fringes and phase-shifted sinusoidal fringes for high speed three-dimensional shape measurement,” Opt. Eng. 55, 024105 (2016).
[Crossref]

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).
[Crossref]

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, 10541–10551 (2015).
[Crossref]

Li, B. W.

B. W. Li, Y. J. Wang, J. F. 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).
[Crossref]

Li, R. B.

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

Liu, M.

M. Liu, S. B. Yin, S. R. Yang, and Z. H. Zhang, “An accurate projector gamma correction method for phase-measuring profilometry based on direct optical power detection,” Proc. SPIE 9677, 96771D (2015).
[Crossref]

Liu, Y. K.

J. P. Zhu, X. Y. Su, Z. S. You, and Y. K. Liu, “Temporal-spatial encoding binary fringes toward three-dimensional shape measurement without projector nonlinearity,” Opt. Eng. 54, 054108 (2015).
[Crossref]

Lohry, W.

B. W. Li, Y. J. Wang, J. F. 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).
[Crossref]

W. Lohry and S. Zhang, “Genetic method to optimize binary dithering technique for high-quality fringe generation,” Opt. Lett. 38, 540–542 (2013).
[Crossref]

W. Lohry and S. Zhang, “3D shape measurement with 2D area modulated binary patterns,” Opt. Lasers Eng. 50, 917–921 (2012).
[Crossref]

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).
[Crossref]

Martino, J. M. D.

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).
[Crossref]

S. Heist, P. Kühmstedt, A. Tünnermann, and G. Notni, “Experimental comparison of aperiodic sinusoidal fringes and phase-shifted sinusoidal fringes for high speed three-dimensional shape measurement,” Opt. Eng. 55, 024105 (2016).
[Crossref]

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, 10541–10551 (2015).
[Crossref]

Perciante, C. D.

Rastogi, P.

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

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).
[Crossref]

Schmitt, R.

Shen, G. C.

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

Song, W.

X. Y. Su, W. Song, Y. Cao, and L. Q. Xiang, “Phase-height mapping and coordinate calibration simultaneously in phase-measuring profilometry,” Opt. Eng. 43, 708–712 (2004).
[Crossref]

Su, X. Y.

J. P. Zhu, P. Zhou, X. Y. Su, and Z. S. You, “Accurate and fast 3D surface measurement with temporal-spatial binary encoding structured illumination,” Opt. Express 24, 28549–28560 (2016).
[Crossref]

J. P. Zhu, X. Y. Su, Z. S. You, and Y. K. Liu, “Temporal-spatial encoding binary fringes toward three-dimensional shape measurement without projector nonlinearity,” Opt. Eng. 54, 054108 (2015).
[Crossref]

X. Y. Su, W. Song, Y. Cao, and L. Q. Xiang, “Phase-height mapping and coordinate calibration simultaneously in phase-measuring profilometry,” Opt. Eng. 43, 708–712 (2004).
[Crossref]

Tao, T. Y.

Tünnermann, A.

S. Heist, P. Kühmstedt, A. Tünnermann, and G. Notni, “Experimental comparison of aperiodic sinusoidal fringes and phase-shifted sinusoidal fringes for high speed three-dimensional shape measurement,” Opt. Eng. 55, 024105 (2016).
[Crossref]

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).
[Crossref]

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, 10541–10551 (2015).
[Crossref]

Wang, Y.

Wang, Y. J.

B. W. Li, Y. J. Wang, J. F. 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).
[Crossref]

Wissmann, P.

Xiang, L. Q.

X. Y. Su, W. Song, Y. Cao, and L. Q. Xiang, “Phase-height mapping and coordinate calibration simultaneously in phase-measuring profilometry,” Opt. Eng. 43, 708–712 (2004).
[Crossref]

Xu, Y.

Yang, S. R.

M. Liu, S. B. Yin, S. R. Yang, and Z. H. Zhang, “An accurate projector gamma correction method for phase-measuring profilometry based on direct optical power detection,” Proc. SPIE 9677, 96771D (2015).
[Crossref]

Yin, S. B.

M. Liu, S. B. Yin, S. R. Yang, and Z. H. Zhang, “An accurate projector gamma correction method for phase-measuring profilometry based on direct optical power detection,” Proc. SPIE 9677, 96771D (2015).
[Crossref]

You, Z. S.

J. P. Zhu, P. Zhou, X. Y. Su, and Z. S. You, “Accurate and fast 3D surface measurement with temporal-spatial binary encoding structured illumination,” Opt. Express 24, 28549–28560 (2016).
[Crossref]

J. P. Zhu, X. Y. Su, Z. S. You, and Y. K. Liu, “Temporal-spatial encoding binary fringes toward three-dimensional shape measurement without projector nonlinearity,” Opt. Eng. 54, 054108 (2015).
[Crossref]

Zhang, S.

J. S. Hyun and S. Zhang, “Superfast 3D absolute shape measurement using five binary patterns,” Opt. Lasers Eng. 90, 217–224 (2017).
[Crossref]

B. W. Li, Y. J. Wang, J. F. 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).
[Crossref]

J. Dai and S. Zhang, “Phase-optimized dithering technique for high-quality 3D shape measurement,” Opt. Laser Eng. 51, 790–795 (2013).
[Crossref]

W. Lohry and S. Zhang, “Genetic method to optimize binary dithering technique for high-quality fringe generation,” Opt. Lett. 38, 540–542 (2013).
[Crossref]

W. Lohry and S. Zhang, “3D shape measurement with 2D area modulated binary patterns,” Opt. Lasers Eng. 50, 917–921 (2012).
[Crossref]

Y. Wang and S. Zhang, “Three-dimensional shape measurement with binary dithered patterns,” Appl. Opt. 51, 6631–6636 (2012).
[Crossref]

L. Ekstrand and S. Zhang, “Three-dimensional profilometry with nearly focused binary phase-shifting algorithms,” Opt. Lett. 36, 4518–4520 (2011).
[Crossref]

Y. Xu, L. Ekstrand, J. Dai, and S. Zhang, “Phase error compensation for three dimensional shape measurement with projector defocusing,” Appl. Opt. 50, 2572–2581 (2011).
[Crossref]

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

Zhang, Z. H.

M. Liu, S. B. Yin, S. R. Yang, and Z. H. Zhang, “An accurate projector gamma correction method for phase-measuring profilometry based on direct optical power detection,” Proc. SPIE 9677, 96771D (2015).
[Crossref]

Zhou, P.

Zhu, J. P.

J. P. Zhu, P. Zhou, X. Y. Su, and Z. S. You, “Accurate and fast 3D surface measurement with temporal-spatial binary encoding structured illumination,” Opt. Express 24, 28549–28560 (2016).
[Crossref]

J. P. Zhu, X. Y. Su, Z. S. You, and Y. K. Liu, “Temporal-spatial encoding binary fringes toward three-dimensional shape measurement without projector nonlinearity,” Opt. Eng. 54, 054108 (2015).
[Crossref]

Zuo, C.

Appl. Opt. (6)

Opt. Eng. (3)

S. Heist, P. Kühmstedt, A. Tünnermann, and G. Notni, “Experimental comparison of aperiodic sinusoidal fringes and phase-shifted sinusoidal fringes for high speed three-dimensional shape measurement,” Opt. Eng. 55, 024105 (2016).
[Crossref]

J. P. Zhu, X. Y. Su, Z. S. You, and Y. K. Liu, “Temporal-spatial encoding binary fringes toward three-dimensional shape measurement without projector nonlinearity,” Opt. Eng. 54, 054108 (2015).
[Crossref]

X. Y. Su, W. Song, Y. Cao, and L. Q. Xiang, “Phase-height mapping and coordinate calibration simultaneously in phase-measuring profilometry,” Opt. Eng. 43, 708–712 (2004).
[Crossref]

Opt. Express (3)

Opt. Laser Eng. (1)

J. Dai and S. Zhang, “Phase-optimized dithering technique for high-quality 3D shape measurement,” Opt. Laser Eng. 51, 790–795 (2013).
[Crossref]

Opt. Lasers Eng. (6)

J. S. Hyun and S. Zhang, “Superfast 3D absolute shape measurement using five binary patterns,” Opt. Lasers Eng. 90, 217–224 (2017).
[Crossref]

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).
[Crossref]

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

B. W. Li, Y. J. Wang, J. F. 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).
[Crossref]

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

W. Lohry and S. Zhang, “3D shape measurement with 2D area modulated binary patterns,” Opt. Lasers Eng. 50, 917–921 (2012).
[Crossref]

Opt. Lett. (4)

Proc. SPIE (1)

M. Liu, S. B. Yin, S. R. Yang, and Z. H. Zhang, “An accurate projector gamma correction method for phase-measuring profilometry based on direct optical power detection,” Proc. SPIE 9677, 96771D (2015).
[Crossref]

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Figures (10)

Fig. 1.
Fig. 1. Model of low-pass filter of projection optics.
Fig. 2.
Fig. 2. Calibration diagram of phase-height mapping for accuracy evaluation. The reference plane is numbered 0.
Fig. 3.
Fig. 3. Diagram of spatial binary encoding using Eq. (3) in simulation.
Fig. 4.
Fig. 4. Phase error relative to the standard sinusoidal fringe (SF) pattern: (a) the proposed method (TSBE); (b) the conventional spatial encoding (SE) method, combining Eq. (3) with Fig. (3).
Fig. 5.
Fig. 5. Captured experimental images with fringe period 120 pixels: (a) SF (the first four step phase-shifting images); (b) TSBE ( K = 4 ) and (c) SE method ( Q = 4 ).
Fig. 6.
Fig. 6. Phase error w.r.t. the standard sinusoidal fringe versus periods using two binary encoding methods: (a) TSBE method and (b) SE method.
Fig. 7.
Fig. 7. Captured pattern images demodulated by object under test: (a) SF, (b) TSBE, and (c) SE.
Fig. 8.
Fig. 8. Reconstruction results (phase) of a complex object using three methods: (a) SF, (b) TSBE, and (c) SE.
Fig. 9.
Fig. 9. Partially enlarged reconstruction results (phase) of a complex object in Fig. 8 using three methods: (a) SF, (b) TSBE, and (c) SE.
Fig. 10.
Fig. 10. (a) 3D phase reconstructions comparison at 120th row (forehead) of Figs. 8(a)8(c), and the partially enlarged view shown in (b).

Tables (3)

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Table 1. Depth Measurement Results Using SF Method (Units: mm)

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Table 2. Depth Measurement Results Using TSBE Method (Units: mm)

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Table 3. Depth Measurement Results Using SE Method (Units: mm)

Equations (21)

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I ( x , y ) = 0.5 + 0.5 cos ( 2 π f 0 x ) ,
T k = 2 k 1 2 K ( k = 1 , 2 , 3 , , K ) .
H = 1 16 ( * 7 3 5 1 ) ,
I M k ( i , j ) = I k ( i , j ) + m , n L [ H ( m , n ) E k ( i m , j n ) ] ,
E k ( i , j ) = { I M k ( i , j ) k / K , if    I M k ( i , j ) > T k I M k ( i , j ) ( k 1 ) / K , if    I M k ( i , j ) T k ( k = 1 , 2 , 3 , , K ) .
E 1 ( i , j ) = { I M 1 ( i , j ) 1 / 4 , if    I M 1 ( i , j ) > 1 / 8 I M 1 ( i , j ) 0 , if    I M 1 ( i , j ) 1 / 8 .
E 2 ( i , j ) = { I M 2 ( i , j ) 1 / 2 , if    I M 2 ( i , j ) > 3 / 8 I M 2 ( i , j ) 1 / 4 , if    I M 2 ( i , j ) 3 / 8 .
E 3 ( i , j ) = { I M 3 ( i , j ) 3 / 4 , if    I M 3 ( i , j ) > 5 / 8 I M 3 ( i , j ) 1 / 2 , if    I M 3 ( i , j ) 5 / 8 .
E 4 ( i , j ) = { I M 4 ( i , j ) 1 , if    I M 4 ( i , j ) > 7 / 8 I M 4 ( i , j ) 3 / 4 , if    I M 4 ( i , j ) 7 / 8 .
B c k ( x , y ) = B k ( x , y ) psf ( x , y ) , k = 1 , 2 , 3 K .
f ( u , v ) = { t ( u , v ) e j 2 π λ ω ( u , v ) , when    u 2 + v 2 1 0 , when    u 2 + v 2 > 1 ,
f ( u , v ) = { e j 2 π λ ω ( u , v ) , when    u 2 + v 2 1 0 , when    u 2 + v 2 > 1 ,
I ( h , t ) = O ( h , t ) * OTF ( h , t ) .
OTF ( h , t ) = OTF ( h , t ) OTF ( 0 , 0 ) .
OTF ( s ) = 2 J 1 ( 4 π λ ω s ) 4 π λ ω s , ( s = h 2 + t 2 ) ,
I R K ( x , y ) = 1 K k = 1 K B c k ( x , y ) .
I m ( x , y ) = a ( x , y ) + b ( x , y ) cos [ φ ( x , y ) + 2 m π / N ] , ( m = 1 , 2 , 3 , , N ) ,
ϕ w ( x , y ) = arc tan [ m = 0 N I k ( x , y ) sin ( 2 m π / N ) m = 0 N I k ( x , y ) cos ( 2 m π / N ) ] .
{ ϕ u 1 ( x , y ) = ϕ w 1 ( x , y ) , ϕ u N ( x , y ) = ϕ w N ( x , y ) + 2 π × { round [ N ϕ u 1 ( x , y ) ϕ w N ( x , y ) 2 π ] } , ϕ u N ( x , y ) = ϕ w N ( x , y ) + 2 π × { round [ N ϕ u N ( x , y ) ϕ w N ( x , y ) 2 π ] } .
1 Z w ( u , v ) = a ( u , v ) + b ( u , v ) 1 Δ ϕ u ( u , v ) + c ( u , v ) 1 Δ ϕ u 2 ( u , v ) .
Z w ( u , v ) = a 0 + a 1 ϕ u ( u , v ) 1 + a 2 ϕ u ( u , v ) 2 + + a n ϕ u ( u , v ) n .

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