Abstract

Binary defocusing technique has demonstrated various merits for high-speed and high-accuracy three-dimensional measurement. However, the existence of excessive defocusing zone (EDZ) limits the depth range of binary defocusing system. To overcome this problem, this paper proposes a multi-frequency phase merging (MFPM) approach, which makes it possible to measure the object surface in large depth range (LDR). The method is based on our finding that for different fringe frequencies, the associated EDZs of binary defocusing system are different and not totally overlapped. Thus by merging the phase maps of multiple binary fringes, we could effectively enhance the measurement depth range. Meanwhile, a strategy to determine the optimal combination of fringe frequencies is also proposed by analyzing the phase error distribution under different defocusing degrees. Both simulations and experiments verify the effectiveness and robustness of the proposed method.

© 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)

2017 (4)

2016 (1)

2013 (1)

2012 (4)

2011 (3)

2010 (4)

G. A. Ayubi, J. A. Ayubi, M. J. Di, and J. A. Ferrari, “Pulse-width modulation in defocused three-dimensional fringe projection,” Opt. Lett. 35(21), 3682–3684 (2010).
[Crossref]

Y. Gong and S. Zhang, “Ultrafast 3-d shape measurement with an off-the-shelf dlp projector,” Opt. Express 18(19), 19743–19754 (2010).
[Crossref]

S. S. Gorthi and P. Rastogi, “Fringe projection techniques: Whither we are?” Opt. & Lasers Eng. 48(2), 133–140 (2010).
[Crossref]

X. Su and Q. Zhang, “Dynamic 3-d shape measurement method: A review,” Opt. & Lasers Eng. 48(2), 191–204 (2010).
[Crossref]

2009 (2)

2007 (1)

V. P. Namboodiri and S. Chaudhuri, “On defocus, diffusion and depth estimation,” Pattern Recognit. Lett. 28(3), 311–319 (2007).
[Crossref]

2001 (1)

1992 (1)

X. Su, W. Zhou, B. G. Von, and D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a ronchi grating,” Opt. Commun. 94(6), 561–573 (1992).
[Crossref]

1978 (1)

D. Malacara and F. Roddier, “Optical shop testing,” Appl. Opt. 97, 454–464 (1978).
[Crossref]

Anand, A.

Ayubi, G. A.

Ayubi, J. A.

Cao, Y.

Chaudhuri, S.

V. P. Namboodiri and S. Chaudhuri, “On defocus, diffusion and depth estimation,” Pattern Recognit. Lett. 28(3), 311–319 (2007).
[Crossref]

Chen, Q.

Da, F.

Di, M. J.

Ekstrand, L.

Feng, F.

Feng, S.

Ferrari, J. A.

Flores, J. L.

Fujita, H.

H. Fujita, K. Yamatan, M. Yamamoto, Y. Otani, A. Suguro, S. Morokawa, and T. Yoshizawa, “Three-dimensional profilometry using liquid crystal grating,” Proc. SPIE - The Int. Soc. for Opt. Eng. pp. 51–60 (2003).

Gong, Y.

Gorthi, S. S.

S. S. Gorthi and P. Rastogi, “Fringe projection techniques: Whither we are?” Opt. & Lasers Eng. 48(2), 133–140 (2010).
[Crossref]

Gu, G.

Hu, Y.

Huang, L.

Iwai, D.

M. Nagase, D. Iwai, and K. Sato, “Dynamic defocus and occlusion compensation of projected imagery by model-based optimal projector selection in multi-projection environment,” Virtual Real. 15(2-3), 119–132 (2011).
[Crossref]

Jiang, H.

Kamagara, A.

Lei, S.

Li, B.

B. Li and S. Zhang, “Microscopic structured light 3d profilometry: Binary defocusing technique vs. sinusoidal fringe projection,” Opt. & Lasers Eng. 96, 117–123 (2017).
[Crossref]

Li, H.

Li, S.

Li, X.

Lohry, W.

W. Lohry and S. Zhang, “3d shape measurement with 2d area modulated binary patterns,” Opt. & Lasers Eng. 50(7), 917–921 (2012).
[Crossref]

Malacara, D.

D. Malacara and F. Roddier, “Optical shop testing,” Appl. Opt. 97, 454–464 (1978).
[Crossref]

Morokawa, S.

H. Fujita, K. Yamatan, M. Yamamoto, Y. Otani, A. Suguro, S. Morokawa, and T. Yoshizawa, “Three-dimensional profilometry using liquid crystal grating,” Proc. SPIE - The Int. Soc. for Opt. Eng. pp. 51–60 (2003).

Nagase, M.

M. Nagase, D. Iwai, and K. Sato, “Dynamic defocus and occlusion compensation of projected imagery by model-based optimal projector selection in multi-projection environment,” Virtual Real. 15(2-3), 119–132 (2011).
[Crossref]

Namboodiri, V. P.

V. P. Namboodiri and S. Chaudhuri, “On defocus, diffusion and depth estimation,” Pattern Recognit. Lett. 28(3), 311–319 (2007).
[Crossref]

noz, A. M.

Otani, Y.

H. Fujita, K. Yamatan, M. Yamamoto, Y. Otani, A. Suguro, S. Morokawa, and T. Yoshizawa, “Three-dimensional profilometry using liquid crystal grating,” Proc. SPIE - The Int. Soc. for Opt. Eng. pp. 51–60 (2003).

Pan, B.

Qian, K.

Rastogi, P.

S. S. Gorthi and P. Rastogi, “Fringe projection techniques: Whither we are?” Opt. & Lasers Eng. 48(2), 133–140 (2010).
[Crossref]

Roddier, F.

D. Malacara and F. Roddier, “Optical shop testing,” Appl. Opt. 97, 454–464 (1978).
[Crossref]

Sato, K.

M. Nagase, D. Iwai, and K. Sato, “Dynamic defocus and occlusion compensation of projected imagery by model-based optimal projector selection in multi-projection environment,” Virtual Real. 15(2-3), 119–132 (2011).
[Crossref]

Seah, H. S.

Silva, A.

Su, X.

X. Su and Q. Zhang, “Dynamic 3-d shape measurement method: A review,” Opt. & Lasers Eng. 48(2), 191–204 (2010).
[Crossref]

T. Xian and X. Su, “Area modulation grating for sinusoidal structure illumination on phase-measuring profilometry,” Appl. Opt. 40(8), 1201–1206 (2001).
[Crossref]

X. Su, W. Zhou, B. G. Von, and D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a ronchi grating,” Opt. Commun. 94(6), 561–573 (1992).
[Crossref]

Suguro, A.

H. Fujita, K. Yamatan, M. Yamamoto, Y. Otani, A. Suguro, S. Morokawa, and T. Yoshizawa, “Three-dimensional profilometry using liquid crystal grating,” Proc. SPIE - The Int. Soc. for Opt. Eng. pp. 51–60 (2003).

Sui, X.

Tao, T.

Von, B. G.

X. Su, W. Zhou, B. G. Von, and D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a ronchi grating,” Opt. Commun. 94(6), 561–573 (1992).
[Crossref]

Vukicevic, D.

X. Su, W. Zhou, B. G. Von, and D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a ronchi grating,” Opt. Commun. 94(6), 561–573 (1992).
[Crossref]

Wang, X.

Wang, Y.

William, L.

Wu, Y.

Xian, T.

Xiao, Y.

Yamamoto, M.

H. Fujita, K. Yamatan, M. Yamamoto, Y. Otani, A. Suguro, S. Morokawa, and T. Yoshizawa, “Three-dimensional profilometry using liquid crystal grating,” Proc. SPIE - The Int. Soc. for Opt. Eng. pp. 51–60 (2003).

Yamatan, K.

H. Fujita, K. Yamatan, M. Yamamoto, Y. Otani, A. Suguro, S. Morokawa, and T. Yoshizawa, “Three-dimensional profilometry using liquid crystal grating,” Proc. SPIE - The Int. Soc. for Opt. Eng. pp. 51–60 (2003).

Yoshizawa, T.

H. Fujita, K. Yamatan, M. Yamamoto, Y. Otani, A. Suguro, S. Morokawa, and T. Yoshizawa, “Three-dimensional profilometry using liquid crystal grating,” Proc. SPIE - The Int. Soc. for Opt. Eng. pp. 51–60 (2003).

Zhang, M.

Zhang, Q.

X. Su and Q. Zhang, “Dynamic 3-d shape measurement method: A review,” Opt. & Lasers Eng. 48(2), 191–204 (2010).
[Crossref]

Zhang, S.

Zhao, H.

Zheng, D.

Zhou, W.

X. Su, W. Zhou, B. G. Von, and D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a ronchi grating,” Opt. Commun. 94(6), 561–573 (1992).
[Crossref]

Zuo, C.

Appl. Opt. (8)

Opt. & Lasers Eng. (5)

W. Lohry and S. Zhang, “3d shape measurement with 2d area modulated binary patterns,” Opt. & Lasers Eng. 50(7), 917–921 (2012).
[Crossref]

S. S. Gorthi and P. Rastogi, “Fringe projection techniques: Whither we are?” Opt. & Lasers Eng. 48(2), 133–140 (2010).
[Crossref]

X. Su and Q. Zhang, “Dynamic 3-d shape measurement method: A review,” Opt. & Lasers Eng. 48(2), 191–204 (2010).
[Crossref]

S. Zhang, “High-speed 3d shape measurement with structured light methods: A review,” Opt. & Lasers Eng. 106, 119–131 (2018).
[Crossref]

B. Li and S. Zhang, “Microscopic structured light 3d profilometry: Binary defocusing technique vs. sinusoidal fringe projection,” Opt. & Lasers Eng. 96, 117–123 (2017).
[Crossref]

Opt. Commun. (1)

X. Su, W. Zhou, B. G. Von, and D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a ronchi grating,” Opt. Commun. 94(6), 561–573 (1992).
[Crossref]

Opt. Express (4)

Opt. Lett. (5)

Pattern Recognit. Lett. (1)

V. P. Namboodiri and S. Chaudhuri, “On defocus, diffusion and depth estimation,” Pattern Recognit. Lett. 28(3), 311–319 (2007).
[Crossref]

Virtual Real. (1)

M. Nagase, D. Iwai, and K. Sato, “Dynamic defocus and occlusion compensation of projected imagery by model-based optimal projector selection in multi-projection environment,” Virtual Real. 15(2-3), 119–132 (2011).
[Crossref]

Other (1)

H. Fujita, K. Yamatan, M. Yamamoto, Y. Otani, A. Suguro, S. Morokawa, and T. Yoshizawa, “Three-dimensional profilometry using liquid crystal grating,” Proc. SPIE - The Int. Soc. for Opt. Eng. pp. 51–60 (2003).

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Figures (10)

Fig. 1.
Fig. 1. (a) Projector’s defocusing effect corresponding to depth $z$; (b) Defocus kernel $\sigma$ curve as a function of depth $z$: $z_1\,<\,z_2\,<\,z_3\,<\,z_f\,<\,z_4\,<\,z_5\,<\,z_6$.
Fig. 2.
Fig. 2. Multi-frequency phase merging: $\sigma _1, \sigma _2$ are the defocusing kernels at depth $z_1$ and $z_2$, and $\omega _1, \omega _2$ are the fundamental frequencies for fringe periods $T_1, T_2$ with $\omega = \frac {2\pi }{T}$.
Fig. 3.
Fig. 3. Steps for optimal frequency determination.
Fig. 4.
Fig. 4. Simulation results for optimal frequency determination: (a) When $T_1$ = 18 pixels and $T_2$ = 24 pixels; (b) When $T_1$ = 18 pixels and $T_2$ = 36 pixels; (c) When $T_1$ = 18 pixels and $T_2$ = 54 pixels; (d) When $T_1$ = 18 pixels, $T_2$ = 36 pixels and $T_3$ = 54 pixels.
Fig. 5.
Fig. 5. Defocusing degree maps for phase merging: (a) LDR scene consisting of two portrait sculptures of which the male one is placed at the distance of about 23 cm from the focus plane and the female one is placed at the distance of about 52.5 cm from the focus plane; (b) Fringe pattern when $T_1$ = 18 pixels; (c) Corresponding defocusing degree map when $T_1$ = 18 pixels; (d) Fringe pattern when $T_2$ = 36 pixels; (e) Corresponding defocusing degree map when $T_2$ = 36 pixels; (f) Merged fringe pattern calculated by aforementioned defocusing degree maps when $T_1$ = 18 pixels and $T_2$ = 36 pixels.
Fig. 6.
Fig. 6. Experimental setup.
Fig. 7.
Fig. 7. Phase RMS errors in different depth ranges for different fringe period combinations: (a) $T_1$ = 18 pixels and $T_2$ = 24 pixels; (b) $T_1$ = 18 pixels and $T_2$ = 36 pixels; (c) $T_1$ = 18 pixels and $T_2$ = 54 pixels; (d) $T_1$ = 18 pixels, $T_2$ = 36 pixels and $T_3$ = 54 pixels.
Fig. 8.
Fig. 8. 3D reconstruction results for two flat boxes in large depth range: (a) Fringe pattern of $T_1 = 18$ pixels; (b) Corresponding 3D result of (a); (c) Fringe pattern of $T_2 = 36$ pixels; (d) Corresponding 3D result of (c); (e) Merged fringe pattern; (f) Corresponding 3D result based on MFPM method; (g) LDR scene consisting of two boxes; (h) Ideal 3D reconstruction result.
Fig. 9.
Fig. 9. Accuracy evaluation for the MFPM method: (a) Cross sections of absolute phase maps for the upper surface; (b) Corresponding phase error plots when comparing with the ideal phase map; (c)–(d) The cross sections of absolute phase maps and phase error for the lower surface.
Fig. 10.
Fig. 10. 3D reconstruction results for complex sculptures in large depth range. (a) Fringe pattern when $T_1 = 18$ pixels; (b) Corresponding 3D reconstructed result when $T_1 = 18$ pixels; (c) Fringe pattern when $T_2 = 36$ pixels; (d) Corresponding 3D reconstructed result when $T_2 = 36$ pixels; (e) Merged fringe pattern when $T_1 = 18$ pixels and $T_2 = 36$ pixels; (f) Corresponding 3D reconstructed result based on MFPM method; (g) Zoom-in 3D plot for the male statue when $T_1 = 18$ pixels; (h) Zoom-in 3D plot for the female statue when $T_1 = 18$ pixels; (i) Zoom-in 3D plot for the male statue when $T_2 = 36$ pixels; (j) Zoom-in 3D plot for the female statue when $T_2 = 36$ pixels; (k) Zoom-in 3D plot for the male statue based on MFPM method; (l) Zoom-in 3D plot for the female statue based on MFPM method.

Equations (10)

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In(x,y)=I(x,y)+I(x,y)cos(ϕ(x,y)+2nπN),n=0,1,2,,N1.
ϕ(x,y)=tan1[n=0N1In(x,y)sin2nπNn=0N1In(x,y)cos2nπN].
γ(x,y)=2(n=0N1In(x,y)sin2nπN)2+(n=0N1In(x,y)cos2nπN)2n=0N1In(x,y).
Bi(xp,yp)=I(xp,yp)+I(xp,yp)k=012k+1cos[(2k+1)(ϕ(xp,yp)+2πiN)],
G(xp,yp)=12πσ2exp2+yp22σ2G(ω)=eσ2ω22,
σ=kR(z)=k[|D2(zzf1)|+rzv].
γnor(x,y)=γ(x,y)γmax(x,y)=γ(x,y)×I(x,y)Iw(x,y)I(x,y).
{Mt(x,y)=0,ifγnort(x,y)<thresh;Mt(x,y)=1,otherwise.
Φnort(x,y)=tmin(T)Φt(x,y).
ΦLDR(x,y)=Φnortopt(x,y).

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