Abstract

This paper presents a method to unwrap phase pixel by pixel by solely using geometric constraints of the structured light system without requiring additional image acquisition or another camera. Specifically, an artificial absolute phase map, Φmin, at a given virtual depth plane z = zmin, is created from geometric constraints of the calibrated structured light system; the wrapped phase is pixel-by-pixel unwrapped by referring to Φmin. Since Φmin is defined in the projector space, the unwrapped phase obtained from this method is absolute for each pixel. Experimental results demonstrate the success of this proposed novel absolute phase unwrapping method.

© 2016 Optical Society of America

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References

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2016 (2)

K. Song, S. Hu, X. Wen, and Y. Yan, “Fast 3D shape measurement using fourier transform profilometry without phase unwrapping,” Opt. Laser. Eng. 84, 74–81 (2016).
[Crossref]

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

2015 (1)

C. Zhou, T. Liu, S. Si, J. Xu, Y. Liu, and Z. Lei, “An improved stair phase encoding method for absolute phase retrieval,” Opt. Laser Eng. 66, 269–278 (2015).
[Crossref]

2014 (3)

2013 (2)

Z. Li, K. Zhong, Y. Li, X. Zhou, and Y. Shi, “Multiview phase shifting: a full-resolution and high-speed 3d measurement framework for arbitrary shape dynamic objects,” Opt. Lett. 38, 1389–1391 (2013).
[Crossref] [PubMed]

K. Zhong, Z. Li, Y. Shi, C. Wang, and Y. Lei, “Fast phase measurement profilometry for arbitrary shape objects without phase unwrapping,” Opt. Laser Eng. 51, 1213–1222 (2013).
[Crossref]

2012 (3)

2010 (2)

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

S. Zhang, “Flexible 3d shape measurement using projector defocusing: Extended measurement range,” Opt. Lett. 35, 931–933 (2010).

2009 (1)

Y. Li, H. Jin, and H. Wang, “Three-dimensional shape measurement using binary spatio-temporal encoded illumination,” J. Opt. A, Pure Appl. Opt. 11, 075502 (2009).
[Crossref]

2006 (1)

S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45, 083601 (2006).
[Crossref]

2004 (2)

Q. Kemao, “Windowed fourier transform for fringe pattern analysis,” Appl. Opt. 43, 2695–2702 (2004).
[Crossref] [PubMed]

X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Laser Eng. 42, 245–261 (2004).
[Crossref]

2003 (1)

D. P. Towers, J. D. C. Jones, and C. E. Towers, “Optimum frequency selection in multi-frequency interferometry,” Opt. Lett. 28, 1–3 (2003).
[Crossref]

1999 (1)

1985 (1)

1984 (1)

1983 (1)

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. Laser. Eng. 84, 84–103 (2016).
[Crossref]

Bräuer-Burchardt, C.

C. Bräuer-Burchardt, P. Kühmstedt, and G. Notni, “Code minimization for fringe projection based 3d stereo sensors by calibration improvement,” Tech. rep., arXiv (2014). (available at arXiv:1404.7298).

Carocci, M.

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. Laser. Eng. 84, 84–103 (2016).
[Crossref]

Chen, V.

N. Karpinsky, M. Hoke, V. Chen, and S. Zhang, “High-resolution, real-time three-dimensional shape measurement on graphics processing unit,” Opt. Eng. 53, 024105 (2014).
[Crossref]

W. Lohry, V. Chen, and S. Zhang, “Absolute three-dimensional shape measurement using coded fringe patterns without phase unwrapping or projector calibration,” Opt. Express 22, 1287–1301 (2014).
[Crossref] [PubMed]

Chen, W.

X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Laser Eng. 42, 245–261 (2004).
[Crossref]

Cheng, Y.-Y.

Hoke, M.

N. Karpinsky, M. Hoke, V. Chen, and S. Zhang, “High-resolution, real-time three-dimensional shape measurement on graphics processing unit,” Opt. Eng. 53, 024105 (2014).
[Crossref]

Hu, S.

K. Song, S. Hu, X. Wen, and Y. Yan, “Fast 3D shape measurement using fourier transform profilometry without phase unwrapping,” Opt. Laser. Eng. 84, 74–81 (2016).
[Crossref]

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. Laser. Eng. 84, 84–103 (2016).
[Crossref]

Huang, P. S.

S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45, 083601 (2006).
[Crossref]

Jin, H.

Y. Li, H. Jin, and H. Wang, “Three-dimensional shape measurement using binary spatio-temporal encoded illumination,” J. Opt. A, Pure Appl. Opt. 11, 075502 (2009).
[Crossref]

Jones, J. D. C.

D. P. Towers, J. D. C. Jones, and C. E. Towers, “Optimum frequency selection in multi-frequency interferometry,” Opt. Lett. 28, 1–3 (2003).
[Crossref]

Karpinsky, N.

N. Karpinsky, M. Hoke, V. Chen, and S. Zhang, “High-resolution, real-time three-dimensional shape measurement on graphics processing unit,” Opt. Eng. 53, 024105 (2014).
[Crossref]

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]

Kemao, Q.

Kühmstedt, P.

C. Bräuer-Burchardt, P. Kühmstedt, and G. Notni, “Code minimization for fringe projection based 3d stereo sensors by calibration improvement,” Tech. rep., arXiv (2014). (available at arXiv:1404.7298).

Lei, Y.

K. Zhong, Z. Li, Y. Shi, C. Wang, and Y. Lei, “Fast phase measurement profilometry for arbitrary shape objects without phase unwrapping,” Opt. Laser Eng. 51, 1213–1222 (2013).
[Crossref]

Lei, Z.

C. Zhou, T. Liu, S. Si, J. Xu, Y. Liu, and Z. Lei, “An improved stair phase encoding method for absolute phase retrieval,” Opt. Laser Eng. 66, 269–278 (2015).
[Crossref]

C. Zhou, T. Liu, S. Si, J. Xu, Y. Liu, and Z. Lei, “Phase coding method for absolute phase retrieval with a large number of codewords,” Opt. Express 20, 24139–24150 (2012).
[Crossref]

Li, B.

Li, Y.

Z. Li, K. Zhong, Y. Li, X. Zhou, and Y. Shi, “Multiview phase shifting: a full-resolution and high-speed 3d measurement framework for arbitrary shape dynamic objects,” Opt. Lett. 38, 1389–1391 (2013).
[Crossref] [PubMed]

Y. Li, H. Jin, and H. Wang, “Three-dimensional shape measurement using binary spatio-temporal encoded illumination,” J. Opt. A, Pure Appl. Opt. 11, 075502 (2009).
[Crossref]

Li, Z.

K. Zhong, Z. Li, Y. Shi, C. Wang, and Y. Lei, “Fast phase measurement profilometry for arbitrary shape objects without phase unwrapping,” Opt. Laser Eng. 51, 1213–1222 (2013).
[Crossref]

Z. Li, K. Zhong, Y. Li, X. Zhou, and Y. Shi, “Multiview phase shifting: a full-resolution and high-speed 3d measurement framework for arbitrary shape dynamic objects,” Opt. Lett. 38, 1389–1391 (2013).
[Crossref] [PubMed]

Liu, T.

C. Zhou, T. Liu, S. Si, J. Xu, Y. Liu, and Z. Lei, “An improved stair phase encoding method for absolute phase retrieval,” Opt. Laser Eng. 66, 269–278 (2015).
[Crossref]

C. Zhou, T. Liu, S. Si, J. Xu, Y. Liu, and Z. Lei, “Phase coding method for absolute phase retrieval with a large number of codewords,” Opt. Express 20, 24139–24150 (2012).
[Crossref]

Liu, Y.

C. Zhou, T. Liu, S. Si, J. Xu, Y. Liu, and Z. Lei, “An improved stair phase encoding method for absolute phase retrieval,” Opt. Laser Eng. 66, 269–278 (2015).
[Crossref]

C. Zhou, T. Liu, S. Si, J. Xu, Y. Liu, and Z. Lei, “Phase coding method for absolute phase retrieval with a large number of codewords,” Opt. Express 20, 24139–24150 (2012).
[Crossref]

Lohry, W.

Mutoh, K.

Notni, G.

C. Bräuer-Burchardt, P. Kühmstedt, and G. Notni, “Code minimization for fringe projection based 3d stereo sensors by calibration improvement,” Tech. rep., arXiv (2014). (available at arXiv:1404.7298).

Rodella, R.

Sansoni, G.

Shi, Y.

Z. Li, K. Zhong, Y. Li, X. Zhou, and Y. Shi, “Multiview phase shifting: a full-resolution and high-speed 3d measurement framework for arbitrary shape dynamic objects,” Opt. Lett. 38, 1389–1391 (2013).
[Crossref] [PubMed]

K. Zhong, Z. Li, Y. Shi, C. Wang, and Y. Lei, “Fast phase measurement profilometry for arbitrary shape objects without phase unwrapping,” Opt. Laser Eng. 51, 1213–1222 (2013).
[Crossref]

Si, S.

C. Zhou, T. Liu, S. Si, J. Xu, Y. Liu, and Z. Lei, “An improved stair phase encoding method for absolute phase retrieval,” Opt. Laser Eng. 66, 269–278 (2015).
[Crossref]

C. Zhou, T. Liu, S. Si, J. Xu, Y. Liu, and Z. Lei, “Phase coding method for absolute phase retrieval with a large number of codewords,” Opt. Express 20, 24139–24150 (2012).
[Crossref]

Song, K.

K. Song, S. Hu, X. Wen, and Y. Yan, “Fast 3D shape measurement using fourier transform profilometry without phase unwrapping,” Opt. Laser. Eng. 84, 74–81 (2016).
[Crossref]

Su, X.

Q. Zhang, X. Su, L. Xiang, and X. Sun, “3-D shape measurement based on complementary gray-code light,” Opt. Laser Eng. 50, 574–579 (2012).
[Crossref]

X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Laser Eng. 42, 245–261 (2004).
[Crossref]

Sun, X.

Q. Zhang, X. Su, L. Xiang, and X. Sun, “3-D shape measurement based on complementary gray-code light,” Opt. Laser Eng. 50, 574–579 (2012).
[Crossref]

Takeda, M.

Towers, C. E.

D. P. Towers, J. D. C. Jones, and C. E. Towers, “Optimum frequency selection in multi-frequency interferometry,” Opt. Lett. 28, 1–3 (2003).
[Crossref]

Towers, D. P.

D. P. Towers, J. D. C. Jones, and C. E. Towers, “Optimum frequency selection in multi-frequency interferometry,” Opt. Lett. 28, 1–3 (2003).
[Crossref]

Wang, C.

K. Zhong, Z. Li, Y. Shi, C. Wang, and Y. Lei, “Fast phase measurement profilometry for arbitrary shape objects without phase unwrapping,” Opt. Laser Eng. 51, 1213–1222 (2013).
[Crossref]

Wang, H.

Y. Li, H. Jin, and H. Wang, “Three-dimensional shape measurement using binary spatio-temporal encoded illumination,” J. Opt. A, Pure Appl. Opt. 11, 075502 (2009).
[Crossref]

Wang, Y.

Wen, X.

K. Song, S. Hu, X. Wen, and Y. Yan, “Fast 3D shape measurement using fourier transform profilometry without phase unwrapping,” Opt. Laser. Eng. 84, 74–81 (2016).
[Crossref]

Wyant, J. C.

Xiang, L.

Q. Zhang, X. Su, L. Xiang, and X. Sun, “3-D shape measurement based on complementary gray-code light,” Opt. Laser Eng. 50, 574–579 (2012).
[Crossref]

Xu, J.

C. Zhou, T. Liu, S. Si, J. Xu, Y. Liu, and Z. Lei, “An improved stair phase encoding method for absolute phase retrieval,” Opt. Laser Eng. 66, 269–278 (2015).
[Crossref]

C. Zhou, T. Liu, S. Si, J. Xu, Y. Liu, and Z. Lei, “Phase coding method for absolute phase retrieval with a large number of codewords,” Opt. Express 20, 24139–24150 (2012).
[Crossref]

Yan, Y.

K. Song, S. Hu, X. Wen, and Y. Yan, “Fast 3D shape measurement using fourier transform profilometry without phase unwrapping,” Opt. Laser. Eng. 84, 74–81 (2016).
[Crossref]

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. Laser. Eng. 84, 84–103 (2016).
[Crossref]

Zhang, Q.

Q. Zhang, X. Su, L. Xiang, and X. Sun, “3-D shape measurement based on complementary gray-code light,” Opt. Laser Eng. 50, 574–579 (2012).
[Crossref]

Zhang, S.

Zhong, K.

K. Zhong, Z. Li, Y. Shi, C. Wang, and Y. Lei, “Fast phase measurement profilometry for arbitrary shape objects without phase unwrapping,” Opt. Laser Eng. 51, 1213–1222 (2013).
[Crossref]

Z. Li, K. Zhong, Y. Li, X. Zhou, and Y. Shi, “Multiview phase shifting: a full-resolution and high-speed 3d measurement framework for arbitrary shape dynamic objects,” Opt. Lett. 38, 1389–1391 (2013).
[Crossref] [PubMed]

Zhou, C.

C. Zhou, T. Liu, S. Si, J. Xu, Y. Liu, and Z. Lei, “An improved stair phase encoding method for absolute phase retrieval,” Opt. Laser Eng. 66, 269–278 (2015).
[Crossref]

C. Zhou, T. Liu, S. Si, J. Xu, Y. Liu, and Z. Lei, “Phase coding method for absolute phase retrieval with a large number of codewords,” Opt. Express 20, 24139–24150 (2012).
[Crossref]

Zhou, X.

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. Laser. Eng. 84, 84–103 (2016).
[Crossref]

Appl. Opt. (6)

J. Opt. A, Pure Appl. Opt. (1)

Y. Li, H. Jin, and H. Wang, “Three-dimensional shape measurement using binary spatio-temporal encoded illumination,” J. Opt. A, Pure Appl. Opt. 11, 075502 (2009).
[Crossref]

Opt. Eng. (2)

S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45, 083601 (2006).
[Crossref]

N. Karpinsky, M. Hoke, V. Chen, and S. Zhang, “High-resolution, real-time three-dimensional shape measurement on graphics processing unit,” Opt. Eng. 53, 024105 (2014).
[Crossref]

Opt. Express (2)

Opt. Laser Eng. (5)

C. Zhou, T. Liu, S. Si, J. Xu, Y. Liu, and Z. Lei, “An improved stair phase encoding method for absolute phase retrieval,” Opt. Laser Eng. 66, 269–278 (2015).
[Crossref]

K. Zhong, Z. Li, Y. Shi, C. Wang, and Y. Lei, “Fast phase measurement profilometry for arbitrary shape objects without phase unwrapping,” Opt. Laser Eng. 51, 1213–1222 (2013).
[Crossref]

Q. Zhang, X. Su, L. Xiang, and X. Sun, “3-D shape measurement based on complementary gray-code light,” Opt. Laser Eng. 50, 574–579 (2012).
[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 W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Laser Eng. 42, 245–261 (2004).
[Crossref]

Opt. Laser. Eng. (2)

K. Song, S. Hu, X. Wen, and Y. Yan, “Fast 3D shape measurement using fourier transform profilometry without phase unwrapping,” Opt. Laser. Eng. 84, 74–81 (2016).
[Crossref]

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

Opt. Lett. (4)

Other (3)

C. Bräuer-Burchardt, P. Kühmstedt, and G. Notni, “Code minimization for fringe projection based 3d stereo sensors by calibration improvement,” Tech. rep., arXiv (2014). (available at arXiv:1404.7298).

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

D. C. Ghiglia and M. D. Pritt, eds., Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (John Wiley and Sons, 1998).

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Figures (10)

Fig. 1
Fig. 1 By using geometric constraint of a structured light system, one can establish the mapping between the camera image sensor (e.g., charge-coupled device, or CCD) and the corresponding region on the projector sensor (e.g., digital micro-mirror device, or DMD) for a virtual zmin plane.
Fig. 2
Fig. 2 Conceptual idea of removing 2π jump of low-frequency phase map by using the minimum phase map determined from geometric constraints. (a) Windowed regions shows phase map that is acquired by the camera at different depths z: the red dashed window shows zmin and the solid blue window shows z > zmin; (b) Corresponding Φmin and Φ defined on the projector; (c) Cross sections of Φmin and Φ and the phase maps with 2π discontinuities.
Fig. 3
Fig. 3 Determination of fringe order K, for multiple periods of fringe patterns. (a) Example of having three periods of fringe patterns; (b) Example of having four periods of fringe patterns.
Fig. 4
Fig. 4 Photograph of the experimental system. The experimental system only uses one single projector and one single camera that is the same as a typical structured light system.
Fig. 5
Fig. 5 Measurement result of a single 3D object. (a) Photograph of the measured object; (b) One of three phase-shifted fringe patterns; (c) Wrapped phase map ϕ; (d) Artificially generated minimum phase map, Φmin, using geometric constraints of the structured light system; (e) Unwrapped phase map Φ; (f) Reconstructed 3D geometry.
Fig. 6
Fig. 6 Measurement result of two separate 3D objects. (a) Photograph of the objects; (b) One of the three phase-shifted fringe patterns; (c) Wrapped phase map ϕ; (d) Unwrapped phase map Φ; (e) Reconstructed 3D geometry.
Fig. 7
Fig. 7 Measurement results using the conventional temporal phase unwrapping approach. (a) Photograph of the measured objects; (b) Wrapped phase map ϕ; (c) Unwrapped phase map by applying the conventional temporal phase unwrapping method; (d) Reconstructed 3D geometry by the conventional temporal phase unwrapping method without filter; (e) Unwrapped phase map using the conventional temporal phase unwrapping method after applying a 11 × 11 median filter; (f) Reconstructed 3D geometry by the conventional temporal phase unwrapping method with filter.
Fig. 8
Fig. 8 Measurement result by our proposed method. (a) Artificially generated minimum phase map, Φmin, using geometric constraints of the structured light system; (b) Unwrapped phase map Φ by our proposed method; (c) Reconstructed 3D geometry; (d) Unwrapped phase comparison in a cross section between our proposed method and the conventional phase unwrapping one.
Fig. 9
Fig. 9 Measurement result of a large sphere. For this large depth range sphere, our proposed method fails, while the conventional temporal phase unwrapping approach can work well. (a) Reconstructed 3D geometry by our proposed method; (b) Reconstructed 3D geometry by the conventional temporal phase unwrapping approach; (c) Cross section of the 3D geometry reconstructed by our proposed method; (d) Cross section of the 3D geometry reconstructed by the conventional temporal phase unwrapping approach.
Fig. 10
Fig. 10 The maximum depth range that the proposed absolute phase unwrapping method can handle is defined by the angle between the projector and the camera, the projection matrices for the camera and projector, as well as the projected fringe periods in space.

Equations (20)

Equations on this page are rendered with MathJax. Learn more.

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 ] .
Φ ( x , y ) = ϕ ( x , y ) + 2 π × K ( x , y ) .
s [ u v 1 ] = [ f u γ u 0 0 f v v 0 0 0 1 ] [ r 11 r 12 r 13 t 1 r 21 r 22 r 23 t 2 r 31 r 32 r 33 t 3 ] [ x w y w z w 1 ] .
P = [ f u γ u 0 0 f v v 0 0 0 1 ] [ r 11 r 12 r 13 t 1 r 21 r 22 r 23 t 2 r 31 r 32 r 33 t 3 ] ,
= [ p 11 p 12 p 13 p 14 p 21 p 22 p 23 p 24 p 31 p 32 p 33 p 34 ] .
s c [ u c v c 1 ] t = P c [ x w y w z w 1 ] t ,
s p [ u p v p 1 ] t = P p [ x w y w z w 1 ] t .
u p = Φ × T / ( 2 π ) ,
Φ = 2 π × u p / T
Φ m i n ( u c , v c ) = f ( z m i n , T , P c , P p ) .
[ x w y w ] = M 1 b ,
M = [ p 31 c u c p 11 c p 32 c u c p 12 c p 31 c v c p 21 c p 32 c v c p 22 c ] ,
b = [ p 14 c p 34 c u c ( p 33 c u c p 13 c ) z m i n p 24 c p 34 c v c ( p 33 c v c p 23 c ) z m i n ] .
s p [ u p v p 1 ] t = P p [ x w y w z m i n 1 ] t .
2 π × ( K 1 ) < Φ m i n ϕ < 2 π × K .
K ( x , y ) = c e i l [ Φ m i n ϕ 2 π ] .
Δ z m a x = Δ y / tan θ .

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