Abstract

Typical single-pixel imaging techniques inherently consume a large number of measurements to reconstruct a high-quality and high-resolution image. Three-dimensional (3-D) single-pixel imaging with both high sampling efficiency and high depth accuracy remains a challenge. We implement fringe projection virtually by exploiting Helmholtz reciprocity. Depth information is modulated into a deformed fringe pattern whose Fourier spectrum is sampled by using sinusoidal intensity pattern illumination and single-pixel detection. The fringe pattern has a highly focused first-order component in its Fourier spectrum, which allows us to efficiently acquire the depth information from measurements far fewer than illumination pattern pixels. The 3-D information is retrieved through Fourier analysis. We experimentally obtained a 3-D reconstruction of a complex object with 599×599 effective pixels, achieving a measurement-to-pixel ratio of 5.78%. The depth accuracy is evaluated at sub-millimetric level by using a test object.

© 2016 Optical Society of America

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References

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2016 (1)

2015 (4)

W. Yu, X. Yao, X. Liu, L. Li, and G. Zhai, Appl. Opt. 54, 363 (2015).
[Crossref]

Z. Zhang, X. Ma, and J. Zhong, Nat. Commun. 6, 6225 (2015).
[Crossref]

S. Welsh, M. P. Edgar, R. Bowman, B. Sun, and M. J. Padgett, J. Opt. 17, 025705 (2015).
[Crossref]

M. P. Edgar, G. M. Gibson, R. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. Welsh, and M. J. Padgett, Sci. Rep. 5, 10669 (2015).
[Crossref]

2013 (2)

G. Howland, D. Lum, M. Ware, and J. Howell, Opt. Express 21, 23822 (2013).
[Crossref]

B. Sun, M. Edgar, R. Bowman, L. Vittert, S. Welsh, A. Bowman, and M. Padgett, Science 340, 844 (2013).
[Crossref]

2012 (1)

2011 (1)

2008 (2)

J. Shapiro, Phys. Rev. A 78, 061802 (2008).
[Crossref]

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, IEEE Signal Process. Mag. 25(2), 83 (2008).
[Crossref]

2007 (1)

2005 (2)

J. Zhong and J. Weng, Opt. Lett. 30, 2560 (2005).
[Crossref]

P. Sen, B. Chen, G. Garg, S. Marschner, M. Horowitz, M. Levoy, and H. Lensch, ACM Trans. Graph. 24, 745 (2005).
[Crossref]

2004 (1)

2002 (1)

S. Bennink, S. Bentley, and R. Boyd, Phys. Rev. Lett. 89, 113601 (2002).
[Crossref]

1995 (1)

T. Pittman, Phys. Rev. A 52, R3429 (1995).
[Crossref]

1983 (1)

Baraniuk, R.

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, IEEE Signal Process. Mag. 25(2), 83 (2008).
[Crossref]

Bennink, S.

S. Bennink, S. Bentley, and R. Boyd, Phys. Rev. Lett. 89, 113601 (2002).
[Crossref]

Bentley, S.

S. Bennink, S. Bentley, and R. Boyd, Phys. Rev. Lett. 89, 113601 (2002).
[Crossref]

Born, M.

M. Born and E. Wolf, in Principles of Optics (Pergamon, 1959).

Bowman, A.

B. Sun, M. Edgar, R. Bowman, L. Vittert, S. Welsh, A. Bowman, and M. Padgett, Science 340, 844 (2013).
[Crossref]

Bowman, R.

S. Welsh, M. P. Edgar, R. Bowman, B. Sun, and M. J. Padgett, J. Opt. 17, 025705 (2015).
[Crossref]

M. P. Edgar, G. M. Gibson, R. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. Welsh, and M. J. Padgett, Sci. Rep. 5, 10669 (2015).
[Crossref]

B. Sun, M. Edgar, R. Bowman, L. Vittert, S. Welsh, A. Bowman, and M. Padgett, Science 340, 844 (2013).
[Crossref]

Boyd, R.

S. Bennink, S. Bentley, and R. Boyd, Phys. Rev. Lett. 89, 113601 (2002).
[Crossref]

Chen, B.

P. Sen, B. Chen, G. Garg, S. Marschner, M. Horowitz, M. Levoy, and H. Lensch, ACM Trans. Graph. 24, 745 (2005).
[Crossref]

Chen, M.

Clemente, P.

Davenport, M.

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, IEEE Signal Process. Mag. 25(2), 83 (2008).
[Crossref]

Du, H.

Duarte, M.

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, IEEE Signal Process. Mag. 25(2), 83 (2008).
[Crossref]

Edgar, M.

B. Sun, M. Edgar, R. Bowman, L. Vittert, S. Welsh, A. Bowman, and M. Padgett, Science 340, 844 (2013).
[Crossref]

Edgar, M. P.

M. P. Edgar, G. M. Gibson, R. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. Welsh, and M. J. Padgett, Sci. Rep. 5, 10669 (2015).
[Crossref]

S. Welsh, M. P. Edgar, R. Bowman, B. Sun, and M. J. Padgett, J. Opt. 17, 025705 (2015).
[Crossref]

Garg, G.

P. Sen, B. Chen, G. Garg, S. Marschner, M. Horowitz, M. Levoy, and H. Lensch, ACM Trans. Graph. 24, 745 (2005).
[Crossref]

Geng, J.

Gibson, G. M.

M. P. Edgar, G. M. Gibson, R. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. Welsh, and M. J. Padgett, Sci. Rep. 5, 10669 (2015).
[Crossref]

Guo, H.

He, H.

Horowitz, M.

P. Sen, B. Chen, G. Garg, S. Marschner, M. Horowitz, M. Levoy, and H. Lensch, ACM Trans. Graph. 24, 745 (2005).
[Crossref]

Howell, J.

Howland, G.

Kelly, K.

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, IEEE Signal Process. Mag. 25(2), 83 (2008).
[Crossref]

Lancis, J.

Laska, J.

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, IEEE Signal Process. Mag. 25(2), 83 (2008).
[Crossref]

Lensch, H.

P. Sen, B. Chen, G. Garg, S. Marschner, M. Horowitz, M. Levoy, and H. Lensch, ACM Trans. Graph. 24, 745 (2005).
[Crossref]

Levoy, M.

P. Sen, B. Chen, G. Garg, S. Marschner, M. Horowitz, M. Levoy, and H. Lensch, ACM Trans. Graph. 24, 745 (2005).
[Crossref]

Li, L.

Liu, X.

Lum, D.

Ma, X.

Z. Zhang, X. Ma, and J. Zhong, Nat. Commun. 6, 6225 (2015).
[Crossref]

Marschner, S.

P. Sen, B. Chen, G. Garg, S. Marschner, M. Horowitz, M. Levoy, and H. Lensch, ACM Trans. Graph. 24, 745 (2005).
[Crossref]

Mitchell, K. J.

M. P. Edgar, G. M. Gibson, R. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. Welsh, and M. J. Padgett, Sci. Rep. 5, 10669 (2015).
[Crossref]

Mutoh, K.

Padgett, M.

B. Sun, M. Edgar, R. Bowman, L. Vittert, S. Welsh, A. Bowman, and M. Padgett, Science 340, 844 (2013).
[Crossref]

Padgett, M. J.

M. P. Edgar, G. M. Gibson, R. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. Welsh, and M. J. Padgett, Sci. Rep. 5, 10669 (2015).
[Crossref]

S. Welsh, M. P. Edgar, R. Bowman, B. Sun, and M. J. Padgett, J. Opt. 17, 025705 (2015).
[Crossref]

Pan, B.

Pan, T.

Pittman, T.

T. Pittman, Phys. Rev. A 52, R3429 (1995).
[Crossref]

Pla, F.

Radwell, N.

M. P. Edgar, G. M. Gibson, R. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. Welsh, and M. J. Padgett, Sci. Rep. 5, 10669 (2015).
[Crossref]

Salvador-Balaguer, E.

Sen, P.

P. Sen, B. Chen, G. Garg, S. Marschner, M. Horowitz, M. Levoy, and H. Lensch, ACM Trans. Graph. 24, 745 (2005).
[Crossref]

Shapiro, J.

J. Shapiro, Phys. Rev. A 78, 061802 (2008).
[Crossref]

Sun, B.

S. Welsh, M. P. Edgar, R. Bowman, B. Sun, and M. J. Padgett, J. Opt. 17, 025705 (2015).
[Crossref]

M. P. Edgar, G. M. Gibson, R. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. Welsh, and M. J. Padgett, Sci. Rep. 5, 10669 (2015).
[Crossref]

B. Sun, M. Edgar, R. Bowman, L. Vittert, S. Welsh, A. Bowman, and M. Padgett, Science 340, 844 (2013).
[Crossref]

Sun, T.

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, IEEE Signal Process. Mag. 25(2), 83 (2008).
[Crossref]

Tajauerce, E.

Takeda, M.

Takhar, D.

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, IEEE Signal Process. Mag. 25(2), 83 (2008).
[Crossref]

Vittert, L.

B. Sun, M. Edgar, R. Bowman, L. Vittert, S. Welsh, A. Bowman, and M. Padgett, Science 340, 844 (2013).
[Crossref]

Vo, M.

Wang, Z.

Ware, M.

Welsh, S.

M. P. Edgar, G. M. Gibson, R. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. Welsh, and M. J. Padgett, Sci. Rep. 5, 10669 (2015).
[Crossref]

S. Welsh, M. P. Edgar, R. Bowman, B. Sun, and M. J. Padgett, J. Opt. 17, 025705 (2015).
[Crossref]

B. Sun, M. Edgar, R. Bowman, L. Vittert, S. Welsh, A. Bowman, and M. Padgett, Science 340, 844 (2013).
[Crossref]

Weng, J.

Wolf, E.

M. Born and E. Wolf, in Principles of Optics (Pergamon, 1959).

Yao, X.

Yu, W.

Zhai, G.

Zhang, Z.

Z. Zhang, X. Ma, and J. Zhong, Nat. Commun. 6, 6225 (2015).
[Crossref]

Zhong, J.

Z. Zhang, X. Ma, and J. Zhong, Nat. Commun. 6, 6225 (2015).
[Crossref]

J. Zhong and J. Weng, Opt. Lett. 30, 2560 (2005).
[Crossref]

ACM Trans. Graph. (1)

P. Sen, B. Chen, G. Garg, S. Marschner, M. Horowitz, M. Levoy, and H. Lensch, ACM Trans. Graph. 24, 745 (2005).
[Crossref]

Adv. Opt. Photon. (1)

Appl. Opt. (3)

IEEE Signal Process. Mag. (1)

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, IEEE Signal Process. Mag. 25(2), 83 (2008).
[Crossref]

J. Display Technol. (1)

J. Opt. (1)

S. Welsh, M. P. Edgar, R. Bowman, B. Sun, and M. J. Padgett, J. Opt. 17, 025705 (2015).
[Crossref]

Nat. Commun. (1)

Z. Zhang, X. Ma, and J. Zhong, Nat. Commun. 6, 6225 (2015).
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. A (2)

J. Shapiro, Phys. Rev. A 78, 061802 (2008).
[Crossref]

T. Pittman, Phys. Rev. A 52, R3429 (1995).
[Crossref]

Phys. Rev. Lett. (1)

S. Bennink, S. Bentley, and R. Boyd, Phys. Rev. Lett. 89, 113601 (2002).
[Crossref]

Sci. Rep. (1)

M. P. Edgar, G. M. Gibson, R. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. Welsh, and M. J. Padgett, Sci. Rep. 5, 10669 (2015).
[Crossref]

Science (1)

B. Sun, M. Edgar, R. Bowman, L. Vittert, S. Welsh, A. Bowman, and M. Padgett, Science 340, 844 (2013).
[Crossref]

Other (2)

M. Sun, M. Edgar, G. Gibson, B. Sun, N. Radwell, R. Lamb, and M. Padgett, “Single-pixel 3D imaging with time-based depth resolution,” (2016), http://arxiv.org/abs/1603.00726 .

M. Born and E. Wolf, in Principles of Optics (Pergamon, 1959).

Supplementary Material (1)

NameDescription
» Visualization 1: MP4 (14074 KB)      Illustration of the proposed technique.

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Figures (4)

Fig. 1.
Fig. 1. (a) Experimental configuration and (b) its reciprocal.
Fig. 2.
Fig. 2. (a) Fully sampled Fourier spectrum (modulus) and (b) the corresponding reconstructed image. (c) Fourier spectrum with only the zero-order component and (d) the corresponding reconstructed image. (e) Fourier spectrum with only the first-order component and (f) the corresponding reconstructed image. Scale bar = 20    mm . Note that we show the absolute value of the Fourier spectra on a logarithm scale to render them visible.
Fig. 3.
Fig. 3. (a) Image of the prism and the hemisphere. (b) Deformed fringe pattern of the hemisphere, reconstructed from 13,316 measurements ( MPR = 1 % ). (c) Estimated fringe phase map. (d) 3-D reconstruction. (e) Derived height distribution versus true values at the row that crosses the center of the hemisphere and (f) the corresponding height error distribution.
Fig. 4.
Fig. 4. (a) Image of the target object. (b) First-order component marginally sampled from 20,740 measurements ( MPR = 5.78 % ). (c) Estimated fringe phase map. (d) 3-D reconstruction. The result is also shown in Visualization 1.

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