Abstract

The introduction of compressed sensing (CS) effectively pushes the development of single-pixel THz imaging due to reducing the experimental time and avoiding raster scanning. In this work, a CS method based on photoinduced dynamic masks is employed to recover a THz diffraction field in the time domain, and an inverse Fresnel diffraction (IFD) integral is adopted to remove the influence of the diffraction and reconstruct the sharp THz spectral image in a single-pixel THz imaging system. The compatibility of the CS and IFD algorithms are validated on the simulation and experiment. Besides, the reconstruction effects are also systematically analyzed by reducing the measurement number and varying the diffraction distance, respectively. This work supplies a novel thinking for improving the practicability of single-pixel THz imaging.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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2018 (1)

S. Augustin, S. Frohmann, P. Jung, and H. W. Hübers, “Mask responses for single-pixel terahertz imaging,” Sci. Rep. 8(1), 4886 (2018).
[Crossref] [PubMed]

2017 (1)

2016 (1)

R. I. Stantchev, B. Sun, S. M. Hornett, P. A. Hobson, G. M. Gibson, M. J. Padgett, and E. Hendry, “Noninvasive, near-field terahertz imaging of hidden objects using a single-pixel detector,” Sci. Adv. 2(6), e1600190 (2016).
[Crossref] [PubMed]

2015 (2)

K. Krügener, M. Schwerdtfeger, S. F. Busch, A. Soltani, E. Castro-Camus, M. Koch, and W. Viöl, “Terahertz meets sculptural and architectural art: Evaluation and conservation of stone objects with T-ray technology,” Sci. Rep. 5(1), 14842 (2015).
[Crossref] [PubMed]

Y. B. Ji, C. H. Park, H. Kim, S. H. Kim, G. M. Lee, S. K. Noh, T. I. Jeon, J. H. Son, Y. M. Huh, S. Haam, S. J. Oh, S. K. Lee, and J. S. Suh, “Feasibility of terahertz reflectometry for discrimination of human early gastric cancers,” Biomed. Opt. Express 6(4), 1398–1406 (2015).
[Crossref] [PubMed]

2014 (1)

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8(8), 605–609 (2014).
[Crossref]

2013 (1)

2008 (2)

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93(12), 121105 (2008).
[Crossref]

L. L. Zhang, H. Zhong, C. Deng, C. L. Zhang, and Y. J. Zhao, “Terahertz wave reference-free phase imaging for identification of explosives,” Appl. Phys. Lett. 92(9), 091117 (2008).
[Crossref]

1996 (1)

Q. Wu and X.-C. Zhang, “Ultrafast electro-optic field sensors,” Appl. Phys. Lett. 68(12), 1604–1606 (1996).
[Crossref]

Augustin, S.

S. Augustin, S. Frohmann, P. Jung, and H. W. Hübers, “Mask responses for single-pixel terahertz imaging,” Sci. Rep. 8(1), 4886 (2018).
[Crossref] [PubMed]

Baraniuk, R. G.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93(12), 121105 (2008).
[Crossref]

Busch, S. F.

K. Krügener, M. Schwerdtfeger, S. F. Busch, A. Soltani, E. Castro-Camus, M. Koch, and W. Viöl, “Terahertz meets sculptural and architectural art: Evaluation and conservation of stone objects with T-ray technology,” Sci. Rep. 5(1), 14842 (2015).
[Crossref] [PubMed]

Castro-Camus, E.

K. Krügener, M. Schwerdtfeger, S. F. Busch, A. Soltani, E. Castro-Camus, M. Koch, and W. Viöl, “Terahertz meets sculptural and architectural art: Evaluation and conservation of stone objects with T-ray technology,” Sci. Rep. 5(1), 14842 (2015).
[Crossref] [PubMed]

Chan, W. L.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93(12), 121105 (2008).
[Crossref]

Charan, K.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93(12), 121105 (2008).
[Crossref]

Cui, Y.

Deng, C.

L. L. Zhang, H. Zhong, C. Deng, C. L. Zhang, and Y. J. Zhao, “Terahertz wave reference-free phase imaging for identification of explosives,” Appl. Phys. Lett. 92(9), 091117 (2008).
[Crossref]

Feng, S.

Frohmann, S.

S. Augustin, S. Frohmann, P. Jung, and H. W. Hübers, “Mask responses for single-pixel terahertz imaging,” Sci. Rep. 8(1), 4886 (2018).
[Crossref] [PubMed]

Gibson, G. M.

R. I. Stantchev, B. Sun, S. M. Hornett, P. A. Hobson, G. M. Gibson, M. J. Padgett, and E. Hendry, “Noninvasive, near-field terahertz imaging of hidden objects using a single-pixel detector,” Sci. Adv. 2(6), e1600190 (2016).
[Crossref] [PubMed]

Haam, S.

Hendry, E.

R. I. Stantchev, D. B. Phillips, P. Hobson, S. M. Hornett, M. J. Padgett, and E. Hendry, “Compressed sensing with near-field THz radiation,” Optica 4(8), 989–992 (2017).
[Crossref]

R. I. Stantchev, B. Sun, S. M. Hornett, P. A. Hobson, G. M. Gibson, M. J. Padgett, and E. Hendry, “Noninvasive, near-field terahertz imaging of hidden objects using a single-pixel detector,” Sci. Adv. 2(6), e1600190 (2016).
[Crossref] [PubMed]

Hobson, P.

Hobson, P. A.

R. I. Stantchev, B. Sun, S. M. Hornett, P. A. Hobson, G. M. Gibson, M. J. Padgett, and E. Hendry, “Noninvasive, near-field terahertz imaging of hidden objects using a single-pixel detector,” Sci. Adv. 2(6), e1600190 (2016).
[Crossref] [PubMed]

Hornett, S. M.

R. I. Stantchev, D. B. Phillips, P. Hobson, S. M. Hornett, M. J. Padgett, and E. Hendry, “Compressed sensing with near-field THz radiation,” Optica 4(8), 989–992 (2017).
[Crossref]

R. I. Stantchev, B. Sun, S. M. Hornett, P. A. Hobson, G. M. Gibson, M. J. Padgett, and E. Hendry, “Noninvasive, near-field terahertz imaging of hidden objects using a single-pixel detector,” Sci. Adv. 2(6), e1600190 (2016).
[Crossref] [PubMed]

Hübers, H. W.

S. Augustin, S. Frohmann, P. Jung, and H. W. Hübers, “Mask responses for single-pixel terahertz imaging,” Sci. Rep. 8(1), 4886 (2018).
[Crossref] [PubMed]

Huh, Y. M.

Hunt, J.

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8(8), 605–609 (2014).
[Crossref]

Jeon, T. I.

Ji, Y. B.

Jung, P.

S. Augustin, S. Frohmann, P. Jung, and H. W. Hübers, “Mask responses for single-pixel terahertz imaging,” Sci. Rep. 8(1), 4886 (2018).
[Crossref] [PubMed]

Kelly, K. F.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93(12), 121105 (2008).
[Crossref]

Kim, H.

Kim, S. H.

Koch, M.

K. Krügener, M. Schwerdtfeger, S. F. Busch, A. Soltani, E. Castro-Camus, M. Koch, and W. Viöl, “Terahertz meets sculptural and architectural art: Evaluation and conservation of stone objects with T-ray technology,” Sci. Rep. 5(1), 14842 (2015).
[Crossref] [PubMed]

Krishna, S.

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8(8), 605–609 (2014).
[Crossref]

Krügener, K.

K. Krügener, M. Schwerdtfeger, S. F. Busch, A. Soltani, E. Castro-Camus, M. Koch, and W. Viöl, “Terahertz meets sculptural and architectural art: Evaluation and conservation of stone objects with T-ray technology,” Sci. Rep. 5(1), 14842 (2015).
[Crossref] [PubMed]

Lee, G. M.

Lee, S. K.

Lipworth, G.

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8(8), 605–609 (2014).
[Crossref]

Mittleman, D. M.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93(12), 121105 (2008).
[Crossref]

Montoya, J.

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8(8), 605–609 (2014).
[Crossref]

Noh, S. K.

Oh, S. J.

Padgett, M. J.

R. I. Stantchev, D. B. Phillips, P. Hobson, S. M. Hornett, M. J. Padgett, and E. Hendry, “Compressed sensing with near-field THz radiation,” Optica 4(8), 989–992 (2017).
[Crossref]

R. I. Stantchev, B. Sun, S. M. Hornett, P. A. Hobson, G. M. Gibson, M. J. Padgett, and E. Hendry, “Noninvasive, near-field terahertz imaging of hidden objects using a single-pixel detector,” Sci. Adv. 2(6), e1600190 (2016).
[Crossref] [PubMed]

Padilla, W. J.

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8(8), 605–609 (2014).
[Crossref]

Park, C. H.

Phillips, D. B.

Schwerdtfeger, M.

K. Krügener, M. Schwerdtfeger, S. F. Busch, A. Soltani, E. Castro-Camus, M. Koch, and W. Viöl, “Terahertz meets sculptural and architectural art: Evaluation and conservation of stone objects with T-ray technology,” Sci. Rep. 5(1), 14842 (2015).
[Crossref] [PubMed]

Shrekenhamer, D.

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8(8), 605–609 (2014).
[Crossref]

Sleasman, T.

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8(8), 605–609 (2014).
[Crossref]

Smith, D. R.

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8(8), 605–609 (2014).
[Crossref]

Soltani, A.

K. Krügener, M. Schwerdtfeger, S. F. Busch, A. Soltani, E. Castro-Camus, M. Koch, and W. Viöl, “Terahertz meets sculptural and architectural art: Evaluation and conservation of stone objects with T-ray technology,” Sci. Rep. 5(1), 14842 (2015).
[Crossref] [PubMed]

Son, J. H.

Stantchev, R. I.

R. I. Stantchev, D. B. Phillips, P. Hobson, S. M. Hornett, M. J. Padgett, and E. Hendry, “Compressed sensing with near-field THz radiation,” Optica 4(8), 989–992 (2017).
[Crossref]

R. I. Stantchev, B. Sun, S. M. Hornett, P. A. Hobson, G. M. Gibson, M. J. Padgett, and E. Hendry, “Noninvasive, near-field terahertz imaging of hidden objects using a single-pixel detector,” Sci. Adv. 2(6), e1600190 (2016).
[Crossref] [PubMed]

Suh, J. S.

Sun, B.

R. I. Stantchev, B. Sun, S. M. Hornett, P. A. Hobson, G. M. Gibson, M. J. Padgett, and E. Hendry, “Noninvasive, near-field terahertz imaging of hidden objects using a single-pixel detector,” Sci. Adv. 2(6), e1600190 (2016).
[Crossref] [PubMed]

Sun, W.

Takhar, D.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93(12), 121105 (2008).
[Crossref]

Viöl, W.

K. Krügener, M. Schwerdtfeger, S. F. Busch, A. Soltani, E. Castro-Camus, M. Koch, and W. Viöl, “Terahertz meets sculptural and architectural art: Evaluation and conservation of stone objects with T-ray technology,” Sci. Rep. 5(1), 14842 (2015).
[Crossref] [PubMed]

Wang, X.

Watts, C. M.

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8(8), 605–609 (2014).
[Crossref]

Wu, Q.

Q. Wu and X.-C. Zhang, “Ultrafast electro-optic field sensors,” Appl. Phys. Lett. 68(12), 1604–1606 (1996).
[Crossref]

Xie, Z.

Ye, J.

Zhang, C. L.

L. L. Zhang, H. Zhong, C. Deng, C. L. Zhang, and Y. J. Zhao, “Terahertz wave reference-free phase imaging for identification of explosives,” Appl. Phys. Lett. 92(9), 091117 (2008).
[Crossref]

Zhang, L. L.

L. L. Zhang, H. Zhong, C. Deng, C. L. Zhang, and Y. J. Zhao, “Terahertz wave reference-free phase imaging for identification of explosives,” Appl. Phys. Lett. 92(9), 091117 (2008).
[Crossref]

Zhang, X.-C.

Q. Wu and X.-C. Zhang, “Ultrafast electro-optic field sensors,” Appl. Phys. Lett. 68(12), 1604–1606 (1996).
[Crossref]

Zhang, Y.

Zhao, Y. J.

L. L. Zhang, H. Zhong, C. Deng, C. L. Zhang, and Y. J. Zhao, “Terahertz wave reference-free phase imaging for identification of explosives,” Appl. Phys. Lett. 92(9), 091117 (2008).
[Crossref]

Zhong, H.

L. L. Zhang, H. Zhong, C. Deng, C. L. Zhang, and Y. J. Zhao, “Terahertz wave reference-free phase imaging for identification of explosives,” Appl. Phys. Lett. 92(9), 091117 (2008).
[Crossref]

Appl. Phys. Lett. (3)

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93(12), 121105 (2008).
[Crossref]

L. L. Zhang, H. Zhong, C. Deng, C. L. Zhang, and Y. J. Zhao, “Terahertz wave reference-free phase imaging for identification of explosives,” Appl. Phys. Lett. 92(9), 091117 (2008).
[Crossref]

Q. Wu and X.-C. Zhang, “Ultrafast electro-optic field sensors,” Appl. Phys. Lett. 68(12), 1604–1606 (1996).
[Crossref]

Biomed. Opt. Express (1)

Nat. Photonics (1)

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8(8), 605–609 (2014).
[Crossref]

Opt. Lett. (1)

Optica (1)

Sci. Adv. (1)

R. I. Stantchev, B. Sun, S. M. Hornett, P. A. Hobson, G. M. Gibson, M. J. Padgett, and E. Hendry, “Noninvasive, near-field terahertz imaging of hidden objects using a single-pixel detector,” Sci. Adv. 2(6), e1600190 (2016).
[Crossref] [PubMed]

Sci. Rep. (2)

S. Augustin, S. Frohmann, P. Jung, and H. W. Hübers, “Mask responses for single-pixel terahertz imaging,” Sci. Rep. 8(1), 4886 (2018).
[Crossref] [PubMed]

K. Krügener, M. Schwerdtfeger, S. F. Busch, A. Soltani, E. Castro-Camus, M. Koch, and W. Viöl, “Terahertz meets sculptural and architectural art: Evaluation and conservation of stone objects with T-ray technology,” Sci. Rep. 5(1), 14842 (2015).
[Crossref] [PubMed]

Other (2)

J. Romberg, “l1magic,” http://statweb.stanford.edu/~candes/l1magic/ .

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996), Chap. 4.

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Figures (7)

Fig. 1
Fig. 1 (a) Schematic illustration of single-pixel THz imaging based on photoinduced dynamic masks. (b) Procedure of the proposed image reconstruction scheme. (c)-(h) give the simulation results, including (c) sample, (d) original THz temporal image, (e) THz diffraction image at temporal peak position, (f) THz temporal image recovered by CS, (g) THz spectral image at 0.3 THz, (h) THz image reconstructed by the IFD algorithm.
Fig. 2
Fig. 2 Reconstruction effect with under-sampling in the simulation. (a) give the recovered THz temporal images of the letter “T” with 100%, 75%, 50%, 20% of all measurements at the peak position. (b) and (c) present the corresponding THz spectral images at 0.3 THz and reconstructed images with different measurement numbers, respectively. (d) shows the normalized mean squared error (MSE) between the reconstructed and original images with varying the measurement number.
Fig. 3
Fig. 3 Influence of the diffraction distance d to the reconstruction effect in the simulation. (a) gives the photo of a resolution chart with four periods, including p = 1.34 mm, 2.68 mm, 4.02 mm and 5.36 mm. (b) presents the original THz temporal image on the output facet of the resolution chart. (c)-(f) show the reconstructed images with d = 10 mm, 15 mm, 26 mm 32 mm at 0.3 THz, respectively. (g) gives the normalized amplitude curves extracted from (b)-(f). The position of these curves is marked by the white dashed line in (b).
Fig. 4
Fig. 4 (a) Optical configuration of a single-pixel THz imaging system in which a photoexcited high-resistance silicon wafer is adopted to implement multiplex sampling to the THz wave front. (b) Variance of the THz temporal peak signal with adjusting the time delay between the control and THz beams. (c) THz temporal signal modulated by photoinduced carriers.
Fig. 5
Fig. 5 (a) Photos of the samples, including three metallic hollow letters “T”, “H”, and “Z”. (b) THz temporal images recovered by CS at the peak position. (c) THz spectral images at 0.3 THz by operating the Fourier transformation. (d) Reconstructed THz images by the IFD algorithm.
Fig. 6
Fig. 6 Reconstruction effect with an under-sampled measurement in the experiment. (a) gives the recovered THz images of the letter “T” with 100%, 75%, 50%, 29% measurements at the temporal peak position. (b) and (c) exhibit the corresponding THz spectral images at 0.3 THz and reconstructed images. (d) shows the MSE between the reconstructed and reference images with varying the measurement number. The reference image is obtained from a photo of the sample.
Fig. 7
Fig. 7 Influence of the diffraction distance d to the reconstruction effect in the experiment. (a) gives THz temporal images recovered by CS with d = 10 mm, 15 mm, and 20 mm for a metallic hollow letter “T”. (b) and (c) present the THz spectral images at 0.3 THz and reconstructed images with d = 10 mm, 15 mm, and 20 mm, respectively.

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U( x 1 , y 1 )= exp( jkd ) jλd U( x 0 , y 0 )exp{ j k 2d [ ( x 0 x 1 ) 2 + ( y 0 y 1 ) 2 ] } d x 0 d y 0 ,

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