Abstract

We demonstrate high-resolution and high-quality terahertz (THz) in-line digital holography based on the synthetic aperture method. The setup is built on a self-developed THz quantum cascade laser, and a lateral resolution better than 70 μm (λ) is achieved at 4.3 THz. To correct intensity differences between sub-holograms before aperture stitching, a practical algorithm with global optimization is proposed. To address the twin-image problem for in-line holography, a sparsity-based phase retrieval algorithm is applied to perform the high-quality reconstruction. Furthermore, a new autofocusing criterion termed “reconstruction objective function” is introduced to obtain the best in-focus reconstruction distance, so the autofocusing procedure and the reconstruction are unified within the same framework. Both simulation and experiment prove its accuracy and robustness. Note that all the methods proposed here can be applied to other wavebands as well. We demonstrate the success of this THz synthetic aperture in-line holography on biological and semiconductor samples, showing its potential applications in bioimaging and materials analysis.

© 2019 Chinese Laser Press

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References

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2019 (5)

2018 (8)

W. Zhang, L. Cao, D. J. Brady, H. Zhang, J. Cang, H. Zhang, and G. Jin, “Twin-image-free holography: a compressive sensing approach,” Phys. Rev. Lett. 121, 093902 (2018).
[Crossref]

F. Jolivet, F. Momey, L. Denis, L. Méès, N. Faure, N. Grosjean, F. Pinston, J.-L. Marié, and C. Fournier, “Regularized reconstruction of absorbing and phase objects from a single in-line hologram, application to fluid mechanics and micro-biology,” Opt. Express 26, 8923–8940 (2018).
[Crossref]

L. Valzania, T. Feurer, P. Zolliker, and E. Hack, “Terahertz ptychography,” Opt. Lett. 43, 543–546 (2018).
[Crossref]

D. M. Mittleman, “Twenty years of terahertz imaging [Invited],” Opt. Express 26, 9417–9431 (2018).
[Crossref]

L. Olivieri, J. S. Totero Gongora, A. Pasquazi, and M. Peccianti, “Time-resolved nonlinear ghost imaging,” ACS Photon. 5, 3379–3388 (2018).
[Crossref]

M. Yamagiwa, T. Ogawa, T. Minamikawa, D. G. Abdelsalam, K. Okabe, N. Tsurumachi, Y. Mizutani, T. Iwata, H. Yamamoto, and T. Yasui, “Real-time amplitude and phase imaging of optically opaque objects by combining full-field off-axis terahertz digital holography with angular spectrum reconstruction,” J. Infrared Millim. Terahertz Waves 39, 561–572 (2018).
[Crossref]

M. Humphreys, J. Grant, I. Escorcia-Carranza, C. Accarino, M. Kenney, Y. Shah, K. Rew, and D. Cumming, “Video-rate terahertz digital holographic imaging system,” Opt. Express 26, 25805–25813 (2018).
[Crossref]

H. Huang, D. Wang, L. Rong, S. Panezai, D. Zhang, P. Qiu, L. Gao, H. Gao, H. Zheng, and Z. Zheng, “Continuous-wave off-axis and in-line terahertz digital holography with phase unwrapping and phase autofocusing,” Opt. Commun. 426, 612–622 (2018).
[Crossref]

2017 (3)

X. C. Zhang, A. Shkurinov, and Y. Zhang, “Extreme terahertz science,” Nat. Photonics 11, 16–18 (2017).
[Crossref]

Q. Deng, W. Li, X. Wang, Z. Li, H. Huang, C. Shen, Z. Zhan, R. Zou, T. Jiang, and W. Wu, “High-resolution terahertz inline digital holography based on quantum cascade laser,” Opt. Eng. 56, 113102 (2017).
[Crossref]

Y. Zhang, H. Wang, Y. Wu, M. Tamamitsu, and A. Ozcan, “Edge sparsity criterion for robust holographic autofocusing,” Opt. Lett. 42, 3824–3827 (2017).
[Crossref]

2016 (6)

2015 (5)

P. Zolliker and E. Hack, “THz holography in reflection using a high resolution microbolometer array,” Opt. Express 23, 10957–10967 (2015).
[Crossref]

M. Locatelli, M. Ravaro, S. Bartalini, L. Consolino, M. S. Vitiello, R. Cicchi, F. Pavone, and P. De Natale, “Real-time terahertz digital holography with a quantum cascade laser,” Sci. Rep. 5, 13566 (2015).
[Crossref]

L. Rong, T. Latychevskaia, C. Chen, D. Wang, Z. Yu, X. Zhou, Z. Li, H. Huang, Y. Wang, and Z. Zhou, “Terahertz in-line digital holography of human hepatocellular carcinoma tissue,” Sci. Rep. 5, 8445 (2015).
[Crossref]

Y. Li, Q. Li, J. Hu, and Y. Zhao, “Compressive sensing algorithm for 2D reconstruction of THz digital holography,” Chin. Opt. Lett. 13, S11101 (2015).
[Crossref]

W. Luo, A. Greenbaum, Y. Zhang, and A. Ozcan, “Synthetic aperture-based on-chip microscopy,” Light: Sci. Appl. 4, e261 (2015).
[Crossref]

2012 (2)

2011 (1)

2008 (2)

2007 (1)

T. Latychevskaia and H.-W. Fink, “Solution to the twin image problem in holography,” Phys. Rev. Lett. 98, 233901 (2007).
[Crossref]

1949 (1)

D. Gabor, “Microscopy by reconstructed wave-fronts,” Proc. R. Soc. London Ser. A 197, 454–487 (1949).
[Crossref]

Abdelsalam, D. G.

M. Yamagiwa, T. Ogawa, T. Minamikawa, D. G. Abdelsalam, K. Okabe, N. Tsurumachi, Y. Mizutani, T. Iwata, H. Yamamoto, and T. Yasui, “Real-time amplitude and phase imaging of optically opaque objects by combining full-field off-axis terahertz digital holography with angular spectrum reconstruction,” J. Infrared Millim. Terahertz Waves 39, 561–572 (2018).
[Crossref]

Accarino, C.

Bartalini, S.

M. Locatelli, M. Ravaro, S. Bartalini, L. Consolino, M. S. Vitiello, R. Cicchi, F. Pavone, and P. De Natale, “Real-time terahertz digital holography with a quantum cascade laser,” Sci. Rep. 5, 13566 (2015).
[Crossref]

Brady, D. J.

W. Zhang, L. Cao, D. J. Brady, H. Zhang, J. Cang, H. Zhang, and G. Jin, “Twin-image-free holography: a compressive sensing approach,” Phys. Rev. Lett. 121, 093902 (2018).
[Crossref]

Cang, J.

W. Zhang, L. Cao, D. J. Brady, H. Zhang, J. Cang, H. Zhang, and G. Jin, “Twin-image-free holography: a compressive sensing approach,” Phys. Rev. Lett. 121, 093902 (2018).
[Crossref]

Cao, L.

W. Zhang, L. Cao, D. J. Brady, H. Zhang, J. Cang, H. Zhang, and G. Jin, “Twin-image-free holography: a compressive sensing approach,” Phys. Rev. Lett. 121, 093902 (2018).
[Crossref]

Çetin, M.

H. E. Güven, A. Güngör, and M. Çetin, “An augmented Lagrangian method for complex-valued compressed sar imaging,” IEEE Trans. Comput. Imaging 2, 235–250 (2016).
[Crossref]

Chen, C.

L. Rong, T. Latychevskaia, C. Chen, D. Wang, Z. Yu, X. Zhou, Z. Li, H. Huang, Y. Wang, and Z. Zhou, “Terahertz in-line digital holography of human hepatocellular carcinoma tissue,” Sci. Rep. 5, 8445 (2015).
[Crossref]

Chen, N.

Chen, S.

Chu, W.

X. Wang, C. Shen, T. Jiang, Z. Zhan, Q. Deng, W. Li, W. Wu, N. Yang, W. Chu, and S. Duan, “High-power terahertz quantum cascade lasers with ∼0.23  W in continuous wave mode,” AIP Adv. 6, 075210 (2016).
[Crossref]

Cicchi, R.

M. Locatelli, M. Ravaro, S. Bartalini, L. Consolino, M. S. Vitiello, R. Cicchi, F. Pavone, and P. De Natale, “Real-time terahertz digital holography with a quantum cascade laser,” Sci. Rep. 5, 13566 (2015).
[Crossref]

Consolino, L.

M. Locatelli, M. Ravaro, S. Bartalini, L. Consolino, M. S. Vitiello, R. Cicchi, F. Pavone, and P. De Natale, “Real-time terahertz digital holography with a quantum cascade laser,” Sci. Rep. 5, 13566 (2015).
[Crossref]

Cumming, D.

De Natale, P.

M. Locatelli, M. Ravaro, S. Bartalini, L. Consolino, M. S. Vitiello, R. Cicchi, F. Pavone, and P. De Natale, “Real-time terahertz digital holography with a quantum cascade laser,” Sci. Rep. 5, 13566 (2015).
[Crossref]

Deng, Q.

T. Jiang, C. Shen, Z. Zhan, R. Zou, J. Li, L. Fan, T. Xiao, W. Li, Q. Deng, L. Peng, X. Wang, and W. Wu, “Fabrication of 4.4  THz quantum cascade laser and its demonstration in high-resolution digital holographic imaging,” J. Alloys Compd. 771, 106–110 (2019).
[Crossref]

Q. Deng, W. Li, X. Wang, Z. Li, H. Huang, C. Shen, Z. Zhan, R. Zou, T. Jiang, and W. Wu, “High-resolution terahertz inline digital holography based on quantum cascade laser,” Opt. Eng. 56, 113102 (2017).
[Crossref]

H. Huang, L. Rong, D. Wang, W. Li, Q. Deng, B. Li, Y. Wang, Z. Zhan, X. Wang, and W. Wu, “Synthetic aperture in terahertz in-line digital holography for resolution enhancement,” Appl. Opt. 55, A43–A48 (2016).
[Crossref]

X. Wang, C. Shen, T. Jiang, Z. Zhan, Q. Deng, W. Li, W. Wu, N. Yang, W. Chu, and S. Duan, “High-power terahertz quantum cascade lasers with ∼0.23  W in continuous wave mode,” AIP Adv. 6, 075210 (2016).
[Crossref]

Denis, L.

Ding, S.

Dirksen, D.

Du, L.

Duan, S.

X. Wang, C. Shen, T. Jiang, Z. Zhan, Q. Deng, W. Li, W. Wu, N. Yang, W. Chu, and S. Duan, “High-power terahertz quantum cascade lasers with ∼0.23  W in continuous wave mode,” AIP Adv. 6, 075210 (2016).
[Crossref]

Escorcia-Carranza, I.

Fan, L.

T. Jiang, C. Shen, Z. Zhan, R. Zou, J. Li, L. Fan, T. Xiao, W. Li, Q. Deng, L. Peng, X. Wang, and W. Wu, “Fabrication of 4.4  THz quantum cascade laser and its demonstration in high-resolution digital holographic imaging,” J. Alloys Compd. 771, 106–110 (2019).
[Crossref]

Faure, N.

Feurer, T.

Fiadeiro, P. T.

Fienup, J. R.

Fink, H.-W.

T. Latychevskaia and H.-W. Fink, “Solution to the twin image problem in holography,” Phys. Rev. Lett. 98, 233901 (2007).
[Crossref]

Fonseca, E. S. R.

Fournier, C.

Gabor, D.

D. Gabor, “Microscopy by reconstructed wave-fronts,” Proc. R. Soc. London Ser. A 197, 454–487 (1949).
[Crossref]

Gao, H.

H. Huang, D. Wang, L. Rong, S. Panezai, D. Zhang, P. Qiu, L. Gao, H. Gao, H. Zheng, and Z. Zheng, “Continuous-wave off-axis and in-line terahertz digital holography with phase unwrapping and phase autofocusing,” Opt. Commun. 426, 612–622 (2018).
[Crossref]

Gao, L.

H. Huang, D. Wang, L. Rong, S. Panezai, D. Zhang, P. Qiu, L. Gao, H. Gao, H. Zheng, and Z. Zheng, “Continuous-wave off-axis and in-line terahertz digital holography with phase unwrapping and phase autofocusing,” Opt. Commun. 426, 612–622 (2018).
[Crossref]

Grant, J.

Greenbaum, A.

Grosjean, N.

Guizar-Sicairos, M.

Güngör, A.

H. E. Güven, A. Güngör, and M. Çetin, “An augmented Lagrangian method for complex-valued compressed sar imaging,” IEEE Trans. Comput. Imaging 2, 235–250 (2016).
[Crossref]

Güven, H. E.

H. E. Güven, A. Güngör, and M. Çetin, “An augmented Lagrangian method for complex-valued compressed sar imaging,” IEEE Trans. Comput. Imaging 2, 235–250 (2016).
[Crossref]

Hack, E.

Hu, J.

Y. Li, Q. Li, J. Hu, and Y. Zhao, “Compressive sensing algorithm for 2D reconstruction of THz digital holography,” Chin. Opt. Lett. 13, S11101 (2015).
[Crossref]

Huang, H.

H. Huang, D. Wang, L. Rong, S. Panezai, D. Zhang, P. Qiu, L. Gao, H. Gao, H. Zheng, and Z. Zheng, “Continuous-wave off-axis and in-line terahertz digital holography with phase unwrapping and phase autofocusing,” Opt. Commun. 426, 612–622 (2018).
[Crossref]

Q. Deng, W. Li, X. Wang, Z. Li, H. Huang, C. Shen, Z. Zhan, R. Zou, T. Jiang, and W. Wu, “High-resolution terahertz inline digital holography based on quantum cascade laser,” Opt. Eng. 56, 113102 (2017).
[Crossref]

H. Huang, L. Rong, D. Wang, W. Li, Q. Deng, B. Li, Y. Wang, Z. Zhan, X. Wang, and W. Wu, “Synthetic aperture in terahertz in-line digital holography for resolution enhancement,” Appl. Opt. 55, A43–A48 (2016).
[Crossref]

L. Rong, T. Latychevskaia, C. Chen, D. Wang, Z. Yu, X. Zhou, Z. Li, H. Huang, Y. Wang, and Z. Zhou, “Terahertz in-line digital holography of human hepatocellular carcinoma tissue,” Sci. Rep. 5, 8445 (2015).
[Crossref]

Humphreys, M.

Iwata, T.

M. Yamagiwa, T. Ogawa, T. Minamikawa, D. G. Abdelsalam, K. Okabe, N. Tsurumachi, Y. Mizutani, T. Iwata, H. Yamamoto, and T. Yasui, “Real-time amplitude and phase imaging of optically opaque objects by combining full-field off-axis terahertz digital holography with angular spectrum reconstruction,” J. Infrared Millim. Terahertz Waves 39, 561–572 (2018).
[Crossref]

Jiang, T.

T. Jiang, C. Shen, Z. Zhan, R. Zou, J. Li, L. Fan, T. Xiao, W. Li, Q. Deng, L. Peng, X. Wang, and W. Wu, “Fabrication of 4.4  THz quantum cascade laser and its demonstration in high-resolution digital holographic imaging,” J. Alloys Compd. 771, 106–110 (2019).
[Crossref]

Q. Deng, W. Li, X. Wang, Z. Li, H. Huang, C. Shen, Z. Zhan, R. Zou, T. Jiang, and W. Wu, “High-resolution terahertz inline digital holography based on quantum cascade laser,” Opt. Eng. 56, 113102 (2017).
[Crossref]

X. Wang, C. Shen, T. Jiang, Z. Zhan, Q. Deng, W. Li, W. Wu, N. Yang, W. Chu, and S. Duan, “High-power terahertz quantum cascade lasers with ∼0.23  W in continuous wave mode,” AIP Adv. 6, 075210 (2016).
[Crossref]

Jin, G.

W. Zhang, L. Cao, D. J. Brady, H. Zhang, J. Cang, H. Zhang, and G. Jin, “Twin-image-free holography: a compressive sensing approach,” Phys. Rev. Lett. 121, 093902 (2018).
[Crossref]

Jolivet, F.

Kemper, B.

Kenney, M.

Kong, W.

Kuwata-Gonokami, M.

K. E. Peiponen, J. A. Zeitler, and M. Kuwata-Gonokami, Terahertz Spectroscopy and Imaging (Springer, 2013).

Lam, E. Y.

Langehanenberg, P.

Latychevskaia, T.

L. Rong, T. Latychevskaia, C. Chen, D. Wang, Z. Yu, X. Zhou, Z. Li, H. Huang, Y. Wang, and Z. Zhou, “Terahertz in-line digital holography of human hepatocellular carcinoma tissue,” Sci. Rep. 5, 8445 (2015).
[Crossref]

T. Latychevskaia and H.-W. Fink, “Solution to the twin image problem in holography,” Phys. Rev. Lett. 98, 233901 (2007).
[Crossref]

Li, B.

Li, G.

Li, J.

T. Jiang, C. Shen, Z. Zhan, R. Zou, J. Li, L. Fan, T. Xiao, W. Li, Q. Deng, L. Peng, X. Wang, and W. Wu, “Fabrication of 4.4  THz quantum cascade laser and its demonstration in high-resolution digital holographic imaging,” J. Alloys Compd. 771, 106–110 (2019).
[Crossref]

S. Chen, L. Du, K. Meng, J. Li, Z. Zhai, Q. Shi, Z. Li, and L. Zhu, “Terahertz wave near-field compressive imaging with a spatial resolution of over λ/100,” Opt. Lett. 44, 21–24 (2019).
[Crossref]

Li, L.

Li, Q.

Li, W.

T. Jiang, C. Shen, Z. Zhan, R. Zou, J. Li, L. Fan, T. Xiao, W. Li, Q. Deng, L. Peng, X. Wang, and W. Wu, “Fabrication of 4.4  THz quantum cascade laser and its demonstration in high-resolution digital holographic imaging,” J. Alloys Compd. 771, 106–110 (2019).
[Crossref]

Q. Deng, W. Li, X. Wang, Z. Li, H. Huang, C. Shen, Z. Zhan, R. Zou, T. Jiang, and W. Wu, “High-resolution terahertz inline digital holography based on quantum cascade laser,” Opt. Eng. 56, 113102 (2017).
[Crossref]

H. Huang, L. Rong, D. Wang, W. Li, Q. Deng, B. Li, Y. Wang, Z. Zhan, X. Wang, and W. Wu, “Synthetic aperture in terahertz in-line digital holography for resolution enhancement,” Appl. Opt. 55, A43–A48 (2016).
[Crossref]

X. Wang, C. Shen, T. Jiang, Z. Zhan, Q. Deng, W. Li, W. Wu, N. Yang, W. Chu, and S. Duan, “High-power terahertz quantum cascade lasers with ∼0.23  W in continuous wave mode,” AIP Adv. 6, 075210 (2016).
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Li, Z.

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M. Locatelli, M. Ravaro, S. Bartalini, L. Consolino, M. S. Vitiello, R. Cicchi, F. Pavone, and P. De Natale, “Real-time terahertz digital holography with a quantum cascade laser,” Sci. Rep. 5, 13566 (2015).
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W. Luo, A. Greenbaum, Y. Zhang, and A. Ozcan, “Synthetic aperture-based on-chip microscopy,” Light: Sci. Appl. 4, e261 (2015).
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Méès, L.

Meng, K.

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M. Yamagiwa, T. Ogawa, T. Minamikawa, D. G. Abdelsalam, K. Okabe, N. Tsurumachi, Y. Mizutani, T. Iwata, H. Yamamoto, and T. Yasui, “Real-time amplitude and phase imaging of optically opaque objects by combining full-field off-axis terahertz digital holography with angular spectrum reconstruction,” J. Infrared Millim. Terahertz Waves 39, 561–572 (2018).
[Crossref]

Mittleman, D. M.

Mizutani, Y.

M. Yamagiwa, T. Ogawa, T. Minamikawa, D. G. Abdelsalam, K. Okabe, N. Tsurumachi, Y. Mizutani, T. Iwata, H. Yamamoto, and T. Yasui, “Real-time amplitude and phase imaging of optically opaque objects by combining full-field off-axis terahertz digital holography with angular spectrum reconstruction,” J. Infrared Millim. Terahertz Waves 39, 561–572 (2018).
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Ogawa, T.

M. Yamagiwa, T. Ogawa, T. Minamikawa, D. G. Abdelsalam, K. Okabe, N. Tsurumachi, Y. Mizutani, T. Iwata, H. Yamamoto, and T. Yasui, “Real-time amplitude and phase imaging of optically opaque objects by combining full-field off-axis terahertz digital holography with angular spectrum reconstruction,” J. Infrared Millim. Terahertz Waves 39, 561–572 (2018).
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M. Yamagiwa, T. Ogawa, T. Minamikawa, D. G. Abdelsalam, K. Okabe, N. Tsurumachi, Y. Mizutani, T. Iwata, H. Yamamoto, and T. Yasui, “Real-time amplitude and phase imaging of optically opaque objects by combining full-field off-axis terahertz digital holography with angular spectrum reconstruction,” J. Infrared Millim. Terahertz Waves 39, 561–572 (2018).
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L. Olivieri, J. S. Totero Gongora, A. Pasquazi, and M. Peccianti, “Time-resolved nonlinear ghost imaging,” ACS Photon. 5, 3379–3388 (2018).
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Ozcan, A.

Panezai, S.

H. Huang, D. Wang, L. Rong, S. Panezai, D. Zhang, P. Qiu, L. Gao, H. Gao, H. Zheng, and Z. Zheng, “Continuous-wave off-axis and in-line terahertz digital holography with phase unwrapping and phase autofocusing,” Opt. Commun. 426, 612–622 (2018).
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L. Olivieri, J. S. Totero Gongora, A. Pasquazi, and M. Peccianti, “Time-resolved nonlinear ghost imaging,” ACS Photon. 5, 3379–3388 (2018).
[Crossref]

Pavone, F.

M. Locatelli, M. Ravaro, S. Bartalini, L. Consolino, M. S. Vitiello, R. Cicchi, F. Pavone, and P. De Natale, “Real-time terahertz digital holography with a quantum cascade laser,” Sci. Rep. 5, 13566 (2015).
[Crossref]

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L. Olivieri, J. S. Totero Gongora, A. Pasquazi, and M. Peccianti, “Time-resolved nonlinear ghost imaging,” ACS Photon. 5, 3379–3388 (2018).
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K. E. Peiponen, J. A. Zeitler, and M. Kuwata-Gonokami, Terahertz Spectroscopy and Imaging (Springer, 2013).

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T. Jiang, C. Shen, Z. Zhan, R. Zou, J. Li, L. Fan, T. Xiao, W. Li, Q. Deng, L. Peng, X. Wang, and W. Wu, “Fabrication of 4.4  THz quantum cascade laser and its demonstration in high-resolution digital holographic imaging,” J. Alloys Compd. 771, 106–110 (2019).
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Pinheiro, A.

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Qin, Y.

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H. Huang, D. Wang, L. Rong, S. Panezai, D. Zhang, P. Qiu, L. Gao, H. Gao, H. Zheng, and Z. Zheng, “Continuous-wave off-axis and in-line terahertz digital holography with phase unwrapping and phase autofocusing,” Opt. Commun. 426, 612–622 (2018).
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M. Locatelli, M. Ravaro, S. Bartalini, L. Consolino, M. S. Vitiello, R. Cicchi, F. Pavone, and P. De Natale, “Real-time terahertz digital holography with a quantum cascade laser,” Sci. Rep. 5, 13566 (2015).
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Rew, K.

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L. Rong, C. Tang, D. Wang, B. Li, F. Tan, Y. Wang, and X. Shi, “Probe position correction based on overlapped object wavefront cross-correlation for continuous-wave terahertz ptychography,” Opt. Express 27, 938–950 (2019).
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Shen, C.

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L. Olivieri, J. S. Totero Gongora, A. Pasquazi, and M. Peccianti, “Time-resolved nonlinear ghost imaging,” ACS Photon. 5, 3379–3388 (2018).
[Crossref]

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M. Yamagiwa, T. Ogawa, T. Minamikawa, D. G. Abdelsalam, K. Okabe, N. Tsurumachi, Y. Mizutani, T. Iwata, H. Yamamoto, and T. Yasui, “Real-time amplitude and phase imaging of optically opaque objects by combining full-field off-axis terahertz digital holography with angular spectrum reconstruction,” J. Infrared Millim. Terahertz Waves 39, 561–572 (2018).
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Q. Deng, W. Li, X. Wang, Z. Li, H. Huang, C. Shen, Z. Zhan, R. Zou, T. Jiang, and W. Wu, “High-resolution terahertz inline digital holography based on quantum cascade laser,” Opt. Eng. 56, 113102 (2017).
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T. Jiang, C. Shen, Z. Zhan, R. Zou, J. Li, L. Fan, T. Xiao, W. Li, Q. Deng, L. Peng, X. Wang, and W. Wu, “Fabrication of 4.4  THz quantum cascade laser and its demonstration in high-resolution digital holographic imaging,” J. Alloys Compd. 771, 106–110 (2019).
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M. Yamagiwa, T. Ogawa, T. Minamikawa, D. G. Abdelsalam, K. Okabe, N. Tsurumachi, Y. Mizutani, T. Iwata, H. Yamamoto, and T. Yasui, “Real-time amplitude and phase imaging of optically opaque objects by combining full-field off-axis terahertz digital holography with angular spectrum reconstruction,” J. Infrared Millim. Terahertz Waves 39, 561–572 (2018).
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M. Yamagiwa, T. Ogawa, T. Minamikawa, D. G. Abdelsalam, K. Okabe, N. Tsurumachi, Y. Mizutani, T. Iwata, H. Yamamoto, and T. Yasui, “Real-time amplitude and phase imaging of optically opaque objects by combining full-field off-axis terahertz digital holography with angular spectrum reconstruction,” J. Infrared Millim. Terahertz Waves 39, 561–572 (2018).
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M. Yamagiwa, T. Ogawa, T. Minamikawa, D. G. Abdelsalam, K. Okabe, N. Tsurumachi, Y. Mizutani, T. Iwata, H. Yamamoto, and T. Yasui, “Real-time amplitude and phase imaging of optically opaque objects by combining full-field off-axis terahertz digital holography with angular spectrum reconstruction,” J. Infrared Millim. Terahertz Waves 39, 561–572 (2018).
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H. Huang, D. Wang, L. Rong, S. Panezai, D. Zhang, P. Qiu, L. Gao, H. Gao, H. Zheng, and Z. Zheng, “Continuous-wave off-axis and in-line terahertz digital holography with phase unwrapping and phase autofocusing,” Opt. Commun. 426, 612–622 (2018).
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Q. Deng, W. Li, X. Wang, Z. Li, H. Huang, C. Shen, Z. Zhan, R. Zou, T. Jiang, and W. Wu, “High-resolution terahertz inline digital holography based on quantum cascade laser,” Opt. Eng. 56, 113102 (2017).
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ACS Photon. (1)

L. Olivieri, J. S. Totero Gongora, A. Pasquazi, and M. Peccianti, “Time-resolved nonlinear ghost imaging,” ACS Photon. 5, 3379–3388 (2018).
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AIP Adv. (1)

X. Wang, C. Shen, T. Jiang, Z. Zhan, Q. Deng, W. Li, W. Wu, N. Yang, W. Chu, and S. Duan, “High-power terahertz quantum cascade lasers with ∼0.23  W in continuous wave mode,” AIP Adv. 6, 075210 (2016).
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Appl. Opt. (4)

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Figures (14)

Fig. 1.
Fig. 1. Schematic layout of the experimental setup. A Si lens was used to collimate the output THz beam. The wave scattered by the sample forms the object wave, and the unscattered part of the illumination forms the reference wave. The interference pattern recorded by the detector array is called the in-line hologram. The object wave in dark blue represents the low-frequency components, and the object wave in light blue denotes the high-frequency parts. By moving the detector, multiple sub-aperture holograms can be recorded and combined to be a synthetic aperture hologram for the resolution enhancement.
Fig. 2.
Fig. 2. Schematic diagram of the aperture synthesis. (a) Four potential overlapped regions within a sub-hologram. (b) Synthetic aperture hologram with 3×3 tiles numbered by 1–9.
Fig. 3.
Fig. 3. Iterative sparse reconstruction scheme. SA_HN is the normalized synthetic aperture hologram, which is composed of the normalized sub-holograms with intensity correction.
Fig. 4.
Fig. 4. Simulated three types of objects with a THz pattern. (a) Type A: complex amplitude object. (b) Type B: pure amplitude object. (c) Type C: pure phase object.
Fig. 5.
Fig. 5. Autofocusing curves (left column) and their zoomed-in local counterparts (right column) for (a) the complex amplitude object (type A), (b) the pure amplitude object (type B), and (c) the pure phase object (type C). The black dashed lines show the correct position.
Fig. 6.
Fig. 6. Autofocusing curves for the pure amplitude object (type B) with d=6  mm.
Fig. 7.
Fig. 7. Synthetic aperture hologram with intensity correction for a dragonfly forewing. (a) Nine normalized sub-holograms with intensity correction. (b) Synthetic aperture hologram composed of (a). (c) Synthetic aperture hologram without intensity correction. (d) Optical image of the dragonfly forewing sample. (e) Amplitude distribution reconstructed from (b) with 20 iterations. (f) Amplitude distribution reconstructed from (c) with 20 iterations. The effect of non-uniform intensity on reconstruction can be seen from the parts marked by the white and blue dotted circles.
Fig. 8.
Fig. 8. Sparsity-based autofocusing reconstruction for a dragonfly forewing with 20 iterations. (a) Autofocusing curves for three criteria. (b) Complex amplitude reconstruction at d=14.55  mm. (c) Complex amplitude reconstruction at d=14.85  mm. (d) Complex amplitude reconstruction at d=14.93  mm. The regions in (b) marked by the dotted circles show sharper and clearer details than their counterparts.
Fig. 9.
Fig. 9. Optical images of the three samples for the resolution quantification. (a) 100 μm resolution target with a measured width and separation of 99  μm. (b) 80 μm resolution target with a measured width and separation of 77  μm. (c) 70 μm resolution target with a measured width and separation of 69  μm.
Fig. 10.
Fig. 10. Reconstructions of the 100 μm resolution target with and without synthetic aperture. (a), (b) The amplitude and phase-contrast distributions reconstructed by the sparse phase retrieval algorithm with 20 iterations based on the synthetic aperture hologram. (c), (d) The amplitude and phase-contrast distributions reconstructed by the sparse phase retrieval algorithm with 20 iterations based on the center sub-hologram. On the right side of each reconstruction, the intensity distributions along the black lines are displayed.
Fig. 11.
Fig. 11. Reconstructions of the 80 μm resolution target: the amplitude and phase-contrast distributions reconstructed by the sparse phase retrieval algorithm with 20 iterations.
Fig. 12.
Fig. 12. Reconstructions of the 70 μm resolution target: the amplitude and phase-contrast distributions reconstructed by the sparse phase retrieval algorithm with 20 iterations.
Fig. 13.
Fig. 13. Reconstructions of three biological samples with the proposed methods. (a) Complex amplitude reconstructions of a beetle’s leg. (b) Complex amplitude reconstructions of a cicada’s wing. (c) Complex amplitude reconstructions of a spider.
Fig. 14.
Fig. 14. Reconstructed (a) amplitude and (b) phase distributions of a silicon wafer, where the internal non-uniformity can be observed.

Tables (1)

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Table 1. Absolute Errors (mm) of Three Criteria on Different Object Types with Various Recording Distances

Equations (18)

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E1,2=(β1T1,2β2T2,4)2,
E=E1,2+E2,3+E1,4+E2,5+E3,6+E4,5+E5,6+E4,7+E5,8+E6,9+E7,8+E8,9.
E=E1+E2+E3,
E1=E1,2+E2,3+E1,4+E3,6+E4,7+E6,9+E7,8+E8,9+β22T2,32+β42T4,22+β62T6,42+β82T8,12,
E2=2β2(T2,3T5,1)2β4(T4,2T5,4)2β6(T6,4T5,2)2β8(T8,1T5,3),
E3=T5,12+T5,22+T5,32+T5,42,
E=βTAβ2βTB+E3,
A=[A11A120A140000A21A22A23000000A32A330A35000A4100A440A460000A530A5500A58000A640A66A67000000A76A77A780000A850A87A88],
argminβE=βTAβ2βTB+E3.
Eβ=2Aβ2B=0,
β=A1B.
argminX,W,μL(X,W,μ)=12HWT(d)*(X+μ1)22+τX1s.t.  Ps(X)=X,|W|=1,
μk+1=argminμL(Xk,Wk,μ)=1mn|T(d)*(HWk)Xk|,1,
Wk+1=argminWL(Xk,W,μk+1)=T(d)*(Xk+μk+11)|T(d)*(Xk+μk+11)|,
Xk+1=argminXL(X,Wk+1,μk+1)=Ps{SFTτ[T(d)*(HWk+1)μk+11]},
SFTτ(Z)[i,j]={(|Z[i,j]|τ)Z[i,j]|Z[i,j]||Z[i,j]|>τ0|Z[i,j]|τ,
τ=1mn|T(d)*(HW1)μ11|,1.
R=λ2NA=λ2sinθmax,

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