Abstract

In contrast to imaging using position-resolving cameras, single-pixel imaging uses a bucket detector along with spatially structured illumination to compressively recover images. This emerging imaging technique is a promising candidate for a broad range of applications due to the high signal-to-noise ratio (SNR) and sensitivity, and applicability in a wide range of frequency bands. Here, inspired by single-pixel imaging in the spatial domain, we demonstrate a time-domain single-pixel imaging (TSPI) system that covers frequency bands including both terahertz (THz) and near-infrared (NIR) regions. By implementing a programmable temporal fan-out gate based on a digital micromirror device, we can deterministically prepare temporally structured pulses with a temporal sampling size down to $16.00 \pm 0.01\,\,\rm fs$. By inheriting the advantages of detection efficiency and sensitivity from spatial single-pixel imaging, TSPI enables the recovery of a 5 fJ THz pulse and two NIR pulses with over $97\%$ fidelity via compressive sensing. We demonstrate that the TSPI is robust against temporal distortions in the probe pulse train as well. As a direct application, we apply TSPI to machine-learning-aided THz spectroscopy and demonstrate a high sample identification accuracy (97.5%) even under low SNRs (SNR ${\sim}10$).

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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2020 (3)

G. M. Gibson, S. D. Johnson, and M. J. Padgett, “Single-pixel imaging 12 years on: a review,” Opt. Express 28, 28190–28208 (2020).
[Crossref]

Y. Tian, H. Ge, X.-J. Zhang, X.-Y. Xu, M.-H. Lu, Y. Jing, and Y.-F. Chen, “Acoustic ghost imaging in the time domain,” Phys. Rev. Appl. 13, 064044 (2020).
[Crossref]

R. I. Stantchev, X. Yu, T. Blu, and E. Pickwell-MacPherson, “Real-time terahertz imaging with a single-pixel detector,” Nat. Commun. 11, 2535 (2020).
[Crossref]

2019 (3)

J. Zhao, E. Yiwen, K. Williams, X.-C. Zhang, and R. W. Boyd, “Spatial sampling of terahertz fields with sub-wavelength accuracy via probe-beam encoding,” Light Sci. Appl. 8, 55 (2019).
[Crossref]

H. Wu, P. Ryczkowski, A. T. Friberg, J. M. Dudley, and G. Genty, “Temporal ghost imaging using wavelength conversion and two-color detection,” Optica 6, 902–906 (2019).
[Crossref]

M. P. Edgar, G. M. Gibson, and M. J. Padgett, “Principles and prospects for single-pixel imaging,” Nat. Photonics 13, 13–20 (2019).
[Crossref]

2018 (4)

Y. Altmann, S. McLaughlin, M. J. Padgett, V. K. Goyal, A. O. Hero, and D. Faccio, “Quantum-inspired computational imaging,” Science 361, eaat2298 (2018).
[Crossref]

A. Tikan, S. Bielawski, C. Szwaj, S. Randoux, and P. Suret, “Single-shot measurement of phase and amplitude by using a heterodyne time-lens system and ultrafast digital time-holography,” Nat. Photonics 12, 228–234 (2018).
[Crossref]

Y.-K. Xu, S.-H. Sun, W.-T. Liu, G.-Z. Tang, J.-Y. Liu, and P.-X. Chen, “Detecting fast signals beyond bandwidth of detectors based on computational temporal ghost imaging,” Opt. Express 26, 99–107 (2018).
[Crossref]

K. Murate, M. J. Roshtkhari, X. Ropagnol, and F. Blanchard, “Adaptive spatiotemporal optical pulse front tilt using a digital micromirror device and its terahertz application,” Opt. Lett. 43, 2090–2093 (2018).
[Crossref]

2017 (4)

M.-J. Sun, L.-T. Meng, M. P. Edgar, M. J. Padgett, and N. Radwell, “A Russian dolls ordering of the Hadamard basis for compressive single-pixel imaging,” Sci. Rep. 7, 3464 (2017).
[Crossref]

Y. O-oka and S. Fukatsu, “Differential ghost imaging in time domain,” Appl. Phys. Lett. 111, 061106 (2017).
[Crossref]

P. Ryczkowski, M. Barbier, A. T. Friberg, J. M. Dudley, and G. Genty, “Magnified time-domain ghost imaging,” APL Photon. 2, 046102 (2017).
[Crossref]

S. Zheng, X. Pan, Y. Cai, Q. Lin, Y. Li, S. Xu, J. Li, and D. Fan, “Common-path spectral interferometry for single-shot terahertz electro-optics detection,” Opt. Lett. 42, 4263–4266 (2017).
[Crossref]

2016 (2)

P. Ryczkowski, M. Barbier, A. T. Friberg, J. M. Dudley, and G. Genty, “Ghost imaging in the time domain,” Nat. Photonics 10, 167–170 (2016).
[Crossref]

F. Devaux, P.-A. Moreau, S. Denis, and E. Lantz, “Computational temporal ghost imaging,” Optica 3, 698–701 (2016).
[Crossref]

2015 (1)

S. M. Teo, B. K. Ofori-Okai, C. A. Werley, and K. A. Nelson, “Invited article: single-shot THz detection techniques optimized for multidimensional thz spectroscopy,” Rev. Sci. Instrum. 86, 051301 (2015).
[Crossref]

2013 (1)

M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital angular momentum eigenstates of light,” Nat. Commun. 4, 2781 (2013).
[Crossref]

2012 (1)

2011 (1)

2010 (1)

2009 (1)

M. A. Foster, R. Salem, Y. Okawachi, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Ultrafast waveform compression using a time-domain telescope,” Nat. Photonics 3, 581–585 (2009).
[Crossref]

2008 (3)

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Optical time lens based on four-wave mixing on a silicon chip,” Opt. Lett. 33, 1047–1049 (2008).
[Crossref]

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456, 81–84 (2008).
[Crossref]

E. J. Candès and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Processing Magazine 25(2), 21–30 (2008).
[Crossref]

2007 (3)

2006 (1)

K. Kim, B. Yellampalle, G. Rodriguez, R. Averitt, A. Taylor, and J. Glownia, “Single-shot, interferometric, high-resolution, terahertz field diagnostic,” Appl. Phys. Lett. 88, 041123 (2006).
[Crossref]

2005 (1)

T. Yasui, E. Saneyoshi, and T. Araki, “Asynchronous optical sampling terahertz time-domain spectroscopy for ultrahigh spectral resolution and rapid data acquisition,” Appl. Phys. Lett. 87, 061101 (2005).
[Crossref]

2000 (1)

1999 (1)

1998 (2)

1995 (1)

Q. Wu and X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67, 3523–3525 (1995).
[Crossref]

1994 (2)

M. Kauffman, W. Banyai, A. Godil, and D. Bloom, “Time-to-frequency converter for measuring picosecond optical pulses,” Appl. Phys. Lett. 64, 270–272 (1994).
[Crossref]

B. H. Kolner, “Space-time duality and the theory of temporal imaging,” IEEE J. Quantum Electron. 30, 1951–1963 (1994).
[Crossref]

1993 (1)

D. J. Kane and R. Trebino, “Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating,” IEEE J. Quantum Electron. 29, 571–579 (1993).
[Crossref]

1992 (1)

1989 (1)

1971 (1)

H. Dammann and K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[Crossref]

Akiyama, K.

Altmann, Y.

Y. Altmann, S. McLaughlin, M. J. Padgett, V. K. Goyal, A. O. Hero, and D. Faccio, “Quantum-inspired computational imaging,” Science 361, eaat2298 (2018).
[Crossref]

Araki, T.

T. Yasui, E. Saneyoshi, and T. Araki, “Asynchronous optical sampling terahertz time-domain spectroscopy for ultrahigh spectral resolution and rapid data acquisition,” Appl. Phys. Lett. 87, 061101 (2005).
[Crossref]

Averitt, R.

K. Kim, B. Yellampalle, G. Rodriguez, R. Averitt, A. Taylor, and J. Glownia, “Single-shot, interferometric, high-resolution, terahertz field diagnostic,” Appl. Phys. Lett. 88, 041123 (2006).
[Crossref]

Banyai, W.

M. Kauffman, W. Banyai, A. Godil, and D. Bloom, “Time-to-frequency converter for measuring picosecond optical pulses,” Appl. Phys. Lett. 64, 270–272 (1994).
[Crossref]

Barbier, M.

P. Ryczkowski, M. Barbier, A. T. Friberg, J. M. Dudley, and G. Genty, “Magnified time-domain ghost imaging,” APL Photon. 2, 046102 (2017).
[Crossref]

P. Ryczkowski, M. Barbier, A. T. Friberg, J. M. Dudley, and G. Genty, “Ghost imaging in the time domain,” Nat. Photonics 10, 167–170 (2016).
[Crossref]

Bartels, A.

A. Bartels, R. Cerna, C. Kistner, A. Thoma, F. Hudert, C. Janke, and T. Dekorsy, “Ultrafast time-domain spectroscopy based on high-speed asynchronous optical sampling,” Rev. Sci. Instrum. 78, 035107 (2007).
[Crossref]

Bartels, L.

Bennett, C.

Bielawski, S.

A. Tikan, S. Bielawski, C. Szwaj, S. Randoux, and P. Suret, “Single-shot measurement of phase and amplitude by using a heterodyne time-lens system and ultrafast digital time-holography,” Nat. Photonics 12, 228–234 (2018).
[Crossref]

Blanchard, F.

Bloom, D.

M. Kauffman, W. Banyai, A. Godil, and D. Bloom, “Time-to-frequency converter for measuring picosecond optical pulses,” Appl. Phys. Lett. 64, 270–272 (1994).
[Crossref]

Blu, T.

R. I. Stantchev, X. Yu, T. Blu, and E. Pickwell-MacPherson, “Real-time terahertz imaging with a single-pixel detector,” Nat. Commun. 11, 2535 (2020).
[Crossref]

Bonn, M.

Boyd, R. W.

J. Zhao, E. Yiwen, K. Williams, X.-C. Zhang, and R. W. Boyd, “Spatial sampling of terahertz fields with sub-wavelength accuracy via probe-beam encoding,” Light Sci. Appl. 8, 55 (2019).
[Crossref]

M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital angular momentum eigenstates of light,” Nat. Commun. 4, 2781 (2013).
[Crossref]

Cai, Y.

Candès, E. J.

E. J. Candès and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Processing Magazine 25(2), 21–30 (2008).
[Crossref]

Cerna, R.

A. Bartels, R. Cerna, C. Kistner, A. Thoma, F. Hudert, C. Janke, and T. Dekorsy, “Ultrafast time-domain spectroscopy based on high-speed asynchronous optical sampling,” Rev. Sci. Instrum. 78, 035107 (2007).
[Crossref]

Chen, P.-X.

Chen, Y.-F.

Y. Tian, H. Ge, X.-J. Zhang, X.-Y. Xu, M.-H. Lu, Y. Jing, and Y.-F. Chen, “Acoustic ghost imaging in the time domain,” Phys. Rev. Appl. 13, 064044 (2020).
[Crossref]

Dammann, H.

H. Dammann and K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[Crossref]

Dändliker, R.

Dekorsy, T.

A. Bartels, R. Cerna, C. Kistner, A. Thoma, F. Hudert, C. Janke, and T. Dekorsy, “Ultrafast time-domain spectroscopy based on high-speed asynchronous optical sampling,” Rev. Sci. Instrum. 78, 035107 (2007).
[Crossref]

Denis, S.

Devaux, F.

Dickey, F. M.

Dudley, J. M.

H. Wu, P. Ryczkowski, A. T. Friberg, J. M. Dudley, and G. Genty, “Temporal ghost imaging using wavelength conversion and two-color detection,” Optica 6, 902–906 (2019).
[Crossref]

P. Ryczkowski, M. Barbier, A. T. Friberg, J. M. Dudley, and G. Genty, “Magnified time-domain ghost imaging,” APL Photon. 2, 046102 (2017).
[Crossref]

P. Ryczkowski, M. Barbier, A. T. Friberg, J. M. Dudley, and G. Genty, “Ghost imaging in the time domain,” Nat. Photonics 10, 167–170 (2016).
[Crossref]

Edgar, M. P.

M. P. Edgar, G. M. Gibson, and M. J. Padgett, “Principles and prospects for single-pixel imaging,” Nat. Photonics 13, 13–20 (2019).
[Crossref]

M.-J. Sun, L.-T. Meng, M. P. Edgar, M. J. Padgett, and N. Radwell, “A Russian dolls ordering of the Hadamard basis for compressive single-pixel imaging,” Sci. Rep. 7, 3464 (2017).
[Crossref]

Faccio, D.

Y. Altmann, S. McLaughlin, M. J. Padgett, V. K. Goyal, A. O. Hero, and D. Faccio, “Quantum-inspired computational imaging,” Science 361, eaat2298 (2018).
[Crossref]

Fan, D.

Foster, M. A.

M. A. Foster, R. Salem, Y. Okawachi, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Ultrafast waveform compression using a time-domain telescope,” Nat. Photonics 3, 581–585 (2009).
[Crossref]

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456, 81–84 (2008).
[Crossref]

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Optical time lens based on four-wave mixing on a silicon chip,” Opt. Lett. 33, 1047–1049 (2008).
[Crossref]

Friberg, A. T.

H. Wu, P. Ryczkowski, A. T. Friberg, J. M. Dudley, and G. Genty, “Temporal ghost imaging using wavelength conversion and two-color detection,” Optica 6, 902–906 (2019).
[Crossref]

P. Ryczkowski, M. Barbier, A. T. Friberg, J. M. Dudley, and G. Genty, “Magnified time-domain ghost imaging,” APL Photon. 2, 046102 (2017).
[Crossref]

P. Ryczkowski, M. Barbier, A. T. Friberg, J. M. Dudley, and G. Genty, “Ghost imaging in the time domain,” Nat. Photonics 10, 167–170 (2016).
[Crossref]

T. Shirai, T. Setälä, and A. T. Friberg, “Temporal ghost imaging with classical non-stationary pulsed light,” J. Opt. Soc. Am. B 27, 2549–2555 (2010).
[Crossref]

Fukatsu, S.

Y. O-oka and S. Fukatsu, “Differential ghost imaging in time domain,” Appl. Phys. Lett. 111, 061106 (2017).
[Crossref]

Gaeta, A. L.

Y. Okawachi, R. Salem, A. R. Johnson, K. Saha, J. S. Levy, M. Lipson, and A. L. Gaeta, “Asynchronous single-shot characterization of high-repetition-rate ultrafast waveforms using a time-lens-based temporal magnifier,” Opt. Lett. 37, 4892–4894 (2012).
[Crossref]

M. A. Foster, R. Salem, Y. Okawachi, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Ultrafast waveform compression using a time-domain telescope,” Nat. Photonics 3, 581–585 (2009).
[Crossref]

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Optical time lens based on four-wave mixing on a silicon chip,” Opt. Lett. 33, 1047–1049 (2008).
[Crossref]

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456, 81–84 (2008).
[Crossref]

Gale, M. T.

Ge, H.

Y. Tian, H. Ge, X.-J. Zhang, X.-Y. Xu, M.-H. Lu, Y. Jing, and Y.-F. Chen, “Acoustic ghost imaging in the time domain,” Phys. Rev. Appl. 13, 064044 (2020).
[Crossref]

Genty, G.

H. Wu, P. Ryczkowski, A. T. Friberg, J. M. Dudley, and G. Genty, “Temporal ghost imaging using wavelength conversion and two-color detection,” Optica 6, 902–906 (2019).
[Crossref]

P. Ryczkowski, M. Barbier, A. T. Friberg, J. M. Dudley, and G. Genty, “Magnified time-domain ghost imaging,” APL Photon. 2, 046102 (2017).
[Crossref]

P. Ryczkowski, M. Barbier, A. T. Friberg, J. M. Dudley, and G. Genty, “Ghost imaging in the time domain,” Nat. Photonics 10, 167–170 (2016).
[Crossref]

Geraghty, D. F.

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456, 81–84 (2008).
[Crossref]

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Optical time lens based on four-wave mixing on a silicon chip,” Opt. Lett. 33, 1047–1049 (2008).
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G. M. Gibson, S. D. Johnson, and M. J. Padgett, “Single-pixel imaging 12 years on: a review,” Opt. Express 28, 28190–28208 (2020).
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M. P. Edgar, G. M. Gibson, and M. J. Padgett, “Principles and prospects for single-pixel imaging,” Nat. Photonics 13, 13–20 (2019).
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K. Kim, B. Yellampalle, A. Taylor, G. Rodriguez, and J. Glownia, “Single-shot terahertz pulse characterization via two-dimensional electro-optic imaging with dual echelons,” Opt. Lett. 32, 1968–1970 (2007).
[Crossref]

K. Kim, B. Yellampalle, G. Rodriguez, R. Averitt, A. Taylor, and J. Glownia, “Single-shot, interferometric, high-resolution, terahertz field diagnostic,” Appl. Phys. Lett. 88, 041123 (2006).
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M. Kauffman, W. Banyai, A. Godil, and D. Bloom, “Time-to-frequency converter for measuring picosecond optical pulses,” Appl. Phys. Lett. 64, 270–272 (1994).
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H. Dammann and K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
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Y. Altmann, S. McLaughlin, M. J. Padgett, V. K. Goyal, A. O. Hero, and D. Faccio, “Quantum-inspired computational imaging,” Science 361, eaat2298 (2018).
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Hero, A. O.

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Hudert, F.

A. Bartels, R. Cerna, C. Kistner, A. Thoma, F. Hudert, C. Janke, and T. Dekorsy, “Ultrafast time-domain spectroscopy based on high-speed asynchronous optical sampling,” Rev. Sci. Instrum. 78, 035107 (2007).
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Janke, C.

A. Bartels, R. Cerna, C. Kistner, A. Thoma, F. Hudert, C. Janke, and T. Dekorsy, “Ultrafast time-domain spectroscopy based on high-speed asynchronous optical sampling,” Rev. Sci. Instrum. 78, 035107 (2007).
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Jing, Y.

Y. Tian, H. Ge, X.-J. Zhang, X.-Y. Xu, M.-H. Lu, Y. Jing, and Y.-F. Chen, “Acoustic ghost imaging in the time domain,” Phys. Rev. Appl. 13, 064044 (2020).
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Johnson, S. D.

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D. J. Kane and R. Trebino, “Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating,” IEEE J. Quantum Electron. 29, 571–579 (1993).
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M. Kauffman, W. Banyai, A. Godil, and D. Bloom, “Time-to-frequency converter for measuring picosecond optical pulses,” Appl. Phys. Lett. 64, 270–272 (1994).
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Kim, K.

K. Kim, B. Yellampalle, A. Taylor, G. Rodriguez, and J. Glownia, “Single-shot terahertz pulse characterization via two-dimensional electro-optic imaging with dual echelons,” Opt. Lett. 32, 1968–1970 (2007).
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K. Kim, B. Yellampalle, G. Rodriguez, R. Averitt, A. Taylor, and J. Glownia, “Single-shot, interferometric, high-resolution, terahertz field diagnostic,” Appl. Phys. Lett. 88, 041123 (2006).
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A. Bartels, R. Cerna, C. Kistner, A. Thoma, F. Hudert, C. Janke, and T. Dekorsy, “Ultrafast time-domain spectroscopy based on high-speed asynchronous optical sampling,” Rev. Sci. Instrum. 78, 035107 (2007).
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B. H. Kolner, “Space-time duality and the theory of temporal imaging,” IEEE J. Quantum Electron. 30, 1951–1963 (1994).
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B. H. Kolner and M. Nazarathy, “Temporal imaging with a time lens,” Opt. Lett. 14, 630–632 (1989).
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Y. Okawachi, R. Salem, A. R. Johnson, K. Saha, J. S. Levy, M. Lipson, and A. L. Gaeta, “Asynchronous single-shot characterization of high-repetition-rate ultrafast waveforms using a time-lens-based temporal magnifier,” Opt. Lett. 37, 4892–4894 (2012).
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M. A. Foster, R. Salem, Y. Okawachi, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Ultrafast waveform compression using a time-domain telescope,” Nat. Photonics 3, 581–585 (2009).
[Crossref]

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456, 81–84 (2008).
[Crossref]

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Optical time lens based on four-wave mixing on a silicon chip,” Opt. Lett. 33, 1047–1049 (2008).
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Liu, W.-T.

Lu, M.-H.

Y. Tian, H. Ge, X.-J. Zhang, X.-Y. Xu, M.-H. Lu, Y. Jing, and Y.-F. Chen, “Acoustic ghost imaging in the time domain,” Phys. Rev. Appl. 13, 064044 (2020).
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M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital angular momentum eigenstates of light,” Nat. Commun. 4, 2781 (2013).
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Y. Altmann, S. McLaughlin, M. J. Padgett, V. K. Goyal, A. O. Hero, and D. Faccio, “Quantum-inspired computational imaging,” Science 361, eaat2298 (2018).
[Crossref]

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M.-J. Sun, L.-T. Meng, M. P. Edgar, M. J. Padgett, and N. Radwell, “A Russian dolls ordering of the Hadamard basis for compressive single-pixel imaging,” Sci. Rep. 7, 3464 (2017).
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M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital angular momentum eigenstates of light,” Nat. Commun. 4, 2781 (2013).
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Murate, K.

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S. M. Teo, B. K. Ofori-Okai, C. A. Werley, and K. A. Nelson, “Invited article: single-shot THz detection techniques optimized for multidimensional thz spectroscopy,” Rev. Sci. Instrum. 86, 051301 (2015).
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Y. Okawachi, R. Salem, A. R. Johnson, K. Saha, J. S. Levy, M. Lipson, and A. L. Gaeta, “Asynchronous single-shot characterization of high-repetition-rate ultrafast waveforms using a time-lens-based temporal magnifier,” Opt. Lett. 37, 4892–4894 (2012).
[Crossref]

M. A. Foster, R. Salem, Y. Okawachi, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Ultrafast waveform compression using a time-domain telescope,” Nat. Photonics 3, 581–585 (2009).
[Crossref]

O-oka, Y.

Y. O-oka and S. Fukatsu, “Differential ghost imaging in time domain,” Appl. Phys. Lett. 111, 061106 (2017).
[Crossref]

Padgett, M. J.

G. M. Gibson, S. D. Johnson, and M. J. Padgett, “Single-pixel imaging 12 years on: a review,” Opt. Express 28, 28190–28208 (2020).
[Crossref]

M. P. Edgar, G. M. Gibson, and M. J. Padgett, “Principles and prospects for single-pixel imaging,” Nat. Photonics 13, 13–20 (2019).
[Crossref]

Y. Altmann, S. McLaughlin, M. J. Padgett, V. K. Goyal, A. O. Hero, and D. Faccio, “Quantum-inspired computational imaging,” Science 361, eaat2298 (2018).
[Crossref]

M.-J. Sun, L.-T. Meng, M. P. Edgar, M. J. Padgett, and N. Radwell, “A Russian dolls ordering of the Hadamard basis for compressive single-pixel imaging,” Sci. Rep. 7, 3464 (2017).
[Crossref]

Pan, X.

Pickwell-MacPherson, E.

R. I. Stantchev, X. Yu, T. Blu, and E. Pickwell-MacPherson, “Real-time terahertz imaging with a single-pixel detector,” Nat. Commun. 11, 2535 (2020).
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Prongué, D.

Radwell, N.

M.-J. Sun, L.-T. Meng, M. P. Edgar, M. J. Padgett, and N. Radwell, “A Russian dolls ordering of the Hadamard basis for compressive single-pixel imaging,” Sci. Rep. 7, 3464 (2017).
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A. Tikan, S. Bielawski, C. Szwaj, S. Randoux, and P. Suret, “Single-shot measurement of phase and amplitude by using a heterodyne time-lens system and ultrafast digital time-holography,” Nat. Photonics 12, 228–234 (2018).
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Reider, G. A.

Rodriguez, G.

K. Kim, B. Yellampalle, A. Taylor, G. Rodriguez, and J. Glownia, “Single-shot terahertz pulse characterization via two-dimensional electro-optic imaging with dual echelons,” Opt. Lett. 32, 1968–1970 (2007).
[Crossref]

K. Kim, B. Yellampalle, G. Rodriguez, R. Averitt, A. Taylor, and J. Glownia, “Single-shot, interferometric, high-resolution, terahertz field diagnostic,” Appl. Phys. Lett. 88, 041123 (2006).
[Crossref]

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Ropagnol, X.

Roshtkhari, M. J.

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H. Wu, P. Ryczkowski, A. T. Friberg, J. M. Dudley, and G. Genty, “Temporal ghost imaging using wavelength conversion and two-color detection,” Optica 6, 902–906 (2019).
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P. Ryczkowski, M. Barbier, A. T. Friberg, J. M. Dudley, and G. Genty, “Magnified time-domain ghost imaging,” APL Photon. 2, 046102 (2017).
[Crossref]

P. Ryczkowski, M. Barbier, A. T. Friberg, J. M. Dudley, and G. Genty, “Ghost imaging in the time domain,” Nat. Photonics 10, 167–170 (2016).
[Crossref]

Saha, K.

Salem, R.

Y. Okawachi, R. Salem, A. R. Johnson, K. Saha, J. S. Levy, M. Lipson, and A. L. Gaeta, “Asynchronous single-shot characterization of high-repetition-rate ultrafast waveforms using a time-lens-based temporal magnifier,” Opt. Lett. 37, 4892–4894 (2012).
[Crossref]

M. A. Foster, R. Salem, Y. Okawachi, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Ultrafast waveform compression using a time-domain telescope,” Nat. Photonics 3, 581–585 (2009).
[Crossref]

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456, 81–84 (2008).
[Crossref]

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Optical time lens based on four-wave mixing on a silicon chip,” Opt. Lett. 33, 1047–1049 (2008).
[Crossref]

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T. Yasui, E. Saneyoshi, and T. Araki, “Asynchronous optical sampling terahertz time-domain spectroscopy for ultrahigh spectral resolution and rapid data acquisition,” Appl. Phys. Lett. 87, 061101 (2005).
[Crossref]

Setälä, T.

Shan, J.

Shi, Z.

M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital angular momentum eigenstates of light,” Nat. Commun. 4, 2781 (2013).
[Crossref]

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Stantchev, R. I.

R. I. Stantchev, X. Yu, T. Blu, and E. Pickwell-MacPherson, “Real-time terahertz imaging with a single-pixel detector,” Nat. Commun. 11, 2535 (2020).
[Crossref]

Sun, M.-J.

M.-J. Sun, L.-T. Meng, M. P. Edgar, M. J. Padgett, and N. Radwell, “A Russian dolls ordering of the Hadamard basis for compressive single-pixel imaging,” Sci. Rep. 7, 3464 (2017).
[Crossref]

Sun, S.-H.

Suret, P.

A. Tikan, S. Bielawski, C. Szwaj, S. Randoux, and P. Suret, “Single-shot measurement of phase and amplitude by using a heterodyne time-lens system and ultrafast digital time-holography,” Nat. Photonics 12, 228–234 (2018).
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A. Tikan, S. Bielawski, C. Szwaj, S. Randoux, and P. Suret, “Single-shot measurement of phase and amplitude by using a heterodyne time-lens system and ultrafast digital time-holography,” Nat. Photonics 12, 228–234 (2018).
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Tang, G.-Z.

Taylor, A.

K. Kim, B. Yellampalle, A. Taylor, G. Rodriguez, and J. Glownia, “Single-shot terahertz pulse characterization via two-dimensional electro-optic imaging with dual echelons,” Opt. Lett. 32, 1968–1970 (2007).
[Crossref]

K. Kim, B. Yellampalle, G. Rodriguez, R. Averitt, A. Taylor, and J. Glownia, “Single-shot, interferometric, high-resolution, terahertz field diagnostic,” Appl. Phys. Lett. 88, 041123 (2006).
[Crossref]

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S. M. Teo, B. K. Ofori-Okai, C. A. Werley, and K. A. Nelson, “Invited article: single-shot THz detection techniques optimized for multidimensional thz spectroscopy,” Rev. Sci. Instrum. 86, 051301 (2015).
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A. Bartels, R. Cerna, C. Kistner, A. Thoma, F. Hudert, C. Janke, and T. Dekorsy, “Ultrafast time-domain spectroscopy based on high-speed asynchronous optical sampling,” Rev. Sci. Instrum. 78, 035107 (2007).
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Y. Tian, H. Ge, X.-J. Zhang, X.-Y. Xu, M.-H. Lu, Y. Jing, and Y.-F. Chen, “Acoustic ghost imaging in the time domain,” Phys. Rev. Appl. 13, 064044 (2020).
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A. Tikan, S. Bielawski, C. Szwaj, S. Randoux, and P. Suret, “Single-shot measurement of phase and amplitude by using a heterodyne time-lens system and ultrafast digital time-holography,” Nat. Photonics 12, 228–234 (2018).
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D. J. Kane and R. Trebino, “Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating,” IEEE J. Quantum Electron. 29, 571–579 (1993).
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Turner-Foster, A. C.

M. A. Foster, R. Salem, Y. Okawachi, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Ultrafast waveform compression using a time-domain telescope,” Nat. Photonics 3, 581–585 (2009).
[Crossref]

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456, 81–84 (2008).
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E. J. Candès and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Processing Magazine 25(2), 21–30 (2008).
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Weling, A. S.

Werley, C. A.

S. M. Teo, B. K. Ofori-Okai, C. A. Werley, and K. A. Nelson, “Invited article: single-shot THz detection techniques optimized for multidimensional thz spectroscopy,” Rev. Sci. Instrum. 86, 051301 (2015).
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J. Zhao, E. Yiwen, K. Williams, X.-C. Zhang, and R. W. Boyd, “Spatial sampling of terahertz fields with sub-wavelength accuracy via probe-beam encoding,” Light Sci. Appl. 8, 55 (2019).
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Wu, Q.

Q. Wu and X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67, 3523–3525 (1995).
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Xu, X.-Y.

Y. Tian, H. Ge, X.-J. Zhang, X.-Y. Xu, M.-H. Lu, Y. Jing, and Y.-F. Chen, “Acoustic ghost imaging in the time domain,” Phys. Rev. Appl. 13, 064044 (2020).
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Xu, Y.-K.

Yasuda, T.

Yasui, T.

T. Yasui, E. Saneyoshi, and T. Araki, “Asynchronous optical sampling terahertz time-domain spectroscopy for ultrahigh spectral resolution and rapid data acquisition,” Appl. Phys. Lett. 87, 061101 (2005).
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K. Kim, B. Yellampalle, A. Taylor, G. Rodriguez, and J. Glownia, “Single-shot terahertz pulse characterization via two-dimensional electro-optic imaging with dual echelons,” Opt. Lett. 32, 1968–1970 (2007).
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K. Kim, B. Yellampalle, G. Rodriguez, R. Averitt, A. Taylor, and J. Glownia, “Single-shot, interferometric, high-resolution, terahertz field diagnostic,” Appl. Phys. Lett. 88, 041123 (2006).
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J. Zhao, E. Yiwen, K. Williams, X.-C. Zhang, and R. W. Boyd, “Spatial sampling of terahertz fields with sub-wavelength accuracy via probe-beam encoding,” Light Sci. Appl. 8, 55 (2019).
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R. I. Stantchev, X. Yu, T. Blu, and E. Pickwell-MacPherson, “Real-time terahertz imaging with a single-pixel detector,” Nat. Commun. 11, 2535 (2020).
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J. Zhao, E. Yiwen, K. Williams, X.-C. Zhang, and R. W. Boyd, “Spatial sampling of terahertz fields with sub-wavelength accuracy via probe-beam encoding,” Light Sci. Appl. 8, 55 (2019).
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Y. Tian, H. Ge, X.-J. Zhang, X.-Y. Xu, M.-H. Lu, Y. Jing, and Y.-F. Chen, “Acoustic ghost imaging in the time domain,” Phys. Rev. Appl. 13, 064044 (2020).
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Zhao, J.

J. Zhao, E. Yiwen, K. Williams, X.-C. Zhang, and R. W. Boyd, “Spatial sampling of terahertz fields with sub-wavelength accuracy via probe-beam encoding,” Light Sci. Appl. 8, 55 (2019).
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APL Photon. (1)

P. Ryczkowski, M. Barbier, A. T. Friberg, J. M. Dudley, and G. Genty, “Magnified time-domain ghost imaging,” APL Photon. 2, 046102 (2017).
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Appl. Opt. (1)

Appl. Phys. Lett. (5)

K. Kim, B. Yellampalle, G. Rodriguez, R. Averitt, A. Taylor, and J. Glownia, “Single-shot, interferometric, high-resolution, terahertz field diagnostic,” Appl. Phys. Lett. 88, 041123 (2006).
[Crossref]

T. Yasui, E. Saneyoshi, and T. Araki, “Asynchronous optical sampling terahertz time-domain spectroscopy for ultrahigh spectral resolution and rapid data acquisition,” Appl. Phys. Lett. 87, 061101 (2005).
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Y. O-oka and S. Fukatsu, “Differential ghost imaging in time domain,” Appl. Phys. Lett. 111, 061106 (2017).
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Q. Wu and X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67, 3523–3525 (1995).
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M. Kauffman, W. Banyai, A. Godil, and D. Bloom, “Time-to-frequency converter for measuring picosecond optical pulses,” Appl. Phys. Lett. 64, 270–272 (1994).
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IEEE J. Quantum Electron. (2)

B. H. Kolner, “Space-time duality and the theory of temporal imaging,” IEEE J. Quantum Electron. 30, 1951–1963 (1994).
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IEEE Signal Processing Magazine (1)

E. J. Candès and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Processing Magazine 25(2), 21–30 (2008).
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J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

Light Sci. Appl. (1)

J. Zhao, E. Yiwen, K. Williams, X.-C. Zhang, and R. W. Boyd, “Spatial sampling of terahertz fields with sub-wavelength accuracy via probe-beam encoding,” Light Sci. Appl. 8, 55 (2019).
[Crossref]

Nat. Commun. (2)

R. I. Stantchev, X. Yu, T. Blu, and E. Pickwell-MacPherson, “Real-time terahertz imaging with a single-pixel detector,” Nat. Commun. 11, 2535 (2020).
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M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital angular momentum eigenstates of light,” Nat. Commun. 4, 2781 (2013).
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Nat. Photonics (4)

P. Ryczkowski, M. Barbier, A. T. Friberg, J. M. Dudley, and G. Genty, “Ghost imaging in the time domain,” Nat. Photonics 10, 167–170 (2016).
[Crossref]

M. P. Edgar, G. M. Gibson, and M. J. Padgett, “Principles and prospects for single-pixel imaging,” Nat. Photonics 13, 13–20 (2019).
[Crossref]

M. A. Foster, R. Salem, Y. Okawachi, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Ultrafast waveform compression using a time-domain telescope,” Nat. Photonics 3, 581–585 (2009).
[Crossref]

A. Tikan, S. Bielawski, C. Szwaj, S. Randoux, and P. Suret, “Single-shot measurement of phase and amplitude by using a heterodyne time-lens system and ultrafast digital time-holography,” Nat. Photonics 12, 228–234 (2018).
[Crossref]

Nature (1)

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456, 81–84 (2008).
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Opt. Commun. (1)

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Phys. Rev. Appl. (1)

Y. Tian, H. Ge, X.-J. Zhang, X.-Y. Xu, M.-H. Lu, Y. Jing, and Y.-F. Chen, “Acoustic ghost imaging in the time domain,” Phys. Rev. Appl. 13, 064044 (2020).
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Sci. Rep. (1)

M.-J. Sun, L.-T. Meng, M. P. Edgar, M. J. Padgett, and N. Radwell, “A Russian dolls ordering of the Hadamard basis for compressive single-pixel imaging,” Sci. Rep. 7, 3464 (2017).
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Science (1)

Y. Altmann, S. McLaughlin, M. J. Padgett, V. K. Goyal, A. O. Hero, and D. Faccio, “Quantum-inspired computational imaging,” Science 361, eaat2298 (2018).
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Supplementary Material (1)

NameDescription
Supplement 1       Supplemental document

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (7)

Fig. 1.
Fig. 1. Comparison of single-pixel imaging and time-domain single-pixel imaging. (a) Typical single-pixel imaging configuration. The photodiode is the bucket detector, which has only one pixel and hence provides no spatial resolution. (b) Our proposed single-pixel temporal imaging configuration. Analogously, the slow photodiode, which lacks the temporal bandwidth to resolve ultrafast signals by itself, works as the “single-pixel” detector in the time domain.
Fig. 2.
Fig. 2. Schematics of the experimental setup and the structure of the TFO gate. (a) Experimental configuration. The yellow dashed box indicates our TFO gate, and the blue dashed box indicates the prepared ultrafast pulse train at the detection ZnTe crystal plane. (b) A detailed sketch illustrates the layout of the DMD and how its geometry leads to our TFO gate. The dark red arrow shows the propagation direction of input ultrafast pulse. $\alpha = 0.21\,\,\rm rad$ is the tilt angle of each micromirror, while $d = 10.8\,\,\unicode{x00B5}{\rm m}$ is the separation between two micromirrors. Dark red lines represent the corresponding pulse front. The $\Delta \tau$ between two TFO copies is given by $\Delta \tau = {\rm \sin}(2\alpha)d/c = 14.66\,\,\rm fs$, where $c$ is the speed of light in air. Note that, in the experiment, the light is normally incident on the DMD. (c) Examples showing how the TFO works. Each effective TFO replica consists of five DMD columns. Due to the long pulse duration of the NIR pulse, the separation between two effective replicas is 240 fs (15 DMD columns) to explicitly show the structure of pulse trains. The red dashed trace indicates that the TFO copies at those temporal position are turned off by modulating the TFO gate. All cross-correlation traces of pulse trains are averaged over nine measurements.
Fig. 3.
Fig. 3. Walsh-ordered Hadamard matrix and the flow chart of the sampling and data processing based on CS. (a) 128-dimensional Walsh-ordered Hadamard matrix, which is used to sample the temporal object in our experiment. (b) Flow chart of the experiment. The probe pulse is temporally modulated by the TFO gate, which is controlled by the computer, based on the row vectors of the Walsh-ordered Hadamard matrix. By correlating the row vectors and the corresponding signals registered on the detector, we can recover the temporal object on the computer. Note that all the arrows shown are used to guide the viewer through the sampling and signal recovery process, but not indicate the propagation direction of light pulse.
Fig. 4.
Fig. 4. Recovered THz electric fields and spectra at different CRs (blue curves). The THz fields and spectra measured by raster scanning a mechanical delay stage (red curves) are shown for comparison. (a), (d) Recovered THz field and spectrum at 20% CR. The fidelity in THz field is 84.30%. and the root mean square error (RMSE) is 14.92%. (b), (e) Recovered THz field and spectrum at 30% CR. The fidelity in THz field is 97.43%, and the RMSE is 7.69%. (c), (f) Recovered THz field and spectrum at 40% CR. The fidelity in THz field is 97.76%, and the RMSE is 7.17%. THz pulses recovered by both CS and raster scanning are measured without averaging and use the same $\Delta \tau$ (64 fs). Due to the limited detection bandwidth of ZnTe crystal, we show the spectra only in 0–4 THz range. (g) Raster scanning using the TFO gate. The sampling rate and acquisition time of each measurement are set to be the same as CS data. Fidelity is 87.35% and RMSE is 13.11%. (h) Measured and theoretical fidelities and RMSEs as functions of CR. The RMSE is mainly limited by the measurement noise.
Fig. 5.
Fig. 5. Recovered THz electric fields and spectra using the distorted TFO gate at 40% CR. Red arrows illustrate the propagation direction of NIR pulses. (a) How we distort the TFO gate with an asymmetric illumination. (b) Measured asymmetric pulse train formed by the distorted TFO copies. The ratio between the maximal and minimal intensities in (b) is about 10. As a comparison, this ratio is about three in Fig. 2(c), while the SNR is the same (${\sim}350$). (c), (d) Corresponding recovered THz field and spectrum. The RMSE in field is 7.21%. (e) How we move the Fourier plane of the DMD 25 mm away from the detection ZnTe plane by moving the TFO gate in the direction as the blue arrow shows. (f) Measured pulse train when the detection ZnTe crystal is 25 mm out of the Fourier plane of the DMD. The intensity envelope becomes irregular and SNR is poor (${\sim}80$). (g), (h) Recovered THz pulse and spectrum using the distorted pulse train in (f). The RMSE in field is 7.66%. (b), (f) Averaged results of nine measurements, while THz pulses recovered by CS and raster scanning have no averaging. All results shown are consistent with theoretical predictions in Supplement 1 Section 5.
Fig. 6.
Fig. 6. Recovered NIR pulses (blue curves) and measured results using raster scanning (red curves). (a) Recovered NIR pulse with 90 fs pulse duration at 80% CR. (b) Recovered NIR pulse with 125 fs pulse duration at 80% CR. (c) Two pulse trains used for NIR measurement. By shifting one DMD column, we shift pulse train 1 16 fs forward to get pulse train 2. (d) Details of the measured pulse trains shown in the black dashed box in (c). One can find that the displacement between two pulse trains is 16 fs, while the separation between two peaks in one pulse train is 256 fs.
Fig. 7.
Fig. 7. CNN-enhanced THz spectroscopy. (a) The sample classification is based on a CNN. Due to the poor SNR, the fingerprints of each sample are lost and cannot be identified from spectra (blue curves), which leads to a classification accuracy of 34.2% without the use of ML. Red curves are desired spectra that we are trying to match. After training the CNN, we have an average classification accuracy of 96.8% at 40% CR. (b) Accuracy as a function of CR. When the sampling rate is 20 Hz, the accuracy rises quickly when the CR increases from 5% to 20%, and then starts to converge, which has a very similar behavior as the fidelity shown in Fig. 4(h). As a comparison, when sampling rate is 50 Hz, the SNR in each measurement becomes 1.73 times smaller than the 20 Hz sampling rate case, and accuracy curve does not start converging even when CR is 100%. All identification accuracies are averaged over five CNN trainings.

Equations (4)

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E i n ( x , y , z , ω 0 , t ) = A 0 ( x , y ) exp ( t 2 τ w 2 ) exp ( i ω 0 t + i k r ) ,
E T F O ( x , y , z , ω 0 , t ) = j = 1 N A j ( x , y ) exp ( ( t j Δ τ ) 2 τ w 2 ) × exp ( i ω 0 ( t j Δ τ ) + i k j r ) ,
E T F O ( x , y , z , ω 0 , t ) = j = 1 N A j ( x , y ) exp ( ( t j Δ τ ) 2 τ w 2 ) × exp ( i ω 0 ( t j Δ τ ) + i k z ) ,
F = E C S | E R S E C S | E C S E R S | E R S .

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