Abstract

Here, we present a comprehensive study of the reconstruction quality in terahertz (THz) pulse time-domain holography. We look into single wavelength reconstructions, as well as broadband recovery enabled by the ultrabroadband nature of radiation and coherent detection enabled by electro-optic or photoconductive sensing. We demonstrate the transverse resolution dependence for amplitude and phase objects on the solid angle of the inline recorded time-domain THz hologram, and then turn to the contrast of reconstructed binary amplitude objects, and further to longitudinal resolution of phase objects. We show that transverse resolution can reach values comparable to the wavelength of the radiation used, and longitudinally, phase objects can be resolved with even greater precision. We compare the obtained resolution with theoretical estimates and show that THz pulse time-domain holography is a powerful non-contact imaging tool.

© 2019 Optical Society of America

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2019 (3)

N. S. Balbekin, M. S. Kulya, A. V. Belashov, A. Gorodetsky, and N. V. Petrov, “Increasing the resolution of the reconstructed image in terahertz pulse time-domain holography,” Sci. Rep. 9, 1–9 (2019).
[Crossref]

M. Kulya, V. Semenova, A. Gorodetsky, V. G. Bespalov, and N. V. Petrov, “Spatio-temporal and spatiospectral metrology of terahertz broadband uniformly topologically charged vortex beams,” Appl. Opt. 58, A90 (2019).
[Crossref]

S. Keren-Zur, M. Tal, S. Fleischer, D. M. Mittleman, and T. Ellenbogen, “Generation of spatiotemporally tailored terahertz wavepackets by nonlinear metasurfaces,” Nat. Commun. 10, 1778 (2019).
[Crossref]

2018 (4)

M. S. Kulya, V. A. Semenova, V. G. Bespalov, and N. V. Petrov, “On terahertz pulsed broadband Gauss-Bessel beam free-space propagation,” Sci. Rep. 8, 1390 (2018).
[Crossref]

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

O. Smolyanskaya, N. Chernomyrdin, A. Konovko, K. Zaytsev, I. Ozheredov, O. Cherkasova, M. Nazarov, J.-P. Guillet, S. Kozlov, Y. Kistenev, J.-L. Coutaz, P. Mounaix, V. Vaks, J.-H. Son, H. Cheon, V. Wallace, Y. Feldman, I. Popov, A. Yaroslavsky, A. Shkurinov, and V. Tuchin, “Terahertz biophotonics as a tool for studies of dielectric and spectral properties of biological tissues and liquids,” Prog. Quantum Electron. 62, 1–77 (2018).
[Crossref]

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

2017 (3)

S. Lepeshov, A. Gorodetsky, A. Krasnok, E. Rafailov, and P. Belov, “Enhancement of terahertz photoconductive antenna operation by optical nanoantennas,” Laser Photon. Rev. 11, 1600199 (2017).
[Crossref]

S. S. Dhillon, M. S. Vitiello, E. H. Linfield, A. G. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, G. P. Williams, E. Castro-Camus, D. R. S. Cumming, F. Simoens, I. Escorcia-Carranza, J. Grant, S. Lucyszyn, M. Kuwata-Gonokami, K. Konishi, M. Koch, C. A. Schmuttenmaer, T. L. Cocker, R. Huber, A. G. Markelz, Z. D. Taylor, V. P. Wallace, J. A. Zeitler, J. Sibik, T. M. Korter, B. Ellison, S. Rea, P. Goldsmith, K. B. Cooper, R. Appleby, D. Pardo, P. G. Huggard, V. Krozer, H. Shams, M. Fice, C. Renaud, A. Seeds, A. Stöhr, M. Naftaly, N. Ridler, R. Clarke, J. E. Cunningham, and M. B. Johnston, “The 2017 terahertz science and technology roadmap,” J. Phys. D 50, 043001 (2017).
[Crossref]

M. Kulya, N. Balbekin, I. Gredyuhina, M. Uspenskaya, A. Nechiporenko, and N. Petrov, “Computational terahertz imaging with dispersive objects,” J. Mod. Opt. 64, 1283–1288 (2017).
[Crossref]

2016 (4)

N. V. Petrov, M. S. Kulya, A. N. Tsypkin, V. G. Bespalov, and A. Gorodetsky, “Application of terahertz pulse time-domain holography for phase imaging,” IEEE Trans. Terahertz Sci. Technol. 6, 464–472 (2016).
[Crossref]

A. Koulouklidis, V. Y. Fedorov, and S. Tzortzakis, “Spectral bandwidth scaling laws and reconstruction of THz wave packets generated from two-color laser plasma filaments,” Phys. Rev. A 93, 033844 (2016).
[Crossref]

Y. A. Kapoyko, A. A. Drozdov, S. A. Kozlov, and X.-C. Zhang, “Evolution of few-cycle pulses in nonlinear dispersive media: velocity of the center of mass and root-mean-square duration,” Phys. Rev. A 94, 033803 (2016).
[Crossref]

J. Hu, Q. Li, and G. Chen, “Reconstruction of double-exposed terahertz hologram of non-isolated object,” J. Infrared Millim. Terahertz Waves 37, 328–339 (2016).
[Crossref]

2015 (9)

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

H. Huang, “Application of autofocusing methods in continuous-wave terahertz in-line digital holography,” Opt. Commun. 346, 93–98 (2015).
[Crossref]

G. Chen and Q. Li, “Markov chain Monte Carlo sampling based terahertz holography image denoising,” Appl. Opt. 54, 4345–4351 (2015).
[Crossref]

L. Rong, “Terahertz in-line digital holography of human hepatocellular carcinoma tissue,” Sci. Rep. 5, 8445 (2015).
[Crossref]

M. S. Heimbeck, W. R. Ng, D. R. Golish, M. E. Gehm, and H. O. Everitt, “Terahertz digital holographic imaging of voids within visibly opaque dielectrics,” IEEE Trans. Terahertz Sci. Technol. 5, 110–116 (2015).
[Crossref]

Y. Y. Choporova, B. A. Knyazev, and M. S. Mitkov, “Classical holography in the terahertz range: recording and reconstruction techniques,” IEEE Trans. Terahertz Sci. Technol. 5, 836–844 (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]

E. P. Parrott and J. A. Zeitler, “Terahertz time-domain and low-frequency Raman spectroscopy of organic materials,” Appl. Spectrosc. 69, 1–25 (2015).
[Crossref]

N. S. Balbekin, E. V. Novoselov, P. V. Pavlov, V. G. Bespalov, and N. V. Petrov, “Nondestructive monitoring of aircraft composites using terahertz radiation,” Proc. SPIE 9448, 94482D (2015).
[Crossref]

2014 (4)

J. P. Guillet, B. Recur, L. Frederique, B. Bousquet, L. Canioni, I. Manek-Hönninger, P. Desbarats, and P. Mounaix, “Review of terahertz tomography techniques,” J. Infrared Millim. Terahertz Waves 35, 382–411 (2014).
[Crossref]

L. Rong, T. Latychevskaia, D. Wang, X. Zhou, H. Huang, Z. Li, and Y. Wang, “Terahertz in-line digital holography of dragonfly hindwing: amplitude and phase reconstruction at enhanced resolution by extrapolation,” Opt. Express 22, 17236–17245 (2014).
[Crossref]

J. Hu, Q. Li, and S. Cui, “Research on object-plane constraints and hologram expansion in phase retrieval algorithms for continuous-wave terahertz inline digital holography reconstruction,” Appl. Opt. 53, 7112–7119 (2014).
[Crossref]

I. A. Shevkunov, N. S. Balbekin, and N. V. Petrov, “Comparison of digital holography and iterative phase retrieval methods for wavefront reconstruction,” Proc. SPIE 9271, 927128 (2014).
[Crossref]

2013 (1)

N. V. Petrov, A. A. Gorodetsky, and V. Bespalov, “Holography and phase retrieval in terahertz imaging,” Proc. SPIE 8846, 88460S (2013).
[Crossref]

2012 (2)

2011 (4)

M. S. Heimbeck, M. K. Kim, D. A. Gregory, and H. O. Everitt, “Terahertz digital holography using angular spectrum and dual wavelength reconstruction methods,” Opt. Express 19, 9192 (2011).
[Crossref]

B. A. Knyazev, V. S. Cherkassky, Y. Y. Choporova, V. V. Gerasimov, M. G. Vlasenko, M. A. Demyanenko, and D. G. Esaev, “Real-time imaging using a high-power monochromatic terahertz source: comparative description of imaging techniques with examples of application,” J. Infrared Millim. Terahertz Waves 32, 1207–1222 (2011).
[Crossref]

S.-H. Ding, Q. Li, Y.-D. Li, and Q. Wang, “Continuous-wave terahertz digital holography by use of a pyroelectric array camera,” Opt. Lett. 36, 1993–1995 (2011).
[Crossref]

P. Jepsen, D. Cooke, and M. Koch, “Terahertz spectroscopy and imaging - modern techniques and applications,” Laser Photon. Rev. 5, 124–166 (2011).
[Crossref]

2010 (2)

A. Tamminen, J. Ala-Laurinaho, and A. V. Räisänen, “Indirect holographic imaging: evaluation of image quality at 310  GHz,” Proc. SPIE 7670, 76700A (2010).
[Crossref]

A. Gorodetsky and V. Bespalov, “THz pulse time-domain holography,” Proc. SPIE 7601, 760107 (2010).
[Crossref]

2009 (2)

W. L. Chan, H.-T. Chen, A. J. Taylor, I. Brener, M. J. Cich, and D. M. Mittleman, “A spatial light modulator for terahertz beams,” Appl. Phys. Lett. 94, 213511 (2009).
[Crossref]

A. A. Andreev, V. G. Bespalov, A. A. Gorodetskii, S. A. Kozlov, V. N. Krylov, G. V. Lukomskii, E. V. Novoselov, N. V. Petrov, S. E. Putilin, and S. A. Stumpf, “Generation of ultrabroadband terahertz radiation under optical breakdown of air by two femtosecond pulses of different frequencies,” Opt. Spectrosc. 107, 538–544 (2009).
[Crossref]

2008 (2)

P. Picart and J. Leval, “General theoretical formulation of image formation in digital Fresnel holography,” J. Opt. Soc. Am. A 25, 1744 (2008).
[Crossref]

Y. Zhang, W. Zhou, X. Wang, Y. Cui, and W. Sun, “Terahertz digital holography,” Strain 44, 380–385 (2008).
[Crossref]

2007 (6)

V. G. Bespalov and A. A. Gorodetskii, “Modeling of referenceless holographic recording and reconstruction of images by means of pulsed terahertz radiation,” J. Opt. Technol. 74, 745 (2007).
[Crossref]

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1, 97–105 (2007).
[Crossref]

W. Chan, J. Deibel, and D. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys. 70, 1325–1379 (2007).
[Crossref]

M. Leahy-Hoppa, M. Fitch, X. Zheng, L. Hayden, and R. Osiander, “Wideband terahertz spectroscopy of explosives,” Chem. Phys. Lett. 434, 227–230 (2007).
[Crossref]

J. Zeitler, “Terahertz pulsed spectroscopy and imaging in the pharmaceutical setting-a review,” J. Pharm. Pharmacol. 59, 209–223 (2007).
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Petrov, N. V.

M. Kulya, V. Semenova, A. Gorodetsky, V. G. Bespalov, and N. V. Petrov, “Spatio-temporal and spatiospectral metrology of terahertz broadband uniformly topologically charged vortex beams,” Appl. Opt. 58, A90 (2019).
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N. V. Petrov, M. S. Kulya, A. N. Tsypkin, V. G. Bespalov, and A. Gorodetsky, “Application of terahertz pulse time-domain holography for phase imaging,” IEEE Trans. Terahertz Sci. Technol. 6, 464–472 (2016).
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N. S. Balbekin, E. V. Novoselov, P. V. Pavlov, V. G. Bespalov, and N. V. Petrov, “Nondestructive monitoring of aircraft composites using terahertz radiation,” Proc. SPIE 9448, 94482D (2015).
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Figures (8)

Fig. 1.
Fig. 1. General layout for THz PTDH.
Fig. 2.
Fig. 2. Reconstruction of a binary amplitude object in THz PTDH: (a) test object; (b) test object hologram at the distance of 80 mm; (c) reconstruction of the test object; (d) hologram spatial angle dependence on distance from the object.
Fig. 3.
Fig. 3. (a)–(f) Reconstruction of a binary amplitude object in THz PTDH for different spatial angles; $ z = {\rm const} $ represents the spatial angles for the fixed distance, while $ A = {\rm const} $ shows the dependence on spatial angle for the fixed hologram area. Reconstruction is shown for the frequency of $ \nu = 1.3\,\,{\rm THz} $ . (g)–(i) Reconstruction resolution for the same spatial angles and all spectral components, $ z = {\rm const} $ represents the dependence on spatial angle for the fixed distance, while $ A = {\rm const} $ shows the dependence on spatial angle for the fixed hologram area.
Fig. 4.
Fig. 4. (a)–(f) Reconstruction of a binary phase object in THz PTDH for different spatial angles; $ z = {\rm const} $ represents the spatial angles for the fixed distance, while $ A = {\rm const} $ shows the dependence on spatial angle for the fixed hologram area. Reconstruction is shown for the frequency of $ \nu = 1.3\,\,{\rm THz} $ . (g)–(i) Transverse resolution for different spatial angles and all spectral components. $ z = {\rm const} $ represents the dependence on spatial angle for the fixed distance, while $ A = {\rm const} $ shows the dependence on spatial angle for the fixed hologram area.
Fig. 5.
Fig. 5. (a), (b) Reconstructed profiles for $ A = {\rm const} $ and $ z = {\rm const} $ spatial angle variations from Fig. 3, and (c) reconstruction contrast of a binary amplitude object in THz PTDH for different spatial angles and frequencies; $ z = {\rm const} $ represents the spatial angles for the fixed distance, while $ A = {\rm const} $ shows the dependence on spatial angle for the fixed hologram area.
Fig. 6.
Fig. 6. Reconstruction of transparent objects with the thickness of 1 µm (a), (b); 10 µm (c), (d); and 100 µm (e), (f). Left parts of the profiles are shown for the frequency of 2 THz, and the right parts are the result of averaging between $ 1\,\,{\rm THz} - 2\,\,{\rm THz} $ . (g), (h) Reconstructed profile cross sections at the lines shown in (c) and (d), correspondingly. Reconstruction of a phase object thickness in THz PTDH for different frequencies performed with (i) single 2 THz spectral component, and (j) with broadband radiation covering frequency range of $ 1 - 2\,\,{\rm THz} $ .
Fig. 7.
Fig. 7. Estimation of the resolution in inline PTDH. (a) Illustration of the layout, (b) analytical (blue line) and numerical resolution dependence on the spatial angle.
Fig. 8.
Fig. 8. Resolution (a), (b) and contrast (e), (f) of a binary amplitude object reconstructed by THz PTDH at various spatial angles varied by distance ( $ A = {\rm const} $ ) or hologram area ( $ z = {\rm const} $ ) variation, and resolution (c), (d) of binary phase object reconstruction.

Equations (14)

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E t h z ( t ) = E 0 t τ exp ( t 2 τ 2 ) ,
G t h z ( ν ) = E t h z ( t ) exp ( i 2 π ν t ) d t .
G t h z ( x , y , ν ) = G t h z ( ν ) exp ( x 2 + y 2 ρ 2 ) .
G ( x , y , ν , z = 0 ) = G t h z ( x , y , ν ) O ( x , y , ν ) = G t h z ( x , y , ν ) T ( x , y , ν ) × exp ( i 2 π ν c ( n o b j ( x , y , ν ) 1 ) H ( x , y ) ) ,
C ( f x , f y , ν , z = 0 ) = G ( x , y , ν , z = 0 ) exp ( 2 π i ( x f x + y f y ) ) d x d y .
g ( f x , f y , ν , z ) = C ( f x , f y , ν , z = 0 ) exp ( i 2 π ν n ( ν ) c 1 c 2 ν 2 n 2 ( ν ) ( f x 2 + f y 2 ) z ) .
G ( x , y , ν , z ) = g ( f x , f y , ν , z ) × exp ( 2 π i ( x f x + y f y ) ) d f x d f y .
E ( x , y , t , z ) = G ( x , y , ν , z ) exp ( i 2 π ν t ) d ν ,
Ω = 4 arctan ( A 2 z A 2 + z 2 ) ,
C = A w A b A w + A b ,
H i = φ w i c 2 π ν i ( n 1 ) φ b i c 2 π ν i ( n 1 ) ,
I ( x ) = O , H δ ( x ) h ( x , η ) h ( η , x ) d x d η ,
Δ Φ = 2 π λ × ( ( x η ) 2 + z 2 ( x η ) 2 + z 2 )
d x ( Ω ) = π λ Ω ( 4 π Ω ) .

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