Abstract

Imaging with THz radiation has proved an important tool for both fundamental science and industrial use. Here we review a class of THz imaging implementations, named coherent lensless imaging, that reconstruct the coherent response of arbitrary samples with a minimized experimental setup based only on a coherent source and a camera. After discussing the appropriate sources and detectors to perform them, we detail the fundamental principles and implementations of THz digital holography and phase retrieval. These techniques owe a lot to imaging with different wavelengths, yet innovative concepts are also being developed in the THz range and are ready to be applied in other spectral ranges. This makes our review useful for both the THz and imaging communities, and we hope it will foster their interaction.

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

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J. Wang, J. Zhang, T. Chang, L. Liu, and H.-L. Cui, “Terahertz nondestructive imaging for foreign object detection in glass fibre-reinforced polymer composite panels,” Infrared Phys. Technol. 98, 36–44 (2019).
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Y. L. Lim, K. Bertling, T. Taimre, T. Gillespie, C. Glenn, A. Robinson, D. Indjin, Y. Han, L. Li, E. H. Linfield, A. G. Davies, P. Dean, and A. D. Rakić, “Coherent imaging using laser feedback interferometry with pulsed-mode terahertz quantum cascade lasers,” Opt. Express 27, 10221–10233 (2019).
[Crossref]

L. Valzania, P. Zolliker, and E. Hack, “Coherent reconstruction of a textile and a hidden object with terahertz radiation,” Optica 6, 518–523 (2019).
[Crossref]

M. Jazbinsek, U. Puc, A. Abina, and A. Zidansek, “Organic crystals for THz photonics,” Appl. Sci. 9, 882 (2019).
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Z. Li, Q. Yan, Y. Qin, W. Kong, G. Li, M. Zou, D. Wang, Z. You, and X. Zhou, “Sparsity-based continuous-wave terahertz lens-free on-chip holography with sub-wavelength resolution,” Opt. Express 27, 702–713 (2019).
[Crossref]

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).
[Crossref]

T. Jiang, C. Shen, Z. Zhan, R. Zou, J. Li, L. Fan, T. Xiao, W. Li, Q. Hua 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]

D. Wang, Y. Zhao, L. Rong, M. Wan, X. Shi, Y. Wang, and J. T. Sheridan, “Expanding the field-of-view and profile measurement of covered objects in continuous-wave terahertz reflective digital holography,” Opt. Eng. 58, 023111 (2019).
[Crossref]

F. Blanchard, J. E. Nkeck, D. Matte, R. Nechache, and D. G. Cooke, “A low-cost terahertz camera,” Appl. Sci. 9, 2531 (2019).

2018 (12)

L. Valzania, E. Hack, P. Zolliker, R. Brönnimann, and T. Feurer, “Resolution limits of terahertz ptychography,” Proc. SPIE 10677, 1067720 (2018).
[Crossref]

F. Pfeiffer, “X-ray ptychography,” Nat. Photonics 12, 9–17 (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]

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]

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]

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

Y. Jin, L. Gao, J. Chen, C. Z. Wu, J. L. Reno, and S. Kumar, “High power surface emitting terahertz laser with hybrid second- and fourth-order Bragg gratings,” Nat. Commun. 9, 1407 (2018).
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F. Sizov, “Terahertz radiation detectors: the state-of-the-art,” Semicond. Sci. Technol. 33, 123001 (2018).
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D. M. Mittleman, “Twenty years of terahertz imaging,” Opt. Express 26, 9417–9431 (2018).
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H. Guerboukha, K. Nallappan, and M. Skorobogatiy, “Toward real-time terahertz imaging,” Adv. Opt. Photon. 10, 843–938 (2018).
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D. M. Mackenzie, P. R. Whelan, P. Bøggild, P. U. Jepsen, A. Redo-Sanchez, D. Etayo, N. Fabricius, and D. H. Petersen, “Quality assessment of terahertz time-domain spectroscopy transmission and reflection modes for graphene conductivity mapping,” Opt. Express 26, 9220–9229 (2018).
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P. Dwivedi, A. Konijnenberg, S. Pereira, and H. Urbach, “An alternative method to correct translation positions in ptychography,” Proc. SPIE 10677, 106772A (2018).
[Crossref]

2017 (11)

L.-H. Yeh, L. Tian, and L. Waller, “Structured illumination microscopy with unknown patterns and a statistical prior,” Biomed. Opt. Express 8, 695–711 (2017).
[Crossref]

P. Bøggild, D. M. Mackenzie, P. R. Whelan, D. H. Petersen, J. D. Buron, A. Zurutuza, J. Gallop, L. Hao, and P. U. Jepsen, “Mapping the electrical properties of large-area graphene,” 2D Mater. 4, 042003 (2017).
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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).
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P. Zolliker, M. Rüggeberg, L. Valzania, and E. Hack, “Extracting wood properties from structured THz spectra: birefringence and water content,” IEEE Trans. Terahertz Sci. Technol. 7, 722–731 (2017).
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L. Valzania, P. Zolliker, and E. Hack, “Topography of hidden objects using THz digital holography with multi-beam interferences,” Opt. Express 25, 11038–11047 (2017).
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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. Bowman, Y. Wu, J. Gauch, L. K. Campbell, and M. El-Shenawee, “Terahertz imaging of three-dimensional dehydrated breast cancer tumors,” J. Infrared Millim. Terahertz Waves 38, 766–786 (2017).
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M. Wan, I. Muniraj, R. Malallah, L. Zhao, J. P. Ryle, L. Rong, J. J. Healy, D. Wang, and J. T. Sheridan, “Sparsity based terahertz reflective off-axis digital holography,” Proc. SPIE 10233, 102330T (2017).
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H. Huang, D. Wang, W. Li, L. Rong, Z. D. Taylor, Q. Deng, B. Li, Y. Wang, W. Wu, and S. Panezai, “Continuous-wave terahertz multi-plane in-line digital holography,” Opt. Lasers Eng. 94, 76–81 (2017).
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D. F. Gardner, M. Tanksalvala, E. R. Shanblatt, X. Zhang, B. R. Galloway, C. L. Porter, and R. Karl, C. Bevis, D. E. Adams, H. C. Kapteyn, M. M. Murnane, and G. F. Mancini, “Subwavelength coherent imaging of periodic samples using a 13.5 nm tabletop high-harmonic light source,” Nat. Photonics 11, 259–263 (2017).
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D. F. Gardner, M. Tanksalvala, E. R. Shanblatt, X. Zhang, B. R. Galloway, C. L. Porter, and R. Karl, C. Bevis, D. E. Adams, H. C. Kapteyn, M. M. Murnane, and G. F. Mancini, “Subwavelength coherent imaging of periodic samples using a 13.5 nm tabletop high-harmonic light source,” Nat. Photonics 11, 259–263 (2017).
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A. Maiden, D. Johnson, and P. Li, “Further improvements to the ptychographical iterative engine,” Optica 4, 736–745 (2017).
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2016 (8)

E. H. Tsai, I. Usov, A. Diaz, A. Menzel, and M. Guizar-Sicairos, “X-ray ptychography with extended depth of field,” Opt. Express 24, 29089–29108 (2016).
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Z. Li, L. Li, Y. Qin, G. Li, D. Wang, and X. Zhou, “Resolution and quality enhancement in terahertz in-line holography by sub-pixel sampling with double-distance reconstruction,” Opt. Express 24, 21134–21146 (2016).
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J. Hu, Q. Li, and Y. Zhou, “Support-domain constrained phase retrieval algorithms in terahertz in-line digital holography reconstruction of a nonisolated amplitude object,” Appl. Opt. 55, 379–386 (2016).
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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).
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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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A. Redo-Sanchez, B. Heshmat, A. Aghasi, S. Naqvi, M. Zhang, J. Romberg, and R. Raskar, “Terahertz time-gated spectral imaging for content extraction through layered structures,” Nat. Commun. 7, 12665 (2016).
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X. M. Wang, C. L. Shen, T. Jiang, Z. Q. Zhan, Q. H. Deng, W. H. Li, W. D. Wu, N. Yang, W. D. Chu, and S. Q. Duan, “High-power terahertz quantum cascade lasers with similar to 0.23  W in continuous-wave mode,” AIP Adv. 6, 075210 (2016).
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E. Hack, L. Valzania, G. Gäumann, M. Shalaby, C. P. Hauri, and P. Zolliker, “Comparison of thermal detector arrays for off-axis THz holography and real-time THz imaging,” Sensors 16, 221 (2016).
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2015 (12)

P. Zolliker and E. Hack, “THz holography in reflection using a high resolution microbolometer array,” Opt. Express 23, 10957–10967 (2015).
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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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D. Dufour, L. Marchese, M. Terroux, H. Oulachgar, F. Généreux, M. Doucet, L. Mercier, B. Tremblay, C. Alain, P. Beaupré, N. Blanchard, M. Bolduc, C. Chevalier, D. D’Amato, Y. Desroches, F. Duchesne, L. Gagnon, S. Ilias, H. Jerominek, F. Lagacé, J. Lambert, F. Lamontagne, L. Le Noc, A. Martel, O. Pancrati, J.-E. Paultre, T. Pope, F. Provençal, P. Topart, C. Vachon, S. Verreault, and A. Bergeron,” Review of terahertz technology development at INO,” J. Infrared Millim. Terahertz Wavesc 36, 922–946 (2015).
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N. Oda, S. Kurashina, M. Miyoshi, K. Doi, T. Ishi, T. Sudou, T. Morimoto, H. Goto, and T. Sasaki, “Microbolometer terahertz focal plane array and camera with improved sensitivity in the sub-terahertz region,” J. Infrared Millim. Terahertz Waves 36, 947–960 (2015).
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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).
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M. A. Belkin and F. Capasso, “New frontiers in quantum cascade lasers: high performance room temperature terahertz sources,” Phys. Scripta 90, 118002 (2015).
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S. Y. Jung, Y. F. Jiang, K. Vijayraghavan, A. T. Jiang, F. Demmerle, G. Boehm, X. J. Wang, M. Troccoli, M. C. Amann, and M. A. Belkin, “Recent progress in widely tunable single-mode room temperature terahertz quantum cascade laser sources,” IEEE J. Sel. Top. Quantum Electron. 21, 134–143 (2015).
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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).
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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).
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H. Huang, D. Wang, L. Rong, X. Zhou, Z. Li, and Y. Wang, “Application of autofocusing methods in continuous-wave terahertz in-line digital holography,” Opt. Commun. 346, 93–98 (2015).
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G. Chen and Q. Li, “Markov chain Monte Carlo sampling based terahertz holography image denoising,” Appl. Opt. 54, 4345–4351 (2015).
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R. Horstmeyer, H. Ruan, and C. Yang, “Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue,” Nat. Photonics 9, 563–571 (2015).
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2014 (10)

M. D. Seaberg, B. Zhang, D. F. Gardner, E. R. Shanblatt, M. M. Murnane, H. C. Kapteyn, and D. E. Adams, “Tabletop nanometer extreme ultraviolet imaging in an extended reflection mode using coherent Fresnel ptychography,” Optica 1, 39–44 (2014).
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T. Nguyen, J. Valera, and A. Moore, “Optical thickness measurement with multi-wavelength THz interferometry,” Opt. Lasers Eng. 61, 19–22 (2014).
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L. E. Marchese, M. Terroux, D. Dufour, M. Bolduc, C. Chevalier, F. Généreux, H. Jerominek, and A. Bergeron, “Case study of concealed weapons detection at stand-off distances using a compact, large field-of-view THz camera,” Proc. SPIE 9083, 90832G (2014).
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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).
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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).
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Y. J. Ding, “Progress in terahertz sources based on difference-frequency generation,” J. Opt. Soc. Am. B 31, 2696–2711 (2014).
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F. D. J. Brunner, S. H. Lee, O. P. Kwon, and T. Feurer, “THz generation by optical rectification of near-infrared laser pulses in the organic nonlinear optical crystal HMQ-TMS,” Opt. Mater. Express 4, 1586–1592 (2014).
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E. Hack and P. Zolliker, “Terahertz holography for imaging amplitude and phase objects,” Opt. Express 22, 16079–16086 (2014).
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W. Withayachumnankul and M. Naftaly, “Fundamentals of measurement in terahertz time-domain spectroscopy,” J. Infrared Millim. Terahertz Waves 35, 610–637 (2014).
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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).
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2013 (13)

M. Suga, Y. Sasaki, T. Sasahara, T. Yuasa, and C. Otani, “THz phase-contrast computed tomography based on Mach-Zehnder interferometer using continuous-wave source: proof of the concept,” Opt. Express 21, 25389–25402 (2013).
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É. Hérault, M. Hofman, F. Garet, and J.-L. Coutaz, “Observation of terahertz beam diffraction by fabrics,” Opt. Lett. 38, 2708–2710 (2013).
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A. Redo-Sanchez, N. Laman, B. Schulkin, and T. Tongue, “Review of terahertz technology readiness assessment and applications,” J. Infrared Millim. Terahertz Waves 34, 500–518 (2013).
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T. L. Cocker, V. Jelic, M. Gupta, S. J. Molesky, J. A. Burgess, G. De Los Reyes, L. V. Titova, Y. Y. Tsui, M. R. Freeman, and F. A. Hegmann, “An ultrafast terahertz scanning tunnelling microscope,” Nat. Photonics 7, 620–625 (2013).
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J. Oden, J. Meilhan, J. Lalanne-Dera, J.-F. Roux, F. Garet, J.-L. Coutaz, and F. Simoens, “Imaging of broadband terahertz beams using an array of antenna-coupled microbolometers operating at room temperature,” Opt. Express 21, 4817–4825 (2013).
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F. Simoens, J. Meilhan, S. Gidon, G. Lasfargues, J. L. Dera, J. L. Ouvrier-Buffet, S. Pocas, W. Rabaud, F. Guellec, B. Dupont, S. Martin, and A. C. Simon, “Antenna-coupled microbolometer based uncooled 2D array and camera for 2D real-time terahertz imaging,” Proc. SPIE 8846, 88460O (2013).
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M. Sakhno, A. Golenkov, and F. Sizov, “Uncooled detector challenges: millimeter-wave and terahertz long channel field effect transistor and Schottky barrier diode detectors,” J. Appl. Phys. 114, 164503 (2013).
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R. Han, Y. Zhang, Y. Kim, D. Y. Kim, H. Shichijo, E. Afshari, and K. O. Kenneth, “Active terahertz imaging using Schottky diodes in CMOS: array and 860-GHz pixel,” IEEE J. Solid-State Circuits 48, 2296–2308 (2013).
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I. Alexeenko, J.-F. Vandenrijt, G. Pedrini, C. Thizy, B. Vollheim, W. Osten, and M. P. Georges, “Nondestructive testing by using long-wave infrared interferometric techniques with CO2 lasers and microbolometer arrays,” Appl. Opt. 52, A56–A67 (2013).
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F. Zhang, I. Peterson, J. Vila-Comamala, A. Diaz, F. Berenguer, R. Bean, B. Chen, A. Menzel, I. K. Robinson, and J. M. Rodenburg, “Translation position determination in ptychographic coherent diffraction imaging,” Opt. Express 21, 13592–13606 (2013).
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P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494, 68–71 (2013).
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L. Rong, Y. Li, S. Liu, W. Xiao, F. Pan, and D. Wang, “Iterative solution to twin image problem in in-line digital holography,” Opt. Lasers Eng. 51, 553–559 (2013).
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T. Latychevskaia and H.-W. Fink, “Resolution enhancement in digital holography by self-extrapolation of holograms,” Opt. Express 21, 7726–7733 (2013).
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2012 (10)

K. Xue, Q. Li, Y.-D. Li, and Q. Wang, “Continuous-wave terahertz in-line digital holography,” Opt. Lett. 37, 3228–3230 (2012).
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A. Maiden, M. Humphry, M. Sarahan, B. Kraus, and J. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120, 64–72 (2012).
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N. V. Petrov, V. G. Bespalov, and M. V. Volkov, “Phase retrieval of THz radiation using set of 2D spatial intensity measurements with different wavelengths,” Proc. SPIE 8281, 82810J (2012).
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N. V. Petrov, A. N. Galiaskarov, T. Y. Nikolaeva, and V. G. Bespalov, “The features of optimization of a phase retrieval technique in THz frequency range,” Proc. SPIE 8413, 84131T (2012).
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Q. Li, S. Ding, Y. Li, K. Xue, and Q. Wang, “Experimental research on resolution improvement in CW THz digital holography,” Appl. Phys. B 107, 103–110 (2012).
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D. Fast, W. Hurlbut, and V. G. Kozlov, “Extending spectral coverage of BWOs combined with frequency multipliers to 2.6  THz,” Proc. SPIE 8261, 82610L (2012).
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L. Mahler, A. Tredicucci, and M. S. Vitiello, “Quantum cascade laser: a compact, low cost, solid-state source for plasma diagnostics,” J. Instrum. 7, C02018 (2012).
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M. Heimbeck, D. Marks, D. Brady, and H. Everitt, “Terahertz interferometric synthetic aperture tomography for confocal imaging systems,” Opt. Lett. 37, 1316–1318 (2012).
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A. M. Maiden, M. J. Humphry, and J. Rodenburg, “Ptychographic transmission microscopy in three dimensions using a multi-slice approach,” J. Opt. Soc. Am. A 29, 1606–1614 (2012).
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A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6, 283–292 (2012).
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2011 (7)

S. Preu, G. H. Dohler, S. Malzer, L. J. Wang, and A. C. Gossard, “Tunable, continuous-wave terahertz photomixer sources and applications,” J. Appl. Phys. 109, 061301 (2011).
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R. K. May, M. J. Evans, S. Zhong, I. Warr, L. F. Gladden, Y. Shen, and J. A. Zeitler, “Terahertz in-line sensor for direct coating thickness measurement of individual tablets during film coating in real-time,” J. Pharm. Sci. 100, 1535–1544 (2011).
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S. Kumar, “Recent progress in terahertz quantum cascade lasers,” IEEE J. Sel. Top. Quantum Electron. 17, 38–47 (2011).
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J. H. Booske, R. J. Dobbs, C. D. Joye, C. L. Kory, G. R. Neil, G. S. Park, J. Park, and R. J. Temkin, “Vacuum electronic high power terahertz sources,” IEEE Trans. Terahertz Sci. Technol. 1, 54–75 (2011).
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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, 9192–9200 (2011).
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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).
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M. C. Kemp, “Explosives detection by terahertz spectroscopy—a bridge too far?” IEEE Trans. Terahertz Sci. Technol. 1, 282–292 (2011).
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2010 (7)

N. Oda, “Uncooled bolometer-type terahertz focal plane array and camera for real-time imaging,” C. R. Phys. 11, 496–509 (2010).
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C. F. Cull, D. A. Wikner, J. N. Mait, M. Mattheiss, and D. J. Brady, “Millimeter-wave compressive holography,” Appl. Opt. 49, E67–E82 (2010).
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X. Wang, L. Hou, and Y. Zhang, “Continuous-wave terahertz interferometry with multiwavelength phase unwrapping,” Appl. Opt. 49, 5095–5102 (2010).
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L. Le Noc, B. Tremblay, A. Martel, C. Chevalier, N. Blanchard, M. Morissette, L. Mercier, F. Duchesne, L. Gagnon, P. Couture, F. Lévesque, N. Desnoyers, M. Demers, F. Lamontage, H. Jerominek, and A. Bergeron, “1280 × 960  pixel microscanned infrared imaging module,” Proc. SPIE 7660, 766021 (2010).
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A. A. Danylov, T. M. Goyette, J. Waldman, M. J. Coulombe, A. J. Gatesman, R. H. Giles, X. F. Qian, N. Chandrayan, S. Vangala, K. Termkoa, W. D. Goodhue, and W. E. Nixon, “Coherent imaging at 2.4  THz with a CW quantum cascade laser transmitter,” Proc. SPIE 7601, 760105 (2010).
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A. Maestrini, B. Thomas, H. Wang, C. Jung, J. Treuttel, Y. Jin, G. Chattopadhyay, I. Mehdi, and G. Beaudin, “Schottky diode-based terahertz frequency multipliers and mixers,” C. R. Phys. 11, 480–495 (2010).
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H. Minamide and H. Ito, “Frequency-agile terahertz-wave generation and detection using a nonlinear optical conversion, and their applications for imaging,” C. R. Phys. 11, 457–471 (2010).
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2009 (6)

A. Bitzer, H. Merbold, A. Thoman, T. Feurer, H. Helm, and M. Walther, “Terahertz near-field imaging of electric and magnetic resonances of a planar metamaterial,” Opt. Express 17, 3826–3834 (2009).
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S. Martens, B. Gompf, and M. Dressel, “Characterization of continuous-wave terahertz sources: laser mixing versus backward-wave oscillators,” Appl. Opt. 48, 5490–5496 (2009).
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P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
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A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109, 1256–1262 (2009).
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G. Hislop, L. Li, and A. Hellicar, “Phase retrieval for millimeter-and submillimeter-wave imaging,” IEEE Trans. Antennas Propag. 57, 286–290 (2009).
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M. Dem’yanenko, D. Esaev, V. Ovsyuk, B. Fomin, A. Aseev, B. Knyazev, G. Kulipanov, and N. Vinokurov, “Microbolometer detector arrays for the infrared and terahertz ranges,” J. Opt. Technol. 76, 739–743 (2009).
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2008 (11)

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
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O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical iterative engine,” Ultramicroscopy 108, 481–487 (2008).
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M. Guizar-Sicairos, S. T. Thurman, and J. R. Fienup, “Efficient subpixel image registration algorithms,” Opt. Lett. 33, 156–158 (2008).
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K. Matsushima, “Formulation of the rotational transformation of wave fields and their application to digital holography,” Appl. Opt. 47, D110–D116 (2008).
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B. N. Behnken, G. Karunasiri, D. R. Chamberlin, P. R. Robrish, and J. Faist, “Real-time imaging using a 2.8  THz quantum cascade laser and uncooled infrared microbolometer camera,” Opt. Lett. 33, 440–442 (2008).
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Y. He, P. I. Ku, J. Knab, J. Chen, and A. Markelz, “Protein dynamical transition does not require protein structure,” Phys. Rev. Lett. 101, 178103 (2008).
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S. Leinß, T. Kampfrath, K. V. Volkmann, M. Wolf, J. T. Steiner, M. Kira, S. W. Koch, A. Leitenstorfer, and R. Huber, “Terahertz coherent control of optically dark paraexcitons in Cu2O,” Phys. Rev. Lett. 101, 246401 (2008).
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J. M. Rodenburg, “Ptychography and related diffractive imaging methods,” Adv. Imaging Electron Phys. 150, 87–184 (2008).
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E. J. Candès and M. B. Wakin, “An introduction to compressive sampling [a sensing/sampling paradigm that goes against the common knowledge in data acquisition],” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
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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, 121105 (2008).
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W. L. Chan, M. L. Moravec, R. G. Baraniuk, and D. M. Mittleman, “Terahertz imaging with compressed sensing and phase retrieval,” Opt. Lett. 33, 974–976 (2008).
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2007 (7)

R. Piesiewicz, C. Jansen, S. Wietzke, D. Mittleman, M. Koch, and T. Kürner, “Properties of building and plastic materials in the THz range,” Int. J. Infrared Millim. Waves 28, 363–371 (2007).
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B. N. Behnken, M. Lowe, G. Karunasiri, D. Chamberlain, P. Robrish, and J. Faist, “Detection of 3.4  THz radiation from a quantum cascade laser using a microbolometer infrared camera,” Proc. SPIE 6549, 65490C (2007).
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B. S. Williams, “Terahertz quantum-cascade lasers,” Nat. Photonics 1, 517–525 (2007).
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T. Latychevskaia and H.-W. Fink, “Solution to the twin image problem in holography,” Phys. Rev. Lett. 98, 233901 (2007).
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G. Hislop, G. C. James, and A. Hellicar, “Phase retrieval of scattered fields,” IEEE Trans. Antennas Propag. 55, 2332–2341 (2007).
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M. Naftaly and R. E. Miles, “Terahertz time-domain spectroscopy for material characterization,” Proc. IEEE 95, 1658–1665 (2007).
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J. Rodenburg, A. Hurst, and A. Cullis, “Transmission microscopy without lenses for objects of unlimited size,” Ultramicroscopy 107, 227–231 (2007).
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2006 (5)

R. J. Mahon, J. A. Murphy, and W. Lanigan, “Digital holography at millimetre wavelengths,” Opt. Commun. 260, 469–473 (2006).
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Y.-S. Jin, G.-J. Kim, and S.-G. Jeon, “Terahertz dielectric properties of polymers,” J. Korean Phys. Soc. 49, 513–517 (2006).

P. Almoro, G. Pedrini, and W. Osten, “Complete wavefront reconstruction using sequential intensity measurements of a volume speckle field,” Appl. Opt. 45, 8596–8605 (2006).
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X. Xie, J. M. Dai, and X. C. Zhang, “Coherent control of THz wave generation in ambient air,” Phys. Rev. Lett. 96, 075005 (2006).
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A. J. Gatesman, A. Danylov, T. M. Goyette, J. C. Dickinson, R. H. Giles, W. Goodhue, J. Waldman, W. E. Nixon, and W. Hoen, “Terahertz behavior of optical components and common materials,” Proc. SPIE 6212, 62120E (2006).
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2005 (4)

V. Cherkassky, B. Knyazev, V. Kubarev, G. Kulipanov, G. Kuryshev, A. Matveenko, A. Petrov, V. Popik, M. Scheglov, O. Shevchenko, and N. Vinokurov, “Imaging techniques for a high-power THz free electron laser,” Nucl. Instrum. Methods Phys. Res. A 543, 102–109 (2005).
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Y. U. Jeong, G. M. Kazakevitch, H. J. Cha, S. H. Park, and B. C. Lee, “Application of a wide-band compact FEL on THz imaging,” Nucl. Instrum. Methods Phys. Res. A 543, 90–95 (2005).
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H. J. Cha, Y. U. Jeong, S. H. Park, B. C. Lee, and S. H. Park, “Power spectrum and coherence length measurements of a compact terahertz free-electron laser,” J. Korean Phys. Soc. 47, 798–802 (2005).

G. Pedrini, W. Osten, and Y. Zhang, “Wave-front reconstruction from a sequence of interferograms recorded at different planes,” Opt. Lett. 30, 833–835 (2005).
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2004 (4)

J. M. Rodenburg and H. M. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85, 4795–4797 (2004).
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J. Bjarnason, T. Chan, A. Lee, M. Celis, and E. Brown, “Millimeter-wave, terahertz, and mid-infrared transmission through common clothing,” Appl. Phys. Lett. 85, 519–521 (2004).
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A. Dobroiu, M. Yamashita, Y. N. Ohshima, Y. Morita, C. Otani, and K. Kawase, “Terahertz imaging system based on a backward-wave oscillator,” Appl. Opt. 43, 5637–5646 (2004).
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J. Dai, J. Zhang, W. Zhang, and D. Grischkowsky, “Terahertz time-domain spectroscopy characterization of the far-infrared absorption and index of refraction of high-resistivity, float-zone silicon,” J. Opt. Soc. Am. B 21, 1379–1386 (2004).
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2003 (1)

2002 (1)

M. Rochat, L. Ajili, H. Willenberg, J. Faist, H. Beere, G. Davies, E. Linfield, and D. Ritchie, “Low-threshold terahertz quantum-cascade lasers,” Appl. Phys. Lett. 81, 1381–1383 (2002).
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2001 (1)

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1993 (1)

1988 (1)

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1982 (2)

1972 (1)

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Figures (10)

Fig. 1.
Fig. 1. Schematic of off-axis digital holography (simulations). (a) Experimental setup; (b) hologram and (c) modulus of its Fourier transform; (d) amplitude and (e) phase of the reconstructed object function. The inset of (a) shows the average wavevectors of the object beam and reference beam, as well as their difference. Wavelength: 96.5 µm. Scale bars in (b), (d), and (e): 2 mm; scale bar in (c): $ 5{\text{mm}^{ - 1}} $. Adapted with permission from [136].
Fig. 2.
Fig. 2. THz off-axis digital holographic reconstructions in reflection mode of an object moving at 5 mm/s. (a) Photograph of the object, a metallic plate with inscriptions; (b) reconstructed amplitude of the object at one position during its movement; (c) photograph of the plate covered by an optically opaque mask; (d) reconstructed amplitude of the hidden object at the same position as in (b). Scale bars: 4 mm. Adapted from [85] under the terms of the Creative Commons Attribution 4.0 License.
Fig. 3.
Fig. 3. Schematic of in-line digital holography (simulations). (a) Experimental setup; (b) simulated phase object and (c) corresponding hologram; (d) reconstruction where the (d) real [(e) twin] image is brought to focus. In (e), the complex conjugate of the reconstruction is shown, to favor its comparison with (d). Wavelength: 96.5 µm. Scale bars: 2 mm.
Fig. 4.
Fig. 4. THz in-line digital holographic reconstructions. (a) Photograph of the object, a human hepatocellular carcinoma tissue; (b) reconstructed absorption and (c) phase shift from a single $ 12.4 \times 12.4\,\,{\text{mm}^2} $ hologram; (d) reconstructed absorption and (e) phase shift from a larger hologram obtained through aperture synthesis; (f) reconstructed absorption and (g) phase shift after numerically extrapolating the holograms used for reconstructions (d) and (e). The green arrow indicates a cut across a vessel or a region damaged after freezing the object. The blue arrow indicates a vertical line that is a sign of tissue fibrosis, which can be resolved only in (g). Adapted from [108] under the terms of the Creative Commons Attribution 4.0 License.
Fig. 5.
Fig. 5. Steps of a typical phase retrieval technique, using three diffraction patterns recorded at different distances from the object (simulations). Wavelength: 96.5 µm. Scale bars: 2 mm.
Fig. 6.
Fig. 6. Two-intensity phase retrieval. (a) Schematic experimental setup, featuring: a BWO (A) with its waveguide opening (B), a chopper (C), a beam splitter made of non-conducting silicon (D), a detector to monitor the stability of the source (E), a beam stopper to prevent the THz radiation emitted by the source from directly reaching the receiver (F), mirrors (G), (H), a metallic thumbtack used as the object (I), and the receiver (J) moved longitudinally through two sliding blocks (K), (L) and transversely through a 2D stage (M). (b) Amplitude of the reconstructed object and (c) phase of the object and of the incident beam. Adapted with permission from [120] 2019 IEEE.
Fig. 7.
Fig. 7. Phase retrieval imaging behind a moving and scattering barrier. (a) Schematic experimental setup; (b) reconstruction of the wavefronts at the exit of the barrier plane through the SBMIR method; (c) reconstruction of the hidden object and the barrier (top row) assuming that the transversal shifts of the barrier are known a priori, (middle row) retrieving the shifts via cross-correlation, and (bottom row) assuming unknown shifts, which allows the reconstruction of the hidden object only. Scale bars: 2 mm. Adapted with permission from [159] The Optical Society.
Fig. 8.
Fig. 8. Schematic of ptychography (simulations). (a) Experimental setup. (b) Amplitude and (c) phase of the object transmission function reconstructed from only the top-left diffraction pattern. (d) , (f) Amplitude and (e) , (g) phase of the object transmission function after 1 [100] iteration[s]. Wavelength: 96.5 µm. The white scale bar in the top-right panel holds for all the diffraction patterns, while the reconstructions share the same black scale bar in (d). All the scale bars equal 2 mm. Adapted with permission from [136].
Fig. 9.
Fig. 9. Ptychographic reconstruction of a pure amplitude object in the shape of a nine-spoked Siemens star, shown in (a). (b), (d), (f), (c), (e), (g) Diffraction patterns obtained by illuminating the simulated [real] object at the positions enclosed by the circles shown in (a) with the corresponding color. (h) , (i) Amplitude and (j) , (k) phase of the reconstructed object. The insets show the reconstructed probes (left column: simulated probe; right column: real probe; top: amplitude; bottom: phase). All the amplitude distributions share the same color bar next to (a), and all the phase distributions share the same color bar between (j) and (k). Adapted with permission from [86] The Optical Society.
Fig. 10.
Fig. 10. Intensity (label 1) and phase (label 2) of the ptychographic reconstructions with and without correction of the scan positions. (a) Reconstruction of the object after 30 iterations of the ePIE algorithm and (b) after 30 iterations of the ccPIE algorithm; (c) , (d) reconstruction of the object [probe] after 30 iterations of the ccPIE algorithm and 20 iterations of the pcPIE algorithm. Scale bars: 1 mm. Adapted with permission from [109] The Optical Society.

Tables (1)

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Table 1. Combinations of Sources and Detectors Used for THz Lensless Imaging

Equations (32)

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G ( x ) = g ( x ) h L ( x ) .
h L ( x ) | L | i λ exp [ 2 π i sgn ( L ) | x | 2 + L 2 / λ ] | x | 2 + L 2 ,
ρ lat = λ 2 sin ( η ) ,
ρ depth = ρ ϕ λ 2 π ( n 1 ) ,
I ( x ) | R ( x ) + O ( x ) | 2 .
I ( x ) A R 2 ( x ) + A O 2 ( x ) + 2 A R ( x ) A O ( x ) × cos [ ( k R k O ) x + ϕ R ( x ) ϕ O ( x ) ] .
o ( x ) = O ( x ) h d ( x ) .
I ( x ) = | R ( x ) | 2 + | O ( x ) | 2 + O ( x ) R ( x ) + R ( x ) O ( x ) .
R ( x ) I ( x ) = R ( x ) | R ( x ) | 2 + R ( x ) | O ( x ) | 2 + O ( x ) R 2 ( x ) + | R ( x ) | 2 O ( x ) O ( x ) + O ( x ) ,
[ R ( x ) I ( x ) ] h d ( x ) o ( x ) h 2 d ( x ) + o ( x ) ,
I j ( x ) = | o ( x ) h d j ( x ) | 2 .
σ total number of pixels number of pixels of unknown value = N 2 M 2 ,
A j ( x ) ( 1 β ) A j ( x ) + β I j ( x ) .
D O F λ ( d w ) 2 .
Ψ ( x ) = { [ o ( x ) h u ( x ) ] b ( x ) } h d ( x ) ,
Ψ k ( x ) = { [ o ( x ) h u ( x ) ] b ( x x k ) } h d ( x ) .
ψ k ( x ) [ o ( x ) h u ( x ) ] b ( x x k ) .
| Ψ k j ( x ) | 2 | ψ k ( x ) h d j ( x ) | 2 .
| b ( x ) | S k = 1 K [ | ψ k ( x ) | ] ,
ϕ b ( x ) S k = 1 K [ ϕ ψ k ( x ) ] .
o ( x ) = ψ k ( x ) b ( x x k ) k h u ( x ) ,
ψ k ( x ) = p ( x ) o k ( x x k ) ,
Ψ k ( x ) = ψ k ( x ) h d ( x ) .
Ψ k ( x ) = I k ( x ) Ψ k ( x ) | Ψ k ( x ) | ;
ψ k ( x ) = Ψ k ( x ) h d ( x ) .
o k + 1 ( x ) = o k ( x ) + α ( o ) p k ( x + x k ) max | p k ( x + x k ) | 2 × [ ψ k ( x + x k ) ψ k ( x + x k ) ] ,
ψ k ( x ) = p k ( x ) o k ( x x k ) ,
p k + 1 ( x ) = p k ( x ) + α ( p ) o k ( x x k ) max | o k ( x x k ) | 2 [ ψ k ( x ) ψ k ( x ) ] ,
ψ k 0 ( x ) = p k ( x ) o k ( x ( x k + c k ) ) .
ψ km ( x ) = p k ( x ) o k ( x ( x k + c k + c Δ m ) ) ,
Ψ k n ( x ) = ψ k n ( x ) h d ( x ) , n = 0 , 1 , , M ,
x k arg max ξ [ ψ k ( x ) ψ 1 ( x ) ] ( ξ ) ,