Abstract

Continuous-wave (cw) terahertz (THz) phase imaging can accurately and noninvasively present the depth information of an object’s surface and interior. However, a 2π ambiguity limits the measurement of a sample with a thickness larger than the detection wavelength of THz waves. A multiwavelength phase unwrapping method is introduced to the cw THz phase imaging to reconstruct the exact phase map of the object. By using this method, three different types of high-density polyethylene samples were measured, and their phase profiles were well extracted. The result shows that this method is effective in cw THz phase imaging and has the potential to improve the applications of cw THz imaging.

© 2010 Optical Society of America

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2010 (1)

M. Scheller, K. Baaske, and M. Koch, “Multifrequency continuous wave terahertz spectroscopy for absolute thickness determination,” Appl. Phys. Lett. 96, 151112 (2010).
[CrossRef]

2009 (6)

2008 (6)

2007 (3)

2006 (5)

2005 (3)

2004 (1)

2003 (1)

2002 (2)

K. J. Siebert, H. Quast, R. Leonhardt, T. Loffler, M. Thomson, T. Bauer, H. G. Roskos, and S. Czasch, “Continuous-wave all-optoelectronic terahertz imaging,” Appl. Phys. Lett. 80, 3003–3005 (2002).
[CrossRef]

B. Ferguson, S. H. Wang, D. Gray, D. Abbot, and X.-C. Zhang, “T-ray computed tomography,” Opt. Lett. 27, 1312–1314 (2002).
[CrossRef]

2001 (1)

2000 (2)

1998 (2)

1997 (1)

1995 (1)

1971 (1)

Abbot, D.

Alcin, A.

T. Loffler, T. May, C. am Weg, A. Alcin, B. Hils, and H. G. Roskos, “Continuous-wave terahertz imaging with a hybrid system,” Appl. Phys. Lett. 90, 091111 (2007).
[CrossRef]

Alton, J.

am Weg, C.

T. Loffler, T. May, C. am Weg, A. Alcin, B. Hils, and H. G. Roskos, “Continuous-wave terahertz imaging with a hybrid system,” Appl. Phys. Lett. 90, 091111 (2007).
[CrossRef]

Andrianov, A. V.

N. N. Zinov’ev and A. V. Andrianov, “Confocal terahertz imaging,” Appl. Phys. Lett. 95, 011114 (2009).
[CrossRef]

Ariyoshi, S.

S. Ariyoshi, C. Otani, A. Dobroiu, H. Sato, K. Kawase, H. M. Shimizu, T. Taino, and H. Matsuo, “Terahertz imaging with a direct detector based on superconducting tunnel junctions,” Appl. Phys. Lett. 88, 203503 (2006).
[CrossRef]

Arnaud, J. A.

Baaske, K.

M. Scheller, K. Baaske, and M. Koch, “Multifrequency continuous wave terahertz spectroscopy for absolute thickness determination,” Appl. Phys. Lett. 96, 151112 (2010).
[CrossRef]

Baker, C.

Bandyopadhyay, A.

Barat, R.

Barbieri, S.

Bauer, T.

K. J. Siebert, H. Quast, R. Leonhardt, T. Loffler, M. Thomson, T. Bauer, H. G. Roskos, and S. Czasch, “Continuous-wave all-optoelectronic terahertz imaging,” Appl. Phys. Lett. 80, 3003–3005 (2002).
[CrossRef]

Beck, M.

Beere, H. E.

Behnken, B. N.

Bingham, P. R.

Boivin, L.

Breitfeld, F.

Brener, I.

S. Hunsche, M. Koch, I. Brener, and M. C. Nuss, “THz near-field imaging,” Opt. Commun. 150, 22–26 (1998).
[CrossRef]

Buma, T.

Chamberlin, D. R.

Chen, H. W.

Chen, Q.

Chiu, C. M.

Cho, G. G.

Cuevas, F. J.

Cui, Y.

Czasch, S.

K. J. Siebert, H. Quast, R. Leonhardt, T. Loffler, M. Thomson, T. Bauer, H. G. Roskos, and S. Czasch, “Continuous-wave all-optoelectronic terahertz imaging,” Appl. Phys. Lett. 80, 3003–3005 (2002).
[CrossRef]

Dakoff, A.

Darmo, J.

de la Claviere, B.

Debbage, P.

Dem’yanenko, M. A.

M. A. Dem’yanenko, D. G. Esaev, B. A. Knyazev, G. N. Kulipanov, and N. A. Vinokurov, “Imaging with a 90frames/s microbolometer focal plane array and high-power terahertz free electron laser,” Appl. Phys. Lett. 92, 131116 (2008).
[CrossRef]

Dobroiu, A.

S. Ariyoshi, C. Otani, A. Dobroiu, H. Sato, K. Kawase, H. M. Shimizu, T. Taino, and H. Matsuo, “Terahertz imaging with a direct detector based on superconducting tunnel junctions,” Appl. Phys. Lett. 88, 203503 (2006).
[CrossRef]

Esaev, D. G.

M. A. Dem’yanenko, D. G. Esaev, B. A. Knyazev, G. N. Kulipanov, and N. A. Vinokurov, “Imaging with a 90frames/s microbolometer focal plane array and high-power terahertz free electron laser,” Appl. Phys. Lett. 92, 131116 (2008).
[CrossRef]

Faist, J.

Fasching, G.

Federici, J. F.

Federici, M. D.

Ferguson, B.

Franke, E. A.

Franke, J. M.

Gary, D.

Gass, J.

Giovannini, M.

Gray, D.

Han, P. Y.

Hendargo, H. C.

Hils, B.

T. Loffler, T. May, C. am Weg, A. Alcin, B. Hils, and H. G. Roskos, “Continuous-wave terahertz imaging with a hybrid system,” Appl. Phys. Lett. 90, 091111 (2007).
[CrossRef]

Hu, B. B.

Hu, Q.

A. W. M. Lee, Q. Qin, S. Kumar, B. S. Williams, Q. Hu, and J. L. Reno, “Real-time terahertz imaging over a standoff distance (>25 meters),” Appl. Phys. Lett. 89, 141125 (2006).
[CrossRef]

Hubbard, W. M.

Hunsche, S.

S. Hunsche, M. Koch, I. Brener, and M. C. Nuss, “THz near-field imaging,” Opt. Commun. 150, 22–26 (1998).
[CrossRef]

D. M. Mittleman, S. Hunsche, L. Boivin, and M. C. Nuss, “T-ray tomography,” Opt. Lett. 22, 904–906 (1997).
[CrossRef] [PubMed]

Hwang, J. S.

N. Karpowicz, H. Zhong, J. Z. Xu, K. I. Lin, J. S. Hwang, and X.-C. Zhang, “Comparison between pulsed terahertz time-domain imaging and continuous wave terahertz imaging,” Semicond. Sci. Technol. 20, S293–S299 (2005).
[CrossRef]

Hwang, Y. J.

Ichino, S.

Izatt, J. A.

Jiang, Z. P.

Jinno, H.

Karpowicz, N.

N. Karpowicz, H. Zhong, J. Z. Xu, K. I. Lin, J. S. Hwang, and X.-C. Zhang, “Comparison between pulsed terahertz time-domain imaging and continuous wave terahertz imaging,” Semicond. Sci. Technol. 20, S293–S299 (2005).
[CrossRef]

Karunasiri, G.

Kasai, S.

Kawai, M.

Kawase, K.

J. Takayanagi, H. Jinno, S. Ichino, K. Suizu, M. Yamashita, T. Ouchi, S. Kasai, H. Ohtake, H. Uchida, N. Nishizawa, and K. Kawase, “High-resolution time-of-flight terahertz tomography using a femtosecond fiber laser,” Opt. Express 17, 7533–7539 (2009).
[CrossRef]

S. Ariyoshi, C. Otani, A. Dobroiu, H. Sato, K. Kawase, H. M. Shimizu, T. Taino, and H. Matsuo, “Terahertz imaging with a direct detector based on superconducting tunnel junctions,” Appl. Phys. Lett. 88, 203503 (2006).
[CrossRef]

Kim, M. K.

Knyazev, B. A.

M. A. Dem’yanenko, D. G. Esaev, B. A. Knyazev, G. N. Kulipanov, and N. A. Vinokurov, “Imaging with a 90frames/s microbolometer focal plane array and high-power terahertz free electron laser,” Appl. Phys. Lett. 92, 131116 (2008).
[CrossRef]

Koch, M.

M. Scheller, K. Baaske, and M. Koch, “Multifrequency continuous wave terahertz spectroscopy for absolute thickness determination,” Appl. Phys. Lett. 96, 151112 (2010).
[CrossRef]

R. Wilk, F. Breitfeld, M. Mikulics, and M. Koch, “Continuous wave terahertz spectrometer as a noncontact thickness measuring device,” Appl. Opt. 47, 3023–3026(2008).
[CrossRef] [PubMed]

S. Hunsche, M. Koch, I. Brener, and M. C. Nuss, “THz near-field imaging,” Opt. Commun. 150, 22–26 (1998).
[CrossRef]

Kremser, C.

Kroll, J.

Kulipanov, G. N.

M. A. Dem’yanenko, D. G. Esaev, B. A. Knyazev, G. N. Kulipanov, and N. A. Vinokurov, “Imaging with a 90frames/s microbolometer focal plane array and high-power terahertz free electron laser,” Appl. Phys. Lett. 92, 131116 (2008).
[CrossRef]

Kumar, S.

A. W. M. Lee, Q. Qin, S. Kumar, B. S. Williams, Q. Hu, and J. L. Reno, “Real-time terahertz imaging over a standoff distance (>25 meters),” Appl. Phys. Lett. 89, 141125 (2006).
[CrossRef]

Kuo, C. C.

Lee, A. W. M.

A. W. M. Lee, Q. Qin, S. Kumar, B. S. Williams, Q. Hu, and J. L. Reno, “Real-time terahertz imaging over a standoff distance (>25 meters),” Appl. Phys. Lett. 89, 141125 (2006).
[CrossRef]

Leonhardt, R.

K. J. Siebert, H. Quast, R. Leonhardt, T. Loffler, M. Thomson, T. Bauer, H. G. Roskos, and S. Czasch, “Continuous-wave all-optoelectronic terahertz imaging,” Appl. Phys. Lett. 80, 3003–3005 (2002).
[CrossRef]

Lin, K. I.

N. Karpowicz, H. Zhong, J. Z. Xu, K. I. Lin, J. S. Hwang, and X.-C. Zhang, “Comparison between pulsed terahertz time-domain imaging and continuous wave terahertz imaging,” Semicond. Sci. Technol. 20, S293–S299 (2005).
[CrossRef]

Liu, X. H.

Q. Song, Y. J. Zhao, A. R. Sanchez, C. L. Zhang, and X. H. Liu, “Fast continuous terahertz wave imaging system for security,” Opt. Commun. 282, 2019–2022 (2009).
[CrossRef]

L. L. Zhang, Y. Zhang, C. L. Zhang, Y. J. Zhao, and X. H. Liu, “Terahertz multiwavelength phase imaging without 2π ambiguity,” Opt. Lett. 31, 3668–3670 (2006).
[CrossRef] [PubMed]

Lo, T.

Loffler, T.

T. Loffler, T. May, C. am Weg, A. Alcin, B. Hils, and H. G. Roskos, “Continuous-wave terahertz imaging with a hybrid system,” Appl. Phys. Lett. 90, 091111 (2007).
[CrossRef]

K. J. Siebert, H. Quast, R. Leonhardt, T. Loffler, M. Thomson, T. Bauer, H. G. Roskos, and S. Czasch, “Continuous-wave all-optoelectronic terahertz imaging,” Appl. Phys. Lett. 80, 3003–3005 (2002).
[CrossRef]

Lu, J. Y.

Maikusa, N.

Malacara, D.

Mandeville, G. D.

Mann, C. J.

Marroquin, J. L.

Matsuo, H.

S. Ariyoshi, C. Otani, A. Dobroiu, H. Sato, K. Kawase, H. M. Shimizu, T. Taino, and H. Matsuo, “Terahertz imaging with a direct detector based on superconducting tunnel junctions,” Appl. Phys. Lett. 88, 203503 (2006).
[CrossRef]

May, T.

T. Loffler, T. May, C. am Weg, A. Alcin, B. Hils, and H. G. Roskos, “Continuous-wave terahertz imaging with a hybrid system,” Appl. Phys. Lett. 90, 091111 (2007).
[CrossRef]

Michalopoulou, Z. H.

Mikulics, M.

Mittleman, D. M.

Nishizawa, N.

Nuss, M. C.

Ohtake, H.

Otani, C.

N. Sunaguchi, Y. Sasaki, N. Maikusa, M. Kawai, T. Yuasa, and C. Otani, “Depth-resolving THz imaging with tomosynthesis,” Opt. Express 17, 9558–9570 (2009).
[CrossRef] [PubMed]

S. Ariyoshi, C. Otani, A. Dobroiu, H. Sato, K. Kawase, H. M. Shimizu, T. Taino, and H. Matsuo, “Terahertz imaging with a direct detector based on superconducting tunnel junctions,” Appl. Phys. Lett. 88, 203503 (2006).
[CrossRef]

Ouchi, T.

Pan, C. L.

Paquit, V. C.

Planken, P. C. M.

Qin, Q.

A. W. M. Lee, Q. Qin, S. Kumar, B. S. Williams, Q. Hu, and J. L. Reno, “Real-time terahertz imaging over a standoff distance (>25 meters),” Appl. Phys. Lett. 89, 141125 (2006).
[CrossRef]

Quast, H.

K. J. Siebert, H. Quast, R. Leonhardt, T. Loffler, M. Thomson, T. Bauer, H. G. Roskos, and S. Czasch, “Continuous-wave all-optoelectronic terahertz imaging,” Appl. Phys. Lett. 80, 3003–3005 (2002).
[CrossRef]

Redo-Sanchez, A.

Reno, J. L.

A. W. M. Lee, Q. Qin, S. Kumar, B. S. Williams, Q. Hu, and J. L. Reno, “Real-time terahertz imaging over a standoff distance (>25 meters),” Appl. Phys. Lett. 89, 141125 (2006).
[CrossRef]

Ritchie, D.

Robrish, P. R.

Roskos, H. G.

T. Loffler, T. May, C. am Weg, A. Alcin, B. Hils, and H. G. Roskos, “Continuous-wave terahertz imaging with a hybrid system,” Appl. Phys. Lett. 90, 091111 (2007).
[CrossRef]

K. J. Siebert, H. Quast, R. Leonhardt, T. Loffler, M. Thomson, T. Bauer, H. G. Roskos, and S. Czasch, “Continuous-wave all-optoelectronic terahertz imaging,” Appl. Phys. Lett. 80, 3003–3005 (2002).
[CrossRef]

Sanchez, A. R.

Q. Song, Y. J. Zhao, A. R. Sanchez, C. L. Zhang, and X. H. Liu, “Fast continuous terahertz wave imaging system for security,” Opt. Commun. 282, 2019–2022 (2009).
[CrossRef]

Sasaki, Y.

Sato, H.

S. Ariyoshi, C. Otani, A. Dobroiu, H. Sato, K. Kawase, H. M. Shimizu, T. Taino, and H. Matsuo, “Terahertz imaging with a direct detector based on superconducting tunnel junctions,” Appl. Phys. Lett. 88, 203503 (2006).
[CrossRef]

Scheller, M.

M. Scheller, K. Baaske, and M. Koch, “Multifrequency continuous wave terahertz spectroscopy for absolute thickness determination,” Appl. Phys. Lett. 96, 151112 (2010).
[CrossRef]

Schulkin, B.

Sengupta, A.

Servin, M.

Shepherd, N.

Shimizu, H. M.

S. Ariyoshi, C. Otani, A. Dobroiu, H. Sato, K. Kawase, H. M. Shimizu, T. Taino, and H. Matsuo, “Terahertz imaging with a direct detector based on superconducting tunnel junctions,” Appl. Phys. Lett. 88, 203503 (2006).
[CrossRef]

Siebert, K. J.

K. J. Siebert, H. Quast, R. Leonhardt, T. Loffler, M. Thomson, T. Bauer, H. G. Roskos, and S. Czasch, “Continuous-wave all-optoelectronic terahertz imaging,” Appl. Phys. Lett. 80, 3003–3005 (2002).
[CrossRef]

Song, Q.

Q. Song, Y. J. Zhao, A. R. Sanchez, C. L. Zhang, and X. H. Liu, “Fast continuous terahertz wave imaging system for security,” Opt. Commun. 282, 2019–2022 (2009).
[CrossRef]

Stepanov, A.

Suizu, K.

Sun, C. K.

Sun, W. F.

Sunaguchi, N.

Taino, T.

S. Ariyoshi, C. Otani, A. Dobroiu, H. Sato, K. Kawase, H. M. Shimizu, T. Taino, and H. Matsuo, “Terahertz imaging with a direct detector based on superconducting tunnel junctions,” Appl. Phys. Lett. 88, 203503 (2006).
[CrossRef]

Takayanagi, J.

Tamosiunas, V.

Tani, M.

Thomson, M.

K. J. Siebert, H. Quast, R. Leonhardt, T. Loffler, M. Thomson, T. Bauer, H. G. Roskos, and S. Czasch, “Continuous-wave all-optoelectronic terahertz imaging,” Appl. Phys. Lett. 80, 3003–3005 (2002).
[CrossRef]

Tobin, K. W.

Uchida, H.

Unterrainer, K.

van der Marel, W. A. M.

van der Valk, N. C. J.

Vinokurov, N. A.

M. A. Dem’yanenko, D. G. Esaev, B. A. Knyazev, G. N. Kulipanov, and N. A. Vinokurov, “Imaging with a 90frames/s microbolometer focal plane array and high-power terahertz free electron laser,” Appl. Phys. Lett. 92, 131116 (2008).
[CrossRef]

Wang, S. H.

Wang, X. K.

Warnasooriya, N.

Wilk, R.

Williams, B. S.

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N. Karpowicz, H. Zhong, J. Z. Xu, K. I. Lin, J. S. Hwang, and X.-C. Zhang, “Comparison between pulsed terahertz time-domain imaging and continuous wave terahertz imaging,” Semicond. Sci. Technol. 20, S293–S299 (2005).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Experimental setup. L1, L2, L3, L4, HDPE lenses; BS1, BS2, silicon wafers; M1, M2, metallic mirrors; Stage1, Stage2, Stage3, computer-controlled linear stages.

Fig. 2
Fig. 2

Schematic diagram of the twice-scanning method. (a) First scanning and (b) second scanning with the slight shift of M2.

Fig. 3
Fig. 3

(a) THz interference waveform and (b) spectrum of the interference wave generated by 0.10 and 0.12 THz sources.

Fig. 4
Fig. 4

Distribution of the THz signal intensity along the cross direction of the object arm on the focus of (a) 0.10 and (b) 0.12 THz waves, and their first derivatives.

Fig. 5
Fig. 5

Focal depths of focused 0.10 and 0.12 THz waves.

Fig. 6
Fig. 6

Axial resolution for multiwavelength phase imaging. (a) and (b) Single wavelength depth profiles of 0.10 and 0.12 THz waves; (c) depth profile of the coarse map; (d) depth profile of the final fine map; (e) and (f) standard deviation of the single wavelength maps of 0.10 and 0.12 THz waves, respectively; (g) standard deviation of the coarse map; (f) standard deviation of the fine map.

Fig. 7
Fig. 7

(a) and (c) Photos of a HDPE wedge and a HDPE lens, respectively; (b) unwrapped distorted phase map (red dashed curve) of the wedge, and its wrapped fine phase (blue solid curve), which is processed by the twice-scanning method at 0.12 THz ; (d) unwrapped distorted phase map (red dashed curve) of the lens, and its wrapped fine phase (blue solid curve), which is processed by the twice-scanning method at 0.10 THz .

Fig. 8
Fig. 8

Multiwavelength phase imaging of a wedge and a lens. (a) and (e) are wrapped phase profiles of 0.10 (blue solid curve) and 0.12 THz (red dashed curve) waves; (b) and (f) are subtracted results between phase profiles of 0.10 and 0.12 THz waves; (c) and (g) are relative depth coarse maps; (d) and (h) are final relative depth fine maps.

Fig. 9
Fig. 9

Multiwavelength phase imaging of a HDPE plate with two different height steps. (a) Photo of the sample; (b) the wrapped phase maps of 0.10 THz wave (blue dashed curve) and 0.12 THz wave (red dotted curve) and their subtracted result (green solid curve); (c) the relative depth coarse map; (d) the final relative depth fine map.

Equations (5)

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Z i = λ i ϕ i 2 π ,
L i = 2 ln ( 2 ) π n i λ i 2 Δ λ i ,
S 1 A 1 A 4 cos ( φ 1 k l 4 ) + A 2 A 4 cos ( φ 2 k l 4 ) + A 3 A 4 cos ( φ 3 k l 4 ) ,
S 2 A 1 A 4 cos ( φ 1 k l 4 ) + A 2 A 4 cos ( φ 2 k l 4 ) + A 3 A 4 c o s ( φ 3 + φ d - k l 4 ) ,
S = S 1 S 2 2 A 3 A 4 sin ( φ d 2 ) sin ( φ 3 + φ d 2 k l 4 ) .

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