Abstract

Terahertz phase imaging can reveal the depth information of an optically opaque object and provide much better contrast for weak-absorption materials. We demonstrate a continuous-wave terahertz interferometric imaging method in which a far-infrared laser interferometer is used to measure the phase distribution with diffraction-limited lateral resolution and subwavelength axial resolution. An improved four-step phase-shifting algorithm is introduced to retrieve the phase map with very high accuracy and low distortion. The relative depth profiles of two transparent samples are successfully extracted by using this method. Experimental results verify that terahertz interferometric imaging in combination with the phase-shifting technique enables effective reconstruction of the phase image of the object under test.

© 2011 Optical Society of America

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2010 (3)

2009 (1)

2008 (5)

2007 (1)

S. Nakajima, H. Hoshina, M. Yamashita, C. Otani, and N. Miyoshi, “Terahertz imaging diagnostics of cancer tissues with a chemometrics technique,” Appl. Phys. Lett. 90, 041102(2007).
[CrossRef]

2006 (3)

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

Y. Ino, J. B. Hroux, T. Mukaiyama, and M. Kuwata-Gonokami, “Reflection-type pulsed terahertz imaging with a phase-retrieval algorithm,” Appl. Phys. Lett. 88, 041114 (2006).
[CrossRef]

Y.-S. Jin, G.-J. Kim, and S.-G. Jeon, “Terahertz dielectric properties of polymers,” J. Korean Phys. Soc. 49, 513–517 (2006).

2005 (3)

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]

A. W. M. Lee and Q. Hu, “Real-time, continuous-wave terahertz imaging by use of a microbolometer focal-plane array,” Opt. Lett. 30, 2563–2565 (2005).
[CrossRef] [PubMed]

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86, 241116 (2005).
[CrossRef]

2003 (2)

K. Kawase, Y. Ogawa, and Y. Watanabe, “Non-destructive terahertz imaging of illicit drugs using spectral fingerprints,” Opt. Express 11, 2549–2554 (2003).
[CrossRef] [PubMed]

P. D. Jewell, R. J. Smith, and T. R. Jarboe, “Martin-Puplett multichannel far infrared heterodyne interferometer on the Helicity Injected Torus II,” Rev. Sci. Instrum. 74, 80–87 (2003).
[CrossRef]

2002 (2)

K. J. Siebert, H. Quast, R. Leonhardt, T. Löffler, 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]

1995 (1)

1994 (1)

1991 (1)

1988 (1)

1987 (1)

1983 (1)

1982 (1)

1974 (1)

Abbot, D.

Ai, C.

Araki, T.

Baraniuk, R. G.

Bauer, T.

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

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

Brangaccio, D. J.

Brown, E. R.

Bruning, J. H.

Burow, R.

Chan, W. L.

Chen, H.-W.

Chen, Z.

Chiu, C.-M.

Cole, B. E.

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86, 241116 (2005).
[CrossRef]

Culjat, M. O.

Czasch, S.

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

Doyle, D.

Elssner, K.-E.

Federici, J. F.

Ferguson, B.

Frankena, H. J.

Gallagher, J. E.

Geckeler, R. D.

Ghiglia, D. C.

Gray, D.

Grundfest, W. S.

Grzanna, J.

Hariharan, P.

Herriott, D. R.

Hils, B.

Hochrein, T.

Hor, Y. L.

Hoshina, H.

S. Nakajima, H. Hoshina, M. Yamashita, C. Otani, and N. Miyoshi, “Terahertz imaging diagnostics of cancer tissues with a chemometrics technique,” Appl. Phys. Lett. 90, 041102(2007).
[CrossRef]

Hou, L.

Hroux, J. B.

Y. Ino, J. B. Hroux, T. Mukaiyama, and M. Kuwata-Gonokami, “Reflection-type pulsed terahertz imaging with a phase-retrieval algorithm,” Appl. Phys. Lett. 88, 041114 (2006).
[CrossRef]

Hu, B. B.

Hu, Q.

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.

Ina, H.

Ino, Y.

Y. Ino, J. B. Hroux, T. Mukaiyama, and M. Kuwata-Gonokami, “Reflection-type pulsed terahertz imaging with a phase-retrieval algorithm,” Appl. Phys. Lett. 88, 041114 (2006).
[CrossRef]

Jansen, C.

Jarboe, T. R.

P. D. Jewell, R. J. Smith, and T. R. Jarboe, “Martin-Puplett multichannel far infrared heterodyne interferometer on the Helicity Injected Torus II,” Rev. Sci. Instrum. 74, 80–87 (2003).
[CrossRef]

Jeon, S.-G.

Y.-S. Jin, G.-J. Kim, and S.-G. Jeon, “Terahertz dielectric properties of polymers,” J. Korean Phys. Soc. 49, 513–517 (2006).

Jewell, P. D.

P. D. Jewell, R. J. Smith, and T. R. Jarboe, “Martin-Puplett multichannel far infrared heterodyne interferometer on the Helicity Injected Torus II,” Rev. Sci. Instrum. 74, 80–87 (2003).
[CrossRef]

Jin, Y.-S.

Y.-S. Jin, G.-J. Kim, and S.-G. Jeon, “Terahertz dielectric properties of polymers,” J. Korean Phys. Soc. 49, 513–517 (2006).

Jördens, C.

Kabetani, Y.

Kang, K.

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]

Kawase, K.

Kemp, M. C.

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86, 241116 (2005).
[CrossRef]

Kim, G.-J.

Y.-S. Jin, G.-J. Kim, and S.-G. Jeon, “Terahertz dielectric properties of polymers,” J. Korean Phys. Soc. 49, 513–517 (2006).

Kobayashi, S.

Koch, M.

Krumbholz, N.

Kuo, C.-C.

Kuwata-Gonokami, M.

Y. Ino, J. B. Hroux, T. Mukaiyama, and M. Kuwata-Gonokami, “Reflection-type pulsed terahertz imaging with a phase-retrieval algorithm,” Appl. Phys. Lett. 88, 041114 (2006).
[CrossRef]

Lee, A. W. M.

Lee, H.

Leonhardt, R.

K. J. Siebert, H. Quast, R. Leonhardt, T. Löffler, 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.

Lo, T.

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86, 241116 (2005).
[CrossRef]

Löffler, T.

B. Hils, M. D. Thomson, T. Löffler, W. Spiegel, C. Weg, H. G. Roskos, P. Maagt, D. Doyle, and R. D. Geckeler, “Terahertz profilometry at 600 GHz with 0.5 μm depth resolution,” Opt. Express 16, 11289–11293 (2008).
[CrossRef] [PubMed]

K. J. Siebert, H. Quast, R. Leonhardt, T. Löffler, 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.

Maagt, P.

Merkel, K.

Mittleman, D. M.

Miyoshi, N.

S. Nakajima, H. Hoshina, M. Yamashita, C. Otani, and N. Miyoshi, “Terahertz imaging diagnostics of cancer tissues with a chemometrics technique,” Appl. Phys. Lett. 90, 041102(2007).
[CrossRef]

Moravec, M. L.

Mukaiyama, T.

Y. Ino, J. B. Hroux, T. Mukaiyama, and M. Kuwata-Gonokami, “Reflection-type pulsed terahertz imaging with a phase-retrieval algorithm,” Appl. Phys. Lett. 88, 041114 (2006).
[CrossRef]

Nakajima, S.

S. Nakajima, H. Hoshina, M. Yamashita, C. Otani, and N. Miyoshi, “Terahertz imaging diagnostics of cancer tissues with a chemometrics technique,” Appl. Phys. Lett. 90, 041102(2007).
[CrossRef]

Nuss, M. C.

Ogawa, Y.

Ohgi, Y.

Otani, C.

S. Nakajima, H. Hoshina, M. Yamashita, C. Otani, and N. Miyoshi, “Terahertz imaging diagnostics of cancer tissues with a chemometrics technique,” Appl. Phys. Lett. 90, 041102(2007).
[CrossRef]

Pan, C.-L.

Peters, O.

Quast, H.

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

Romero, L. A.

Rosenfeld, D. P.

Roskos, H. G.

B. Hils, M. D. Thomson, T. Löffler, W. Spiegel, C. Weg, H. G. Roskos, P. Maagt, D. Doyle, and R. D. Geckeler, “Terahertz profilometry at 600 GHz with 0.5 μm depth resolution,” Opt. Express 16, 11289–11293 (2008).
[CrossRef] [PubMed]

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

Salhi, M.

Scheller, M.

Schwider, J.

Shen, Y. C.

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86, 241116 (2005).
[CrossRef]

Siebert, K. J.

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

Singh, R. S.

Smith, R. J.

P. D. Jewell, R. J. Smith, and T. R. Jarboe, “Martin-Puplett multichannel far infrared heterodyne interferometer on the Helicity Injected Torus II,” Rev. Sci. Instrum. 74, 80–87 (2003).
[CrossRef]

Smorenburg, C.

Spiegel, W.

Spolaczyk, R.

Suen, J. Y.

Sun, C.-K.

Taday, P. F.

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86, 241116 (2005).
[CrossRef]

Takeda, M.

Taylor, Z. D.

Thomson, M.

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

Thomson, M. D.

Tribe, W. R.

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86, 241116 (2005).
[CrossRef]

van Wingerden, J.

Vieweg, N.

Wample, R. L.

Wang, S. H.

Wang, X.

Wang, Y.

Watanabe, Y.

Weg, C.

White, A. D.

Wietzke, S.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

Wyant, J. C.

Xu, J. Z.

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]

Yamashita, M.

S. Nakajima, H. Hoshina, M. Yamashita, C. Otani, and N. Miyoshi, “Terahertz imaging diagnostics of cancer tissues with a chemometrics technique,” Appl. Phys. Lett. 90, 041102(2007).
[CrossRef]

Yasui, T.

Yokoyama, S.

Zhang, C.

Zhang, L.

Zhang, X.-C.

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]

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

Zhang, Y.

Zhao, Y.

Zhao, Z.

Zhong, H.

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]

Appl. Opt. (9)

Y. L. Hor, J. F. Federici, and R. L. Wample, “Nondestructive evaluation of cork enclosures using terahertz/millimeter wave spectroscopy and imaging,” Appl. Opt. 47, 72–78 (2008).
[CrossRef]

C. Jansen, S. Wietzke, O. Peters, M. Scheller, N. Vieweg, M. Salhi, N. Krumbholz, C. Jördens, T. Hochrein, and M. Koch, “Terahertz imaging: applications and perspectives,” Appl. Opt. 49, E48 –E57 (2010).
[CrossRef] [PubMed]

X. Wang, L. Hou, and Y. Zhang, “Continuous-wave terahertz interferometry with multiwavelength phase unwrapping,” Appl. Opt. 49, 5095–5102 (2010).
[CrossRef] [PubMed]

J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Appl. Opt. 13, 2693–2703 (1974).
[CrossRef] [PubMed]

J. Schwider, R. Burow, K.-E. Elssner, J. Grzanna, R. Spolaczyk, and K. Merkel, “Digital wave-front measuring interferometry: some systematic error sources,” Appl. Opt. 22, 3421–3432(1983).
[CrossRef] [PubMed]

P. Hariharan, “Digital phase-stepping interferometry: effects of multiply reflected beams,” Appl. Opt. 26, 2506–2507 (1987).
[CrossRef] [PubMed]

J. van Wingerden, H. J. Frankena, and C. Smorenburg, “Linear approximation for measurement errors in phase shifting interferometry,” Appl. Opt. 30, 2718–2729 (1991).
[CrossRef] [PubMed]

C. Ai and J. C. Wyant, “Effect of spurious reflection on phase shift interferometry,” Appl. Opt. 27, 3039–3045 (1988).
[CrossRef] [PubMed]

T. Yasui, Y. Kabetani, Y. Ohgi, S. Yokoyama, and T. Araki, “Absolute distance measurement of optically rough objects using asynchronous-optical-sampling terahertz impulse ranging,” Appl. Opt. 49, 5262–5270 (2010).
[CrossRef] [PubMed]

Appl. Phys. Lett. (4)

Y. Ino, J. B. Hroux, T. Mukaiyama, and M. Kuwata-Gonokami, “Reflection-type pulsed terahertz imaging with a phase-retrieval algorithm,” Appl. Phys. Lett. 88, 041114 (2006).
[CrossRef]

S. Nakajima, H. Hoshina, M. Yamashita, C. Otani, and N. Miyoshi, “Terahertz imaging diagnostics of cancer tissues with a chemometrics technique,” Appl. Phys. Lett. 90, 041102(2007).
[CrossRef]

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86, 241116 (2005).
[CrossRef]

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

Chin. Opt. Lett. (1)

J. Korean Phys. Soc. (1)

Y.-S. Jin, G.-J. Kim, and S.-G. Jeon, “Terahertz dielectric properties of polymers,” J. Korean Phys. Soc. 49, 513–517 (2006).

J. Opt. Soc. Am. (1)

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

Opt. Express (3)

Opt. Lett. (6)

Rev. Sci. Instrum. (1)

P. D. Jewell, R. J. Smith, and T. R. Jarboe, “Martin-Puplett multichannel far infrared heterodyne interferometer on the Helicity Injected Torus II,” Rev. Sci. Instrum. 74, 80–87 (2003).
[CrossRef]

Semicond. Sci. Technol. (1)

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]

Other (1)

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram of the experimental setup. A, attenuator; PM1, PM2, parabolic mirrors; L1, L2, HDPE lenses; M, M1, M2, metallic mirrors; C, chopper; BS, beam splitter; S1, S2, linear translation stages.

Fig. 2
Fig. 2

Extraneous reflections from (a) the sample and (b) the lens surfaces.

Fig. 3
Fig. 3

Measurement (circle points) of the interference intensity variation with the OPD of the reference beam and the corresponding cosine fit (solid curve).

Fig. 4
Fig. 4

Measurement of the FIR beam spot size at the sample plane along the (a) horizontal and (b) vertical directions. The dashed curves represent the intensity distributions of the terahertz signal. The square points are their first derivatives, and the solid curves are the Gaussian fits.

Fig. 5
Fig. 5

TIPI of a HDPE wedge. (a) Photograph of the sample; (b) two fringe patterns measured when the object beam undergoes a π phase shift; (c) wrapped distorted phase map (dashed curve) retrieved by the simple algorithm, and wrapped phase map (solid curve) retrieved by the improved algorithm; (d) and (e) are relative depth profiles (dashed curves) reconstructed from the distorted and improved phase maps in (c), respectively, and their linear fits (solid curves), where k denotes the slope; (f) fitting residuals of the data in (d) (dashed curve) and (e) (solid curve).

Fig. 6
Fig. 6

TIPI of a plastic sheet with concave patterns. (a) Photograph of the sample, where the red square indicates the scanned area; (b) intensity image of the sample; (c) and (d) unwrapped phase maps retrieved by the simple and improved algorithms, respectively; (e) phase profiles of the scans across AB in (c) (dashed curve) and (d) (solid curve); (f) phase profiles of the scan across CD in (d) obtained by TIPI (solid curve) and THz-TDS (dashed curve).

Fig. 7
Fig. 7

Three-dimensional plot of the relative depth profile of the plastic sheet.

Equations (9)

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I ( x , y ) = a ( x , y ) + b ( x , y ) cos [ φ ( x , y ) ] ,
I i ( x , y ) = a ( x , y ) + b ( x , y ) cos [ φ ( x , y ) + ( i 1 ) π / 2 ] , i = 1 , 2 , 3 , 4.
φ = arg [ ( I 1 I 3 ) + j ( I 4 I 2 ) ] ,
S 1 = ( 1 R ) 4 S 0 ,
S i = R ( 1 R ) 2 ( i 2 ) S 0 , i = 2 , 3 , 4 , 5 ,
R = ( n 1 n + 1 ) 2 ,
S r 1 = S r 2 = R S r 4 ,
I A r 2 + A o 2 + 2 A r A o cos ( φ r φ o ) + 2 A r A S cos ( φ r φ S ) + 2 A r A M cos ( φ r φ M ) + 2 A o A S cos ( φ o φ S ) + 2 A o A M cos ( φ o φ M ) ,
φ = arg [ ( I 1 I 3 ) ( I 1 I 3 ) + j ( I 4 I 2 ) j ( I 4 I 2 ) ] .

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