Abstract

Single-point imagery of 2D objects is proposed by exploiting the extreme broadband nature of an ultrafast terahertz wave. In the proposed imagery, a collimated terahertz beam is illuminated on an object, and the scattered fields are measured through a hole at the Fourier plane in a conventional terahertz time-domain spectroscope. This arrangement allows conversion of radial spatial frequencies of the object to the temporal spectrum of the pulse. Hence, a 2D image can be readily obtained by rotating a hole around the optical axis. Experimental results confirm that a complicated object can be reliably imaged using only 30 waveform measurements.

© 2010 Optical Society of America

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2009

2008

B. Pradarutti, R. Muller, W. Freese, G. Matthäus, S. Riehemann, G. Notni, S. Nolte, and A. Tünnermann, Opt. Express 16, 18443 (2008).
[CrossRef] [PubMed]

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, Appl. Phys. Lett. 93, 121105 (2008).
[CrossRef]

2006

J. Xu and X.-C. Zhang, Appl. Phys. Lett. 88, 151107 (2006).
[CrossRef]

D. L. Donoho, IEEE Trans. Inf. Theory 52, 1289 (2006).
[CrossRef]

2005

T. Yasui, E. Saneyoshi, and T. Araki, Appl. Phys. Lett. 87, 061101 (2005).
[CrossRef]

A. Dreyhaupt, S. Winnerl, T. Dekorsy, and M. Helm, Appl. Phys. Lett. 86, 121114 (2005).
[CrossRef]

2003

J. Ahn, A. V. Efimov, R. D. Averitt, and A. J. Taylor, Opt. Express 11, 2486 (2003).
[CrossRef] [PubMed]

S. Wang, B. Ferguson, D. Abbott, and X. C. Zhang, J. Biol. Phys. 29, 247 (2003).
[CrossRef]

2001

M. T. Reiten, D. Grischkowsky, and R. A. Cheville, Appl. Phys. Lett. 78, 1146 (2001).
[CrossRef]

1999

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, Appl. Phys. B 68, 1085 (1999).
[CrossRef]

1996

Q. Wu, T. D. Hewitt, and X.-C. Zhang, Appl. Phys. Lett. 69, 1026 (1996).
[CrossRef]

1995

1991

B. I. Greene, J. F. Federici, D. R. Dykaar, R. R. Jones, and P. H. Bucksbaum, Appl. Phys. Lett. 59, 893 (1991).
[CrossRef]

1988

P. R. Smith, D. H. Auston, and M. C. Nuss, IEEE J. Quantum Electron. 24, 255 (1988).
[CrossRef]

1979

D. Casasent, Computer 12, 27 (1979).
[CrossRef]

Abbott, D.

S. Wang, B. Ferguson, D. Abbott, and X. C. Zhang, J. Biol. Phys. 29, 247 (2003).
[CrossRef]

Ahn, J.

J. Ahn, A. V. Efimov, R. D. Averitt, and A. J. Taylor, Opt. Express 11, 2486 (2003).
[CrossRef] [PubMed]

D.-S. Yee, Y. Kim, and J. Ahn, in Conference on Lasers and Electro-Optics (Optical Society of America, 2009), paper JWA17.

Araki, T.

T. Yasui, E. Saneyoshi, and T. Araki, Appl. Phys. Lett. 87, 061101 (2005).
[CrossRef]

Auston, D. H.

P. R. Smith, D. H. Auston, and M. C. Nuss, IEEE J. Quantum Electron. 24, 255 (1988).
[CrossRef]

Averitt, R. D.

Baraniuk, R. G.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, Appl. Phys. Lett. 93, 121105 (2008).
[CrossRef]

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, Appl. Phys. B 68, 1085 (1999).
[CrossRef]

Bucksbaum, P. H.

B. I. Greene, J. F. Federici, D. R. Dykaar, R. R. Jones, and P. H. Bucksbaum, Appl. Phys. Lett. 59, 893 (1991).
[CrossRef]

Casasent, D.

D. Casasent, Computer 12, 27 (1979).
[CrossRef]

Chan, W. L.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, Appl. Phys. Lett. 93, 121105 (2008).
[CrossRef]

Charan, K.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, Appl. Phys. Lett. 93, 121105 (2008).
[CrossRef]

Cheville, R. A.

M. T. Reiten, D. Grischkowsky, and R. A. Cheville, Appl. Phys. Lett. 78, 1146 (2001).
[CrossRef]

Ciampa, M.

J. Olenewa and M. Ciampa, Wireless Guide to Wireless Communications, 2nd ed. (Course Technology, 2007).

Dekorsy, T.

A. Dreyhaupt, S. Winnerl, T. Dekorsy, and M. Helm, Appl. Phys. Lett. 86, 121114 (2005).
[CrossRef]

Donoho, D. L.

D. L. Donoho, IEEE Trans. Inf. Theory 52, 1289 (2006).
[CrossRef]

Dreyhaupt, A.

A. Dreyhaupt, S. Winnerl, T. Dekorsy, and M. Helm, Appl. Phys. Lett. 86, 121114 (2005).
[CrossRef]

Dykaar, D. R.

B. I. Greene, J. F. Federici, D. R. Dykaar, R. R. Jones, and P. H. Bucksbaum, Appl. Phys. Lett. 59, 893 (1991).
[CrossRef]

Efimov, A. V.

Ersoy, O. K.

O. K. Ersoy, Diffraction, Fourier Optics and Imaging (Wiley-Interscience, 2006).

Federici, J. F.

B. I. Greene, J. F. Federici, D. R. Dykaar, R. R. Jones, and P. H. Bucksbaum, Appl. Phys. Lett. 59, 893 (1991).
[CrossRef]

Ferguson, B.

S. Wang, B. Ferguson, D. Abbott, and X. C. Zhang, J. Biol. Phys. 29, 247 (2003).
[CrossRef]

Freese, W.

Greene, B. I.

B. I. Greene, J. F. Federici, D. R. Dykaar, R. R. Jones, and P. H. Bucksbaum, Appl. Phys. Lett. 59, 893 (1991).
[CrossRef]

Grischkowsky, D.

M. T. Reiten, D. Grischkowsky, and R. A. Cheville, Appl. Phys. Lett. 78, 1146 (2001).
[CrossRef]

Gupta, M.

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, Appl. Phys. B 68, 1085 (1999).
[CrossRef]

Hecht, E.

E. Hecht, Optics, 4th ed. (Addison Wesley, 2002).

Helm, M.

A. Dreyhaupt, S. Winnerl, T. Dekorsy, and M. Helm, Appl. Phys. Lett. 86, 121114 (2005).
[CrossRef]

Hewitt, T. D.

Q. Wu, T. D. Hewitt, and X.-C. Zhang, Appl. Phys. Lett. 69, 1026 (1996).
[CrossRef]

Hu, B. B.

Ipatov, V.

V. Ipatov, Spread Spectrum and CDMA (Wiley, 2005).
[CrossRef]

Jin, K. H.

Jones, R. R.

B. I. Greene, J. F. Federici, D. R. Dykaar, R. R. Jones, and P. H. Bucksbaum, Appl. Phys. Lett. 59, 893 (1991).
[CrossRef]

Kelly, K. F.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, Appl. Phys. Lett. 93, 121105 (2008).
[CrossRef]

Kim, Y.

D.-S. Yee, Y. Kim, and J. Ahn, in Conference on Lasers and Electro-Optics (Optical Society of America, 2009), paper JWA17.

Kim, Y. C.

Koch, M.

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, Appl. Phys. B 68, 1085 (1999).
[CrossRef]

Lee, O. K.

Matthäus, G.

Mittleman, D. M.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, Appl. Phys. Lett. 93, 121105 (2008).
[CrossRef]

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, Appl. Phys. B 68, 1085 (1999).
[CrossRef]

Muller, R.

Neelamani, R.

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, Appl. Phys. B 68, 1085 (1999).
[CrossRef]

Nolte, S.

Notni, G.

Nuss, M. C.

B. B. Hu and M. C. Nuss, Opt. Lett. 20, 1716 (1995).
[CrossRef] [PubMed]

P. R. Smith, D. H. Auston, and M. C. Nuss, IEEE J. Quantum Electron. 24, 255 (1988).
[CrossRef]

Olenewa, J.

J. Olenewa and M. Ciampa, Wireless Guide to Wireless Communications, 2nd ed. (Course Technology, 2007).

Pradarutti, B.

Reiten, M. T.

M. T. Reiten, D. Grischkowsky, and R. A. Cheville, Appl. Phys. Lett. 78, 1146 (2001).
[CrossRef]

Riehemann, S.

Rudd, J. V.

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, Appl. Phys. B 68, 1085 (1999).
[CrossRef]

Saneyoshi, E.

T. Yasui, E. Saneyoshi, and T. Araki, Appl. Phys. Lett. 87, 061101 (2005).
[CrossRef]

Smith, P. R.

P. R. Smith, D. H. Auston, and M. C. Nuss, IEEE J. Quantum Electron. 24, 255 (1988).
[CrossRef]

Takhar, D.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, Appl. Phys. Lett. 93, 121105 (2008).
[CrossRef]

Taylor, A. J.

Tünnermann, A.

Wang, S.

S. Wang, B. Ferguson, D. Abbott, and X. C. Zhang, J. Biol. Phys. 29, 247 (2003).
[CrossRef]

Winnerl, S.

A. Dreyhaupt, S. Winnerl, T. Dekorsy, and M. Helm, Appl. Phys. Lett. 86, 121114 (2005).
[CrossRef]

Wu, Q.

Q. Wu, T. D. Hewitt, and X.-C. Zhang, Appl. Phys. Lett. 69, 1026 (1996).
[CrossRef]

Xu, J.

J. Xu and X.-C. Zhang, Appl. Phys. Lett. 88, 151107 (2006).
[CrossRef]

Yasui, T.

T. Yasui, E. Saneyoshi, and T. Araki, Appl. Phys. Lett. 87, 061101 (2005).
[CrossRef]

Ye, J. C.

Yee, D. S.

Yee, D.-S.

D.-S. Yee, Y. Kim, and J. Ahn, in Conference on Lasers and Electro-Optics (Optical Society of America, 2009), paper JWA17.

Zhang, X. C.

S. Wang, B. Ferguson, D. Abbott, and X. C. Zhang, J. Biol. Phys. 29, 247 (2003).
[CrossRef]

Zhang, X.-C.

J. Xu and X.-C. Zhang, Appl. Phys. Lett. 88, 151107 (2006).
[CrossRef]

Q. Wu, T. D. Hewitt, and X.-C. Zhang, Appl. Phys. Lett. 69, 1026 (1996).
[CrossRef]

Appl. Phys. B

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, Appl. Phys. B 68, 1085 (1999).
[CrossRef]

Appl. Phys. Lett.

M. T. Reiten, D. Grischkowsky, and R. A. Cheville, Appl. Phys. Lett. 78, 1146 (2001).
[CrossRef]

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, Appl. Phys. Lett. 93, 121105 (2008).
[CrossRef]

Q. Wu, T. D. Hewitt, and X.-C. Zhang, Appl. Phys. Lett. 69, 1026 (1996).
[CrossRef]

J. Xu and X.-C. Zhang, Appl. Phys. Lett. 88, 151107 (2006).
[CrossRef]

T. Yasui, E. Saneyoshi, and T. Araki, Appl. Phys. Lett. 87, 061101 (2005).
[CrossRef]

A. Dreyhaupt, S. Winnerl, T. Dekorsy, and M. Helm, Appl. Phys. Lett. 86, 121114 (2005).
[CrossRef]

B. I. Greene, J. F. Federici, D. R. Dykaar, R. R. Jones, and P. H. Bucksbaum, Appl. Phys. Lett. 59, 893 (1991).
[CrossRef]

Computer

D. Casasent, Computer 12, 27 (1979).
[CrossRef]

IEEE J. Quantum Electron.

P. R. Smith, D. H. Auston, and M. C. Nuss, IEEE J. Quantum Electron. 24, 255 (1988).
[CrossRef]

IEEE Trans. Inf. Theory

D. L. Donoho, IEEE Trans. Inf. Theory 52, 1289 (2006).
[CrossRef]

J. Biol. Phys.

S. Wang, B. Ferguson, D. Abbott, and X. C. Zhang, J. Biol. Phys. 29, 247 (2003).
[CrossRef]

Opt. Express

Opt. Lett.

Other

J. Olenewa and M. Ciampa, Wireless Guide to Wireless Communications, 2nd ed. (Course Technology, 2007).

V. Ipatov, Spread Spectrum and CDMA (Wiley, 2005).
[CrossRef]

D.-S. Yee, Y. Kim, and J. Ahn, in Conference on Lasers and Electro-Optics (Optical Society of America, 2009), paper JWA17.

O. K. Ersoy, Diffraction, Fourier Optics and Imaging (Wiley-Interscience, 2006).

E. Hecht, Optics, 4th ed. (Addison Wesley, 2002).

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Figures (3)

Fig. 1
Fig. 1

Concepts of (a) conventional usage of monochromatic wave for image formation and (b) single-point imagery using extreme broadband source.

Fig. 2
Fig. 2

(a) Setup of THz single-point imagery and (b) mask geometry. The signal corresponds to the Fourier transform of the projection of the image.

Fig. 3
Fig. 3

Image reconstruction process. (a) Target object U ( x , y ) with a Korean word meaning “light.” (b) Measured terahertz temporal profile V ( t , θ ) presented as a function of the angle θ of the mask. (c) Corresponding terahertz spectra V ( ω ; θ ) . (d)–(f) Reconstructed images using inverse Radon transform using (d) 10 waveforms measuring per 18°, (e) 15 waveforms measuring per 12° and (f) 30 waveforms per 6°, respectively.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

V ( x , y ) = F 1 [ M ( k x , k y ) F { U ( x , y ) } ] ,
V ( ω ) = C ( ω ) Σ t d ξ d η Σ o d x d y × [ M ( ξ , η ) U ( x , y ) e i k ( x ξ + y η ) f ] ,
V ( ω ; θ ) = C ( ω ) Σ o d x d y U ( x , y ) e i k d f ( x cos θ + y sin θ ) .
S ̃ ( u , θ ) = Σ o d x d y U ( x , y ) δ ( x cos θ + y sin θ f u d ) ,
U ( x , y ) = π a 2 U ( x , y ) 2 J 1 ( k a ρ f ) k a ρ f ,

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