Abstract

We demonstrate pulse-echo mode terahertz (THz) reflectance tomography, where scattered THz waveforms are measured using a high-resolution asynchronous-optical-sampling THz time domain spectroscopy (AOS THz-TDS) technique, and 3-D tomographic reconstruction is accomplished using a compressed sensing approach. One of the main advantages of the proposed system is a significant reduction of acquisition time without sacrificing the reconstruction quality, thanks to the sufficient incoherency in the pulse-echo mode-sensing matrix and the fast sampling scheme in AOS THz-TDS.

© 2009 Optical Society of America

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References

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    [CrossRef]
  2. S. Wang and X.-C. Zhang, J. Phys. D 37, R1 (2004).
    [CrossRef]
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    [CrossRef] [PubMed]
  4. E. Candes, J. Romberg, and T. Tao, IEEE Trans. Inf. Theory 52, 489 (2006).
    [CrossRef]
  5. T. Yasui, E. Saneyoshi, and T. Araki, Appl. Phys. Lett. 87, 061101 (2005).
    [CrossRef]
  6. J. Tropp, IEEE Trans. Inf. Theory 50, 2231 (2004).
    [CrossRef]
  7. Y. Kim, D. S. Yee, M. Yi, and J. Ahn, “High speed resolution terahertz spectrometers,” J. Korean Phys. Soc. (to be published).

2008 (1)

2006 (1)

E. Candes, J. Romberg, and T. Tao, IEEE Trans. Inf. Theory 52, 489 (2006).
[CrossRef]

2005 (1)

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

2004 (2)

J. Tropp, IEEE Trans. Inf. Theory 50, 2231 (2004).
[CrossRef]

S. Wang and X.-C. Zhang, J. Phys. D 37, R1 (2004).
[CrossRef]

2001 (1)

Ahn, J.

Y. Kim, D. S. Yee, M. Yi, and J. Ahn, “High speed resolution terahertz spectrometers,” J. Korean Phys. Soc. (to be published).

Araki, T.

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

Baraniuk, R. G.

Candes, E.

E. Candes, J. Romberg, and T. Tao, IEEE Trans. Inf. Theory 52, 489 (2006).
[CrossRef]

Chan, W. L.

Dorney, T. D.

Johnson, J. L.

Kim, Y.

Y. Kim, D. S. Yee, M. Yi, and J. Ahn, “High speed resolution terahertz spectrometers,” J. Korean Phys. Soc. (to be published).

Mittleman, D. M.

Moravec, M. L.

Romberg, J.

E. Candes, J. Romberg, and T. Tao, IEEE Trans. Inf. Theory 52, 489 (2006).
[CrossRef]

Rudd, J. V.

Saneyoshi, E.

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

Symes, W. W.

Tao, T.

E. Candes, J. Romberg, and T. Tao, IEEE Trans. Inf. Theory 52, 489 (2006).
[CrossRef]

Tropp, J.

J. Tropp, IEEE Trans. Inf. Theory 50, 2231 (2004).
[CrossRef]

Wang, S.

S. Wang and X.-C. Zhang, J. Phys. D 37, R1 (2004).
[CrossRef]

Yasui, T.

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

Yee, D. S.

Y. Kim, D. S. Yee, M. Yi, and J. Ahn, “High speed resolution terahertz spectrometers,” J. Korean Phys. Soc. (to be published).

Yi, M.

Y. Kim, D. S. Yee, M. Yi, and J. Ahn, “High speed resolution terahertz spectrometers,” J. Korean Phys. Soc. (to be published).

Zhang, X.-C.

S. Wang and X.-C. Zhang, J. Phys. D 37, R1 (2004).
[CrossRef]

Appl. Phys. Lett. (1)

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

IEEE Trans. Inf. Theory (2)

J. Tropp, IEEE Trans. Inf. Theory 50, 2231 (2004).
[CrossRef]

E. Candes, J. Romberg, and T. Tao, IEEE Trans. Inf. Theory 52, 489 (2006).
[CrossRef]

J. Korean Phys. Soc. (1)

Y. Kim, D. S. Yee, M. Yi, and J. Ahn, “High speed resolution terahertz spectrometers,” J. Korean Phys. Soc. (to be published).

J. Phys. D (1)

S. Wang and X.-C. Zhang, J. Phys. D 37, R1 (2004).
[CrossRef]

Opt. Lett. (2)

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Figures (4)

Fig. 1
Fig. 1

Geometry of (a) pulse-echo mode THz tomography and (b) equidistance plane and transmit/receive antenna trajectory plane.

Fig. 2
Fig. 2

Experimental setup using AOS THz-TDS. DT, detector; EM, emitter; PM, parabolic mirror.

Fig. 3
Fig. 3

(a) “K” character sample and (b) scattered field measurement, while scanning along the dashed line in (a).

Fig. 4
Fig. 4

Simulation results by (a) Kirchoff migration and (b) l 1 minimization. Real measurement results by (c) Kirchoff migration and (d) l 1 minimization. The threshold values for 3-D volume rendering were chosen as one-fifth of the maximum value.

Equations (11)

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ψ ( r , r s ; k ) k 2 S ( k ) d r f ( r ; k ) g k ( r | r ) g k ( r | r s ) ,
g k ( r | r ) = e i k r r 4 π r r
y ( r , r s ; k ) ψ ( r , r s ; k ) k 2 n ( k ) S ( k ) = d r χ ( r ) g k ( r | r ) g k ( r | r s ) .
y ( r , r s ; t ¯ ) = d r χ ( r ) δ ( t ¯ | r r | | r r s | ) ( 4 π ) 2 | r r | | r r s | ,
y ( n ) = G ( n ) χ , n = 1 , , N ,
[ δ ( t 1 | r n r 1 | | r n s r 1 | ) | r n r 1 | | r n s r 1 | δ ( t 1 | r n r P | | r n s r P | ) | r n r P | | r n s r P | δ ( t L | r n r 1 | | r n s r 1 | ) | r n r 1 | | r n s r 1 | δ ( t L | r n r P | | r n s r P | ) | r n r P | | r n s r P | ] ,
y = G f ,
( P 0 ) : min f 0 , subject to y = G f ,
f 0 < ( μ ( G ) 1 + 1 ) 2 ,
max p q n N p q 1 | r n r p | | r n s r p | | r n r q | | r n s r q | ( n = 1 N 1 | r n r p | | r n s r p | ) 1 2 ( n = 1 N 1 | r n r q | | r n s r q | ) 1 2 ,
N p q = { n { 1 , , N } : | r p r n + r n s 2 | = | r q r n + r n s 2 | } .

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