Abstract

We demonstrate the reconstruction of one- and two-dimensional objects by numerically backpropagating measured scattered terahertz transients. The spatial resolution determined by the Sparrow criterion is found to correspond to approximately 30% of the peak wavelength and 85% of the mean wavelength of the power spectrum of the single-cycle waveform.

© 2001 Optical Society of America

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References

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  1. J. Bromage, S. Radic, G. Agrawal, C. R. Stroud, P. M. Fauchet, and R. Sobolewski, J. Opt. Soc. Am. B 15, 1399 (1998).
    [Crossref]
  2. E. Budiarto, N.-W. Pu, S. Jeong, and J. Bokor, Opt. Lett. 23, 213 (1998).
    [Crossref]
  3. R. A. Cheville and D. Grischkowsky, Appl. Phys. Lett. 67, 1960 (1995).
    [Crossref]
  4. D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, Appl. Phys. B 68, 1085 (1999).
    [Crossref]
  5. M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, 1997).
  6. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996).
  7. J. V. Rudd, D. Zimdars, and M. Warmuth, Proc. SPIE 3934, 27 (2000).
    [Crossref]
  8. M. van Exter and D. Grischkowsky, IEEE Trans. Microwave Theory Tech. 38, 1684 (1990).
    [Crossref]
  9. R. Guenther, Modern Optics (Wiley, New York, 1990).

2000 (1)

J. V. Rudd, D. Zimdars, and M. Warmuth, Proc. SPIE 3934, 27 (2000).
[Crossref]

1999 (1)

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

1998 (2)

1995 (1)

R. A. Cheville and D. Grischkowsky, Appl. Phys. Lett. 67, 1960 (1995).
[Crossref]

1990 (1)

M. van Exter and D. Grischkowsky, IEEE Trans. Microwave Theory Tech. 38, 1684 (1990).
[Crossref]

Agrawal, G.

Baraniuk, R. G.

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

Bokor, J.

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, 1997).

Bromage, J.

Budiarto, E.

Cheville, R. A.

R. A. Cheville and D. Grischkowsky, Appl. Phys. Lett. 67, 1960 (1995).
[Crossref]

Fauchet, P. M.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996).

Grischkowsky, D.

R. A. Cheville and D. Grischkowsky, Appl. Phys. Lett. 67, 1960 (1995).
[Crossref]

M. van Exter and D. Grischkowsky, IEEE Trans. Microwave Theory Tech. 38, 1684 (1990).
[Crossref]

Guenther, R.

R. Guenther, Modern Optics (Wiley, New York, 1990).

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]

Jeong, S.

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]

Mittleman, D. M.

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

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]

Pu, N.-W.

Radic, S.

Rudd, J. V.

J. V. Rudd, D. Zimdars, and M. Warmuth, Proc. SPIE 3934, 27 (2000).
[Crossref]

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

Sobolewski, R.

Stroud, C. R.

van Exter, M.

M. van Exter and D. Grischkowsky, IEEE Trans. Microwave Theory Tech. 38, 1684 (1990).
[Crossref]

Warmuth, M.

J. V. Rudd, D. Zimdars, and M. Warmuth, Proc. SPIE 3934, 27 (2000).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, 1997).

Zimdars, D.

J. V. Rudd, D. Zimdars, and M. Warmuth, Proc. SPIE 3934, 27 (2000).
[Crossref]

Appl. Phys. B (1)

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. (1)

R. A. Cheville and D. Grischkowsky, Appl. Phys. Lett. 67, 1960 (1995).
[Crossref]

IEEE Trans. Microwave Theory Tech. (1)

M. van Exter and D. Grischkowsky, IEEE Trans. Microwave Theory Tech. 38, 1684 (1990).
[Crossref]

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

Opt. Lett. (1)

Proc. SPIE (1)

J. V. Rudd, D. Zimdars, and M. Warmuth, Proc. SPIE 3934, 27 (2000).
[Crossref]

Other (3)

R. Guenther, Modern Optics (Wiley, New York, 1990).

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, 1997).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996).

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Figures (5)

Fig. 1
Fig. 1

One-dimensional (1-D) experimental setup. A collimated input field diffracts in all directions from an object. (The input field shown represents a field measured in the near field of the THz emitter.) These scattered transients are then recorded at different azimuths along the intermediate (detection) screen. For the numerical backpropagation, the positions at the intermediate screen are locations for virtual sources, uP0,t+r01/ν, that will propagate in the reverse direction to the object plane.

Fig. 2
Fig. 2

One-dimensional experimental results: (a) the diffracted fields at the intermediate screen. These waveforms were used as input sources in Eq.  (2) to reproduce the transmission function of the object (Fig.  1, inset); the result is shown in (b).

Fig. 3
Fig. 3

2D experimental setup. Diffracted electric fields are measured at one off-axis position θd=12° as the object (spiral) is rotated about the z axis from 0 to 2π. This figure also demonstrates how measuring at one off-axis position while rotating the object is equivalent to measuring the fields on a spherical screen.

Fig. 4
Fig. 4

(a) Time-reversal imaging simulation. Here the scattered field distribution of the electric field incident upon the object was calculated with Eq.  (1). The field was then time reversed and backpropagated by use of Eq.  (2) under the same conditions as in the experiment. (b) Image obtained from the experimental data after the backpropagation algorithm described in the text has been performed.

Fig. 5
Fig. 5

Two electric field measurements at the intermediate screen for the ϕ=0° and ϕ=15° orientations. From delay between the waveforms and Eq.  (3), the spatial resolution was determined to be 674 μm.

Equations (3)

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

uP0,t=Σcosθ2πcr01tuP1,t-r01cdσ,
uP1,t=-14πcΣ1+cosθ×tuP0,t+r01cdσ,
Δx=cΔt/sinθd.

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