Abstract

We demonstrate tomographic T-ray imaging, using the timing information present in terahertz (THz) pulses in a reflection geometry. THz pulses are reflected from refractive-index discontinuities inside an object, and the time delays of these pulses are used to determine the positions of the discontinuities along the propagation direction. In this fashion a tomographic image can be constructed.

© 1997 Optical Society of America

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References

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  1. B. B. Hu and M. C. Nuss, Opt. Lett. 20, 1716 (1995).
    [Crossref]
  2. D. Grischkowsky, S. Keiding, M. van Exter, and C. Fattinger, J. Opt. Soc. Am. B 7, 2006 (1990); N. Katzenellenbogen and D. Grischkowsky, Appl. Phys. Lett. 61, 840 (1992).
    [Crossref]
  3. M. C. Nuss and J. Orenstein, in Millimeter-Wave Spectroscopy of Solids, G. Gruener, ed. (Springer-Verlag, Berlin, 1997).
  4. D. M. Mittleman, R. H. Jacobsen, and M. C. Nuss, IEEE J. Sel. Topics Quantum Electron. 2, 679 (1997).
    [Crossref]
  5. R. H. Jacobsen, D. M. Mittleman, and M. C. Nuss, Opt. Lett. 21, 2011 (1996).
    [Crossref] [PubMed]
  6. M. van Exter, C. Fattinger, and D. Grischkowsky, Opt. Lett. 14, 1128 (1989).
    [Crossref]
  7. Wavelet processing was performed with the WaveLab software package of J. Buckheit, S. Chen, D. Donoho, I. Johnstone, and J. Scargle, of the Department of Statistics at Stanford University, available on the World Wide Web at http://playfair.stanford.edu/~wavelab/ .
  8. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, New York, 1988).

1997 (1)

D. M. Mittleman, R. H. Jacobsen, and M. C. Nuss, IEEE J. Sel. Topics Quantum Electron. 2, 679 (1997).
[Crossref]

1996 (1)

1995 (1)

1990 (1)

1989 (1)

Fattinger, C.

Grischkowsky, D.

Hu, B. B.

Jacobsen, R. H.

D. M. Mittleman, R. H. Jacobsen, and M. C. Nuss, IEEE J. Sel. Topics Quantum Electron. 2, 679 (1997).
[Crossref]

R. H. Jacobsen, D. M. Mittleman, and M. C. Nuss, Opt. Lett. 21, 2011 (1996).
[Crossref] [PubMed]

Kak, A. C.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, New York, 1988).

Keiding, S.

Mittleman, D. M.

D. M. Mittleman, R. H. Jacobsen, and M. C. Nuss, IEEE J. Sel. Topics Quantum Electron. 2, 679 (1997).
[Crossref]

R. H. Jacobsen, D. M. Mittleman, and M. C. Nuss, Opt. Lett. 21, 2011 (1996).
[Crossref] [PubMed]

Nuss, M. C.

D. M. Mittleman, R. H. Jacobsen, and M. C. Nuss, IEEE J. Sel. Topics Quantum Electron. 2, 679 (1997).
[Crossref]

R. H. Jacobsen, D. M. Mittleman, and M. C. Nuss, Opt. Lett. 21, 2011 (1996).
[Crossref] [PubMed]

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

M. C. Nuss and J. Orenstein, in Millimeter-Wave Spectroscopy of Solids, G. Gruener, ed. (Springer-Verlag, Berlin, 1997).

Orenstein, J.

M. C. Nuss and J. Orenstein, in Millimeter-Wave Spectroscopy of Solids, G. Gruener, ed. (Springer-Verlag, Berlin, 1997).

Slaney, M.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, New York, 1988).

van Exter, M.

IEEE J. Sel. Topics Quantum Electron. (1)

D. M. Mittleman, R. H. Jacobsen, and M. C. Nuss, IEEE J. Sel. Topics Quantum Electron. 2, 679 (1997).
[Crossref]

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

Opt. Lett. (3)

Other (3)

Wavelet processing was performed with the WaveLab software package of J. Buckheit, S. Chen, D. Donoho, I. Johnstone, and J. Scargle, of the Department of Statistics at Stanford University, available on the World Wide Web at http://playfair.stanford.edu/~wavelab/ .

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, New York, 1988).

M. C. Nuss and J. Orenstein, in Millimeter-Wave Spectroscopy of Solids, G. Gruener, ed. (Springer-Verlag, Berlin, 1997).

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Figures (2)

Fig. 1
Fig. 1

(a) Input THz waveform and (b) reflected waveform from a single point on a 3.5-in.  floppy disk. Each of the reflected pulses identifies a dielectric discontinuity along the propagation direction of the beam normal to the floppy disk, as labeled in the figure. Curve (c) is the reflected waveform after signal processing, as described in the text. Curve (d) is the refractive-index profile of the medium (right-hand axis), derived from curve (c) by Eqs.  (3) and (4) below. Curve (b) has been scaled up by a factor of 3 relative to the left (photocurrent) axis and vertically offset for clarity.

Fig. 2
Fig. 2

(a) Conventional reflective T-ray image of the 3.5-in.  floppy disk and (b) tomographic image of the same disk at a constant vertical position, indicated by the dashed line at y=15 mm in (a). Darker stripes indicate positive refractive-index steps (Δn>0), and lighter stripes indicate negative steps (Δn<0). The vertical axis (optical delay) is related to the waveform delay by Eq.  (2), neglecting all refractive-index variations.

Equations (4)

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Bj=k=0Mgj-kAk.
dj=c2njΔt,
nj=i=1j1-ri1+ri,
rk=gkj=1k-111-rj2.

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