Abstract

We describe a new imaging method using single-cycle pulses of terahertz (THz) radiation. This technique emulates the data collection and image processing procedures developed for geophysical prospecting and is made possible by the availability of fiber-coupled THz receiver antennas. We use a migration procedure to solve the inverse problem; this permits us to reconstruct the location, the shape, and the refractive index of targets. We show examples for both metallic and dielectric model targets, and we perform velocity analysis on dielectric targets to estimate the refractive indices of imaged components. These results broaden the capabilities of THz imaging systems and also demonstrate the viability of the THz system as a test bed for the exploration of new seismic processing methods.

© 2002 Optical Society of America

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  1. B. B. Hu, M. Nuss, “Imaging with terahertz waves,” Opt. Lett. 20, 1716–1718 (1995).
    [CrossRef] [PubMed]
  2. D. Mittleman, R. Jacobsen, M. Nuss, “T-ray imaging,” IEEE J. Sel. Top. Quantum Electron. 2, 679–692 (1996).
    [CrossRef]
  3. D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, M. Koch, “Recent advances in terahertz imaging,” Appl. Phys. B 68, 1085–1094 (1999).
    [CrossRef]
  4. M. Brucherseifer, P. Haring Bolivar, H. Klingenberg, H. Kurz, “Angle-dependent THz tomography characterization of thin ceramic oxide films for fuel cell applications,” Appl. Phys. B 72, 361–366 (2001).
    [CrossRef]
  5. R. A. Cheville, D. Grischkowsky, “Time domain terahertz impulse ranging studies,” Appl. Phys. Lett. 67, 1960–1963 (1995).
    [CrossRef]
  6. D. Mittleman, S. Hunsche, L. Boivin, M. Nuss, “T-ray tomography,” Opt. Lett. 22, 904–906 (1997).
    [CrossRef] [PubMed]
  7. M. Tonouchi, M. Yamashita, M. Hangyo, “Terahertz radiation imaging of supercurrent distribution in vortex-penetrated YBa2Cu3O7-δ thin film strips,” J. Appl. Phys. 87, 7366–7375 (2000).
    [CrossRef]
  8. S. Hunsche, M. Koch, I. Brener, M. C. Nuss, “THz near-field imaging,” Opt. Commun. 150, 22–26 (1998).
    [CrossRef]
  9. Q. Chen, Z. Jiang, G. Xu, X.-C. Zhang, “Near-field terahertz imaging with a dynamic aperture,” Opt. Lett. 25, 1122–1124 (2000).
    [CrossRef]
  10. J. L. Johnson, T. D. Dorney, D. M. Mittleman, “Enhanced depth resolution in terahertz imaging using phase-shift interferometry,” Appl. Phys. Lett. 78, 835–837 (2001).
    [CrossRef]
  11. M. Herrmann, M. Tani, K. Sakai, “Display modes in time-resolved terahertz imaging,” Jpn. J. Appl. Phys. Part 1 39, 6254–6258 (2000).
    [CrossRef]
  12. J. V. Rudd, J. L. Johnson, D. M. Mittleman, “Quadrupole radiation from terahertz dipole antennas,” Opt. Lett. 25, 1556–1558 (2000).
    [CrossRef]
  13. J. V. Rudd, J. L. Johnson, D. M. Mittleman, “Cross-polarized angular emission patterns from lens-coupled terahertz antennas,” J. Opt. Soc. Am. B 18, 1524–1533 (2001).
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  14. J. V. Rudd, D. M. Mittleman, “The influence of substrate lens design in terahertz time-domain spectroscopy,” J. Opt. Soc. Am. B 19, 319–329 (2002).
    [CrossRef]
  15. A. Ruffin, J. Decker, L. Sanchez-Palencia, L. LeHors, J. Whitaker, T. Norris, J. Rudd, “Time reversal and object reconstruction with single-cycle pulses,” Opt. Lett. 26, 681–683 (2001).
    [CrossRef]
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    [CrossRef]
  18. J. Scales, Theory of Seismic Imaging (Springer-Verlag, Berlin, 1995).
  19. M. Dobrin, C. Savit, Introduction to Geophysical Prospecting, 4th ed. (McGraw-Hill, New York, 1988).
  20. G. W. Purnell, “Observations of wave velocity and attenuation in two-phase media,” Geophysics 51, 2193–2199 (1986).
    [CrossRef]
  21. J.-M. Ass’ad, T. M. Kusky, J. A. McDonald, R. H. Tatham, “Implications of scale model seismology in the detection of natural fractures and microcracks,” J. Seismic Explor. 1, 61–76 (1992).
  22. C. Macdonald, P. M. Davis, D. D. Jackson, “Inversion of reflection traveltimes and amplitudes,” Geophysics 52, 606–617 (1987).
    [CrossRef]
  23. W. A. Schneider, “Integral formulation for migration in two and three dimensions,” Geophysics 43, 49–76 (1978).
    [CrossRef]
  24. K. Waters, Reflection Seismology: A Tool for Energy Resource Exploration (Wiley, New York, 1981).
  25. R. McGowan, R. Cheville, D. Grischkowsky, “Experimental study of the surface waves on a dielectric cylinder via terahertz impulse radar ranging,” IEEE Trans. Microwave Theory Tech. 48, 417–422 (2000).
    [CrossRef]
  26. R. Sullivan, Microwave Radar: Imaging and Advanced Concepts (Artech House, Norwood, Mass., 2000).
  27. M. Brühl, J. Vermeer, M. Kiehn, “Fresnel zones for broadband data,” Geophysics 61, 600–604 (1996).
    [CrossRef]
  28. R. E. Sheriff, Geophysical Methods (Prentice-Hall, Englewood Cliffs, N.J., 1989).
  29. J. R. Birch, J. D. Dromey, J. Lesurf, “The optical constants of some common low-loss polymers between 4 and 40 cm-1,” Infrared Phys. 21, 225–228 (1981).
    [CrossRef]
  30. C. H. Green, “Velocity determinations by means of reflection profiles,” Geophysics 3, 295–305 (1938).
    [CrossRef]
  31. W. W. Symes, M. Kern, “Inversion of reflection seismograms by differential semblance analysis: algorithm structure and synthetic examples,” Geophys. Prospect. 42, 565–614 (1994).
    [CrossRef]
  32. R. Versteeg, “The Marmousi experience: velocity model determination on a synthetic complex data set,” Leading Edge 13, 927–936 (1994).
    [CrossRef]
  33. M. T. Taner, F. Koehler, “Velocity spectra: digital computer derivation and applications of velocity functions,” Geophysics 34, 859–881 (1969).
    [CrossRef]
  34. N. S. Neidell, M. T. Taner, “Semblance and other coherency measures for multichannel data,” Geophysics 36, 482–497 (1971).
    [CrossRef]
  35. C. H. Dix, “Seismic velocities from surface measurements,” Geophysics 20, 68–86 (1955).
    [CrossRef]

2002

2001

2000

M. Herrmann, M. Tani, K. Sakai, “Display modes in time-resolved terahertz imaging,” Jpn. J. Appl. Phys. Part 1 39, 6254–6258 (2000).
[CrossRef]

R. McGowan, R. Cheville, D. Grischkowsky, “Experimental study of the surface waves on a dielectric cylinder via terahertz impulse radar ranging,” IEEE Trans. Microwave Theory Tech. 48, 417–422 (2000).
[CrossRef]

M. Tonouchi, M. Yamashita, M. Hangyo, “Terahertz radiation imaging of supercurrent distribution in vortex-penetrated YBa2Cu3O7-δ thin film strips,” J. Appl. Phys. 87, 7366–7375 (2000).
[CrossRef]

Q. Chen, Z. Jiang, G. Xu, X.-C. Zhang, “Near-field terahertz imaging with a dynamic aperture,” Opt. Lett. 25, 1122–1124 (2000).
[CrossRef]

J. V. Rudd, J. L. Johnson, D. M. Mittleman, “Quadrupole radiation from terahertz dipole antennas,” Opt. Lett. 25, 1556–1558 (2000).
[CrossRef]

1999

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, M. Koch, “Recent advances in terahertz imaging,” Appl. Phys. B 68, 1085–1094 (1999).
[CrossRef]

1998

S. Hunsche, M. Koch, I. Brener, M. C. Nuss, “THz near-field imaging,” Opt. Commun. 150, 22–26 (1998).
[CrossRef]

1997

1996

D. Mittleman, R. Jacobsen, M. Nuss, “T-ray imaging,” IEEE J. Sel. Top. Quantum Electron. 2, 679–692 (1996).
[CrossRef]

M. Brühl, J. Vermeer, M. Kiehn, “Fresnel zones for broadband data,” Geophysics 61, 600–604 (1996).
[CrossRef]

1995

R. A. Cheville, D. Grischkowsky, “Time domain terahertz impulse ranging studies,” Appl. Phys. Lett. 67, 1960–1963 (1995).
[CrossRef]

B. B. Hu, M. Nuss, “Imaging with terahertz waves,” Opt. Lett. 20, 1716–1718 (1995).
[CrossRef] [PubMed]

1994

W. W. Symes, M. Kern, “Inversion of reflection seismograms by differential semblance analysis: algorithm structure and synthetic examples,” Geophys. Prospect. 42, 565–614 (1994).
[CrossRef]

R. Versteeg, “The Marmousi experience: velocity model determination on a synthetic complex data set,” Leading Edge 13, 927–936 (1994).
[CrossRef]

1992

J.-M. Ass’ad, T. M. Kusky, J. A. McDonald, R. H. Tatham, “Implications of scale model seismology in the detection of natural fractures and microcracks,” J. Seismic Explor. 1, 61–76 (1992).

1987

C. Macdonald, P. M. Davis, D. D. Jackson, “Inversion of reflection traveltimes and amplitudes,” Geophysics 52, 606–617 (1987).
[CrossRef]

1986

G. W. Purnell, “Observations of wave velocity and attenuation in two-phase media,” Geophysics 51, 2193–2199 (1986).
[CrossRef]

1981

J. R. Birch, J. D. Dromey, J. Lesurf, “The optical constants of some common low-loss polymers between 4 and 40 cm-1,” Infrared Phys. 21, 225–228 (1981).
[CrossRef]

1978

W. A. Schneider, “Integral formulation for migration in two and three dimensions,” Geophysics 43, 49–76 (1978).
[CrossRef]

1971

N. S. Neidell, M. T. Taner, “Semblance and other coherency measures for multichannel data,” Geophysics 36, 482–497 (1971).
[CrossRef]

1969

M. T. Taner, F. Koehler, “Velocity spectra: digital computer derivation and applications of velocity functions,” Geophysics 34, 859–881 (1969).
[CrossRef]

1955

C. H. Dix, “Seismic velocities from surface measurements,” Geophysics 20, 68–86 (1955).
[CrossRef]

1938

C. H. Green, “Velocity determinations by means of reflection profiles,” Geophysics 3, 295–305 (1938).
[CrossRef]

Ass’ad, J.-M.

J.-M. Ass’ad, T. M. Kusky, J. A. McDonald, R. H. Tatham, “Implications of scale model seismology in the detection of natural fractures and microcracks,” J. Seismic Explor. 1, 61–76 (1992).

Baraniuk, R. G.

T. D. Dorney, J. L. Johnson, J. V. Rudd, R. G. Baraniuk, W. W. Symes, D. M. Mittleman, “Terahertz reflection imaging using Kirchhoff migration,” Opt. Lett. 26, 1513–1515 (2001).
[CrossRef]

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, M. Koch, “Recent advances in terahertz imaging,” Appl. Phys. B 68, 1085–1094 (1999).
[CrossRef]

Birch, J. R.

J. R. Birch, J. D. Dromey, J. Lesurf, “The optical constants of some common low-loss polymers between 4 and 40 cm-1,” Infrared Phys. 21, 225–228 (1981).
[CrossRef]

Boivin, L.

Born, M.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, New York, 1999).

Brener, I.

S. Hunsche, M. Koch, I. Brener, M. C. Nuss, “THz near-field imaging,” Opt. Commun. 150, 22–26 (1998).
[CrossRef]

Brucherseifer, M.

M. Brucherseifer, P. Haring Bolivar, H. Klingenberg, H. Kurz, “Angle-dependent THz tomography characterization of thin ceramic oxide films for fuel cell applications,” Appl. Phys. B 72, 361–366 (2001).
[CrossRef]

Brühl, M.

M. Brühl, J. Vermeer, M. Kiehn, “Fresnel zones for broadband data,” Geophysics 61, 600–604 (1996).
[CrossRef]

Chen, Q.

Cheville, R.

R. McGowan, R. Cheville, D. Grischkowsky, “Experimental study of the surface waves on a dielectric cylinder via terahertz impulse radar ranging,” IEEE Trans. Microwave Theory Tech. 48, 417–422 (2000).
[CrossRef]

Cheville, R. A.

R. A. Cheville, D. Grischkowsky, “Time domain terahertz impulse ranging studies,” Appl. Phys. Lett. 67, 1960–1963 (1995).
[CrossRef]

Davis, P. M.

C. Macdonald, P. M. Davis, D. D. Jackson, “Inversion of reflection traveltimes and amplitudes,” Geophysics 52, 606–617 (1987).
[CrossRef]

Decker, J.

Dix, C. H.

C. H. Dix, “Seismic velocities from surface measurements,” Geophysics 20, 68–86 (1955).
[CrossRef]

Dobrin, M.

M. Dobrin, C. Savit, Introduction to Geophysical Prospecting, 4th ed. (McGraw-Hill, New York, 1988).

Dorney, T. D.

T. D. Dorney, J. L. Johnson, J. V. Rudd, R. G. Baraniuk, W. W. Symes, D. M. Mittleman, “Terahertz reflection imaging using Kirchhoff migration,” Opt. Lett. 26, 1513–1515 (2001).
[CrossRef]

J. L. Johnson, T. D. Dorney, D. M. Mittleman, “Enhanced depth resolution in terahertz imaging using phase-shift interferometry,” Appl. Phys. Lett. 78, 835–837 (2001).
[CrossRef]

Dromey, J. D.

J. R. Birch, J. D. Dromey, J. Lesurf, “The optical constants of some common low-loss polymers between 4 and 40 cm-1,” Infrared Phys. 21, 225–228 (1981).
[CrossRef]

Green, C. H.

C. H. Green, “Velocity determinations by means of reflection profiles,” Geophysics 3, 295–305 (1938).
[CrossRef]

Grischkowsky, D.

R. McGowan, R. Cheville, D. Grischkowsky, “Experimental study of the surface waves on a dielectric cylinder via terahertz impulse radar ranging,” IEEE Trans. Microwave Theory Tech. 48, 417–422 (2000).
[CrossRef]

R. A. Cheville, D. Grischkowsky, “Time domain terahertz impulse ranging studies,” Appl. Phys. Lett. 67, 1960–1963 (1995).
[CrossRef]

Gupta, M.

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, M. Koch, “Recent advances in terahertz imaging,” Appl. Phys. B 68, 1085–1094 (1999).
[CrossRef]

Hangyo, M.

M. Tonouchi, M. Yamashita, M. Hangyo, “Terahertz radiation imaging of supercurrent distribution in vortex-penetrated YBa2Cu3O7-δ thin film strips,” J. Appl. Phys. 87, 7366–7375 (2000).
[CrossRef]

Haring Bolivar, P.

M. Brucherseifer, P. Haring Bolivar, H. Klingenberg, H. Kurz, “Angle-dependent THz tomography characterization of thin ceramic oxide films for fuel cell applications,” Appl. Phys. B 72, 361–366 (2001).
[CrossRef]

Herrmann, M.

M. Herrmann, M. Tani, K. Sakai, “Display modes in time-resolved terahertz imaging,” Jpn. J. Appl. Phys. Part 1 39, 6254–6258 (2000).
[CrossRef]

Hu, B. B.

Hunsche, S.

S. Hunsche, M. Koch, I. Brener, M. C. Nuss, “THz near-field imaging,” Opt. Commun. 150, 22–26 (1998).
[CrossRef]

D. Mittleman, S. Hunsche, L. Boivin, M. Nuss, “T-ray tomography,” Opt. Lett. 22, 904–906 (1997).
[CrossRef] [PubMed]

Jackson, D. D.

C. Macdonald, P. M. Davis, D. D. Jackson, “Inversion of reflection traveltimes and amplitudes,” Geophysics 52, 606–617 (1987).
[CrossRef]

Jacobsen, R.

D. Mittleman, R. Jacobsen, M. Nuss, “T-ray imaging,” IEEE J. Sel. Top. Quantum Electron. 2, 679–692 (1996).
[CrossRef]

Jiang, Z.

Johnson, J. L.

Kern, M.

W. W. Symes, M. Kern, “Inversion of reflection seismograms by differential semblance analysis: algorithm structure and synthetic examples,” Geophys. Prospect. 42, 565–614 (1994).
[CrossRef]

Kiehn, M.

M. Brühl, J. Vermeer, M. Kiehn, “Fresnel zones for broadband data,” Geophysics 61, 600–604 (1996).
[CrossRef]

Klingenberg, H.

M. Brucherseifer, P. Haring Bolivar, H. Klingenberg, H. Kurz, “Angle-dependent THz tomography characterization of thin ceramic oxide films for fuel cell applications,” Appl. Phys. B 72, 361–366 (2001).
[CrossRef]

Koch, M.

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, M. Koch, “Recent advances in terahertz imaging,” Appl. Phys. B 68, 1085–1094 (1999).
[CrossRef]

S. Hunsche, M. Koch, I. Brener, M. C. Nuss, “THz near-field imaging,” Opt. Commun. 150, 22–26 (1998).
[CrossRef]

Koehler, F.

M. T. Taner, F. Koehler, “Velocity spectra: digital computer derivation and applications of velocity functions,” Geophysics 34, 859–881 (1969).
[CrossRef]

Kurz, H.

M. Brucherseifer, P. Haring Bolivar, H. Klingenberg, H. Kurz, “Angle-dependent THz tomography characterization of thin ceramic oxide films for fuel cell applications,” Appl. Phys. B 72, 361–366 (2001).
[CrossRef]

Kusky, T. M.

J.-M. Ass’ad, T. M. Kusky, J. A. McDonald, R. H. Tatham, “Implications of scale model seismology in the detection of natural fractures and microcracks,” J. Seismic Explor. 1, 61–76 (1992).

LeHors, L.

Lesurf, J.

J. R. Birch, J. D. Dromey, J. Lesurf, “The optical constants of some common low-loss polymers between 4 and 40 cm-1,” Infrared Phys. 21, 225–228 (1981).
[CrossRef]

Macdonald, C.

C. Macdonald, P. M. Davis, D. D. Jackson, “Inversion of reflection traveltimes and amplitudes,” Geophysics 52, 606–617 (1987).
[CrossRef]

McDonald, J. A.

J.-M. Ass’ad, T. M. Kusky, J. A. McDonald, R. H. Tatham, “Implications of scale model seismology in the detection of natural fractures and microcracks,” J. Seismic Explor. 1, 61–76 (1992).

McGowan, R.

R. McGowan, R. Cheville, D. Grischkowsky, “Experimental study of the surface waves on a dielectric cylinder via terahertz impulse radar ranging,” IEEE Trans. Microwave Theory Tech. 48, 417–422 (2000).
[CrossRef]

Mittleman, D.

D. Mittleman, S. Hunsche, L. Boivin, M. Nuss, “T-ray tomography,” Opt. Lett. 22, 904–906 (1997).
[CrossRef] [PubMed]

D. Mittleman, R. Jacobsen, M. Nuss, “T-ray imaging,” IEEE J. Sel. Top. Quantum Electron. 2, 679–692 (1996).
[CrossRef]

Mittleman, D. M.

Neelamani, R.

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, M. Koch, “Recent advances in terahertz imaging,” Appl. Phys. B 68, 1085–1094 (1999).
[CrossRef]

Neidell, N. S.

N. S. Neidell, M. T. Taner, “Semblance and other coherency measures for multichannel data,” Geophysics 36, 482–497 (1971).
[CrossRef]

Norris, T.

Nuss, M.

Nuss, M. C.

S. Hunsche, M. Koch, I. Brener, M. C. Nuss, “THz near-field imaging,” Opt. Commun. 150, 22–26 (1998).
[CrossRef]

Purnell, G. W.

G. W. Purnell, “Observations of wave velocity and attenuation in two-phase media,” Geophysics 51, 2193–2199 (1986).
[CrossRef]

Rudd, J.

Rudd, J. V.

Ruffin, A.

Sakai, K.

M. Herrmann, M. Tani, K. Sakai, “Display modes in time-resolved terahertz imaging,” Jpn. J. Appl. Phys. Part 1 39, 6254–6258 (2000).
[CrossRef]

Sanchez-Palencia, L.

Savit, C.

M. Dobrin, C. Savit, Introduction to Geophysical Prospecting, 4th ed. (McGraw-Hill, New York, 1988).

Scales, J.

J. Scales, Theory of Seismic Imaging (Springer-Verlag, Berlin, 1995).

Schneider, W. A.

W. A. Schneider, “Integral formulation for migration in two and three dimensions,” Geophysics 43, 49–76 (1978).
[CrossRef]

Sheriff, R. E.

R. E. Sheriff, Geophysical Methods (Prentice-Hall, Englewood Cliffs, N.J., 1989).

Sullivan, R.

R. Sullivan, Microwave Radar: Imaging and Advanced Concepts (Artech House, Norwood, Mass., 2000).

Symes, W. W.

T. D. Dorney, J. L. Johnson, J. V. Rudd, R. G. Baraniuk, W. W. Symes, D. M. Mittleman, “Terahertz reflection imaging using Kirchhoff migration,” Opt. Lett. 26, 1513–1515 (2001).
[CrossRef]

W. W. Symes, M. Kern, “Inversion of reflection seismograms by differential semblance analysis: algorithm structure and synthetic examples,” Geophys. Prospect. 42, 565–614 (1994).
[CrossRef]

Taner, M. T.

N. S. Neidell, M. T. Taner, “Semblance and other coherency measures for multichannel data,” Geophysics 36, 482–497 (1971).
[CrossRef]

M. T. Taner, F. Koehler, “Velocity spectra: digital computer derivation and applications of velocity functions,” Geophysics 34, 859–881 (1969).
[CrossRef]

Tani, M.

M. Herrmann, M. Tani, K. Sakai, “Display modes in time-resolved terahertz imaging,” Jpn. J. Appl. Phys. Part 1 39, 6254–6258 (2000).
[CrossRef]

Tatham, R. H.

J.-M. Ass’ad, T. M. Kusky, J. A. McDonald, R. H. Tatham, “Implications of scale model seismology in the detection of natural fractures and microcracks,” J. Seismic Explor. 1, 61–76 (1992).

Tonouchi, M.

M. Tonouchi, M. Yamashita, M. Hangyo, “Terahertz radiation imaging of supercurrent distribution in vortex-penetrated YBa2Cu3O7-δ thin film strips,” J. Appl. Phys. 87, 7366–7375 (2000).
[CrossRef]

Vermeer, J.

M. Brühl, J. Vermeer, M. Kiehn, “Fresnel zones for broadband data,” Geophysics 61, 600–604 (1996).
[CrossRef]

Versteeg, R.

R. Versteeg, “The Marmousi experience: velocity model determination on a synthetic complex data set,” Leading Edge 13, 927–936 (1994).
[CrossRef]

Waters, K.

K. Waters, Reflection Seismology: A Tool for Energy Resource Exploration (Wiley, New York, 1981).

Whitaker, J.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, New York, 1999).

Xu, G.

Yamashita, M.

M. Tonouchi, M. Yamashita, M. Hangyo, “Terahertz radiation imaging of supercurrent distribution in vortex-penetrated YBa2Cu3O7-δ thin film strips,” J. Appl. Phys. 87, 7366–7375 (2000).
[CrossRef]

Zhang, X.-C.

Appl. Phys. B

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, M. Koch, “Recent advances in terahertz imaging,” Appl. Phys. B 68, 1085–1094 (1999).
[CrossRef]

M. Brucherseifer, P. Haring Bolivar, H. Klingenberg, H. Kurz, “Angle-dependent THz tomography characterization of thin ceramic oxide films for fuel cell applications,” Appl. Phys. B 72, 361–366 (2001).
[CrossRef]

Appl. Phys. Lett.

R. A. Cheville, D. Grischkowsky, “Time domain terahertz impulse ranging studies,” Appl. Phys. Lett. 67, 1960–1963 (1995).
[CrossRef]

J. L. Johnson, T. D. Dorney, D. M. Mittleman, “Enhanced depth resolution in terahertz imaging using phase-shift interferometry,” Appl. Phys. Lett. 78, 835–837 (2001).
[CrossRef]

Geophys. Prospect.

W. W. Symes, M. Kern, “Inversion of reflection seismograms by differential semblance analysis: algorithm structure and synthetic examples,” Geophys. Prospect. 42, 565–614 (1994).
[CrossRef]

Geophysics

G. W. Purnell, “Observations of wave velocity and attenuation in two-phase media,” Geophysics 51, 2193–2199 (1986).
[CrossRef]

C. Macdonald, P. M. Davis, D. D. Jackson, “Inversion of reflection traveltimes and amplitudes,” Geophysics 52, 606–617 (1987).
[CrossRef]

W. A. Schneider, “Integral formulation for migration in two and three dimensions,” Geophysics 43, 49–76 (1978).
[CrossRef]

M. Brühl, J. Vermeer, M. Kiehn, “Fresnel zones for broadband data,” Geophysics 61, 600–604 (1996).
[CrossRef]

C. H. Green, “Velocity determinations by means of reflection profiles,” Geophysics 3, 295–305 (1938).
[CrossRef]

M. T. Taner, F. Koehler, “Velocity spectra: digital computer derivation and applications of velocity functions,” Geophysics 34, 859–881 (1969).
[CrossRef]

N. S. Neidell, M. T. Taner, “Semblance and other coherency measures for multichannel data,” Geophysics 36, 482–497 (1971).
[CrossRef]

C. H. Dix, “Seismic velocities from surface measurements,” Geophysics 20, 68–86 (1955).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

D. Mittleman, R. Jacobsen, M. Nuss, “T-ray imaging,” IEEE J. Sel. Top. Quantum Electron. 2, 679–692 (1996).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

R. McGowan, R. Cheville, D. Grischkowsky, “Experimental study of the surface waves on a dielectric cylinder via terahertz impulse radar ranging,” IEEE Trans. Microwave Theory Tech. 48, 417–422 (2000).
[CrossRef]

Infrared Phys.

J. R. Birch, J. D. Dromey, J. Lesurf, “The optical constants of some common low-loss polymers between 4 and 40 cm-1,” Infrared Phys. 21, 225–228 (1981).
[CrossRef]

J. Appl. Phys.

M. Tonouchi, M. Yamashita, M. Hangyo, “Terahertz radiation imaging of supercurrent distribution in vortex-penetrated YBa2Cu3O7-δ thin film strips,” J. Appl. Phys. 87, 7366–7375 (2000).
[CrossRef]

J. Opt. Soc. Am. B

J. Seismic Explor.

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Figures (10)

Fig. 1
Fig. 1

(a) Schematic of a common shot experimental arrangement emulated by terahertz (THz) system. Multiple symmetrically placed receivers are arranged to collect a series of reflected waveforms from a point scatterer. The travel time increases hyperbolically with the receiver offset from the transmitter. (b) Kirchhoff migration reconstructs the location and the shape of a reflector by calculating the appropriate hyperbola and summing the values of the recorded traces along that hyperbola, for an array of guessed locations. Incorrect locations generate a small summation, since their hyperbolas do not pass through many reflected pulses. Two such incorrect guesses, and their corresponding hyperbolas, are shown.

Fig. 2
Fig. 2

We acquire data by using the Picometrix fiber-coupled THz system that provides a constant temporal delay as the transmitter and/or the receiver is translated. The system includes dispersion compensation to offset the effects of the optical fiber and a separate enclosure for fiber splitting, delay rail, and data acquisition. To simulate simultaneous multistatic data acquisition, we translate and rotate the receiver along a line. A photograph of a packaged antenna module is shown.

Fig. 3
Fig. 3

Kirchhoff migration images from five metal cylinder targets with diameters of (a) 2.4 mm, (b) 3.2 mm, (c) 4.7 mm, (d) 6.2 mm, and (e) 12.7 mm. The dashed curves represent the outlines of the targets for comparison with the migration images. In (a) and (b), the objects are correctly located, but their surface curvature cannot be resolved, since their diameters are close to the resolution. In (c), the location of the object and a very faint surface curvature are resolved. In (d) and (e), the cylindrical surfaces are reconstructed over a limited region on account of the finite range of receiver offsets.

Fig. 4
Fig. 4

Reconstruction of a planar reflector using a single transmitter and a group of receivers on one side of the transmitter with different receiver spacings, demonstrating the effect of aliasing. In (a), (b), (c), and (d), the receivers are spaced every 1, 2, 3, and 4 mm, respectively, within an offset range of 38–157 mm.

Fig. 5
Fig. 5

Data acquisition of a synthetic planar, homogeneous dielectric material using a moving group of one transmitter and 20 receivers. This arrangement allows common offset, common midpoint, and common shot gathers. We use a refractive index of 1.525, similar to that of high-density polyethylene (HDPE).

Fig. 6
Fig. 6

The absolute propagation time for the THz system is determined by plotting the squared receiver offset for a flat plate while adjusting the squared two-way travel time until the slope equals 1/vair2. Green’s technique28 is used to determine the wave velocity v0 when the absolute time is known. We know precisely the wave velocity but do not have an absolute time reference.

Fig. 7
Fig. 7

Kirchhoff (diffraction) summation of the synthetic data collected in Fig. 5 by using a 50-μm grid clearly shows the two surfaces of the flat plate. The top surface is accurately placed; however, the z-distance separation between the two surfaces is larger than the simulated thickness of 10 mm. Velocity analysis is required and is performed over the region indicated. Figure 8 below displays the results.

Fig. 8
Fig. 8

(a) A comparison of eight different velocity fields applied to the Kirchhoff migration of the second interface in Fig. 7 shows a dramatic change in the placement of the layer. We note a generally decreasing spread of the reconstructed interface as the guessed velocity decreases; however, there is no simple way to distinguish among these guesses. The background has been amplified to display the artifacts. (b) We apply the semblance coherency metric to each column of the migration indicated in Fig. 7 from 95 to 110 mm. The maximum semblance values for each column increase with decreasing velocity but show a curve that is due to the artifacts on both the left and right sides of the reconstruction. The maximum semblance value occurs at 2.0×108 m/s, close to the actual value of 1.97×108 m/s.

Fig. 9
Fig. 9

(a) Construction of an experimental, composite target includes a top layer of Teflon followed by high-density polyethylene (HDPE) and another layer of Teflon. The second and third layers are machined to have the same optical delay at normal incidence. This stack creates a smaller change in velocity between layers compared with that of the simulated air/HDPE interface in Fig. 5. (b) Common offset data after filtering show a large amount of noise. The interfaces are hard to discern; however, the constant-velocity migration results in (c) dramatically reduce the noise and reconstruct the image. The indicators at left denote the expected locations of each interface. These demonstrate the need for velocity analysis to properly locate the interfaces.

Fig. 10
Fig. 10

The normalized semblance averages for the second, third, and fourth interfaces are shown in (a), (b), and (c), respectively. The semblance values were calculated for each 50-μm-wide column over an approximately 3-mm-high window encompassing each interface. The average semblance for each velocity bin was taken over 30 columns. Unlike the results in Fig. 8, noise and multiple oscillations at the interfaces create a challenge for the semblance metric. The final Kirchhoff migration using the velocities taken from (a)–(c) is displayed in (d). The indicators, unlike those in Fig. 9(c), match the locations of the reconstructed interfaces.

Equations (9)

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D(x)=v0τ=(x02+z02)1/2+[(x-x0)2+z02]1/2,
Δx=v02τfmean,
Δz=v04Δf,
ΔDn=|D(xn)-D(xn+1)|v02Δf,
Tx2=T02+x2v02,
ΔT=Tx-T0=T02+x2vg21/2-T0,
vrms2=v12t1+v22t2+v32t3++vn2tnt1+t2+t3++tn=k=1nvk2tkk=1ntk.
I(x, z)=TRf(R, t(R, T, x, z)),
S=MIM(x, z)2MMIM2(x, z),

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