Abstract

Characterization of the topography of materials by interferometry in the visible or near-IR wavelength regime becomes difficult or impossible if the surface is rough on the length scale of a tenth of the wavelength and more. In this case, THz radiation can provide an interesting alternative. We demonstrate heterodyne profilometry at 600 GHz as a method for the accurate determination of surface topography with an achievable expanded standard uncertainty of 0.5 μm.

© 2008 Optical Society of America

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  1. Q. Chen and X.-C. Zhang, "Polarization modulation in optoelectronic generation and detection of terahertz beams," Appl. Phys. Lett. 23, 3435 (1999).
    [CrossRef]
  2. Q. Chen, M. Tani, Z. Jiang, and X.-C. Zhang, "Electro-optic transceivers for terahertz-wave applications," J. Opt. Soc. Am. B 18, 823 (2001).
    [CrossRef]
  3. J. L. Johnson, T. D. Dorney, and D. M. Mittleman, "Enhanced depth resolution in terahertz imaging using phase-shift interferometry," Appl. Phys. Lett. 78, 835 (2001).
    [CrossRef]
  4. J. L. Johnson, T. D. Dorney, and D. M. Mittleman, "Interferometric imaging with THz pulses," IEEE J. Sel. Top. Quantum Electron. 4, 592 (2001).
  5. N. Hasegawa, T. Löffler, M. D. Thomson and H. G. Roskos, "Remote identification of protrusions and dents on surfaces by terahertz reflectometry with spatial beam filtering and out-of-focus detection," Appl. Phys. Lett. 83, 3996 (2003).
    [CrossRef]
  6. T. Löffler, K. J. Siebert, N. Hasegawa, T. Hahn, and H. G. Roskos, "All-optoelectronic terahertz imaging systems and examples of their application," Proceedings of the IEEE 95, 1576 (2007).
    [CrossRef]
  7. T. Löffler, T. Bauer, K. Siebert, H. G. Roskos, A. Fitzgerald, and S. Czasch, "Terahertz dark-field imaging of biomedical tissue," Opt. Express 9, 616 (2001).
    [CrossRef] [PubMed]
  8. K. Siebert, T. Löffler, H. Quast, M. Thomson, T. Bauer, R. Leonhardt, S. Czasch, and H. G. Roskos, "All-optoelectronic continuous-wave terahertz imaging for biomedical applications," Phys. Med. Biol. 47, 3743 (2002).
    [CrossRef] [PubMed]
  9. K. J. Siebert, H. Quast, R. Leonhardt, T. Löffler, M. Thomson, T. Bauer, H. G. Roskos, and S. Czasch, "Continuous-wave all-optoelectronic terahertz imaging," Appl. Phys. Lett. 80, 3003 (2002).
    [CrossRef]
  10. T. Löffler, T. May, C. am Weg, A. Alcin, B. Hils and H. G. Roskos. "Continuous-wave terahertz imaging with a hybrid system," Appl. Phys. Lett. 90, 091111 (2007).
    [CrossRef]
  11. T. Bauer, J. S. Kolb, T. Löffler, E. Mohler, H. G. Roskos, and U. C. Pernisz, "Indium-tin-oxide-coated glass as dichroic mirror for far-infrared electromagnetic radiation," J. Appl. Phys. 92, 2210 (2002).
    [CrossRef]
  12. P. L. Heydemann, "Determination and correction of quadrature fringe measurement errors in interferometers," Appl. Opt. 20, 3382 (1981).
    [CrossRef] [PubMed]
  13. Guide to the Expression of Uncertainty in Measurement (Geneva: International Organization for Standardization (ISO)) 1995

2007 (2)

T. Löffler, K. J. Siebert, N. Hasegawa, T. Hahn, and H. G. Roskos, "All-optoelectronic terahertz imaging systems and examples of their application," Proceedings of the IEEE 95, 1576 (2007).
[CrossRef]

T. Löffler, T. May, C. am Weg, A. Alcin, B. Hils and H. G. Roskos. "Continuous-wave terahertz imaging with a hybrid system," Appl. Phys. Lett. 90, 091111 (2007).
[CrossRef]

2003 (1)

N. Hasegawa, T. Löffler, M. D. Thomson and H. G. Roskos, "Remote identification of protrusions and dents on surfaces by terahertz reflectometry with spatial beam filtering and out-of-focus detection," Appl. Phys. Lett. 83, 3996 (2003).
[CrossRef]

2002 (3)

K. Siebert, T. Löffler, H. Quast, M. Thomson, T. Bauer, R. Leonhardt, S. Czasch, and H. G. Roskos, "All-optoelectronic continuous-wave terahertz imaging for biomedical applications," Phys. Med. Biol. 47, 3743 (2002).
[CrossRef] [PubMed]

K. J. Siebert, H. Quast, R. Leonhardt, T. Löffler, M. Thomson, T. Bauer, H. G. Roskos, and S. Czasch, "Continuous-wave all-optoelectronic terahertz imaging," Appl. Phys. Lett. 80, 3003 (2002).
[CrossRef]

T. Bauer, J. S. Kolb, T. Löffler, E. Mohler, H. G. Roskos, and U. C. Pernisz, "Indium-tin-oxide-coated glass as dichroic mirror for far-infrared electromagnetic radiation," J. Appl. Phys. 92, 2210 (2002).
[CrossRef]

2001 (4)

T. Löffler, T. Bauer, K. Siebert, H. G. Roskos, A. Fitzgerald, and S. Czasch, "Terahertz dark-field imaging of biomedical tissue," Opt. Express 9, 616 (2001).
[CrossRef] [PubMed]

Q. Chen, M. Tani, Z. Jiang, and X.-C. Zhang, "Electro-optic transceivers for terahertz-wave applications," J. Opt. Soc. Am. B 18, 823 (2001).
[CrossRef]

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

J. L. Johnson, T. D. Dorney, and D. M. Mittleman, "Interferometric imaging with THz pulses," IEEE J. Sel. Top. Quantum Electron. 4, 592 (2001).

1999 (1)

Q. Chen and X.-C. Zhang, "Polarization modulation in optoelectronic generation and detection of terahertz beams," Appl. Phys. Lett. 23, 3435 (1999).
[CrossRef]

1981 (1)

Bauer, T.

K. Siebert, T. Löffler, H. Quast, M. Thomson, T. Bauer, R. Leonhardt, S. Czasch, and H. G. Roskos, "All-optoelectronic continuous-wave terahertz imaging for biomedical applications," Phys. Med. Biol. 47, 3743 (2002).
[CrossRef] [PubMed]

K. J. Siebert, H. Quast, R. Leonhardt, T. Löffler, M. Thomson, T. Bauer, H. G. Roskos, and S. Czasch, "Continuous-wave all-optoelectronic terahertz imaging," Appl. Phys. Lett. 80, 3003 (2002).
[CrossRef]

T. Bauer, J. S. Kolb, T. Löffler, E. Mohler, H. G. Roskos, and U. C. Pernisz, "Indium-tin-oxide-coated glass as dichroic mirror for far-infrared electromagnetic radiation," J. Appl. Phys. 92, 2210 (2002).
[CrossRef]

T. Löffler, T. Bauer, K. Siebert, H. G. Roskos, A. Fitzgerald, and S. Czasch, "Terahertz dark-field imaging of biomedical tissue," Opt. Express 9, 616 (2001).
[CrossRef] [PubMed]

Chen, Q.

Q. Chen, M. Tani, Z. Jiang, and X.-C. Zhang, "Electro-optic transceivers for terahertz-wave applications," J. Opt. Soc. Am. B 18, 823 (2001).
[CrossRef]

Q. Chen and X.-C. Zhang, "Polarization modulation in optoelectronic generation and detection of terahertz beams," Appl. Phys. Lett. 23, 3435 (1999).
[CrossRef]

Czasch, S.

K. Siebert, T. Löffler, H. Quast, M. Thomson, T. Bauer, R. Leonhardt, S. Czasch, and H. G. Roskos, "All-optoelectronic continuous-wave terahertz imaging for biomedical applications," Phys. Med. Biol. 47, 3743 (2002).
[CrossRef] [PubMed]

K. J. Siebert, H. Quast, R. Leonhardt, T. Löffler, M. Thomson, T. Bauer, H. G. Roskos, and S. Czasch, "Continuous-wave all-optoelectronic terahertz imaging," Appl. Phys. Lett. 80, 3003 (2002).
[CrossRef]

T. Löffler, T. Bauer, K. Siebert, H. G. Roskos, A. Fitzgerald, and S. Czasch, "Terahertz dark-field imaging of biomedical tissue," Opt. Express 9, 616 (2001).
[CrossRef] [PubMed]

Dorney, T. D.

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

J. L. Johnson, T. D. Dorney, and D. M. Mittleman, "Interferometric imaging with THz pulses," IEEE J. Sel. Top. Quantum Electron. 4, 592 (2001).

Fitzgerald, A.

Hahn, T.

T. Löffler, K. J. Siebert, N. Hasegawa, T. Hahn, and H. G. Roskos, "All-optoelectronic terahertz imaging systems and examples of their application," Proceedings of the IEEE 95, 1576 (2007).
[CrossRef]

Hasegawa, N.

T. Löffler, K. J. Siebert, N. Hasegawa, T. Hahn, and H. G. Roskos, "All-optoelectronic terahertz imaging systems and examples of their application," Proceedings of the IEEE 95, 1576 (2007).
[CrossRef]

N. Hasegawa, T. Löffler, M. D. Thomson and H. G. Roskos, "Remote identification of protrusions and dents on surfaces by terahertz reflectometry with spatial beam filtering and out-of-focus detection," Appl. Phys. Lett. 83, 3996 (2003).
[CrossRef]

Heydemann, P. L.

Jiang, Z.

Johnson, J. L.

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

J. L. Johnson, T. D. Dorney, and D. M. Mittleman, "Interferometric imaging with THz pulses," IEEE J. Sel. Top. Quantum Electron. 4, 592 (2001).

Kolb, J. S.

T. Bauer, J. S. Kolb, T. Löffler, E. Mohler, H. G. Roskos, and U. C. Pernisz, "Indium-tin-oxide-coated glass as dichroic mirror for far-infrared electromagnetic radiation," J. Appl. Phys. 92, 2210 (2002).
[CrossRef]

Leonhardt, R.

K. J. Siebert, H. Quast, R. Leonhardt, T. Löffler, M. Thomson, T. Bauer, H. G. Roskos, and S. Czasch, "Continuous-wave all-optoelectronic terahertz imaging," Appl. Phys. Lett. 80, 3003 (2002).
[CrossRef]

K. Siebert, T. Löffler, H. Quast, M. Thomson, T. Bauer, R. Leonhardt, S. Czasch, and H. G. Roskos, "All-optoelectronic continuous-wave terahertz imaging for biomedical applications," Phys. Med. Biol. 47, 3743 (2002).
[CrossRef] [PubMed]

Löffler, T.

T. Löffler, K. J. Siebert, N. Hasegawa, T. Hahn, and H. G. Roskos, "All-optoelectronic terahertz imaging systems and examples of their application," Proceedings of the IEEE 95, 1576 (2007).
[CrossRef]

T. Löffler, T. May, C. am Weg, A. Alcin, B. Hils and H. G. Roskos. "Continuous-wave terahertz imaging with a hybrid system," Appl. Phys. Lett. 90, 091111 (2007).
[CrossRef]

N. Hasegawa, T. Löffler, M. D. Thomson and H. G. Roskos, "Remote identification of protrusions and dents on surfaces by terahertz reflectometry with spatial beam filtering and out-of-focus detection," Appl. Phys. Lett. 83, 3996 (2003).
[CrossRef]

K. Siebert, T. Löffler, H. Quast, M. Thomson, T. Bauer, R. Leonhardt, S. Czasch, and H. G. Roskos, "All-optoelectronic continuous-wave terahertz imaging for biomedical applications," Phys. Med. Biol. 47, 3743 (2002).
[CrossRef] [PubMed]

K. J. Siebert, H. Quast, R. Leonhardt, T. Löffler, M. Thomson, T. Bauer, H. G. Roskos, and S. Czasch, "Continuous-wave all-optoelectronic terahertz imaging," Appl. Phys. Lett. 80, 3003 (2002).
[CrossRef]

T. Bauer, J. S. Kolb, T. Löffler, E. Mohler, H. G. Roskos, and U. C. Pernisz, "Indium-tin-oxide-coated glass as dichroic mirror for far-infrared electromagnetic radiation," J. Appl. Phys. 92, 2210 (2002).
[CrossRef]

T. Löffler, T. Bauer, K. Siebert, H. G. Roskos, A. Fitzgerald, and S. Czasch, "Terahertz dark-field imaging of biomedical tissue," Opt. Express 9, 616 (2001).
[CrossRef] [PubMed]

May, T.

T. Löffler, T. May, C. am Weg, A. Alcin, B. Hils and H. G. Roskos. "Continuous-wave terahertz imaging with a hybrid system," Appl. Phys. Lett. 90, 091111 (2007).
[CrossRef]

Mittleman, D. M.

J. L. Johnson, T. D. Dorney, and D. M. Mittleman, "Interferometric imaging with THz pulses," IEEE J. Sel. Top. Quantum Electron. 4, 592 (2001).

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

Mohler, E.

T. Bauer, J. S. Kolb, T. Löffler, E. Mohler, H. G. Roskos, and U. C. Pernisz, "Indium-tin-oxide-coated glass as dichroic mirror for far-infrared electromagnetic radiation," J. Appl. Phys. 92, 2210 (2002).
[CrossRef]

Pernisz, U. C.

T. Bauer, J. S. Kolb, T. Löffler, E. Mohler, H. G. Roskos, and U. C. Pernisz, "Indium-tin-oxide-coated glass as dichroic mirror for far-infrared electromagnetic radiation," J. Appl. Phys. 92, 2210 (2002).
[CrossRef]

Quast, H.

K. J. Siebert, H. Quast, R. Leonhardt, T. Löffler, M. Thomson, T. Bauer, H. G. Roskos, and S. Czasch, "Continuous-wave all-optoelectronic terahertz imaging," Appl. Phys. Lett. 80, 3003 (2002).
[CrossRef]

K. Siebert, T. Löffler, H. Quast, M. Thomson, T. Bauer, R. Leonhardt, S. Czasch, and H. G. Roskos, "All-optoelectronic continuous-wave terahertz imaging for biomedical applications," Phys. Med. Biol. 47, 3743 (2002).
[CrossRef] [PubMed]

Roskos, H. G.

T. Löffler, K. J. Siebert, N. Hasegawa, T. Hahn, and H. G. Roskos, "All-optoelectronic terahertz imaging systems and examples of their application," Proceedings of the IEEE 95, 1576 (2007).
[CrossRef]

N. Hasegawa, T. Löffler, M. D. Thomson and H. G. Roskos, "Remote identification of protrusions and dents on surfaces by terahertz reflectometry with spatial beam filtering and out-of-focus detection," Appl. Phys. Lett. 83, 3996 (2003).
[CrossRef]

K. Siebert, T. Löffler, H. Quast, M. Thomson, T. Bauer, R. Leonhardt, S. Czasch, and H. G. Roskos, "All-optoelectronic continuous-wave terahertz imaging for biomedical applications," Phys. Med. Biol. 47, 3743 (2002).
[CrossRef] [PubMed]

K. J. Siebert, H. Quast, R. Leonhardt, T. Löffler, M. Thomson, T. Bauer, H. G. Roskos, and S. Czasch, "Continuous-wave all-optoelectronic terahertz imaging," Appl. Phys. Lett. 80, 3003 (2002).
[CrossRef]

T. Bauer, J. S. Kolb, T. Löffler, E. Mohler, H. G. Roskos, and U. C. Pernisz, "Indium-tin-oxide-coated glass as dichroic mirror for far-infrared electromagnetic radiation," J. Appl. Phys. 92, 2210 (2002).
[CrossRef]

T. Löffler, T. Bauer, K. Siebert, H. G. Roskos, A. Fitzgerald, and S. Czasch, "Terahertz dark-field imaging of biomedical tissue," Opt. Express 9, 616 (2001).
[CrossRef] [PubMed]

Siebert, K.

K. Siebert, T. Löffler, H. Quast, M. Thomson, T. Bauer, R. Leonhardt, S. Czasch, and H. G. Roskos, "All-optoelectronic continuous-wave terahertz imaging for biomedical applications," Phys. Med. Biol. 47, 3743 (2002).
[CrossRef] [PubMed]

T. Löffler, T. Bauer, K. Siebert, H. G. Roskos, A. Fitzgerald, and S. Czasch, "Terahertz dark-field imaging of biomedical tissue," Opt. Express 9, 616 (2001).
[CrossRef] [PubMed]

Siebert, K. J.

T. Löffler, K. J. Siebert, N. Hasegawa, T. Hahn, and H. G. Roskos, "All-optoelectronic terahertz imaging systems and examples of their application," Proceedings of the IEEE 95, 1576 (2007).
[CrossRef]

K. J. Siebert, H. Quast, R. Leonhardt, T. Löffler, M. Thomson, T. Bauer, H. G. Roskos, and S. Czasch, "Continuous-wave all-optoelectronic terahertz imaging," Appl. Phys. Lett. 80, 3003 (2002).
[CrossRef]

Tani, M.

Thomson, M.

K. Siebert, T. Löffler, H. Quast, M. Thomson, T. Bauer, R. Leonhardt, S. Czasch, and H. G. Roskos, "All-optoelectronic continuous-wave terahertz imaging for biomedical applications," Phys. Med. Biol. 47, 3743 (2002).
[CrossRef] [PubMed]

K. J. Siebert, H. Quast, R. Leonhardt, T. Löffler, M. Thomson, T. Bauer, H. G. Roskos, and S. Czasch, "Continuous-wave all-optoelectronic terahertz imaging," Appl. Phys. Lett. 80, 3003 (2002).
[CrossRef]

Thomson, M. D.

N. Hasegawa, T. Löffler, M. D. Thomson and H. G. Roskos, "Remote identification of protrusions and dents on surfaces by terahertz reflectometry with spatial beam filtering and out-of-focus detection," Appl. Phys. Lett. 83, 3996 (2003).
[CrossRef]

Zhang, X.-C.

Q. Chen, M. Tani, Z. Jiang, and X.-C. Zhang, "Electro-optic transceivers for terahertz-wave applications," J. Opt. Soc. Am. B 18, 823 (2001).
[CrossRef]

Q. Chen and X.-C. Zhang, "Polarization modulation in optoelectronic generation and detection of terahertz beams," Appl. Phys. Lett. 23, 3435 (1999).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (5)

K. J. Siebert, H. Quast, R. Leonhardt, T. Löffler, M. Thomson, T. Bauer, H. G. Roskos, and S. Czasch, "Continuous-wave all-optoelectronic terahertz imaging," Appl. Phys. Lett. 80, 3003 (2002).
[CrossRef]

T. Löffler, T. May, C. am Weg, A. Alcin, B. Hils and H. G. Roskos. "Continuous-wave terahertz imaging with a hybrid system," Appl. Phys. Lett. 90, 091111 (2007).
[CrossRef]

Q. Chen and X.-C. Zhang, "Polarization modulation in optoelectronic generation and detection of terahertz beams," Appl. Phys. Lett. 23, 3435 (1999).
[CrossRef]

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

N. Hasegawa, T. Löffler, M. D. Thomson and H. G. Roskos, "Remote identification of protrusions and dents on surfaces by terahertz reflectometry with spatial beam filtering and out-of-focus detection," Appl. Phys. Lett. 83, 3996 (2003).
[CrossRef]

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

J. L. Johnson, T. D. Dorney, and D. M. Mittleman, "Interferometric imaging with THz pulses," IEEE J. Sel. Top. Quantum Electron. 4, 592 (2001).

J. Appl. Phys. (1)

T. Bauer, J. S. Kolb, T. Löffler, E. Mohler, H. G. Roskos, and U. C. Pernisz, "Indium-tin-oxide-coated glass as dichroic mirror for far-infrared electromagnetic radiation," J. Appl. Phys. 92, 2210 (2002).
[CrossRef]

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

Opt. Express (1)

Phys. Med. Biol. (1)

K. Siebert, T. Löffler, H. Quast, M. Thomson, T. Bauer, R. Leonhardt, S. Czasch, and H. G. Roskos, "All-optoelectronic continuous-wave terahertz imaging for biomedical applications," Phys. Med. Biol. 47, 3743 (2002).
[CrossRef] [PubMed]

Proceedings of the IEEE (1)

T. Löffler, K. J. Siebert, N. Hasegawa, T. Hahn, and H. G. Roskos, "All-optoelectronic terahertz imaging systems and examples of their application," Proceedings of the IEEE 95, 1576 (2007).
[CrossRef]

Other (1)

Guide to the Expression of Uncertainty in Measurement (Geneva: International Organization for Standardization (ISO)) 1995

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Figures (3)

Fig. 1.
Fig. 1.

Schematic view of the THz profilometer.

Fig. 2.
Fig. 2.

False-color plot of the topography of a nominally flat light-weight satellite telescope mirror.

Fig. 3.
Fig. 3.

Cyclic error (circles), correction of the displacement measured by the THz heterodyne profilometer (solid line) and the least-squares approximation of the cyclic error (dashed line).

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