Abstract

We report on a real-time terahertz (THz) impulse ranging (IPR) system based on a combination of time-of-flight measurement of pulsed THz radiation and the asynchronous-optical-sampling (ASOPS) tech nique. The insensitivity of THz radiation to optical scattering enables the detection of various objects having optically rough surfaces. The temporal magnification capability unique to ASOPS achieves precise distance measurements of a stationary target at an accuracy of 551μm and a resolution of 113μm. Furthermore, ASOPS THz IPR is effectively applied to real-time distance measurements of a moving target at a scan rate of 10Hz. Finally, we demonstrate the application of ASOPS THz IPR to a shape measurement of an optically rough surface and a thickness measurement of a paint film, showing the promise of further expanding the application scope of ASOPS THz IPR. The reported method will become a powerful tool for nondestructive inspection of large-scale structures.

© 2010 Optical Society of America

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References

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    [CrossRef]
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  23. D. M. Mittleman, S. Hunsche, L. Boivin, and M. C. Nuss, “T-ray tomography,” Opt. Lett. 22, 904–906 (1997).
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  24. T. Yasui, T. Yasuda, K. Sawanaka, and T. Araki, “A terahertz paintmeter for non-contact monitoring of thickness and drying progress in paint film,” Appl. Opt. 44, 6849–6856 (2005).
    [CrossRef] [PubMed]
  25. T. Yasuda, T. Iwata, T. Araki, and T. Yasui, “Improvement of minimum paint film thickness for THz paintmeters by multiple regression analysis,” Appl. Opt. 46, 7518–7526 (2007).
    [CrossRef] [PubMed]
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    [CrossRef]
  27. B. Sartorius, H. Roehle, H. Künzel, J. Böttcher, M. Schlak, D. Stanze, H. Venghaus, and M. Schell, “All-fiber terahertz time-domain spectrometer operating at 1.5 μm telecom wavelengths,” Opt. Express 16, 9565–9570 (2008).
    [CrossRef] [PubMed]

2010

2009

2008

2007

T. Yasuda, T. Iwata, T. Araki, and T. Yasui, “Improvement of minimum paint film thickness for THz paintmeters by multiple regression analysis,” Appl. Opt. 46, 7518–7526 (2007).
[CrossRef] [PubMed]

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photon. 1, 97–105 (2007).
[CrossRef]

J. Kim, S.-G. Jeon, J.-I. Kim, and Y.-S. Jin, “Terahertz pulse detection using rotary optical delay line,” Jpn. J. Appl. Phys. 46, 7332–7335 (2007).
[CrossRef]

A. Bartels, R. Cerna, C. Kistner, A. Thoma, F. Hudert, C. Janke, and T. Dekorsy, “Ultrafast time-domain spectroscopy based on high-speed asynchronous optical sampling,” Rev. Sci. Instrum. 78, 035107 (2007).
[CrossRef] [PubMed]

2006

T. Yasuda, T. Yasui, T. Araki, and E. Abraham, “Real-time two-dimensional terahertz tomography of moving objects,” Opt. Commun. 267, 128–136 (2006).
[CrossRef]

A. Bartels, A. Thoma, C. Janke, T. Dekorsy, A. Dreyhaupt, S. Winnerl, and M. Helm, “High-resolution THz spectrometer with kHz scan rates,” Opt. Express 14, 430–437 (2006).
[CrossRef] [PubMed]

2005

T. Yasui, T. Yasuda, K. Sawanaka, and T. Araki, “A terahertz paintmeter for non-contact monitoring of thickness and drying progress in paint film,” Appl. Opt. 44, 6849–6856 (2005).
[CrossRef] [PubMed]

T. Yasui, E. Saneyoshi, and T. Araki, “Asynchronous optical sampling terahertz time-domain spectroscopy for ultrahigh spectral resolution and rapid data acquisition,” Appl. Phys. Lett. 87, 061101 (2005).
[CrossRef]

2004

2000

D. L. Maskell and G. S. Woods, “A frequency modulated envelope delay FSCW radar for multiple-target applications,” IEEE Trans. Instrum. Meas. 49, 710–715 (2000).
[CrossRef]

M. Mitsumoto, N. Uehara, S. Inatsune, and T. Kirimoto, “Target distance and velocity measurement algorithm to reduce false target in FMCW automotive radar,” IEICE Trans. Commun. E83-B, 1983–1989 (2000).

K. Minoshima and H. Matsumoto, “High-accuracy measurement of 240 m distance in an optical tunnel by use of a compact femtosecond laser,” Appl. Opt. 39, 5512–5517 (2000).
[CrossRef]

1999

Y. Takagi and S. Adachi, “Subpicosecond optical sampling spectrometer using asynchronous tunable mode-locked lasers,” Rev. Sci. Instrum. 70, 2218–2224 (1999).
[CrossRef]

1998

I. Fujima, S. Iwasaki, and K. Seta, “High-resolution distance meter using optical intensity modulation at 28 GHz,” Meas. Sci. Technol. 9, 1049–1052 (1998).
[CrossRef]

1997

1995

R. A. Cheville and D. Grischkowsky, “Time domain THz impulse ranging studies,” Appl. Phys. Lett. 67, 1960–1962(1995).
[CrossRef]

1991

G. A. Ybarra, S. H. Ardalan, C. P. Hearn, R. E. Marshall, and R. T. Neece, “Detection of target distance in the presence of an interfering reflection using a frequency-stepped double side-band suppressed carrier microwave radar system,” IEEE Trans. Microwave Theory Tech. 39, 809–818 (1991).
[CrossRef]

1987

1985

K. Seta, T. Oh’ishi, and S. Seino, “Optical distance measurement using inter-mode beat of laser,” Jpn. J. Appl. Phys. 24, 1374–1375 (1985).
[CrossRef]

Abraham, E.

T. Yasuda, T. Yasui, T. Araki, and E. Abraham, “Real-time two-dimensional terahertz tomography of moving objects,” Opt. Commun. 267, 128–136 (2006).
[CrossRef]

Adachi, S.

Y. Takagi and S. Adachi, “Subpicosecond optical sampling spectrometer using asynchronous tunable mode-locked lasers,” Rev. Sci. Instrum. 70, 2218–2224 (1999).
[CrossRef]

Anastasi, R. F.

R. F. Anastasi and E. I. Madaras, “Terahertz NDE for metallic surface roughness evaluation,” in Proceedings of 4th International Workshop on Ultrasonic and Advanced Methods for Nondestructive Testing and Material Characterization, C.H.Chen, ed. (NDT.net, 2006), pp. 57–62.

Araki, T.

Ardalan, S. H.

G. A. Ybarra, S. H. Ardalan, C. P. Hearn, R. E. Marshall, and R. T. Neece, “Detection of target distance in the presence of an interfering reflection using a frequency-stepped double side-band suppressed carrier microwave radar system,” IEEE Trans. Microwave Theory Tech. 39, 809–818 (1991).
[CrossRef]

Bartels, A.

A. Bartels, R. Cerna, C. Kistner, A. Thoma, F. Hudert, C. Janke, and T. Dekorsy, “Ultrafast time-domain spectroscopy based on high-speed asynchronous optical sampling,” Rev. Sci. Instrum. 78, 035107 (2007).
[CrossRef] [PubMed]

A. Bartels, A. Thoma, C. Janke, T. Dekorsy, A. Dreyhaupt, S. Winnerl, and M. Helm, “High-resolution THz spectrometer with kHz scan rates,” Opt. Express 14, 430–437 (2006).
[CrossRef] [PubMed]

Boivin, L.

Böttcher, J.

Cerna, R.

A. Bartels, R. Cerna, C. Kistner, A. Thoma, F. Hudert, C. Janke, and T. Dekorsy, “Ultrafast time-domain spectroscopy based on high-speed asynchronous optical sampling,” Rev. Sci. Instrum. 78, 035107 (2007).
[CrossRef] [PubMed]

Cheville, R. A.

R. A. Cheville and D. Grischkowsky, “Time domain THz impulse ranging studies,” Appl. Phys. Lett. 67, 1960–1962(1995).
[CrossRef]

Coddington, I.

I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photon. 3, 351–356 (2009).
[CrossRef]

Dekorsy, T.

A. Bartels, R. Cerna, C. Kistner, A. Thoma, F. Hudert, C. Janke, and T. Dekorsy, “Ultrafast time-domain spectroscopy based on high-speed asynchronous optical sampling,” Rev. Sci. Instrum. 78, 035107 (2007).
[CrossRef] [PubMed]

A. Bartels, A. Thoma, C. Janke, T. Dekorsy, A. Dreyhaupt, S. Winnerl, and M. Helm, “High-resolution THz spectrometer with kHz scan rates,” Opt. Express 14, 430–437 (2006).
[CrossRef] [PubMed]

Dreyhaupt, A.

Dudley, R.

Elzinga, P. A.

Fujima, I.

I. Fujima, S. Iwasaki, and K. Seta, “High-resolution distance meter using optical intensity modulation at 28 GHz,” Meas. Sci. Technol. 9, 1049–1052 (1998).
[CrossRef]

Grischkowsky, D.

R. A. Cheville and D. Grischkowsky, “Time domain THz impulse ranging studies,” Appl. Phys. Lett. 67, 1960–1962(1995).
[CrossRef]

Hagihara, Y.

Hearn, C. P.

G. A. Ybarra, S. H. Ardalan, C. P. Hearn, R. E. Marshall, and R. T. Neece, “Detection of target distance in the presence of an interfering reflection using a frequency-stepped double side-band suppressed carrier microwave radar system,” IEEE Trans. Microwave Theory Tech. 39, 809–818 (1991).
[CrossRef]

Helm, M.

Hudert, F.

A. Bartels, R. Cerna, C. Kistner, A. Thoma, F. Hudert, C. Janke, and T. Dekorsy, “Ultrafast time-domain spectroscopy based on high-speed asynchronous optical sampling,” Rev. Sci. Instrum. 78, 035107 (2007).
[CrossRef] [PubMed]

Hunsche, S.

Ihara, A.

Inaba, H.

Inatsune, S.

M. Mitsumoto, N. Uehara, S. Inatsune, and T. Kirimoto, “Target distance and velocity measurement algorithm to reduce false target in FMCW automotive radar,” IEICE Trans. Commun. E83-B, 1983–1989 (2000).

Iwasaki, S.

I. Fujima, S. Iwasaki, and K. Seta, “High-resolution distance meter using optical intensity modulation at 28 GHz,” Meas. Sci. Technol. 9, 1049–1052 (1998).
[CrossRef]

Iwata, T.

Janke, C.

A. Bartels, R. Cerna, C. Kistner, A. Thoma, F. Hudert, C. Janke, and T. Dekorsy, “Ultrafast time-domain spectroscopy based on high-speed asynchronous optical sampling,” Rev. Sci. Instrum. 78, 035107 (2007).
[CrossRef] [PubMed]

A. Bartels, A. Thoma, C. Janke, T. Dekorsy, A. Dreyhaupt, S. Winnerl, and M. Helm, “High-resolution THz spectrometer with kHz scan rates,” Opt. Express 14, 430–437 (2006).
[CrossRef] [PubMed]

Jeon, S.-G.

J. Kim, S.-G. Jeon, J.-I. Kim, and Y.-S. Jin, “Terahertz pulse detection using rotary optical delay line,” Jpn. J. Appl. Phys. 46, 7332–7335 (2007).
[CrossRef]

Jian, Y.

Jin, Y.-S.

J. Kim, S.-G. Jeon, J.-I. Kim, and Y.-S. Jin, “Terahertz pulse detection using rotary optical delay line,” Jpn. J. Appl. Phys. 46, 7332–7335 (2007).
[CrossRef]

Kawamoto, K.

Kim, J.

J. Kim, S.-G. Jeon, J.-I. Kim, and Y.-S. Jin, “Terahertz pulse detection using rotary optical delay line,” Jpn. J. Appl. Phys. 46, 7332–7335 (2007).
[CrossRef]

Kim, J.-I.

J. Kim, S.-G. Jeon, J.-I. Kim, and Y.-S. Jin, “Terahertz pulse detection using rotary optical delay line,” Jpn. J. Appl. Phys. 46, 7332–7335 (2007).
[CrossRef]

King, G. B.

Kirimoto, T.

M. Mitsumoto, N. Uehara, S. Inatsune, and T. Kirimoto, “Target distance and velocity measurement algorithm to reduce false target in FMCW automotive radar,” IEICE Trans. Commun. E83-B, 1983–1989 (2000).

Kistner, C.

A. Bartels, R. Cerna, C. Kistner, A. Thoma, F. Hudert, C. Janke, and T. Dekorsy, “Ultrafast time-domain spectroscopy based on high-speed asynchronous optical sampling,” Rev. Sci. Instrum. 78, 035107 (2007).
[CrossRef] [PubMed]

Kneisler, R. J.

Künzel, H.

Laurendeau, N. M.

Liebe, H. J.

H. J. Liebe, “Atmospheric water vapor: a nemesis for millimeter wave propagation,” in Atmospheric Water Vapor, A.Deepak, Th.D.Wilkerson, and L.H.Ruhnke, eds. (Academic, 1980), pp. 143–201.

Lytle, F. E.

Madaras, E. I.

R. F. Anastasi and E. I. Madaras, “Terahertz NDE for metallic surface roughness evaluation,” in Proceedings of 4th International Workshop on Ultrasonic and Advanced Methods for Nondestructive Testing and Material Characterization, C.H.Chen, ed. (NDT.net, 2006), pp. 57–62.

Marshall, R. E.

G. A. Ybarra, S. H. Ardalan, C. P. Hearn, R. E. Marshall, and R. T. Neece, “Detection of target distance in the presence of an interfering reflection using a frequency-stepped double side-band suppressed carrier microwave radar system,” IEEE Trans. Microwave Theory Tech. 39, 809–818 (1991).
[CrossRef]

Maskell, D. L.

D. L. Maskell and G. S. Woods, “A frequency modulated envelope delay FSCW radar for multiple-target applications,” IEEE Trans. Instrum. Meas. 49, 710–715 (2000).
[CrossRef]

Matsumoto, H.

Minoshima, K.

Mitsumoto, M.

M. Mitsumoto, N. Uehara, S. Inatsune, and T. Kirimoto, “Target distance and velocity measurement algorithm to reduce false target in FMCW automotive radar,” IEICE Trans. Commun. E83-B, 1983–1989 (2000).

Mittleman, D. M.

Naftaly, M.

Neece, R. T.

G. A. Ybarra, S. H. Ardalan, C. P. Hearn, R. E. Marshall, and R. T. Neece, “Detection of target distance in the presence of an interfering reflection using a frequency-stepped double side-band suppressed carrier microwave radar system,” IEEE Trans. Microwave Theory Tech. 39, 809–818 (1991).
[CrossRef]

Nenadovic, L.

I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photon. 3, 351–356 (2009).
[CrossRef]

Newbury, N. R.

I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photon. 3, 351–356 (2009).
[CrossRef]

Nose, M.

Nuss, M. C.

Oh’ishi, T.

K. Seta, T. Oh’ishi, and S. Seino, “Optical distance measurement using inter-mode beat of laser,” Jpn. J. Appl. Phys. 24, 1374–1375 (1985).
[CrossRef]

Roehle, H.

Saneyoshi, E.

T. Yasui, E. Saneyoshi, and T. Araki, “Asynchronous optical sampling terahertz time-domain spectroscopy for ultrahigh spectral resolution and rapid data acquisition,” Appl. Phys. Lett. 87, 061101 (2005).
[CrossRef]

Sartorius, B.

Sawanaka, K.

Schell, M.

Schlak, M.

Seino, S.

K. Seta, T. Oh’ishi, and S. Seino, “Optical distance measurement using inter-mode beat of laser,” Jpn. J. Appl. Phys. 24, 1374–1375 (1985).
[CrossRef]

Seta, K.

I. Fujima, S. Iwasaki, and K. Seta, “High-resolution distance meter using optical intensity modulation at 28 GHz,” Meas. Sci. Technol. 9, 1049–1052 (1998).
[CrossRef]

K. Seta, T. Oh’ishi, and S. Seino, “Optical distance measurement using inter-mode beat of laser,” Jpn. J. Appl. Phys. 24, 1374–1375 (1985).
[CrossRef]

Stanze, D.

Swann, W. C.

I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photon. 3, 351–356 (2009).
[CrossRef]

Takagi, Y.

Y. Takagi and S. Adachi, “Subpicosecond optical sampling spectrometer using asynchronous tunable mode-locked lasers,” Rev. Sci. Instrum. 70, 2218–2224 (1999).
[CrossRef]

Thoma, A.

A. Bartels, R. Cerna, C. Kistner, A. Thoma, F. Hudert, C. Janke, and T. Dekorsy, “Ultrafast time-domain spectroscopy based on high-speed asynchronous optical sampling,” Rev. Sci. Instrum. 78, 035107 (2007).
[CrossRef] [PubMed]

A. Bartels, A. Thoma, C. Janke, T. Dekorsy, A. Dreyhaupt, S. Winnerl, and M. Helm, “High-resolution THz spectrometer with kHz scan rates,” Opt. Express 14, 430–437 (2006).
[CrossRef] [PubMed]

Tonouchi, M.

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photon. 1, 97–105 (2007).
[CrossRef]

Uehara, N.

M. Mitsumoto, N. Uehara, S. Inatsune, and T. Kirimoto, “Target distance and velocity measurement algorithm to reduce false target in FMCW automotive radar,” IEICE Trans. Commun. E83-B, 1983–1989 (2000).

Venghaus, H.

Winnerl, S.

Woods, G. S.

D. L. Maskell and G. S. Woods, “A frequency modulated envelope delay FSCW radar for multiple-target applications,” IEEE Trans. Instrum. Meas. 49, 710–715 (2000).
[CrossRef]

Xu, J.

Yasuda, T.

Yasui, T.

Ybarra, G. A.

G. A. Ybarra, S. H. Ardalan, C. P. Hearn, R. E. Marshall, and R. T. Neece, “Detection of target distance in the presence of an interfering reflection using a frequency-stepped double side-band suppressed carrier microwave radar system,” IEEE Trans. Microwave Theory Tech. 39, 809–818 (1991).
[CrossRef]

Ye, J.

Yokoyama, S.

Yokoyama, T.

Zhang, X.-C.

Appl. Opt.

Appl. Phys. Lett.

T. Yasui, E. Saneyoshi, and T. Araki, “Asynchronous optical sampling terahertz time-domain spectroscopy for ultrahigh spectral resolution and rapid data acquisition,” Appl. Phys. Lett. 87, 061101 (2005).
[CrossRef]

R. A. Cheville and D. Grischkowsky, “Time domain THz impulse ranging studies,” Appl. Phys. Lett. 67, 1960–1962(1995).
[CrossRef]

IEEE Trans. Instrum. Meas.

D. L. Maskell and G. S. Woods, “A frequency modulated envelope delay FSCW radar for multiple-target applications,” IEEE Trans. Instrum. Meas. 49, 710–715 (2000).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

G. A. Ybarra, S. H. Ardalan, C. P. Hearn, R. E. Marshall, and R. T. Neece, “Detection of target distance in the presence of an interfering reflection using a frequency-stepped double side-band suppressed carrier microwave radar system,” IEEE Trans. Microwave Theory Tech. 39, 809–818 (1991).
[CrossRef]

IEICE Trans. Commun.

M. Mitsumoto, N. Uehara, S. Inatsune, and T. Kirimoto, “Target distance and velocity measurement algorithm to reduce false target in FMCW automotive radar,” IEICE Trans. Commun. E83-B, 1983–1989 (2000).

Jpn. J. Appl. Phys.

K. Seta, T. Oh’ishi, and S. Seino, “Optical distance measurement using inter-mode beat of laser,” Jpn. J. Appl. Phys. 24, 1374–1375 (1985).
[CrossRef]

J. Kim, S.-G. Jeon, J.-I. Kim, and Y.-S. Jin, “Terahertz pulse detection using rotary optical delay line,” Jpn. J. Appl. Phys. 46, 7332–7335 (2007).
[CrossRef]

Meas. Sci. Technol.

I. Fujima, S. Iwasaki, and K. Seta, “High-resolution distance meter using optical intensity modulation at 28 GHz,” Meas. Sci. Technol. 9, 1049–1052 (1998).
[CrossRef]

Nat. Photon.

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photon. 1, 97–105 (2007).
[CrossRef]

I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photon. 3, 351–356 (2009).
[CrossRef]

Opt. Commun.

T. Yasuda, T. Yasui, T. Araki, and E. Abraham, “Real-time two-dimensional terahertz tomography of moving objects,” Opt. Commun. 267, 128–136 (2006).
[CrossRef]

Opt. Express

Opt. Lett.

Rev. Sci. Instrum.

A. Bartels, R. Cerna, C. Kistner, A. Thoma, F. Hudert, C. Janke, and T. Dekorsy, “Ultrafast time-domain spectroscopy based on high-speed asynchronous optical sampling,” Rev. Sci. Instrum. 78, 035107 (2007).
[CrossRef] [PubMed]

Y. Takagi and S. Adachi, “Subpicosecond optical sampling spectrometer using asynchronous tunable mode-locked lasers,” Rev. Sci. Instrum. 70, 2218–2224 (1999).
[CrossRef]

Other

R. F. Anastasi and E. I. Madaras, “Terahertz NDE for metallic surface roughness evaluation,” in Proceedings of 4th International Workshop on Ultrasonic and Advanced Methods for Nondestructive Testing and Material Characterization, C.H.Chen, ed. (NDT.net, 2006), pp. 57–62.

H. J. Liebe, “Atmospheric water vapor: a nemesis for millimeter wave propagation,” in Atmospheric Water Vapor, A.Deepak, Th.D.Wilkerson, and L.H.Ruhnke, eds. (Academic, 1980), pp. 143–201.

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Figures (10)

Fig. 1
Fig. 1

Principle of distance measurement. (a) Timing chart for SFG signal and THz echo signal when target distance d is shorter and longer than half of the spatial period L hsp of a THz pulse train. (b) Timing chart for SFG signal and THz echo signal when the pulse period is set to T and T + Δ T .

Fig. 2
Fig. 2

Experimental setup: pump and probe lasers, mode-locked Ti:sapphire lasers; PD, photodiodes; PLL1 and PLL2, phase-locked loop control systems; Rb FS, rubidium frequency standard; BS, beam splitter; THz PCA emitter, planar, large-area GaAs photoconductive antenna with an interdigitated electrode structure for THz generation; THz PCA detector, bowtie-shaped, low-temperature-grown GaAs photoconductive antenna for THz detection; OAPM-1 and OAPM-2, off-axis parabolic mirrors; M, plane mirror.

Fig. 3
Fig. 3

Temporal waveforms of the THz echo signal returned from the machined surface of a metal plate. The upper and lower horizontal coordinates indicate the actual time scale measured by the digitizer and the real time scale calibrated using a temporal magnification factor of f 1 / Δ f , respectively.

Fig. 4
Fig. 4

Relationship between stage displacement and measured displacement (black circle) and discrepancy between them (red triangle).

Fig. 5
Fig. 5

Relationship between time delay ϕ and timing jitter. Distance resolution calculated by the timing jitter is given at the right vertical coordinate.

Fig. 6
Fig. 6

Absolute distance measurement of the target located at a distance greater than L hsp . The temporal waveform after shift of T (lower green curve) is offset for clarity.

Fig. 7
Fig. 7

Six consecutive measurements of the THz echo signal when a target was continuously moved by 200 mm at a speed of 25 mm / s using a translation stage (Media 1). The lower horizontal coordinate indicates the time delay ϕ between the THz echo signal and the SFG signal. The target distance d determined from ϕ is given at the upper horizontal scale.

Fig. 8
Fig. 8

Relationship between the sample speed and the distance resolution with respect to three different scan rates of 10 Hz (red solid line), 100 Hz (blue dotted line), and 1000 Hz (green broken line).

Fig. 9
Fig. 9

Shape measurement of a stepped metal object: (a) schematic drawing of the object and scanned THz beam and (b) temporal waveform of the THz echo signal measured at five different steps on the object (Media 2).

Fig. 10
Fig. 10

(a) Original signal and (b) impulse response signal of THz echo pulse returned from a single-layer paint film on an Al plate.

Equations (6)

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L hsp = c T 2 n g ,
d = c ϕ 2 n g .
d = c ( m T + ϕ ) 2 n g ,
d = c ( m T + ϕ ) 2 n g = c [ m ( T + Δ T ) + ϕ + Δ ϕ ] 2 n g .
Δ ϕ = m Δ T .
Δ t = 2 n g D c .

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