Abstract

The ability to retrieve information from different layers within a stratified sample using terahertz pulsed reflection imaging and spectroscopy has traditionally been resolution limited by the pulse width available. In this paper, a deconvolution algorithm is presented which circumvents this resolution limit, enabling deep sub-wavelength and sub-pulse width depth resolution. The algorithm is explained through theoretical investigation, and demonstrated by reconstructing signals reflected from boundaries in stratified materials that cannot be resolved directly from the unprocessed time-domain reflection signal. Furthermore, the deconvolution technique has been used to recreate sub-surface images from a stratified sample: imaging the reverse side of a piece of paper.

© 2012 OSA

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References

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    [CrossRef]

2010

2009

2007

1996

J. T. Kindt and C. A. Schmuttenmaer, “Far-infrared dielectric properties of polar liquids probed by femtosecond pulsed terahertz spectroscopy,” J. Phys. Chem.100(24), 10373–10379 (1996).
[CrossRef]

Bowen, J. W.

Chen, Y.

Dudley, R.

Galvão, R. K.

Hadjiloucas, S.

Huang, S.

Ichino, S.

Jinno, H.

Kasai, S.

Kawase, K.

Kindt, J. T.

J. T. Kindt and C. A. Schmuttenmaer, “Far-infrared dielectric properties of polar liquids probed by femtosecond pulsed terahertz spectroscopy,” J. Phys. Chem.100(24), 10373–10379 (1996).
[CrossRef]

Nishizawa, N.

Ohtake, H.

Ouchi, T.

Pickwell-MacPherson, E.

Schmuttenmaer, C. A.

J. T. Kindt and C. A. Schmuttenmaer, “Far-infrared dielectric properties of polar liquids probed by femtosecond pulsed terahertz spectroscopy,” J. Phys. Chem.100(24), 10373–10379 (1996).
[CrossRef]

Suizu, K.

Takayanagi, J.

Uchida, H.

Walker, G. C.

Yamashita, M.

Zafiropoulos, A.

J. Phys. Chem.

J. T. Kindt and C. A. Schmuttenmaer, “Far-infrared dielectric properties of polar liquids probed by femtosecond pulsed terahertz spectroscopy,” J. Phys. Chem.100(24), 10373–10379 (1996).
[CrossRef]

Opt. Express

Opt. Lett.

Other

P. R. Griffiths and J. A. de Haseth, Fourier Transform Infrared Spectrometry (New York, Wiley 1986), Chap. 3.

R. N. Bracewell, The Fourier Transform and its Applications (New York: London: McGraw-Hill 1978) Chap. 18.

G. C. Walker, J. B. Jackson, W. Matthews, J. W. Bowen, J. Labaune, G. A. Mourou, J. F. Whitaker, M. Menu, and I. Hodder, “Seeing Through Walls: Sub-surface imaging at Çatalhöyük”, Presented at the Raman and Infrared User Group Meeting, Barcelona, March 2012.

E. Berry, R. D. Boyle, A. J. Fitzgerald, and J. W. Handley, Computer Vision Beyond the Visible Spectrum, (Springer 2004), Chap. 9.

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Figures (8)

Fig. 1
Fig. 1

Illustration of the Nyquist sampling theorem in the recovery of a two peak feature in the impulse response function following deconvolution.

Fig. 2
Fig. 2

Illustration of the effect of padding on the signal to noise ratio of the recovered impulse response function following deconvolution.

Fig. 3
Fig. 3

Schematic diagram illustrating the deconvolution process.

Fig. 4
Fig. 4

(a) shows a reflection signal from two sheets of modern papyrus, each 150 µm thick, separated by 2 mm. Figure 4(b) shows the resulting impulse response function calculated using the deconvolution routine.

Fig. 5
Fig. 5

shows reconvolved signals representing reflections from the front and back surfaces of two sheets of papyrus separated by 2 mm. These add to match the measured signal reflected from the two sheets.

Fig. 6
Fig. 6

shows the sum of the reconvolved signals in Fig. 5 compared to the measured signal reflected from two sheets of papyrus.

Fig. 7
Fig. 7

(a) Time domain pulse measured following reflection from a 57 µm plastic sheet. Figure 7 (b) Impulse response function for a 57 µm plastic sheet.

Fig. 8
Fig. 8

shows a typical data series from the reflection image from a stack of three sheets of paper, each 100 µm thick.

Equations (12)

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P o ( t )= P i ( t )IRF( t )
S o ( υ )= S i ( υ )×T( υ )
IRF( t )=iFT( S o ( υ ) S i ( υ ) )
X k = 1 N n=0 N1 x n e i2π k N n
x n = 1 N k=0 N1 X k e i2π n N k
X k = S k ± E k
x n = s n ± e n = 1 pN ( s n ± e n )
s n pN
e n ( E 0 2 + E 1 2 + E 2 2 + E pN1 2 ) 1/2
e n pN E k
s n 1 pN s n pN
e n 1 pN e n E k

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