Abstract

We improve the existing data extraction algorithms for THz time-domain spectroscopy (THz TDS) in two aspects. On the one hand, we merge the up-to-date knowledge of THz TDS signal processing into a single powerful optical material parameter extraction algorithm. On the other hand, we introduce a novel iterative algorithm that further enhances the accuracy of the parameter extraction. In contrast to most of the published experiments, we are able to reliably investigate samples with thicknesses as small as 100μm, samples with low indexes of refraction, i.e. close to 1, as well as samples with sharp peaks in the material parameter curves.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L. Duvillaret, F. Garet, and J.-L. Coutaz, "A reliable method for extraction of material parameters in Terahertz Time-Domain Spectroscopy," IEEE J. Sel. Top. Quantum Electron. 2, 739 - 746 (1996).
    [CrossRef]
  2. L. Duvillaret, F. Garet, and J.-L. Coutaz, "Highly precise determination of Optical Constants and sample thickness in Terahertz Time-Domain Spectroscopy," Appl. Opt. 38, 409 - 415 (1999).
    [CrossRef]
  3. T. Dorney, R. Baraniuk, and D. Mittleman, "Material parameter estimation with Terahertz Time-Domain Spectroscopy," J. Opt. Soc. Am. A 18, 1562 - 1571 (2001).
    [CrossRef]
  4. B. Ferguson and D. Abbott, "Signal processing for T-Ray Biosensor Systems," Smart Electronics and MEMS II 4236, 157 - 169 (2001).
  5. P. U. Jepsen and B. M. Fischer, "Dynamic range in Terahertz Time-Domain Transmission and Reflection Spectroscopy," Opt. Lett. 30, 29 - 31 (2005).
    [CrossRef] [PubMed]
  6. D. Grischkowsky, S. Keiding, M. van Exter, and C. Fattinger, "Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors," J. Opt. Soc. Am. B 7, 2006 - 2015 (1990).
    [CrossRef]
  7. B. Ferguson and D. Abbott, "Wavelet de-noising of optical terahertz pulse imaging data," Fluct. Noise Lett. 1, L65 - L69 (2001).
    [CrossRef]
  8. B. Ferguson and D. Abbott, "De-noising techniques for terahertz responses of biological samples," Microelectron. J. (Elsevier) 32, 943 - 953 (2001).
  9. D. L. Donoho, "De-noising by Soft-Thresholding," IEEE Trans. Inf. Theory 41, 613 - 627 (1995).
    [CrossRef]
  10. J. C. Lagarias, J. A. Reeds,M. H. Wright and P. E. Wright, "Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions," SIAM J. Optim. 9, 112 - 147 (1998).
    [CrossRef]
  11. S. Mickan, K.-S. Lee, T.-M. Lu, J. Munch, X.-C. Zhang and D. Abbott, "Thin Film Characterization using Terahertz Differential Time-Domain Spectroscopy and Double Modulation," Electronics and Structures for MEMS II Proc.SPIE 4591, 197 - 209 (2001).
  12. DIN Deutsches Institut f¨ur Normung, "DIN 1319 Fundamentals of metrology - Part 4: Evaluation of measurements; uncertainty of measurement," (Beuth Verlag GmbH, 1999).
  13. M. N. Afsar, "Dielectric Measurements of Millimeter-Wave Materials," IEEE Trans. Microwave Theory Tech. 12, 1598 - 1609 (1984).
    [CrossRef]
  14. B. M. Fischer, M. Hoffmann, R. Wilk, F. Rutz, T. Kleine-Ostmann, M. Koch, and P. Uhd Jepsen, "Terahertz time-domain spectroscopy and imaging of artificial RNA," Opt. Express 13, 5205 - 5215 (2005).
    [CrossRef] [PubMed]

2005

2001

T. Dorney, R. Baraniuk, and D. Mittleman, "Material parameter estimation with Terahertz Time-Domain Spectroscopy," J. Opt. Soc. Am. A 18, 1562 - 1571 (2001).
[CrossRef]

B. Ferguson and D. Abbott, "Signal processing for T-Ray Biosensor Systems," Smart Electronics and MEMS II 4236, 157 - 169 (2001).

B. Ferguson and D. Abbott, "Wavelet de-noising of optical terahertz pulse imaging data," Fluct. Noise Lett. 1, L65 - L69 (2001).
[CrossRef]

B. Ferguson and D. Abbott, "De-noising techniques for terahertz responses of biological samples," Microelectron. J. (Elsevier) 32, 943 - 953 (2001).

S. Mickan, K.-S. Lee, T.-M. Lu, J. Munch, X.-C. Zhang and D. Abbott, "Thin Film Characterization using Terahertz Differential Time-Domain Spectroscopy and Double Modulation," Electronics and Structures for MEMS II Proc.SPIE 4591, 197 - 209 (2001).

1999

1998

J. C. Lagarias, J. A. Reeds,M. H. Wright and P. E. Wright, "Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions," SIAM J. Optim. 9, 112 - 147 (1998).
[CrossRef]

1996

L. Duvillaret, F. Garet, and J.-L. Coutaz, "A reliable method for extraction of material parameters in Terahertz Time-Domain Spectroscopy," IEEE J. Sel. Top. Quantum Electron. 2, 739 - 746 (1996).
[CrossRef]

1995

D. L. Donoho, "De-noising by Soft-Thresholding," IEEE Trans. Inf. Theory 41, 613 - 627 (1995).
[CrossRef]

1990

1984

M. N. Afsar, "Dielectric Measurements of Millimeter-Wave Materials," IEEE Trans. Microwave Theory Tech. 12, 1598 - 1609 (1984).
[CrossRef]

Abbott, D.

B. Ferguson and D. Abbott, "De-noising techniques for terahertz responses of biological samples," Microelectron. J. (Elsevier) 32, 943 - 953 (2001).

B. Ferguson and D. Abbott, "Signal processing for T-Ray Biosensor Systems," Smart Electronics and MEMS II 4236, 157 - 169 (2001).

S. Mickan, K.-S. Lee, T.-M. Lu, J. Munch, X.-C. Zhang and D. Abbott, "Thin Film Characterization using Terahertz Differential Time-Domain Spectroscopy and Double Modulation," Electronics and Structures for MEMS II Proc.SPIE 4591, 197 - 209 (2001).

B. Ferguson and D. Abbott, "Wavelet de-noising of optical terahertz pulse imaging data," Fluct. Noise Lett. 1, L65 - L69 (2001).
[CrossRef]

Afsar, M. N.

M. N. Afsar, "Dielectric Measurements of Millimeter-Wave Materials," IEEE Trans. Microwave Theory Tech. 12, 1598 - 1609 (1984).
[CrossRef]

Baraniuk, R.

Coutaz, J.-L.

L. Duvillaret, F. Garet, and J.-L. Coutaz, "Highly precise determination of Optical Constants and sample thickness in Terahertz Time-Domain Spectroscopy," Appl. Opt. 38, 409 - 415 (1999).
[CrossRef]

L. Duvillaret, F. Garet, and J.-L. Coutaz, "A reliable method for extraction of material parameters in Terahertz Time-Domain Spectroscopy," IEEE J. Sel. Top. Quantum Electron. 2, 739 - 746 (1996).
[CrossRef]

Donoho, D. L.

D. L. Donoho, "De-noising by Soft-Thresholding," IEEE Trans. Inf. Theory 41, 613 - 627 (1995).
[CrossRef]

Dorney, T.

Duvillaret, L.

L. Duvillaret, F. Garet, and J.-L. Coutaz, "Highly precise determination of Optical Constants and sample thickness in Terahertz Time-Domain Spectroscopy," Appl. Opt. 38, 409 - 415 (1999).
[CrossRef]

L. Duvillaret, F. Garet, and J.-L. Coutaz, "A reliable method for extraction of material parameters in Terahertz Time-Domain Spectroscopy," IEEE J. Sel. Top. Quantum Electron. 2, 739 - 746 (1996).
[CrossRef]

Fattinger, C.

Ferguson, B.

B. Ferguson and D. Abbott, "Signal processing for T-Ray Biosensor Systems," Smart Electronics and MEMS II 4236, 157 - 169 (2001).

B. Ferguson and D. Abbott, "De-noising techniques for terahertz responses of biological samples," Microelectron. J. (Elsevier) 32, 943 - 953 (2001).

B. Ferguson and D. Abbott, "Wavelet de-noising of optical terahertz pulse imaging data," Fluct. Noise Lett. 1, L65 - L69 (2001).
[CrossRef]

Fischer, B. M.

Garet, F.

L. Duvillaret, F. Garet, and J.-L. Coutaz, "Highly precise determination of Optical Constants and sample thickness in Terahertz Time-Domain Spectroscopy," Appl. Opt. 38, 409 - 415 (1999).
[CrossRef]

L. Duvillaret, F. Garet, and J.-L. Coutaz, "A reliable method for extraction of material parameters in Terahertz Time-Domain Spectroscopy," IEEE J. Sel. Top. Quantum Electron. 2, 739 - 746 (1996).
[CrossRef]

Grischkowsky, D.

Hoffmann, M.

Jepsen, P. U.

Keiding, S.

Kleine-Ostmann, T.

Koch, M.

Lagarias, J. C.

J. C. Lagarias, J. A. Reeds,M. H. Wright and P. E. Wright, "Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions," SIAM J. Optim. 9, 112 - 147 (1998).
[CrossRef]

Lee, K.-S.

S. Mickan, K.-S. Lee, T.-M. Lu, J. Munch, X.-C. Zhang and D. Abbott, "Thin Film Characterization using Terahertz Differential Time-Domain Spectroscopy and Double Modulation," Electronics and Structures for MEMS II Proc.SPIE 4591, 197 - 209 (2001).

Lu, T.-M.

S. Mickan, K.-S. Lee, T.-M. Lu, J. Munch, X.-C. Zhang and D. Abbott, "Thin Film Characterization using Terahertz Differential Time-Domain Spectroscopy and Double Modulation," Electronics and Structures for MEMS II Proc.SPIE 4591, 197 - 209 (2001).

Mickan, S.

S. Mickan, K.-S. Lee, T.-M. Lu, J. Munch, X.-C. Zhang and D. Abbott, "Thin Film Characterization using Terahertz Differential Time-Domain Spectroscopy and Double Modulation," Electronics and Structures for MEMS II Proc.SPIE 4591, 197 - 209 (2001).

Mittleman, D.

Munch, J.

S. Mickan, K.-S. Lee, T.-M. Lu, J. Munch, X.-C. Zhang and D. Abbott, "Thin Film Characterization using Terahertz Differential Time-Domain Spectroscopy and Double Modulation," Electronics and Structures for MEMS II Proc.SPIE 4591, 197 - 209 (2001).

Reeds, J. A.

J. C. Lagarias, J. A. Reeds,M. H. Wright and P. E. Wright, "Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions," SIAM J. Optim. 9, 112 - 147 (1998).
[CrossRef]

Rutz, F.

Uhd Jepsen, P.

van Exter, M.

Wilk, R.

Wright, M. H.

J. C. Lagarias, J. A. Reeds,M. H. Wright and P. E. Wright, "Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions," SIAM J. Optim. 9, 112 - 147 (1998).
[CrossRef]

Wright, P. E.

J. C. Lagarias, J. A. Reeds,M. H. Wright and P. E. Wright, "Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions," SIAM J. Optim. 9, 112 - 147 (1998).
[CrossRef]

Zhang, X.-C.

S. Mickan, K.-S. Lee, T.-M. Lu, J. Munch, X.-C. Zhang and D. Abbott, "Thin Film Characterization using Terahertz Differential Time-Domain Spectroscopy and Double Modulation," Electronics and Structures for MEMS II Proc.SPIE 4591, 197 - 209 (2001).

Appl. Opt.

Fluct. Noise Lett.

B. Ferguson and D. Abbott, "Wavelet de-noising of optical terahertz pulse imaging data," Fluct. Noise Lett. 1, L65 - L69 (2001).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

L. Duvillaret, F. Garet, and J.-L. Coutaz, "A reliable method for extraction of material parameters in Terahertz Time-Domain Spectroscopy," IEEE J. Sel. Top. Quantum Electron. 2, 739 - 746 (1996).
[CrossRef]

IEEE Trans. Inf. Theory

D. L. Donoho, "De-noising by Soft-Thresholding," IEEE Trans. Inf. Theory 41, 613 - 627 (1995).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

M. N. Afsar, "Dielectric Measurements of Millimeter-Wave Materials," IEEE Trans. Microwave Theory Tech. 12, 1598 - 1609 (1984).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Microelectron. J. (Elsevier)

B. Ferguson and D. Abbott, "De-noising techniques for terahertz responses of biological samples," Microelectron. J. (Elsevier) 32, 943 - 953 (2001).

Opt. Express

Opt. Lett.

SIAM J. Optim.

J. C. Lagarias, J. A. Reeds,M. H. Wright and P. E. Wright, "Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions," SIAM J. Optim. 9, 112 - 147 (1998).
[CrossRef]

Smart Electronics and MEMS II

B. Ferguson and D. Abbott, "Signal processing for T-Ray Biosensor Systems," Smart Electronics and MEMS II 4236, 157 - 169 (2001).

SPIE

S. Mickan, K.-S. Lee, T.-M. Lu, J. Munch, X.-C. Zhang and D. Abbott, "Thin Film Characterization using Terahertz Differential Time-Domain Spectroscopy and Double Modulation," Electronics and Structures for MEMS II Proc.SPIE 4591, 197 - 209 (2001).

Other

DIN Deutsches Institut f¨ur Normung, "DIN 1319 Fundamentals of metrology - Part 4: Evaluation of measurements; uncertainty of measurement," (Beuth Verlag GmbH, 1999).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1.

Ray propagation through a planar, homogenous sample.

Fig. 2.
Fig. 2.

Illustration of the mode of operation of the SVMAF

Fig. 3.
Fig. 3.

Material parameter extraction of a 543μm Si wafer

Fig. 4.
Fig. 4.

Material parameter extraction of a 1252μm leu-gly-gly pellet

Fig. 5.
Fig. 5.

Material parameter extraction of a 145μm artificial RNA pressing

Equations (39)

Equations on this page are rendered with MathJax. Learn more.

H experiment ( ω ) = E samp ex ( ω ) E ref ex ( ω ) .
M ( ω ) = H theory ( ω ) H expriment ( ω ) ,
A ( ω ) = H theory ( ω ) H expriment ( ω ) ,
Err = Σ ω ( M ( ω ) + A ( ω ) )
R 12 = n 2 ˜ n 1 ˜ n 1 ˜ + n 2 ˜ ,
T 12 = 2 n ˜ 1 n ˜ 1 + n ˜ 2 .
E ( z ) = E init P 1 ( z ) ,
P 1 ( z ) = exp ( n ˜ 1 z c 0 ) ,
E samp = E inint P 0 T 01 P 1 T 10 [ 1 + Σ i = 1 δ ( R 10 2 P 1 2 ) i ]
E ref = E init P 0 ( x )
H theory = E samp E ref = P 0 ( ) T 01 P 1 T 10 [ 1 + Σ i = 1 δ ( R 10 2 P 1 2 ) i ]
E s , max = E r , max exp ( ω c 0 κ 1 ) ,
κ 1 = 1 c 0 ω log E s , max E r , max .
Δ t = Δ n c 0 .
n 1 = c 0 Δ t + n 0 .
t max n 1 c 0 ( 1 + 2 δ ) .
D ( m ) = n 1 ( m 1 ) n 1 ( m ) + κ 1 ( m 1 ) κ 1 ( m ) ,
TV ( ) = m S D ( m ) .
H = E samp ex ¯ ( ω ) E ref ex ¯ ( ω ) .
E samp ex ¯ ( ω ) = a + jb
E ref ex ¯ ( ω ) = c + jd .
H = a + jb c + jd = ac + bd + j ( bc ad ) c 2 + d 2 .
m x = 1 k Σ i = 1 k N i .
Δ N x = 1 k 1 Σ i = 1 k ( N i m x ) 2 .
x ( mean ) = 1 u Σ i = 1 u x ( i ) .
Δ S x = 1 u 1 Σ i = 1 u ( x ( i ) x ( mean ) ) 2 .
Δ x = ( Δ N x ) 2 + ( Δ S x ) 2 .
{ H } = ac + bd c 2 + d 2 f ( a , b , c , d ) ,
{ H } = bc ad c 2 + d 2 g ( a , b , c , d ) ,
Δℜ { H } = ( Δ a f a ) 2 + ( Δ b f b ) 2 + ( Δ c f c ) 2 + ( Δ d f d ) 2 ,
Δℑ { H } = ( Δ a g a ) 2 + ( Δ b g b ) 2 + ( Δ c g c ) 2 + ( Δ d g d ) 2 ,
f a = c c 2 + d 2 ,
f b = c c 2 + d 2 ,
f c = ad 2 ac 2 2 bcd ( c 2 + d 2 ) 2 ,
f d = bc 2 bd 2 2a cd ( c 2 + d 2 ) 2 ,
g a = d c 2 + d 2 ,
g b = c c 2 + d 2 ,
g c = bc 2 bd 2 2a cd ( c 2 + d 2 ) 2 ,
g d = ad 2 ac 2 2 bcd ( c 2 + d 2 ) 2 .

Metrics