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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 17 — Aug. 26, 2013
  • pp: 19943–19950
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Pre- and post-processing for tomographic reconstruction of terahertz time-domain spectroscopy

Hye-Jin Hong, Jinho Park, Hochong Park, Joo-Hiuk Son, and Chang-Beom Ahn  »View Author Affiliations


Optics Express, Vol. 21, Issue 17, pp. 19943-19950 (2013)
http://dx.doi.org/10.1364/OE.21.019943


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Abstract

Reflection-type terahertz tomography is obtained using time-domain spectroscopy. Due to different velocities of the terahertz ray in free space and inside a sample, the tomographic transverse plane is not obtained by a simple reconstruction using time index. A pre-processing method is proposed to compensate for the different velocities of the terahertz ray for tomographic reconstruction. Maximum intensity projection, averaging, and short-time Fourier transform are proposed as post-processing methods along the depth direction for the terahertz tomography. Log-scale display is also suggested for a better visualization. Some experimental results with the pre- and post-processing are demonstrated.

© 2013 OSA

1. Introduction

Terahertz ray (T-ray) is an electromagnetic wave between infra-red and micro waves. It has applications in many areas such as security, nondestructive test, and biomedical imaging [1

1. B. B. Hu and M. C. Nuss, “Imaging with terahertz waves,” Opt. Lett. 20(16), 1716–1718 (1995). [CrossRef] [PubMed]

4

4. S. J. Oh, J. Choi, I. Maeng, J. Y. Park, K. Lee, Y.-M. Huh, J.-S. Suh, S. Haam, and J.-H. Son, “Molecular imaging with terahertz waves,” Opt. Express 19(5), 4009–4016 (2011). [CrossRef] [PubMed]

]. T-ray tomographic imaging using the delay time of the time-domain spectroscopy has emerged as a new imaging method because it can be a non-invasive technique to probe bio-terahertz interaction [5

5. D. M. Mittleman, S. Hunsche, L. Boivin, and M. C. Nuss, “T-ray tomography,” Opt. Lett. 22(12), 904–906 (1997). [CrossRef] [PubMed]

8

8. K. W. Kim, K.-S. Kim, H. Kim, S. H. Lee, J.-H. Park, J.-H. Han, S.-H. Seok, J. Park, Y. Choi, Y. I. Kim, J. K. Han, and J.-H. Son, “Terahertz dynamic imaging of skin drug absorption,” Opt. Express 20(9), 9476–9484 (2012). [CrossRef] [PubMed]

].

The delay time of the time-domain spectroscopy provides depth information in the reflection-type T-ray tomography. The refractive index is a ratio of the velocity of the T-ray in free space divided by that inside a sample. If the refractive index is greater than 1, velocity inside the sample is less than that in free space.

There have been several terahertz tomography approaches. Among them are: time-of-flight tomography using the delay time of pulsed T-ray [5

5. D. M. Mittleman, S. Hunsche, L. Boivin, and M. C. Nuss, “T-ray tomography,” Opt. Lett. 22(12), 904–906 (1997). [CrossRef] [PubMed]

,6

6. S. H. Cho, S. H. Lee, C. Nam-Gung, S. J. Oh, J. H. Son, H. Park, and C. B. Ahn, “Fast terahertz reflection tomography using block-based compressed sensing,” Opt. Express 19(17), 16401–16409 (2011). [CrossRef] [PubMed]

,9

9. J. Takayanagi, H. Jinno, S. Ichino, K. Suizu, M. Yamashita, T. Ouchi, S. Kasai, H. Ohtake, H. Uchida, N. Nishizawa, and K. Kawase, “High-resolution time-of-flight terahertz tomography using a femtosecond fiber laser,” Opt. Express 17(9), 7533–7555 (2009). [CrossRef] [PubMed]

,10

10. K. Iwaszczuk, H. Heiselberg, and P. U. Jepsen, “Terahertz radar cross section measurements,” Opt. Express 18(25), 26399–26408 (2010). [CrossRef] [PubMed]

], terahertz computed tomography similar to the x-ray computed tomography acquiring projection data from various rotational angles [11

11. B. Ferguson, S. Wang, D. Gray, D. Abbot, and X. C. Zhang, “T-ray computed tomography,” Opt. Lett. 27(15), 1312–1314 (2002). [CrossRef] [PubMed]

,12

12. B. Recur, A. Younus, S. Salort, P. Mounaix, B. Chassagne, P. Desbarats, J.-P. Caumes, and E. Abraham, “Investigation on reconstruction methods applied to 3D terahertz computed tomography,” Opt. Express 19(6), 5105–5117 (2011). [CrossRef] [PubMed]

], and terahertz diffraction tomography [13

13. S. Wang and X. C. Zhang, “Pulsed terahertz tomography,” J. Phys. D Appl. Phys. 37(4), R1–R36 (2004). [CrossRef]

]. The terahertz computed tomography and the diffraction tomography may be applicable more generally, since they use a more general formulation of terahertz signal and employ mechanisms for rotational and translational motions of source and detector pairs to record position-dependent terahertz signal. In time-of-flight tomography, since it acquires depth information solely from the delay time of terahertz pulse, it has been applied only to simple planar objects composed of well defined planes [5

5. D. M. Mittleman, S. Hunsche, L. Boivin, and M. C. Nuss, “T-ray tomography,” Opt. Lett. 22(12), 904–906 (1997). [CrossRef] [PubMed]

,9

9. J. Takayanagi, H. Jinno, S. Ichino, K. Suizu, M. Yamashita, T. Ouchi, S. Kasai, H. Ohtake, H. Uchida, N. Nishizawa, and K. Kawase, “High-resolution time-of-flight terahertz tomography using a femtosecond fiber laser,” Opt. Express 17(9), 7533–7555 (2009). [CrossRef] [PubMed]

] or measurements of radar cross section from surface [10

10. K. Iwaszczuk, H. Heiselberg, and P. U. Jepsen, “Terahertz radar cross section measurements,” Opt. Express 18(25), 26399–26408 (2010). [CrossRef] [PubMed]

]. If the technique is applied to the tomography of non-planar bio-samples, it is necessary to measure the travel time of T-ray in free space before the sample and that inside the sample to compensate for the different velocities of the T-ray for each scan point.

To illustrate the tomographic reconstruction with a two-dimensional scanning of the time-domain spectroscopy, the wave fronts inside a phantom composed of several layers with homogeneous refractive index are shown in Fig. 1
Fig. 1 Illustration of a phantom (a), recorded wave front as a function of time in the vertical direction (refractive index, n = 2) (b), and a reconstructed plane on a time index (c). The location of the reconstructed plane and the time index are shown in (a) and (b) with red dotted lines, respectively.
.

In Fig. 1, a conceptual phantom is shown in (a), which was piled up by squares with equal thickness. We assumed that the refractive indices of the squares are 2. The Terahertz beam is assumed to be incident from above (z). The vertical and horizontal axes in (a) are arbitrarily chosen as z and x, and the axis normal to the sheet is assumed as y. A corresponding wave front recorded is shown in (b) as a function of time in the vertical direction. Due to a lower velocity of the T-ray inside the sample, it takes a longer time for the T-ray to pass the sample. Therefore, a plane (c) is reconstructed on the time index shown in (b) with a dotted line. As one can see, (c) is not a proper cross sectional plane of the phantom at the location shown in (a) with a dotted line. To acquire distortion-free tomographic planes, the different velocities of the T-ray in free space and inside a sample should be properly compensated for. In other words, the data recorded as a function of time should be converted to the data as a function of depth.

In this paper, we report on a simple method to measure the refractive index of the sample and the velocity compensation method necessary for the tomographic reconstruction of the T-ray time domain spectroscopic image of non-planar bio samples.

2. Measurement of refractive index

A schematic diagram to measure the refractive index of the sample using one-dimensional measured data (time-domain spectroscopy) is shown in Fig. 2
Fig. 2 Schematic diagram to measure the refractive index of a sample is shown.
.

Aluminum tape was placed on the table to serve as a highly-reflective reference surface beneath the sample. One terahertz measurement was taken with the sample in place and another in free space without the sample. The T-ray passing through the sample shows highly reflected signals at the surface (t1) and at the boundary between the sample and the table (t2) due to the large impedance differences between free space and the sample.

On the other hand, the T-ray passing through free space is reflected highly from the table (t3). If the sample is homogeneous with an equal refractive index, the refractive index of the sample may be expressed as
n=vairvsample=dairtairdsampletsample
(1)
where vair and vsample are velocities of the T-ray in free space and inside the sample; dair and dsample are distances from the sample surface to the floor and the sample as shown in Fig. 2; tair and tsample are transit times for the T-rays in free space and inside the sample for the distances dair and dsample, respectively.

In Eq. (1), dair may be expressed as
dair=dsample+dgapdsample
(2)
where dgap, the distance between the bottom of the sample and the floor is assumed to be much smaller than dsample, and is neglected. Thus, Eq. (1) may be approximately expressed as
ntsampletair=t2t1t3t1
(3)
where t1 is the reflected time of the T-ray at the surface of the sample; t2 is the reflected time at the boundary of the sample adjoining to the floor; t3 is the reflected time at the floor without passing through the sample.

3. Compensation method by the refractive index

The depth of the T-ray data is given by the integral length of the velocity of the T-ray multiplied by a unit time. Generally, a sample may be composed of many elements and structures having different refractive indices. However, we assumed a homogeneous sample with a constant refractive index. So only two media, free space and a sample, are considered.

The depth of the data at (l1+l2)Δt may be given by
d=l1Δtvair+l2Δtvsample=l1Δtnvsample+l2Δtvsample=l1nΔd+l2Δd=(l1n+l2)Δd
(4)
Where
Δd=Δtvsample
(5)
In Eq. (4), l1 is the number of time units for the T-ray to travel in free space before the surface of the sample; l2 is the number of time units for the T-ray to travel inside the sample to reach the location; Δt is the unit time; and Δd is the unit distance in the sample.

From Eq. (4), the data acquired at the time of (l1+l2)Δt is converted to the one with the depth of (l1n+l2)Δd. Disregarding the units for now, the difference between the distance and time indices is (l1n+l2)(l1+l2)=(n1)l1. Thus the two-dimensional terahertz spectroscopy data as a function of time can be converted to the one as a function of depth by simply shifting the data by (n1)l1 points and changing the time unit to the depth unit given by Eq. (5). The time index l1 can be detected by the first peak signal reflected at the surface of the sample.

The recorded wave fronts shown in Fig. 1(b) are transformed as a function of depth using the velocity compensation method and are shown in Fig. 3
Fig. 3 Restored wave front as a function of depth after the compensation (n = 2) (a) and a reconstructed plane (b) for the location shown in (a) with a dotted line.
. Since the velocity of the T-ray in free space is double the speed inside the sample (n = 2), compensation can be done by shifting the data by l1 grids as previously described. The grid in Fig. 3(a) is the unit distance of the T-ray inside the phantom. Perfect reconstruction can be made as shown in Fig. 3(b).

4. Experiment

The proposed pre-processing method is applied to two-dimensional multi slice tomography with a reflection-type T-ray time-domain spectroscopy system with a pulsed mode laser source [6

6. S. H. Cho, S. H. Lee, C. Nam-Gung, S. J. Oh, J. H. Son, H. Park, and C. B. Ahn, “Fast terahertz reflection tomography using block-based compressed sensing,” Opt. Express 19(17), 16401–16409 (2011). [CrossRef] [PubMed]

]. The sample is a parched anchovy in 10 x 38 mm. The image matrix size is 56 x 170 pixels. Transverse resolution is 250μm x 250μm. The number of sampling points in the temporal direction is 512 with the sampling interval of 70.3fs [6

6. S. H. Cho, S. H. Lee, C. Nam-Gung, S. J. Oh, J. H. Son, H. Park, and C. B. Ahn, “Fast terahertz reflection tomography using block-based compressed sensing,” Opt. Express 19(17), 16401–16409 (2011). [CrossRef] [PubMed]

]. Using Eq. (3), the average refractive index of the parched anchovy is 1.6. Thus, the depth resolution is 21μm in free space, and is 13μm inside the anchovy.

Photographs of the sample, dissection image, and positive peak image of the T-ray are shown in Fig. 4
Fig. 4 Photograph of the patched anchovy (a), dissection image (b) and positive peak image of the T-ray in log scale (c). Horizontal and vertical dotted lines are added in (c) for profile plot.
. A positive peak image is displayed in log scale for a better visualization.

Cut views of the sample are shown in Fig. 5
Fig. 5 Cut views of the sample in horizontal (a) and vertical (b) directions.
along the dotted lines shown in Fig. 4(c). Two vertical axes in Fig. 5 represent the time of the delay (left) and the depth (right) of the first reflected signal. The first peak time of the T-ray is plotted with a blue solid line, and the corresponding depth of the surface of the sample is shown with a red solid line after the velocity compensation. Note that the depth profile is not obtainable by simply scaling of the time profile as demonstrated in Fig. 1.

Four tomographic images of the parched anchovy are shown in Figs. 6
Fig. 6 The Maximum intensity projection (MIP) images of the T-ray tomography are shown in log scale before the velocity compensation.
and 7
Fig. 7 The MIP images of the T-ray tomography in log scale after the velocity compensation. The resolution in the transverse plane is 250μm x 250μm, and the depth resolution is 65μm.
before and after the velocity compensation. The maximum intensity is projected (MIP) among 5 adjacent depth images with a depth resolution of 13μm, which makes the depth resolution or equivalent slice thickness 65μm. By comparing Figs. 6 and 7, the tomographic images after the velocity compensation (Fig. 7) have better defined boundaries and show the internal structures more clearly. Log scale is taken to make for severe attenuation inside the sample. The log scale reduces the large reflected signal at the surface, which enhances the small signal inside the sample. The velocity compensated images in linear scale are also shown in Fig. 8
Fig. 8 The MIP images of the T-ray tomography in linear scale.
for comparison.

Since the depth resolution (13μm) inside the sample is much higher compared to the transverse resolution (250μm) [9

9. J. Takayanagi, H. Jinno, S. Ichino, K. Suizu, M. Yamashita, T. Ouchi, S. Kasai, H. Ohtake, H. Uchida, N. Nishizawa, and K. Kawase, “High-resolution time-of-flight terahertz tomography using a femtosecond fiber laser,” Opt. Express 17(9), 7533–7555 (2009). [CrossRef] [PubMed]

], some post-processing along the depth direction is desirable. For instance, T-ray tomography with an isotropic resolution in both the transverse plane and the depth direction (250μm x 250μm x 250μm) is reconstructed from 19 adjacent depth images after the velocity compensation. Reconstructed images by the maximum intensity projection, averaging, and the short-time Fourier transform along the depth direction are shown in Figs. 9-11 in log scale. The images shown in Fig. 9
Fig. 9 Five MIP images of the T-ray tomography of the anchovy are shown with an isotropic resolution of 250 μm in both the transverse plane and the depth direction.
are obtained by the maximum intensity projection. The technique is a nonlinear process, which may reduce the contribution from small signal. The images shown in Fig. 10
Fig. 10 Five average images of T-ray tomography of the anchovy with an isotropic resolution of 250 μm.
are done by averaging, which improves signal-to-noise ratio. The images shown in Fig. 11
Fig. 11 Narrow band spectral responses (0.374THz ~1.123THz) of the T-ray tomographic images of the anchovy are shown with an isotropic resolution of 250 μm by the short-time Fourier transform.
are the average spectral responses of the terahertz wave in the range of 0.374THz~1.123THz obtained by the short-time Fourier transform. By using a narrow spectral width rather than the whole spectra of the terahertz wave, the responses have higher resolution. The technique also improves signal-to-noise ratio similar to the averaging method. Although the three post-processing methods do not make significant differences in the reconstructed images, they have distinct characters in improving the signal-to-noise ratio and resolution in the reconstructed images, which will be useful in the terahertz tomography depending on the sample and measurement conditions.

5. Conclusion

Terahertz tomography is obtained for a biological sample. Due to different velocities of the terahertz wave in free space and inside the sample, compensation is necessary to obtain tomographic images. A simple method to measure the refractive index of the sample is proposed. By the suggestive velocity compensation method, tomographic images are successfully obtained. To make isotropic resolution, several image processing methods such as the maximum intensity projection, averaging, and the short-time Fourier transform along the slice direction (the propagation direction of the terahertz wave) are suggested. Log scale display of the terahertz tomography is also suggested.

Acknowledgments

This research was conducted during the sabbatical year, 2011 supported by Kwangwoon University. This research was also supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 2011-0001291) and by a grant from the Korean Health Technology R&D Project of the Ministry for Health, Welfare & Family Affairs, Republic of Korea (A101954).

References and links

1.

B. B. Hu and M. C. Nuss, “Imaging with terahertz waves,” Opt. Lett. 20(16), 1716–1718 (1995). [CrossRef] [PubMed]

2.

A. J. Fitzgerald, V. P. Wallace, M. Jimenez-Linan, L. Bobrow, R. J. Pye, A. D. Purushotham, and D. D. Arnone, “Terahertz pulsed imaging of human breast tumors,” Radiology 239(2), 533–540 (2006). [CrossRef] [PubMed]

3.

M. M. Nazarov, A. P. Shkurinov, E. A. Kuleshov, and V. V. Tuchin, “Terahertz time-domain spectroscopy of biological tissues,” Quantum Electron. 38(7), 647–654 (2008). [CrossRef]

4.

S. J. Oh, J. Choi, I. Maeng, J. Y. Park, K. Lee, Y.-M. Huh, J.-S. Suh, S. Haam, and J.-H. Son, “Molecular imaging with terahertz waves,” Opt. Express 19(5), 4009–4016 (2011). [CrossRef] [PubMed]

5.

D. M. Mittleman, S. Hunsche, L. Boivin, and M. C. Nuss, “T-ray tomography,” Opt. Lett. 22(12), 904–906 (1997). [CrossRef] [PubMed]

6.

S. H. Cho, S. H. Lee, C. Nam-Gung, S. J. Oh, J. H. Son, H. Park, and C. B. Ahn, “Fast terahertz reflection tomography using block-based compressed sensing,” Opt. Express 19(17), 16401–16409 (2011). [CrossRef] [PubMed]

7.

B.-M. Hwang, S. H. Lee, W.-T. Lim, C. B. Ahn, J.-H. Son, and H. Park, “A fast spatial-domain terahertz imaging using block-based compressed sensing,” J. Infrared, Millimeter, Terahertz Waves 32(11), 1328–1336 (2011). [CrossRef]

8.

K. W. Kim, K.-S. Kim, H. Kim, S. H. Lee, J.-H. Park, J.-H. Han, S.-H. Seok, J. Park, Y. Choi, Y. I. Kim, J. K. Han, and J.-H. Son, “Terahertz dynamic imaging of skin drug absorption,” Opt. Express 20(9), 9476–9484 (2012). [CrossRef] [PubMed]

9.

J. Takayanagi, H. Jinno, S. Ichino, K. Suizu, M. Yamashita, T. Ouchi, S. Kasai, H. Ohtake, H. Uchida, N. Nishizawa, and K. Kawase, “High-resolution time-of-flight terahertz tomography using a femtosecond fiber laser,” Opt. Express 17(9), 7533–7555 (2009). [CrossRef] [PubMed]

10.

K. Iwaszczuk, H. Heiselberg, and P. U. Jepsen, “Terahertz radar cross section measurements,” Opt. Express 18(25), 26399–26408 (2010). [CrossRef] [PubMed]

11.

B. Ferguson, S. Wang, D. Gray, D. Abbot, and X. C. Zhang, “T-ray computed tomography,” Opt. Lett. 27(15), 1312–1314 (2002). [CrossRef] [PubMed]

12.

B. Recur, A. Younus, S. Salort, P. Mounaix, B. Chassagne, P. Desbarats, J.-P. Caumes, and E. Abraham, “Investigation on reconstruction methods applied to 3D terahertz computed tomography,” Opt. Express 19(6), 5105–5117 (2011). [CrossRef] [PubMed]

13.

S. Wang and X. C. Zhang, “Pulsed terahertz tomography,” J. Phys. D Appl. Phys. 37(4), R1–R36 (2004). [CrossRef]

OCIS Codes
(100.6950) Image processing : Tomographic image processing
(110.6795) Imaging systems : Terahertz imaging
(110.6955) Imaging systems : Tomographic imaging

ToC Category:
Imaging Systems

History
Original Manuscript: May 31, 2013
Revised Manuscript: July 18, 2013
Manuscript Accepted: August 5, 2013
Published: August 16, 2013

Virtual Issues
Vol. 8, Iss. 9 Virtual Journal for Biomedical Optics

Citation
Hye-Jin Hong, Jinho Park, Hochong Park, Joo-Hiuk Son, and Chang-Beom Ahn, "Pre- and post-processing for tomographic reconstruction of terahertz time-domain spectroscopy," Opt. Express 21, 19943-19950 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-17-19943


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References

  1. B. B. Hu and M. C. Nuss, “Imaging with terahertz waves,” Opt. Lett.20(16), 1716–1718 (1995). [CrossRef] [PubMed]
  2. A. J. Fitzgerald, V. P. Wallace, M. Jimenez-Linan, L. Bobrow, R. J. Pye, A. D. Purushotham, and D. D. Arnone, “Terahertz pulsed imaging of human breast tumors,” Radiology239(2), 533–540 (2006). [CrossRef] [PubMed]
  3. M. M. Nazarov, A. P. Shkurinov, E. A. Kuleshov, and V. V. Tuchin, “Terahertz time-domain spectroscopy of biological tissues,” Quantum Electron.38(7), 647–654 (2008). [CrossRef]
  4. S. J. Oh, J. Choi, I. Maeng, J. Y. Park, K. Lee, Y.-M. Huh, J.-S. Suh, S. Haam, and J.-H. Son, “Molecular imaging with terahertz waves,” Opt. Express19(5), 4009–4016 (2011). [CrossRef] [PubMed]
  5. D. M. Mittleman, S. Hunsche, L. Boivin, and M. C. Nuss, “T-ray tomography,” Opt. Lett.22(12), 904–906 (1997). [CrossRef] [PubMed]
  6. S. H. Cho, S. H. Lee, C. Nam-Gung, S. J. Oh, J. H. Son, H. Park, and C. B. Ahn, “Fast terahertz reflection tomography using block-based compressed sensing,” Opt. Express19(17), 16401–16409 (2011). [CrossRef] [PubMed]
  7. B.-M. Hwang, S. H. Lee, W.-T. Lim, C. B. Ahn, J.-H. Son, and H. Park, “A fast spatial-domain terahertz imaging using block-based compressed sensing,” J. Infrared, Millimeter, Terahertz Waves32(11), 1328–1336 (2011). [CrossRef]
  8. K. W. Kim, K.-S. Kim, H. Kim, S. H. Lee, J.-H. Park, J.-H. Han, S.-H. Seok, J. Park, Y. Choi, Y. I. Kim, J. K. Han, and J.-H. Son, “Terahertz dynamic imaging of skin drug absorption,” Opt. Express20(9), 9476–9484 (2012). [CrossRef] [PubMed]
  9. J. Takayanagi, H. Jinno, S. Ichino, K. Suizu, M. Yamashita, T. Ouchi, S. Kasai, H. Ohtake, H. Uchida, N. Nishizawa, and K. Kawase, “High-resolution time-of-flight terahertz tomography using a femtosecond fiber laser,” Opt. Express17(9), 7533–7555 (2009). [CrossRef] [PubMed]
  10. K. Iwaszczuk, H. Heiselberg, and P. U. Jepsen, “Terahertz radar cross section measurements,” Opt. Express18(25), 26399–26408 (2010). [CrossRef] [PubMed]
  11. B. Ferguson, S. Wang, D. Gray, D. Abbot, and X. C. Zhang, “T-ray computed tomography,” Opt. Lett.27(15), 1312–1314 (2002). [CrossRef] [PubMed]
  12. B. Recur, A. Younus, S. Salort, P. Mounaix, B. Chassagne, P. Desbarats, J.-P. Caumes, and E. Abraham, “Investigation on reconstruction methods applied to 3D terahertz computed tomography,” Opt. Express19(6), 5105–5117 (2011). [CrossRef] [PubMed]
  13. S. Wang and X. C. Zhang, “Pulsed terahertz tomography,” J. Phys. D Appl. Phys.37(4), R1–R36 (2004). [CrossRef]

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