## Identification and classification of chemicals using terahertz reflective spectroscopic focal-plane imaging system

Optics Express, Vol. 14, Issue 20, pp. 9130-9141 (2006)

http://dx.doi.org/10.1364/OE.14.009130

Acrobat PDF (246 KB)

### Abstract

We present terahertz (THz) reflective spectroscopic focal-plane imaging of four explosive and bio-chemical materials (2, 4-DNT, Theophylline, RDX and Glutamic Acid) at a standoff imaging distance of 0.4 m. The 2 dimension (2-D) nature of this technique enables a fast acquisition time and is very close to a camera-like operation, compared to the most commonly used point emission-detection and raster scanning configuration. The samples are identified by their absorption peaks extracted from the negative derivative of the reflection coefficient respect to the frequency (-*dr/dv*) of each pixel. Classification of the samples is achieved by using minimum distance classifier and neural network methods with a rate of accuracy above 80% and a false alarm rate below 8%. This result supports the future application of THz time-domain spectroscopy (TDS) in standoff distance sensing, imaging, and identification.

© 2006 Optical Society of America

## 1. Introduction

19. Q. Wu, T. Hewitt, and X.-C. Zhang, “Two-dimensional electro-optic imaging of THz beams,” Appl. Phys. Lett. **69**, 1026–1028 (1996). [CrossRef]

20. M. Usami, M. Yamashita, M, K. Fukushima, C. Otani, and K. Kawase, “Terahertz wideband spectroscopic imaging based on two-dimensional electro-optic sampling technique,” Appl. Phys. Lett. **86**, 141109-1–3 (2005). [CrossRef]

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

19. Q. Wu, T. Hewitt, and X.-C. Zhang, “Two-dimensional electro-optic imaging of THz beams,” Appl. Phys. Lett. **69**, 1026–1028 (1996). [CrossRef]

21. R. Rungsawang, K. Ohta, K. Tukamoto, and T. Hattori, “Ring formation of focused half-cycle terahertz pulses,” J. Phys. D: Appl. Phys. **36**229–235 (2003). [CrossRef]

## 2. Method

*r*̃ is given by the relation between the reflected beam

*E*and the incident beam

_{2}*E*. It can be derived through the complex refractive index of the material

_{1}*ñ=n+iκ*by Eq. (1) [24]:

*Φ*between

*E*and

_{1}*E*and the reflectance R are known, then the refractive index

_{2}*n*and the absorption coefficient

*κ*can be calculated as Eq. (2):

*Φ*is affected by sample surface roughness and sensor crystal non-homogeneity, leading to erroneous results when being applied to Eq. (2) [25

25. E. M. Vartiainen, Y. Ino, R. Shimano, M. Kuwata-Gonokami, Y. P. Svirko, and K.-E. Peiponen, “Numerical phase correction method for terahertz time-domain reflection spectroscopy,” J. Appl. Phys. **96**, 4171–4175 (2004). [CrossRef]

*r*=√

*R*respect to the frequency can also provide the positions of absorption frequencies with peak position deviations within 0.02 THz. It is noteworthy that this property only holds to weakly polarized organic material, which has moderate absorption compared to dispersion in THz range, such as ERCs, bio-chemicals, etc. [26

26. K. Yamamoto, A. Masui, and H. Ishida, “Kramers-Kronig analysis of infrared reflection spectra with perpendicular polarization,” Appl. Opt. **33**, 6285–6293 (1994). [CrossRef] [PubMed]

*κ*and -

*dr/dv*of RDX. It is noted that the curve -

*dr/dν*also presents peaks around the absorption frequencies.

## 3. Experimental setup

^{3}). Both the distance of image and distance of object are 0.4 m (2f-2f). The probe beam has an expanded diameter of 25 mm and copropagates with THz beam through the sensor crystal. A Princeton Instrument CCD camera is used to capture the image of the probe beam. The spatial resolution of the imaging system is 2 mm. To ensure the best imaging quality, images of each sample were taken separately but concatenated together as a whole image.

9. Y. Chen, H. Liu, Y. Deng, D. Veksler, M. Shur, X. -C. Zhang, D. Schauki, M. J. Fitch, and R. Osiander, “Spectroscopic characterization of explosives in the far infrared region,” in *Terahertz for Military and Security Applications II*,
R. J. Hwu and D. L. Woolard, eds., Proc. SPIE **5411**, 1–8 (2004). [CrossRef]

11. K. Yamamoto, M. Yamaguchi, F. Miyamaru, M. Tani, M. Hangyo, T. Ikeda, A. Matsushita, K. Koide, M. Tatsuno, and Y. Minami, “Noninvasive inspection of C-4 explosive in mails by terahertz time-domain spectroscopy,” Jpn. J. Appl. Phys. **43**, n 3B, L414–417 (2004). [CrossRef]

12. M. C. Kemp, P. F. Taday, B. E. Cole, J. A. Cluff, A. J. Fitzgerald, and W. R. Tribe, “Security applications of terahertz technology,” in *Terahertz for Military and Security Applications*,
R. J. Hwu and D. L. Woolard, eds., Proc. SPIE **5070**, 44–52 (2003). [CrossRef]

13. F. Huang, B. Schulkin, H. Altan, J. F. Federici, D. Gary, R. Barat, D. Zimdars, M. Chen, and D. B. Tanner, “Terahertz study of 1,3,5-trinitro-s-triazine by time-domain and Fourier transform infrared spectroscopy,” Appl. Phys. Lett. **85**, 5535–5537 (2004). [CrossRef]

*κ*~0.3) and 1.33 THz (

*κ*~0.1) [11

11. K. Yamamoto, M. Yamaguchi, F. Miyamaru, M. Tani, M. Hangyo, T. Ikeda, A. Matsushita, K. Koide, M. Tatsuno, and Y. Minami, “Noninvasive inspection of C-4 explosive in mails by terahertz time-domain spectroscopy,” Jpn. J. Appl. Phys. **43**, n 3B, L414–417 (2004). [CrossRef]

*κ*~0.2), Theophylline at 0.96 THz (

*κ*~0.06) and Glutamic Acid at 1.21 THz (

*κ*~0.1) are the most prominent within the spectral window between 0.4 THz to 1.6 THz.

## 4. Results

### 4.1 THz spectra of the reference and imaging targets

*E*to calculate -

_{1}*dr/dv*for all samples.

### 4.2 Optical image

### 4.3 Spectroscopic image

*dr/dv*of five pixels randomly chosen from the image of each sample. Three absorption peaks of RDX, one of 2, 4-DNT and one of Glutamic Acid are well identified. However, there is no significant absorption features extracted from the plot of Theophylline.

*dr/dv*spectra, the peak areas around 0.82 THz, 0.96 THz, 1.08 THz and 1.21 THz are integrated for each pixel with a width of 0.15 THz. Analytically, the value of each pixel is calculated as Eq. (3):

*v*and

_{2}*v*indicate the range of the integration. The pixels with peak within the window appear brighter and the ones without appear darker. The background value of the image is set to be 0. The results are illustrated in Fig. 8, which show that at 0.82 THz, 1.08 THz and 1.21 THz, the samples that have the corresponding absorption peak at each frequency appear to be the brightest. No significant cluttered distribution at 0.96 THz (the absorption peak of Theophylline) is addressed. The failure to identify Theophylline is due to the fact that its absorption peak at 0.96 THz is too weak to be resolved under the current dynamic range (discussions are given at the end of this paper).

_{1}### 4.4 Contrast of the image

*I*is the mean value of the “bright” area and

_{peak}*I*is the mean value of the background. Both values can be extracted from the histogram of the image. To fairly compare all four images, the pixel values of each image are normalized linearly to range from 1 to 10. Figure 9 shows an example of the histogram of the spectroscopic image at 1.21 THz [Fig. 8(d)]. The pixel value on X-axis is normalized linearly to range from 1 to 10. The value of

_{floor}*I*is the peak position of the normal distribution on the left and

_{floor}*I*is the one on the right. Both are marked with dashed lines. Table 1 lists the contrast of all four images in Fig 8. It is noticed that the contrast value of the image at 0.96 THz is 0 as a result of a single normal of the histogram, which means that there is not any sample identified. The image at 0.82 THz has the highest contrast, which is also understood because the extinction coefficient

_{peak}*κ*of RDX is the highest among all. Therefore, the calculations of image contrast provide a measure to evaluate the identification result.

### 4.5 Classification

*dr/dv*for each sample is use to perform such identification and classification. The frequency ranges from 0.4 THz to 1.6 THz with 15 GHz resolution (80 frequencies). Supervised classification is adopted by selecting 50 training vectors randomly from each class (2, 4-DNT, Theophylline, RDX, Glutamic Acid and glass).

### 4.6 Mahalanobis classifier

34. G. Seber, *Multivariate observations*, (Wiley & Sons, New York, 1984). [CrossRef]

*E*[(

*x-µ*)(

*x-µ*)

^{T}] is the mean of the class

*i*and

*µ*is the covariance matrix of the class

*i*(

*E*means expectation) calculated from the training dataset. For a given sample vector, the classification is done by assigning the vector to the class in which the MD is the minimum.

*P*), negative identification rate (

*W*), and false alarm rate (

*F*). Mathematically they can be expressed by Eq. (6):

*N*is the total number of vectors in the category

_{i}*i, r*accounts for the number of waveforms correctly identified into the category,

_{i}*t*represents the quantity of waveforms mistakenly labeled as other categories,

_{i}*o*indicates those not identified and

_{i}*u*is the number of waveforms that are wrongly assigned to class

_{i}*i*while belong to other categories. Table 2 gives the

*P, W*and

*F*rates of this classifier. Each category is classified with a rate of accuracy higher than 99%.

### 4.7 Neural network based classifier

*A*and criterion

*B*. Criterion

*A*considers all outputs between

*Y*±0.5, Y={0,1,2,3,4} belong to

_{i}*i*; criterion

*B*assigns outputs within the standard deviation range

*Y*±σ, Y={0,1,2,3,4} into class

_{i}*i*. This standard deviation is obtained from the output of the neural network when training data is used as the input. In criterion

*A, o*=0 because all outputs will be classified into any existing class. For criterion

_{i}*B*, it is possible that some outputs will not be classified into any category. Criterion

*A*is more restricted in terms of making the decision which implies that

*P, W*and

*F*are lower than using criterion

*B*. Table 3 summarizes the

*P, W*and

*F*rates of classification based on each criterion.

*A*and

*B*, respectively.

## 5. Discussion

### 5.1 Limitation of surface morphology

7. D. M. Mittleman, R. H. Jacobsen, R. Neelamani, R. G. Baraniuk, and M. C. Nuss, “Gas sensing using terahertz time-domain spectroscopy,” Appl. Phys. B **67**, 379–390 (1998). [CrossRef]

### 5.2 Limitation of sensitivity

*δr~r/D*where

*D*is the dynamic range at that frequency [38

38. J. Xu, T. Yuan, S. Mickan, and X.-C. Zhang, “Limit of spectral resolution in terahertz time-domain spectroscopy,” Chin. Phys. Lett. **20**, 1266–1268 (2003). [CrossRef]

*v*and

_{2}*v*mark the range of the absorption peak area and SNR is the signal to noise ratio of the image. For example, to identify the absorption peak of Theophylline at 0.96 THz, given

_{1}*r/Δr*~9 and

*SNR*>2, the dynamic range of each pixel at 0.96 THz has to be bigger than 20, which was not satisfied in our current system.

### 5.3 Classifier selection

## 6. Conclusion

## Acknowledgments

## References

1. | H. Zhong, J. Xu, X. Xie, T. Y. R. Reightler, E. Madaras, and X.-C. Zhang, “Nondestructive defect identification with terahertz time-of-flight tomography,” IEEE Sens. |

2. | Y. Watanabe, K. Kawase, T. Ikari, H. Ito, Y. Ishikawa, and H. Minamide, “Component spatial pattern analysis of chemicals using terahertz spectroscopic imaging,” Appl. Phys. Lett. |

3. | D. M. Mittleman, S. Hunsche, L. Boivin, and M. C. Nuss, “T-ray tomography,” Opt. Lett. |

4. | B. Ferguson and X.-C. Zhang, “Materials for terahertz science and technology,” Nat. Mater. |

5. | D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, “Recent advances in terahertz imaging,” Appl. Phys. B |

6. | D. Zimdars, J. Valdmanis, J. White, and G. Stuk, “Time domain terahertz detection of flaws within space shuttle sprayed on foam insulation,” |

7. | D. M. Mittleman, R. H. Jacobsen, R. Neelamani, R. G. Baraniuk, and M. C. Nuss, “Gas sensing using terahertz time-domain spectroscopy,” Appl. Phys. B |

8. | R. Woodward, V. Wallace, R. Pye, B. Cole, D. Arnone, E. Linfield, and M. Pepper, “Terahertz pulse imaging of ex vivo basal cell carcinoma samples,” J. Invest. Dermatol. |

9. | Y. Chen, H. Liu, Y. Deng, D. Veksler, M. Shur, X. -C. Zhang, D. Schauki, M. J. Fitch, and R. Osiander, “Spectroscopic characterization of explosives in the far infrared region,” in |

10. | M. K. Choi, A. Bettermann, and D. W. van der Weide, “Potential for detection of explosive and biological hazards with electronic terahertz systems,” Phil. Trans. R. Soc. Lond. A |

11. | K. Yamamoto, M. Yamaguchi, F. Miyamaru, M. Tani, M. Hangyo, T. Ikeda, A. Matsushita, K. Koide, M. Tatsuno, and Y. Minami, “Noninvasive inspection of C-4 explosive in mails by terahertz time-domain spectroscopy,” Jpn. J. Appl. Phys. |

12. | M. C. Kemp, P. F. Taday, B. E. Cole, J. A. Cluff, A. J. Fitzgerald, and W. R. Tribe, “Security applications of terahertz technology,” in |

13. | F. Huang, B. Schulkin, H. Altan, J. F. Federici, D. Gary, R. Barat, D. Zimdars, M. Chen, and D. B. Tanner, “Terahertz study of 1,3,5-trinitro-s-triazine by time-domain and Fourier transform infrared spectroscopy,” Appl. Phys. Lett. |

14. | H. Liu, “Terahertz spectroscopy for chemical and biological sensing applications”, Ph.D. thesis (2006). |

15. | D. Arnone, “Terahertz pulsed imaging and spectroscopy for chemical detection and security,” The Joint 30th International Conference on Infrared and Millimeter Waves , |

16. | D. Zimdars, J. White, G. Stuk, A. Chernovsky, G. Fichter, and S. Williamson, “Large area high speed time domain THz imager for security and nondestructive evaluation imaging,” the Joint 30th International Conference on Infrared and Millimeter Waves , |

17. | H. Zhong, A. Redo, Y. Chen, and X.-C. Zhang, “Standoff distance detection of explosive materials with THz waves,” the Joint 30th International Conference on Infrared and Millimeter Waves , |

18. | Y. Shen, P. Taday, D. Newnham, and M. Pepper, “Chemical mapping using reflection terahertz pulsed imaging,” Semicond. Sci. Technol. |

19. | Q. Wu, T. Hewitt, and X.-C. Zhang, “Two-dimensional electro-optic imaging of THz beams,” Appl. Phys. Lett. |

20. | M. Usami, M. Yamashita, M, K. Fukushima, C. Otani, and K. Kawase, “Terahertz wideband spectroscopic imaging based on two-dimensional electro-optic sampling technique,” Appl. Phys. Lett. |

21. | R. Rungsawang, K. Ohta, K. Tukamoto, and T. Hattori, “Ring formation of focused half-cycle terahertz pulses,” J. Phys. D: Appl. Phys. |

22. | F. Ferguson, S. Wang, D. Gray, D. Abbot, and X.-C. Zhang, “T-ray computed tomography,” Opt. Lett. |

23. | National Research Council of the National Academies, “Existing and potential standoff explosives detection techniques,” (National Academies Press2004). |

24. | J. Jackson, |

25. | E. M. Vartiainen, Y. Ino, R. Shimano, M. Kuwata-Gonokami, Y. P. Svirko, and K.-E. Peiponen, “Numerical phase correction method for terahertz time-domain reflection spectroscopy,” J. Appl. Phys. |

26. | K. Yamamoto, A. Masui, and H. Ishida, “Kramers-Kronig analysis of infrared reflection spectra with perpendicular polarization,” Appl. Opt. |

27. | F. Wooten, |

28. | H. Zhong, “Terahertz wave reflective sensing and imaging,” Ph.D. thesis (2006). |

29. | E. Hecht, |

30. | D. Michie, D. Spiegelhalter, and C. Taylor, |

31. | L. Zheng and X. He, “Classification techniques in pattern recognition,” |

32. | J. Edward Jackson, |

33. | B. Ferguson, S. Wang, H. Zhong, D. Abbott, and X.-C. Zhang, “Powder detection with T-ray imaging,” in |

34. | G. Seber, |

35. | Z. Bian and X. Zhang, |

36. | F. Oliveira, R. Barat, B. Schulkin, F. Huang, J. Federici, D. Gary, and D. Zimdars, “Analysis of THz spectral images of explosives and bio-agents using trained neural networks,” in |

37. | T. Globus, D. Woolard, M. Bykhovskaia, B. Gelmont, L. Werbos, and A. Samuels, “THz-frequency spectroscopic sensing of DNA and related biological materials,” International Journal of High Speed Electronics and Systems , |

38. | J. Xu, T. Yuan, S. Mickan, and X.-C. Zhang, “Limit of spectral resolution in terahertz time-domain spectroscopy,” Chin. Phys. Lett. |

39. | B. Ferguson, “Three-dimensional T-ray inspection systems,” Ph.D. thesis (2003). |

**OCIS Codes**

(070.4560) Fourier optics and signal processing : Data processing by optical means

(100.5010) Image processing : Pattern recognition

(120.6200) Instrumentation, measurement, and metrology : Spectrometers and spectroscopic instrumentation

(300.6270) Spectroscopy : Spectroscopy, far infrared

**ToC Category:**

Imaging Systems

**History**

Original Manuscript: August 1, 2006

Revised Manuscript: September 11, 2006

Manuscript Accepted: September 12, 2006

Published: October 2, 2006

**Virtual Issues**

Vol. 1, Iss. 11 *Virtual Journal for Biomedical Optics*

**Citation**

Hua Zhong, Albert Redo-Sanchez, and X.-C. Zhang, "Identification and classification of chemicals using terahertz reflective spectroscopic focal-plane imaging system," Opt. Express **14**, 9130-9141 (2006)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-14-20-9130

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### References

- H. Zhong, J. Xu, X. Xie, T. Y. R. Reightler, E. Madaras, and X.-C. Zhang, "Nondestructive defect identification with terahertz time-of-flight tomography," IEEE Sens. J. 5, 203-208 (2005). [CrossRef]
- Y. Watanabe, K. Kawase, T. Ikari, H. Ito, Y. Ishikawa, and H. Minamide, "Component spatial pattern analysis of chemicals using terahertz spectroscopic imaging," Appl. Phys. Lett. 83, 800-802 (2003). [CrossRef]
- D. M. Mittleman, S. Hunsche, L. Boivin, and M. C. Nuss, "T-ray tomography," Opt. Lett. 22, 904-906 (1997). [CrossRef] [PubMed]
- B. Ferguson, and X.-C. Zhang, "Materials for terahertz science and technology," Nat. Mater. 1, 26-33 (2002). [CrossRef]
- D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, "Recent advances in terahertz imaging," Appl. Phys. B 68, 1085-1094 (1999). [CrossRef]
- D. Zimdars, J. Valdmanis, J. White, and G. Stuk, "Time domain terahertz detection of flaws within space shuttle sprayed on foam insulation," in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2004), paper CThN4.
- D. M. Mittleman, R. H. Jacobsen, R. Neelamani, R. G. Baraniuk, and M. C. Nuss, "Gas sensing using terahertz time-domain spectroscopy," Appl. Phys. B 67, 379-390 (1998). [CrossRef]
- R. Woodward, V. Wallace, R. Pye, B. Cole, D. Arnone, E. Linfield, and M. Pepper, "Terahertz pulse imaging of ex vivo basal cell carcinoma samples," J. Invest. Dermatol. 120, 72-78 (2003). [CrossRef] [PubMed]
- Y. Chen, H. Liu, Y. Deng, D. Veksler, M. Shur, X. -C. Zhang, D. Schauki, M. J. Fitch, and R. Osiander, "Spectroscopic characterization of explosives in the far infrared region," in Terahertz for Military and Security Applications II, R. J. Hwu, D. L. Woolard, eds., Proc. SPIE 5411, 1-8 (2004). [CrossRef]
- M. K. Choi, A. Bettermann, and D. W. van der Weide, "Potential for detection of explosive and biological hazards with electronic terahertz systems," Phil. Trans. R. Soc. Lond. A 362, 337-349 (2004). [CrossRef]
- K. Yamamoto, M. Yamaguchi, F. Miyamaru, M. Tani, M. Hangyo, T. Ikeda, A. Matsushita, K. Koide, M. Tatsuno and Y. Minami, "Noninvasive inspection of C-4 explosive in mails by terahertz time-domain spectroscopy," Jpn. J. Appl. Phys. 43, n 3B, L414-417 (2004). [CrossRef]
- M. C. Kemp, P. F. Taday, B. E. Cole, J. A. Cluff, A. J. Fitzgerald, and W. R. Tribe, "Security applications of terahertz technology," in Terahertz for Military and Security Applications, R. J. Hwu, D. L. Woolard, eds., Proc. SPIE 5070, 44-52 (2003). [CrossRef]
- F. Huang, B. Schulkin, H. Altan, J. F. Federici, D. Gary, R. Barat, D. Zimdars, M. Chen, and D. B. Tanner, "Terahertz study of 1,3,5-trinitro-s-triazine by time-domain and Fourier transform infrared spectroscopy," Appl. Phys. Lett. 85, 5535-5537 (2004). [CrossRef]
- H. Liu, "Terahertz spectroscopy for chemical and biological sensing applications", Ph.D. thesis (2006).
- D. Arnone, "Terahertz pulsed imaging and spectroscopy for chemical detection and security," The Joint 30th International Conference on Infrared and Millimeter Waves, 1, 198 (2005). [CrossRef]
- D. Zimdars, J. White, G. Stuk, A. Chernovsky, G. Fichter, and S. Williamson, "Large area high speed time domain THz imager for security and nondestructive evaluation imaging," the Joint 30th International Conference on Infrared and Millimeter Waves, 1, 5-6 (2005). [CrossRef]
- H. Zhong, A. Redo, Y. Chen, and X.-C. Zhang, "Standoff distance detection of explosive materials with THz waves," the Joint 30th International Conference on Infrared and Millimeter Waves, 1, 42-3 (2005). [CrossRef]
- Y. Shen, P. Taday, D. Newnham, and M. Pepper, "Chemical mapping using reflection terahertz pulsed imaging," Semicond. Sci. Technol. 20, S254-257 (2005). [CrossRef]
- Q. Wu, T. Hewitt, and X.-C. Zhang, "Two-dimensional electro-optic imaging of THz beams," Appl. Phys. Lett. 69, 1026-1028 (1996). [CrossRef]
- M. Usami, M. Yamashita, M. K. Fukushima, C. Otani, and K. Kawase, "Terahertz wideband spectroscopic imaging based on two-dimensional electro-optic sampling technique," Appl. Phys. Lett. 86, 141109-1-3 (2005). [CrossRef]
- R. Rungsawang, K. Ohta, K. Tukamoto, and T. Hattori, "Ring formation of focused half-cycle terahertz pulses," J. Phys. D: Appl. Phys. 36229-235 (2003). [CrossRef]
- F. Ferguson, S. Wang, D. Gray, D. Abbot and X.-C. Zhang, "T-ray computed tomography," Opt. Lett. 27, 1312-1314 (2002). [CrossRef]
- National Research Council of the National Academies, "Existing and potential standoff explosives detection techniques," (National Academies Press 2004).
- J. Jackson, Classical Electrodynamics, (Wiley & Sons, New York, 1975).
- E. M. Vartiainen, Y. Ino, R. Shimano, M. Kuwata-Gonokami, Y. P. Svirko, and K.-E. Peiponen, "Numerical phase correction method for terahertz time-domain reflection spectroscopy," J. Appl. Phys. 96, 4171-4175 (2004). [CrossRef]
- K. Yamamoto, A. Masui and H. Ishida, "Kramers-Kronig analysis of infrared reflection spectra with perpendicular polarization," Appl. Opt. 33, 6285-6293 (1994). [CrossRef] [PubMed]
- F. Wooten, Optical properties of solids, (Academic New York, 1972).
- H. Zhong, "Terahertz wave reflective sensing and imaging," Ph.D. thesis (2006).
- E. Hecht, Optics, (Addison Wesley Longman 1998).
- D. Michie, D. Spiegelhalter, C. Taylor, Machine learning, neural and statistical classification, (Ellis Horwood, 1994).
- L. Zheng, and X. He, "Classification techniques in pattern recognition," WSCG, conference proceedings, ISBN 80-903100-8-7 (2005).
- J. Edward Jackson, A user's Guide to principal components, and subspaces, (Wiley & Sons, New York, 1991). [CrossRef]
- B. Ferguson, S. Wang, H. Zhong, D. Abbott, and X.-C. Zhang, "Powder detection with T-ray imaging," in Terahertz for Military and Security Applications, R. J. Hwu, D. L. Woolard, eds., Proc. SPIE 5070, 7-16 (2003). [CrossRef]
- G. Seber, Multivariate observations, (Wiley & Sons, New York, 1984). [CrossRef]
- Z. Bian, and X. Zhang, Pattern recognition, (Tsinghua University Press, Beijing, 1999).
- F. Oliveira, R. Barat, B. Schulkin, F. Huang, J. Federici, D. Gary, and D. Zimdars, "Analysis of THz spectral images of explosives and bio-agents using trained neural networks," in Terahertz for Military and Security Applications II, R. J. Hwu, D. L. Woolard, eds., Proc. SPIE 5411, 45 (2004). [CrossRef]
- T. Globus, D. Woolard, M. Bykhovskaia, B. Gelmont, L. Werbos, and A. Samuels, "THz-frequency spectroscopic sensing of DNA and related biological materials," International Journal of High Speed Electronics and Systems, 13, 903-936 (2003). [CrossRef]
- J. Xu, T. Yuan, S. Mickan, and X.-C. Zhang, "Limit of spectral resolution in terahertz time-domain spectroscopy," Chin. Phys. Lett. 20, 1266-1268 (2003). [CrossRef]
- B. Ferguson, "Three-dimensional T-ray inspection systems," Ph.D. thesis (2003).

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