Open Access
Add to BibSonomyAbstract
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
Sensing and imaging using pulsed terahertz (THz) radiation has been widely and rapidly recognized as a promising non-destructive and non-contact detection technique. THz radiation can penetrate through most of the commonly used dielectric materials, such as paper, plastic, leather and wood [1–8]. Many chemical materials, such as explosives and related compounds (ERCs) and bio-chemicals have resonant peaks due to intermolecular or phonon vibrations within the THz region [9–14]. A number of sensing and imaging modalities using pulsed THz wave have been developed in the past [15–18]. 2-D chemical mapping of heterogeneous mixtures with reflective THz-TDS has also been achieved [18]. However, most of the available sensing and imaging geometries adopt the raster scanning method by focusing the THz beam onto the sample surface. The main reason for using this configuration is that a reflective spectroscopy system requires a high signal-to-noise-ratio (SNR) and scanning with the THz beam focused ensures the best collection efficiency of the reflected signal. Moreover, the reference beam is easier to control with this configuration. Nonetheless, raster scanning geometry is difficult to be applied in sensing and imaging at large scale and at standoff distance [15, 16, 18]. Although data acquisition speed can be 20 pixels per second or even faster, this speed cannot provide the amount of data required for classification within a short period of time.
One solution for chemical explosive sensing at standoff distance is THz focal-plane imaging in reflection geometry [19]. The technique of THz focal-plane imaging was first developed in late 90s. Rather than focusing the THz pulse on the sample, both THz and probe beams are expanded and a THz quasi-plane wave is used to illuminate the target. The THz beam is modified by the target (either in transmission or reflection) and overlaps with the probe beam in a large sensor crystal. Each point on the probe beam wave front is modulated by the local THz field, which carries the information of the target. The wave front is then captured by a CCD camera. By taking the 2-D image at once and only scanning the time delay, the data acquisition speed is dramatically improved [20–22]. For example, it takes less than 10 minutes to acquire an image of 288 by 384 pixels with 300 time steps, by averaging each frame for 100 times, which means that it is possible to acquire almost 200 waveforms per second.
Short distance THz focal-plane imaging is not new [19–21]. However, in the real scenario, many target materials appear in large quantity and sit on non-transparent substrate. Therefore a more practical imaging geometry for sensing application would be conducted in reflection mode and at longer imaging distance [23].
This work aims at presenting a THz focal-plane imaging system in reflection geometry which is able to identify multiple spectroscopic features of biological chemicals and ERCs, such as 2, 4-DNT, Theophylline, RDX, and Glutamic Acid within the THz frequency range, at a standoff distance of 0.4 m. Minimum distance based classifier and a neural network will be used for sample classification. The investigation of this feasibility will greatly benefit the advancing of THz imaging technique at standoff distance for chemical and biological materials sensing and screening.
2. Method
At normal incidence, the complex reflection coefficient r̃ is given by the relation between the reflected beam E2 and the incident beam E1. It can be derived through the complex refractive index of the material ñ=n+iκ by Eq. (1) [24]:
If the phase shift Φ between E1 and E2 and the reflectance R are known, then the refractive index n and the absorption coefficient κ can be calculated as Eq. (2):
In THz reflective focal-plane imaging, the phase shift Φ is affected by sample surface roughness and sensor crystal non-homogeneity, leading to erroneous results when being applied to Eq. (2) [25]. However, calculations show that the derivative of 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, 27, 28].
Figure 1 shows the extinction coefficient κ and -dr/dv of RDX. It is noted that the curve -dr/dν also presents peaks around the absorption frequencies.
Fig. 1. The absorption coefficient κ and -dr/dν of RDX. Both curves show the absorption peak around 0.82 THz and 1.05 THz, which are indicated by arrows.
3. Experimental setup
The schematic layout of the setup is illustrated in Fig. 2. The laser used is a Spectra Physics Hurricane with 1 KHz repetition rate, 100 fs pulse duration, 700 mW output power, and 795 nm center wavelength. The THz beam is generated from a 2.5 mm thick ZnTe crystal and is expanded to a diameter of 25 mm. The incident angle of THz beam onto the sample’s surface is 15°. A polyethylene lens with 200 mm focal length is used to image the sample target onto a large ZnTe sensor crystal (50 by 50 by 5 mm3). 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.
The imaging targets are 2, 4-DNT, Theophylline, RDX, Glutamic Acid and glass. All of them except the glass are prepared as compressed pellets with a thickness of ~1.5 mm and a diameter of 13 mm. However, the RDX material is extremely brittle and only a small piece is used as imaging target. Glass does not have any absorption features within THz region and is used as a contrast sample. Figure 3 shows the extinction coefficients of 2, 4-DNT, Theophylline, RDX and Glutamic Acid measured with the same sample pellets, in transmission geometry by a standard THz-TDS system. Each curve is plotted at the same scale. All labeled absorption peaks have been confirmed by other measurements [9,11,12,13,14]. It is noteworthy that the absorption peaks of RDX at 0.82 THz (κ~0.3) and 1.33 THz (κ~0.1) [11], 2, 4-DNT at 1.08 THz (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.
Fig. 3. The extinction coefficient κ of RDX, Theophylline, 2, 4-DNT, and Glutamic Acid measured by transmission THz-TDS in nitrogen purged cell. Data is shifted for clarity. The arrows indicate the absorption peaks of each target.
4. Results
4.1 THz spectra of the reference and imaging targets
The waveform and spectrum of the THz beam taken without the presence of any sample (averaged over all pixels) are given in Fig. 4. This spectrum is used as reference E1 to calculate -dr/dv for all samples.
Fig. 4. Time domain waveform (top) and spectrum (bottom) of the reference THz wave (averaged over all pixels).
4.2 Optical image
Figure 5 is the optical picture of all five imaging samples. Figure 6 shows the THz image obtained by taking the peak amplitude of the THz pulse at each pixel. Samples can not be identified from this THz image.
Fig. 6. THz peak amplitude image of 2, 4-DNT, Theophylline RDX, Glutamic Acid and glass. Identification of the samples is not possible in this image.
4.3 Spectroscopic image
Figure 7 shows the plot of -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.
Fig. 7. -dr/dv of RDX, Theophylline, 2, 4-DNT, Glutamic Acid and glass from five randomly selected pixels on each sample image. The arrows indicate the absorption peaks. Three absorption peaks of RDX, one of 2, 4-DNT and one of Glutamic Acid are located by comparing with Fig 6.2. No significant absorption features are found in Theophylline’s plot.
In order to identify each sample from their -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):
Where v2 and v1 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).
Fig. 8. The images of the sample targets formed by integrating the peak area around (a) 0.82 THz; (b) 0.96 THz; (c) 1.08 THz and (d) 1.21 THz, with a width of 0.15 THz. Except for the image at 0.96 THz, which is supposed to be the absorption peak location of Theophylline, all three other samples can be identified at the images of their corresponding absorption peak frequencies.
4.4 Contrast of the image
The contrast of the spectroscopic image is defined as Eq. (4) [29]:
Where Ipeak is the mean value of the “bright” area and Ifloor 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 Ifloor is the peak position of the normal distribution on the left and Ipeak 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 κ of RDX is the highest among all. Therefore, the calculations of image contrast provide a measure to evaluate the identification result.
Fig. 9. Histogram of the spectroscopic image at 1.21 THz on Fig. 8 (d). The pixel value is normalized from 1 to 10. The position of the peak on the left Ifloor represents the pixel value of the background, whereas the position of the peak on the right Ipeak indicates the pixel value of the foreground, which is the sample being identified.
Table 1. Contrast of each image on Fig. 8. The image at 0.82 THz has the highest contrast because the extinction coefficient κ of RDX is measured to be the highest among the four. The image at 0.96 THz has zero contrast resulting from the single normal distribution on its histogram. The failure to identify any absorption feature at 0.96 THz image is due to insufficient dynamic range of the imaging system.
4.5 Classification
The spectroscopic images shown in Fig. 8 help to identify the sample material. Although assigning a threshold pixel value on each image can greatly enhance the contrast, the identification task is still largely based on vision. A more general method is to apply classification or pattern recognition methods [30, 31]. In this paper, the spectrum of -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).
It has been shown that the Theophylline sample fails to stand out at its absorption frequency at 0.96 THz due to insufficient contrast. Therefore, the conventional absorption peak-based features will not be applicable in this case [7]. However, there may still be characteristic spectral features for each sample which are not necessarily related with absorption resonance, such as reflection variations caused by different surface morphology [14]. By using statistical based multi-variable classification methods such as Mahalanobis distance classifier, or mapping techniques such as neural network, it is still possible to distinguish each sample from the rest. In that case, the features selected may not have physical meaning [31]. By applying principal component analysis (PCA) to the training dataset, over 99% of the total variance is found in the first 19 dimensions in the 80-dimension principal component (PC) space [32]. Thus by selecting the first 19 PC scores in the classification analysis, most of the information is retained while greatly reducing the redundancy and mathematical instabilities. Moreover, after performing PCA, the new set of data is maximally uncorrelated.
4.6 Mahalanobis classifier
Mahalanobis distance (MD) is defined as the distance from a given point to the mean value for a certain class normalized by the variance of the training vectors in that direction [34]. For the class i, this distance is given by Eq. (5):
Where ∑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.
The Mahalanobis classifier was constructed using 50 training vectors from each of the five classes. All pixels on the entire image are tested with the classifier (2248 pixels from 2, 4-DNT, 3157 pixels from Theophylline, 483 pixels from RDX, 2717 pixels from Glutamic Acid and 2570 from glass).
To evaluate the classification, one could calculate the positive identification rate (P), negative identification rate (W), and false alarm rate (F). Mathematically they can be expressed by Eq. (6):
Where Ni is the total number of vectors in the category i, ri accounts for the number of waveforms correctly identified into the category, ti represents the quantity of waveforms mistakenly labeled as other categories, oi indicates those not identified and ui is the number of waveforms that are wrongly assigned to class 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%.
Table 2. Positive (P), negative (W) and false (F) identification percentage of the classification using the first derivative of reflective coefficient -dr/dv.
4.7 Neural network based classifier
Artificial neural network provides another powerful tool for classification [35]. One significant advantage of neural network classification is that it does not assume any a priori knowledge of the probability distribution, while in other statistic method a priori knowledge is necessary. Neural network assisted THz-TDS have been reported in the past [33,36,37]. This method is also applied to the classification of the spectroscopic imaging data. The training dataset is the same as the previous method. The neural network is a forward-feed type with 19 neurons in the input layer, 3 hidden layers containing 10, 8, and 5 neurons respectively, and 1 neuron in the output layer. The response function of the neurons in the hidden layers is sigmoid, while the response of the output neuron is linear. The Levenberg-Marquardt back-propagation method is used to train the network.
When evaluating this classifier, two identification criteria have to be considered: criterion A and criterion B. Criterion A considers all outputs between Yi±0.5, Y={0,1,2,3,4} belong to i; criterion B assigns outputs within the standard deviation range Yi±σ, Y={0,1,2,3,4} into class i. This standard deviation is obtained from the output of the neural network when training data is used as the input. In criterion A, oi=0 because all outputs will be classified into any existing class. For criterion 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.
Table 3. Positive (P), negative (W) and false (F) identification rate using both A and B criteria.
These results show that for both criteria, the positive identification rate is above 80%, and the false identification for any sample is less than 3%. The total false identification rate is 8% and 4% for A and B, respectively.
5. Discussion
5.1 Limitation of surface morphology
Multiple reflections within the time window will cause severe distortions in the spectrum through Fabry-Perrot effect [7]. In order to correctly measure the reflection spectrum from the sample surface, the scale of sample surface variation within the area limited by spatial resolution should not exceed the time window determined by spectral range and resolution. For example, in an imaging system with 2 mm spatial resolution, the time window has to be at least 1.5 mm with 20 µm step size in order to have 7 THz of spectral window with 0.2 THz resolution. Hence, a surface variation smaller than 20 µm or beyond 1.5 mm is desired. This requirement may not be so unrealistic considering in many cases explosive chemicals such as RDX are transported in bulk and solid shape [23].
5.2 Limitation of sensitivity
The failure to address any absorption feature of Theophylline indicates that the modulation depth of the suspect material within the absorption region has to be higher than the dynamic range of the imaging system. Indeed, knowing the noise floor δr~r/D where D is the dynamic range at that frequency [38], Eq. (7) must be satisfied in order to see the absorption peak:
In which , v2 and v1 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 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
The accuracy of the MD classifier is slightly higher than that of the neural network, which is understood because the neural network structure may not be optimized. However, it is still justified to believe that the performance of the two classifiers are comparable, which also supports the validity of the experimental data [39].
6. Conclusion
To conclude, the results demonstrate that this THz reflective focal-plane imaging system is able to identify multiple spectroscopic features of 2,4-DNT, Theophylline, RDX, and Glutamic Acid at a distance up to 0.4 m. By using either MD or neural network classifiers, it is possible to distinguish between any of the samples with a positive rate higher than 80%. Surface morphology and dynamic range are the two most important factors that limit the sensitivity of the imaging system.
Acknowledgments
This work is supported by Army Research Office and the National Science Foundation. We greatly acknowledge the generous help offered by Mr. Gary Young, Dr. Yunqing Chen, Dr. Xin He, Mr. Jian Chen, Dr. Glenn Bastiaans and Dr. Charles Davis.
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. J. 5, 203–208 (2005). [CrossRef]
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. 83, 800–802 (2003). [CrossRef]
3. D. M. Mittleman, S. Hunsche, L. Boivin, and M. C. Nuss, “T-ray tomography,” Opt. Lett. 22, 904–906 (1997). [CrossRef] [PubMed]
4. B. Ferguson and X.-C. Zhang, “Materials for terahertz science and technology,” Nat. Mater. 1, 26–33 (2002). [CrossRef]
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 68, 1085–1094 (1999). [CrossRef]
6. D. Zimdars, J. Valdmanis, J. White, and G. Stuk, “Time domain terahertz detection of flaws within space shuttle sprayed on foam insulation,” CLEO, CThN4 (2004).
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]
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. 120, 72–78 (2003). [CrossRef] [PubMed]
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]
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 362, 337–349 (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]
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 , 1, 198 (2005). [CrossRef]
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 , 1, 5–6 (2005). [CrossRef]
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 , 1, 42–3 (2005). [CrossRef]
18. Y. Shen, P. Taday, D. Newnham, and M. Pepper, “Chemical mapping using reflection terahertz pulsed imaging,” Semicond. Sci. Technol. 20, S254–257 (2005). [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]
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]
21. 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]
22. F. Ferguson, S. Wang, D. Gray, D. Abbot, and X.-C. Zhang, “T-ray computed tomography,” Opt. Lett. 27, 1312–1314 (2002). [CrossRef]
23. National Research Council of the National Academies, “Existing and potential standoff explosives detection techniques,” (National Academies Press2004).
24. J. Jackson, Classical Electrodynamics, (Wiley & Sons, New York, 1975).
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]
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]
27. F. Wooten, Optical properties of solids, (Academic New York, 1972).
28. H. Zhong, “Terahertz wave reflective sensing and imaging,” Ph.D. thesis (2006).
29. E. Hecht, Optics, (Addison Wesley Longman1998).
30. D. Michie, D. Spiegelhalter, and C. Taylor, Machine learning, neural and statistical classification, (Ellis Horwood, 1994).
31. L. Zheng and X. He, “Classification techniques in pattern recognition,” WSCG, conference proceedings, ISBN 80-903100-8-7 (2005).
32. J. Edward Jackson, A user’s Guide to principal components, and subspaces, (Wiley & Sons, New York, 1991). [CrossRef]
33. 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 and D. L. Woolard, eds., Proc. SPIE 5070, 7–16 (2003). [CrossRef]
34. G. Seber, Multivariate observations, (Wiley & Sons, New York, 1984). [CrossRef]
35. Z. Bian and X. Zhang, Pattern recognition, (Tsinghua University Press, Beijing, 1999).
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 Terahertz for Military and Security Applications II, R. J. Hwu and D. L. Woolard, eds., Proc. SPIE 5411, 45 (2004). [CrossRef]
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 , 13, 903–936 (2003). [CrossRef]
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]
39. B. Ferguson, “Three-dimensional T-ray inspection systems,” Ph.D. thesis (2003).
