| Terahertz (THz) is the frequency of the electromagnetic wave between0.1～10THz (1THz=1012Hz). The region of the electromagnetic spectrum corresponding to the vibrational and rotational energy levels of molecules, contains a wealth of physical and chemical information, and it is very suitable for low-frequency identification and the study of dynamic characteristics of the molecule.Especially the developing of terahertz time-domain spectroscopy technology (THz-TDS) which based on ultrafast femtosecond laser pulses. Utilizing this technology can measure the amplitude and phase of Terahertz electric field, get the sample refractive index, dielectric constant and absorption coefficient of the measured samples directly. And then forming fingerprints of samples based on Terahertz spectral as the identification parameters of samples on this basis.The low frequency vibrations were usually investigated by means of absorption coefficient regardless of the refractive index. It leads to the disregard of some inherent low-frequency vibrational information of the chemical compounds. It leads to the Incomplete of the research. Moreover, due to the scattering inside the sample, there are some distortions of the absorption features, so that the absorption dependent material identification is not valid enough and cannot serve as the sole basis for the identification of samples.To solve the problems above, the study of this paper commence in the following manner, on the basis of the refractive index and absorption coefficient of samples in Terahertz region, the absorption linear shape function I(v) based on statistical mechanics is established as a contact between the two parameters, and then using a multivariate linear model-principal component analysis (PCA) to model the linear shape function. I(v) is a combination of the refractive index and the absorption coefficient and is related to the Fourier transform of the time-correlation function of the total dipole moment of the system. It contains information on the low-frequency dynamics and the structural flexibility of the samples. The log plot of I(v) show power-law behavior I(v) oc vα, and there is a linear relation between the wavenumber and I(v) in the double logarithmic plot. The big differences of the exponents a between different samples can be seen visually from the slopes of the I(v) curves. So we can use I(v) analytical method to distinguish some complex compounds in THz region. This identification method has greatly improved in terms of precision and accuracy than only using absorption characteristics in the aspects of sample identification. The exponents a of different samples that have similar structure are very close, but there is a large difference with the other samples. So we can use this method to classify the samples which have similar structure.Multiple linear principal component analysis is construct with orthogonal the principal component. Principal component fits the significantly variance and random measurement error in statistics of the data set. A major purpose of the PCA is to present the random error in the principal component, thereby reducing the dimension of the complex data and minimizing the amount of measurement errors. We can use PCA to deal with the Terahertz data, after that we can obtain a more efficient and accurate method to identify samples.As a complement to the two methods above, we have introduced the Terahertz two-dimension correlation spectroscopy. The spectral differences between samples can be expressed more intuitive. Compared with the absorption linear shape function and principal component analysis methods, two-dimension correlation spectroscopy requires only a simple qualitative comparison to distinguish the sample. It is a more convenient and intuitive method of identifying samples.Finally, we summarized the work we did, specifically we discussed the pros and cons of the3statistical methods that be used, analyzed the application, and made a specific plan about the next work we would do. |
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