The Continuous Wavelet Transform In Terahertz Time-domain Spectroscopy

Wavelet analysis is a mathematics branch that started to develop and mature gradually from the 1980s.The main characteristic of wavelet transform is that it has the double domain determined ability both to the time domain and frequency domain and multi-resolving power analyse ability, for which it is called mathematics microscope. Wavelet transform has become a strong tool for signal analysis after Fourier transform. In this paper, the realization of continuous wavelet transforms (CWT) besides its advantages and applications in terahertz time-domain spectroscopy (THz-TDS) technology were president.THz-TDS combined with continuous wavelet transform can realize time-frequency analysis for THz wave. In this paper, CWT in THz control system of THz-TDS based on LabVIEW was realized. By CWT, planar time-frequency distribution graph can be got, which decomposeTHz wave in time-frequency domain. Compared with time domain oscillation waveform and Fourier transform spectrum, CWT has both time and frequency-domain resolution, which can not only reflect the frequency components, but also show relative time delay of all the frequency components.We choose Gabor wavelet as the"mother wavelet"to analyze THz wave . we focus our attention on shaping factor of Gabor wavelet including its property and affection on CWT. The research indicated that shaping factor influence time-frequency resolution of Gabor wavelet transform. The larger the shaping factor is, the higher the frequency resolution will be, and corresponding, time resolution will decrease, vice versa. Besides , in this paper , we also analyze some extreme situation and conclude that when shaping factor is quite small, the property of CWT is close to time domain oscillation property,and when shaping factor is large enough , CWT result is semblable to Fourier transform.THz-TDS combined with CWT open new application field for THz-TDS. In this paper, based on time-resolved measurement of ultra-fast terahertz radiation pulses combined with wavelet analysis, an experimental system for magnetically confined (tokomak) plasma density measurement is designed. The ultra-fast terahertz signal transmitted through the under tested plasma can be measured based on phase coherence technique of electromagnetic wave. By analyzing the measured THz pulses signal with continuous wavelet transform, the group velocity under tested plasma can be obtained. And thus plasma density can be derived according to the relationship between the group velocity and refractive index of plasma. The schematic diagram of the experimental system designed is given. The measured ultra-fast terahertz signal in our experiment, ranging from 0.2 THz to 1 THz, is used as the input to simulate the whole experimental process, and the plasma density obtained is close to that we designed, which proves the feasibility of this design, which indicate that ultrafast THz system combined with wavelet analysis may have potential applications in high density plasma diagnostics.