# Research on the Application of THz-TDS in Coal-Rock Interface Recognition
## 3 Results and Discussion  
### THz Spectral Properties of Coal-Rock and Coal-Rock Mixtures  
#### 3.1.1 THz Spectral Properties of Coal and Rock  
Before starting the sample test, it is necessary to wait for the femtosecond laser to stabilize and recalibrate in advance to ensure the safe stability of the measurement. First, the reference THz signal is obtained without placing the sample on the sample table. Then, different coal and rock samples are tested separately. The THz spectral scan range was 218-232 ps with a step size of 0.02 ps to obtain the time-domain spectrum of the sample as shown in Figure 2a. THz-TDS is a coherent detection technology that can simultaneously obtain information of the THz pulse amplitude and phase. As such, it relies on the THz wave reflection to detect changes in the THz time-domain pulse wave in the sample before and after irradiation, called the reference and sample waveforms, respectively. It can be observed that the THz amplitudes of coal-rock samples decrease to varying degrees compared with the reference signal due to surface reflection and absorption. Because the four samples have different refractive index, the wave speed and light path of the THz pulse passing through the sample are different, leading to differences in the time delay and the appearance of the signal at different times [28]. It is pointed out that the waveforms starting at 218 ps are not offset or intrinsic results from our method, which is determined by the motorized stages, phase-lock amplifier and detection antenna of THz-TDS. The reason is that the peaks occur in THz band, and only through this band are we able to see a full and useful time-domain waveform. Fast Fourier transform (FFT) was used to convert the time-domain signals of coal and rock into the frequency domain to obtain the frequency domain spectrum, as shown in Figure 2b. It can be found that the amplitude of temporal waveform for samples has some oscillation and attenuation relative to the reference waveform. This may be due to the sample's reflection, dispersion and absorption. In addition, it should be pointed out that the echoes were cut off in the THz time-domain spectra before the THz frequency domain spectra was obtained by Fourier transform, which can effectively avoid the Fabry-Perot effect. THz frequency domain spectra reveal significant differences between the sample's signal and reference signal, which is caused by the different propagating velocity in the sample relative to the reference path, which gives rise to the different time delay. Meanwhile, the reduced THz pulse intensity results from the sample's reflectivity and absorption, as well as the THz pulse which broaden with sample dispersion. In general, there is a critical value for the sample's absorption of high-frequency signals greater than that of low-frequency signals. Below the critical value, the signal strength of the sample is greater than the noise signal, and the spectral information of the sample can be truly reflected. Once the value is greater than the critical value, because the signal strength of the strongly absorbed sample is less than the noise signal, the sample information is submerged in the noise, and the sample information cannot be truly reflected. Therefore, we intercepted the effective frequency range according to the critical value. It can be seen from Figure 2b that the effective frequency range is 0.3-1.1 THz. Accordingly, the frequency band of 0.3-1.1 THz was selected to analyze the absorption coefficient and refractive index of the sample. Then, we analyzed the optical signal of the coal mixture sample within the 0.3-1.11 THz frequency band. Figure 2: The THz spectra of coal and rock. (**a**) Time-domain spectra. (**b**) Frequency domain spectra. (**c**) Refractive index spectra. (**d**) Absorption coefficient spectra. Therefore, the refractive index and absorption coefficient of coal and rock samples can be calculated using Formulas (12) and (13). From Figure 2c, the refractive index of coal and rock samples is relatively stable.