# A Contactless Liquor Level Detection Method Using Terahertz Time-Domain Spectroscopy

Authors: Boqin Yang; Hu Deng; Quancheng Liu; LinYu Chen; Liang Xiong; Zhixiang Wu; Weiwei Qu; Liping Shang
Journal: Journal of Sensors
 (2021)

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## Abstract

In this paper, we proposed the terahertz technique to measure the liquid level of Chinese liquor in sealed pots. We analyzed the transmission process of terahertz pulse in the sealed pots and established a model of the relationship between terahertz pulse interval and liquor level. The measurement results are in good agreement with the theoretical model. The results show that the terahertz technique can realize the high precision measurement of liquor level. The absolute and relative errors are less than ±40μm and 0.014%, respectively. In addition, we also evaluated the influence of dewdrop on the measurement accuracy. The results show that dewdrop only leads to a deviation of 18 μm. The results prove the value of terahertz technology in the field of liquid level monitoring.


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## Body

## 1. Introduction

Chinese liquor is one of the oldest distillates in the world and has been popular in China for centuries. The growing sales indicated liquor still plays a major social role in China [1, 2]. Before being sold, the liquor is commonly stored in the ceramic pot for the hoard to improve its taste and enhance its value. In this process, the liquid level of the liquor in the pot is one of the key indicators that represent its states. Since hundreds to thousands of pots are sealed with polyethylene (PE) films, it is challenging to find an appropriate method and adequate instruments to measure the liquid level of the liquor. Firstly, the fragility of the ceramic pots requires a contactless measurement method. Additionally, it is better not to remove the PE film that ensures that the liquor in the cylinder is in a stable state when measuring the liquid level of the liquor. Finally, measurement methods with low energy consumption and high precision are needed to avoid damaging the product. Therefore, the liquid level measurement is of great significance in the liquor-brewing process.At present, most liquid level sensors are in contact, including pressure liquor meters [3], magnetostriction liquid meters [4], floating sensors [5], capacitance sensors [6, 7], and fiber optic liquid meters using an in-fiber Mach-Zehnder interferometer [8–10], an in-fiber Fabry-Perot interferometer [11, 12], or fiber Bragg gratings [13–15]. All the contact-based methods are unable to meet the requirements for a satisfactory measurement of the liquid level of the liquor. And the contactless sensors include ultrasonic liquid meters [16], radar liquid meters [17], microwave liquid meters [18–20], and optical liquid meters [21], of which are easily perturbed by dust, steam, bubbles, and the variations in the dielectric constant of the liquid and the temperature, which leads to large uncertainties in the measurement.Terahertz (THz) radiation, which refers to the region of 0.1-10 THz, has the advantage of directivity and low photon energy. Thus, the terahertz time-domain spectroscopy (THz-TDS) technology has become widely used in the nondestructive field [22, 23]. In this study, we developed the research of liquor level measurement using THz-TDS technology. The liquor level measurement model is established, which has a good consistency with the experimental results. Additionally, we evaluated the stability of the system. The results show that THz-TDS has application value in the field of liquor level monitoring.


## 2. Theory of Liquor Level Measurement

### 2.1. Experimental Setup

The traditional THz-TDS mainly includes a femtosecond laser, a THz source, a THz detector, and a time-delay stage. Generally, the femtosecond laser is focused on the THz source to produce THz pulses. The pump-probe technology is employed to detect ultrafast THz pulses. The THz-TDS setup in this study is plotted in Figure1. The femtosecond pulses (MaiTai SP, Spectra-Physics) are divided into pump and probe pulses by a half-wave plate (HWP) and a polarization beam splitter (PBS), with an energy ratio of 5 : 1. The pump pulses are reflected by M1-M3 and then focused onto a photoconductive antenna (PCA-LTGAAS-LT50, Zomega) to produce THz pulses. The THz pulses are collected with a lens (TL1) to form a parallel beam. Then, the parallel beam is reflected vertically by a THz mirror (TM1) for object detection. The reflective THz beam is collected with beam splitter mirror (TBS), THz mirrors (TM2 and TM3), and then focused on the ZnTe (110, 2 mm). The probe pulses are collected with mirrors (M4, M5, and M6) and silicon chip and finally focused on the ZnTe collinearly with THz beam. The probe pulses modulated by the THz beam are measured by a Wollaston prism and a balanced detector. The output signal from the detector is amplified by a phase-locked amplifier (SR830, SRS). The time-delay stage is realized with two mirrors (M1 and M2) and a motorized linear stage (GTS150, Newport). In the experiment, the motion control and signal acquisition are realized by the LabVIEW software.Figure 1
The schematic diagram of the experimental setup.


### 2.2. Theoretical Analysis

Figure2 shows the transmission model of the THz wave in the sealed pot. The THz wave (Eiω) generated by the photoconductive antenna is normal incidence on the sealed pot. Part of the THz wave is reflected from the air-PE interface, and the rest of the THz wave penetrates the air-PE interface. According to the Fresnel equation [24], the propagation coefficient Ppω,h+da inside the air and the reflection coefficient Rapω of the air-PE film interface are
(1)Paω,h+da=exp−in~aωωh+da/c,(2)Rapω=n~aω−n~pωn~aω+n~pω,Figure 2
The transmission model of THz wave in the sealed pot.The part of the wave reflected from the air-PE film interface serves as the reference signalErω, which is described by
(3)Erω=EiωPa2ω,h+daRapω.To simplify the calculation, we ignore the effect of the frequency on the refractive index. Equation (3) is transformed by a Fourier inversion as
(4)Ert=12π∫−∞+∞RapEiωexp−i2naωh+daceiωt,dω=RapEt−2nah+dac,Rap=na−npna+np.Another part of wave penetrating the air-PE interface transmits into two media (PE film and ethanol gas): the transmission coefficientTapω at the air-PE film interface, propagation coefficient Ppω,dp inside the PE film, and transmission coefficient Tpeω of the PE film-ethanol gas interface are
(5)Tap=2n~aωn~aω+n~pω,(6)Ppω,dp=exp−in~pωωdp/c,(7)Tpe=2n~pωn~pω+n~eω.Additionally, it is reflected (by ethanol gas-liquor interface) back into ethanol gas and PE film again, which the liquor level signalEoω is obtained. According to the Fresnel equation, the propagation coefficient Peω,de inside the ethanol gas, reflection coefficient Relω of the ethanol gas-liquor interface, transmission coefficient Tepω of the ethanol gas-PE film interface, and transmission coefficient Tpaω of the PE film-air interface are
(8)Peω,de=exp−in~eωωde/c,Relω=n~eω−n~lωn~eω+n~lω,(9)Tep=2n~eωn~eω+n~pω,(10)Tpa=2n~pωn~pω+n~aω.According to Equations (1) and (5)–(10), the liquor level signal Eoω is expressed as
(11)Eoω=EiωTapωTpeωRelωTepωTpaωPa2ω,h+daPp2ω,dpPe2ω,de.Ignoring the effect of the frequency on the refractive index, Equation (11) is transformed by a Fourier inversion as
(12)Eot=12π∫−∞+∞kEiωeiωte−i2ωnah+da+npdp+nede/c,dω=kEt−2nah+nada+npdp+nedec,k=16nanp2nene−nlna+np2np+ne2ne+nl.As Equations (4) and (12) show, by comparing Eot with Ert, the time-domain spectroscopy moves to the right 2npdp+nede/c, where c indicates the speed of light, np, dp, and ne are known quantities, and only de is unknown. The terahertz pulse interval Δt between the reference signal Ert and the liquor level signal Eot is
(13)Δt=npdp+nedec.According to Equation (13), the liquor level dl can be written as
(14)dl=L−de=L−cΔt−2npdp2ne,where c=3×108m/s, ne≈1, np=1.518 [25], dp=0.1mm, and L is the depth of container.


## 2.1. Experimental Setup

The traditional THz-TDS mainly includes a femtosecond laser, a THz source, a THz detector, and a time-delay stage. Generally, the femtosecond laser is focused on the THz source to produce THz pulses. The pump-probe technology is employed to detect ultrafast THz pulses. The THz-TDS setup in this study is plotted in Figure1. The femtosecond pulses (MaiTai SP, Spectra-Physics) are divided into pump and probe pulses by a half-wave plate (HWP) and a polarization beam splitter (PBS), with an energy ratio of 5 : 1. The pump pulses are reflected by M1-M3 and then focused onto a photoconductive antenna (PCA-LTGAAS-LT50, Zomega) to produce THz pulses. The THz pulses are collected with a lens (TL1) to form a parallel beam. Then, the parallel beam is reflected vertically by a THz mirror (TM1) for object detection. The reflective THz beam is collected with beam splitter mirror (TBS), THz mirrors (TM2 and TM3), and then focused on the ZnTe (110, 2 mm). The probe pulses are collected with mirrors (M4, M5, and M6) and silicon chip and finally focused on the ZnTe collinearly with THz beam. The probe pulses modulated by the THz beam are measured by a Wollaston prism and a balanced detector. The output signal from the detector is amplified by a phase-locked amplifier (SR830, SRS). The time-delay stage is realized with two mirrors (M1 and M2) and a motorized linear stage (GTS150, Newport). In the experiment, the motion control and signal acquisition are realized by the LabVIEW software.Figure 1
The schematic diagram of the experimental setup.


## 2.2. Theoretical Analysis

Figure2 shows the transmission model of the THz wave in the sealed pot. The THz wave (Eiω) generated by the photoconductive antenna is normal incidence on the sealed pot. Part of the THz wave is reflected from the air-PE interface, and the rest of the THz wave penetrates the air-PE interface. According to the Fresnel equation [24], the propagation coefficient Ppω,h+da inside the air and the reflection coefficient Rapω of the air-PE film interface are
(1)Paω,h+da=exp−in~aωωh+da/c,(2)Rapω=n~aω−n~pωn~aω+n~pω,Figure 2
The transmission model of THz wave in the sealed pot.The part of the wave reflected from the air-PE film interface serves as the reference signalErω, which is described by
(3)Erω=EiωPa2ω,h+daRapω.To simplify the calculation, we ignore the effect of the frequency on the refractive index. Equation (3) is transformed by a Fourier inversion as
(4)Ert=12π∫−∞+∞RapEiωexp−i2naωh+daceiωt,dω=RapEt−2nah+dac,Rap=na−npna+np.Another part of wave penetrating the air-PE interface transmits into two media (PE film and ethanol gas): the transmission coefficientTapω at the air-PE film interface, propagation coefficient Ppω,dp inside the PE film, and transmission coefficient Tpeω of the PE film-ethanol gas interface are
(5)Tap=2n~aωn~aω+n~pω,(6)Ppω,dp=exp−in~pωωdp/c,(7)Tpe=2n~pωn~pω+n~eω.Additionally, it is reflected (by ethanol gas-liquor interface) back into ethanol gas and PE film again, which the liquor level signalEoω is obtained. According to the Fresnel equation, the propagation coefficient Peω,de inside the ethanol gas, reflection coefficient Relω of the ethanol gas-liquor interface, transmission coefficient Tepω of the ethanol gas-PE film interface, and transmission coefficient Tpaω of the PE film-air interface are
(8)Peω,de=exp−in~eωωde/c,Relω=n~eω−n~lωn~eω+n~lω,(9)Tep=2n~eωn~eω+n~pω,(10)Tpa=2n~pωn~pω+n~aω.According to Equations (1) and (5)–(10), the liquor level signal Eoω is expressed as
(11)Eoω=EiωTapωTpeωRelωTepωTpaωPa2ω,h+daPp2ω,dpPe2ω,de.Ignoring the effect of the frequency on the refractive index, Equation (11) is transformed by a Fourier inversion as
(12)Eot=12π∫−∞+∞kEiωeiωte−i2ωnah+da+npdp+nede/c,dω=kEt−2nah+nada+npdp+nedec,k=16nanp2nene−nlna+np2np+ne2ne+nl.As Equations (4) and (12) show, by comparing Eot with Ert, the time-domain spectroscopy moves to the right 2npdp+nede/c, where c indicates the speed of light, np, dp, and ne are known quantities, and only de is unknown. The terahertz pulse interval Δt between the reference signal Ert and the liquor level signal Eot is
(13)Δt=npdp+nedec.According to Equation (13), the liquor level dl can be written as
(14)dl=L−de=L−cΔt−2npdp2ne,where c=3×108m/s, ne≈1, np=1.518 [25], dp=0.1mm, and L is the depth of container.


## 3. Experimental Results and Discussion

In this research, we adopted a cylindrical glass container (the diameter and height are 116.19 mm and 300 mm, respectively) and a PE film (the thickness is 0.1 mm, the state of PE film is dry) to simulate the storage conditions of liquor. To simulate the variations of liquor level, we used a pipette to inject 10 mL liquor into the container each time with a liquor level change (Δdl) of 0.943 mm. Here, we measured the liquor level with a path of approach 120 mm.In Section2.2, we established a predictive model based on the Δt between the reference signal Ert and the liquor level signal Eot. Figure 3(a) plots the comparison of the predictive model with measured results. The measured results have a good consistency with the predictive model in both intercept and slope. Further, Figure 3(b) shows that the absolute and relative errors are less than ±40 μm and 0.014%, respectively. This indicated that the THz-TDS method is of high precision in liquor level measurement.Figure 3
(a) The comparison of the predictive model with measured results. (b) Error analysis.
(a)(b)To evaluate the systematic error on measurement accuracy, we performed 20 times repeated measurements of the liquor level signal with dry of PE film. As Figure4 shows, the maximum and the minimum peak positions are 5.86 ps and 5.82 ps, respectively, with a mean value of 5.84 ps. The standard deviation is 0.012 ps, which indicates that the measurements are of high repeatability.Figure 4
Twenty times repeated measurements of the liquor level signal.As mentioned, the dewdrop is one of the major factors that affect measurement accuracy. After being stored for two days, dewdrops have occurred on the PE film’s inside as shown in Figure5(a). The reflected signal of the liquor surface has been measured repeatedly for 20 times, as illustrated in Figure 5(b). Comparing with Figures 4 and 5(b), it could be seen that the terahertz signal intensities are reduced from 2.35×10−4 to 1.99×10−4 (Figure 5(c)), due to the extra absorption of dewdrops. Meanwhile, the average peak position is delayed 0.06 ps from 5.78 ps to 5.84 ps (Figure 5(d)), which gives rise to about 18 μm measuring error. Since terahertz waves have longer wavelengths than visible-infrared rays and better penetration than microwaves, the dewdrop of the PE film has less effect on measurement accuracy and error. This indicates that the THz technology has the advantage of field detection.Figure 5
The influence of dewdrop phenomenon: (a) dewdrop phenomenon on the PE film’s inside, (b) THz time-domain spectra for 20 times repeated measurements with dewdrops of the PE film, (c) comparison of peak terahertz signal intensity between dry and dewy PE films, and (d) comparison of peak position between dry and dewy PE films.
(a)(b)(c)(d)


## 4. Conclusion

To meet the demand for liquor level measurements of stored liquor, we proposed a new liquor level detection method using the THz technology. Firstly, we designed a reflective THz-TDS system for measurements. Secondly, we deduced the predictive model of THz signals with the liquor level based on the propagation coefficients of the multilayered medium. Finally, we verified the model with the measurements. The results show that the predictive model has a good consistency with measurements in both intercept and slope. Additionally, the absolute and relative errors are less than ±40μm and 0.014%, respectively, which indicates that this method is of high accuracy. Moreover, we also evaluated the effects of systematic error and dewdrop. The repeatable experiment shows that the system has good repeatability with a small standard deviation of 0.012 ps, and the dewdrop results in an 18 μm measuring error. This indicates that the THz-TDS method is an accurate, nondestructive tool for the liquor level measurements.



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