WO2021184760A1 - 一种在太赫兹波段测量材料折射率的系统及方法 - Google Patents

一种在太赫兹波段测量材料折射率的系统及方法 Download PDF

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WO2021184760A1
WO2021184760A1 PCT/CN2020/123740 CN2020123740W WO2021184760A1 WO 2021184760 A1 WO2021184760 A1 WO 2021184760A1 CN 2020123740 W CN2020123740 W CN 2020123740W WO 2021184760 A1 WO2021184760 A1 WO 2021184760A1
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terahertz
signal
refractive index
detector
signals
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PCT/CN2020/123740
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French (fr)
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涂学凑
吴雅倩
陈健
邵智豪
贾小氢
赵清源
张蜡宝
康琳
吴培亨
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南京大学
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
    • G01N21/41—Refractivity; Phase-affecting properties, e.g. optical path length

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  • the invention relates to a normal temperature terahertz detection technology, in particular to a system and method for measuring the refractive index of different materials in the terahertz wave band.
  • Terahertz (Terahertz, THz for short) waves generally refer to electromagnetic waves with a frequency in the range of 0.3 T to 10 THz (wavelengths of 30 ⁇ m to 1 mm), and the electromagnetic wave band is between sub-millimeter waves and far-infrared. Because terahertz waves have strong penetrating power for many non-polar materials, such as some dielectric materials, plastic films, paper, cloth, etc., terahertz detection technology has also been applied to quality inspection, safety inspection, and industrial non-destructive testing, etc. In the scene.
  • the measurement by reflection or transmission is currently only suitable for measuring the dielectric constant of materials in the optical band.
  • the terahertz source in this terahertz measurement system is pulsed rather than continuous terahertz light source.
  • the optical path of this pulsed terahertz system is complicated, many optical components are used, the system debugging is time-consuming, the efficiency is low, and the cost is high. Therefore, the development of a measurement system based on a continuous terahertz source has significant advantages.
  • the purpose of the present invention is to provide a system and method for measuring the refractive index of a material in the terahertz band.
  • the technical solution to achieve the objective of the present invention is: a system for measuring the refractive index of a material in the terahertz band, which includes a terahertz source fixed on an optical platform, a detector fixed on a motorized translation stage, and an electronic optical system. :
  • the terahertz source uses a continuous wave terahertz source for generating continuous terahertz radiation waves
  • the detector is fixed on the electric displacement stage, and is used for collimating the terahertz signal in the scanning light path, including the terahertz signal that has not passed through the dielectric material and the terahertz signal after passing through the dielectric material;
  • the electronic optical system includes an electric displacement control module, a signal readout module, and a signal processing module.
  • the electric displacement control module is used to control the detector to maintain collimation in the optical path and move away from the terahertz source, collimatingly Scan the terahertz signal in the path;
  • the signal readout module is used to convert the terahertz signal received by the detector into an electrical signal and read it out with a lock-in amplifier;
  • the signal processing module is used to digitize and process the response signal of the detector. Filter to obtain the final periodically changing terahertz signal, analyze and determine the refractive index of the material.
  • the continuous wave terahertz source includes a VDI terahertz band signal source, a frequency multiplier and a function signal generator.
  • the detector adopts a Schottky detector.
  • a method for measuring the refractive index of different materials in the terahertz band including the following steps:
  • Step 1 The terahertz source generates a continuous wave terahertz signal, which is received by the detector collimatedly through an optical path in free space;
  • Step 2 When scanning the free space optical path between the terahertz source and the detector, the detector first scans half the distance close to the terahertz source, then inserts the dielectric material in the middle of the scanning path, and then continues to the distance away from the terahertz source In the other half of the distance, the terahertz signal passes through the dielectric material and is collimatedly received by the detector fixed on the electric stage and moving backward during the scanning process;
  • Step 3 The detector converts the received terahertz signal into an electrical signal, and reads out the response signal information through the lock-in amplifier;
  • Step 4 Filter the two segments of signals scanned by the detector before and after inserting the material first to filter out the DC component, and then perform signal analysis and processing through Hilbert and other mathematical transformations to obtain the instantaneous phase of the signal, and then according to the insertion
  • the phase jump value before and after the material calculates the refractive index.
  • step 4 after two-segment scanning, it is necessary to ensure that a signal of more than 8 complete cycles is obtained after the optical path is completely scanned.
  • step 4 when the signal is filtered in sections, the detection signals corresponding to the two optical paths are first subjected to Fourier transform to filter out the DC component, the zero frequency component of the original signal is filtered out, and then the inverse Fourier transform is used to The signal is restored.
  • step 4 the Hilbert transform expression is:
  • the instantaneous phase expression of the transformed signal is:
  • S(x) is the Hilbert transform signal
  • s(x) Are the real and imaginary parts of the signal, Is the phase of the signal.
  • step 4 the method for calculating the refractive index of the material according to the phase change is:
  • n mat is the refractive index of the material
  • C is the speed of light
  • L mat is the material thickness
  • ⁇ THz is the terahertz signal frequency
  • step 4 increase the thickness of the material, and by accumulating the thickness of the material, the phase jump value, that is, the phase change caused by inserting materials of different thicknesses in the terahertz path, is measured So as to find the material thickness and the slope of the phase fitting line
  • the refractive index of the material can be calculated, and the specific formula is:
  • n mat is the refractive index of the material
  • c is the speed of light
  • L mat is the material thickness
  • ⁇ THz is the terahertz signal frequency
  • the present invention has significant advantages: 1) Using a simple optical path system, the refractive index and other parameters of a variety of non-polar substances can be measured at room temperature, and the measurement resolution reaches the micron level; 2 ) Calculate the material refractive index by statistically calculating the instantaneous phase mutation of the signal when inserting the material, and accumulate the material thickness for multiple repeated measurements, which improves the accuracy, stability and efficiency of the measurement; 3) It has good technical portability, It is not only suitable for refractive index detection of some materials, but also suitable for industrial inspection, especially non-destructive inspection.
  • Fig. 1 is a schematic diagram of the optical path of the material refractive index measurement system of the present invention.
  • Figure 2 is an example diagram of the voltage response of the detected terahertz signal.
  • Figure 3 is an example diagram of a filtered terahertz signal.
  • Figure 4 is an example diagram of phase jump after Hilbert transform.
  • Figure 5 is an example diagram of the corresponding relationship between the thickness of the superimposed material and the phase jump value.
  • the system for measuring the refractive index of different materials in the terahertz band includes: a terahertz source fixed on an optical platform, a detector fixed on a motorized translation stage, and an electronic optical system, including:
  • the terahertz source uses a continuous wave terahertz source, which can efficiently and stably generate continuous terahertz radiation waves.
  • the continuous wave terahertz source uses a VDI terahertz band signal source expansion system at room temperature, and cooperates with a frequency multiplier and a function signal generator to stably amplify the signal to the terahertz band.
  • the function signal generator can generate specific periodic time function waveforms with different frequencies.
  • the function signal generator uses TTL pulse waves for signal modulation.
  • the frequency of TTL pulse modulation depends on the response speed of the detector (10-100k), and the selected operating frequency is 0.18T-0.6THz.
  • the detector is fixed on the electric displacement stage to maintain the alignment of the optical path, so that the terahertz signal (including the terahertz signal that has not passed through the dielectric material and the terahertz signal after passing through the dielectric material) is received by the detector in collimation.
  • the Schottky detector has the advantages of strong nonlinearity, fast speed, and ability to work at room temperature.
  • a Schottky detector with a cut-off frequency up to the terahertz band is used to achieve frequency multiplication or mixing of the terahertz signal. This is because the Schottky detector has frequency-selective characteristics and can be smaller at certain frequencies.
  • the terahertz signal is detected lossy, and the signal is multiplied.
  • the electro-optical system includes an electric displacement control module, a signal readout module, and a signal processing module.
  • the electric displacement control module controls the detector to maintain collimation in the optical path and move backward (away from the terahertz source) to collimate. Scan the terahertz signal in the path; the signal readout module uses a lock-in amplifier to convert the terahertz signal received by the detector into an electrical signal (periodically changing voltage signal) and read it out; the signal processing module responds to the detector's response signal Perform digital processing, uniformly digitally filter the signal, filter out the DC component, and obtain the final periodically changing terahertz signal, and analyze and determine the refractive index of the material.
  • the electronic optical system uses a Labview control program to interconnect the terahertz source, the function signal generator, the detector, and the lock-in amplifier to read out the signal.
  • the method of measuring the refractive index of different materials in the terahertz band includes the following steps:
  • Step 1 The terahertz source generates a continuous wave terahertz signal, which is received by the detector collimatedly through an optical path in free space;
  • Step 2 When scanning the free space optical path between the terahertz source and the detector, the detector first scans the first half of the optical path (the half of the path close to the terahertz source) distance, and then inserts the dielectric material in the middle of the scanning path, and continues again Scan the second half of the optical path backward (the other half of the distance away from the terahertz source).
  • the terahertz signal passes through the dielectric material and is received by the detector fixed on the electric stage and moving backward;
  • Step 3 The detector converts the received terahertz signal into an electrical signal, and reads out the response signal information through the lock-in amplifier;
  • terahertz (THz) signal As the distance between the terahertz source and the detector changes, the terahertz (THz) signal will continue to change.
  • the sine expression of a terahertz signal can be written as:
  • K THz is the wave number
  • ⁇ THZ is the terahertz wavelength
  • S 1 is the original signal generated by the terahertz source
  • L THz is the distance of the free path between the terahertz source and the detector
  • the formula (2) is the expression for accumulating and summing the odd multiples of the THz signal S n , where n is the refractive index and nodd is the number of S n;
  • Step 4 Perform segmental filtering on the two segments of signals obtained above (the two segments of signals scanned by the detector before and after inserting the material) to filter out the DC component, and then perform signal analysis and processing through Hilbert and other mathematical transformations to obtain The instantaneous phase of the signal, and then the refractive index is calculated based on the phase jump value when the material is inserted.
  • the signal obtained after scanning is a periodic voltage signal.
  • the detection signals corresponding to the two optical paths are first subjected to Fourier transform (FFT) to filter out the DC component and the zero of the original signal.
  • FFT Fourier transform
  • IFFT inverse Fourier transform
  • Hilbert transform can delay the phase of all frequency components of the signal by 90 degrees, and is mainly used to solve the envelope, instantaneous phase and instantaneous frequency of the signal.
  • the signal Hilbert transform expression is:
  • the instantaneous phase expression of the transformed signal is:
  • the optical path length is n air L, n air ⁇ 1, L is the optical path length, and n air is the refractive index of the air medium;
  • the optical path length is n air (LL mat )+ n mat L mat , n mat is the refractive index of the material, and L mat is the material thickness;
  • ⁇ THz is the signal frequency. It can be seen from the formula (6) that the phase change caused by the insertion of the dielectric material is detected The refractive index n mat of the material can be calculated.
  • the present invention proposes a terahertz detection system based on continuous wave coherent measurement.
  • the system uses only continuous terahertz sources and detectors without other additional optical components. It scans the space path of the detector to obtain phase-related voltage signals. By analyzing the phase signal, the dielectric constant of the sample can be obtained.
  • This system and method for measuring the refractive index of materials by using the phase coherence effect of terahertz has the advantages of simple optical path system, high measurement efficiency, high precision, and strong reusability. It can be used for testing and testing the dielectric constant of terahertz band materials. Characterization, especially for the non-destructive online detection of industrial products, such as paper, plastic, paint, glass, oily gas, etc., has great commercial value.
  • the signal is then subjected to Hilbert transform (Hilbert), and the instantaneous phase of the signal can be obtained after the transformation.
  • Hilbert transform Hilbert transform
  • matlab software is used to perform the Hilbert transform to obtain the instantaneous phase of the signal.
  • the arctangent function expressing the instantaneous phase is a periodic function
  • the unwrap function is used here to unwrap the obtained instantaneous phase.
  • the arctangent function in the computer stipulates that the angle in the first and second quadrants is 0 ⁇ , and the angle in the third and fourth quadrants is 0 ⁇ - ⁇ . If an angle changes from 0 to 2 ⁇ , the actual result is 0 ⁇ , Then from - ⁇ to 0, the phase of the signal is wrapped.
  • the unwrap function makes the phase not jump at ⁇ , thereby reflecting the real phase change, and can check the data phase jump, and correct the jump.
  • the unwrap function checks that the difference between the two points before and after the data exceeds ⁇ . , It is considered that there is a jump, and +2 ⁇ or -2 ⁇ will be used to correct the jump to make the data continuous.
  • Figure 4 is the instantaneous phase of the signal obtained after phase unwrapping.
  • Figure 4 can read the jump value of the signal phase.
  • the phase jump value read out is calculated by formula (4) to obtain the refractive index of the sample material.
  • the thickness of the material is increased.
  • the phase jump value caused by the insertion of materials of different thicknesses in the terahertz path is measured, the slope of the fitting straight line is calculated, and the refractive index is further calculated.
  • Figure 5 shows the phase jump value of the cumulative paper thickness, and the refractive index of the material is calculated by calculating the slope of the fitted straight line.
  • the final measured refractive index of the paper sheet at 0.216THz is 1.632, and the refractive index of the glass sheet and plastic film at 0.216THz are shown in Table 1.
  • the refractive index measured in this experiment at 0.216THz is 1.632, which is within a reasonable range compared with the published value measured by other methods.
  • the published value of the refractive index of the polyester film at 194.4GHz is 2.19, 1.83 at 140GHz, and 2.0 to 2.2 in the range of 225-250GHz.
  • the refractive index of the plastic film measured in this experiment is 2.04, and the measured value is in the open Within range.
  • the present invention fills the gap in the measurement of the refractive index of materials by the terahertz continuous wave, and ensures the measurement accuracy of the refractive index compared with other measurement methods.

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Abstract

一种在太赫兹波段测量材料折射率的系统及方法，系统包括太赫兹源(1)、探测器(3)和电子光学系统，其中太赫兹源(1)产生连续的太赫兹辐射波；探测器(3)接收太赫兹信号；电子光学系统中电动位移控制模块控制探测器保持准直并向远离太赫兹源的方向移动；信号读出模块将接收到的太赫兹信号转化为电信号；信号处理模块对电信号进行数字化处理和滤波，得到周期性变化的太赫兹信号分析确定折射率。方法为先对插入样品材料(2)前后探测器(3)扫描到的两段信号进行分段滤波，滤除其中的直流分量，然后通过希尔伯特等数学变换进行信号分析处理，得到信号的瞬时相位，再根据插入样品材料(2)前后的相位跳变值计算出折射率。该系统和方法实现了基于太赫兹连续波的高精度材料折射率测量。

Description

一种在太赫兹波段测量材料折射率的系统及方法 技术领域
本发明涉及常温太赫兹探测技术，具体涉及一种在太赫兹波段测量不同材料折射率的系统及方法。
背景技术
太赫兹(Terahertz，简称THz)波一般是指频率在0.3T到10THz(波长为30μm到1mm)范围内的电磁波，该电磁波段介于亚毫米波和远红外之间。由于太赫兹波对于很多非极性物质，如部分电介质材料、塑料薄膜、纸张、布料等有较强的穿透力，因此太赫兹检测技术也被应用于质检、安全检查以及工业无损检测等场景当中。
在过去的二十年中，太赫兹技术的许多应用已经被讨论过，从生物分子的光谱学、国土安全、太赫兹通信等领域到工业检测都有广泛应用。在工业检测当中，材料参数的表征对于近年来的半导体工业和纳米光子技术非常重要。在光学波段，测量材料介电常数的方法和设备有很多，比如说椭偏仪、光谱仪等常用设备，通过测试能迅速获得材料的介电常数，但是这些设备通过材料对入射光的反射或透射来反演材料的光学参数。然而，目前的太赫兹源和探测器的性能还远达不到光学波段的光源和探测器的性能，因此通过反射或透射的测量目前只适合测量材料光学波段的介电常数，在太赫兹波段的实现还存在困难。尽管基于昂贵的飞秒激光器的太赫兹时域光谱仪已经问世，这种太赫兹测量系统中太赫兹源是脉冲式的，而非连续太赫兹光源。但是这种脉冲太赫兹系统光路复杂，使用了很多光学元件，系统调试耗时长，效率较低，成本很高，因此开发基于连续太赫兹源的测量系统具有显著优势。此外，微波波段测量材料的介电常数的方法也有很多，比如说矩形波导法、准光耦合方法，这些矩形波导系统和准光部件在微波波段尺寸大机械加工容易，但到了太赫兹波段，入射波长变小，对应的测量系统部件尺寸也相应减少，加工精度要求10微米以上，这给机械加工带来了极大的困难。因此，在太赫兹测量领域，高效率且高精度地表征材料参数仍然是目前研究的难题之一。
发明内容
本发明的目的在于提供一种在太赫兹波段测量材料折射率的系统及方法。
实现本发明目的的技术解决方案为：一种在太赫兹波段测量材料折射率的系统，包括固定于光学平台上的太赫兹源，固定于电动位移台上的探测器，以及电子光学系统，其中：
所述太赫兹源使用连续波太赫兹源，用于产生连续的太赫兹辐射波；
所述探测器固定在电动位移台上，用于准直的扫描光路中的太赫兹信号，包括未通过介质材料的太赫兹信号和通过介质材料后的太赫兹信号；
所述电子光学系统包括电动位移控制模块、信号读出模块和信号处理模块，其中电动位移控制模块用于控制探测器在光路中保持准直并向远离太赫兹源的方向移动，准直地在路径中扫描太赫兹信号；信号读出模块用于将探测器接收到的太赫兹信号转化为电信号，并利用锁相放大器读出；信号处理模块用于对探测器的响应信号进行数字化处理和滤波，得到最终的周期性变化的太赫兹信号，分析确定材料折射率。
进一步的，所述连续波太赫兹源包括VDI太赫兹频段信号源、倍频器与函数信号发生器。
进一步的，所述探测器采用肖特基探测器。
一种在太赫兹波段测量不同材料折射率的方法，包括以下步骤：
步骤一：太赫兹源产生连续波太赫兹信号，通过自由空间的光学路径准直地被探测器接收到；
步骤二：在扫描太赫兹源和探测器之间的自由空间光路时，探测器先扫描靠近太赫兹源的一半距离，然后在扫描路径的中间位置插入介质材料，继续再向远离太赫兹源的另一半距离，扫描过程中太赫兹信号透过介质材料准直地被固定在电动位移台上并向后移动的探测器接收到；
步骤三：探测器将接收到的太赫兹信号转换为电信号，并通过锁相放大器读出响应信号信息；
步骤四：对插入材料前后探测器扫描到的两段信号先进行分段滤波，滤除其中的直流分量，然后通过希尔伯特等数学变换进行信号分析处理，得到信号的瞬时相位，再根据插入材料前后的相位跳变值计算出折射率。
进一步的，步骤4中，经过两段扫描后，需要保证完整扫描光路后得到8个以上的完整周期的信号。
进一步的，步骤4中，对信号进行分段滤波时，先对两段光路对应的检测信号分别进行傅立叶变换滤除其中的直流分量，滤除原始信号的零频分量后再通过傅立叶反变换将信号恢复。
进一步的，步骤4中，希尔伯特变换表达式为：
Figure PCTCN2020123740-appb-000001
经过变换得到的虚部为：
Figure PCTCN2020123740-appb-000002
变换后信号的瞬时相位表达式为：
Figure PCTCN2020123740-appb-000003
其中，S(x)为进行希尔伯特变换的信号，s(x)、
Figure PCTCN2020123740-appb-000004
分别为信号的实部和虚部，
Figure PCTCN2020123740-appb-000005
为信号的相位。
进一步的，步骤4中，根据相位变化计算出材料折射率的方法为：
Figure PCTCN2020123740-appb-000006
其中，n mat为材料的折射率，
Figure PCTCN2020123740-appb-000007
为插入介质材料带来的相位变化，C为光速，L mat为材料厚度，ν THz为太赫兹信号频率。
进一步的，步骤4中，增加材料的厚度，通过对材料的厚度进行累计，测出在太赫兹路径中插入不同厚度材料引起的相位跳变值即相位变化
Figure PCTCN2020123740-appb-000008
从而求出材料厚度和相位拟合直线的斜率
Figure PCTCN2020123740-appb-000009
即可计算材料的折射率，具体公式为：
Figure PCTCN2020123740-appb-000010
其中，n mat为材料的折射率，
Figure PCTCN2020123740-appb-000011
为插入介质材料带来的相位变化，c为光速，L mat为材料厚度，ν THz为太赫兹信号频率。
本发明与现有技术相比，其显著优点在于：1)采用简洁的光路系统，在室温下即可测量多种非极性物质的折射率等参数，测量的分辨率达到了微米级别；2)利用插入材料时带来的信号瞬时相位突变统计计算材料折射率，并累计材料厚度多次重复测量，提高了测量的精度、稳定性和和效率；3)具有很好的技术 可移植性，不仅适用于部分材料的折射率检测，也适用于工业检测尤其是无损检测。
附图说明
图1为本发明材料折射率测量系统的光路示意图。
图2为检测的太赫兹信号电压响应示例图。
图3为滤波后的太赫兹信号示例图。
图4为希尔伯特变换后的相位跳变示例图。
图5为叠加材料厚度与相位跳变值的对应关系示例图。
具体实施方式
下面结合附图和具体实施例，进一步说明本发明方案。
如图1所示，在太赫兹波段测量不同材料折射率的系统，包括：固定于光学平台上的太赫兹源，固定于电动位移台上的探测器，以及电子光学系统，其中：
所述太赫兹源使用连续波太赫兹源，其能高效、稳定地产生连续的太赫兹辐射波。所述连续波太赫兹源在常温下，使用VDI太赫兹频段信号源扩展系统，配合倍频器与函数信号发生器将信号稳定放大至太赫兹波段。所述函数信号发生器能产生不同频率的特定的周期性时间函数波形。一些实施例中，函数信号发生器使用TTL脉冲波进行信号调制，TTL脉冲调制的频率取决于探测器的响应速度(10-100k)，选取的工作频率为0.18T-0.6THz。
所述探测器固定在电动位移台上保持光路的准直，使得太赫兹信号(包括未通过介质材料的太赫兹信号和通过介质材料后的太赫兹信号)准直地被探测器接收到。由于肖特基探测器具有非线性强、速度快、能够常温工作的优点。一些实施例中，利用截止频率达太赫兹波段的肖特基探测器实现太赫兹信号的倍频或混频，这是由于肖特基探测器具有选频特性，在某些频率上能较小损耗地探测到太赫兹信号，实现信号的倍频。
所述电子光学系统包括电动位移控制模块、信号读出模块和信号处理模块，其中电动位移控制模块控制探测器在光路中保持准直并向后(远离太赫兹源的方向)移动，准直地在路径中扫描太赫兹信号；信号读出模块利用锁相放大器将探测器接收到的太赫兹信号转化为电信号(周期性变化的电压信号)并读出；信号处理模块对探测器的响应信号进行数字化处理，将信号统一进行数字滤波，滤除其中直流分量，得到最终的周期性变化的太赫兹信号，分析确定材料折射率。作 为一种具体实施方式，所述电子光学系统通过使用Labview控制程序将太赫兹源、函数信号发生器、探测器以及锁相放大器互联，从而读出信号。
由于光路中插入材料时，探测器检测到的信号也将发生变化，因此，可以通过检测插入材料带来的相位跳变可以快速提取样品材料的折射率。此外，由于太赫兹波的高度相干性，太赫兹波在光路中多次往返传播，检测到的信号为太赫兹相干波。因此，对检测的相干波进行频谱分析，从而获得信号的幅度和相位等信息，进一步可以计算出材料的折射率。基于上述分析，在太赫兹波段测量不同材料折射率的方法，包括以下步骤：
步骤一：太赫兹源产生连续波太赫兹信号，通过自由空间的光学路径准直地被探测器接收到；
步骤二：在扫描太赫兹源和探测器之间的自由空间光路时，探测器先扫描前一半光路(靠近太赫兹源的一半路径)距离，然后在扫描路径的中间位置插入介质材料，继续再向后扫描光路的后一半(远离太赫兹源的另一半距离)距离，扫描过程中太赫兹信号透过介质材料准直地被固定在电动位移台上并向后移动的探测器接收到；
步骤三：探测器将接收到的太赫兹信号转换为电信号，并通过锁相放大器读出响应信号信息；
由于太赫兹源和探测器之间的距离的改变，太赫兹(THz)信号将不断变化。太赫兹信号的正弦表达式可以写为：
Figure PCTCN2020123740-appb-000012
其中，K THz为波数，
Figure PCTCN2020123740-appb-000013
λ THZ为太赫兹波长；S 1为太赫兹源产生的原始信号；L THz为太赫兹源到探测器之间的自由路径的距离；
Figure PCTCN2020123740-appb-000014
为信号的初相，
Figure PCTCN2020123740-appb-000015
与自由路径的光路距离有关。
通过移动探测器，L THz将不断改变。由于天线之间的反射会经过奇数倍次的光路距离，即会导致奇数倍的THz检测信号。因此公式(1)实际需要写成：
Figure PCTCN2020123740-appb-000016
公式(2)即为对奇数倍的THz信号S n进行累加求和的表达式，其中n为折射率，nodd为S n的个数；
步骤四：对上述获取的两段信号(插入材料前后探测器扫描到的两段信号)先进行分段滤波，滤除其中的直流分量，然后通过希尔伯特等数学变换进行信号分析处理，得到信号的瞬时相位，再根据插入材料时的相位跳变值计算出折射率。
经过两段扫描后，需要保证完整扫描光路后可以得到8个以上的完整周期的信号。扫描后得出的信号为周期性的电压信号，对信号进行分段滤波时，先对两段光路对应的检测信号分别进行傅立叶变换(FFT)滤除其中的直流分量，滤除原始信号的零频分量后再通过傅立叶反变换(IFFT)将信号恢复。信号的傅立叶变换可以表示为：
Figure PCTCN2020123740-appb-000017
其中a为电动位移台移动速度，x为移动的距离，x＝at，x与a成正比。
Hilbert变换能把信号的所有频率分量的相位推迟90度，主要用于求解信号的包络、瞬时相位以及瞬时频率。信号希尔伯特变换表达式为：
Figure PCTCN2020123740-appb-000018
经过变换得到的虚部为：
Figure PCTCN2020123740-appb-000019
变换后信号的瞬时相位表达式为：
Figure PCTCN2020123740-appb-000020
由公式(5)，即可获得信号的瞬时相位。因此，信号的相位变化就可以直接获得。
当光路中没有材料时的光程为n airL,n air≈1，L为光程，n air为空气介质的折射率；当光路中插入材料后的光程为n air(L-L mat)+n matL mat，n mat为材料折射率，L mat为材料厚度；光程差则为△L＝(n mat-1)L mat，相位差为
Figure PCTCN2020123740-appb-000021
进一步相位差
Figure PCTCN2020123740-appb-000022
可以改写为：
Figure PCTCN2020123740-appb-000023
其中，ν THz为信号频率。通过公式(6)可以看出，检测插入介质材料带来的相位变化
Figure PCTCN2020123740-appb-000024
可以计算出材料的折射率n mat。
进一步，为了提高实验结果精度，减小系统实验的偶然性误差，通过不断累积样品材料的厚度，从一片样品累计到多片样品，扫描光路插入不同样品厚度的时的太赫兹信号，并重复上述的实验步骤来以此方法可以减小系统实验的偶然性误差，提高测量精度。
对公式6进行变形，可以得到：
Figure PCTCN2020123740-appb-000025
从公式(7)可以看出，增加材料的厚度，通过对材料的厚度L mat进行累计，测出在太赫兹路径中插入不同厚度材料引起的相位跳变值即相位变化值
Figure PCTCN2020123740-appb-000026
求出拟合直线的斜率
Figure PCTCN2020123740-appb-000027
即可计算出折射率。
本发明提出基于连续波相干测量的太赫兹检测系统，该系统仅使用连续太赫兹源和探测器而不需要其他额外的光学部件，通过探测器空间路径扫描，获得与相位有关的电压信号，通过对该相位信号进行分析就可以获得样品的介电常数。这种利用太赫兹的相位相干效应测量材料折射率的系统和方法具有光路系统简单、测量效率高、精度高、可复用性强等优点，可用于太赫兹波段材料的介电常数的测试和表征，尤其可以用于工业产品，如纸张，塑料，油漆，玻璃，油污气体等的无损在线检测，商业价值很大。
实施例
为了验证本发明方案的有效性，选取不同厚度的标准A4纸片、塑料薄膜、玻璃片进行仿真实验。在扫描太赫兹路径时，控制电动位移台移动探测器，先扫描光学路径的前一半距离，如图1所示的材料右侧的L1表示的这段距离，再将介质材料固定在扫描光路的中间放置，控制电动位移台向继续向后(远离太赫兹源的方向)移动探测器，移动距离为L2，如图1所示。本实施例中，设置移动步数为200步，步长为25μm。在第100步的位置(L1与L2的中间位置)插入材料，图2展示了随着探测器的移动检测到的响应电压。
然后对l1，L2这两段光路对应的检测信号进行分段滤波。对两段信号分别进行傅立叶变换滤除直流分量，通过FFT(傅立叶变换)滤除原始信号的零频分量后再通过IFFT(傅立叶反变换)将信号恢复。图3展示了滤波之后的太赫兹信号，可以从图中看出在插入材料的位置有明显的相位跳变。
为了求出信号的相位变化，接着对信号进行希尔伯特变换(Hilbert)，变换后即可获得信号的瞬时相位。本实施例使用matlab软件进行希尔伯特变换，求出信号的瞬时相位。由于表达瞬时相位的反正切函数是一个周期函数，这里使用unwrap函数对求出的瞬时相位进行解包裹。计算机中反正切函数规定，在一、二象限中的角度为0～π，三四象限的角度为0～-π，若一个角度从0变到2π，但实际得到的结果是0～π，再由-π～0，信号的相位就产生了包裹。unwrap函数使相位在π处不发生跳变，从而反应出真实的相位变化，并能够检查出数据相位跳变，并纠正跳变，unwrap函数在检查到数据前后两点的差距在超过π的时候，就认为有跳变，并会+2π或者-2π来纠正跳变，使得数据连续。如图4所示，图4是相位解包裹后得到信号的瞬时相位。通过图4可以读出信号相位的跳变值。进一步将读出的相位跳变值通过公式(4)，求出样品材料的折射率。
为了进一步提高精度，减小误差。本实施例增加材料的厚度，通过对材料的厚度L mat进行累计，测出在太赫兹路径中插入不同厚度材料引起的相位跳变值，求出拟合直线的斜率，进一步计算出折射率，如图5所示。图5展示了累计纸片厚度的相位跳变值，通过计算拟合直线的斜率求出材料的折射率。最终测得纸片在0.216THz下的折射率为1.632，以及玻璃片、塑料薄膜在0.216THz下的折射率如表1所示。
表1各材料测得的折射率
材料 密度(g/cm^3) 折射率
标准A4纸片 0.75 1.632
玻璃片 2.53 1.549
塑料薄膜 0.96 2.04
对于纸张来说，本实验在0.216THz下测得的折射率为1.632，跟其他方法测量的公开值相比，测量值处于合理的范围内。聚脂薄膜在194.4GHz处的折射率公开值为2.19，在140GHz时为1.83，在225–250GHz的范围内为2.0至2.2，本实验中测得的塑料薄膜折射率为2.04，测量值处于公开范围内。综上所述，本发明填补了太赫兹连续波测量材料折射率的空白，相比其他测量方法，保证了折射率的测量精度。

Claims (10)

  1. 一种在太赫兹波段测量材料折射率的系统，其特征在于，包括固定于光学平台上的太赫兹源，固定于电动位移台上的探测器，以及电子光学系统，其中：
    所述太赫兹源使用连续波太赫兹源，用于产生连续的太赫兹辐射波；
    所述探测器固定在电动位移台上，用于准直的扫描光路中的太赫兹信号，包括未通过介质材料的太赫兹信号和通过介质材料后的太赫兹信号；
    所述电子光学系统包括电动位移控制模块、信号读出模块和信号处理模块，其中电动位移控制模块用于控制探测器在光路中保持准直并向远离太赫兹源的方向移动，准直地在路径中扫描太赫兹信号；信号读出模块用于将探测器接收到的太赫兹信号转化为电信号，并利用锁相放大器读出；信号处理模块用于对探测器的响应信号进行数字化处理和滤波，得到最终的周期性变化的太赫兹信号，分析确定材料折射率。
  2. 根据权利要求1所述的在太赫兹波段测量材料折射率的系统，其特征在于，所述连续波太赫兹源包括VDI太赫兹频段信号源、倍频器与函数信号发生器。
  3. 根据权利要求1所述的在太赫兹波段测量材料折射率的系统，其特征在于，所述探测器采用肖特基探测器。
  4. 一种在太赫兹波段测量不同材料折射率的方法，其特征在于，包括以下步骤：
    步骤一：太赫兹源产生连续波太赫兹信号，通过自由空间的光学路径准直地被探测器接收到；
    步骤二：在扫描太赫兹源和探测器之间的自由空间光路时，探测器先扫描靠近太赫兹源的一半距离，然后在扫描路径的中间位置插入介质材料，继续再向远离太赫兹源的另一半距离，扫描过程中太赫兹信号透过介质材料准直地被固定在电动位移台上并向后移动的探测器接收到；
    步骤三：探测器将接收到的太赫兹信号转换为电信号，并通过锁相放大器读出响应信号信息；
    步骤四：对插入材料前后探测器扫描到的两段信号先进行分段滤波，滤除其中的直流分量，然后通过希尔伯特等数学变换进行信号分析处理，得到信号的瞬时相位，再根据插入材料前后的相位跳变值计算出折射率。
  5. 根据权利要求4所述的在太赫兹波段测量不同材料折射率的方法，其特征在于，步骤2中，两段扫瞄的距离相等。
  6. 根据权利要求4所述的在太赫兹波段测量不同材料折射率的方法，其特征在于，步骤4中，经过两段扫描后，需要保证完整扫描光路后得到8个以上的完整周期的信号。
  7. 根据权利要求4所述的在太赫兹波段测量不同材料折射率的方法，其特征在于，步骤4中，对信号进行分段滤波时，先对两段光路对应的检测信号分别进行傅立叶变换滤除其中的直流分量，滤除原始信号的零频分量后再通过傅立叶反变换将信号恢复。
  8. 根据权利要求4所述的在太赫兹波段测量不同材料折射率的方法，其特征在于，步骤4中，希尔伯特变换表达式为：
    Figure PCTCN2020123740-appb-100001
    经过变换得到的虚部为：
    Figure PCTCN2020123740-appb-100002
    变换后信号的瞬时相位表达式为：
    Figure PCTCN2020123740-appb-100003
    其中，S(x)为进行希尔伯特变换的信号，s(x)、
    Figure PCTCN2020123740-appb-100004
    分别为信号的实部和虚部，
    Figure PCTCN2020123740-appb-100005
    为信号的相位。
  9. 根据权利要求4所述的在太赫兹波段测量不同材料折射率的方法，其特征在于，步骤4中，根据相位变化计算出材料折射率的方法为：
    Figure PCTCN2020123740-appb-100006
    其中，n mat为材料的折射率，
    Figure PCTCN2020123740-appb-100007
    为插入介质材料带来的相位变化，C为光速，L mat为材料厚度，ν THz为太赫兹信号频率。
  10. 根据权利要求4所述的在太赫兹波段测量不同材料折射率的方法，其特征在于，步骤4中，增加材料的厚度，通过对材料的厚度进行累计，测出在太赫兹路径中插入不同厚度材料引起的相位跳变值，即相位变化
    Figure PCTCN2020123740-appb-100008
    从而求出材料厚度和相位拟合直线的斜率
    Figure PCTCN2020123740-appb-100009
    即可计算材料的折射率，具体公式为：
    Figure PCTCN2020123740-appb-100010
    其中，n mat为材料的折射率，
    Figure PCTCN2020123740-appb-100011
    为插入介质材料带来的相位变化，c为光速，L mat为材料厚度，ν THz为太赫兹信号频率。
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