CN105181624A - Scattering analogy-based terahertz spectroscopy quantitative analysis method - Google Patents

Abstract

The invention relates to a terahertz spectrum quantitative analysis method based on scattering analogy, and belongs to the technical field of terahertz spectrum application. The present invention performs terahertz time-domain spectrum detection on three pure polyethylene (PE) tablet samples with different concentrations, obtains their terahertz absorption spectra and performs average calculation, and uses the average calculated PE terahertz absorption spectra to characterize the scattering effect ; Obtain the terahertz absorption spectrum of the mixture sample and the simple substances in the mixture respectively; the terahertz absorption spectrum of the sample measured in the experiment is actually composed of two parts: the absorption of the terahertz wave by the sample itself and the attenuation caused by the scattering effect. Establish the terahertz absorption spectrum model of the mixture sample measured in the experiment; establish the relationship between the terahertz absorption spectrum of the mixture sample, the terahertz absorption spectrum of each component in the mixture and the PE terahertz absorption spectrum based on the principle of analog scattering; use The least square algorithm calculates the concentration of each component in the mixture.

Description

A Quantitative Analysis Method of Terahertz Spectroscopy Based on Scattering Analogy

technical field

The invention relates to a terahertz spectrum quantitative analysis method based on scattering analogy, and belongs to the technical field of terahertz spectrum application.

Background technique

In recent years, with the development of ultrafast laser technology, a series of effective methods have been provided for the generation and detection of terahertz waves. As a band in the electromagnetic spectrum, terahertz (THz, 1THz=10 ¹² Hz) waves have not been deeply developed and utilized for a long time due to the lack of effective generation sources and detection devices, so that they have been ignored for a long time. Called the "terahertz gap". Due to the unique characteristics of terahertz waves, it has shown great potential in many fields, such as material identification, medicine, security inspection and astronomical observation. Among them, quantitative analysis based on terahertz absorption spectrum is one of the most important application directions of terahertz technology.

At present, the methods applied in the field of terahertz quantitative analysis mainly include least squares and partial least squares. As early as 2007, Professor Zhang Zhaohui of Beijing University of Science and Technology and others analyzed the terahertz absorption spectra of three L-type amino acids such as cysteine, asparagine and threonine and their mixtures, and used the least squares method to analyze the The concentration of each component was calculated and good results were obtained. Chen Tao from Guilin University of Electronic Science and Technology studied the application of the partial least squares-based characteristic spectral region screening method in the quantitative analysis of terahertz spectroscopy. Experiments show that the root mean square error of interactive verification using the moving window partial least squares method can reach 0.9803, which proves that this method can effectively detect the component content of multivariate mixtures quickly.

However, the prior art has neglected the influence of the scattering effect in the field of terahertz quantitative analysis. Especially when the particle size of the sample is close to the wavelength of the incident wave, severe scattering will occur. The absorption spectrum measured at this time is composed of two parts, that is, the absorption of the incident light by the sample itself and the attenuation caused by the scattering effect. The previous analytical methods only considered the absorption of the sample itself, but ignored the scattering effect, which made the accuracy of quantitative analysis not high.

Contents of the invention

The purpose of the present invention is to provide a terahertz spectral quantitative analysis method based on scattering analogy, to solve the problem that only the absorption of the sample itself is considered in the current terahertz spectral quantitative analysis, and the scattering effect is ignored, which leads to the problem of quantitative analysis. A technical problem with low accuracy of results.

In order to solve the above technical problems, the present invention provides a method for quantitative analysis of terahertz spectrum based on scattering analogy. The method includes the following steps:

1) Perform terahertz time-domain spectral detection on three pure polyethylene (PE) tablet samples with different concentrations, obtain their terahertz absorption spectra and perform average calculations, and use the averaged PE terahertz absorption spectra to characterize the scattering effect ;

2) Perform terahertz time-domain spectral detection on the mixture sample and each component element in the mixture to obtain its terahertz absorption spectrum;

3) The terahertz absorption spectrum of the sample measured in the experiment includes two parts, namely the absorption of the terahertz wave by the sample itself and the attenuation caused by the scattering effect, based on which the model of the terahertz absorption spectrum of the mixture sample measured in the experiment is established;

4) According to the principle of analog scattering, transform the terahertz absorption spectrum model of the mixture sample in step 3) to obtain the transformed terahertz absorption spectrum model of the mixture sample, so as to establish the terahertz absorption spectrum model of the mixture sample and The relationship between the terahertz absorption spectrum of each component in the mixture and the PE terahertz absorption spectrum;

5) Use the least squares algorithm to calculate the concentration of each component in the mixture.

The terahertz absorption spectrum model of the mixture sample in step 3) is:

(1)

Where ω _i is the frequency, α _{mix_e} is the terahertz absorption coefficient of the mixture sample obtained through experiments, α _{mix_s} is the scattering coefficient of the mixture sample, the subscripts 1, 2,..., n represent various components in the mixture, and the subscript e Indicates obtained through experiments, subscript s represents the scattering coefficient of the sample, that is, α _{1_e} is the terahertz absorption coefficient of the first component obtained through the experiment, α _{2_e} is the terahertz absorption coefficient of the second component obtained through the experiment, α _{1_s} is the scattering coefficient of the first component, α _{2_s} is the scattering coefficient of the second component, and so on. c1 is the concentration of the _first sample in the mixture, c2 is the concentration of the _second sample in the mixture, and so on.

The principle of analog scattering in step 4) is:

(2)

Where α _PE is the averaged PE absorption coefficient, k ₁ , k ₂ ,..., k _n , k _mix are dimensionless coefficients related to the scattering of each component in the mixture and the mixture.

The terahertz absorption spectrum model of the transformed mixture sample in step 4) is:

(3)

(4)

where K is a dimensionless coefficient related to scattering.

The least squares algorithm in the step 5) is:

make , , ,

Then formula (3) can be expressed as:

(5)

Among them, MIX is the absorption coefficient matrix of the mixture sample, A is the absorption coefficient matrix of each component simple substance and PE in the mixture, and C is the concentration matrix of each component in the mixture including the scattering coefficient K. Then there are:

(6)

The beneficial effects of the present invention are: the present invention proposes a terahertz absorption spectrum model of the mixture on the basis of analyzing the terahertz band scattering effect of the mixture sample and adopting an analogy method. When the least square method is used to quantitatively analyze the mixture, the influence of the scattering effect is considered, thereby improving the accuracy of the quantitative analysis. A good application effect has been achieved. At the same time, it is verified through quantitative analysis experiments that the invention can realize accurate quantitative analysis of the concentration of the mixture.

Description of drawings

Fig. 1. Algorithm flow chart of the present invention

Figure 2. SEM images of mixture samples (glutamine, histidine)

Fig. 3. Terahertz absorption spectrum (dashed line) and its average value (solid line) of pure PE pellets

Figure 4. Molar absorption coefficient spectra of glutamine, histidine, and threonine

Figure 5. Terahertz absorption spectra of a glutamine-histidine mixture sample (dashed line) and a histidine-threonine mixture sample (solid line).

Detailed ways

The specific embodiments of the present invention will be further described below in conjunction with the accompanying drawings. The invention provides a method for quantitative analysis of terahertz spectrum based on scattering analogy, in which influence caused by scattering is considered when quantitatively analyzing terahertz spectrum. Through a series of experiments, it is proved that taking the scattering effect into account in the quantitative analysis of the mixture can improve the accuracy of quantitative analysis.

Severe scattering occurs when the particle size of the sample is close to the wavelength of the incident wave. The absorption spectrum of the sample measured at this time consists of two parts, namely the absorption of the incident light by the sample itself and the attenuation caused by the scattering effect:

where α _e is the terahertz absorption coefficient of the sample, α _in is the absorption of the sample itself, and α _s is the attenuation caused by the scattering effect, also known as the scattering coefficient.

According to the description of Lambert Beer's law, the absorption of light by a substance is proportional to its concentration, and the absorption coefficient of a mixture sample composed of multiple components can be expressed by the following formula:

(1)

Where ω _i is the frequency, α _{mix_e} is the terahertz absorption coefficient of the mixture sample obtained through experiments, α _{mix_s} is the scattering coefficient of the mixture sample, the subscripts 1, 2,..., n represent various components in the mixture, and the subscript e The subscript in indicates the absorption of the terahertz wave by the sample itself, and the subscript s indicates the scattering coefficient of the sample, that is, α _{1_e} is the terahertz absorption coefficient of the first component obtained through the experiment, and α _{2_e} is the terahertz absorption coefficient obtained through the experiment The obtained terahertz absorption coefficient of the second component, α _{1_in} is the absorption coefficient of the first component itself to the terahertz wave, α _{2_in} is the absorption coefficient of the second component itself to the terahertz wave, α _{1_s} is the first The scattering coefficient of the component, α _{2_s} is the scattering coefficient of the second component, and so on. c1 is the concentration of the _first sample in the mixture, c2 is the concentration of the _second sample in the mixture, and so on. Equation (1) can also be called the terahertz absorption spectrum model of the mixture.

All samples were diluted with polyethylene (PE) and compressed into pellets for testing. Since PE does not absorb terahertz waves, it can be considered that the experimentally measured absorption spectrum of PE is entirely caused by the scattering effect. Since the size of the sample particles is close to that of PE particles, and the scattering effect is mainly related to the particle size, we tested three pellets composed of pure PE and averaged the obtained terahertz absorption spectra. Then, the average calculated PE absorption spectrum is used to characterize the scattering effect of the sample in the terahertz band by analogy, that is, the scattering effect of the sample is expressed as a linear function of the PE absorption spectrum with coefficients:

(2)

_Wherein α _PE is the averaged PE absorption _coefficient , k ₁ , k ₂ , . Therefore, formula (1) can be written in the following form:

(3)

(4)

where K is a dimensionless coefficient related to scattering. Using formula (3), combined with the least squares algorithm, the quantitative analysis of the mixture with known components can be carried out, and accurate results can be obtained.

make , , ,

Then formula (3) can be expressed as:

(5)

Among them, MIX is the absorption coefficient matrix of the mixture sample, A is the absorption coefficient matrix of each component simple substance and PE in the mixture, and C is the concentration matrix of each component in the mixture including the scattering coefficient K. Then there are:

(6)

In order to verify the superiority of this method, a series of quantitative analysis experiments were designed. Three kinds of amino acids were selected as samples, namely glutamine, histidine and threonine, and they were mixed in pairs, and then the index qe was used to characterize the error of quantitative analysis. The definition of qe is as follows:

Where qe represents the error of quantitative analysis, n is the number of different component species in the mixture sample, ci_real and _{ci_cal} are the real and calculated concentrations of each component _, respectively, and are expressed in percentages .

The composition of the samples and the results of quantitative analysis are shown in the table below.

Table 1. Composition of samples and errors of quantitative analysis

The above experimental data show that the algorithm can be used to achieve accurate quantitative analysis of the concentration of the mixture, with an error of approximately less than 3%, and excellent results have been achieved.

Claims (4)

1. A terahertz spectrum quantitative analysis method based on scattering analogy, is characterized in that, the analysis method comprises the following steps: 1) Perform terahertz time-domain spectral detection on three pure polyethylene (PE) tablet samples with different concentrations, obtain their terahertz absorption spectra and perform average calculations, and use the averaged PE terahertz absorption spectra to characterize the scattering effect ; 2) Perform terahertz time-domain spectral detection on the mixture sample and each component element in the mixture to obtain its terahertz absorption spectrum; 3) The terahertz absorption spectrum of the sample measured in the experiment includes two parts, namely the absorption of the terahertz wave by the sample itself and the attenuation caused by the scattering effect, based on which the model of the terahertz absorption spectrum of the mixture sample measured in the experiment is established; 4) According to the principle of analog scattering, transform the terahertz absorption spectrum model of the mixture sample in step 3) to obtain the transformed terahertz absorption spectrum model of the mixture sample, so as to establish the terahertz absorption spectrum model of the mixture sample and The relationship between the terahertz absorption spectrum of each component in the mixture and the PE terahertz absorption spectrum; 5) Use the least squares algorithm to calculate the concentration of each component in the mixture. 2. The terahertz quantitative analysis method based on scattering analogy according to claim 1, characterized in that, the terahertz absorption spectrum model of the mixture sample in the step 3) is: (1) where ω _i is the frequency, α _{mix_e} is the terahertz absorption coefficient of the mixture sample obtained through experiments, α _{mix_s} is the scattering coefficient of the mixture sample, the subscripts 1, 2, ..., n represent various components in the mixture, and the subscript e Indicates obtained through experiments, and the subscript s indicates the scattering coefficient of the sample, that is, c ₁ is the concentration of the first sample in the mixture, c ₂ is the concentration of the second sample in the mixture, and so on; α _{1_e} is obtained by the experiment The obtained terahertz absorption coefficient of the first component, α _{2_e} is the terahertz absorption coefficient of the second component obtained through experiments; α _{1_s} is the scattering coefficient of the first component, α _{2_s} is the scattering coefficient of the second component , and so on. 3. The quantitative analysis method of terahertz spectrum based on scattering analogy according to claim 1, characterized in that the principle of analogy scattering in step 4) is: (2) Where α _PE is the averaged PE absorption coefficient, k ₁ , k ₂ ,..., k _n , k _mix are the components in the mixture and the dimensionless coefficients related to the scattering of the mixture, and the terahertz absorption spectrum model of the mixture sample is : (3) (4) where K is a dimensionless coefficient related to scattering. 4. The terahertz spectral quantitative analysis method based on scattering analogy according to claim 1, characterized in that the least squares algorithm in step 5) is: make , , , Then formula (3) can be expressed as: (5) Where MIX is the absorption coefficient matrix of the mixture sample, A is the absorption coefficient matrix of each component in the mixture and PE, and C is the concentration matrix of each component in the mixture including the scattering coefficient K, then: (6).