CN112748140A - Trace element XRF determination method based on iterative discrete wavelet background subtraction - Google Patents

Trace element XRF determination method based on iterative discrete wavelet background subtraction Download PDF

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CN112748140A
CN112748140A CN202011534473.1A CN202011534473A CN112748140A CN 112748140 A CN112748140 A CN 112748140A CN 202011534473 A CN202011534473 A CN 202011534473A CN 112748140 A CN112748140 A CN 112748140A
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李福生
马骞
程惠珠
赵彦春
杨婉琪
何星华
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University of Electronic Science and Technology of China
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Abstract

The invention discloses a trace element XRF (X-ray fluorescence) determination method based on iterative discrete wavelet background subtraction, which is characterized in that an original detection spectral line signal of a sample to be detected is subjected to L-layer one-dimensional discrete wavelet decomposition to obtain a primary low-frequency approximation coefficient of each layer, and an optimal decomposition layer and a corresponding primary low-frequency approximation coefficient a are selectedv(ii) a Then, the coefficient a is approximated to the first low frequencyvPerforming iterative discrete wavelet decomposition, stopping iteration when the difference values of the continuous N adjacent two iteration results are smaller than the preset precision, and taking the latest iteration result as an approximate background signal to further obtain a signal after background subtraction; respectively calculating the Compton peak scattering intensity and the characteristic X-ray fluorescence intensity of the target element, and obtaining the quantitative analysis value of the target element after approximate processing. The method can effectively avoid the influence of the deviation of the peak value and the peak area of the original spectrogram signal, improve the quantitative detection precision of the trace elements, and improve the detection signal-to-noise ratioAnd over three times, the detection limit of trace elements is reduced.

Description

Trace element XRF determination method based on iterative discrete wavelet background subtraction
Technical Field
The invention relates to the field of improvement of an analysis processing technology of spectral data, in particular to a trace element XRF determination method based on iterative discrete wavelet background subtraction.
Background
The energy dispersion X-ray fluorescence spectrum detection technology can meet various requirements of trace element detection due to the capability of almost no need of sample pretreatment, no pollution and quick and convenient analysis, and a detection spectrogram of a spectrometer contains information such as background information, characteristic X-rays, escape peaks, superposition peaks and the like. Due to the influence of many factors such as instrument systems, detection environments and the nature of the sample, background interference of different degrees always exists in the spectrum signal. In addition, the metal element-containing components on each instrument can influence the spectrogram in the empty measurement, such as metal elements contained in a light pipe, a collimator and a head shell flip cover, which inevitably influence the test result. Therefore, the influence of spectral line background is removed, effective and accurate spectral peak net strength is obtained, and the method has important significance for improving the test signal-to-noise ratio and reducing the detection limit so as to accurately and quantitatively detect the trace elements.
In addition to improving hardware test circuitry, background subtraction calculations for continuum and scattered radiation from air, samples, instruments, etc. are often performed in conventional applications by: peak stripping, polynomial fitting, fourier transform, etc. The background is deducted by adopting a peak stripping method, so that the position of the original peak can be well kept, but the operation process of the method has certain influence on the peak area of the original spectral line and depends on the shape of the original spectral line to a great extent. Polynomial fitting often results in distortion of the sample spectra due to overfitting. Classical fourier transforms can reflect the overall connotation of the signal, but their representation is often not intuitive and noise can complicate the spectrogram. The traditional background subtraction method can cause the deviation of a peak value and influence the peak area of a primary spectrum signal, and the detection precision is not high, so that the invention provides a trace element XRF (X Ray Fluorescence spectroscopy) determination method based on iterative discrete wavelet background subtraction.
Disclosure of Invention
Aiming at the technical problems in the prior art, the invention provides a trace element XRF determination method based on iterative discrete wavelet background subtraction, which can obviously improve the signal-to-noise ratio of element detection under the condition of not influencing peak values and the peak areas of original spectrogram signals, thereby accurately obtaining the content information of trace elements and reducing the element detection limit.
In order to achieve the purpose, the invention adopts the technical scheme that:
a trace element XRF determination method based on iterative discrete wavelet background subtraction is characterized by comprising the following steps:
step 1: obtaining original detection spectral line signal f of sample to be detected0；
Step 2: using wavelet base to the original detection spectral line signal f obtained in step 10Performing L-layer one-dimensional discrete wavelet decomposition to obtain L-layer discrete wavelet decomposition layers, and reconstructing corresponding one-time low-frequency approximation coefficient a according to each discrete wavelet decomposition layerjJ is 1, …, L, where L is derived from the original detected line signal f0Determining the length of the spectral line channel;
and step 3: according to the original detection spectral line signal f obtained in the step 10Is selected to be closest to but not exceeding the original detected spectral signal f0Optimal decomposition layer v of middle characteristic peak wave valley position and corresponding primary low-frequency approximation coefficient a thereofv；
And 4, step 4: the first low frequency approximation coefficient a of the optimal decomposition layer v obtained in the step 3vPerforming iterative discrete wavelet decomposition, defining k as iteration number, and when k is 1, fitting the low-frequency approximation coefficient a oncevPerforming discrete wavelet decomposition to obtain a secondary low-frequency approximation coefficient av 1Approximating the second order low frequency to a coefficient av 1As the background of the iteration, the next iteration is carried out;
and 5: let k be k +1, and for the last iteration result av k-1Performing discrete wavelet decomposition to further obtain the current secondary low-frequency approximation coefficient av k；
Step 6: if the difference value between the kth iteration result and the kth-1 th iteration result is greater than the preset precision epsilon, returning to the step 5; if the difference value between the kth iteration result of N continuous times and the kth-1 th iteration result is less than the preset precision epsilon, the iteration result is considered to be reliable, the iteration is stopped, and the latest iteration result a is obtainedv k+N(ii) a Otherwise, returning to the step 5; wherein N is determined by actual accuracy requirements;
and 7: the last iteration result a obtained in the step 6v k+NAs an approximate background signal, the original detection line signal f0Subtracting the approximate background signal to realize background subtraction and obtain a background-subtracted signal;
and 8: calculating Compton peak scattering intensity I of interference elements in to-be-detected samplec；
And step 9: selecting target elements of the sample to be detected from the signals obtained in the step 7 after the background is deducted, and calculating the characteristic X-ray fluorescence intensity I of the target elementsp；
Step 10: respectively comparing the Compton peak scattering intensity I obtained in the step 8cAnd the characteristic X-ray fluorescence intensity I obtained in step 9pAnd performing approximate processing to obtain a correction equation of the target element, namely a quantitative analysis value of the target element.
Further, Compton peak scattering intensity I in step 8cThe calculation formula of (2) is as follows:
Figure BDA0002852925580000021
where K is a constant determined by the X-ray source, the sample to be measured,. psi.and phi, I0Intensity of primary radiation, σ, of X-rayscCompton scattering cross section area, mu, of interfering elements0For the mass absorption coefficient of the interfering element for the primary radiation, musAnd psi and phi are respectively an incident angle and an emergent angle of the X-ray and the sample to be detected.
Further, the characteristic X-ray of the target element in step 9Fluorescence intensity IpThe calculation formula of (2) is as follows:
Figure BDA0002852925580000031
in the formula, KpIs a constant determined by the overall efficiency of the XRF detector, the fluorescence yield of the X-ray probe, psi and phi, CpIs the concentration of the target element in the sample to be tested, mukIs the mass absorption coefficient of the target element to the characteristic X-rays.
Further, the approximation processing in step 10 is specifically as follows:
for Compton peak scattering intensity IcWhen neglecting the elements whose X-ray absorption energy is greater than the Compton scattering energy, mu0And musHas linear relation, and after approximate treatment, the obtained treated Compton peak scattering intensity Ic' is:
Figure BDA0002852925580000032
in the formula (I), the compound is shown in the specification,
Figure BDA0002852925580000033
r is mu0And musLinear scaling coefficient of (a);
for characteristic X-ray fluorescence intensity IpWhen the change of the background information of the sample to be measured is ignored, mu0And mukThe obtained processed characteristic X-ray fluorescence intensity I after approximate processing has linear relationp' is:
Figure BDA0002852925580000034
in the formula (I), the compound is shown in the specification,
Figure BDA0002852925580000035
r' is mu0And mukLinear scaling coefficient of (a);
further, the correction equation of the target element is the processed characteristic X-ray fluorescence intensity Ip' division by the Compton peak scattering intensity I after treatmentc′：
Figure BDA0002852925580000036
Wherein C is a quantitative analysis value of the target element.
The invention has the beneficial effects that:
the method carries out background subtraction and matrix effect correction by adopting a mode of combining iterative discrete wavelet decomposition and a Compton normalization method, reduces the calculated amount while effectively avoiding the deviation of a peak value and the influence of the peak area of an original spectrogram signal, improves the quantitative detection precision of the trace elements, improves the detection signal-to-noise ratio by more than three times, reduces the matrix effect caused by an instrument or air to a certain extent, and reduces the detection limit of the trace elements.
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FIG. 1 is a schematic diagram of 7 discrete wavelet decomposition layers obtained in example 1 of the present invention;
FIG. 2 is a graph comparing the original detection line signal and the approximate background signal obtained by testing a soil sample of GBW07380(GSD-29) under a light pipe voltage of 45kV in example 1 of the present invention;
FIG. 3 is a graph comparing the original detection line signal obtained by detecting a soil sample GBW07380(GSD-29) under a light tube voltage of 45kV and the signal after background subtraction in example 1 of the present invention;
FIG. 4 is a schematic diagram of a target element peak and an Ag element Compton peak in example 1 of the present invention;
fig. 5 is a comparison graph of a linear fit curve of the original data of Cu element in example 1 of the present invention and the data obtained by combining the iterative discrete wavelet decomposition and compton normalization.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be further described with reference to the following embodiments and the accompanying drawings.
Example 1
The embodiment provides a trace element XRF (X-ray fluorescence) determination method based on iterative discrete wavelet background subtraction, which takes a GBW07380(GSD-29) soil sample as a sample to be detected and calculates a quantitative analysis value of a Cu element, and comprises the following steps:
step 1: detecting GBW07380(GSD-29) soil samples by adopting a TS-XH4000-P type handheld X-ray fluorescence analyzer provided with an Ag anode X-ray tube, wherein the fitting degree and the signal-to-noise ratio of detection spectral lines reach the optimal value under the light tube voltage of 45kV, and then obtaining original detection spectral line signals f of the GBW07380(GSD-29) soil samples0；
Step 2: using wavelet base to the original detection spectral line signal f obtained in step 10Performing 7-layer one-dimensional discrete wavelet decomposition to obtain 7 discrete wavelet decomposition layers, and reconstructing corresponding primary low-frequency approximation coefficient a according to each discrete wavelet decomposition layer as shown in FIG. 1j，j＝1,…,7；
And step 3: according to the original detection spectral line signal f obtained in the step 10Is selected to be closest to but not exceeding the original detected spectral line signal f0The optimal decomposition layer of the peak-valley position of each feature in the system, in this embodiment, the 7 th discrete wavelet decomposition layer is the optimal decomposition layer, and the first-order low-frequency approximation coefficient a corresponding to the 7 th discrete wavelet decomposition layer is obtained7；
And 4, step 4: for the first low frequency approximation coefficient a obtained in the step 37Performing iterative discrete wavelet decomposition, defining k as iteration number, and when k is 1, fitting the low-frequency approximation coefficient a once7Performing discrete wavelet decomposition to obtain a secondary low-frequency approximation coefficient a7 1At this time a7＞a7 1Approximating the second order low frequency to a coefficient a7 1As the background of the iteration, the next iteration is carried out;
and 5: let k be k +1, and for the last iteration result a7 k-1Performing discrete wavelet decomposition to further obtain the current secondary low-frequency approximation coefficient a7 k；
Step 6: if the difference value between the kth iteration result and the (k-1) th iteration result is greater thanIf the precision epsilon is preset, returning to the step 5; if the difference value between the kth iteration result of N continuous times and the kth-1 th iteration result is less than the preset precision epsilon, the iteration result is considered to be reliable, the iteration is stopped, and the latest iteration result a is obtained7 k+N(ii) a Otherwise, returning to the step 5; wherein N is determined by actual accuracy requirements;
and 7: the last iteration result a7 k+NAs an approximate background signal, the original detection line signal f, as shown in fig. 20Subtracting the approximate background signal can realize background subtraction to obtain the signal after background subtraction, as shown in FIG. 3, the original detection spectral line signal f can be seen0The background information of the image is effectively removed;
and 8: taking the peak of the interfering element Ag in the GBW07380(GSD-29) soil sample as the Compton peak, as shown in FIG. 4, calculating the Compton peak scattering intensity I according to the peak value and the nature of the Ag elementc：
Figure BDA0002852925580000051
Wherein K is a constant determined by the X-ray radiation source, GBW07380(GSD-29) soil sample, psi and phi, I0Intensity of primary radiation, σ, of X-rayscIs the Compton scattering cross section area, mu, of Ag element0Is the mass absorption coefficient of Ag element to primary radiation, musThe mass absorption coefficient of Ag element to Compton scattered ray, psi and phi are respectively the incident angle and the emergent angle of X ray and GBW07380(GSD-29) soil sample;
and step 9: selecting a target element Cu element of the GBW07380(GSD-29) soil sample from the signal obtained in the step 7 after the background is subtracted, and calculating the characteristic X-ray fluorescence intensity I of the Cu elementp：
Figure BDA0002852925580000052
In the formula, KpThe total efficiency of the XRF detector, the fluorescence yield of the X-ray probeC, phi and phi determined constantpConcentration of Cu element in soil sample of GBW07380(GSD-29) (. mu.)kThe mass absorption coefficient of Cu element to characteristic X-ray;
step 10: for Compton peak scattering intensity I obtained in step 8cBy performing approximation processing, when neglecting the element with X-ray absorption energy larger than Compton scattering energy, mu0And musHas linear relation, and after approximate treatment, the obtained treated Compton peak scattering intensity Ic' is:
Figure BDA0002852925580000061
in the formula (I), the compound is shown in the specification,
Figure BDA0002852925580000062
r is mu0And musLinear scaling coefficient of (a);
for the characteristic X-ray fluorescence intensity I obtained in the step 9pAn approximation is made, when neglecting the background information change of GBW07380(GSD-29) soil sample, mu0And mukThe obtained processed characteristic X-ray fluorescence intensity I after approximate processing has linear relationp' is:
Figure BDA0002852925580000063
in the formula (I), the compound is shown in the specification,
Figure BDA0002852925580000064
r' is mu0And mukLinear scaling coefficient of (a);
further, the correction equation of the Cu element is the processed characteristic X-ray fluorescence intensity Ip' division by the Compton peak scattering intensity I after treatmentc′：
Figure BDA0002852925580000065
In the formula, C is a quantitative analysis value of the Cu element, namely the quantitative analysis value of the Cu element processed by combining the iterative discrete wavelet decomposition and the Compton normalization method is finally obtained.
The quantitative analysis value of the processed Cu element and the original detection spectral line signal f0Comparing the extracted quantitative analysis raw data of the Cu element, and obtaining a corresponding fitting curve comparison graph, as shown in fig. 5, it can be known that the goodness of fit (R) of the Cu element is obtained after the processing by combining the iterative discrete wavelet decomposition and compton normalization method described in this embodiment2) The lifting is from 0.89 to 0.97, and the lifting is large;
furthermore, by calculating the original detection line signal f0And the signal-to-noise ratio of the signal processed by the combination of the iterative discrete wavelet decomposition and the compton normalization method in this embodiment is known, the method in this embodiment can effectively improve the detection signal-to-noise ratio from 4.47 to 12.201, and further improve the detection accuracy of the trace elements.

Claims (4)

1. A trace element XRF determination method based on iterative discrete wavelet background subtraction is characterized by comprising the following steps:
step 1: obtaining original detection spectral line signal f of sample to be detected0；
Step 2: using wavelet base to the original detection spectral line signal f obtained in step 10Performing L-layer one-dimensional discrete wavelet decomposition to obtain L-layer discrete wavelet decomposition layers, and reconstructing corresponding one-time low-frequency approximation coefficient a according to each discrete wavelet decomposition layerjJ is 1, …, L; wherein L is derived from the original detected spectral line signal f0Determining the length of the spectral line channel;
and step 3: according to the original detection spectral line signal f obtained in the step 10Selecting the optimal decomposition layer v nearest to but not exceeding the valley position of each characteristic peak and the corresponding first low-frequency approximation coefficient a thereofv；
And 4, step 4: for the first low frequency approximation coefficient a obtained in the step 3vPerforming iterative discrete wavelet decomposition when the results of two adjacent iterations are performed for N consecutive timesStopping iteration when the difference values are smaller than the preset precision epsilon, taking the obtained latest iteration result as an approximate background signal, and obtaining the original detection spectral line signal f0Subtracting the approximate background signal to obtain a background-subtracted signal; wherein N is determined by actual precision requirements;
and 5: calculating Compton peak scattering intensity I of interference elements in to-be-detected samplec；
Step 6: selecting target elements of the sample to be detected from the signals obtained in the step 4 after the background is deducted, and calculating the characteristic X-ray fluorescence intensity I of the target elementsp；
And 7: respectively comparing the Compton peak scattering intensity I obtained in the step 5cAnd the characteristic X-ray fluorescence intensity I obtained in step 6pAnd performing approximate processing to obtain a quantitative analysis value of the target element.
2. The method for XRF trace element determination based on iterative discrete wavelet background subtraction as claimed in claim 1 wherein Compton peak scattering intensity I in step 5cThe calculation formula of (2) is as follows:
Figure FDA0002852925570000011
where K is a constant determined by the X-ray source, the sample to be measured,. psi.and phi, I0Intensity of primary radiation, σ, of X-rayscCompton scattering cross section area, mu, of interfering elements0For the mass absorption coefficient of the interfering element for the primary radiation, musAnd psi and phi are respectively an incident angle and an emergent angle of the X-ray and the sample to be detected.
3. The method for detecting trace element XRF based on background subtraction of iterative discrete wavelet as claimed in claims 1 and 2 wherein the characteristic X-ray fluorescence intensity I of target element in step 6pThe calculation formula of (2) is as follows:
Figure FDA0002852925570000021
in the formula, KpIs a constant determined by the overall efficiency of the XRF detector, the fluorescence yield of the X-ray probe, psi and phi, I0Intensity of primary radiation as X-rays, CpIs the concentration of the target element in the sample to be tested, mu0For the mass absorption coefficient of the interfering element for the primary radiation, mukThe mass absorption coefficient of the target element to the characteristic X-ray is psi and phi which are respectively the incident angle and the emergent angle of the X-ray and the sample to be detected.
4. The method for XRF trace element determination based on iterative discrete wavelet background subtraction as claimed in claim 1 wherein the procedure of the approximation process in step 7 is as follows:
for Compton peak scattering intensity IcWhen neglecting the elements whose X-ray absorption energy is greater than the Compton scattering energy, mu0And musHas linear relation, and after approximate treatment, the obtained treated Compton peak scattering intensity Ic' is:
Figure FDA0002852925570000022
in the formula (I), the compound is shown in the specification,
Figure FDA0002852925570000023
r is mu0And musLinear scaling coefficient of (a);
for characteristic X-ray fluorescence intensity IpWhen the change of the background information of the sample to be measured is ignored, mu0And mukThe obtained processed characteristic X-ray fluorescence intensity I after approximate processing has linear relationp' is:
Figure FDA0002852925570000024
in the formula (I), the compound is shown in the specification,
Figure FDA0002852925570000025
r' is mu0And mukLinear scaling coefficient of (a);
further, the correction equation of the target element is the processed characteristic X-ray fluorescence intensity Ip' division by the Compton peak scattering intensity I after treatmentc′：
Figure FDA0002852925570000031
Wherein C is a quantitative analysis value of the target element.
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