X-ray fluorescence spectroscopy multi-energy state sample superposition method and system

Abstract

The application discloses an X-ray fluorescence spectrum multi-energy state sample superposition method and system, and belongs to the technical field of optics and spectroscopy. The method first simulates the X-ray fluorescence spectrum analysis process multiple times by using the Monte Carlo method to obtain a multi-stage energy state spectrum, then determines the maximum value points of each channel address in the multi-stage energy state spectrum by using an extreme value method, splices the maximum value points of all the channel addresses into a spectrum sequence, and finally extracts an important sampling area from the spectrum sequence by using importance sampling, samples in the channel address corresponding to the important sampling area in the multi-stage energy state spectrum, obtains the sampling spectrum of different energy states, and finally splices into a complete spectrum. The application simulates the physical model of the X-ray fluorescence spectrum element detection method based on the Monte Carlo method, obtains the theoretical data of the energy spectrum, and makes the multi-stage energy state spectrum well fused by using the importance sampling, that is, the local accurate spectrum data is fitted into a complete spectrum.

Description

Technical Field

[0001] This invention relates to the fields of optics and spectroscopy, and in particular to a method and system for superimposing multi-energy state samples in X-ray fluorescence spectroscopy. Background Technology

[0002] With the increasing severity of environmental pollution, the demand for elemental analysis of air, soil, and water is gradually increasing, placing higher demands on measurement accuracy and speed. Therefore, the detection of pollutant elements in various environments has become a key technology with future development potential. X-ray fluorescence spectrometry is a commonly used elemental analysis technique that can be used to determine the composition and concentration of elements in a sample. However, to improve the accuracy of measurements in a specific area, experiments often involve multiple measurements of the same sample based on different X-ray emission energies. The resulting multi-level energy states in the spectra obtained from these multiple measurements are not clearly delineated. Therefore, how to fit locally accurate spectral data into a complete spectrum has become an urgent problem to be solved. Summary of the Invention

[0003] The purpose of this invention is to provide a method and system for superimposing X-ray fluorescence spectrometer multi-energy state samples, which can fit local precise spectral data into a complete spectrum.

[0004] To achieve the above objectives, the present invention provides the following solution:

[0005] A method for superimposing multi-energy state samples in X-ray fluorescence spectroscopy includes:

[0006] Based on different inter-tube voltages, and using an energy-dispersive X-ray fluorescence analysis system as a framework, the Monte Carlo method was employed to repeatedly simulate the X-ray fluorescence spectral analysis process, resulting in multi-level energy state spectra. The multi-level energy state spectra include the spectra of different energy states. The multi-level energy state spectra are plotted with channel address on the x-axis and count rate on the y-axis.

[0007] Differentiate the count rate sequence corresponding to each channel in the multi-level energy state spectrum to obtain the maximum point of each channel;

[0008] The maxima of all the path addresses are stitched together to form a spectral sequence;

[0009] Importance sampling is used to extract important sampling regions from the spectral sequence;

[0010] Sampling is performed according to the channel address corresponding to the important sampling region in the multi-level energy state spectrum to obtain the sampling spectrum of different energy states, and the sampling spectra of different energy states are stitched together to form a complete spectrum.

[0011] Optionally, based on different inter-tube voltages, and using an energy-dispersive X-ray fluorescence analysis system as a framework, the Monte Carlo method is employed to repeatedly simulate the X-ray fluorescence spectral analysis process, obtaining multi-level energy state spectra, specifically including:

[0012] Starting from voltage 0 to voltage T3, multiple inter-transistor voltages are set in steps of v; where (0, T1) represents the low-energy state, (T1, T2) represents the medium-energy state, and (T2, T3) represents the high-energy state. <T2<T3;

[0013] Based on each inter-tube voltage, using an energy-dispersive X-ray fluorescence analysis system as a framework, the Monte Carlo method is employed to simulate the X-ray fluorescence spectroscopy analysis process, obtaining the spectrum of the energy state corresponding to the inter-tube voltage. The X-ray fluorescence spectroscopy analysis process includes: X-ray generation, monochromatization, fluorescence process, Compton scattering and Rayleigh scattering, and detector response.

[0014] By plotting all the spectra obtained from the simulation in the same coordinate system, a multi-level energy state spectrum is obtained;

[0015] The energy-dispersive X-ray fluorescence analysis system includes an X-ray tube, a fully focusing hyperbolic flexural crystal, a sample to be tested, and a detector. The X-ray tube generates X-rays, which are incident on the fully focusing hyperbolic flexural crystal. The incident fully focusing hyperbolic flexural crystal monochromates the wavelength of the incident X-rays, and the emitted single-wavelength X-rays are incident on the sample to be tested. The incident photons of the single-wavelength X-rays react with the target elements in the sample to produce multiple fluorescence through the photoelectric effect, and / or Compton scattering and Rayleigh scattering to produce scattered light. The detector receives the multiple fluorescence and / or scattered light and converts the optical signals into electrical signals. The multiple fluorescence includes primary fluorescence, secondary fluorescence, and tertiary fluorescence.

[0016] Optionally, the Monte Carlo method is used to simulate the generation of X-rays during X-ray fluorescence spectroscopy analysis, specifically including:

[0017] Based on the geometric parameters of the X-ray tube and the fully focused hyperbolic curved crystal, according to the formula... and Calculate the minimum azimuth angle corresponding to the visible portion of the X-ray tube's radiation source photon and the fully focused hyperbolic curved crystal. and maximum azimuth Where a1 is the radius of the upper collimation hole, a2 is the vertical distance between the radiation source target and the point of action of the refractive surface, and a3 is the vertical distance between the radiation source target and the bottom surface of the lower collimation hole.

[0018] Based on the minimum azimuth angle and maximum azimuth According to the formula Determine the azimuth angle φ0 of the incident photons of the X-ray tube's radiation source onto the visible portion of the fully focused hyperbolic curved crystal; where x is a random number in (0,1);

[0019] The X-ray tube emits X-rays according to the preset inter-tube voltage and azimuth angle φ0.

[0020] Based on the minimum azimuth angle and maximum azimuth According to the formula Calculate the probability W1 of the X-ray tube's radiation source photons incident on the fully focused hyperbolic curved crystal;

[0021] Combining probability W1 and X-ray energy E1 generated by the X-ray tube based on a preset inter-tube voltage, the incident X-ray energy E2 on the fully focused hyperbolic curved crystal is determined according to the formula E2 = W1·E1.

[0022] Optionally, the monochromaticization process in X-ray fluorescence spectroscopy is simulated using the Monte Carlo method, specifically including:

[0023] When a fully focused hyperbolic curved crystal receives X-rays, it will diffract single-wavelength X-rays that satisfy Bragg's law.

[0024] Based on the incident X-ray energy E2 on the fully focused hyperbolic curved crystal, the X-ray energy E3 exiting the fully focused hyperbolic curved crystal is determined according to the formula E3=E2(λ-σ,λ+σ); where λ is the wavelength of a single-wavelength X-ray and σ is the distribution variance.

[0025] Optionally, the Monte Carlo method is used to simulate the fluorescence process during X-ray fluorescence spectroscopy analysis, specifically including:

[0026] Based on the azimuth angle φ0, and according to the formulas Z0=t0cosφ0 and t0=-ln[1-x+xexp(-μt)], max The perpendicular distance Z0 from the incident photon through the sample is determined by the formula: t0 = [[cosφ0] / μ] / μ. Here, t0 is the distance between the incident point and the point of first action of the incident photon in the sample, μ is the mass absorption coefficient of the sample to the incident photon, and t... max The thickness of the sample to be tested;

[0027] According to azimuth According to the formula W2=1-exp(-μt) max / cosφ0), determine the probability W2 that the point of action is limited to the thickness range of the sample to be measured;

[0028] According to the formula W3 = Y i C i (1-1 / r i )σi / μ i The probability W3 of a single fluorescence produced by the interaction of an incident photon with an atom of element i in the sample to be tested is determined; where Y i For the fluorescence yield of the element, C i Let r be the concentration of element i in the sample to be tested. i σ is the abrupt change coefficient of the absorption limit of element i. i Let μ be the photoelectric absorption cross section of element i with respect to incident rays. i The absorption coefficient of the sample to be tested on the characteristic line of element i;

[0029] Based on the azimuth angle φ1 corresponding to the primary fluorescence characteristic X-ray, according to the formula... Determine the probability W4 that the secondary action point is within the thickness range of the sample to be tested;

[0030] Based on the formula Z1=t1cosφ1, the penetration distance Z1 between the primary and secondary points of action is determined; where t1 is the distance between the primary and secondary points of action.

[0031] According to the formula W5=(1 / μ i )Y j C j (1-1 / r j )σ ij Determine the probability W5 of secondary fluorescence produced by the interaction of the characteristic rays of element i with atoms of element j; where Y j Let C be the fluorescence yield of element j. j Let r be the concentration of element j. j σ is the abrupt change coefficient of the absorption limit of element j. ij Let J be the cross section of the characteristic ray acting on element i by element j.

[0032] According to the formula Determine the probability W6 that the tertiary action point falls within the thickness range of the sample to be tested; where φ2 is the azimuth angle corresponding to the secondary fluorescence characteristic X-ray, μ j The mass absorption coefficient of the sample to be tested for the characteristic rays of element j;

[0033] According to the formula W7=(1 / μ j )Y k C k (1-1 / r k )σ jk Determine the probability W7 of the third fluorescence produced by the interaction between the characteristic line of element j and the atom of element k; where Y k For the fluorescence yield of element k, C k r represents the concentration of element k in the sample. k σ is the abrupt change coefficient of the absorption limit of element k.jk Let k be the cross section of the characteristic line acting on element j;

[0034] The probability of a single fluorescence emission, W'1, is W'1 = W2·W3, and the fluorescence energy of a single fluorescence emission, E4, is E4 = W3·E3.

[0035] The probability of secondary fluorescence W'2 is W'2 = W2·W3·W4·W5, and the fluorescence energy E5 of secondary fluorescence is E5 = W5·E4;

[0036] The probability of three fluorescence events, W'3, is W'3 = W2·W3·W4·W5·W6·W7, and the fluorescence energy of the three fluorescence events, E6, is E6 = W7·E5.

[0037] If primary fluorescence, secondary fluorescence, and tertiary fluorescence occur simultaneously, the energy E7 of the fluorescent rays emitted from the sample to be tested is E7 = E4 + E5 + E6.

[0038] Optionally, the Monte Carlo method is used to simulate Compton scattering and Rayleigh scattering during X-ray fluorescence spectroscopy analysis, specifically including:

[0039] According to the formula Determine the probability W that the point of action for generating Rayleigh scattering rays falls within the thickness range of the sample under test. 8A ;

[0040] According to the formula Determine the probability W that the point of action of the Compton scattering ray is within the thickness range of the sample under test. 8B ;

[0041] The fluorescence energy E8 after energy loss due to Rayleigh scattering is E8 = W. 8A E3;

[0042] The fluorescence energy E9 after energy loss due to Compton scattering is E9 = W. 8B E3;

[0043] If Rayleigh scattering and Compton scattering are both present, then the fluorescence energy distribution E 10 For E 10 =E8+E9.

[0044] Optionally, the Monte Carlo method is used to simulate the detector response during X-ray fluorescence spectroscopy analysis, specifically including:

[0045] When the incident spectral energy is E S The Gaussian distribution of energy when a photon is detected by a detector is: Among them, E D Let c1 represent the energy of the detected spectrum, and σ represent the first linear distribution function. 2Represents variance. This indicates the effect of charge sharing.

[0046] Incident light angle into the detector The expression is

[0047] The probability W9 of incident light entering the detector is

[0048] The incident spectral energy E of the detector S and detection spectral energy E D Satisfy E D =W9·E S Among them, E S =E7+E 10 .

[0049] Optionally, the maximum point satisfies:

[0050]

[0051]

[0052] Where j' is the maximum point, y ij Let be the count rate corresponding to the i-th address in the j-th spectrum.

[0053] Optionally, important sampling regions are extracted from the spectral sequence using importance sampling, specifically including:

[0054] Regions in the spectral sequence with count rates greater than the threshold are designated as important sampling areas, while regions with count rates less than the threshold are designated as background noise areas.

[0055] A multi-energy state sample overlay system for X-ray fluorescence spectroscopy includes:

[0056] The simulation module is used to simulate the X-ray fluorescence spectroscopy analysis process multiple times using the Monte Carlo method based on different inter-tube voltages and an energy-dispersive X-ray fluorescence analysis system as a framework, to obtain multi-level energy state spectra. The multi-level energy state spectra include the spectra of different energy states. The multi-level energy state spectra are plotted with channel address as the abscissa and count rate as the ordinate.

[0057] The differentiation module is used to differentiate the count rate sequence corresponding to each channel in the multi-level energy state spectrum to obtain the maximum point of each channel.

[0058] The maximum point stitching module is used to stitch together the maximum points of all channels into a spectral sequence;

[0059] An extraction module is used to extract important sampling regions from the spectral sequence using importance sampling;

[0060] The sampling module is used to sample the multi-level energy state spectrum according to the channel address corresponding to the important sampling region, obtain the sampling spectrum of different energy states, and stitch the sampling spectra of different energy states into a complete spectrum.

[0061] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0062] This invention discloses a method and system for superimposing multi-energy-state samples in X-ray fluorescence spectroscopy. First, the Monte Carlo method is used to simulate the X-ray fluorescence spectroscopy analysis process multiple times to obtain multi-level energy-state spectra. Then, the extreme value method is used to determine the maximum point of each channel in the multi-level energy-state spectra, and the maximum points of all channels are stitched together to form a spectral sequence. Finally, important sampling regions are extracted from the spectral sequence using importance sampling. Sampling is performed in the multi-level energy-state spectra according to the channels corresponding to the important sampling regions to obtain sampled spectra of different energy states, which are then stitched together to form a complete spectrum. This invention is based on the Monte Carlo method to simulate the physical model of X-ray fluorescence spectroscopy elemental detection, obtaining theoretical data of the energy spectrum. Importance sampling enables good fusion of multi-level energy-state spectra, that is, fitting locally precise spectral data into a complete spectrum. Attached Figure Description

[0063] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0064] Figure 1 A flowchart of a method for superimposing X-ray fluorescence spectrometer multi-energy state samples provided in an embodiment of the present invention;

[0065] Figure 2 A schematic diagram illustrating the principle of a multi-energy state sample superposition method for X-ray fluorescence spectroscopy provided in an embodiment of the present invention;

[0066] Figure 3 A structural diagram of the energy-dispersive X-ray fluorescence analysis system provided in an embodiment of the present invention;

[0067] Figure 4 A schematic diagram of the exit section of an X-ray tube provided in an embodiment of the present invention;

[0068] Figure 5 This is a schematic diagram of the structure of a fully focused hyperbolic curved crystal provided in an embodiment of the present invention;

[0069] Figure 6 A schematic diagram illustrating the principle of Bragg's law provided for embodiments of the present invention;

[0070] Figure 7 This is a schematic diagram of the structure of an X-ray incident sample provided in an embodiment of the present invention;

[0071] Figure 8 A schematic diagram of the Compton scattering principle provided in an embodiment of the present invention;

[0072] Figure 9 A schematic diagram of Rayleigh scattering principle provided for an embodiment of the present invention;

[0073] Figure 10 This is a structural diagram of the detection process provided in an embodiment of the present invention;

[0074] Figure 11 A schematic diagram illustrating the principle of the importance sampling method in spectral processing provided in this embodiment of the invention. Detailed Implementation

[0075] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0076] To address the problem of unclear spectral range division in multi-level energy states of X-ray tubes, which makes it impossible to fit locally accurate spectral data into a complete spectrum, this invention combines importance sampling from the Monte Carlo method with multi-level energy state separation technology in X-ray fluorescence spectroscopy. The former is used to supplement and optimize the latter. A physical model based on the Monte Carlo method to simulate elemental detection in X-ray fluorescence spectroscopy is presented. Theoretical energy spectrum data are obtained based on this model, and importance sampling ultimately achieves good fusion of multi-level energy state spectra.

[0077] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0078] like Figure 1 As shown, this embodiment of the invention provides a method for superimposing X-ray fluorescence spectrometer multi-energy state samples, including:

[0079] Step 1: Based on different inter-tube voltages, using an energy-dispersive X-ray fluorescence analysis system as a framework, the Monte Carlo method is used to simulate the X-ray fluorescence spectral analysis process multiple times to obtain multi-level energy state spectra; the multi-level energy state spectra include the spectra of different energy states; the multi-level energy state spectra are plotted with channel address as the abscissa and count rate as the ordinate.

[0080] The Monte Carlo method is a numerical computation method based on random sampling and statistical inference, often used to solve complex problems and perform numerical simulations. Its core idea is to approximate models that are difficult to solve analytically through random sampling. In the analysis of X-ray fluorescence spectra, a large number of random numbers are used to simulate the generation and motion of X-ray photons, as well as collisions and scattering during these processes, including: X-ray generation, monochromatization, fluorescence processes, Compton and Rayleigh scattering, and detector response. The Monte Carlo method is independent of the dimensionality and complexity of the problem, thus it can adapt to problems with strong nonlinearity and randomness in photon motion. Increasing the number of photons can refine the model of the measurement system and improve the accuracy of the method.

[0081] Importance sampling is an optimization strategy in Monte Carlo simulations. By selecting a subset of high-weighted sample points for simulation, the overall picture can be predicted from the local sample, reducing computational load and improving simulation efficiency. In X-ray fluorescence spectroscopy, the simulated spectra across different energy states can be viewed as probability density functions of energy. By using a Monte Carlo model to traverse the spectrum within a specific energy state range, the region with the highest probability density on the abscissa—the sampling interval with higher weight—can be identified. Based on the weights of different energy states, the spectral data can be weighted and summed to obtain a more reliable spectrum.

[0082] This invention employs an energy-dispersive X-ray fluorescence analysis system as the framework of a Monte Carlo model, comprising an X-ray tube, a fully focusing hyperbolic curved crystal, a sufficiently thick sample, and a detector. The X-ray tube generates X-rays, which are incident on the fully focusing hyperbolic curved crystal. The incident fully focusing hyperbolic curved crystal monochromates the wavelength of the incident X-rays, and the emitted single-wavelength X-rays are incident on the sample. The incident photons of the single-wavelength X-rays react with the target elements in the sample through a photoelectric effect, emitting multiple fluorescence, and / or undergoing Compton scattering and Rayleigh scattering to generate scattered light. The detector receives the multiple fluorescence and / or scattered light and converts the optical signals into electrical signals. The multiple fluorescence includes primary fluorescence, secondary fluorescence, and tertiary fluorescence.

[0083] like Figure 3The diagram shows the structure of an energy-dispersive X-ray fluorescence analysis system (energy-dispersive spectroscopy elemental detection platform). The X-ray tube is the radiation source, emitting X-rays of different wavelengths by charging particles bombarding the target material. The X-ray energy is controlled by the inter-tube voltage. The fully focusing hyperboloidal crystal is the X-ray monochromator, diffracting X-rays of a specific wavelength that conforms to Bragg's law, filtering out noise wavelengths. The sample, the carrier of the element to be analyzed, can be collected from the environment, such as the atmosphere, soil, or water. The detector absorbs the X-ray fluorescence reflected from the sample, as well as various scattered light, and converts the optical signals into electrical signals for analysis.

[0084] The specific working process of the energy-dispersive X-ray fluorescence analysis system is as follows:

[0085] The X-ray generation is initialized by setting the number of incident photons, the voltage between X-ray tubes, and the distance between the bent crystal and the X-ray tube. The generated X-rays are incident at a certain angle on the fully focused hyperbolic bent crystal to monochromate the wavelength. The bending principle of the crystal satisfies Bragg's law. The wavelength that meets the emission conditions can be obtained based on the set X-ray energy, crystal plane spacing, and incident angle, and the emission angle is consistent with the incident angle.

[0086] When a single-wavelength X-ray is emitted and enters the sample, for a sufficiently thick sample, the probability that the point of action of the X-ray is confined within the sample area can be calculated based on parameters such as the sample absorption coefficient and thickness.

[0087] Incident photons interact with target elements in the sample via the photoelectric effect, emitting primary, secondary, and tertiary fluorescence. The probability of primary fluorescence generation can be calculated based on the concentration of the excitation element in the sample and the element's photoelectric absorption parameters to the incident light. The probability of secondary fluorescence generation is calculated by using the distance between the primary and secondary fluorescence activation sites as a variable, within the sample area. Similarly, the generation process of tertiary fluorescence can be simulated and its probability calculated.

[0088] During the interaction between photons and sample element atoms, Compton scattering and Rayleigh scattering may occur, causing secondary fluorescence of the sample by the scattered photons, which introduces noise into the emitted spectrum. The probability of secondary fluorescence generated by these two types of scattering can be calculated based on the mass absorption coefficient of the sample for the incident photons, and the scattering process can be simulated.

[0089] In the receiving section, the azimuth angle between the characteristic rays emitted from the sample surface and the visible part of the detector can be obtained through random simulation calculation. By modeling the size of the detector window and the parameters of the absorbing crystal, the detection efficiency for photons of a specific energy can be obtained based on the detector's response function.

[0090] The above simulation process only considers the excitation of one element. In practical applications, it is necessary to consider the superposition effect of multiple elements. The characteristic intensities of different elements in different energy ranges are inconsistent, which makes the situation complicated.

[0091] Exemplarily, the specific process of step 1 is as follows:

[0092] Starting from 0 to voltage T3, with v as the step size, a plurality of inter-tube voltages are set; wherein, (0, T1) is a low energy state, (T1, T2) is a medium energy state, (T2, T3) is a high energy state, and T1<T2<T3; based on each inter-tube voltage, with an energy dispersive X-ray fluorescence analysis system as a framework, the Monte Carlo method is used to simulate the X-ray fluorescence spectrum analysis process once, to obtain the spectrum of the energy state corresponding to the inter-tube voltage; the X-ray fluorescence spectrum analysis process includes: generation of X-rays, monochromatization, fluorescence process, Compton scattering and Rayleigh scattering, and detector response; all spectra obtained by simulation are drawn in the same coordinate system to obtain a multi-level energy state spectrogram.

[0093] Simulating the X-ray fluorescence spectrum analysis process once by using the Monte Carlo method includes the following processes:

[0094] (1) One-time simulation of X-ray generation

[0095] Figure 4 is shown as a structural schematic diagram of the emission part of an X-ray tube. The entire radioactive source is axially symmetric with respect to the center, and the radioactive source photons correspond to the visible part of the fully focusing hyperbolic curved crystal with a minimum azimuth angle and a maximum azimuth angle wherein the azimuth angle φ0 satisfies Let a1 be the radius of the upper collimation hole (generally taken as the radius of the curved crystal surface), a2 be the vertical distance between the radioactive source target material and the action point on the refraction surface, a3 be the vertical distance between the radioactive source target material and the bottom surface of the lower collimation hole, x be a random number selected in the interval (0,1), it is assumed that the ray energy generated based on the inter-tube voltage during incidence conforms to a normal distribution, let E1~N(λ,σ 2 ), wherein λ is the center wavelength and σ is the distribution variance, and the corresponding calculation formulas are as follows:

[0096]

[0097]

[0098]

[0099] If the probability that a photon is incident at φ0 is W1 and the energy of the emitted X-ray is E2, then

[0100]

[0101] E2 = W1·E1

[0102] (II) Monochrome Simulation

[0103] Figure 5 This is a schematic diagram of the structure of a fully focused hyperboloid crystal. The radius of curvature of the crystal surface is R, the radius of curvature of the crystal orientation plane is 2R, and the radius of rotation is r. The incident source S, the hyperboloid crystal, and the exit port F are on a Rowland circle with a radius of R.

[0104] The incident light source is a line source parallel to the crystal cylinder on the focusing circle. X-rays emitted from a point on the Rowland circle (incident focus S) onto any point on the crystal surface can be focused at the same point F after reflection by the crystal. Simultaneously, the fully focusing hyperbolic curved crystal enables X-ray diffraction that satisfies Bragg's law. Utilizing the "strong focusing" effect of the diffracted rays, each diffracted ray converges on a line parallel to the cylinder on the other side of the focusing circle, achieving wavelength selection and enhanced diffraction.

[0105] The principle of Bragg's Law is as follows: Figure 6 As shown, the formula can be expressed as:

[0106] 2dsin(θ)=nλ

[0107] Where λ represents the wavelength of the diffracted X-rays; d is the interplanar spacing of the crystal; n is the diffraction order, usually taken as the first order. θ represents the incident angle of the X-rays. The exit angle is equal to the incident angle. Bragg's law states that when X-rays are incident at an angle θ on a crystal with an interplanar spacing of d, only X-rays with wavelength λ that satisfy Bragg's law are diffracted; otherwise, no diffraction occurs. Based on the structural properties of hyperbolic curved crystals, X-rays incident at an angle φ0 will also exit at φ0. X-rays of specific wavelengths that satisfy Bragg's law will diffract. If we assume that the incident X-rays are approximately ideal pulses, we can use the interval (λ-σ, λ+σ) to approximate the energy percentage of wavelengths λ that satisfy Bragg's law, thus obtaining the exit energy E3 from the curved crystal.

[0108] E3=E2(λ-σ,λ+σ)

[0109] (III) Simulation of the fluorescence process

[0110] Figure 7 This is a schematic diagram of the structure of an X-ray incident sample. The X-rays are incident on the sample from the incident source, with the first point of impact being P. Let μ be the mass absorption coefficient of the sample to the incident photons, and the thickness of the sample be t. max Let t0 be the distance between the incident point and the point of first action of the photon in the sample, and Z0 be the perpendicular distance the incident photon travels through the sample. Let x be a random number selected from (0,1). Then:

[0111] t0=-ln[1-x+xexp(-μtmax / cosφ0)] / μ

[0112] Z0=t0cosφ0

[0113] The probability W2 that a photon does not penetrate the sample before interacting with atom i (i.e., the interaction point is confined within the sample thickness) is:

[0114] W2=1-exp(-μt) max / cosφ0)

[0115] Let C i Let σ be the concentration of element i in the sample. i Let σ be the photoelectric absorption cross section of element i with respect to incident rays. i Y is the absorption coefficient of the sample to the characteristic line of element i. i t represents the fluorescence yield of the element. i Let be the abrupt change coefficient of the absorption limit of the element. Then, the probability W3 of a single fluorescence produced by the interaction of an incident photon with atom i of element i is:

[0116] W3 = Y i C i (1-1 / r i )σ i / μ i

[0117] The primary fluorescence characteristic X-ray also has a corresponding azimuth angle φ1, where φ1 is... Figure 7 The angle between the arrow pointing from P to O and the vertically upward dashed line with P as its endpoint. Let a2 be the distance between the primary point of action and the central axis of the sample, and t1 be the distance between the primary fluorescence point and the secondary fluorescence point O. The probability W4 that restricts the secondary point of action to be within the sample is:

[0118]

[0119] t1=-(1 / μ i )ln{1-x+xexp[-μ i (t max -Z0) / cosφ1]}(cosφ1≥0)

[0120] W4 = 1 - exp[-μ i (t max -Z0) / cosφ1](cosφ1≥0)

[0121] t1=-(1 / μ i )ln[1-xexp(μ i Z0 / cosφ1)](cosφ1<0)

[0122] W4 = 1 - exp(μi Z0 / cosφ1)(cosφ1<0)

[0123] At this point, the penetration distance corresponding to t1 is Z1 = t1cosφ1.

[0124] For the second fluorescence generation process, let C j Let σ be the concentration of the element in sample j. ij Y is the cross section of the characteristic ray of element j on element i. j Let r be the fluorescence yield of element j. j Let be the abrupt change coefficient of the absorption limit of element j. Then the probability of secondary fluorescence produced by the interaction of the characteristic rays of element i with atoms of element j is:

[0125] W5=(1 / μ i )Y j C j (1-1 / r j )σ ij

[0126] For the third fluorescence generation process, let μ j Let W6 be the mass absorption coefficient of the sample for the characteristic rays of element j, and let W6 be the probability that the point of action of the third element is within the sample thickness range.

[0127] W6 = 1 - exp[-μ j (t max -Z0-Z1) / cosφ2](cosφ2≥0)

[0128] W6 = 1 - exp[μ j [(Z0+Z1) / cosφ2](cosφ2<0)

[0129] Let C k Let σ be the concentration of element k in the sample. jk Let Y be the cross section of the characteristic line acting on element k with respect to element j. k r represents the fluorescence yield of element k. k Let be the abrupt change coefficient of the absorption limit of element k. The probability W7 of the third fluorescence produced by the interaction between the characteristic line of element j and the atom of element k is:

[0130] W7=(1 / μ j )Y k C k (1-1 / r k )σ jk

[0131] Based on the above process, the probability of primary fluorescence generation is W2·W3, and the fluorescence intensity E4 = W3·E3; ​​the probability of secondary fluorescence generation is W2·W3·W4·W5, and the fluorescence intensity E5 = W5·E4; the probability of tertiary fluorescence generation is W2·W3·W4·W5·W6·W7, and the fluorescence intensity E6 = W7·E5. Finally, if all three fluorescence events occur simultaneously, the energy E7 of the fluorescent rays emitted from the sample is:

[0132] E7 = E4 + E5 + E6

[0133] Fluorescence intensity can be understood as the magnitude of energy. When X-rays enter a sample, they react with the elements in the sample to produce fluorescent rays, which are then detected by a detector. Essentially, fluorescent rays are also a type of radiation.

[0134] Based on the X-ray fluorescence excitation process model described above, the probabilities can be classified and discussed in the Monte Carlo method to simulate different situations.

[0135] (iv) A Simulation of Compton Scattering and Rayleigh Scattering

[0136] Figure 8 and Figure 9 This diagram illustrates the principles of Compton scattering and Rayleigh scattering. The Compton scattering principle states that when a photon collides with a free electron, energy and momentum are exchanged; some of the photon's energy is transferred to the electron, its own energy decreases, its wavelength increases, and scattered light is formed. The Rayleigh scattering principle states that when an electromagnetic wave passes through a region where the energy distribution does not change significantly, scattering occurs, and the waveform is cone-shaped.

[0137] Let μ C Let φ be the mass absorption coefficient of the sample for Compton scattered photons, φ1 be the incident angle, and W be the probability that the point of action of the Rayleigh scattering ray is within the sample thickness range. 8A The probability that the Compton scattering line occurs within the sample thickness range is W. 8B .

[0138] W 8A =1-exp[-μ(t) max -Z0) / cosφ1](cosφ1<0)

[0139] W 8A =1-exp(μZ0 / cosφ1)(cosφ1≥0)

[0140] W 8B =1-exp(-μ C Z0 / cosφ1)(cosφ1<0)

[0141] W 8B =1-exp(μ CZ0 / cosφ1)(cosφ1≥0)

[0142] After the energy loss due to Rayleigh scattering, the fluorescence energy is E8 = W. 8A After energy loss due to Compton scattering, the fluorescence energy of E3 is E9 = W. 8B •E3, the energy distribution where both types of scattering coexist. 10 =E8+E9.

[0143] (v) Simulation of the detector's response

[0144] Figure 10 The diagram illustrates the detection process structure. The detector's response is a system matrix representing the probability distribution of the counts in the output spectrum when the incident photon is detected. The response of a monochromatic photon can be described as follows:

[0145]

[0146] in,

[0147] E S and E D These represent the energies of the incident and detected spectra, respectively; c1 and c2 represent the linear distribution functions; σ 2 R(E) represents variance. D E S ) represents when the energy is E S The Gaussian distribution of energy when a photon is detected. A baseline for the monochromatic response spectrum is provided to describe the effect of charge sharing, since the energies of all incident photons are above E. D This may affect E D Count the positions on the detection spectrum.

[0148] x is a random number in (0,1), given by Figure 6 It can be seen that the characteristic X-rays are angular The expression for the incident detector is:

[0149]

[0150] The probability of occurrence is:

[0151]

[0152] Therefore, the incident spectrum E can be obtained. S and detection spectrum E D Satisfy E D =W9·E S Based on the above discussion, from formula E S =E7+E 10The fluorescence energy of the incident spectrum can be calculated.

[0153] Step 2: Derive the count rate sequence corresponding to each channel address in the multi-level energy state spectrogram to obtain the maximum value point of each channel address.

[0154] Figure 11 It represents the application of importance sampling in spectrum processing. First, assume that the energy state division range is the inter-tube voltage V g the range (0, T1) is a low energy state, (T1, T2) is a medium energy state, and (T2, T3) is a high energy state, where T1<T2<T3. Taking v as the step size, the inter-tube voltage is changed for simulation in the Monte Carlo model, and feature spectra are obtained, is a floor function, if y ij is the count rate (ordinate) corresponding to the i-th channel address (abscissa) in the j-th spectrum, derive the count rate sequence corresponding to each channel address in the j spectra to obtain the maximum value point j', which satisfies:

[0155]

[0156]

[0157] Step 3: Splice the maximum value points of all channel addresses into a spectral sequence.

[0158] Splice the new maximum count rate points into a new spectral sequence, thus N is the number of channel addresses. Due to the distortion of the detection process and the influence of key voltages, the obtained Y can be considered as the spectrum whose contained information amount is closest to the actual situation, including noise and characteristic X-rays.

[0159] Step 4: Extract an important sampling region from the spectral sequence by using importance sampling.

[0160] Take the spectral sequence as the probability density function for importance sampling, separate characteristic peaks and background noise according to a certain count rate threshold Q. The part larger than Q can be considered to contain characteristic X-ray fluorescence information, and the channel addresses corresponding to this region are taken as the important sampling region; the part smaller than Q is regarded as a background noise region and taken as an unimportant sampling region. Based on this, sampling is performed on the corresponding regions of low, medium and high energy states of real samples respectively, so as to retain important information and remove noise interference.

[0161] Step 5: Perform sampling according to the channel addresses corresponding to the important sampling region in the multi-level energy state spectrogram to obtain sampling spectra of different energy states, and splice the sampling spectra of different energy states into a complete spectrogram.

[0162] Figure 2The flowchart of the scheme is shown. Since the generation of X-rays, the ability to excite element atoms, the generation of scattering and the detection can be reduced to a probability problem in practice, it can be classified and discussed in the Monte Carlo method. Corresponding to different probabilities, the finally detected fluorescence components include all three characteristic fluorescences, as well as the scattered light from the scattering of the three fluorescences, etc., which constitute a complete spectrum.

[0163] Importance sampling, based on the model, finds the characteristic X-ray sampling region with a high probability density according to the spectrum with the maximum information content. It samples the actual spectrum, which not only retains the important spectral information but also filters out some noise components, realizing the scientific fusion of multi-energy state spectra and laying the foundation for subsequent spectral analysis.

[0164] To execute the methods corresponding to the above embodiments and achieve the corresponding functions and technical effects, an X-ray fluorescence spectroscopy multi-energy state sample overlay system is provided below, comprising:

[0165] The simulation module is used to simulate the X-ray fluorescence spectroscopy analysis process multiple times using the Monte Carlo method based on different inter-tube voltages and an energy-dispersive X-ray fluorescence analysis system as a framework, to obtain multi-level energy state spectra. The multi-level energy state spectra include the spectra of different energy states. The multi-level energy state spectra are plotted with channel address as the abscissa and count rate as the ordinate.

[0166] The differentiation module is used to differentiate the count rate sequence corresponding to each channel address in the multi-level energy state spectrum to obtain the maximum point of each channel address.

[0167] The maximum point stitching module is used to stitch together the maximum points of all channels into a spectral sequence.

[0168] An extraction module is used to extract important sampling regions from the spectral sequence using importance sampling.

[0169] The sampling module is used to sample the multi-level energy state spectrum according to the channel address corresponding to the important sampling region, obtain the sampling spectrum of different energy states, and stitch the sampling spectra of different energy states into a complete spectrum.

[0170] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.

[0171] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. An X-ray fluorescence spectroscopy multi-energy state sample superposition method, characterized in that, include: Based on different inter-tube voltages, and using an energy-dispersive X-ray fluorescence analysis system as a framework, the Monte Carlo method was employed to repeatedly simulate the X-ray fluorescence spectral analysis process, resulting in multi-level energy state spectra. The multi-level energy state spectra include the spectra of different energy states. The multi-level energy state spectra are plotted with channel address on the x-axis and count rate on the y-axis. Differentiate the count rate sequence corresponding to each channel in the multi-level energy state spectrum to obtain the maximum point of each channel; The maxima of all the path addresses are stitched together to form a spectral sequence; Importance sampling is used to extract important sampling regions from the spectral sequence; Sampling is performed according to the channel address corresponding to the important sampling region in the multi-level energy state spectrum to obtain the sampling spectrum of different energy states, and the sampling spectra of different energy states are stitched together into a complete spectrum. Based on different inter-tube voltages and using an energy-dispersive X-ray fluorescence analysis system as a framework, the Monte Carlo method was employed to repeatedly simulate the X-ray fluorescence spectral analysis process, obtaining multi-level energy state spectra, specifically including: from 0 to voltage T 3. setting a plurality of inter-tube voltages with a step of v ; wherein, is a low energy state, is a medium energy state, is a high energy state, ; Based on each inter-tube voltage, using an energy-dispersive X-ray fluorescence analysis system as a framework, the Monte Carlo method is employed to simulate the X-ray fluorescence spectroscopy analysis process, obtaining the spectrum of the energy state corresponding to the inter-tube voltage. The X-ray fluorescence spectroscopy analysis process includes: X-ray generation, monochromatization, fluorescence process, Compton scattering and Rayleigh scattering, and detector response. By plotting all the spectra obtained from the simulation in the same coordinate system, a multi-level energy state spectrum is obtained; The energy-dispersive X-ray fluorescence analysis system includes an X-ray tube, a fully focusing hyperbolic flexural crystal, a sample to be tested, and a detector. The X-ray tube generates X-rays, which are incident on the fully focusing hyperbolic flexural crystal. The incident fully focusing hyperbolic flexural crystal monochromates the wavelength of the incident X-rays, and the emitted single-wavelength X-rays are incident on the sample to be tested. The incident photons of the single-wavelength X-rays react with the target elements in the sample to produce multiple fluorescence through the photoelectric effect, and / or Compton scattering and Rayleigh scattering to produce scattered light. The detector receives the multiple fluorescence and / or scattered light and converts the optical signals into electrical signals. The multiple fluorescence includes primary fluorescence, secondary fluorescence, and tertiary fluorescence.

2. The X-ray fluorescence spectrometry multi-energy state sample superposition method according to claim 1, characterized in that, A simulation of X-ray generation during X-ray fluorescence spectroscopy analysis was performed using the Monte Carlo method, specifically including: Based on the geometric parameters of the X-ray tube and the fully focused hyperbolic curved crystal, according to the formula... and Calculate the minimum azimuth angle between the radiation source photon of the X-ray tube and the visible portion of the fully focused hyperbolic curved crystal. and maximum azimuth ;in, The radius of the upper collimation hole. The perpendicular distance between the point of interaction between the radiation source target and the refractive surface. This is the vertical distance between the radiation source target and the bottom surface of the lower collimation hole; Based on the minimum azimuth angle and maximum azimuth According to the formula Determine the azimuth angle of the incident photons from the X-ray tube's radiation source onto the visible portion of the fully focusing hyperbolic curved crystal. ;in, for Random numbers; According to the preset inter-tube voltage and azimuth angle of the X-ray tube To make the X-ray tube emit X-rays; Based on the minimum azimuth angle and maximum azimuth According to the formula Calculate the probability that photons from the X-ray tube's radiation source will be incident on the fully focusing hyperbolic curved crystal. ; Associative probability X-ray energy generated by the X-ray tube based on the preset inter-tube voltage According to the formula Determine the energy of the rays incident on the fully focused hyperbolic curved crystal. .

3. The X-ray fluorescence spectrometry multi-energy state sample superposition method according to claim 2, characterized in that, A simulation of monochromatization in X-ray fluorescence spectroscopy analysis was performed using the Monte Carlo method, specifically including: When a fully focused hyperbolic curved crystal receives X-rays, it will diffract single-wavelength X-rays that satisfy Bragg's law. Based on the energy of the rays incident on the fully focused hyperbolic spherical crystal According to the formula Determine the energy of the rays emitted from the fully focused hyperbolic curved crystal. ;in, The wavelength of a single-wavelength X-ray. Let be the distribution variance.

4. The X-ray fluorescence spectrometry multi-energy state sample superposition method according to claim 3, characterized in that, A simulation of the fluorescence process in X-ray fluorescence spectroscopy analysis was performed using the Monte Carlo method, specifically including: According to azimuth According to the formula and Determine the vertical distance at which the incident photon penetrates the sample under test. ;in, Let be the distance between the incident point and the point of first action of the incident photon in the sample under test. The mass absorption coefficient of the sample to be tested for incident photons is denoted as . The thickness of the sample to be tested; According to azimuth According to the formula Determine the probability that the point of action is confined to the thickness range of the sample being tested. ; According to the formula To determine the interaction between the incident photon and the elements in the sample. The probability of producing a single burst of fluorescence due to atomic interaction. ;in, The fluorescence yield of the element, Elements in the sample to be tested concentration, For elements The mutation coefficient of the absorption limit, For elements For the photoelectric absorption cross section of the incident beam, For the element pair of the sample to be tested The absorption coefficient of the characteristic line; Based on the corresponding azimuth angle of a single fluorescence characteristic X-ray According to the formula Determine the probability that the secondary action point is within the thickness range of the sample to be tested. ; According to the formula Determine the penetration distance between the primary and secondary points of action. ;in, The distance between the primary point of action and the secondary point of action; According to the formula Determine the element Characteristic rays and elements The probability of secondary fluorescence produced by atomic interaction ;in, For elements fluorescent output, For elements concentration, For elements The mutation coefficient of the absorption limit, For elements For elements The cross section through which the characteristic rays act; According to the formula Determine the probability that the three application points fall within the thickness range of the sample to be tested. ;in, The azimuth angle corresponding to the secondary fluorescence characteristic X-rays. For the element pair of the sample to be tested Mass absorption coefficient of characteristic rays; According to the formula Determine the element Feature lines and elements The probability of third-order fluorescence produced by atomic interactions ;in, For elements fluorescent output, Element in the sample concentration, For elements The absorption limit mutation coefficient, For elements For elements The characteristic line acts on the cross section; Probability of primary fluorescence generation for Fluorescence energy of a single fluorescence event for ; Probability of secondary fluorescence generation for fluorescence energy of secondary fluorescence for ; Probability of three-dimensional fluorescence generation for fluorescence energy of tertiary fluorescence for ; If primary fluorescence, secondary fluorescence, and tertiary fluorescence occur simultaneously, the energy of the fluorescent rays emitted from the sample to be tested... for .

5. The X-ray fluorescence spectrometry multi-energy state sample superposition method according to claim 4, characterized in that, A simulation of Compton and Rayleigh scattering in X-ray fluorescence spectroscopy analysis was performed using the Monte Carlo method, specifically including: According to the formula Determine the probability that the point of action for Rayleigh scattering occurs within the thickness range of the sample under test. ; According to the formula Determine the probability that the point of action of the Compton scattering ray is within the thickness range of the sample under test. ; Fluorescence energy after energy loss due to Rayleigh scattering for ; Fluorescence energy after Compton scattering energy loss for ; If Rayleigh scattering and Compton scattering are both present, then the fluorescence energy distribution... for .

6. The X-ray fluorescence spectrometry multi-energy state sample superposition method according to claim 5, characterized in that, A simulation of the detector response during X-ray fluorescence spectroscopy analysis was performed using the Monte Carlo method, specifically including: When the incident spectral energy is The Gaussian distribution of energy when a photon is detected by a detector is: ;in, This indicates the energy of the detected spectrum. Denotes the first linear distribution function. Represents variance. This indicates the effect of charge sharing. ; Incident light angle into the detector The expression is ; Probability of incident light entering the detector for ; Incident spectral energy of the detector and detection spectral energy satisfy ;in, .

7. The X-ray fluorescence spectrometry multi-energy state sample superposition method according to claim 1, characterized in that, The maximum point satisfies: ； ； in, It is a maximum point. For the first The corresponding spectrum The counting rate of road addresses.

8. The X-ray fluorescence spectrometry multi-energy state sample superposition method according to claim 1, characterized in that, Importance sampling is used to extract important sampling regions from the spectral sequence, specifically including: Regions in the spectral sequence with count rates greater than the threshold are designated as important sampling areas, while regions with count rates less than the threshold are designated as background noise areas.

9. A multi-energy state sample superposition system for X-ray fluorescence spectroscopy, characterized in that, include: The simulation module is used to simulate the X-ray fluorescence spectroscopy analysis process multiple times using the Monte Carlo method based on different inter-tube voltages and an energy-dispersive X-ray fluorescence analysis system as a framework, to obtain multi-level energy state spectra. The multi-level energy state spectra include the spectra of different energy states. The multi-level energy state spectra are plotted with channel address as the abscissa and count rate as the ordinate. The differentiation module is used to differentiate the count rate sequence corresponding to each channel in the multi-level energy state spectrum to obtain the maximum point of each channel. The maximum point stitching module is used to stitch together the maximum points of all channels into a spectral sequence; An extraction module is used to extract important sampling regions from the spectral sequence using importance sampling; The sampling module is used to sample the multi-level energy state spectrum according to the channel address corresponding to the important sampling region, obtain the sampling spectrum of different energy states, and stitch the sampling spectra of different energy states into a complete spectrum. Based on different inter-tube voltages and using an energy-dispersive X-ray fluorescence analysis system as a framework, the Monte Carlo method was employed to repeatedly simulate the X-ray fluorescence spectral analysis process, obtaining multi-level energy state spectra, specifically including: Starting from 0 to voltage T 3, with v Multiple inter-transistor voltages are set as step sizes; among them, It is in a low-energy state. It is a medium energy state. It is a high-energy state. ; Based on each inter-tube voltage, using an energy-dispersive X-ray fluorescence analysis system as a framework, the Monte Carlo method is employed to simulate the X-ray fluorescence spectroscopy analysis process, obtaining the spectrum of the energy state corresponding to the inter-tube voltage. The X-ray fluorescence spectroscopy analysis process includes: X-ray generation, monochromatization, fluorescence process, Compton scattering and Rayleigh scattering, and detector response. By plotting all the spectra obtained from the simulation in the same coordinate system, a multi-level energy state spectrum is obtained; The energy-dispersive X-ray fluorescence analysis system includes an X-ray tube, a fully focusing hyperbolic flexural crystal, a sample to be tested, and a detector. The X-ray tube generates X-rays, which are incident on the fully focusing hyperbolic flexural crystal. The incident fully focusing hyperbolic flexural crystal monochromates the wavelength of the incident X-rays, and the emitted single-wavelength X-rays are incident on the sample to be tested. The incident photons of the single-wavelength X-rays react with the target elements in the sample to produce multiple fluorescence through the photoelectric effect, and / or Compton scattering and Rayleigh scattering to produce scattered light. The detector receives the multiple fluorescence and / or scattered light and converts the optical signals into electrical signals. The multiple fluorescence includes primary fluorescence, secondary fluorescence, and tertiary fluorescence.

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