X-ray fluorescence spectrum monochromator multi-objective optimization design method and system

Abstract

The invention relates to the technical field of X-ray optics and spectral analysis, in particular to a multi-objective optimization design method and system for an X-ray fluorescence spectrum monochromator, and the main points of the technical scheme are as follows: S1, parameter and database input, S2, source spectrum generation and calibration, S3, monochromator dynamics solution, S4, multi-scheme comprehensive scoring and optimization selection, and S5, XRF forward modeling and system-level indexes. According to the method, an X-ray tube source parameter library is established to synthesize a real source spectrum containing a continuous spectrum and a characteristic line, an optimal design scheme is automatically searched in a multi-parameter space through a normalized weighted scoring system, and finally a simulated full spectrum is generated and system-level performance indexes are evaluated through an end-to-end'source-monochromatization-sample-detector 'forward modeling link. The problems that in a traditional design method, parameter coupling is complex, and model prediction deviation is large are solved, collaborative optimization of energy resolution, flux and purity is achieved, and technical support is provided for developing a high-performance XRF spectrograph.

Description

Technical Field

[0001] This invention relates to the field of X-ray optics and spectral analysis technology, specifically to a multi-objective optimization design method and system for X-ray fluorescence spectroscopy monochromators. Background Technology

[0002] X-ray fluorescence spectroscopy (XRF) is a non-destructive analytical technique based on the generation of characteristic X-rays from inner-shell electron transitions. It is widely used in environmental monitoring, geological exploration, materials science, and archaeological identification. By measuring the fluorescence spectrum emitted by a sample under X-ray excitation, this technique can quickly and accurately determine the types and contents of elements in the sample. However, traditional energy-dispersive X-ray fluorescence spectrometers (ED-XRF) suffer from technical bottlenecks such as limited energy resolution, scattering background interference, and insufficient excitation efficiency. In recent years, monochromator technology based on crystal diffraction has provided a new approach to solving these problems. Johansson-type bent crystal monochromators can achieve point-to-point focusing by bending the crystal to a specific radius of curvature, while providing high energy resolution and high reflection efficiency. However, monochromator design involves multiple parameters such as crystal material selection (Si, Ge, LiF, quartz, etc.), crystal plane indices (111, 220, 200, etc.), bending radius, and orientation angle. These parameters have complex coupling relationships, and traditional single-parameter optimization methods are difficult to obtain the global optimal solution.

[0003] Multi-objective optimization algorithms have been widely used in engineering design, but their application in the field of X-ray optics is still insufficient. Existing research mainly focuses on the optimization of single performance indicators and lacks systematic analysis of the trade-offs between multiple objectives. To solve the above problems, this invention proposes a multi-objective optimization design method and system for X-ray fluorescence spectrometer monochromators. It can automatically search for optimal design parameters under given constraints and achieve synergistic optimization of multiple performance indicators such as energy resolution, flux, and monochromatic purity, providing technical support for the high performance of XRF spectrometers. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a multi-objective optimization design method and system for X-ray fluorescence spectrometer monochromators, solving the problems mentioned in the background art.

[0005] The above-mentioned technical objective of the present invention is achieved through the following technical solution:

[0006] In a first aspect, this invention proposes a multi-objective optimization design method for X-ray fluorescence spectroscopy monochromators, comprising the following steps:

[0007] S1. Parameters and Database Input: Collect key physical parameters of the source, crystal, detector, and sample, and construct a structured database, unifying them into queryable configuration objects, including tube voltage and current, target and window parameters, source spot geometry, crystal material, and indices. Lattice constant, detector quantum efficiency, and energy range of the target element;

[0008] S2. Source Spectrum Generation and Calibration: Synthesizing Real Source Spectra Including Continuous Spectra and Characteristic Lines Based on Material Properties The flux is calibrated and normalized based on the geometric solid angle and tube power.

[0009] S3. Monochromator Dynamics Solution: Approximate Takagi–Taupin (T–T) dynamics diffraction is performed on the candidate crystal, coupled with the Johansson bending crystal focusing effect and material absorption. An adaptive encrypted sampling strategy is implemented in the energy domain to calculate the output energy spectrum after monochromatization. ;

[0010] S4. Comprehensive evaluation and selection of multiple schemes: Extract flux, energy resolution, monochromatic efficiency and purity indicators, construct a normalized weighted scoring system, and automatically search for the optimal design parameters that meet the constraints from the candidate crystal library.

[0011] S5, XRF forward modeling and system-level metrics: Drive the sample model with optimal monochromatic output, generate simulated full spectrum and calculate system-level performance metrics including peak-to-background ratio (PBR) and signal-to-noise ratio (SNR), achieving end-to-end verification from device optimization to spectroscopic performance.

[0012] Preferably, the source spectrum generation and calibration in step S2 includes:

[0013] Based on Kramers' formula and introducing the Kirkpatrick–Wiedmann modified structure, a braking radiation continuum is constructed.

[0014] The characteristic line components of the anode material are superimposed using the Pseudo-Voigt function, taking into account the natural linewidth and instrument broadening.

[0015] The material mass attenuation coefficient model is used to perform energy-dependent transmission correction on the X-ray tube exit window and filter.

[0016] according to Solid angle measurement yields the flux baseline per spherametric degree. .

[0017] Preferably, the monochromator dynamics solution in step S3 includes:

[0018] Energy-dependent structure factors are constructed using the Cromer–Mann atomic scattering factor, the Debye–Waller factor, and the anomalous dispersion term. ;

[0019] according to The Darwin width, calculated using the cosines of the incident / exit directions, is energy dependent. With extinction depth ;

[0020] Introducing normalized thickness Distinguishing between thin-crystal and thick-crystal grains: Thin-crystal grains are produced using... Type kinematic approximation, thick crystals adopt Type dynamics expression, and based on To achieve a smooth transition from kinematics to dynamics theory.

[0021] Preferably, the adaptive encryption sampling strategy implemented in step S3 is as follows:

[0022] For perfect crystals, a dense sampling window of no less than ±0.1keV is set in the Darwin-width core region, and a three-segment density distribution strategy of core region and left and right wing regions is adopted to eliminate peak position measurement value drift.

[0023] For mosaic crystals, encryption is performed around mosaic broadening, and an engineering upper limit is set for the far-band region to suppress invalid integration.

[0024] Preferably, the modeling of Johansson bending and geometric effects in step S3 includes:

[0025] Based on bending parameters and strain gradient, a piecewise dynamic expression is given in the weak bending region and the strong bending region.

[0026] The focus enhancement factor in piecewise constant form is calculated using the Rowland circle deviation threshold approximation.

[0027] Introducing asymmetric angles Correct the width and intensity scale of the reflection window;

[0028] Applying constraints to optical thickness , as the stabilization boundary, where The absorption coefficient is... For path length, when When the value exceeds this threshold, it is considered to be approximately complete absorption, in order to avoid numerical underflow in the low-energy region.

[0029] Preferably, the multi-solution comprehensive scoring and selection in step S4 includes the following quantitative indicators:

[0030] Monochromatic efficiency: the ratio of output flux to incident flux in the effective energy region;

[0031] Energy resolution: Full width at half maximum (FWHM) of the output peak ;

[0032] Monochromatic purity: main peak The proportion of the flux within the range to the total output flux.

[0033] Preferably, the XRF forward modeling and system-level metrics in step S5 include:

[0034] The simulated full spectrum was obtained by superimposing Rayleigh scattering, Compton scattering, and a continuous background model;

[0035] Calculate the sample self-absorption effect, geometric solid angle weight, and detector quantum efficiency. ;

[0036] The total count rate, peak-to-back ratio, and signal-to-noise ratio are used to evaluate the overall performance of the system.

[0037] Secondly, the present invention provides a multi-objective optimization design system for X-ray fluorescence spectroscopy monochromators, comprising:

[0038] Parameters and Database Module: Used to store source parameters, candidate crystal materials and parameters, detector characteristics, and element line libraries;

[0039] Source spectrum simulation module: used to synthesize and calibrate the incident energy spectrum. ;

[0040] The monochromator dynamics core module is used to perform dynamic theory solutions, adaptive energy sampling, and calculation of bent crystal geometric effects.

[0041] Optimization evaluation module: used for normalized weighted scoring and automatic selection of the best solution from multiple options;

[0042] System-level verification module: used to generate the simulated full spectrum and output system-level performance index data.

[0043] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method described in the first aspect.

[0044] In summary, the present invention has the following main beneficial effects:

[0045] This invention first synthesizes a true source spectrum containing continuous spectrum and characteristic lines by establishing an X-ray tube source parameter library. Then, based on the approximate Takagi–Taupin (T–T) dynamic diffraction theory, it couples the bent crystal geometric focusing effect with material absorption to establish an energy-dependent reflection model of the monochromator. Adaptive encrypted sampling is implemented in the energy domain to balance computational accuracy and efficiency. Through a normalized weighted scoring system, the optimal design scheme is automatically searched in the multi-parameter space. Finally, through an end-to-end "source-monochromatization-sample-detector" forward modeling link, a simulated full spectrum is generated and system-level performance indicators are evaluated. This invention overcomes the problems of complex parameter coupling and large model prediction deviation in traditional design methods, and achieves synergistic optimization of energy resolution, flux, and purity, providing technical support for the development of high-performance XRF spectrometers. Attached Figure Description

[0046] Figure 1 This is an overall flowchart of the monochromator design based on multi-objective optimization of the present invention;

[0047] Figure 2 This is a schematic diagram of the monochromator dynamics diffraction and bent crystal focusing mechanism of the present invention;

[0048] Figure 3 This is the core optimized main flowchart of the present invention. Detailed Implementation

[0049] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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 some embodiments of the present invention, but not all embodiments. Based on the described 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.

[0050] The following embodiments are used to illustrate the present invention, but should not be used to limit the scope of protection of the present invention. The conditions in the embodiments can be further adjusted according to specific conditions, and simple improvements to the method of the present invention under the premise of the concept of the present invention are all within the scope of protection claimed by the present invention.

[0051] Example 1

[0052] refer to Figure 1 The overall process for designing the X-ray fluorescence spectroscopy monochromator based on multi-objective optimization according to this invention is as follows:

[0053] S1, Parameters and Database Input

[0054] This step compiles key physical parameters and material libraries for the source, crystal, detector, and sample, unifying them into a queryable configuration object. First, it unifies the key physical parameters, materials, and wire libraries of the source, crystal, detector, and sample into a queryable configuration object, including tube voltage and current, target and window, source spot and geometry, crystal materials, and... The system outputs a standardized "system configuration object" containing models of lattice and absorption, detector area / quantum efficiency / energy division and dead time, as well as target elements and energy regions, which can be directly called for subsequent spectrum generation and dynamics solving.

[0055] S2. Source spectrum generation and calibration

[0056] This step synthesizes a continuous spectrum and characteristic lines based on material properties, superimposes them through window transmission to obtain the true source spectrum, and calibrates the flux according to tube power and geometric normalization. Based on this, the true source spectrum is synthesized: the continuous spectrum uses the Kramers formula and fully considers target / window self-absorption and transmission effects; the characteristic lines are broadened using a Voigt broadening and superposition instrument, and then geometrically normalized according to solid angle, squared distance, and aperture. Absolute flux calibration is then performed with reference measurements or manufacturer curves to obtain the calibrated original energy spectrum. For subsequent use.

[0057] S3, Monochromator Dynamics Solution

[0058] This step calculates the reflectivity and focusing gain of the candidate crystal, and couples geometry, polarization, and absorption to obtain the monochromatic energy spectrum, extracting core indicators such as flux, efficiency, and purity. The key lies in performing dynamic diffraction on the candidate crystal, including asymmetric parameters. The study investigated Darwin width, extinction depth, and polarization factor, coupled with bent crystal focusing (Johansson and Rowland conditions), thickness absorption, and geometric occlusion. Simultaneously, an adaptive encrypted sampling strategy was implemented in the energy domain to output the monochromatic energy spectrum. And core indicators such as flux, energy FWHM, purity, stray power and coupling efficiency.

[0059] S4. Comprehensive scoring and selection of multiple options

[0060] This step performs a normalized weighted score on flux, efficiency, and purity to select the monochromatic scheme with the best overall performance, in terms of materials / ,thickness Bending radius Asymmetric angles and Generate solutions within the geometric and other design spaces, and increase flux. , ,purity , stray By normalizing and weighting the indicators, the optimal monochromator configuration is finally given, and the key parameters and indicators are output as subsequent system configurations.

[0061] S5, XRF Forward Modeling and System-Level Metrics

[0062] This step drives the sample with the optimal monochromator to generate a simulated spectrum containing characteristic lines and background. System-level performance parameters such as PBR, SNR, and count rate are calculated to evaluate the overall system performance. XRF forward modeling is then performed on the sample using the optimal monochromator. The injected sample model calculates fluorescence generation and self-absorption, and the Rayleigh / Compton and detector responses are superimposed to obtain the simulated spectrum. Then, the system-level PBR, SNR, count rate and linearity margin are evaluated, and a recommended operating point is given, thus forming an end-to-end closed loop of "data input → source spectrum calibration → kinetic solution → scheme optimization → system-level verification".

[0063] Example 2

[0064] refer to Figure 2 To illustrate the monochromator dynamics diffraction and bent crystal focusing mechanism of this invention, the left X-ray tube emits a broad-spectrum unmonochromatic beam (dashed line), which is also when the beam is incident on the marked... When bending crystals, the Bragg condition must be satisfied: The energy fraction undergoes dynamic diffraction within the crystal and is selected, with its direction being... For geometric identification, the output is a solid line "diffraction beam";

[0065] radius of curvature of bent crystal To satisfy these The light rays are focused under approximate Rowland geometry and directed towards the sample;

[0066] At the same time, the angle between the crystal surface normal and the crystal plane normal This indicates asymmetric cutting, which amplifies / compresses the beam width and divergence and changes the effective Darwin width and reflectivity, thus affecting energy resolution and flux tradeoff; finally, the detector completes signal acquisition.

[0067] Example 3

[0068] refer to Figure 3 The core optimization flowchart of this invention clearly illustrates the basis and entire process of crystal selection, as detailed below:

[0069] The first step is to pursue the optimal "overall training performance" under fixed data distribution and engineering constraints. The overall performance is composed of three types of quantifiable indicators:

[0070] Convergence efficiency: The rate of decrease and stability of loss within the unit calculation budget, taking into account both speed and reproducibility;

[0071] Characterization capability: Reconstruction quality at the structural and physical quantity levels (overall error, key peak structure, consistency mapping).

[0072] Operational robustness: numerical stability (no gradient explosion / vanishing), output availability (non-negative, range-controlled), and resistance to noise and disturbances;

[0073] During evaluation, the three types of indicators are normalized and weighted according to preset weights to obtain a single comparable score. Red line constraints are executed simultaneously: the learning rate and gradient norm are within a safe range, the regularization coefficient does not exceed the limit, and all calculations explicitly mask and clean up NaN / Inf to ensure the reliability of the conclusions.

[0074] The second step is to break down the overall goal into three independently verifiable computational branches, which are aligned with each other with clear interfaces to form a traceable closed loop.

[0075] First, the source spectrum generation module transforms the engineering settings into a physically correct incident energy spectrum: we start from tube voltage and current, target material and window parameters, and simultaneously construct a continuous background of braking radiation and characteristic emission lines of the target material, and perform physical broadening using intrinsic broadening and instrument functions; then, the energy dependence attenuation of light in the window, filter, air and related materials is accurately calculated according to the actual geometric path length, and the polarization state is kept consistent.

[0076] Finally, absolute calibration was performed based on the tube power and photon-energy conversion relationship. Then, the full-space flux was normalized to the energy spectrum per unit solid angle according to the actual fixed angle, thus obtaining the energy spectrum that can be directly sampled downstream. shaft and Complete interface information, etc.

[0077] Based on this incident light, the monochromatic dynamics module converts the energy spectrum into a monochromatic and focused output: for candidate crystals and a library of geometric schemes, we rely on interplanar spacing, Bragg angle and structure factor to establish a dynamic model of Johansson bent crystals, which explicitly characterizes the coupled response of Darwin width, extinction length and effective thickness with energy.

[0078] To balance peak shape fidelity and computational efficiency, we implement energy-adaptive encrypted sampling around the target main peak, while sparsely sampling the out-of-band region to capture stray components. Combining Rowland circle geometry, we calculate the focusing gain and correct for energy axis shift and defocusing effects caused by curvature. We also incorporate the incident divergence and detector acceptance angle into the prediction of peak position and shape through convolution.

[0079] At the same time, we incorporate the material absorption along the reflection path and the modulation of reflection intensity by s / p polarization, thus obtaining a geometrically and materially corrected image on the detection surface. Simultaneously, it generates interpretable physical quantities such as peak reflectivity, effective bandwidth, focusing gain, and energy coordinate calibration, establishing a one-to-one causal chain between these quantities and the corresponding incident slices.

[0080] Subsequently, the index evaluation module compresses the spectral shape into a digital representation that can be compared horizontally: we first complete robust peak location and energy band definition on the output spectrum, then integrate the target energy band to obtain the usable flux, and use the incident integral of the same energy band as a reference to calculate the conversion efficiency; in terms of resolution and purity, we use the energy resolution of the main peak at half maximum width (HWHM), and at the same time use the proportion of flux within HWHM to the total flux to characterize the spectral purity, thereby intuitively suppressing stray leakage;

[0081] To ensure that the conclusions are not contaminated by spurious signals, we enforced screening of the physical upper limits of reflectivity and efficiency, removed any outliers at the numerical level, and finally delivered peak position, bandwidth, flux, efficiency, purity, and their boundary markers as a unified interface to the overall evaluation.

[0082] When the outputs of the three branches are brought back to the overall evaluation level, we first normalize the flux, efficiency and purity so that they fall within a consistent dimension range, and then weight them according to the established preferences to form a single total score.

[0083] When selecting the best option, we only retain the solution that satisfies all constraints and has the highest total score. We report the solution along with the complete output spectrum, along with key physical quantities such as peak reflectivity and focusing gain, to support engineering verification and experimental alignment.

[0084] Finally, we directly interfaced the optimal solution and its single-chromatogram directly into the X-ray fluorescence forward modeling module, creating a closed-loop data channel for "design-evaluation-application" and allowing performance improvements to flow back into observables and experimental planning.

[0085] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that, unless otherwise defined, the technical or scientific terms used in this invention should be understood in the ordinary sense by those skilled in the art to which this invention pertains, and the terms "comprising" or "including" or similar terms used in this invention mean that the element or object preceding the word covers the element or object listed after the word and its equivalents.

[0086] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A multi-objective optimization design method for X-ray fluorescence spectroscopy monochromator, characterized in that, Includes the following steps: S1. Parameters and Database Input: Collect key physical parameters of the source, crystal, detector, and sample, and construct a structured database, unifying them into queryable configuration objects, including tube voltage and current, target and window parameters, source spot geometry, crystal material, and indices. Lattice constant, detector quantum efficiency, and energy range of the target element; S2. Source Spectrum Generation and Calibration: Synthesizing Real Source Spectra Including Continuous Spectra and Characteristic Lines Based on Material Properties The flux is calibrated and normalized based on the geometric solid angle and tube power. S3. Monochromator Dynamics Solution: Approximate Takagi–Taupin (T–T) dynamics diffraction is performed on the candidate crystal, coupled with the Johansson bending crystal focusing effect and material absorption. An adaptive encrypted sampling strategy is implemented in the energy domain to calculate the output energy spectrum after monochromatization. ; S4. Comprehensive evaluation and selection of multiple schemes: Extract flux, energy resolution, monochromatic efficiency and purity indicators, construct a normalized weighted scoring system, and automatically search for the optimal design parameters that meet the constraints from the candidate crystal library. S5, XRF forward modeling and system-level metrics: Drive the sample model with optimal monochromatic output, generate simulated full spectrum and calculate system-level performance metrics including peak-to-background ratio (PBR) and signal-to-noise ratio (SNR), achieving end-to-end verification from device optimization to spectroscopic performance.

2. The method according to claim 1, characterized in that, The source spectrum generation and calibration in step S2 includes: Based on Kramers' formula and introducing the Kirkpatrick–Wiedmann modified structure, a braking radiation continuum is constructed. The characteristic line components of the anode material are superimposed using the Pseudo-Voigt function, taking into account the natural linewidth and instrument broadening. The material mass attenuation coefficient model is used to perform energy-dependent transmission correction on the X-ray tube exit window and filter. according to Solid angle measurement yields the flux baseline per spherametric degree. .

3. The method according to claim 1, characterized in that, The monochromator dynamics solution in step S3 includes: Energy-dependent structure factors are constructed using the Cromer–Mann atomic scattering factor, the Debye–Waller factor, and the anomalous dispersion term. ; according to The Darwin width, calculated using the cosines of the incident / exit directions, is energy dependent. With extinction depth ; Introducing normalized thickness Distinguishing between thin-crystal and thick-crystal grains: Thin-crystal grains are produced using... Type kinematic approximation, thick crystals adopt Type dynamics expression, and based on To achieve a smooth transition from kinematics to dynamics theory.

4. The method according to claim 1, characterized in that, The adaptive encryption sampling strategy implemented in step S3 is as follows: For perfect crystals, a dense sampling window of no less than ±0.1keV is set in the Darwin-width core region, and a three-segment density distribution strategy of core region and left and right wing regions is adopted to eliminate peak position measurement value drift. For mosaic crystals, encryption is performed around mosaic broadening, and an engineering upper limit is set for the far-band region to suppress invalid integration.

5. The method according to claim 1, characterized in that, The modeling of Johansson bending and geometric effects in step S3 includes: Based on bending parameters and strain gradient, a piecewise dynamic expression is given in the weak bending region and the strong bending region. The focus enhancement factor in piecewise constant form is calculated using the Rowland circle deviation threshold approximation. Introducing asymmetric angles Correct the width and intensity scale of the reflection window; Applying constraints to optical thickness , as the stabilization boundary, where The absorption coefficient is... For path length, when When the value exceeds this threshold, it is considered to be approximately complete absorption, in order to avoid numerical underflow in the low-energy region.

6. The method according to claim 1, characterized in that, The multi-scheme comprehensive scoring and selection in step S4 includes the following quantitative indicators: Monochromatic efficiency: the ratio of output flux to incident flux in the effective energy region; Energy resolution: Full width at half maximum (FWHM) of the output peak ; Monochromatic purity: main peak The proportion of the flux within the range to the total output flux.

7. The method according to claim 1, characterized in that, The XRF forward modeling and system-level metrics in step S5 include: The simulated full spectrum was obtained by superimposing Rayleigh scattering, Compton scattering, and a continuous background model; Calculate the sample self-absorption effect, geometric solid angle weight, and detector quantum efficiency. ; The total count rate, peak-to-back ratio, and signal-to-noise ratio are used to evaluate the overall performance of the system.

8. A multi-objective optimization design system for an X-ray fluorescence spectroscopy monochromator implementing the method of any one of claims 1-7, characterized in that, include: Parameters and Database Module: Used to store source parameters, candidate crystal materials and parameters, detector characteristics, and element line libraries; Source spectrum simulation module: used to synthesize and calibrate the incident energy spectrum. ; The monochromator dynamics core module is used to perform dynamic theory solutions, adaptive energy sampling, and calculation of bent crystal geometric effects. Optimization evaluation module: used for normalized weighted scoring and automatic selection of the best solution from multiple options; System-level verification module: used to generate the simulated full spectrum and output system-level performance index data.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the program implements the steps of the method according to any one of claims 1-7.

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