A method for optimizing the structure parameters of a small-angle X-ray scattering instrument collimation system

Abstract

The application belongs to the technical field of precise optical measuring instruments, and discloses a kind of small-angle X-ray scattering instrument collimation system structure parameter optimization method.The method comprises the following steps: S1, a simulation model of the scattering instrument collimation system is constructed, and the initial structure parameters of the simulation model are set;S2, the position of the light source is set, the geometric coordinates are constructed with the light source as the origin, and the photons emitted from the light source are constructed in the geometric coordinate system, the process of the photons sequentially passing through the converging light optical device and the slit group and finally falling on the surface grid of the detector is simulated, and the number of photons in each grid of the detector surface grid is determined;S3, an evaluation system of the collimation system structure parameters is constructed, the structure parameters of the collimation system are taken as the input, the evaluation system is used to construct an optimization model for the optimization target, the optimal structure parameters corresponding to the optimization model are solved, and the optimization of the collimation system structure parameters is realized.Through the application, the problem of low accuracy of structure parameters in the small-angle X-ray collimation system is solved.

Description

Technical Field

[0001] This invention belongs to the technical field of precision optical measuring instruments, and more specifically, relates to a method for optimizing the structural parameters of a collimation system for a small-angle X-ray scattering instrument. Background Technology

[0002] Small-angle X-ray scattering (SAXS) is one of the main methods for studying the structure of matter at the nanoscale (1–100 nm). It is suitable for measuring the microstructure of samples such as powder particles, polymers, nanocomposite materials, colloids, biomacromolecules, and semiconductors, and has broad application prospects in fields such as biology, materials science, chemistry, physics, and the semiconductor industry.

[0003] Currently, X-rays emitted by synchrotron radiation sources possess characteristics such as high brightness and high collimation, often resulting in better SAXS experiments conducted on synchrotron radiation sources. However, the construction of synchrotron radiation sources requires a huge amount of land, and the corresponding equipment is large, expensive, and difficult to maintain. Experimental opportunities using synchrotron radiation sources are scarce both domestically and internationally, hindering their widespread application in disciplines such as integrated circuit measurement, medicine, and biology. In research related to the design of laboratory-level SAXS instruments, the optimization design of the collimation system is one of the most crucial aspects. The collimation system not only defines the characteristics of the X-ray beam reaching the sample but also constrains the divergence of the main X-ray beam, thus defining the minimum achievable scattering angle of the instrument, ultimately affecting the overall performance parameters of the instrument. The parameters of the X-ray beam in a small-angle X-ray scatterer, including beam spot diameter, beam divergence, luminous flux, and the periodic range of measurable nanostructures, are the main parameters that need to be constrained in the optimization design of the collimation system.

[0004] Currently, commonly used collimation system optimization methods are based on simple geometric models of the collimation system, and obtain the optimal values ​​of the parameters to be optimized analytically under constraints of a large number of parameters. These commonly used optimization methods have the following drawbacks: this optimization design process completely ignores the beam characteristics of the X-ray beam, including intensity distribution and beam divergence, lacking sufficient flexibility; the beam characteristics calculated based on simple geometric models differ somewhat from the actual beam characteristics, making it difficult to meet the requirements of more refined and accurate collimation system designs. Therefore, developing new design methods for small-angle X-ray collimation systems is of great significance. Summary of the Invention

[0005] In view of the above-mentioned defects or improvement needs of the existing technology, the present invention provides a method for optimizing the structural parameters of the collimation system of a small-angle X-ray scattering instrument, which solves the problems of low accuracy in optimizing the structural parameters of the collimation system and poor performance release of the collimation system in traditional small-angle X-ray scattering instruments.

[0006] To achieve the above objectives, according to the present invention, a method for optimizing the structural parameters of a collimation system for a small-angle X-ray scattering instrument is provided, the method comprising the following steps: S1 Construct a simulation model of the collimation system of the scattering instrument and set the initial structural parameters of the simulation model. The simulation model includes a light source, a light-converging optical device, a slit assembly and a detector arranged from front to back. S2 Set the position of the light source, construct a geometric coordinate system with the light source as the origin, and construct the photons emitted from the light source in the geometric coordinate system. Simulate the process of the photons passing through the optical device and slit group that converge the light in sequence and finally falling on the surface mesh of the detector, and determine the number of photons in each grid of the surface mesh of the detector. S3 constructs an evaluation system for the structural parameters of the collimation system, uses the structural parameters of the collimation system as input, constructs an optimization model with the evaluation system as the optimization objective, and solves for the optimal structural parameters corresponding to the optimization model, thereby achieving the optimization of the structural parameters of the collimation system.

[0007] More preferably, in step S2, determining the number of photons in each grid cell of the detector surface is performed according to the following steps: S21 Obtain the coordinates of each photon at the light source in the geometric coordinate system, and set the photon energy and weight of the photon at the light source according to the initial structural parameters; S22 randomly generates photons at the detector and constructs a photon vector pointing from the light source to the detector. S23 determines the position of the slit group and the size of the slit opening in the geometric coordinate system, and uses the positional relationship between the photon vector and the slit opening to determine whether the photons at the light source are blocked by the slit group. S24 determines the number and weight of photons falling in the grid on the detector surface based on the structure determined in S23.

[0008] More preferably, in step S21, the photons emitted from the light source satisfy a preset spot size and Gaussian distribution.

[0009] More preferably, in step S21, the photons at the light source are generated using the Monte Carlo method, and their coordinates in the geometric coordinate system are determined as follows:

[0010] in, and Photons at the source , Photon coordinate distribution in two directions For distribution The amplitude parameter of the i-th Gaussian distribution. For distribution The location parameters of the i-th Gaussian distribution in the middle. For distribution The scaling parameter of the i-th Gaussian distribution in the distribution. For distribution The amplitude parameter of the j-th Gaussian distribution. For distribution The location parameters of the j-th Gaussian distribution in the middle. For distribution The scale parameter of the j-th Gaussian distribution, and the total number of photon coordinates are It is an integer that can be set freely. For distribution The number of photon coordinates corresponding to the i-th Gaussian distribution. For distribution The number of photon coordinates corresponding to the j-th Gaussian distribution.

[0011] More preferably, in step S22, the photon coordinates at the detector are determined according to the following relationship:

[0012]

[0013] in, For photons at the detector directional coordinate distribution For photons at the detector directional coordinate distribution Corresponding distribution The scaling parameter of the i-th Gaussian distribution in the distribution. Corresponding distribution The scaling parameter of the j-th Gaussian distribution in the distribution. The total length of the collimation system of a small-angle X-ray scattering instrument; The vector of a photon is described by the following formula:

[0014] in, , , These are the unit vectors of the photon in the X, Y, and Z directions of the absolute coordinate system. This represents the difference between the photon coordinates at the detector and the photon coordinates at the source in the X direction. This represents the difference between the photon coordinates at the detector and the photon coordinates at the source in the Y direction. This is the difference between the photon coordinates at the detector and the photon coordinates at the source in the Z direction.

[0015] More preferably, in step S3, the evaluation parameters of the rating system include beam divergence, beam size at the sample, detector beam size, minimum measurable period of the collimation system of the small-angle X-ray scattering instrument, maximum measurable period of the collimation system of the small-angle X-ray scattering instrument, and beam intensity.

[0016] More preferably, the minimum measurable period and the maximum measurable period of the scatterer are respectively determined according to the following formulas:

[0017]

[0018] in, This is the minimum measurable period for a small-angle X-ray scattering instrument. This is the maximum measurable period for a small-angle X-ray scattering instrument. The wavelength of X-rays. This represents the distance from the sample to the detector. The size of the detector pixels. The size of the X-ray beam spot at the detector.

[0019] More preferably, the beam intensity is calculated based on the number of photons in each grid cell of the detector surface.

[0020] More preferably, in step S3, the optimization model is constructed using a multi-constraint differential evolution algorithm.

[0021] More preferably, the multi-constraint differential evolution algorithm uses beam divergence, beam size at the sample, beam size at the detector, and the periodic range of the structure that the scatterometer can measure. As a constraint, beam intensity is used as the optimization objective.

[0022] In summary, the technical solutions conceived by this invention have the following beneficial effects compared with the prior art: 1. This invention simulates the motion of photons in a collimation system by constructing photon coordinates and photon vectors in a simulation system, thereby obtaining the maximum divergence of the X-ray beam at the detector, beam size, total number of photons, and the number of photons in each grid on the detector surface. This method simulates the actual motion of photons in the collimation system, and can obtain parameters such as the maximum divergence of the X-ray beam at the detector, beam size, and total number of photons more accurately and realistically. The performance of the collimation system can be evaluated based on these parameters. The number of photons in each grid on the detector surface is used to describe the distribution of photons arriving at the detector. This distribution can be compared with simulation or experimental results to verify the accuracy of the simulation system. 2. This invention proposes a method for constructing a small-angle X-ray collimation system model based on the Monte Carlo method and a corresponding method for evaluating the performance parameters of the collimation system. On this basis, the structural parameters of the collimation system are optimized by a multi-constraint differential evolution algorithm. The optimization method is accurate, efficient and can meet the laboratory SAXS measurement requirements. 3. This invention novelly employs a multi-constraint differential evolution algorithm to optimize structural parameters and uses a penalty function to penalize solutions that violate constraints, thus ensuring the accuracy, reliability, and efficiency of the multi-constraint differential evolution algorithm; 4. The collimation system model for a small-angle X-ray scatterer based on the Monte Carlo method provided by this invention is applicable to the optimized design of various collimation systems, including but not limited to multi-pinhole slit systems, multi-rectangular slit systems, divergent light collimation systems, and converging light collimation systems. Attached Figure Description

[0023] Figure 1 This is a flowchart of a method for optimizing the structural parameters of a collimation system for a small-angle X-ray scattering instrument according to a preferred embodiment of the present invention. Figure 2 This is a schematic diagram of a laboratory small-angle X-ray scattering device constructed according to a preferred embodiment of the present invention; Figure 3 This is a flowchart illustrating the construction process of a collimation system simulation model based on the Monte Carlo method, according to a preferred embodiment of the present invention. Figure 4 This is a schematic diagram illustrating the construction principle of a collimation system simulation model based on the Monte Carlo method, constructed according to a preferred embodiment of the present invention. Figure 5 This is a comparison chart of the simulation results of the collimation system simulation model and the commercial software McXtrace under certain identical conditions, constructed according to a preferred embodiment of the present invention. Figure 6 This is a diagram of two slit collimation systems constructed according to a preferred embodiment of the present invention; Figure 7 This is a flowchart of the multi-constraint differential evolution algorithm constructed according to a preferred embodiment of the present invention; Figure 8 This is a graph of the objective function of the multi-constraint differential evolution algorithm constructed according to a preferred embodiment of the present invention.

[0024] In all the accompanying drawings, the same reference numerals are used to denote the same elements or structures, wherein: 210 - Light source, 220 - Optical device for converging light, 230 - Slit group, 231 - First non-scattering slit, 232 - First non-scattering slit, 240 - Detector module, 241 - Beam baffle, 242 - Detector. Detailed Implementation

[0025] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0026] like Figure 1 As shown, a method for optimizing the structural parameters of a collimation system for a small-angle X-ray scattering instrument is presented. The Monte Carlo simulation method is used to simulate the collimation system. This simulation model characterizes the performance of the collimation system through statistical information of photons. Based on this simulation model, the structural parameters of the collimation system are optimized using a multi-constraint differential evolution algorithm. The method includes the following three main steps: (1) Identify and analyze the X-ray small-angle scattering collimation system device to be simulated; (2) A simulation model of a small-angle X-ray scatterer was established based on the Monte Carlo simulation method; (3) Establish a parameter system for evaluating the performance of the collimation system based on the simulation model, and use the multi-constraint differential evolution algorithm to optimize the structural parameters of the simulation model; The specific steps are as follows: S1 describes the small-angle X-ray scattering system to be optimized and establishes a simulation model of the collimation system of the small-angle X-ray scatterer based on Monte Carlo simulation.

[0027] It should be noted that the description of the small-angle X-ray scattering system to be optimized includes the type of collimation system and the beam characteristics of the beam input to the collimation system.

[0028] S2. A parameter system for evaluating the performance of a collimation system is established based on a small-angle X-ray scattering system, including: beam divergence. Beam size at the sample Beam size at the detector The range of scattering angles that the beam can reach Beam intensity The beam intensity is determined by the number of photons arriving at the detector. Evaluation is conducted. The range of scattering angles that the beam can reach is converted into the range of periodic structures that can be measured by a small-angle X-ray scattering system. The beam divergence, beam size at the sample, beam size at the detector, and the measurable periodic structure range of the small-angle X-ray scattering system are described and evaluated based on statistical information obtained from Monte Carlo simulations.

[0029] S3. Based on the collimation system simulation model and the collimation system performance parameter evaluation system, a multi-constraint differential evolution algorithm is used to optimize the structural parameters of the collimation system. The multi-constraint differential evolution algorithm employs a penalty function. Used to penalize solutions that violate constraints. This is the scaling factor. These are the expected performance parameters for the collimation system. These are the collimation system performance parameter values ​​obtained from model simulation.

[0030] Furthermore, the measurement system is determined based on the measurement requirements of the X-ray small-angle scattering instrument. In some embodiments, the X-ray small-angle scattering collimation system includes a linear slit optical system, a pinhole slit optical system, a conical slit optical system, a Kratky optical system, and a focusing optical system. Preferably, a two-aperture slit optical system is used, such as... Figure 2 As shown, the two-aperture slit optical system mainly includes a high-brightness and high-stability X-ray source 210, a light-converging optical device 220, a slit assembly 230, and a high-dynamic-range and high-resolution detector module 240.

[0031] In one embodiment, the light source 210 is configured to generate the hard X-ray radiation energy (>15 keV) required for transmission. Any source capable of producing high-brightness X-rays is suitable for T-SAXS measurements, including but not limited to synchrotron radiation sources, liquid metal target X-ray sources, solid anode X-ray sources, rotating anode X-ray sources, microfocusing sources, and inverse Compton sources.

[0032] In one embodiment, the focusing optics 220 are configured to collimate or focus hard X-rays emitted from the light source 210, and include one or more collimating mirrors, apertures, stops, refractive optics, diffractive optics (e.g., zone plates), Montel optics, specular optics (e.g., grazing-incident ellipsoidal mirrors), multi-capillary optics (e.g., hollow capillary X-ray waveguides), or any combination thereof. It should be noted that in the collimation system model constructed based on Monte Carlo simulation, the light source model simulates an X-ray beam emitted by the focusing optics 220 and incident on the slit assembly 230, the characteristics of which are jointly defined by the light source 210 and the focusing optics 220.

[0033] In one embodiment, all slits 230 are non-scattering slits used to collimate the optical path and eliminate parasitic scattering. The first non-scattering slit 231 and the second non-scattering slit 232 are of the same type. In one embodiment, each non-scattering slit in the slit group 230 consists of two sets of mutually perpendicular blades, each blade is individually controlled by a motor, and the slit aperture is defined by all four blades. In one embodiment, the slit blades adopt a hybrid metal structure, consisting of a high-density metal substrate and a single-crystal cutting edge. Preferably, when the X-ray energy is higher than 12 keV, the single-crystal cutting edge is made of germanium (Ge), and when the X-ray energy is lower than 12 keV, the single-crystal cutting edge is made of indium phosphide (InP).

[0034] The non-scattering slits used in slit group 230 have been tested and found to essentially eliminate any potential parasitic scattering. Preferably, the slit group model can be simplified to a rectangular hole defined by four cutting edges, typically a square hole.

[0035] The high dynamic range, high resolution detector module 240 includes a beam baffle 241 and a detector 242 configured to collect X-rays incident on the detector module 240. In some embodiments, the detector module 240 includes one or more photon counters with a high dynamic range for detecting the position and number of detected photons. In some instances, a beam baffle is positioned at the center of the X-ray beam to block excessive X-rays and prevent detector damage. In some instances, damage to the detector system due to overexposure can be avoided by shortening the exposure time or employing a novel two-dimensional detector system.

[0036] In a specific example, the detector module 240 system uses the PILATUS series system with a pixel size of 172μm×172μm. The construction of the two-dimensional detector system model can be simplified to a mesh with a grid size of 172μm×172μm, where each grid acts as a photon counter to detect the position and number of photons being detected.

[0037] In one specific embodiment, the X-ray source employs a liquid metal target made of gallium-indium alloy; the X-ray optics utilize a two-dimensional Montel collimating X-ray focusing lens with a Gaussian beam intensity distribution, a beam size of 1.1 mm × 1.1 mm (FWHM), and a maximum divergence of 0.35 mrad; the slit assembly employs scatter-free slits for collimating the optical path and eliminating parasitic scattering. The slit blades utilize a hybrid metal structure, consisting of a high-density metal substrate and a single-crystal cutting edge. The metal substrate is made of tungsten (W), and the slit blades are made of single-crystal germanium (Ge). The two-dimensional detector system employs a Pilatus 1M detector, with its sensing layer made of cadmium telluride (CdTe), providing near 100% absorption efficiency for Mo, Ag, and In radiation, thus improving sensitivity and accuracy during measurement.

[0038] Further, in step S2, a simulation model of the collimation system of the small-angle X-ray scatterer is established based on the Monte Carlo simulation method. For example... Figure 3 As shown in the figure, the basic principle of constructing a collimation system using the Monte Carlo method is illustrated. Photon coordinates with a certain distribution are generated at the light source and detector, respectively. Connecting the points corresponding to the photon coordinates at the light source and the detector yields a randomly generated ray. The trajectory of this ray in the absolute coordinate system is then obtained, allowing the determination of the interaction between the ray and components such as the slit array and the detector. Figure 4 As shown, the specific construction process of the collimation system simulation model includes: S21 defines the components of the collimation system and constructs the system's absolute coordinate system. The simulation model consists of a light source, a slit, and a detector, with the center of the light source as the origin of the absolute coordinate system. The coordinate axis along the beam propagation direction is the Z-axis, the coordinate axis perpendicular to the plane of the paper is the Y-axis, and the X-axis direction is determined by the right-hand rule.

[0039] (1) Determine the input parameters of the collimation system and the photon information in the collimation system simulation model. The input parameters include the light spot distribution at the light source. Maximum beam divergence at the light source Total number of photons Beam energy Energy bandwidth Total length of the collimation system The length of the geometric center of the first non-scattering slit 231 from the light source The length of the geometric center of the second non-scattering slit 232 from the light source and the aperture size of the slit group Photon information includes geometric coordinates. ,vector and photon energy and photon weight Based on the collimation system input parameters, the positions of the geometric centers of the first non-scattering slit 231, the second non-scattering slit 232, and the detector module 240 in the system's absolute coordinate system are as follows: , , .

[0040] (2) Generate the initial coordinates of photons in the theoretical light source based on the input parameters. 0. Spot distribution Including the coordinate distribution of photons along the X-axis. and coordinate distribution in the Y-axis direction ,distributed and It can be of any shape. Its characteristic is that the distribution... It can be done Approximated by a Gaussian distribution:

[0041] In the formula, , , The distribution consists of the amplitude, location, and scale parameters corresponding to the Gaussian distribution. Similarly, the distribution... It can be done Approximated by a Gaussian distribution:

[0042] For distribution Based on distribution The number of random coordinates generated along the X-axis is equal to the total number of photons. Based on the fitted distribution of The number of random coordinates generated by the Gaussian distribution are respectively , is defined by the following formula:

[0043] In the formula, Represents distribution The area enclosed by the coordinate axes, based on the above analysis, is similarly based on the fitted distribution. of The number of random coordinates generated by the Gaussian fitted distributions are respectively :

[0044] For distribution Its characteristic is that it is based on distribution generated Each random coordinate along the X-axis is determined by... It consists of groups of random coordinates that satisfy different Gaussian distributions, and the different Gaussian distributions satisfy the distribution... The corresponding number of random coordinates is .

[0045] Based on distribution generated A random Y-axis coordinate, from It consists of groups of random coordinates that satisfy different Gaussian distributions, and the different Gaussian distributions satisfy the distribution... The corresponding number of random coordinates is By combining the two sets of coordinates one-to-one, the location of the light source can be obtained. Photon coordinate information .

[0046] (3) Generate the photon energy and weight at the light source based on the input parameters. The energy of a single photon is defined by the following formula:

[0047] in, Satisfy distribution The weight of a single photon is set to... The weight of a photon changes after undergoing optical processes such as reflection, absorption, and refraction. Therefore, complete information about a single photon can be obtained. .

[0048] S22 generates the photon coordinates at the theoretical detector and the photon vector at the source based on the input parameters. The coordinates in the X and Y directions satisfy a Gaussian distribution. and Photons, at maximum divergence Transmission distance Subsequently, the coordinate distribution of photons in the X and Y directions satisfies a Gaussian distribution. and Among them, variance and Defined by the following formula:

[0049] Based on the initial coordinate method of photons in the generative theory light source, the detector coordinates can be obtained. Photon coordinate information Vector in photon parameters Defined by the following formula:

[0050] S23 determines whether a photon has passed through the slits and reached the detector system based on the photon information and the slit group information. Based on the photon information, the position of the photon within the slit group can be calculated. and coordinates of and This allows us to determine whether a photon is blocked by the slit; the weight of an unblocked photon is... The weight of the blocked photon remains unchanged. Preferably, in actual calculations, the step of changing the photon weight can be replaced by deleting information about the blocked photons, thereby reducing the computational load and improving the calculation speed. It should be noted that the non-scattering slit composed of four blades is typically a square aperture in applications, with the four blades symmetrically arranged in pairs around the z-axis, and the distance between the blade edge and the z-axis being half the aperture diameter.

[0051] S24 collects information about the photons arriving at the two-dimensional detector. Based on this photon information, the position coordinates of the photons at the detector can be calculated. If the coordinates lie within a grid on the two-dimensional detector's surface, the counter value corresponding to that grid is incremented by 1. The resulting two-dimensional matrix describes the actual characteristics of the light spot at the detector after a light source of a certain shape passes through the collimation system. Figure 5 As shown in the figure, the dots correspond to the light intensity distribution at the detector output by the collimation system simulation model, and the curves correspond to the light intensity distribution output by the existing X-ray simulation software McXtrace under the same conditions. The two are basically consistent.

[0052] Further, in step S3, Figure 6 A schematic diagram of a two-slit system is provided. Based on the geometric relationships presented in the schematic diagram, the structural parameter expressions of the collimation system can be obtained as follows: Table 1. Performance Parameter Evaluation of Collimation System

[0053] in, This indicates the maximum divergence. and Let FWHM represent the full width at half maximum (FWHM) of the photon position coordinate distribution at the sample and detector, respectively. This represents the total number of photons passing through the slit system. This indicates the distance from the sample to the detector. The table represents the detector pixel size, and the range of periodic structures that the scatterometer can measure is calculated based on the formulas in the table. .

[0054] Furthermore, in step S3, after determining the calculation method for the collimation system evaluation parameters, the collimation system structural parameters can be optimized using a multi-constraint differential evolution algorithm. In one embodiment, the beam divergence is used as the optimization parameter. Beam size at the sample Beam size at the detector The scatterometer can measure the periodic range of structures. As a desired performance parameter, beam intensity The optimization objective is to maximize beam intensity of the collimation system while meeting the desired performance parameter constraints. The multi-constraint differential evolution algorithm employs a penalty function. Structural parameter solutions used to penalize those that violate expected performance parameter constraints. This is the scaling factor. These are the expected performance parameters for the collimation system. These are the collimation system performance parameter values ​​obtained from model simulation.

[0055] A multi-constraint differential evolution algorithm is proposed. In this embodiment, the performance parameter evaluation of the two-slit system and the collimation system is the same as that provided in Embodiment 1 above. The specific process of the multi-constraint differential evolution algorithm is as follows: Figure 7 As shown, it includes: Initialize the population. The structural parameters to be optimized for the two-slit system include the slit aperture size. , The distance between the two slits Total length of the collimation system The distance from the second slit to the sample In a two-slit system, and The value is fixed due to limitations imposed by the size of the laboratory space and the sample chamber. , and For the structural parameters to be optimized, set the value range for each parameter and generate an initial population of appropriate size.

[0056] Calculate individual fitness values ​​and penalize individuals that violate constraints. Individual fitness values ​​are determined by light intensity. Indicated by beam divergence Beam size at the sample Beam size at the detector The scatterometer can measure the periodic range of structures. The collimation system performance parameters are used as constraints to penalize individuals whose performance fails to meet the expected target. Both the light intensity and the collimation system performance parameters are described by statistical information from a model of the collimation system based on the Monte Carlo method. In one example, the light intensity... Equivalent to the total number of photons reaching the detector through the collimation system, and the beam size at the sample. Beam size at the detector These are the full width at half maximum (FWHM) of the photon position coordinates at the sample and detector, respectively, representing the range of periodic structures that the scatterometer can measure. It can be obtained through calculation. The fitness value of an individual in the multi-constraint differential evolution algorithm is calculated by the following formula:

[0057] in, , , , , These are simulation performance parameters calculated using a Monte Carlo model of a collimated system under specific structural parameter configurations. , , , These are the expected performance parameters. This is the scaling factor, which can be adjusted according to the convergence of the algorithm.

[0058] Subsequent steps such as crossover mutation, boundary handling, and selection operations are similar to those in commonly used differential evolution algorithms and will not be elaborated upon here. Once the termination condition is met, the optimal structure parameter values ​​can be obtained. It should be noted that, as... Figure 8 As shown, the collimated system model based on the Monte Carlo method has a certain degree of randomness. This is manifested in the fact that after the convergence curve of the multi-constraint differential evolution algorithm converges as a whole, there are still fluctuations within a very small range. The optimal structural parameter values ​​can be selected as the average of several sets of optimal parameter values.

[0059] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for optimizing the structural parameters of a collimation system in a small-angle X-ray scattering instrument, characterized in that, The method includes the following steps: S1 Construct a simulation model of the collimation system of the scattering instrument and set the initial structural parameters of the simulation model. The simulation model includes a light source, a light-converging optical device, a slit assembly and a detector arranged from front to back. S2 Set the position of the light source, construct geometric coordinates with the light source as the origin, and construct the photons emitted from the light source in the geometric coordinate system. Simulate the process of the photons passing through the optical device and slit group that converge the light in sequence and finally falling on the surface mesh of the detector, and determine the number of photons in each grid of the surface mesh of the detector. S3 constructs an evaluation system for the structural parameters of the collimation system, takes the structural parameters of the collimation system as input, constructs an optimization model with the evaluation system as the optimization objective, and solves for the optimal structural parameters corresponding to the optimization model, thereby achieving the optimization of the structural parameters of the collimation system; In step S2, determining the number of photons in each grid cell of the detector surface is performed according to the following steps: S21 Obtain the coordinates of each photon at the light source in the geometric coordinate system, and set the photon energy and weight of the photon at the light source according to the initial structural parameters; S22 randomly generates photons at the detector and constructs a photon vector pointing from the light source to the detector. S23 determines the position of the slit group and the size of the slit opening in the geometric coordinate system, and uses the positional relationship between the photon vector and the slit opening to determine whether the photon at the light source is blocked by the slit group. S24 Determines the number and weight of photons falling in the grid on the detector surface based on the structure determined in S23; In step S21, the photons at the light source are generated using the Monte Carlo method, and their coordinates in the geometric coordinate system are determined as follows: in, and Photons at the source , Photon coordinate distribution in two directions For distribution The amplitude parameter of the i-th Gaussian distribution. i =1,2,3,…, n , For distribution The location parameters of the i-th Gaussian distribution in the middle. For distribution The scaling parameter of the i-th Gaussian distribution in the distribution. For distribution The amplitude parameter of the j-th Gaussian distribution. j =1,2,3,…, m , For distribution The location parameters of the j-th Gaussian distribution in the middle. For distribution The scale parameter of the j-th Gaussian distribution, and the total number of photon coordinates are , is a freely set integer. For distribution The number of photon coordinates corresponding to the i-th Gaussian distribution. For distribution The number of photon coordinates corresponding to the j-th Gaussian distribution in the middle; In step S3, the optimization model is constructed using a multi-constraint differential evolution algorithm; The multi-constraint differential evolution algorithm uses beam divergence, beam size at the sample, beam size at the detector, and the periodic range of the structure that the scatterer can measure as factors. As a constraint, beam intensity is used as the optimization objective.

2. The method for optimizing the structural parameters of a collimation system for a small-angle X-ray scattering instrument as described in claim 1, characterized in that, The photons emitted from the light source satisfy the preset spot size and Gaussian distribution.

3. The method for optimizing the structural parameters of a collimation system for a small-angle X-ray scattering instrument as described in claim 1, characterized in that, In step S22, the photon coordinates at the detector are determined according to the following formula: in, For photons at the detector directional coordinate distribution For photons at the detector directional coordinate distribution Corresponding distribution The scaling parameter of the i-th Gaussian distribution in the distribution. i =1,2,3,…, n , Corresponding distribution The scaling parameter of the j-th Gaussian distribution in the distribution. j =1,2,3,…, m , The total length of the collimation system of a small-angle X-ray scattering instrument; The vector of a photon is described by the following formula: in, , , These are the unit vectors of the photon in the X, Y, and Z directions of the absolute coordinate system. This represents the difference between the photon coordinates at the detector and the photon coordinates at the source in the X direction. This represents the difference between the photon coordinates at the detector and the photon coordinates at the source in the Y direction. This is the difference between the photon coordinates at the detector and the photon coordinates at the source in the Z direction.

4. The method for optimizing the structural parameters of a collimation system for a small-angle X-ray scattering instrument as described in claim 1, characterized in that, In step S3, the evaluation parameters of the evaluation system include beam divergence, beam size at the sample, detector beam size, minimum measurable period of the collimation system of the small-angle X-ray scattering instrument, maximum measurable period of the collimation system of the small-angle X-ray scattering instrument, and beam intensity.

5. The method for optimizing the structural parameters of a collimation system for a small-angle X-ray scattering instrument as described in claim 4, characterized in that, The minimum and maximum measurable periods of the scatterer are determined according to the following formulas: in, This is the minimum measurable period for a small-angle X-ray scattering instrument. This is the maximum measurable period for a small-angle X-ray scattering instrument. The wavelength of X-rays. This represents the distance from the sample to the detector. The size of the detector pixels. The size of the X-ray beam spot at the detector.

6. The method for optimizing the structural parameters of a collimation system for a small-angle X-ray scattering instrument as described in claim 4, characterized in that, The beam intensity is calculated based on the number of photons in each grid cell of the detector surface.

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