Simulation method for x-ray transmission in multiple capillaries

Abstract

The application discloses a simulation method for X-ray transmission in a multi-capillary, and belongs to the technical field of data processing. The method comprises the following steps: S1, a program reads parameters of a light source and a multi-capillary structure from an input file; S2, a 4pi divergent photon source is adopted; S3, a multi-capillary structure is constructed; S4, a sub-capillary structure is constructed, and the sub-capillary is discretized into an inclined circular truncated cone structure; S5, a photon enters the capillary; S6, a collision position and an angle of the photon with a capillary wall are calculated; and S7, the photon is transmitted in the multi-capillary. The simulation method can significantly improve the calculation efficiency and reliability of simulation.

Description

Technical Field

[0001] This invention relates to the field of data processing technology, and in particular to a simulation method for X-ray transmission in multiple capillaries. Background Technology

[0002] Since its discovery, X-rays have been widely used in astronomical observation, non-destructive testing, and medical imaging, leading to the development of X-ray manipulation techniques. Capillaries are devices that utilize the principle of total internal reflection to manipulate X-rays, exhibiting high transmission efficiency and strong resistance to radiation damage. Numerical simulations of X-ray transmission within capillaries can not only guide capillary structural design but also predict their transmission performance.

[0003] Currently, there are many methods for studying X-ray transmission in multi-capillary tubes, most of which combine Monte Carlo and ray tracing methods. Existing methods suffer from at least the following problems:

[0004] First, this method uses a small divergence angle light source, such as synchrotron radiation, for simulation, and only utilizes a portion of the capillary region (e.g., Figure 1 As shown, Figure 1 In the diagram, the hexagon represents the outer contour of the capillary, and the blue area represents the photon distribution region. This does not reflect most practical application scenarios. Secondly, while the considered "internal leakage event" correction improves the results (e.g., Figure 2 (As shown in Figure 3), but this significantly increases computation time, from minutes to hours. However, the correction effect is greatly reduced when using a large divergence angle light source (as shown in Figure 3). This is understandable: only photons entering the central part of the multi-capillary can improve transmission efficiency through leakage correction, while a large divergence angle light source covers the entire area of ​​the multi-capillary, thus the correction effect is naturally weak. Furthermore, this method provides a relatively coarse simulation of the multi-capillary structure, assuming that the radius of the sub-capillaries changes linearly. Although this approximation reduces the computational load, it deviates significantly from reality. When simulating photon collisions with the capillary walls, simply approximating the sub-capillaries as cylinders also introduces errors. Summary of the Invention

[0005] The purpose of this invention is to provide a simulation method for X-ray transmission in multiple capillaries to solve the above-mentioned problems.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows: a simulation method for X-ray transmission in multiple capillaries, comprising the following steps:

[0007] S1. The program reads the parameters of the light source and the multi-capillary structure from the input file;

[0008] S2. The light field distribution of the light source is simulated using a 4π divergent photon source;

[0009] The original method uses a small divergence angle of a synchrotron light source; and the application is improved to use a 4π divergence light source, which is more in line with the laboratory use scene, and the photons have random initial positions and velocity directions;

[0010] S3. Constructing a multi-capillary structure;

[0011] S4. Constructing a sub-capillary structure, and dispersing the sub-capillary into an inclined circular truncated cone structure;

[0012] The original method disperses the sub-capillary into a cylindrical structure, as shown in (a), and the center and radius of each segment are constant. Figure 5 The application improves to disperse the sub-capillary into a circular truncated cone structure (b), and the radius and center position in each segment change linearly, which is more in line with the actual situation. When calculating the collision angle of the photon with the capillary wall, the application is also more accurate. For example, the cylindrical structure approximation of the original method is too rough for the converging capillary lens, which may cause the collision angle of the photon with the capillary wall to be too large. Figure 5 is the reflectivity of 8.4keV photons with SiO2 material at different angles, and it can be seen that the reflectivity is extremely sensitive to the incident angle, and rough approximation may have a great impact on the results. Figure 6

[0013] S5. The photon enters the capillary;

[0014] S6. Calculating the collision position and angle of the photon with the capillary wall;

[0015] S7. The photon is transmitted in the multi-capillary, and after the photon reaches the outlet of the multi-capillary, the coordinates of the photon are rotated back to the original position, i.e. the simulation result is obtained.

[0016] As a preferred technical solution, in step S3, the method for constructing the multi-capillary structure is:

[0017] A cubic curve is used: (1)

[0018] The radius variation of the multi-capillary is fitted, wherein a, b, c, and d are coefficients of the curve, and are all unknown numbers, and z is the distance in the transmission direction, is the radius of the multi-capillary;

[0019] r1 is the multi-capillary inlet radius, r2 is the multi-capillary outlet radius, F1 is the multi-capillary inlet focal length, F2 is the multi-capillary outlet focal length, and L is the multi-capillary length. The above parameters are brought into the curve equation:

[0020] (2) ,

[0021] ​Slope of the outer contour curve of the multi-capillary at both ends ,

[0022] (3),

[0023] Satisfy the radius ratio focal length, can be obtained:

[0024] (4),

[0025] By solving the equation set formula (2) and (4), the values of a, b, c, d can be obtained, so that the curve equation of the above formula (1) is obtained.

[0026] The original method is to use input parameters to design the outer contour of the multi-capillary as an ellipsoid, a cone and the like, and this method needs additional parameters to set the structure type. The application improves the construction of the multi-capillary structure by using the above method, and by using the above method, the converging capillary lens and the parallel lens can be obtained by inputting appropriate parameters without additional parameters to set. In addition, the application also supports customizing the capillary structure.

[0027] As a preferred technical solution, in step S5,

[0028] The photon enters a sub-capillary according to its initial position and velocity direction, and the coordinates of the center of the sub-capillary are , and the coordinates of the photon are ;

[0029] The sub-capillary and the photon are rotated to make the center of the sub-capillary located on the x-axis,

[0030] The coordinates of the center of the sub-capillary change to: ;

[0031] The coordinates of the photon change to: ;

[0032] Wherein, is the rotation angle, ;

[0033] Finally, only the coordinates need to be rotated back to the original position at the end of the calculation. The advantage of this is that it can reduce the calculation difficulty of the subsequent simulation of the collision between the photon and the capillary wall.

[0034] As a preferred technical solution, in step S6, the specific calculation method of the collision position is:

[0035] The distance of the photon from the center of the ion capillary at the front end point :

[0036] (5),

[0037] and These are the coordinates of the photon and the subcapillary center at the front end point, respectively.

[0038] The distance of the photon at the center of the ion capillary at the rear end ,

[0039] ,

[0040] and These are the coordinates of the photon and the subcapillary center at the rear end point, respectively.

[0041] The equation for the change in the center distance of the photon ion capillary is obtained as follows:

[0042] (7),

[0043] dl is a simulated step size, and l is the transmission distance in the transmission direction;

[0044] The radius of the subcapillary at the tip point The radius of the capillary at the rear end point Since this is known during the construction of the sub-capillary, the equation for the change in the sub-capillary radius is obtained:

[0045] , (8),

[0046] This represents the change in the center distance of the photon-ion capillary. The formula for the change in the radius of the subcapillary tube;

[0047] When a photon collides with the capillary wall, that is... By combining formulas (7) and (8), the axial distance of the collision point, i.e. the transmission distance l in the transmission direction, can be obtained. Substituting this into the path equation of the photon, the accurate coordinates can be obtained.

[0048] As a preferred technical solution, in step S6, the specific method for setting the collision angle is as follows:

[0049] Since the cross-section of the subcapillary is circular, the normal vector at the collision point... Pointing towards the center of the circle, The coordinates of the collision point relative to the center of the circle; the axial direction of the sub-capillary forms an angle with the z-axis. Therefore, the normal vector is rotated from the subcapillary coordinate system to the simulation coordinate system: (9),

[0050] wherein, is a rotation matrix, and thus the collision angle is solved by the photon path equation as in formula (7) above and the normal vector, that is,

[0051] The original method calculates the collision position and angle of the photon with the capillary wall by constructing a path equation with the positions before and after a simulation step of the photon, and then bringing it into the cylindrical equation of the capillary wall to solve the collision point coordinates and then the collision angle, but this method is only suitable for simple structures. As described above, the original method is obviously not applicable to the inclined truncated cone structure selected in the present application for closer approximation to the reality, and thus the above calculation method of the present application is required.

[0052] Compared with the prior art, the simulation method of the present application has the advantages that the transmission efficiency obtained by the simulation method of the present application is very close to the actual value, while the transmission efficiency obtained by the original method is only about 10% of the actual value, and thus the simulation method of the present application improves the accuracy of the calculation while maintaining high calculation speed. BRIEF DESCRIPTION OF DRAWINGS

[0053] Figure 1 is a distribution diagram of the photons at the entrance of the multi-capillary when a small divergence angle light source is used in the simulation method of the prior art;

[0054] Figure 2 is the change of the transmission efficiency with the photon energy when a small divergence angle light source is used in the simulation method of the prior art, with or without considering the leakage event;

[0055] Figure 3 is the change of the transmission efficiency with the photon energy when a large divergence angle light source is used in the simulation method of the prior art, with or without considering the leakage event

[0056] Figure 4 is a schematic diagram of the multi-capillary profile of the embodiment of the present application;

[0057] Figure 5 is a schematic diagram of the sub-capillary (a) of the simulation of the prior art and the sub-capillary (b) of the simulation of the embodiment of the present application;

[0058] Figure 6 is the reflectivity of the 8.4keV photon with SiO2 material at different angles in the embodiment of the present application;

[0059] Figure 7 is a schematic diagram of the entrance cross section of the multi-capillary of the embodiment of the present application;

[0060] Figure 8 is a schematic diagram of the rotation of the sub-capillary of the embodiment of the present application;

[0061] Figure 9This is a schematic diagram of the collision between photons and the capillary wall according to an embodiment of the present invention;

[0062] Figure 10 The transmission efficiency of the XOS-1796 capillary tube was simulated and tested using existing technology;

[0063] Figure 11 This is a comparison chart showing the simulated transmission efficiency of the XOS-1796 capillary tube using the embodiments of the present invention and the methods using existing technologies. Detailed Implementation

[0064] To explain the technical content, objectives, and effects of the present invention in detail, the following specific embodiments are provided to further illustrate the content of the present invention. However, the content of the present invention is far more than the following examples.

[0065] Example 1

[0066] A simulation method for X-ray transmission in a multi-capillary tube includes the following steps:

[0067] S1. The program of this invention reads the parameters of the light source and the multi-capillary structure from the input file. These parameters are consistent with those of the original method as shown in Table 1 below.

[0068] S2. The light field distribution of the light source is simulated using a 4π divergent photon source;

[0069] S3. Construct a multi-capillary structure;

[0070] This embodiment uses a cubic curve ( (1)

[0071] Fitting the radius variation of multiple capillaries, such as Figure 4 As shown, a, b, c, and d are the coefficients of the curve, all of which are unknowns; z is the distance in the transmission direction; the inlet diameter of the multi-capillary is 2r1, the outlet diameter is 2r2, the inlet focal length is F1, the outlet focal length is F2, and the capillary length is L; substituting these parameters into the curve equation:

[0072] (2),

[0073] In addition, the slope at both ends of the outer contour curve of the multi-capillary The radius should be proportional to the focal length, where,

[0074] (3),

[0075] We can obtain:

[0076] (4),

[0077] The values of a, b, c and d can be obtained by solving the equation set, and thus the curve equation is obtained ; by inputting appropriate parameters, converging capillary lens and parallel lens can be obtained;

[0078] S4. Constructing a sub-capillary structure, and discretizing the sub-capillary into an inclined circular truncated cone structure;

[0079] In this embodiment, the sub-capillary is discretized into an inclined circular truncated cone structure Figure 5 (b), the radius and the center position linearly change in each section;

[0080] S5. Photons enter the capillary;

[0081] The cross section of the multi-capillary is a honeycomb-like structure, and in this embodiment, it is approximately a circular structure, as shown in Figure 7 . Photons enter a sub-capillary according to their initial positions and velocity directions, the coordinates of the center of the sub-capillary are , and the coordinates of the photons are ; in order to facilitate subsequent calculation, this embodiment performs a rotation operation Figure 8 on the sub-capillary and the photons, so that the center of the sub-capillary is located on the x-axis;

[0082] The coordinates of the center of the sub-capillary change to: ,

[0083] The coordinates of the photons change to: ,

[0084] is the rotation angle, and finally only the coordinates need to be rotated back to the original position at the end of the calculation;

[0085] S6. Calculate the collision position and angle of the photons with the capillary wall;

[0086] First, the distance of the photons from the center of the capillary at the front end point :

[0087] (5),

[0088] and are the coordinates of the photons and the center of the sub-capillary at the front end point, respectively, and the distance of the photons from the center of the capillary at the rear end point :

[0089] (6),

[0090] and respectively, are the coordinates of the photon and the center of the sub-capillary at the back end point; thus the variation equation of the distance between the photon and the center of the sub-capillary can be obtained:

[0091] (7),

[0092] wherein, is a simulation step length, and l is the transmission distance in the transmission direction;

[0093] the radii of the sub-capillary at the front and back end points and When the sub-capillary is constructed, the variation equation of the radius of the sub-capillary can be obtained:

[0094] (8),

[0095] wherein, ;

[0096] When the photon collides with the wall of the sub-capillary, i.e. By simultaneously solving equation (7) and equation (8), the axial distance l of the collision point can be obtained, and the accurate coordinates can be obtained by bringing the path equation of the photon into the axial distance l.

[0097] To obtain the collision angle, the normal vector of the collision point is needed, because the cross section of the sub-capillary is circular, so the normal vector points to the center of the circle, is the coordinate of the collision point relative to the center of the circle. However, the axial direction of the sub-capillary has a certain angle with the z-axis, so it is needed to rotate the normal vector from the coordinate system of the sub-capillary to the coordinate system of the simulation calculation:

[0098] (9),

[0099] wherein, is a rotation matrix,

[0100] Thus, the collision angle is obtained through the path equation of the photon of the above equation (7) and the normal vector.

[0101] S7. Transmission of the photon in the multi-capillary;

[0102] That is, the process of one-time collision reflection, after the photon reaches the outlet of the multi-capillary, the coordinates of the photon are rotated back to the original position to obtain the final result.

[0103] Example 2

[0104] Effect verification

[0105] The above example 1 has explained the main improvement of the present application and the original method, and this example verifies the comparison of the output results and reference data of the two.

[0106] Table 1 below is the multi-capillary parameters used in the prior art, and Figure 10 is the simulation and experimental results thereof.

[0107] Table 1 Multi-capillary parameters of the original method

[0108]

[0109] The simulation results of the method of Embodiment 1 of the present application are very close to the results of Robert et al., while the transmission efficiency obtained by the original method has a significant difference, as shown in Table 2. Figure 11

[0110] The above only describes the preferred embodiments of the present application and is not intended to limit the present application. Those skilled in the art can make various modifications and changes to the present application. Any modification, equivalent replacement, improvement, etc. within the spirit and principles of the present application shall be included in the protection scope of the present application.​​

Claims

1. A simulation method for X-ray transmission in multiple capillaries, characterized in that, Includes the following steps: S1. The program reads the parameters of the light source and the multi-capillary structure from the input file; S2. The light field distribution of the light source is simulated using a 4π divergent photon source; S3. Construct a multi-capillary structure; S4. Construct the subcapillary structure, and discretize the subcapillary into an inclined frustum structure; S5. Photons enter the capillary; S6. Calculate the collision position and angle between the photon and the capillary wall; S7. Photons propagate in the multi-capillary tube. After the photons reach the exit of the multi-capillary tube, the photon coordinates are rotated back to their original positions to obtain the simulation results. In step S4, the radius and center position of each segment of the inclined frustum structure change linearly. In step S6, the specific method for calculating the collision position is as follows: The distance of the photon at the front point of the ion capillary center , （5）， and These are the coordinates of the photon and the subcapillary center at the front end point, respectively. The distance of the photon at the center of the ion capillary at the rear end , ， and These are the coordinates of the photon and the subcapillary center at the rear end point, respectively. The equation for the change in the center distance of the photon ion capillary is obtained as follows: （7）， dl is a simulated step size, and l is the transmission distance in the transmission direction; The radius of the subcapillary at the tip point The radius of the capillary at the rear end point Knowing this during the construction of the sub-capillary, we can obtain the equation for the change in the sub-capillary radius: ， （8）， When a photon collides with the capillary wall, that is... By combining formulas (7) and (8), the axial distance of the collision point, i.e. the transmission distance l in the transmission direction, is obtained. Substituting this into the path equation of the photon, the accurate coordinates are obtained.

2. The method according to claim 1, characterized in that, In step S3, the method for constructing the multi-capillary structure is as follows: Using cubic curves: (1), The radius variation of the fitted multi-capillary tube is shown, where a, b, c, and d are the coefficients of the curve and are all unknowns, and z is the distance in the transmission direction. The radius of the capillary tube; r1 is the inlet radius of the multi-capillary tube, r2 is the outlet radius of the multi-capillary tube, F1 is the inlet focal length of the multi-capillary tube, F2 is the outlet focal length of the multi-capillary tube, and L is the length of the multi-capillary tube. Substitute the above parameters into the curve equation: （2）， The slope at both ends of the outer contour curve of the multi-capillary , （3）， Given that the radius is equal to the focal length, we can obtain: （4）， By solving equations (2) and (4), the values ​​of a, b, c, and d are obtained, thus yielding the curve equation of the above formula (1).

3. The method according to claim 1, characterized in that, In step S5, Based on its initial position and velocity direction, the photon enters a subcapillary tube, the coordinates of which are: Photon coordinates are ; The subcapillary and photon are rotated so that the center of the subcapillary is located on the x-axis. The coordinates of the subcapillary center change are as follows: ; Photon coordinate changes: ( ; in, For rotation angle, .

4. The method according to claim 1, characterized in that, In step S6, the specific method for determining the collision angle is as follows: Since the cross-section of the subcapillary is circular, the normal vector at the collision point... Pointing towards the center of the circle, The coordinates of the collision point relative to the center of the circle; the axial direction of the sub-capillary forms an angle with the z-axis. Therefore, the normal vector is rotated from the subcapillary coordinate system to the simulation coordinate system: （9）， in, Given the rotation matrix, the collision angle can be calculated using the photon path equation and normal vector from the above formula (7).

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