CN112579969A - Two-dimensional small-angle X-ray scattering map calculation method and device - Google Patents

Two-dimensional small-angle X-ray scattering map calculation method and device Download PDF

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CN112579969A
CN112579969A CN202011524314.3A CN202011524314A CN112579969A CN 112579969 A CN112579969 A CN 112579969A CN 202011524314 A CN202011524314 A CN 202011524314A CN 112579969 A CN112579969 A CN 112579969A
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朱才镇
唐正
张昊
乔永娜
刘会超
徐坚
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Abstract

The application discloses a method and a device for calculating a two-dimensional small-angle X-ray scattering 2DSAXS map, wherein the method comprises the following steps: acquiring the shape parameter, the size parameter and the angle parameter of the ith scatterer, wherein i is an integer greater than or equal to zero; determining a target three-dimensional matrix M of the ith scatterer according to the shape parameter, the size parameter and the angle parameter of the ith scattereri(ii) a For target three-dimensional matrix MiProjecting to obtain a two-dimensional projection matrix Ki(ii) a For two-dimensional projection matrix KiPerforming Fourier operation to obtain a 2DSAXS map matrix L of the ith scattereri(ii) a According to a 2DSAXS atlas matrix LiDetermining a target 2DSAXS map.

Description

Two-dimensional small-angle X-ray scattering map calculation method and device
Technical Field
The application relates to the technical field of small-angle X-ray scattering, in particular to a method and a device for calculating a two-dimensional small-angle X-ray scattering map.
Background
Small angle X-ray scattering (SAXS) refers to a coherent scattering phenomenon of electrons to X-rays within a small angle range near an original X-ray beam, and spatial geometrical information such as the shape, size, distribution and content of microstructures (including micro-nano particles, pore structures and the like) within a nano-scale (1-1000nm) range in a material can be effectively detected by analyzing X-ray scattering intensity fluctuation caused by electron density difference between a matrix and the microstructures in a sample. Meanwhile, the SAXS technology has the characteristics of high penetrability, simplicity in sample preparation, nondestructive detection, rapidness in test, good statistics, wide application range and the like, is an indispensable microscopic-mesoscale key analysis characterization means in the current high-throughput characterization technology of the novel material nanoscale microstructure, and is widely applied to various research fields of alloys, suspensions, emulsions, colloids, polymer solutions, natural macromolecules, liquid crystals, films, polyelectrolytes, composites, nanomaterials and the like.
SAXS is simple to test, but data analysis is quite complex. For anisotropic systems with highly preferred orientation of scatterers, data analysis is currently mainly performed by a 2D SAXS (2D SAXS) method. The 2D SAXS method realizes the analysis of the microstructure by directly fitting an experimental two-dimensional scattering map, and key factors for implementing the method are the construction of a reasonable mathematical model and the rapid calculation of a theoretical two-dimensional scattering map. At present, some methods can effectively calculate a theoretical 2D SAXS spectrum of an anisotropic system, but the methods all adopt a technical route for directly calculating a scattering spectrum in an inverted space, seriously depend on shape factors and structural factors of scatterers in the inverted space, are only suitable for simple scatterers with analytical solutions in the inverted space, such as ellipsoids, cylinders, cuboids and the like, and can not meet the requirements of practical experiments.
Therefore, the development of a 2D SAXS spectrum calculation method with more universality is a key technical problem of the current SAXS research of the anisotropic system.
Disclosure of Invention
The embodiment of the application provides a method and a device for calculating a two-dimensional small-angle X-ray scattering spectrum, which can effectively calculate a 2D SAXS spectrum of an anisotropic system and have good universality.
In a first aspect, the present application provides a two-dimensional small-angle X-ray scattering 2DSAXS atlas calculation method, which is applied to a sparse system, and the method includes: s1: acquiring the shape parameter, the size parameter and the angle parameter of the ith scatterer, wherein i is an integer greater than or equal to zero; s2: determining a target three-dimensional matrix M of the ith scatterer according to the shape parameter, the size parameter and the angle parameter of the ith scattereri(ii) a S3: for target three-dimensional matrix MiProjecting to obtain a two-dimensional projection matrix Ki(ii) a S4: for two-dimensional projection matrix KiPerforming Fourier operation to obtain a 2DSAXS map matrix L of the ith scattereri(ii) a S5: according to a 2DSAXS atlas matrix LiDetermining a target 2DSAXS map.
It can be seen that, in the embodiment of the present application, for scatterers with different characteristics, a target three-dimensional matrix representing the shape, size and orientation angle of the scatterer can be easily obtained by using the method in the embodiment of the present application, and further, a target 2DSAXS spectrum of a sample can be quickly determined by projection and fourier transform.
In one possible embodiment, the matrix L is based on a 2DSAXS mapiDetermining a target 2DSAXS map comprising: 2DSAXS map matrix L of ith scattereri2D SCAXS map matrix L with the i-1 st scattereri-1Adding corresponding elements and taking the average value to obtain a matrix Li'; will matrix Li-1And matrix Li' the corresponding elements are subtracted to obtain the matrix Li", when matrix Li"all elements inWhen the maximum value of the pair values is less than or equal to a preset threshold value, the 2DSAXS map matrix L is processediThe corresponding 2DSAXS map is taken as the target 2DSAXS map; otherwise, let i equal to i +1, and repeat the above steps S1-S5.
It can be seen that, in the embodiment of the application, by setting the iteration termination condition, when the iteration termination condition is met, that is, the target 2DSAXS atlas is converged, the atlas calculation process can be stopped, time is saved, and calculation efficiency is improved.
In a possible embodiment, the above-mentioned target three-dimensional matrix M of the ith scatterer is determined according to the shape parameter, the size parameter and the angle parameter of the ith scattereriThe method comprises the following steps: generating an initial three-dimensional matrix of the ith scatterer according to the shape parameter, the size parameter and the angle parameter of the ith scatterer; determining a rotation matrix of the ith scatterer according to the angle parameter of the ith scatterer; multiplying the initial three-dimensional matrix of the ith scatterer by the rotation matrix of the ith scatterer to obtain a target three-dimensional matrix M of the ith scattereri。
In a second aspect, the present application provides a two-dimensional small-angle X-ray scattering 2DSAXS map calculation method, applied to a dense system, the method including: acquiring N groups of shape parameters, size parameters, angle parameters and center coordinates of N scatterers, wherein the N scatterers correspond to the N groups of shape parameters, size parameters, angle parameters and center coordinates one by one; determining a target three-dimensional matrix according to the N groups of shape parameters, size parameters, angle parameters and center coordinates, wherein the target three-dimensional matrix represents the shapes, sizes and orientations of the N scatterers and the positions of the N scatterers in a three-dimensional coordinate system; projecting the target three-dimensional matrix to obtain a two-dimensional projection matrix; performing Fourier operation on the two-dimensional projection matrix to obtain a target 2D SAXS spectrum matrix; and taking the 2D SAXS spectrum corresponding to the target 2D SAXS spectrum matrix as the target 2D SAXS spectrum.
It can be seen that, in the embodiment of the application, for a dense system, based on N groups of shape parameters, size parameters, angle parameters and center coordinates of N scatterers, a target three-dimensional matrix of the N scatterers is obtained, and further, through projection and fourier transform, a target 2DSAXS spectrum of a sample can be quickly determined.
In a possible embodiment, the determining the target three-dimensional matrix according to the N sets of shape parameters, size parameters, angle parameters and center coordinates includes: generating an initial three-dimensional matrix of each scatterer according to the shape parameter, the size parameter, the angle parameter and the center coordinate of each scatterer in the N scatterers; determining a rotation matrix of each scatterer according to the angle parameter of each scatterer; multiplying the initial three-dimensional matrix of each scatterer by the rotation matrix of each scatterer to obtain a reference three-dimensional matrix of each scatterer; and determining a target three-dimensional matrix according to the reference three-dimensional matrix of each scatterer.
In a possible embodiment, the method further includes: after the target three-dimensional matrix is determined according to the reference three-dimensional matrix of each scatterer, when any two scatterers in the N scatterers are overlapped, elements representing the overlapped part in the target three-dimensional matrix are set to be zero.
It can be seen that, in the embodiment of the application, when any two scatterers in the N scatterers overlap, the element representing the overlapping part in the target three-dimensional matrix is set to zero, so that the accuracy of the target three-dimensional matrix can be ensured, and the accurate target 2D SAXS spectrum can be obtained subsequently.
In a possible embodiment, the method further includes: after the target three-dimensional matrix is determined according to the reference three-dimensional matrix of each scatterer, when the size of a three-dimensional model formed by the N scatterers is larger than that of a preset cuboid, the scatterers beyond the range of the preset cuboid are filled from the other end and filled into the preset cuboid, and the target three-dimensional matrix is updated according to the position change of the scatterers.
It can be seen that, in the embodiment of the application, the size of the resolution of the finally obtained target 2D SAXS spectrum is controlled by setting the size of the preset cuboid, then scatterers out of the N scatterers in the range of the preset cuboid are supplemented into the preset cuboid, and elements in the target three-dimensional matrix are adjusted, so that the accuracy of the target 2D SAXS spectrum obtained by subsequent calculation of the target three-dimensional matrix is ensured on the premise that the target 2D SAXS spectrum meets the preset resolution.
In a third aspect, the present application provides a two-dimensional small-angle X-ray scattering 2DSAXS map computing apparatus, which includes corresponding modules for performing all or any one of the methods of the first and second aspects.
In a fourth aspect, the present application provides a computer readable storage medium storing program code for execution by a device, the program code comprising instructions for performing the method of any or all of the first and second aspects described above.
In a fifth aspect, the present application provides a chip comprising a processor and a data interface, wherein the processor reads instructions stored in a memory through the data interface to perform the method according to any one or all of the first and second aspects.
Drawings
The drawings used in the embodiments of the present application are described below.
Fig. 1 is a flowchart of a 2DSAXS atlas calculation method in an embodiment of the present application;
fig. 2 is a flowchart of another 2DSAXS map calculation method in the embodiment of the present application;
fig. 3 is a schematic structural diagram of a 2DSAXS map computing device in an embodiment of the present application;
fig. 4 is a schematic structural diagram of another 2d axs map computing device in the embodiment of the present application;
fig. 5 is a 2d axs map of a scatterer in a sparse system calculated by the embodiment of the present application;
FIG. 6 is a 2DSAXS map of scatterers in a dense system calculated using an embodiment of the present application;
fig. 7 is a schematic hardware structure diagram of a 2d axs map computing device in an embodiment of the present application.
Detailed Description
The embodiments of the present application will be described below with reference to the drawings.
Referring to fig. 1, fig. 1 is a flowchart of a 2DSAXS atlas calculation method 100 in an embodiment of the present application. As shown in fig. 1, the method 100 includes steps S1, S2, S3, S4, and S5.
Step S1: and acquiring the shape parameter, the size parameter and the angle parameter of the ith scatterer, wherein i is an integer greater than or equal to zero.
In one possible embodiment, the shape, size and orientation angle of the scatterer can be characterized by a hyperellipsoid function, where the shape parameters of the scatterer are parameters e and n in the hyperellipsoid function, and the expression of the hyperellipsoid function is shown in formula (1). The scatterer size comprises a short axis size and a long axis size, the size parameters comprise a short axis size parameter and a long axis size parameter, the short axis size parameter is a short axis mean and a short axis variance, and the long axis size parameter is a long axis mean and a long axis variance. The scatterer angle comprises a zenith angle and an azimuth angle, so the angle parameters comprise zenith angle parameters and azimuth comparison parameters, the zenith angle satisfies circular distribution, and the circular distribution has two parameters, namely a mean value and a variance, so the zenith angle parameters of the scatterer are a zenith angle mean value and a zenith angle variance; the azimuth angle of the scatterer meets the requirement of uniform distribution, no actual parameter exists, and the value of the scatterer is any value between 0 and 360 degrees. In summary, eight parameters, i.e., the shape, size (including the size of the long axis and the size of the short axis) and orientation angle (zenith angle and azimuth angle) of a single scatterer can be determined by determining the parameters e and n, the short axis mean, the short axis variance, the long axis mean, the long axis variance, the zenith angle mean and the zenith angle variance.
Specifically, for the ith scatterer, a shape parameter, a size parameter and an angle parameter of the ith scatterer are generated by using a random function. Random function in the numeric computation function library NUMPY or a function in other function libraries similar to the function in random function library in NUMPY.
The orientation of the scattering body refers to the spatial orientation of the single scattering body in the coordinate system, and the orientation is characterized by the angle parameter.
Figure BDA0002848605950000041
Wherein x is0、y0、z0Representing the coordinates of the centre of the scatterer, e and n being shape parameters, respectively, different e and n yielding different shapes, R1And R2For the minor axis dimension, usually taking an equal value, R3The major axis dimension.
Step S2: determining a target three-dimensional matrix M of the ith scatterer according to the shape parameter, the size parameter and the angle parameter of the ith scattereri。
In a possible embodiment, the above-mentioned target three-dimensional matrix M of the ith scatterer is determined according to the shape parameter, the size parameter and the angle parameter of the ith scattereriThe method comprises the following steps: generating an initial three-dimensional matrix of the ith scatterer according to the shape parameter, the size parameter and the angle parameter of the ith scatterer; determining a rotation matrix of the ith scatterer according to the angle parameter of the ith scatterer; multiplying the initial three-dimensional matrix of the ith scatterer by the rotation matrix of the ith scatterer to obtain a target three-dimensional matrix M of the ith scattereri。
Specifically, parameters e and n representing the shape and size of the ith scatterer, a short axis mean value, a short axis variance, a long axis mean value and a long axis variance are substituted into a hyper-ellipsoid function to generate an initial three-dimensional matrix of the ith scatterer; then, generating a rotation matrix of the ith scatterer based on zenith angle parameters and azimuth angles of the scatterers; multiplying the rotation matrix of the ith scatterer by the initial three-dimensional matrix to generate a target three-dimensional matrix M of the ith scatterer under the given angle conditioni。
Step S3: for target three-dimensional matrix MiProjecting to obtain a two-dimensional projection matrix Ki。
Specifically, the target three-dimensional matrix M is divided intoiProjecting along the normal direction of the detector to obtain a two-dimensional projection matrix Ki。
Step S4: for two-dimensional projection matrix KiPerforming Fourier transformCalculating to obtain a 2DSAXS map matrix L of the ith scattereri。
In particular, for a two-dimensional projection matrix KiFourier transform is carried out to obtain a 2DSAXS map matrix L of the ith scattereri。
Step S5: according to a 2DSAXS atlas matrix LiDetermining a target 2DSAXS map.
Specifically, a 2DSAXS map matrix L of the ith scattereri2D SCAXS map matrix L with the i-1 st scattereri-1Adding corresponding elements and taking the average value to obtain a matrix Li'; the matrix LiThe specific acquisition process of' can refer to the 2DSAXS map matrix L of the ith scattereriThe detailed description of the calculation process is omitted here.
After obtaining the matrix Li' thereafter, the matrix L is appliedi-1And matrix Li' the corresponding elements are subtracted to obtain the matrix Li", when matrix LiWhen the maximum value of the absolute value of each element in the 2DSAXS atlas matrix L is less than or equal to a preset threshold valueiThe corresponding 2DSAXS map is taken as the target 2DSAXS map; otherwise, let i equal to i +1, and repeat the above steps S1-S5. It should be understood that the preset threshold may be determined according to a specific application scenario, and this application is not limited thereto.
It should be understood that the foregoing embodiments are mainly applied to a sparse system, in the embodiments of the present application, for scatterers with different characteristics, a target three-dimensional matrix characterizing the shape, size, and orientation angle of the scatterer is easily obtained by using the method in the embodiments of the present application, and then a target 2DSAXS spectrum of a sample can be quickly determined by projection and fourier transform, and since the target three-dimensional matrix of the scatterer is a basic parameter characterizing the characteristics of the scatterer, the embodiments of the present application have strong universality, and can be used for calculation of the 2DSAXS spectrum of an anisotropic system.
Referring to fig. 2, a flowchart of another 2DSAXS atlas calculation method 200 in the embodiment of the present application is shown. As shown in fig. 2, the method 200 includes steps S210, S220, S230, and S240.
Step S210: n groups of shape parameters, size parameters, angle parameters and center coordinates of N scatterers are obtained, and the N scatterers correspond to the N groups of shape parameters, size parameters, angle parameters and center coordinates one to one.
Specifically, a random function may be used to generate the shape parameter, the size parameter, and the angle parameter of each of the N scatterers. The shape parameter, the size parameter and the angle parameter of each scatterer respectively include specific parameters that are the same as those described in the corresponding steps of the embodiment of fig. 1, and are not described herein again. According to eight parameters of the shape parameter (e and n), the short axis mean value, the short axis variance, the long axis mean value, the long axis variance, the zenith angle mean value and the zenith angle variance of each scatterer, the shape, the size (including the long axis size and the short axis size) and the orientation angle (the zenith angle and the azimuth angle) of each scatterer can be determined. And determining the center coordinates of the N scatterers according to the distribution function of the system scatterers. Specifically, the distribution function may be gaussian distribution or random distribution, or the centers of the N scatterers may also be arranged periodically, such as cubic or hexagonal lattice arrangement, which is not specifically limited in this embodiment of the present application. The center coordinates of the N scatterers are used for representing the positions of the centers of the N scatterers in a three-dimensional coordinate system.
Step S220: and determining a target three-dimensional matrix according to the N groups of shape parameters, size parameters, angle parameters and center coordinates, wherein the target three-dimensional matrix represents the shape, size and orientation of the N scatterers and the positions of the N scatterers in a three-dimensional coordinate system.
Specifically, in one possible embodiment, an initial three-dimensional matrix of each scatterer is generated according to the shape parameter, the size parameter, the angle parameter and the center coordinate of each scatterer in the N scatterers; then determining a rotation matrix of each scatterer according to the angle parameter of each scatterer; multiplying the initial three-dimensional matrix of each scatterer by the rotation matrix of each scatterer to obtain a reference three-dimensional matrix of each scatterer; and accumulating all elements in the N reference three-dimensional matrixes of the N scatterers and averaging to obtain a target three-dimensional matrix, wherein the target three-dimensional matrix represents the shapes, sizes and orientations of the N scatterers and the positions of the N scatterers in a three-dimensional coordinate system. That is, a three-dimensional model including the N scatterers can be constructed in a three-dimensional coordinate system by the target three-dimensional matrix.
In a possible embodiment, after the target three-dimensional matrix is determined based on the reference three-dimensional matrix of each scatterer, when any two scatterers of the N scatterers overlap, an element in the target three-dimensional matrix that characterizes the overlapping portion is set to zero.
In a possible embodiment, after determining the target three-dimensional matrix according to the reference three-dimensional matrix of each scatterer, when the size of the three-dimensional model containing the N scatterers is larger than that of the preset cuboid, the scatterers beyond the range of the preset cuboid are filled from the other end, and the target three-dimensional matrix is updated according to the position change of the scatterers.
Step S230: and projecting the target three-dimensional matrix to obtain a two-dimensional projection matrix.
Specifically, the target three-dimensional matrix is projected along a normal direction of the detector to obtain a two-dimensional projection matrix representing the N scatterers.
Step S240: performing Fourier operation on the two-dimensional projection matrix to obtain a target 2D SAXS spectrum matrix; and taking the 2D SAXS spectrum corresponding to the target 2D SAXS spectrum matrix as the target 2D SAXS spectrum.
Specifically, the two-dimensional projection matrix is subjected to fourier transform to obtain a target 2D SAXS spectrum matrix, a 2D SAXS spectrum corresponding to the target 2D SAXS spectrum matrix is taken as a target 2D SAXS spectrum, and the target 2D SAXS spectrum is a 2D SAXS spectrum obtained by performing two-dimensional small-angle X-ray scattering on a sample containing the N scatterers.
It should be understood that the above embodiments are mainly applied to a dense system, in the embodiments of the present application, a target three-dimensional matrix of N scatterers is obtained based on N sets of shape parameters, size parameters, angle parameters, and center coordinates of the N scatterers, and then a target 2DSAXS spectrum of a sample can be quickly determined through projection and fourier transform, and since the target three-dimensional matrix of the scatterer is a basic parameter characterizing characteristics of the scatterer, the embodiments of the present application have strong universality, and can be used for calculation of the 2DSAXS spectrum of an anisotropic system. In addition, the resolution of the finally obtained target 2D SAXS spectrum is controlled by setting the size of a preset cuboid, then scatterers exceeding the range of the preset cuboid in the N scatterers are complemented into the preset cuboid, elements in a target three-dimensional matrix are adjusted, and the accuracy of the target 2D SAXS spectrum obtained through calculation of the target three-dimensional matrix is guaranteed on the premise that the target 2D SAXS spectrum meets the preset resolution.
Referring to fig. 3, fig. 3 is a schematic structural diagram of a 2DSAXS map computing device 300 according to an embodiment of the present application. As shown in fig. 3, the apparatus 300 comprises an obtaining unit 310, a processing unit 320 and a determining unit 330.
An obtaining unit 310, configured to perform step S1: and acquiring the shape parameter, the size parameter and the angle parameter of the ith scatterer, wherein i is an integer greater than or equal to zero.
A processing unit 320 for performing steps S2-S4: s2: determining a target three-dimensional matrix M of the ith scatterer according to the shape parameter, the size parameter and the angle parameter of the ith scattereri(ii) a S3: for target three-dimensional matrix MiProjecting to obtain a two-dimensional projection matrix Ki(ii) a S4: for two-dimensional projection matrix KiPerforming Fourier operation to obtain a 2DSAXS map matrix L of the ith scattereri。
A determination unit 330 configured to perform step S3: according to a 2DSAXS atlas matrix LiDetermining a target 2DSAXS map.
In one possible embodiment, the matrix L is based on the 2DSAXS mapiDetermining an aspect of the target 2DSAXS map, the determining unit 330 is specifically configured to: 2DSAXS map matrix L of ith scattereri2D SCAXS map matrix L with the i-1 st scattereri-1Adding corresponding elements and taking the average value to obtain a matrix Li'; will matrix Li-1And matrix Li' the corresponding elements are subtracted to obtain the matrix Li", when matrix LiWhen the maximum value of the absolute value of each element in the map is less than or equal to a preset threshold value, the 2DSAXS map is usedMatrix LiThe corresponding 2DSAXS map is taken as the target 2DSAXS map; otherwise, let i be i +1, and cause the acquisition unit 310 to repeatedly perform step S1, the processing unit 320 repeatedly performs steps S2-S4, and the determination unit 330 repeatedly performs step S3.
In one possible embodiment, the target three-dimensional matrix M of the ith scatterer is determined as described above based on the shape parameter, the size parameter, and the angle parameter of the ith scattereriIn an aspect, the processing unit 320 is specifically configured to: generating an initial three-dimensional matrix of the ith scatterer according to the shape parameter, the size parameter and the angle parameter of the ith scatterer; determining a rotation matrix of the ith scatterer according to the angle parameter of the ith scatterer; multiplying the initial three-dimensional matrix of the ith scatterer by the rotation matrix of the ith scatterer to obtain a target three-dimensional matrix M of the ith scattereri。
Referring to fig. 4, fig. 4 is a schematic structural diagram of another 2DSAXS map computing device 400 according to an embodiment of the present application. As shown in fig. 4, the apparatus 400 includes an obtaining unit 410, a preprocessing unit 420, and a determining unit 430.
The acquiring unit 410 is configured to acquire N sets of shape parameters, size parameters, angle parameters, and center coordinates of N scatterers, where the N scatterers correspond to the N sets of shape parameters, size parameters, angle parameters, and center coordinates one to one.
The preprocessing unit 420 is configured to determine a target three-dimensional matrix according to the N groups of shape parameters, size parameters, angle parameters, and center coordinates, where the target three-dimensional matrix represents shapes, sizes, orientations of the N scatterers, and positions of the N scatterers in a three-dimensional coordinate system; projecting the target three-dimensional matrix to obtain a two-dimensional projection matrix; and performing Fourier operation on the two-dimensional projection matrix to obtain a target 2D SAXS spectrum matrix.
The determining unit 430 is configured to use the 2D SAXS spectrum corresponding to the target 2D SAXS spectrum matrix as the target 2D SAXS spectrum.
In one possible embodiment, in the aspect of determining the target three-dimensional matrix according to the N sets of shape parameters, size parameters, angle parameters and center coordinates, the preprocessing unit 420 is specifically configured to: generating an initial three-dimensional matrix of each scatterer according to the shape parameter, the size parameter, the angle parameter and the center coordinate of each scatterer in the N scatterers; determining a rotation matrix of each scatterer according to the angle parameter of each scatterer; multiplying the initial three-dimensional matrix of each scatterer by the rotation matrix of each scatterer to obtain a reference three-dimensional matrix of each scatterer; and determining a target three-dimensional matrix according to the reference three-dimensional matrix of each scatterer.
In a possible embodiment, the preprocessing unit 420 is further configured to, after determining the target three-dimensional matrix according to the reference three-dimensional matrix of each scatterer, zero an element in the target three-dimensional matrix that characterizes an overlapping portion when any two scatterers of the N scatterers overlap.
In a possible embodiment, the preprocessing unit 420 is further configured to, after the target three-dimensional matrix is determined according to the reference three-dimensional matrix of each scatterer, when the size of the three-dimensional model formed by the N scatterers is larger than that of the preset cuboid, fill the scatterers beyond the range of the preset cuboid from the other end, fill the preset cuboid, and update the target three-dimensional matrix according to the position change of the scatterers.
Referring to fig. 5, fig. 5 is a 2d axs map of a scatterer in a sparse system calculated by the embodiment of the present application. The shape of the scatterer 1 is shown in fig. 5 (a), where the values of e and n in the shape parameters for describing the scatterer 1 are 1.00 and 1.75, respectively; the minor axis mean and the minor axis variance are 10.0nm and 10.0nm, respectively; the major axis mean and the major axis variance were 50.0nm and 10.0nm, respectively, and the zenith angle mean and the zenith angle variance were 0.0 ° and 100.0, respectively. According to the method in the embodiment of fig. 1, the above parameters are substituted into a hyper-ellipsoid function for calculation, so as to obtain a target 2D SAXS map of a single 128 × 128 pixel, as shown in fig. 5 (b).
The shape of the scatterer 2 is as shown in fig. 5 (c), and the values of e and n in the shape parameters for describing the scatterer 2 are 3.50 and 0.50, respectively; the minor axis mean and the minor axis variance are 10.0nm and 10.0nm, respectively; the major axis mean and the major axis variance were 50.0nm and 10.0nm, respectively, and the zenith angle mean and the zenith angle variance were 0.0 ° and 100.0, respectively. According to the method in the embodiment of fig. 1, the above parameters are substituted into a hyper-ellipsoid function for calculation, so as to obtain a target 2D SAXS map of a single 128 × 128 pixel, as shown in fig. 5 (D).
Referring to fig. 6, fig. 6 is a 2d axs map of scatterers in a dense system calculated by the embodiment of the present application. As shown in fig. 6 (a), 256 scatterers are arranged in a hexagonal arrangement in the XY plane, and the values of the shape parameter e and n characterizing each of the 256 scatterers are 1.00 and 1.00, respectively; the minor axis mean and the minor axis variance are 2.0nm and 0.0nm, respectively; the major axis mean and the major axis variance were 10.0nm and 0.0nm, respectively, and the zenith angle mean and the zenith angle variance were 0.0 ° and 100.0, respectively. According to the method in the embodiment of fig. 2, the above parameters are substituted into a hyper-ellipsoid function for calculation, so as to obtain a target 2D SAXS map of a single 128 × 128 pixel, as shown in (b) of fig. 6.
As shown in fig. 6 (c), 256 scatterers are arranged in a cube in the XY plane, and the values of the shape parameter e and n characterizing each of the 256 scatterers are 1.00 and 1.00, respectively; the minor axis mean and the minor axis variance are 2.0nm and 0.0nm, respectively; the major axis mean and the major axis variance were 10.0nm and the zenith angle mean and the zenith angle variance were 0.0 ° and 100.0, respectively. According to the method in the embodiment of fig. 2, the above parameters are substituted into a hyper-ellipsoid function for calculation, so as to obtain a target 2D SAXS map of a single 128 × 128 pixel, as shown in (D) of fig. 6.
Referring to fig. 7, fig. 7 is a schematic diagram of a hardware structure of a 2d axs map computing device in an embodiment of the present application. As shown in fig. 7, computing device 700 includes a communication interface 701, a processor 702, a memory 703, and at least one communication bus 704 for coupling communication interface 701, processor 702, and memory 703.
The memory 703 includes, but is not limited to, a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM), or a portable read-only memory (CD-ROM), and the memory 703 is used for related instructions and data.
Communication interface 701 is used to receive and transmit data.
The processor 702 may be one or more Central Processing Units (CPUs), and in the case that the processor 702 is one CPU, the CPU may be a single-core CPU or a multi-core CPU.
The processor 702 in the electronic device 700 is configured to read one or more program codes stored in the memory 703 to perform the method as described in the embodiments of fig. 1 and 2.
An embodiment of the present application further provides a computer-readable storage medium, in which a computer program is stored, and when the computer program runs on a terminal, the method flows shown in the foregoing method embodiments are implemented.
The embodiments of the present application further provide a computer program product, and when the computer program product runs on a terminal, the method flows shown in the foregoing method embodiments are implemented.
It should be understood that the Processor mentioned in the embodiments of the present Application may be a Central Processing Unit (CPU), and may also be other general purpose processors, Digital Signal Processors (DSP), Application Specific Integrated Circuits (ASIC), Field Programmable Gate Arrays (FPGA) or other Programmable logic devices, discrete Gate or transistor logic devices, discrete hardware components, and the like. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like.
It will also be appreciated that the memory referred to in the embodiments of the application may be either volatile memory or nonvolatile memory, or may include both volatile and nonvolatile memory. The non-volatile Memory may be a Read-Only Memory (ROM), a Programmable ROM (PROM), an Erasable PROM (EPROM), an Electrically Erasable PROM (EEPROM), or a flash Memory. Volatile Memory can be Random Access Memory (RAM), which acts as external cache Memory. By way of example, but not limitation, many forms of RAM are available, such as Static random access memory (Static RAM, SRAM), Dynamic Random Access Memory (DRAM), Synchronous Dynamic random access memory (Synchronous DRAM, SDRAM), Double Data Rate Synchronous Dynamic random access memory (DDR SDRAM), Enhanced Synchronous SDRAM (ESDRAM), Synchronous link SDRAM (SLDRAM), and Direct Rambus RAM (DR RAM).
It should be noted that when the processor is a general-purpose processor, a DSP, an ASIC, an FPGA or other programmable logic device, a discrete gate or transistor logic device, or a discrete hardware component, the memory (memory module) is integrated in the processor.
It should be noted that the memory described herein is intended to comprise, without being limited to, these and any other suitable types of memory.
It should be understood that, in the various embodiments of the present application, the sequence numbers of the above-mentioned processes do not mean the execution sequence, and the execution sequence of each process should be determined by its function and inherent logic, and should not constitute any limitation to the implementation process of the embodiments of the present application.
Those of ordinary skill in the art will appreciate that the various illustrative elements and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware or combinations of computer software and electronic hardware. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the implementation. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present application.
It is clear to those skilled in the art that, for convenience and brevity of description, the specific working processes of the above-described apparatuses and units may refer to the corresponding processes in the foregoing method embodiments, and are not described herein again.
In the several embodiments provided in the present application, it should be understood that the disclosed apparatus and method may be implemented in other ways. For example, the above-described device embodiments are merely illustrative, and for example, a division of a unit is merely a logical division, and an actual implementation may have another division, for example, a plurality of units or components may be combined or integrated into another device, or some features may be omitted, or not executed. In addition, the shown or discussed mutual coupling or direct coupling or communication connection may be an indirect coupling or communication connection through some interfaces, devices or units, and may be in an electrical, mechanical or other form.
The units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of the embodiment.
In addition, functional units in the embodiments of the present application may be integrated into one processing unit, or each unit may exist alone physically, or two or more units are integrated into one unit.
The above functions, if implemented in the form of software functional units and sold or used as a separate product, may be stored in a computer-readable storage medium. Based on such understanding, the technical solution of the present application or portions thereof that substantially contribute to the prior art may be embodied in the form of a software product stored in a storage medium and including instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present application. And the aforementioned storage medium includes: various media capable of storing program codes, such as a usb disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk, or an optical disk.
The steps in the method of the embodiment of the application can be sequentially adjusted, combined and deleted according to actual needs.
The modules in the device can be merged, divided and deleted according to actual needs.
The above embodiments are only used for illustrating the technical solutions of the present application, and not for limiting the same; although the present application has been described in detail with reference to the foregoing embodiments, it should be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present application.

Claims (10)

1. A method for calculating a two-dimensional small-angle X-ray scattering 2DSAXS map, the method comprising:
s1: acquiring a shape parameter, a size parameter and an angle parameter of an ith scatterer, wherein i is an integer greater than or equal to zero;
s2: determining a target three-dimensional matrix M of the ith scatterer according to the shape parameter, the size parameter and the angle parameter of the ith scattereri；
S3: for the target three-dimensional matrix MiProjecting to obtain a two-dimensional projection matrix Ki；
S4: for the two-dimensional projection matrix KiPerforming Fourier operation to obtain a 2DSAXS map matrix L of the ith scattereri；
S5: according to the 2DSAXS atlas matrix LiDetermining a target 2DSAXS map.
2. The method of claim 1, wherein the map matrix L is the 2DSAXS map matrixiDetermining a target 2DSAXS map comprising:
mapping the 2DSAXS map matrix L of the ith scattereri2D SCAXS map matrix L with the i-1 st scattereri-1Adding corresponding elements and taking the average value to obtain a matrix Li’；
The matrix Li-1And the matrix Li' the corresponding elements are subtracted to obtain the matrix Li", when the matrix L isiWhen the maximum value of the absolute value of each element in the 2DSAXS atlas matrix L is less than or equal to a preset threshold valuei(ii) the corresponding 2DSAXS map as the target 2DSAXS map; otherwise, let i equal to i +1, and repeat the above steps S1-S5.
3. Method according to claim 1 or 2, characterized in that the target three-dimensional matrix M of the ith scatterer is determined from the shape parameter, the size parameter and the angle parameter of the ith scattereriThe method comprises the following steps:
generating an initial three-dimensional matrix of the ith scatterer according to the shape parameter, the size parameter and the angle parameter of the ith scatterer;
determining a rotation matrix of the ith scatterer according to the angle parameter of the ith scatterer;
multiplying the initial three-dimensional matrix of the ith scatterer by the rotation matrix of the ith scatterer to obtain a target three-dimensional matrix M of the ith scattereri。
4. A method for calculating a two-dimensional small-angle X-ray scattering 2DSAXS map, the method comprising:
acquiring N groups of shape parameters, size parameters, angle parameters and center coordinates of N scatterers, wherein the N scatterers correspond to the N groups of shape parameters, size parameters, angle parameters and center coordinates one by one;
determining a target three-dimensional matrix according to the N groups of shape parameters, size parameters, angle parameters and center coordinates, wherein the target three-dimensional matrix represents the shape, size and orientation of the N scatterers and the positions of the N scatterers in a three-dimensional coordinate system;
projecting the target three-dimensional matrix to obtain a two-dimensional projection matrix;
performing Fourier operation on the two-dimensional projection matrix to obtain a target 2D SAXS spectrum matrix; and taking the 2D AXS map corresponding to the target 2D SAXS map matrix as a target 2D AXS map.
5. The method of claim 4, wherein determining the target three-dimensional matrix from the N sets of shape parameters, size parameters, angle parameters, and center coordinates comprises:
generating an initial three-dimensional matrix of each scatterer according to the shape parameter, the size parameter, the angle parameter and the center coordinate of each scatterer in the N scatterers;
determining a rotation matrix of each scatterer according to the angle parameter of each scatterer;
multiplying the initial three-dimensional matrix of each scatterer by the rotation matrix of each scatterer to obtain a reference three-dimensional matrix of each scatterer;
and determining a target three-dimensional matrix according to the reference three-dimensional matrix of each scatterer.
6. The method of claim 4 or 5, further comprising:
after the target three-dimensional matrix is determined according to the reference three-dimensional matrix of each scatterer, when any two scatterers in the N scatterers are overlapped, setting elements in the target three-dimensional matrix for representing the overlapped part to be zero.
7. The method according to any one of claims 4-6, further comprising:
after the target three-dimensional matrix is determined according to the reference three-dimensional matrix of each scatterer, when the size of a three-dimensional model formed by the N scatterers is larger than that of a preset cuboid, the scatterers beyond the range of the preset cuboid are filled from the other end and filled into the preset cuboid, and the target three-dimensional matrix is updated according to the position change of the scatterers.
8. A two-dimensional small-angle X-ray scattering 2DSAXS map computing device, wherein the device comprises corresponding means for performing the method of any of claims 1-7.
9. A computer-readable storage medium, characterized in that the computer-readable medium stores program code for execution by a device, the program code comprising instructions for performing the method of any of claims 1 to 7.
10. A chip comprising a processor and a data interface, the processor reading instructions stored on a memory through the data interface to perform the method of any one of claims 1 to 7.
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