A self-adaptive power-based magnetic lens full-aberration calculation method and system

Abstract

The application relates to the technical field of electron optics simulation, and particularly discloses a magnetic lens full-aberration calculation method and system based on adaptive power, which comprises the following steps: acquiring an axial magnetic field distribution, an acceleration voltage, a relativistic correction voltage and an imaging position, respectively solving a paraxial ray equation based on the acceleration voltage and the relativistic correction voltage to obtain paraxial ray parameters and a Busch rotation angle, calculating Seidel aberration integrals based on the paraxial ray parameters of the relativistic correction voltage and normalizing the Seidel aberration integrals, determining an adaptive power according to a ratio of a magnetic field intensity at the imaging position to a peak magnetic field intensity, mixing Seidel aberration integral results and Glaser aberration reference values according to lens intensity parameters, and outputting full-aberration results. Through double solving, normalization and adaptive mixing, the application makes the aberrations under weak lens, transition zone and strong lens conditions continuous, and distinguishes compatible values from physical values.

Description

Technical Field

[0001] This invention relates to the field of electronic optics simulation technology, specifically to a method and system for calculating total aberrations of a magnetic lens based on adaptive power law. Background Technology

[0002] In the field of electron optics simulation technology, computational models are typically established around electron beams, magnetic lenses, and electromagnetic field environments. Computers simulate the electron motion path, focusing state, and imaging process. The process generally includes model building, field distribution reading, trajectory calculation, image plane determination, and result recording. Among these, the traditional magnetic lens total aberration calculation method and system refers to establishing electron motion calculation relationships based on the lens structure, magnetic field distribution, electron incident conditions, and imaging position within an electron optics system. The electron trajectory and imaging offset are obtained through numerical solutions, and parameters such as spherical aberration, coma, astigmatism, field curvature, distortion, and chromatic aberration are calculated according to preset aberration types. The computer program then stores, retrieves, and displays the calculation results in a simulation.

[0003] Existing calculations of total aberrations of magnetic lenses often rely on fixed-order Seidel integrals or Glaser approximations. The calculation basis is separate under weak and strong lens conditions. Paraxial ray oscillations after the image plane enters the magnetic field region affect the stability of the integral. Inconsistent off-axis aberration normalization rules can cause field curvature and distortion order deviations. The selection of resolving focal length and numerical focal length for strong lenses is not consistent. When the Busch rotation angle adopts a single voltage convention, there is a lack of distinction between the physical calculation value and the compatible output value, resulting in insufficient consistency of total aberration calculation results across different lens strength ranges. Summary of the Invention

[0004] The purpose of this invention is to provide a method and system for calculating total aberrations of magnetic lenses based on adaptive power law, which enables a unified calculation process for total aberrations of magnetic lenses in weak lens regions, strong lens regions, and the transition regions between them, and establishes a clear data correspondence between Seidel aberration integral, Glaser aberration reference value, adaptive power law correction, and Busch rotation angle output, so as to meet the calculation requirements of spherical aberration, chromatic aberration, coma, field curvature, distortion, and fifth-order spherical aberration of magnetic lenses in electro-optics simulation.

[0005] To achieve the above objectives, the present invention adopts the following technical solution.

[0006] This invention provides a method for calculating total aberrations of a magnetic lens based on adaptive power, comprising the following steps: obtaining the axial magnetic field distribution, accelerating voltage, relativistic correction voltage, initial position, and imaging position of the magnetic lens; solving the paraxial ray equation based on the accelerating voltage and the relativistic correction voltage respectively to obtain the first paraxial ray parameter, the second paraxial ray parameter, and the corresponding Busch rotation angle; calculating the Seidel aberration integral based on the second paraxial ray parameter, and normalizing the calculation of spherical aberration, chromatic aberration, coma, field curvature, distortion, and fifth-order spherical aberration according to the rule that the total power of the denominator is consistent with the total power of the Seidel kernel function; and obtaining the magnetic field strength at the imaging position. The ratio of the peak magnetic field strength in the axial magnetic field distribution is used to determine the adaptive power for spherical aberration and chromatic aberration, and the normalized result of the corresponding Seidel aberration integral is corrected using the adaptive power. The lens strength parameter and resolving effective focal length are determined based on the axial magnetic field distribution, and the Glaser aberration reference value is calculated. The lens strength parameter is compared with the preset weak lens threshold and strong lens threshold to determine the mixing weight. Based on the mixing weight, the Seidel aberration integral result that has undergone adaptive power correction is weighted and mixed with the Glaser aberration reference value to output the magnetic lens total aberration result and the corresponding Busch rotation angle.

[0007] In the above method, the axial magnetic field distribution can be obtained from magnetic field data discretely arranged along the optical axis of the magnetic lens. The magnetic field data includes the axial position and the magnetic field strength corresponding to the axial position. The maximum magnetic field strength in the magnetic field data is taken as the peak magnetic field strength, and the half-height position of the magnetic field is determined based on the peak magnetic field strength. Then, the equivalent half-height width is determined based on the half-height positions of the magnetic field located on both sides of the peak magnetic field strength. Finally, the lens strength parameters are calculated based on the peak magnetic field strength, the equivalent half-height width, and the relativistic correction voltage.

[0008] In a further technical solution, when determining the peak magnetic field strength and equivalent half-width at half-maximum (HWHM), the magnetic field data is organized in ascending order of axial position, and magnetic field data that does not contain magnetic field strength or has duplicate axial positions are deleted. When there is a maximum magnetic field strength in the organized magnetic field data, the maximum magnetic field strength is taken as the peak magnetic field strength. When there are multiple identical maximum magnetic field strengths in the organized magnetic field data, the middle position of the axial positions corresponding to the multiple maximum magnetic field strengths is taken as the peak position, and the HWHM positions are determined on both sides of the peak position. When determining the HWHM position, half of the peak magnetic field strength is determined as the HWHM. On one side of the peak position, two adjacent sets of magnetic field data whose magnetic field strength crosses the HWHM are selected from the organized magnetic field data. Interpolation is performed based on the axial position and magnetic field strength in the two adjacent sets of magnetic field data to obtain the HWHM position on that side. The same rule is used to obtain the HWHM position on the other side of the peak position.

[0009] In the above method, when solving the paraxial ray equation based on the accelerating voltage and the relativistic correction voltage respectively, under the same starting position and the same initial ray conditions, the accelerating voltage is substituted into the first paraxial ray equation, and the relativistic correction voltage is substituted into the second paraxial ray equation; the first paraxial ray parameter is obtained by solving the first paraxial ray equation, and the second paraxial ray parameter is obtained by solving the second paraxial ray equation; the first Busch rotation angle is calculated based on the first paraxial ray parameter, and the second Busch rotation angle is calculated based on the second paraxial ray parameter.

[0010] In the above method, when performing normalization calculations according to the rule that the total power of the denominator is consistent with the total power of the Seidel kernel function, the total power of the Seidel kernel function corresponding to each of spherical aberration, coma, field curvature, and distortion is first determined, and the total power of the normalized denominator for each of spherical aberration, coma, field curvature, and distortion is set to be the same as the total power of the corresponding Seidel kernel function; for chromatic aberration, the total power of the chromatic aberration Seidel kernel function is determined, and the total power of the normalized denominator for chromatic aberration is set to be the same as the total power of the chromatic aberration Seidel kernel function; for fifth-order spherical aberration, the total power of the fifth-order Seidel kernel function is determined, and the total power of the normalized denominator for fifth-order spherical aberration is set to be the same as the total power of the fifth-order Seidel kernel function.

[0011] In the above method, the adaptive power function is calculated by inputting the ratio of the magnetic field strength at the imaging position to the peak magnetic field strength into a preset power function. The power function is established by fitting finite element simulation or experimental data of a specific magnetic lens design. The adaptive power function of spherical aberration changes nonlinearly with the square of the magnetic field strength ratio, and its value ranges from four to four point four; the adaptive power function of chromatic aberration changes linearly or with low-order nonlinearity with the magnetic field strength ratio, and its value ranges from 0.7 to one.

[0012] In the above method, when determining the mixing weight according to the lens strength parameter, the lens strength parameter is compared with the weak lens threshold and the strong lens threshold respectively. When the lens strength parameter is not greater than the weak lens threshold, the mixing weight is set to zero, and the Seidel aberration integral result is used as the basis for calculating the total aberration result of the magnetic lens. When the lens strength parameter is not less than the strong lens threshold, the mixing weight is set to one, and the Glaser aberration reference value is used as the basis for calculating the total aberration result of the magnetic lens. When the lens strength parameter is greater than the weak lens threshold and less than the strong lens threshold, the mixing weight is determined according to the cosine transition relationship, and the Seidel aberration integral result and the Glaser aberration reference value are weighted and calculated according to the mixing weight.

[0013] In the above method, when outputting the total aberration result of the magnetic lens and the corresponding Busch rotation angle, the spherical aberration, chromatic aberration, coma, field curvature, distortion and fifth-order spherical aberration in the total aberration result of the magnetic lens are written into the result data set; the Busch rotation angle calculated based on the accelerating voltage is taken as the first Busch rotation angle, and the Busch rotation angle calculated based on the relativistically corrected voltage is taken as the second Busch rotation angle; a voltage convention identifier is written into the result data set, which is used to distinguish the first Busch rotation angle and the second Busch rotation angle.

[0014] The present invention also provides a magnetic lens total aberration calculation system based on adaptive power law, for performing the above-mentioned magnetic lens total aberration calculation method based on adaptive power law. The system includes an input interface, a first paraxial ray solving unit, a second paraxial ray solving unit, a Seidel aberration calculation unit, a Glaser aberration calculation unit, a hybrid calculation unit, and an output interface. The input interface receives the axial magnetic field distribution, accelerating voltage, relativistic correction voltage, starting position, and imaging position of the magnetic lens. The first paraxial ray solving unit solves the paraxial ray equation based on the accelerating voltage and calculates the first Busch rotation angle. The second paraxial ray solving unit solves the paraxial ray equation based on the relativistic correction voltage and calculates the second Busch rotation angle. The Seidel aberration calculation unit calculates the Seidel aberration integral based on the second paraxial ray parameters output by the second paraxial ray solving unit and normalizes it according to the rule that the total power of the denominator is consistent with the total power of the Seidel kernel function. The Glaser aberration calculation unit determines the lens strength parameters and resolving effective focal length based on the axial magnetic field distribution and calculates the Glaser aberration reference value. The hybrid calculation unit determines the adaptive power based on the ratio of the magnetic field strength at the imaging position to the peak magnetic field strength in the axial magnetic field distribution and determines the hybrid weight based on the lens strength parameters to calculate the total aberration result of the magnetic lens. The output interface outputs the total aberration result of the magnetic lens, the first Busch rotation angle, and the second Busch rotation angle.

[0015] The beneficial effects of the technical solutions provided in the embodiments of the present invention include at least the following: In this invention, the paraxial ray equations are solved using accelerating voltage and relativistic correction voltage respectively, resulting in ray parameters and Busch rotation angles that are compatible with both computational and physical calculations. This separates the rotation angle output from the ray parameters used for aberration integration. A normalization rule aligns the total power of the denominator with the total power of the Seidel kernel function, ensuring that spherical aberration, chromatic aberration, coma, field curvature, distortion, and fifth-order spherical aberration are calculated under a unified dimensional relationship. An adaptive power is determined based on the ratio of the image plane magnetic field strength to the peak magnetic field strength. By mixing the Seidel integration results and Glaser reference values ​​according to the lens strength parameters, the overall aberration results remain continuous under weak lens, transition zone, and strong lens conditions. Attached Figure Description

[0016] Figure 1 This is a flowchart of the total aberration calculation for the magnetic lens of the present invention; Figure 2 This is a schematic diagram illustrating the axial magnetic field distribution and the determination of the equivalent half-width at half-maximum (HWHM) of the present invention. Figure 3 This is a schematic diagram of the dual-voltage paraxial ray tracing method of the present invention; Figure 4 This is a schematic diagram illustrating the adaptive power and hybrid weight relationship of the present invention; Figure 5 This is a block diagram of the magnetic lens total aberration calculation system of the present invention. Detailed Implementation

[0017] The technical solution of the present invention will now be described with reference to the accompanying drawings.

[0018] In embodiments of the present invention, words such as "exemplarily," "for example," etc., are used to indicate that something is an example, illustration, or description. Any embodiment or design described as "exemplary" in the present invention should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of the word "exemplary" is intended to present the concept in a concrete manner. Furthermore, in embodiments of the present invention, the meaning expressed by "and / or" can be both, or either one.

[0019] Please see Figures 1 to 4This embodiment provides a method for calculating the total aberration of a magnetic lens based on adaptive power law, which is used for calculating magnetic lens aberrations in electro-optics simulations. The method takes the axial magnetic field distribution, accelerating voltage, relativistic correction voltage, starting position, and imaging position of the magnetic lens as inputs. First, it establishes the paraxial ray calculation relationship under a dual-voltage convention. Then, it calculates the Seidel aberration integral based on the second paraxial ray parameter. Finally, through normalization, adaptive power law correction, and a weighted mixing of the Seidel aberration integral result and the Glaser aberration reference value, the total aberration result of the magnetic lens and the corresponding Busch rotation angle are obtained. In the computational scenario for transmission electron microscope objectives, the accelerating voltage can be taken as 200,000 V, the relativistic correction voltage as 239,100 V, the peak magnetic field strength as 0.5 T to 2.0 T, the equivalent half-width at half-maximum as 2 mm to 5 mm, the lens strength parameter as 0.01 to 5.0, the adaptive power of spherical aberration as 4.0 to 4.4, the adaptive power of chromatic aberration as 0.7 to 1.0, and the mixed weight as 0 to 1. The above data are used to illustrate the typical simulation input range in the design of the magnetic lens for an electron microscope in this embodiment; the actual values ​​are determined by the magnetic lens structure and the axial magnetic field distribution.

[0020] S1, obtain the axial magnetic field distribution, accelerating voltage, relativistic correction voltage, starting position, and imaging position of the magnetic lens.

[0021] The axial magnetic field distribution consists of magnetic field data obtained along the optical axis of the magnetic lens. The magnetic field data are arranged by axial position, and each set of data includes at least one axial position and the corresponding magnetic field strength. The accelerating voltage is the voltage parameter used in electron optics simulation according to non-relativistic conventions; the relativistically corrected voltage is the voltage parameter obtained after relativistically correcting the accelerating voltage. The starting position defines the starting position for solving the paraxial ray equation, and the imaging position defines the axial position corresponding to the image plane in aberration calculations.

[0022] During execution S1, magnetic field data discretely arranged along the optical axis of the magnetic lens is first received. To ensure a unified data basis for determining the subsequent peak magnetic field strength and equivalent half-width at half-maximum, the magnetic field data is organized in ascending order of axial position, and magnetic field data that does not contain magnetic field strength or has duplicate axial positions are deleted. The organized magnetic field data is then used in the peak magnetic field strength determination process. Subsequent determinations of lens strength parameters, magnetic field strength at the imaging position, and adaptive power are all based on the organized magnetic field data.

[0023] S101, the maximum magnetic field strength in the magnetic field data is taken as the peak magnetic field strength, and the half-height position of the magnetic field is determined based on the peak magnetic field strength.

[0024] When a single maximum magnetic field strength exists in the processed magnetic field data, this maximum magnetic field strength is taken as the peak magnetic field strength, and the axial position corresponding to this maximum magnetic field strength is taken as the peak position. When multiple identical maximum magnetic field strengths exist in the processed magnetic field data, the midpoint between the axial positions corresponding to these multiple maximum magnetic field strengths is taken as the peak position, and the multiple identical maximum magnetic field strengths are taken as the peak magnetic field strengths. The peak position is used to determine the decreasing range of magnetic field strength on both sides, and the peak magnetic field strength is used to determine the half-height magnetic field strength.

[0025] S102, determine the half-height position of the magnetic field.

[0026] Half of the peak magnetic field strength is defined as the half-height magnetic field strength. On one side of the peak position, two adjacent sets of magnetic field data are selected from the processed magnetic field data where the magnetic field strength spans the half-height magnetic field strength. One magnetic field strength from each of the two adjacent sets is located on one side of the half-height magnetic field strength, and the other on the other side. Interpolation is performed based on the axial position and magnetic field strength from the two adjacent sets of data to obtain the half-height position of that side. Following the same rule, another half-height position is determined on the other side of the peak position. These two half-height positions are used to determine the equivalent half-height width subsequently.

[0027] S103 determines the equivalent half-height width based on the half-height positions of the magnetic field located on both sides of the peak magnetic field strength, and calculates the lens strength parameters based on the peak magnetic field strength, the equivalent half-height width, and the relativistic correction voltage.

[0028] The equivalent half-width at half-maximum (HWHM) is determined by the distance between the HWHM positions on either side of the peak magnetic field strength. The peak magnetic field strength reflects the maximum intensity of the magnetic field distribution of the magnetic lens, while the HWHM reflects the effective width of the magnetic field distribution along the optical axis. The relativistic correction voltage serves as the voltage basis for calculating the lens strength parameters. These lens strength parameters are subsequently used to determine whether the magnetic lens is located in a weak lens region, a strong lens region, or a transitional region between the two.

[0029] The lens intensity parameters are determined using the following calculation relationship: ; in, For lens intensity parameters, The amount of electron charge. The peak magnetic field strength, For the equivalent half-width, The rest mass of the electron. The relativistic correction voltage is used. A set of objective lens calculation conditions is set with a peak magnetic field strength of 0.5T, an equivalent half-width at half-maximum of 3mm, and a relativistic correction voltage of 239100V. The lens strength parameter can fall within the calculation range of the weak lens to the transition region. When the peak magnetic field strength increases or the equivalent half-width at half-maximum increases, the lens strength parameter increases accordingly and is used as the basis for subsequent mixed weight determination.

[0030] S2, based on the accelerating voltage and the relativistically corrected voltage, solves the paraxial ray equation to obtain the first paraxial ray parameter, the second paraxial ray parameter, and the corresponding Busch rotation angle.

[0031] When executing S2, under the same starting position and initial ray conditions, the first paraxial ray equation and the second paraxial ray equation are established respectively. The first paraxial ray equation uses the accelerating voltage as the voltage term, while the second paraxial ray equation uses the relativistically corrected voltage as the voltage term. The two paraxial ray equations use the same axial magnetic field distribution, the same starting position, and the same initial ray conditions; the difference between the two sets of solutions stems from the different voltage conventions.

[0032] S201, Solve the equation of the first paraxial ray to obtain the parameters of the first paraxial ray.

[0033] The first paraxial ray parameter characterizes the paraxial ray state obtained under the accelerating voltage convention. The first paraxial ray parameter is used in the calculation of the first Busch rotation angle and to preserve the output relationship corresponding to the accelerating voltage convention. The first paraxial ray parameter is not used as the physical integration basis for the Seidel aberration integral.

[0034] S202, Solve the equation of the second paraxial ray to obtain the parameters of the second paraxial ray.

[0035] The second paraxial ray parameter is used to characterize the paraxial ray state obtained under the relativistically corrected voltage convention. The second paraxial ray parameter is incorporated into the Seidel aberration integral calculation. The second paraxial ray parameter is also used to calculate the second Busch rotation angle, ensuring that the Seidel aberration integral and the rotation angle output under the relativistically corrected voltage convention have the same physical calculation basis.

[0036] S203, calculate the first Busch rotation angle based on the first paraxial ray parameters, and calculate the second Busch rotation angle based on the second paraxial ray parameters.

[0037] The first Busch rotation angle corresponds to the accelerating voltage convention, and the second Busch rotation angle corresponds to the relativistic correction voltage convention. When outputting two Busch rotation angles, the subsequent result dataset distinguishes between the first and second Busch rotation angles using voltage convention identifiers, thus avoiding confusion between them in the same output dataset. Under the calculation conditions of an accelerating voltage of 200,000V and a relativistic correction voltage of 239,100V, the first Busch rotation angle can be 15.23 mrad, and the second Busch rotation angle can be 13.93 mrad. Under the calculation conditions of an accelerating voltage of 300,000V, the Busch rotation angles corresponding to the two voltage conventions are still written into the result dataset separately and distinguished by voltage convention identifiers. The above data is used to illustrate the recording method for simultaneously outputting two Busch rotation angles in the same magnetic lens simulation task.

[0038] S3 calculates the Seidel aberration integral based on the second paraxial ray parameters, and normalizes the calculation of spherical aberration, chromatic aberration, coma, field curvature, distortion, and fifth-order spherical aberration according to the rule that the total power of the denominator is consistent with the total power of the Seidel kernel function.

[0039] The inputs to the Seidel aberration integral are the second paraxial ray parameter, the axial magnetic field distribution, the starting position, and the imaging position. The second paraxial ray parameter provides the paraxial ray state under the relativistically corrected voltage convention. The axial magnetic field distribution provides the magnetic field strength at each axial position. The starting position and imaging position define the integration interval. The Seidel aberration integral result is used to characterize the integral value of different aberration types within the Seidel theoretical framework.

[0040] S301 performs normalized calculations for spherical aberration, coma, field curvature, and distortion.

[0041] First, determine the total power of the Seidel kernel function corresponding to each of spherical aberration, coma, field curvature, and distortion. Then, set the total power of the normalized denominator for each of these aberrations to be the same as the total power of the corresponding Seidel kernel function. After aligning the total power of the normalized denominator with the total power of the Seidel kernel function, the integral results of spherical aberration, coma, field curvature, and distortion are placed within the same dimensional constraints. This process ensures that the denominator power in off-axis aberration calculations no longer deviates from the power structure of the corresponding Seidel kernel function. In a set of off-axis aberration calculation data at 200kV with a lens intensity parameter of 0.207, after processing according to the rule of aligning the total power of the denominator with the total power of the Seidel kernel function, the calculated value of coma can be 14.8μm, the calculated value of field curvature can be 13.6μm, and the calculated value of distortion can be 17.6μm. The above data, along with spherical aberration, chromatic aberration, and fifth-order spherical aberration, are written into the total aberration results of the magnetic lens, so that the result dataset can simultaneously carry on-axis and off-axis aberrations.

[0042] S302, normalizes the color difference calculation.

[0043] Determine the total power of the Seidel kernel function for chromatic aberration, and set the total power of the chromatic aberration normalization denominator to be the same as the total power of the Seidel kernel function. The normalization of chromatic aberration is determined separately from spherical aberration, coma, field curvature, and distortion to avoid directly applying the normalization power of the third-order off-axis aberration to the chromatic aberration calculation.

[0044] S303 performs normalization calculations on fifth-order spherical aberrations.

[0045] The total power of the fifth-order Seidel kernel function is determined, and the total power of the normalized denominator for fifth-order spherical aberration is set to be the same as that of the fifth-order Seidel kernel function. The normalization rule for fifth-order spherical aberration is determined according to the total power of the fifth-order Seidel kernel function itself, ensuring that fifth-order spherical aberration does not share a mismatched normalized denominator structure with third-order aberration or chromatic aberration.

[0046] S4. Obtain the ratio of the magnetic field strength at the imaging position to the peak magnetic field strength in the axial magnetic field distribution. Determine the adaptive powers corresponding to spherical aberration and chromatic aberration based on this ratio, and use the adaptive powers to correct the normalization results of the corresponding Seidel aberration integrals.

[0047] During execution S4, the magnetic field strength at the imaging location is obtained from the axial magnetic field distribution based on the imaging location. When the imaging location coincides with the sampling point location in the axial magnetic field distribution, the magnetic field strength of the corresponding sampling point is directly used; when the imaging location is between two adjacent sampling points, the magnetic field strength at the imaging location is determined based on the axial position and magnetic field strength of the two adjacent sampling points. Subsequently, the ratio of the magnetic field strength at the imaging location to the peak magnetic field strength is used as the magnetic field strength ratio.

[0048] The magnetic field strength ratio is determined using the following calculation relationship: ; in, The ratio of magnetic field strength, The magnetic field strength at the imaging location, For imaging position, The magnetic field strength is the peak magnetic field strength. The magnetic field strength ratio is used to indicate the degree to which the imaging location is still within the magnetic field region; when the magnetic field strength ratio is close to 0, the magnetic field influence at the imaging location is weak; when the magnetic field strength ratio is close to 1, the magnetic field strength at the imaging location is close to the peak magnetic field strength.

[0049] S401 calculates an adaptive power by inputting the magnetic field strength ratio into a preset power function.

[0050] The preset power function is established by fitting finite element simulation or experimental data based on a specific magnetic lens design. The power function is used to establish the correspondence between the magnetic field strength ratio and the adaptive power function. Spherical aberration and chromatic aberration each use their respective power functions, and they are not treated as using the same power function.

[0051] S402, determine the adaptive power of spherical aberration.

[0052] The adaptive power of spherical aberration varies nonlinearly with the square of the magnetic field strength ratio, ranging from four to 4.4. The magnetic field strength ratio reflects the field strength state of the imaging position relative to the peak magnetic field strength. By limiting the adaptive power of spherical aberration to this range, the Seidel aberration integral normalization result of spherical aberration can be corrected according to the magnetic field strength state at the imaging position.

[0053] S403 determines the adaptive power of color difference.

[0054] The adaptive power of chromatic aberration varies linearly or with low-order nonlinearity depending on the magnetic field strength ratio, ranging from 0.7 to 1. The adaptive power of chromatic aberration is determined separately from that of spherical aberration, and both are applied to the normalized Seidel aberration integral results corresponding to chromatic aberration and spherical aberration, respectively. The adaptive power applies to the normalized Seidel aberration integral results without altering the integration interval of the Seidel kernel function or the source of the second paraxial ray parameters.

[0055] The adaptive powers of spherical aberration and chromatic aberration are determined using the following calculation relationship: ; in, For the adaptive power of spherical aberration, For the adaptive power of color difference, This represents the magnetic field strength ratio. Taking a magnetic field strength ratio of 0.45 as an example, the adaptive power of spherical aberration is approximately 4.081, and the adaptive power of chromatic aberration is approximately 0.835. The adaptive power of spherical aberration acts on the normalized result of the Seidel integral of spherical aberration, and the adaptive power of chromatic aberration acts on the normalized result of the Seidel integral of chromatic aberration, so that the calculation of spherical aberration and chromatic aberration corresponds to the magnetic field strength state at the imaging position.

[0056] S5. Determine the lens strength parameters and effective focal length based on the axial magnetic field distribution, and calculate the Glaser aberration reference value.

[0057] The lens strength parameters are calculated from the peak magnetic field strength, equivalent half-width at half-maximum (FWHM), and relativistically corrected voltage determined in S103. The resolving effective focal length is determined based on the effective field strength parameters of the axial magnetic field distribution. The Glaser aberration reference value, based on the lens strength parameters and the resolving effective focal length, is used for mixed calculations in the strong lens region and the transition region. The Glaser aberration reference value and the Seidel aberration integral result are derived from different calculation bases, and their participation ratio in the total aberration result of the magnetic lens is subsequently determined by a mixed weighting.

[0058] The effective focal length is determined using the following calculation relationship: ; in, To determine the effective focal length, For the equivalent half-width, Pi The square root of the lens intensity parameter. For lens intensity parameters, This represents the sine term in the Glaser bell-shaped magnetic field analytical relationship. Taking a 200kV objective lens as an example, when the lens strength parameter is 1.5, the spherical aberration reference value calculated using Glaser analysis can be taken as 1.260 mm; when the lens strength parameter is 3.0, the spherical aberration reference value can be taken as 0.312 mm; and when the lens strength parameter is 5.0, the spherical aberration reference value can be taken as 0.128 mm. The above data are used to illustrate the application of Glaser aberration reference values ​​in strong lens regions.

[0059] S6. Compare the lens intensity parameter with the preset weak lens threshold and strong lens threshold to determine the mixing weight.

[0060] The weak lens threshold and strong lens threshold are preset thresholds. The weak lens threshold is used to define the region where the Seidel aberration integral result is used as the main calculation basis, and the strong lens threshold is used to define the region where the Glaser aberration reference value is used as the main calculation basis. The comparison relationship between the lens intensity parameter and the weak lens threshold and strong lens threshold determines the value of the mixing weight.

[0061] The mixed weights are determined using the following calculation relationship: ; in, For mixed weights, For lens intensity parameters, For weak lens threshold, For strong lens threshold, Pi It is a cosine function. The weak lens threshold can be 0.05, and the strong lens threshold can be 1.0. When the lens intensity parameter is not greater than 0.05, the mixing weight is 0; when the lens intensity parameter is not less than 1.0, the mixing weight is 1; when the lens intensity parameter is greater than 0.05 and less than 1.0, the mixing weight takes a value between 0 and 1 according to the cosine transition relationship.

[0062] S601, when the lens intensity parameter is not greater than the weak lens threshold, the mixing weight is set to zero, and the Seidel aberration integral result is used as the basis for calculating the total aberration result of the magnetic lens.

[0063] Under these conditions, the Seidel aberration integral result, which has undergone adaptive power-law correction, is incorporated into the calculation of the total aberration result of the magnetic lens. The Glaser aberration reference value is not used as the primary basis for calculating the total aberration result of the magnetic lens in this region.

[0064] S602, when the lens intensity parameter is not less than the strong lens threshold, the mixing weight is set to one, and the Glaser aberration reference value is used as the basis for calculating the total aberration result of the magnetic lens.

[0065] Under these conditions, the Glaser aberration reference value is incorporated into the calculation of the total aberration of the magnetic lens. The Seidel aberration integral result, which has undergone adaptive power correction, is not used as the primary basis for calculating the total aberration of the magnetic lens in this region.

[0066] S603, when the lens intensity parameter is greater than the weak lens threshold and less than the strong lens threshold, the mixing weight is determined according to the cosine transition relationship, and the Seidel aberration integral result and the Glaser aberration reference value are weighted according to the mixing weight.

[0067] Within the transition region, the mixing weights vary with the lens intensity parameter between the weak lens threshold and the strong lens threshold. The Seidel aberration integral result, which has undergone adaptive power-law correction, and the Glaser aberration reference value are simultaneously included in the calculation of the total magnetic lens aberration result. This weighted calculation connects the weak lens region, the transition region, and the strong lens region within the same computational flow.

[0068] S7 performs a weighted mixing calculation based on the Seidel aberration integral result that has undergone adaptive power correction and the Glaser aberration reference value, and outputs the magnetic lens total aberration result and the corresponding Busch rotation angle.

[0069] The total aberration results from the magnetic lens include at least spherical aberration, chromatic aberration, coma, field curvature, distortion, and fifth-order spherical aberration. For each type of aberration, the corresponding Seidel aberration integral result and the Glaser aberration reference value are weighted and mixed according to the mixing weights determined in S6. The Seidel aberration integral results corresponding to spherical aberration and chromatic aberration have undergone adaptive power correction before entering the weighted mixing calculation. The Seidel aberration integral results corresponding to coma, field curvature, distortion, and fifth-order spherical aberration have undergone normalization calculation consistent with the total power of the Seidel kernel function before entering the weighted mixing calculation.

[0070] In a set of spherical aberration calculation data for a 200kV Glaser-type magnetic lens, with a peak magnetic field strength of 0.5T, an equivalent half-width at half-maximum of 3mm, and a lens strength parameter of 0.207, the calculated spherical aberration value for a fixed power of 4 (Seidel) is 2.856mm. After correction using an adaptive power of approximately 4.08, the calculated spherical aberration value is 2.748mm. This data shows that after the adaptive power correction is applied to the Seidel aberration integral normalization result, the calculated spherical aberration value can be adjusted according to the magnetic field strength at the imaging position.

[0071] S701 writes the spherical aberration, chromatic aberration, coma, field curvature, distortion, and fifth-order spherical aberration from the total aberration results of the magnetic lens into the result data set.

[0072] The results dataset is used to contain the total aberration results of the magnetic lens. Each type of aberration corresponds to a specific data item in the results dataset. The results dataset also carries Busch rotation angle and voltage convention identifiers, ensuring that aberration results and rotation angle results maintain a correspondence within the same output structure. The results dataset can also record aberration items using the Krivanek standardized naming system, where defocus is denoted as C1, double astigmatism as A1, coma as B2, third-order spherical aberration as C3, third-order stellar aberration as S3, fifth-order spherical aberration as C5, and fifth-order stellar aberration as S5. This naming system is stored in parallel with the spherical aberration, chromatic aberration, coma, field curvature, distortion, and fifth-order spherical aberration in the total aberration results of the magnetic lens, for subsequent use in electro-optical simulation programs.

[0073] S702 uses the Busch rotation angle calculated based on the accelerating voltage as the first Busch rotation angle and the Busch rotation angle calculated based on the relativistically corrected voltage as the second Busch rotation angle.

[0074] The first Busch rotation angle is derived from the first paraxial ray parameter, and the second Busch rotation angle is derived from the second paraxial ray parameter. The first Busch rotation angle and the second Busch rotation angle correspond to different voltage conventions and are not combined into a single rotation angle output.

[0075] S703, writes a voltage convention identifier into the result data set. The voltage convention identifier is used to distinguish between the first Busch rotation angle and the second Busch rotation angle.

[0076] The voltage convention identifier, along with the first and second Busch rotation angles, is written into the result data set. When retrieving the result data set, the voltage convention identifier identifies the accelerating voltage convention corresponding to the first Busch rotation angle and the relativistically corrected voltage convention corresponding to the second Busch rotation angle. The result data set can be called by the electron-optics simulation program for subsequent display, saving, or further calculations.

[0077] Please see Figure 5 This embodiment provides a magnetic lens total aberration calculation system based on adaptive power law. This system is used to execute the aforementioned magnetic lens total aberration calculation method based on adaptive power law. The system includes an input interface, a first paraxial ray solving unit, a second paraxial ray solving unit, a Seidel aberration calculation unit, a Glaser aberration calculation unit, a hybrid calculation unit, and an output interface. Data is transferred between the units according to the magnetic lens total aberration calculation process.

[0078] The input interface receives the axial magnetic field distribution, accelerating voltage, relativistic correction voltage, starting position, and imaging position of the magnetic lens. The input interface transmits the axial magnetic field distribution to the first paraxial ray solving unit, the second paraxial ray solving unit, the Glaser aberration calculation unit, and the hybrid calculation unit, respectively; transmits the accelerating voltage to the first paraxial ray solving unit; transmits the relativistic correction voltage to the second paraxial ray solving unit and the Glaser aberration calculation unit; and transmits the starting position and imaging position to the first paraxial ray solving unit, the second paraxial ray solving unit, and the Seidel aberration calculation unit.

[0079] The first paraxial ray solving unit solves the paraxial ray equation based on the accelerating voltage to obtain the first paraxial ray parameters, and calculates the first Busch rotation angle based on the first paraxial ray parameters. The first Busch rotation angle is transmitted to the output interface as the rotation angle output corresponding to the acceleration voltage.

[0080] The second paraxial ray solving unit solves the paraxial ray equation based on the relativistic correction voltage to obtain the second paraxial ray parameters, and calculates the second Busch rotation angle based on the second paraxial ray parameters. The second paraxial ray parameters are passed to the Seidel aberration calculation unit, and the second Busch rotation angle is passed to the output interface as the rotation angle output corresponding to the relativistic correction voltage convention.

[0081] The Seidel aberration calculation unit calculates the Seidel aberration integral based on the second paraxial ray parameters output by the second paraxial ray solving unit, and performs normalization calculation according to the rule that the total power of the denominator is consistent with the total power of the Seidel kernel function. The Seidel aberration calculation unit outputs the Seidel aberration integral result and passes the Seidel aberration integral result to the hybrid calculation unit.

[0082] The Glaser aberration calculation unit determines the lens strength parameters and resolving effective focal length based on the axial magnetic field distribution, and calculates the Glaser aberration reference value. The lens strength parameters and Glaser aberration reference value are then passed to the hybrid calculation unit. The lens strength parameters are used by the hybrid calculation unit to determine the hybrid weights, while the Glaser aberration reference value is used in the calculation of the total aberration result of the magnetic lens.

[0083] The hybrid calculation unit determines an adaptive power factor based on the ratio of the magnetic field strength at the imaging location to the peak magnetic field strength in the axial magnetic field distribution, and determines the hybrid weights based on the lens strength parameters. The hybrid calculation unit uses the adaptive power factor to correct the corresponding Seidel aberration integral results and calculates the total magnetic lens aberration result based on the hybrid weights. The total magnetic lens aberration result is then transmitted to the output interface.

[0084] The output interface outputs the total aberration results of the magnetic lens, the first Busch rotation angle, and the second Busch rotation angle. The total aberration results output include spherical aberration, chromatic aberration, coma, field curvature, distortion, and fifth-order spherical aberration. The output interface also outputs a voltage convention identifier to distinguish between the first and second Busch rotation angles, allowing the caller to identify the voltage basis for the two Busch rotation angles. In the application scenario of a 300kV cryo-electron microscope column design, this system can receive the axial magnetic field distribution corresponding to multiple levels of magnetic lenses and perform total aberration calculations on the magnetic lens under objective conditions. When the mixing weight is 0.82, the spherical aberration in the total aberration results can be 0.48mm, and the chromatic aberration can be 0.51mm. This set of application data illustrates that the total aberration results of the magnetic lens output by the output interface can be used as aberration calculation data in electron optical column simulations.

[0085] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for calculating total aberration of a magnetic lens based on adaptive power law, characterized in that, Includes the following steps: Obtain the axial magnetic field distribution, accelerating voltage, relativistic correction voltage, starting position, and imaging position of the magnetic lens; The paraxial ray equations are solved based on the accelerating voltage and the relativistic correction voltage, respectively, to obtain the first paraxial ray parameters, the second paraxial ray parameters, and the corresponding Busch rotation angles. Based on the second paraxial ray parameters, the Seidel aberration integral is calculated, and the spherical aberration, chromatic aberration, coma, field curvature, distortion, and fifth-order spherical aberration are normalized according to the rule that the total power of the denominator is consistent with the total power of the Seidel kernel function. The ratio of the magnetic field strength at the imaging position to the peak magnetic field strength in the axial magnetic field distribution is obtained. Based on this ratio, the adaptive powers corresponding to the spherical aberration and the chromatic aberration are determined. The adaptive powers are then used to correct the normalization result of the corresponding Seidel aberration integral in order to compensate for the Seidel theoretical approximation error caused by the change in magnetic field strength at the imaging position. Based on the axial magnetic field distribution, determine the lens strength parameters and the effective focal length, and calculate the Glaser aberration reference value; The lens intensity parameter is compared with preset weak lens thresholds and strong lens thresholds to determine the mixing weight; wherein: When the lens intensity parameter is between the weak lens threshold and the strong lens threshold, the mixing weight is determined according to the cosine transition function. When the lens intensity parameter is equal to or less than the weak lens threshold, the mixing weight is considered to be 0. When the lens intensity parameter is equal to or greater than the strong lens threshold, the mixing weight is considered to be 1; Based on the aforementioned weighted calculation, the Seidel aberration integral result that has undergone adaptive power correction is weighted and mixed with the Glaser aberration reference value. This results in the use of numerically integrated Seidel results in weak lens regions, the use of analytically corrected Glaser models in strong lens regions, and a smooth transition in intermediate regions. The hybrid calculation outputs the total aberration result of the magnetic lens and the corresponding Busch rotation angle.

2. The method for calculating total aberration of a magnetic lens based on adaptive power order according to claim 1, characterized in that, The step of obtaining the axial magnetic field distribution includes: receiving magnetic field data discretely arranged along the optical axis of the magnetic lens, wherein the magnetic field data includes the axial position and the magnetic field strength corresponding to the axial position; The maximum magnetic field strength in the magnetic field data is taken as the peak magnetic field strength, and the half-height position of the magnetic field is determined based on the peak magnetic field strength. The equivalent half-height width is determined based on the magnetic field half-height positions located on both sides of the peak magnetic field strength, and the lens strength parameters are calculated based on the peak magnetic field strength, the equivalent half-height width, and the relativistic correction voltage.

3. The method for calculating total aberration of a magnetic lens based on adaptive power order according to claim 2, characterized in that, The steps for determining the peak magnetic field strength and the equivalent full width at half maximum (FWHM) include: The magnetic field data are sorted in ascending order of axial position, and magnetic field data that do not contain magnetic field strength or duplicate axial positions are deleted. When there is a maximum magnetic field strength in the processed magnetic field data, the maximum magnetic field strength is taken as the peak magnetic field strength; When there are multiple identical maximum magnetic field intensities in the processed magnetic field data, the midpoint of the axial position corresponding to the multiple maximum magnetic field intensities is taken as the peak position, and the half-height position of the magnetic field is determined on both sides of the peak position.

4. The method for calculating total aberration of a magnetic lens based on adaptive power as described in claim 3, characterized in that, The steps to determine the half-height of a magnetic field include: Half of the peak magnetic field strength is defined as the half-high magnetic field strength; On one side of the peak position, select two adjacent sets of magnetic field data whose magnetic field strength spans the half-height magnetic field strength from the sorted magnetic field data; Interpolation calculations are performed based on the axial position and magnetic field strength in the two adjacent sets of magnetic field data to obtain the half-height position of the magnetic field on that side, and the half-height position of the magnetic field on the other side of the peak position is obtained according to the same rule.

5. The method for calculating total aberration of a magnetic lens based on adaptive power order according to claim 1, characterized in that, The steps for solving the paraxial ray equations based on the accelerating voltage and the relativistic correction voltage respectively include: Under the same starting position and the same initial ray conditions, the accelerating voltage is substituted into the first paraxial ray equation, and the relativistic correction voltage is substituted into the second paraxial ray equation; The first paraxial ray parameters are obtained by solving the first paraxial ray equation, and the second paraxial ray parameters are obtained by solving the second paraxial ray equation. The first Busch rotation angle is calculated based on the first paraxial ray parameters, and the second Busch rotation angle is calculated based on the second paraxial ray parameters.

6. The method for calculating total aberration of a magnetic lens based on adaptive power order according to claim 1, characterized in that, When performing normalization calculations according to the rule that the total power of the denominator is consistent with the total power of the Seidel kernel function, first determine the total power of the Seidel kernel function corresponding to each of spherical aberration, coma, field curvature and distortion, and set the total power of the normalized denominator of each of spherical aberration, coma, field curvature and distortion to be the same as the total power of the corresponding Seidel kernel function. For color difference, determine the total power of the color difference Seidel kernel function, and set the total power of the color difference normalization denominator to be the same as the total power of the color difference Seidel kernel function; For fifth-order spherical aberration, determine the total power of the fifth-order Seidel kernel function, and set the total power of the normalized denominator of the fifth-order spherical aberration to be the same as the total power of the fifth-order Seidel kernel function.

7. The method for calculating total aberration of a magnetic lens based on adaptive power as described in claim 1, characterized in that, The steps for determining the adaptive exponentiation include: The ratio of the magnetic field strength at the imaging location to the peak magnetic field strength is calculated by inputting it into a preset power function. The power function is established by fitting finite element simulation or experimental data based on a specific magnetic lens design, and its functional form includes: The adaptive power of spherical aberration varies nonlinearly with the square of the magnetic field strength ratio, and its value ranges from four to four point four. The adaptive power of the color difference varies linearly or in a low-order nonlinear manner with the magnetic field strength ratio, and its value ranges from 0.7 to 1.

8. The method for calculating total aberration of a magnetic lens based on adaptive power as described in claim 1, characterized in that, The step of determining the mixing weight according to the lens intensity parameter includes: comparing the lens intensity parameter with the weak lens threshold and the strong lens threshold respectively; When the lens intensity parameter is not greater than the weak lens threshold, the mixing weight is set to zero, and the Seidel aberration integral result is used as the basis for calculating the total aberration result of the magnetic lens. When the lens intensity parameter is not less than the strong lens threshold, the mixing weight is set to one, and the Glaser aberration reference value is used as the basis for calculating the total aberration result of the magnetic lens. When the lens intensity parameter is greater than the weak lens threshold and less than the strong lens threshold, the mixing weight is determined according to the cosine transition relationship, and the Seidel aberration integral result and the Glaser aberration reference value are weighted according to the mixing weight.

9. The method for calculating total aberration of a magnetic lens based on adaptive power order according to claim 1, characterized in that, The steps for outputting the total aberration results of the magnetic lens and the corresponding Busch rotation angle include: Write the spherical aberration, chromatic aberration, coma, field curvature, distortion, and fifth-order spherical aberration from the total aberration results of the magnetic lens into the result data set; The Busch rotation angle calculated based on the accelerating voltage is taken as the first Busch rotation angle, and the Busch rotation angle calculated based on the relativistic correction voltage is taken as the second Busch rotation angle; A voltage convention identifier is written into the result data set, which is used to distinguish between the first Busch rotation angle and the second Busch rotation angle.

10. A magnetic lens total aberration calculation system based on adaptive power law, used to execute the magnetic lens total aberration calculation method according to any one of claims 1 to 9, characterized in that, include: The input interface is used to receive the axial magnetic field distribution of the magnetic lens, the accelerating voltage, the relativistic correction voltage, the starting position, and the imaging position. The first paraxial ray solving unit is used to solve the paraxial ray equation based on the accelerating voltage and calculate the first Busch rotation angle. The second paraxial ray solving unit is used to solve the paraxial ray equation based on the relativistic correction voltage and calculate the second Busch rotation angle. The Seidel aberration calculation unit is used to calculate the Seidel aberration integral based on the second paraxial ray parameters output by the second paraxial ray solving unit, and to perform normalization calculation according to the rule that the total power of the denominator is consistent with the total power of the Seidel kernel function. The Glaser aberration calculation unit is used to determine the lens strength parameters and the resolving effective focal length based on the axial magnetic field distribution, and to calculate the Glaser aberration reference value. The hybrid calculation unit is used to determine an adaptive power based on the ratio of the magnetic field strength at the imaging position to the peak magnetic field strength in the axial magnetic field distribution, and to determine the hybrid weight based on the lens strength parameter, and to calculate the total aberration result of the magnetic lens. The output interface is used to output the total aberration result of the magnetic lens, the first Busch rotation angle, and the second Busch rotation angle.

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