Probe compensation method and system based on e-plane electric field and edge current approximation

CN117741268BActive Publication Date: 2026-09-18CHINA ELECTRONIS TECH INSTR CO LTD
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Patent Information

Application Number
CN202311483335.9
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2023-11-08
Publication Date
2026-09-18
Estimated Expiration
2043-11-08

AI Technical Summary

Technical Problem

[0006]现有的探头补偿方法主要包括边缘电流逼近法和E面电场法,前者由于忽略了一些重要分量,在整个副瓣区域引入了较大误差,后者则在远区引入较大误差,不符合被测天线的实际辐射特性,且上述方法的适用角域范围难以确定

Benefits of technology

[0039] 1. The technical solution provided by this invention combines the E-plane electric field method and the edge current approximation method according to the actual radiation characteristics of the antenna under test, and uses their advantages to perform probe compensation. The compensation effect is more consistent with the actual radiation pattern of the antenna under test than that of a single compensation method, and the accuracy is higher. It is applicable to the planar near-field range, and is therefore particularly suitable for testing narrow-beam phased array antennas. It is applicable to rectangular waveguide probes and square waveguide probes.

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Abstract

This invention discloses a probe compensation method and system based on E-plane electric field and edge current approximation, belonging to the field of probe compensation technology. It includes acquiring the probe's test frequency, size, and angular coordinates; obtaining the full-angle probe far-field radiation pattern using the E-plane electric field method; calculating the elevation angle critical point under each angular section according to a preset critical point determination principle; obtaining H-plane probe far-field radiation pattern compensation data using the E-plane electric field method and edge current approximation method based on the elevation angle critical point; obtaining E-plane probe far-field radiation pattern compensation data using the E-plane electric field method based on the elevation angle critical point; and completing planar near-field probe compensation using a planar near-field and far-field algorithm based on the H-plane and E-plane probe far-field radiation pattern compensation data. It can automatically determine the applicable range of the compensation method according to the characteristics of the antenna under test, achieving high-precision probe compensation effects across the entire angular domain; and solving the problem of large probe compensation errors.
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Description

Technical Field

[0001] This invention relates to the field of probe compensation technology, and in particular to a probe compensation method and system based on E-plane electric field and edge current approximation. Background Technology

[0002] The statements in this section merely refer to the background art related to this invention and do not necessarily constitute prior art.

[0003] Planar near-field measurement involves using a probe with known characteristics to sample the amplitude and phase distribution of the far-field radiation on a specific surface in the near-field region of the antenna. Then, through rigorous mathematical transformations, the far-field characteristics and the amplitude and phase distribution of the aperture field can be determined. The measurement surface is typically a plane, hence the term "planar near-field measurement technique."

[0004] The basic idea of ​​this method is to expand the field established by the antenna under test in space into a sum of planar spectral functions. The weighting function in the expansion contains complete information about the far field. The weighting function is calculated based on the near-field measurement data, and then the antenna pattern is determined. Compared with conventional far-field measurements, planar near-field measurements have advantages such as low cost and high testing efficiency, and are therefore widely used in the measurement of high-gain, narrow-beam antennas such as phased array antennas and waveguide slot antennas.

[0005] In planar near-field antenna testing, because the near-field probe is not an ideal probe, the far-field data after near-field-to-far-field transformation contains not only the parameter information of the antenna under test but also the parameter information of the near-field probe. In order to obtain more accurate antenna parameter information in planar near-field testing, compensation techniques must be used to remove the probe's influence after near-field-to-far-field transformation.

[0006] Existing probe compensation methods mainly include the edge current approximation method and the E-plane electric field method. The former introduces a large error in the entire sidelobe region because it ignores some important components, while the latter introduces a large error in the far region, which does not conform to the actual radiation characteristics of the antenna under test. Moreover, the applicable angular domain range of the above methods is difficult to determine. Summary of the Invention

[0007] To address the shortcomings of existing technologies, this invention provides a probe compensation method, system, electronic device, and computer-readable storage medium based on E-plane electric field and edge current approximation. It accurately determines the application range and limits of the E-plane electric field method and the edge current approximation method, uses the E-plane electric field method to calculate the probe radiation pattern in the near-field range, and uses the edge current approximation method to calculate the probe radiation pattern in the far-field range, thereby improving the probe compensation accuracy across the entire angular domain.

[0008] In a first aspect, the present invention provides a probe compensation method based on E-plane electric field and edge current approximation;

[0009] A probe compensation method based on E-plane electric field and edge current approximation includes:

[0010] The test frequency, size, and angular coordinates of the probe are obtained, and the far-field radiation pattern of the full-angle probe is obtained using the E-plane electric field method.

[0011] Based on the far-field radiation pattern of the full-angle probe, the pitch angle critical point under each directional angle tangent is calculated according to the preset critical point determination principle.

[0012] Based on the pitch angle critical point, the far-field radiation pattern compensation data of the H-plane probe is obtained by using the E-plane electric field method and the edge current approximation method.

[0013] Based on the pitch angle critical point, the far-field radiation pattern compensation data of the E-plane probe is obtained by using the E-plane electric field method.

[0014] Based on the far-field radiation pattern compensation data of the H-plane probe and the far-field radiation pattern compensation data of the E-plane probe, the planar near-field probe compensation is completed using a planar near-field and far-field algorithm.

[0015] Furthermore, the principles for determining the critical point include: the pitch angle critical point is greater than the effective reliable angle domain of the near field in the plane, and the external field region after compensation by the E-plane electric field method is greater than a preset threshold.

[0016] Furthermore, the principle for determining the critical point is expressed as follows:

[0017]

[0018] Where (θ, φ) are the coordinates of the far-field radiation pattern that need to be compensated, ε0 is the threshold, N represents the number of coordinate points of the radiation pattern in the azimuth direction, and represents the far-field radiation pattern obtained by compensation using the E-plane electric field method.

[0019] Furthermore, the acquisition of H-plane probe far-field pattern compensation data based on the pitch angle critical point, using the E-plane electric field method and edge current approximation method, includes:

[0020] Based on the pitch angle critical point, the full-angle domain direction angle compensation function is determined by the E-plane electric field method and the edge current approximation method.

[0021] Based on the probe's test frequency, size, and angular coordinates, the far-field radiation pattern compensation data of the H-plane probe under each angular section is obtained through the full-angular-domain directional angle compensation function.

[0022] Preferably, the full-angle domain direction angle compensation function is expressed as:

[0023]

[0024] Where θ is θ is the angle between the z-axis in the coordinate system and the line connecting any point in space to the origin (0,0), i.e., the pitch angle; a is the long side of the probe, b is the short side of the probe, λ is the wavelength, and θ0 is the critical value of the pitch angle.

[0025] Furthermore, the step of obtaining the far-field radiation pattern compensation data of the E-plane probe based on the pitch angle critical point and the E-plane electric field method specifically involves substituting the pitch angle critical point under each directional angle tangent into the E-plane radiation pattern compensation function to obtain the far-field radiation pattern compensation data of the E-plane probe.

[0026] Preferably, the E-plane pattern compensation function is expressed as:

[0027]

[0028] Where θ = θ0 is the pitch angle critical point, a is the long side of the probe, b is the short side of the probe, and λ is the wavelength.

[0029] Secondly, the present invention provides a probe compensation system based on E-plane electric field and edge current approximation;

[0030] A probe compensation system based on E-plane electric field and edge current approximation includes:

[0031] The critical point range determination module is used to obtain the test frequency, size, and angular coordinates of the probe, and to obtain the full-angle probe far-field radiation pattern using the E-plane electric field method. Based on the full-angle probe far-field radiation pattern, the elevation angle critical point under each angular tangent is calculated according to the preset critical point determination principle.

[0032] The compensation data calculation module is used to obtain H-plane probe far-field pattern compensation data based on the pitch angle critical point using the E-plane electric field method and the edge current approximation method; and to obtain E-plane probe far-field pattern compensation data based on the pitch angle critical point using the E-plane electric field method.

[0033] The probe compensation module is used to complete the planar near-field probe compensation based on the far-field radiation pattern compensation data of the H-plane probe and the far-field radiation pattern compensation data of the E-plane probe, through a planar near-field and far-field algorithm.

[0034] Thirdly, the present invention provides an electronic device;

[0035] An electronic device includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor, wherein the computer instructions, when executed by the processor, perform the steps of the probe compensation method based on E-plane electric field and edge current approximation described above.

[0036] Fourthly, the present invention provides a computer-readable storage medium;

[0037] A computer-readable storage medium for storing computer instructions, which, when executed by a processor, perform the steps of the probe compensation method based on E-plane electric field and edge current approximation described above.

[0038] Compared with the prior art, the beneficial effects of the present invention are:

[0039] 1. The technical solution provided by this invention combines the E-plane electric field method and the edge current approximation method according to the actual radiation characteristics of the antenna under test, and uses their advantages to perform probe compensation. The compensation effect is more consistent with the actual radiation pattern of the antenna under test than that of a single compensation method, and the accuracy is higher. It is applicable to the planar near-field range, and is therefore particularly suitable for testing narrow-beam phased array antennas. It is applicable to rectangular waveguide probes and square waveguide probes.

[0040] 2. The technical solution provided by this invention can automatically determine the applicable scope of the E-plane electric field method and the edge current approximation method based on the characteristics of the antenna under test, thus achieving higher intelligence. Attached Figure Description

[0041] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0042] Figure 1 This is a flowchart provided for an embodiment of the present invention;

[0043] Figure 2 This is a schematic diagram of the structure of the open waveguide probe provided in an embodiment of the present invention. Detailed Implementation

[0044] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0045] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments of the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. Furthermore, it should be understood that the terms “comprising” and “having”, and any variations thereof, are intended to cover non-exclusive inclusion, for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0046] Where there is no conflict, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0047] Example 1

[0048] Existing probe compensation methods introduce significant errors during compensation, which do not conform to the actual radiation characteristics of the antenna under test. Therefore, this invention provides a probe compensation method based on E-plane electric field and edge current approximation.

[0049] First, a brief introduction to the E-plane electric field method and the edge current approximation method will be given.

[0050] Basic principle of the E-plane electric field method:

[0051] Planar near-field antenna testing typically uses a standard rectangular waveguide as the test probe, as shown in the schematic diagram below. Figure 2 As shown in the figure, a and b are the long and narrow sides of the probe, respectively. The X and Y axes are parallel to the long and narrow sides of the waveguide aperture, respectively, and the Z axis represents the direction of wave propagation. In a rectangular waveguide probe, electromagnetic waves are transmitted in transverse electric (TE) and transverse magnetic (TM) modes.

[0052] The E-plane electric field method is mainly obtained by integrating the electric field across the probe's cross-section. The electromagnetic field pattern in the front half of the antenna space can be obtained by performing a double Fourier transform on the antenna's near-field energy. Therefore, the far-field of the probe's H-plane can be obtained by integrating the E-plane electric field.

[0053]

[0054] In the formula, Let represent the integral vector from the origin to the element dx′dy′ in the integral plane. The electric and magnetic fields of the TE10 mode are as follows:

[0055]

[0056]

[0057] Here, E0 is TE 10 The amplitude value of the mode, Γ is the probe reflection coefficient, λ is the wavelength. It can be analyzed that the electric field integral in equation (1) can be represented by E10 in equation (2). After simplification, the H-plane radiation pattern function of the probe can be obtained:

[0058]

[0059] Furthermore, in the E-plane electric field method, the E-plane pattern function of the probe is:

[0060]

[0061] In equation (5), θ is It is the angle between the z-axis in the coordinate system and the line connecting any point in space to the origin (0,0). Studying equation (5), we can conclude that when θ = 90°, cosθ = 0, and the radiation pattern functions of the probe's E-plane and H-plane are both 0, which obviously does not conform to the radiation pattern law of the antenna. Therefore, although the E-plane electric field method is simple, it has a large error and its shortcomings.

[0062] The edge current approximation method is another probe compensation method. Its formula for calculating the probe's H-plane radiation pattern is as follows:

[0063]

[0064] Next, combined Figures 1-2 The probe compensation method based on E-plane electric field and edge current approximation described in this embodiment will be further described in detail. This probe compensation method based on E-plane electric field and edge current approximation includes the following steps:

[0065] S1. Obtain the wavelength, size, and (θ, φ) angular domain coordinates of the probe. Obtain the far-field pattern of the full-angle probe using the E-plane electric field method. The wavelength and test frequency are in a proportional relationship. The wavelength of the probe can be obtained based on the test frequency of the probe. The far-field pattern of the full-angle probe includes the far-field pattern of the H-plane full-angle probe and the far-field pattern of the E-plane full-angle probe.

[0066] The far-field radiation pattern of the H-plane full-angle probe is represented as follows:

[0067]

[0068] The far-field radiation pattern of the E-plane full-angle probe is represented as follows:

[0069]

[0070] S2. Based on the far-field radiation pattern of the full-angle probe, calculate the pitch angle critical point under each directional angle tangent according to the preset critical point determination principle.

[0071] Furthermore, the principles for determining the critical point include:

[0072] First, the compensation accuracy of the main beam pattern should not be affected. Therefore, the pitch angle critical point θ0 should be greater than the effective reliable angle domain of the near field in the plane. The effective reliable angle domain of the near field in the plane is generally within ±60°. Therefore, the value of θ0 should first meet the condition of being greater than 60°.

[0073] Furthermore, the external field region compensated by the E-plane electric field method is greater than the preset threshold. Specifically, the external field region compensated by the E-plane electric field method is searched and judged along the pitch tangent at each fixed direction angle. According to the set threshold, it is generally set to about -40dB after the normalized radiation pattern, and the critical point is set to θ0.

[0074] Specifically, it is expressed as follows:

[0075]

[0076] Where (θ, φ) are the coordinates of the far-field radiation pattern that need to be compensated, ε0 is the threshold, N represents the number of coordinate points of the radiation pattern in the azimuth direction, and represents the far-field radiation pattern obtained by compensation using the E-plane electric field method.

[0077] S3, Discrete azimuth angle φ, where the discrete values ​​of φ are φ1, φ2, ... φ N Based on the pitch angle critical point, compensation data for the far-field radiation pattern of the H-plane probe is obtained using the E-plane electric field method and the edge current approximation method. Specifically, this includes:

[0078] S301. Based on the pitch angle critical point, determine the full-angle domain direction angle compensation function using the E-plane electric field method and the edge current approximation method.

[0079] The full-angle domain direction angle compensation function is expressed as:

[0080]

[0081] Where θ is θ is the angle between the z-axis in the coordinate system and the line connecting any point in space to the origin (0,0), i.e., the pitch angle; a is the long side of the probe, b is the short side of the probe, λ is the wavelength, and θ0 is the critical value of the pitch angle.

[0082] S302. Based on the wavelength, size, and angular coordinates of the probe, obtain the far-field radiation pattern compensation data of the H-plane probe under each angular section using the full-angle directional angle compensation function.

[0083] S4. Based on the pitch angle critical point, obtain the far-field radiation pattern compensation data of the E-plane probe using the E-plane electric field method.

[0084] Specifically, the pitch angle critical point under each azimuth angle tangent is substituted into the E-plane radiation pattern compensation function to obtain the far-field radiation pattern compensation data of the E-plane probe.

[0085] The E-plane pattern compensation function is expressed as:

[0086]

[0087] Where θ = θ0 is the pitch angle critical point, a is the long side of the probe, b is the short side of the probe, and λ is the wavelength.

[0088] S5. Based on the far-field radiation pattern compensation data of the H-plane probe and the far-field radiation pattern compensation data of the E-plane probe, the planar near-field probe compensation is completed using a planar near-field and far-field algorithm.

[0089] Specifically, the planar near-field and far-field algorithm is an existing algorithm used in planar near-field antenna testing to transform the measured near-field data into the antenna far-field radiation pattern, and to calculate the probe radiation pattern data f. E (θ), f H After (θ), the probe compensation can be completed by substituting it into the planar near-field and far-field transformation algorithm.

[0090] Example 2

[0091] This embodiment discloses a probe compensation system based on E-plane electric field and edge current approximation, including:

[0092] The critical point range determination module is used to obtain the test frequency, size, and angular coordinates of the probe, and to obtain the full-angle probe far-field radiation pattern using the E-plane electric field method. Based on the full-angle probe far-field radiation pattern, the elevation angle critical point under each angular tangent is calculated according to the preset critical point determination principle.

[0093] The compensation data calculation module is used to obtain H-plane probe far-field pattern compensation data based on the pitch angle critical point using the E-plane electric field method and the edge current approximation method; and to obtain E-plane probe far-field pattern compensation data based on the pitch angle critical point using the E-plane electric field method.

[0094] The probe compensation module is used to complete the planar near-field probe compensation based on the far-field radiation pattern compensation data of the H-plane probe and the far-field radiation pattern compensation data of the E-plane probe, through a planar near-field and far-field algorithm.

[0095] It should be noted that the aforementioned critical point range determination module, compensation data calculation module, and probe compensation module correspond to the steps in Embodiment 1. The examples and application scenarios implemented by these modules and their corresponding steps are the same, but they are not limited to the content disclosed in Embodiment 1. It should also be noted that these modules, as part of the system, can be executed in a computer system, such as a set of computer-executable instructions.

[0096] Example 3

[0097] Embodiment 3 of the present invention provides an electronic device, including a memory and a processor, as well as computer instructions stored in the memory and running on the processor. When the computer instructions are executed by the processor, they complete the steps of the probe compensation method based on E-plane electric field and edge current approximation described above.

[0098] Example 4

[0099] Embodiment 4 of the present invention provides a computer-readable storage medium for storing computer instructions, which, when executed by a processor, complete the steps of the probe compensation method based on E-plane electric field and edge current approximation described above.

[0100] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0101] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0102] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment, whereby a series of operational steps are performed to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0103] The descriptions of each embodiment in the above embodiments have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.

[0104] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A probe compensation method based on E-plane electric field and edge current approximation, characterized in that, include: The test frequency, size, and angular coordinates of the probe are obtained, and the far-field radiation pattern of the full-angle probe is obtained using the E-plane electric field method. Based on the far-field radiation pattern of the full-angle probe, the pitch angle critical point under each directional angle tangent is calculated according to the preset critical point determination principle. The principles for determining the critical point include: the pitch angle critical point is greater than the effective reliable angle domain of the near field in the plane, and the external field region after compensation by the E-plane electric field method is greater than a preset threshold; the principles for determining the critical point are expressed as follows: in, The coordinates of the far-field radiation pattern that need to be compensated are: The threshold is N, which represents the number of coordinate points of the radiation pattern in the azimuth direction. This represents the far-field radiation pattern obtained using the E-plane electric field method for compensation. Based on the pitch angle critical point, the far-field radiation pattern compensation data of the H-plane probe is obtained by using the E-plane electric field method and the edge current approximation method. Based on the pitch angle critical point, the far-field radiation pattern compensation data of the E-plane probe is obtained by using the E-plane electric field method. Based on the far-field radiation pattern compensation data of the H-plane probe and the far-field radiation pattern compensation data of the E-plane probe, the planar near-field probe compensation is completed using a planar near-field and far-field algorithm.

2. The probe compensation method based on E-plane electric field and edge current approximation as described in claim 1, characterized in that, The process of obtaining H-plane probe far-field pattern compensation data based on the pitch angle critical point using the E-plane electric field method and edge current approximation method includes: Based on the pitch angle critical point, the full-angle domain direction angle compensation function is determined by the E-plane electric field method and the edge current approximation method. Based on the probe's test frequency, size, and angular coordinates, the far-field radiation pattern compensation data of the H-plane probe under each angular section is obtained through the full-angular-domain directional angle compensation function.

3. The probe compensation method based on E-plane electric field and edge current approximation as described in claim 2, characterized in that, The full-angle domain direction angle compensation function is expressed as follows: in, yes( , () is the angle between the z-axis in the coordinate system and the line connecting any point in space to the origin (0,0), i.e., the pitch angle; a is the long side of the probe, and b is the short side of the probe. For wavelength, This is the critical value for the pitch angle.

4. The probe compensation method based on E-plane electric field and edge current approximation as described in claim 1, characterized in that, The specific steps for obtaining far-field radiation pattern compensation data of the E-plane probe based on the pitch angle critical point and using the E-plane electric field method are as follows: Substitute the pitch angle critical point under each directional angle tangent into the E-plane radiation pattern compensation function to obtain the far-field radiation pattern compensation data of the E-plane probe.

5. The probe compensation method based on E-plane electric field and edge current approximation as described in claim 4, characterized in that, The E-plane radiation pattern compensation function is expressed as follows: in, Here, 'a' represents the critical point of elevation angle, 'b' represents the long side of the probe, and 'a' represents the short side of the probe. λ is the wavelength.

6. A probe compensation system based on E-plane electric field and edge current approximation, characterized in that it includes: The critical point range determination module is used to acquire the probe's test frequency, size, and angular coordinates, and obtain the full-angle probe far-field radiation pattern using the E-plane electric field method. Based on the full-angle probe far-field radiation pattern, the elevation angle critical point under each angular tangent is calculated according to preset critical point determination principles. These principles include: the elevation angle critical point is greater than the effective reliable angular domain of the planar near field, and the external field region compensated by the E-plane electric field method is greater than a preset threshold. These principles are expressed as follows: in, The coordinates of the far-field radiation pattern that need to be compensated are: The threshold is N, which represents the number of coordinate points of the radiation pattern in the azimuth direction. This represents the far-field radiation pattern obtained using the E-plane electric field method for compensation. The compensation data calculation module is used to obtain H-plane probe far-field pattern compensation data based on the pitch angle critical point using the E-plane electric field method and the edge current approximation method; and to obtain E-plane probe far-field pattern compensation data based on the pitch angle critical point using the E-plane electric field method. The probe compensation module is used to complete the planar near-field probe compensation based on the far-field radiation pattern compensation data of the H-plane probe and the far-field radiation pattern compensation data of the E-plane probe, through a planar near-field and far-field algorithm.

7. An electronic device, characterized in that, It includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor, which, when executed by the processor, complete the steps of the probe compensation method based on E-plane electric field and edge current approximation as described in any one of claims 1-5.

8. A computer-readable storage medium, characterized in that, Used to store computer instructions, which, when executed by a processor, complete the steps of the probe compensation method based on E-plane electric field and edge current approximation as described in any one of claims 1-5.

Citation Information

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