Inversion method for electromagnetic parameters of non-uniform wave-absorbing material based on arch method test system

Abstract

The invention discloses a non-uniform wave-absorbing material electromagnetic parameter inversion method based on an arch method test system. The method comprises the following steps: step 1, calculating mathematical formula derivation of electromagnetic parameters through reflectivity; step 2, a reflectivity test method and process; and step 3, performing inversion of the electromagnetic parameters of the non-uniform wave-absorbing material. Compared with a traditional transmission / reflection measurement method, the method has the advantages that the sample does not need to be precisely cut and processed in the testing process, and the microstructure of the to-be-tested material cannot be damaged. In the aspect of an inversion algorithm, dual-polarization and oblique incidence reflectivity data are utilized, a reflectivity only amplitude inversion method is adopted, and compared with an NRW method, the problem of multiple solutions caused by phase ambiguity is avoided. According to the method, parameter calibration of the non-uniform wave-absorbing material can be accurately carried out, and more accurate electrical parameter guidance is provided for design and model selection of electromagnetic systems such as radar stealth, electromagnetic shielding and radio frequency matching.

Description

Technical Field

[0001] The present application relates to the fields of radar stealth and electromagnetic technology, and in particular to an electromagnetic parameter inversion method for a non-uniform absorbing material based on a bow method test system. Background Art

[0002] Absorbing materials can effectively convert incident electromagnetic wave energy into heat or other forms of energy, thereby solving problems such as electromagnetic radiation pollution and radar stealth, and are widely used in various fields. Absorbing materials are usually made of a matrix doped with an absorber, or designed into a porous subwavelength structure. Due to the influence of dopant distribution or manufacturing process, absorbing materials are often non-uniform. However, accurately measuring the electromagnetic parameters of non-uniform absorbing materials is a prerequisite for fine design and optimization of absorbers. Therefore, how to accurately measure the electromagnetic parameters of these materials remains a technical challenge faced by this field.

[0003] The electromagnetic parameters of non-uniform absorbing materials cannot be measured directly, and usually need to be calculated by indirect methods, such as establishing the relationship between scattering parameters and electromagnetic parameters. At present, common test methods, such as transmission reflection method, usually use waveguide or coaxial line for measurement, covering a wide frequency range, and the test method is relatively mature. However, since the sample needs to be cut into small pieces or rings during measurement, and the processing accuracy directly affects the test results, especially for non-uniform absorbing materials, the special structure and processing difficulty of the material seriously affect the measurement accuracy. For soft and easily deformed absorbing materials (such as foaming materials), when cutting at the millimeter level, the tolerance of sample size and shape may not meet the standard requirements, thereby affecting the accuracy of the test results. Harder materials (such as shielding cement) are not only difficult to process, but also damage the fixture during testing. In addition, the inhomogeneity of the material microstructure and dopant distribution will also lead to differences in test results in different parts, further reducing the reliability of the measurement.

[0004] In the inversion method of electromagnetic parameters, the existing technology generally relies on traditional inversion algorithms, such as the Nicolson-Ross-Weir (NRW) method, which is widely used in the calculation of electromagnetic parameters and has a faster solution speed and wider applicability. However, due to the influence of phase ambiguity and thickness resonance, the NRW method has certain multi-value problems, which poses a challenge to the accurate inversion of electromagnetic parameters of inhomogeneous materials. Summary of the invention

[0005] The present application provides a method for inverting electromagnetic parameters of non-uniform absorbing materials based on a bow method test system, which can be used to solve the technical problem of challenges in accurately inverting electromagnetic parameters of non-uniform materials.

[0006] The present application provides a method for inverting electromagnetic parameters of non-uniform absorbing materials based on a bow method test system, the method comprising the following steps:

[0007] Step 1, determining the electromagnetic parameter derivation form through reflectivity;

[0008] Step 2, perform reflectivity test through bow frame system test;

[0009] Step 3, invert the electromagnetic parameters of the non-uniform absorbing material.

[0010] Further, step 1, determining the electromagnetic parameter derivation form through reflectivity, comprises:

[0011] Γ pi is the reflectivity of the absorbing material to be tested. The reflectivity is related to the reflection coefficient Γ and the transmission coefficient T of the material to be tested, and is expressed by the following formula:

[0012]

[0013] According to the different polarization modes of the transmitting and receiving antennas, the reflection coefficient Γ and the transmission coefficient T are expressed as:

[0014]

[0015]

[0016] The subscripts VV (Vertical-Vertical Polarization) and HH (Horizontal-Horizontal Polarization) represent the polarization modes of the transmitting and receiving antennas, which are vertical polarization and horizontal polarization respectively; L is the thickness of the absorbing material to be tested, γ is the propagation constant, β is the phase coefficient, ω is the angular frequency, c is the speed of light, θ is the angle between the testing transmitting and receiving antennas and the normal line, ε0 and μ0 are the absolute electromagnetic parameters of vacuum;

[0017] ε r , μ r are electromagnetic parameters, representing the complex permittivity and complex permeability, respectively, which are divided into real and imaginary parts and are represented by the following formula:

[0018]

[0019] Among them, ε' r is the real part of the complex dielectric constant, ε' r ' is the imaginary part of the complex dielectric constant, μ' r is the real part of complex magnetic permeability, μ' r ' is the imaginary part of complex magnetic permeability, j is the imaginary unit;

[0020] From equations (1)-(4), it can be seen that the electromagnetic parameters are related to the reflectivity, and a numerical method is used to solve them.

[0021] Further, step 2, performing a reflectivity test through a bow frame system test, includes:

[0022] First, place the metal calibration plate on the table and test the reflectivity of the calibration plate;

[0023] Then, the absorbing material to be tested is placed on the metal calibration plate to test the reflectivity of the absorbing material backed by the metal plate;

[0024] The difference between the reflectivity of the calibration plate and the reflectivity of the absorbing material of the backing metal plate is the required reflectivity Γ pi ;

[0025] During the test, the test data is time-domain gated to eliminate the influence of background noise; the thickness L of the absorbing material is measured by a vernier caliper; and the oblique incident angle θ is obtained by a high-precision inclinometer on the transceiver antenna.

[0026] Furthermore, step 3, performing inversion of electromagnetic parameters of the non-uniform absorbing material, includes:

[0027] When the thickness of the absorbing material to be tested and the test incident angle are determined, the reflectivity Γ pi Only with the electromagnetic parameter ε r , μ r In formula (1), the real and imaginary parts of the electromagnetic parameters are derived respectively to obtain:

[0028]

[0029] Formula (5) can be abbreviated as:

[0030] JΔX=ΔY (6)

[0031] Where J is the Jacobian matrix, ΔX and ΔY are expressed as:

[0032]

[0033] However, the iteration process is not stable, so equation (7) is modified as follows:

[0034]

[0035] In the above formula, n represents the number of iterations, Γ pmi is the reflectivity of the absorbing material measured at the i-th test, which remains unchanged during the iteration process;

[0036] From (5)-(8), we can get:

[0037] X n+1=X n -J -1 (X n )Y(X n ) (9)

[0038] The iterative method is the Newton-Raphson iterative algorithm of the nonlinear equation system, and the electromagnetic parameters are obtained by equation (9).

[0039] Furthermore, in order to satisfy the Jacobian matrix convergence condition, i.e., the matrix condition number ≤ 10, only the amplitude data of the reflectivity of vertical polarization and horizontal polarization are used instead of single polarization data.

[0040] Furthermore, in step 2, in order to satisfy the Jacobian matrix convergence condition, that is, the matrix condition number ≤ 10, when measuring the reflectivity, it is required that the test angle θ of a certain polarization direction in the i-th and i+1-th tests i or θ i+1 Satisfy θ i ,θ i+1 ≥30°, and the difference between the two test angles satisfies |θ i -θ i+1 |≥10°.

[0041] Compared with the prior art, the present invention has the following significant advantages: 1. The bow method test system is adopted, and the whole test process is non-destructive and non-contact measurement, and the test frequency band is wide (2-40GHz); 2. The bow method test system is a mature test method, and there is no need to rebuild the test system; 3. In the inversion algorithm, the reflectivity only amplitude information is adopted to eliminate the multi-value influence caused by phase ambiguity; 4. In the inversion algorithm, the dual-polarization multi-angle reflectivity only amplitude information is adopted, and the electromagnetic parameters can be obtained by testing only one piece of the measurement to be measured, and the cost is low. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 Schematic diagram of the bow method testing system mentioned in the present invention;

[0043] Figure 2 The bow method test system mentioned in the present invention measures the reflectivity amplitude information of a certain absorbing material;

[0044] Figure 3 It is the electromagnetic parameter (complex dielectric constant) extracted by the inversion algorithm mentioned in the present invention. DETAILED DESCRIPTION

[0045] In order to make the objectives, technical solutions and advantages of the present application clearer, the implementation methods of the present application will be further described in detail below with reference to the accompanying drawings.

[0046] The following first introduces the embodiments of the present application in conjunction with the accompanying drawings.

[0047] The main steps of this method include reflectivity testing and inversion algorithms. In the test system, destructive test methods such as the coaxial method and the waveguide method are abandoned, and the bow method test system is adopted to achieve non-destructive, non-contact, and wide-band measurement. In the inversion algorithm, the reflectivity data of dual polarization and oblique incidence are used, and the reflectivity amplitude-only inversion method is adopted to eliminate the multiple solution problem caused by phase ambiguity. The purpose of this method is to provide a non-contact, non-destructive, and algorithm-stable method for measuring and inverting the electromagnetic parameters of non-uniform absorbing materials.

[0048] Embodiment 1, a method for inverting electromagnetic parameters of a non-uniform absorbing material based on a bow method test system, mainly comprises the following steps:

[0049] Step 1, the derivation form of electromagnetic parameters inverted from reflectivity amplitude information;

[0050] Γ pi is the reflectivity of the absorbing material to be tested in the actual test, which is related to the reflection coefficient Γ and the transmission coefficient T of the material to be tested, and is expressed by the following formula:

[0051]

[0052] According to the different polarization modes of the transmitting and receiving antennas, the reflection coefficient Γ and the transmission coefficient T are expressed as:

[0053]

[0054]

[0055] Wherein, the subscripts VV (Vertical-Vertical Polarization) and HH (Horizontal-Horizontal Polarization) in the letters represent the polarization modes of the transmitting and receiving antennas, which are vertical polarization and horizontal polarization respectively; L is the thickness of the absorbing material to be tested, γ is the propagation constant, β is the phase coefficient, ω is the angular frequency, c is the speed of light, θ is the angle between the testing transmitting and receiving antennas and the normal line, and ε0 and μ0 are the absolute electromagnetic parameters of vacuum;

[0056] ε r , μ r are electromagnetic parameters, representing the complex permittivity and complex permeability, respectively, which are divided into real and imaginary parts and are represented by formula (4).

[0057]

[0058] Among them, ε' r is the real part of the complex dielectric constant, ε' r ' is the imaginary part of the complex dielectric constant, μ' r is the real part of complex magnetic permeability, μ' r' is the imaginary part of complex magnetic permeability, j is the imaginary unit;

[0059] It can be seen from the above formula that there is a mathematical relationship between the electromagnetic parameters and the reflectivity, which can be solved by numerical methods.

[0060] Step 2, reflectivity by bow system test:

[0061] Reflectivity Γ pi It is obtained by testing the bow system. First, place the metal calibration plate on the table to test the reflectivity of the calibration plate; then, place the absorbing material to be tested on the metal calibration plate to test the reflectivity of the absorbing material backing the metal plate. The difference between the two reflectivities is the required reflectivity Γ pi During the test, the main control computer will automatically perform time domain gating on the test data to eliminate the influence of background noise. The thickness L of the absorbing material can be measured by a vernier caliper. The oblique incident angle θ is obtained by the high-precision inclinometer on the transceiver antenna.

[0062] It should be noted that the absorbing material to be tested in this model is infinite in theory, but in actual engineering, the absorbing material to be tested cannot be an infinite medium. Therefore, depending on the test frequency band, the size of the absorbing material to be tested should meet the following requirements:

[0063] (1) 500mm×500mm, dimensional tolerance is ±0.2mm, applicable frequency range is 1GHz~8GHz;

[0064] (2) 300 mm × 300 mm, dimensional tolerance ±0.1 mm, applicable frequency range 2 GHz to 18 GHz;

[0065] (3) 180 mm × 180 mm, dimensional tolerance ± 0.05 mm, applicable frequency range 6 GHz to 40 GHz;

[0066] Step 3, inversion of electromagnetic parameters of non-uniform absorbing materials:

[0067] When the thickness of the absorbing material to be tested and the test incident angle are determined, the reflectivity Γ pi Only with the electromagnetic parameter ε r , μ r In formula (1), the real and imaginary parts of the electromagnetic parameters are derived respectively to obtain:

[0068]

[0069] Formula (5) can be abbreviated as:

[0070] JΔX=ΔY (6)

[0071] Where J is the Jacobian matrix, ΔX and ΔY are expressed as:

[0072]

[0073] However, the iteration process is not stable, so equation (7) is modified as follows:

[0074]

[0075] In the above formula, n represents the number of iterations, Γ pmi is the reflectivity of the absorbing material measured at the i-th test, which remains unchanged during the iteration process;

[0076] The algorithm is a Newton-Raphson iterative algorithm for nonlinear equations, and the electromagnetic parameters can be obtained by equation (7).

[0077] Therefore, in the above-mentioned embodiment, the test and inversion method used is non-contact and non-destructive compared to the previous calculation method. The electromagnetic parameters obtained by the inversion algorithm do not need to consider phase multiple solutions, and only need to test a piece of absorbing material to obtain the electromagnetic parameters, which is lower in cost. Therefore, the test and inversion method of the present invention has good industrial application prospects and scientific research value.

Claims

1. A method for inverting electromagnetic parameters of non-uniform absorbing materials based on a bow method test system, characterized in that: The method comprises the following steps: Step 1, determining the electromagnetic parameter derivation form through reflectivity; Step 2, perform reflectivity test through bow frame system test; Step 3, invert the electromagnetic parameters of the non-uniform absorbing material.

2. The method for measuring and inverting electromagnetic parameters of non-uniform absorbing materials based on the bow method according to claim 1 is characterized in that: Step 1, determining the electromagnetic parameter derivation form through reflectivity; include: Γ pi is the reflectivity of the absorbing material to be tested. The reflectivity is related to the reflection coefficient Γ and the transmission coefficient T of the material to be tested, and is expressed by the following formula: According to the different polarization modes of the transmitting and receiving antennas, the reflection coefficient Γ and the transmission coefficient T are expressed as: The subscripts VV (Vertical-Vertical Polarization) and HH (Horizontal-Horizontal Polarization) represent the polarization modes of the transmitting and receiving antennas, which are vertical polarization and horizontal polarization respectively; L is the thickness of the absorbing material to be tested, γ is the propagation constant, β is the phase coefficient, ω is the angular frequency, c is the speed of light, θ is the angle between the testing transmitting and receiving antennas and the normal line, ε0 and μ0 are the absolute electromagnetic parameters of vacuum; ε r , μ r are electromagnetic parameters, representing the complex permittivity and complex permeability, respectively, which are divided into real and imaginary parts and are represented by the following formula: Among them, ε' r is the real part of the complex dielectric constant, ε″ r is the imaginary part of the complex dielectric constant, μ' r is the real part of complex magnetic permeability, μ″ r is the imaginary part of complex magnetic permeability, j is the imaginary unit; From equations (1)-(4), it can be seen that the electromagnetic parameters are related to the reflectivity, and a numerical method is used to solve them.

3. The method for measuring and inverting electromagnetic parameters of non-uniform absorbing materials based on the bow method according to claim 1 is characterized in that: Step 2, performing reflectivity test through bow system test; including: First, place the metal calibration plate on the table and test the reflectivity of the calibration plate; Then, the absorbing material to be tested is placed on the metal calibration plate to test the reflectivity of the absorbing material backed by the metal plate; The difference between the reflectivity of the calibration plate and the reflectivity of the absorbing material of the backing metal plate is the required reflectivity Γ pi ; During the test, the test data is time-domain gated to eliminate the influence of background noise; the thickness L of the absorbing material is measured by a vernier caliper; and the oblique incident angle θ is obtained by a high-precision inclinometer on the transceiver antenna.

4. The method for measuring and inverting electromagnetic parameters of non-uniform absorbing materials based on the bow method according to claim 1 is characterized in that: Step 3, inverting the electromagnetic parameters of the non-uniform absorbing material, including: When the thickness of the absorbing material to be tested and the test incident angle are determined, the reflectivity Γ pi Only with the electromagnetic parameter ε r , μ r In formula (1), the real and imaginary parts of the electromagnetic parameters are derived respectively to obtain: Formula (5) can be abbreviated as: JΔX=ΔY (6) Where J is the Jacobian matrix, ΔX and ΔY are expressed as: However, the iteration process is not stable, so equation (7) is modified as follows: In the above formula, n represents the number of iterations, Γ pmi is the reflectivity of the absorbing material measured at the i-th test, which remains unchanged during the iteration process; From (5)-(8), we can get: X n+1 =X n -J -1 (X n )Y(X n ) (9) The iterative method is the Newton-Raphson iterative algorithm of the nonlinear equation system, and the electromagnetic parameters are obtained by equation (9).

5. The method for measuring and inverting electromagnetic parameters of non-uniform absorbing materials based on the bow method according to claim 1 is characterized in that: In order to satisfy the Jacobian matrix convergence condition, i.e., the matrix condition number ≤ 10, only the amplitude data of the reflectivity of vertical and horizontal polarizations are used instead of single polarization data.

6. The method for measuring and inverting electromagnetic parameters of non-uniform absorbing materials based on the bow method according to claim 1 is characterized in that: In step 2, in order to meet the Jacobian matrix convergence condition, that is, the matrix condition number ≤ 10, when measuring the reflectivity, it is required that the test angle θ of a certain polarization direction in the i-th and i+1-th tests i or θ i+1 Satisfy θ i ,θ i+1 ≥30°, and the difference between the two test angles satisfies |θ i -θ i+1 |≥10°.

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