A method for correcting the complex permittivity inversion of a free-space focusing system

Abstract

The application aims to provide a complex permittivity inversion correction method of a free space focusing system, and belongs to the technical field of microwave and millimeter wave material complex permittivity testing. The method decomposes a focusing beam into many uniform plane waves, and obtains a correction formula through superposition of reflection fields of each uniform plane wave component, thereby correcting model errors caused by deviation of the focusing beam radiated by an actual focusing system from the uniform plane wave, and improving the precision of the complex permittivity inversion model of the focusing beam system.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of microwave and millimeter wave material complex permittivity testing, and particularly relates to a complex permittivity inversion correction method of a free space focusing system. BACKGROUND

[0002] Microwave materials are widely used in satellite communication, radar navigation, electronic countermeasures, infrared remote sensing and other microwave fields. The complex permittivity of the material characterizes the interaction between the material and the electromagnetic field. The accurate measurement of the complex permittivity of the material is the basis for the application of microwave materials. At present, the methods commonly used for testing the complex permittivity of the material include the resonant cavity method, the network parameter method and the like. The free space method is one of the network parameter methods, can realize wideband testing by improving the antenna, and has the advantages of not contacting and not damaging the sample, and is therefore widely used in the testing of the complex permittivity of the material. The principle of the free space method is that the electromagnetic wave radiated by the transmitting antenna is focused on the surface of the sample to be tested. Due to the discontinuity of the sample surface, the electromagnetic wave will be reflected and transmitted at the interface between the sample and the air. The reflection coefficient or the transmission coefficient of the sample is measured by using a vector network analyzer, and the complex permittivity of the sample to be tested can be obtained based on the complex permittivity inversion model.

[0003] The traditional complex permittivity inversion model of the free space method is a plane wave beam model, that is, the electromagnetic wave incident on the surface of the planar sample is regarded as a uniform plane wave. However, in actual testing, a point focusing lens antenna or a point focusing reflector antenna is usually used to focus the beam, so as to reduce the diffraction effect of the sample edge. Therefore, in actual application, the testing antenna does not transmit a uniform plane wave with a cut-off frequency of zero, but a focused beam with a non-zero cut-off frequency. The propagation constant of the uniform plane wave is not the same as that of the focused beam. Therefore, when the complex permittivity of the sample to be tested is inverted, the model error will be introduced if the focused beam is approximated as a uniform plane wave. SUMMARY

[0004] In view of the model error introduced by approximating the focused beam as a uniform plane wave at the focal plane in the background art, the purpose of the present application is to provide a complex permittivity inversion correction method of a free space focusing system. The method decomposes the focused beam into a plurality of uniform plane waves, and obtains a correction formula through the superposition of the reflection field of each uniform plane wave component, so as to correct the model error caused by the deviation of the focused beam radiated by the actual focusing system from the uniform plane wave, and improve the accuracy of the complex permittivity inversion model of the focused beam system.

[0005] To achieve the above-mentioned purpose, the technical scheme of the present application is as follows:

[0006] A complex permittivity inversion correction method of a free space focusing system, comprising the following steps:

[0007] Step 1: the position of the focal plane of the focused beam radiated by the focusing antenna and the beam waist radius w0 at the focal plane are measured by using near-field probe scanning technology;

[0008] Step 2: two-port calibration is performed on the free-space focusing system, so that the calibration reference plane is located at the focal plane of the focused beam;

[0009] Step 3: the sample to be measured is placed at the focal plane of the focusing system, the receiving antenna is moved so that the calibration reference plane is coincident with the planes on both sides of the sample to be measured, and the scattering parameters S 21 of the sample to be measured are measured by using a vector network analyzer;

[0010] Step 4: the relative complex permittivity ε r of the sample to be measured is calculated by combining the beam waist radius w0 measured in Step 1 and the inversion formula; the inversion formula is specifically:

[0011]

[0012]

[0013] wherein T ⊥ is the Fresnel transmission coefficient of the vertically polarized wave, k0 is the free-space wave number, is the phase change caused by the propagation of the incident wave in the sample to be measured, θ i is the incident angle of the plane wave incident from the air to the surface of the sample.

[0014] Further, the near-field probe in Step 1 is a low-disturbance coaxial probe with a diameter less than 1.5 mm and an absorbing coating on the outside.

[0015] Further, the free-space focusing system in Step 2 includes a vector network analyzer, a receiving antenna, a transmitting antenna and a cable; the transmitting antenna and the receiving antenna are respectively connected to the vector network analyzer through the cable; the relative positions of the transmitting antenna and the receiving antenna are located in the same plane as the focused beam generated by the transmitting antenna; both the receiving antenna and the transmitting antenna are point focusing antennas.

[0016] Further, the point focusing antenna is preferably a point focusing lens antenna or a point focusing reflector antenna.

[0017] Further, the two-port calibration adopts TRL (Through-Reflect-Line) calibration.

[0018] Further, in Step 3, the lateral dimension of the sample to be measured should be greater than 5 times the beam waist radius, so as to reduce the test error caused by the edge diffraction effect of the sample, and the sample to be measured should be placed vertically to the axis of the focused beam.

[0019] Further, in Step 4, λ0 is free space wavelength, and l is sample thickness.

[0020] Therefore, by using the technical scheme, the application has the following beneficial effects:

[0021] The application provides a complex permittivity inversion correction method for a free space focusing system, considers the influence of a focusing beam on a complex permittivity inversion model, brings the measured focusing beam waist radius into a related formula, obtains an inversion formula of the complex permittivity of a sample to be measured under the action of the focusing beam, corrects the model error caused by the deviation of the focusing beam radiated by an actual focusing system from a uniform plane wave, and improves the precision of the complex permittivity inversion model of the focusing beam system. BRIEF DESCRIPTION OF DRAWINGS

[0022] Figure 1 A schematic diagram of a uniform plane wave incident on a sample surface.

[0023] Figure 2 A schematic diagram of a focusing beam incident on a sample surface.

[0024] Figure 3 A schematic diagram of a free space focusing system in the embodiment of the application.

[0025] Figure 4 A curve diagram of the real part of the relative permittivity inversion varying with the waist radius in the embodiment of the application.

[0026] Wherein, 1 is a sample to be measured, 2 is a focusing beam waist radius, 3 is a beam equal phase surface, 4 is a focusing reflection surface, 5 is a horn antenna, 6 is a cable, and 7 is a vector network analyzer. DETAILED DESCRIPTION

[0027] In order to make the purpose, technical scheme and advantages of the application more clear, the application is further described in detail below in combination with the embodiments and the drawings.

[0028] When the material to be measured is far away from the antenna, the electromagnetic wave incident on the surface of the material to be measured is considered as a uniform plane wave. A schematic diagram of a uniform plane wave incident on a sample surface is shown in Figure 1 Wherein, 1 is a sample to be measured, and 3 is a beam equal phase surface of the uniform plane wave. But actually, due to the limitation of the test space, in the near-field measurement, because the antenna is close to the material to be measured, the incident electromagnetic wave is generally a beam with a certain spatial boundary. For example, a point focusing antenna commonly used in the test system, a schematic diagram of the electromagnetic wave radiated by the antenna and incident on the sample surface is shown in Figure 2As shown, it is a typical focused beam, wherein 1 is a sample to be measured, 2 is the waist radius of the focused beam, and 3 is the beam equal phase plane of the focused beam. The propagation constant of the focused beam is different from that of the uniform plane wave, so when the complex permittivity inversion of the sample to be measured is carried out, the existing inversion model needs to be modified.

[0029] A complex permittivity inversion correction method of a free space focusing system, comprising the following steps:

[0030] Step 1: The focused beam focal plane position of the focused antenna radiation and its waist radius w0 at the focal plane are measured by using a near-field probe scanning technology;

[0031] Step 2: The free space focusing system is calibrated by double ports, so that the calibration reference surface is located at the focal plane of the focused beam; wherein the schematic diagram of the focusing system is as shown in Figure 3 , which comprises a vector network analyzer, a receiving antenna, a transmitting antenna and a cable; the transmitting antenna and the receiving antenna are connected with the vector network analyzer through the cable; the relative position of the transmitting antenna and the receiving antenna and the focused beam generated by the transmitting antenna are located in the same plane; the receiving antenna and the transmitting antenna both adopt point focusing antennas, preferably horn antennas;

[0032] Step 3: The sample to be measured is placed at the focal plane of the focusing system, the receiving antenna is moved so that the calibration reference surface is coincided with the planes on both sides of the sample to be measured, and the scattering parameter S 21 of the sample to be measured is measured by using the vector network analyzer;

[0033] Step 4: The relative complex permittivity ε r of the sample to be measured is calculated by combining the waist radius w0 measured in step 1 and the inversion formula; the inversion formula is specifically:

[0034]

[0035]

[0036] Wherein, T ⊥ is the Fresnel transmission coefficient of the vertical polarization wave, k0 is the free space wave number, is the phase change caused by the propagation of the incident wave in the sample to be measured, θ i is the incident angle of the plane wave incident from the air to the sample surface.

[0037] Example 1

[0038] In this example, the free space focusing system shown in Figure 3 is simulated, the sample to be measured has a thickness of 2mm, a relative permittivity ε' r = 3.83, and a relative permeability μ rflat fused quartz with =1.

[0039] The simulation values of the waist radius w0 of the focused beam are obtained by changing the position of the point focusing antenna and the structure of the antenna, and the scattering parameters S 21 The simulation values of the scattering parameters S 21 are respectively brought into the uniform plane wave model and the focused beam model of the application for dielectric inversion.

[0040] Figure 4 For the frequency of 110GHz, the relative permittivity obtained by the inversion of the uniform plane wave model and the focused beam model in the embodiment of the application respectively varies with the waist radius. It can be seen that the relative permittivity obtained by the inversion of the focused beam model is basically consistent with the simulation setting value, and the deviation is less than 0.01, while the relative permittivity obtained by the inversion of the uniform plane wave model has a large deviation from the simulation setting value, especially when the waist radius is small; for example, when the waist radius is 1.3mm, the deviation reaches 0.1. Therefore, when the complex permittivity is inverted by using the free space focusing system, if the uniform plane wave model is still used, the inversion result has a certain error, and the smaller the waist radius of the focused beam is, the larger the error is; while the complex permittivity obtained by using the inversion and correction method of the application has high accuracy, and is basically not affected by the change of the waist radius of the focused beam.

[0041] The above is only a specific embodiment of the application, any feature disclosed in the specification can be replaced by other equivalent or similar purpose alternative features unless specifically described; all features disclosed, or steps in all methods or processes, except for mutually exclusive features and / or steps, can be combined in any way.

Claims

1. A method of complex permittivity inversion correction for a free-space focusing system, characterized by, The method comprises the following steps: Step 1: the position of the focal plane of the focused beam radiated by the focusing antenna and the beam waist radius w0 at the focal plane are measured by using a near-field probe scanning technology; Step 2: a two-port calibration is performed on the free-space focusing system, so that the calibration reference surface is located at the focal plane of the focused beam; Step 3: Place the sample under test at the focal plane of the focusing system, move the receiving antenna so that the calibration reference plane coincides with the planes on both sides of the sample under test, and measure the scattering parameters S of the sample under test using the vector network analyzer 21 ; Step 4: Combine the beam waist radius w0 measured in step 1 and the inversion formula to calculate the relative complex permittivity ε of the sample under test r ; the inversion formula is specifically: where T ⊥ is the Fresnel transmission coefficient for a vertically polarized wave, k0 is the free-space wave number, is the phase change caused by the propagation of the incident wave in the sample to be measured, θ i is the angle of incidence of the plane wave incident from the air to the surface of the sample.

2. The complex permittivity inversion correction method of claim 1, wherein, In step 1, the near-field probe is a low-disturbance coaxial probe with a diameter less than 1.5 mm and a wave-absorbing coating on the outer side.

3. The complex permittivity inversion correction method of claim 1, wherein, In step 2, the free-space focusing system comprises a vector network analyzer, a receiving antenna, a transmitting antenna and a cable; the transmitting antenna and the receiving antenna are connected to the vector network analyzer through the cable; the relative positions of the transmitting antenna and the receiving antenna and the focused beam generated by the transmitting antenna are located in the same plane; the transmitting antenna and the receiving antenna are both point focusing antennas.

4. The complex permittivity inversion correction method of claim 1, wherein, The point focusing antenna is a point focusing lens antenna or a point focusing reflector antenna.

5. The complex permittivity inversion correction method of claim 1, wherein, In step 2, the two-port calibration adopts TRL calibration.

6. The complex permittivity inversion correction method of claim 1, wherein, In step 3, the lateral size of the sample to be measured should be greater than 5 times the beam waist radius, so as to reduce the test error caused by the diffraction effect of the sample edge; the sample to be measured is placed vertically to the axis of the focused beam.

7. The complex permittivity inversion correction method of claim 1, wherein, In step 4, λ0 is the free space wavelength and l is the sample thickness.

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