CN115542017A - Complex dielectric constant inversion correction method of free space focusing system - Google Patents
Complex dielectric constant inversion correction method of free space focusing system Download PDFInfo
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- CN115542017A CN115542017A CN202211198081.1A CN202211198081A CN115542017A CN 115542017 A CN115542017 A CN 115542017A CN 202211198081 A CN202211198081 A CN 202211198081A CN 115542017 A CN115542017 A CN 115542017A
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Abstract
The invention aims to provide a complex dielectric constant inversion correction method of a free space focusing system, and belongs to the technical field of complex dielectric constant testing of microwave and millimeter wave materials. According to the method, the focusing beam is decomposed into a plurality of uniform plane waves, and a correction formula is obtained by superposing the reflection fields of the components of each uniform plane wave, so that model errors caused by deviation of the focusing beam radiated by an actual focusing system and the uniform plane waves are corrected, and the precision of a complex dielectric constant inversion model of the focusing beam system is improved.
Description
Technical Field
The invention belongs to the technical field of microwave and millimeter wave material complex dielectric constant testing, and particularly relates to a complex dielectric constant inversion correction method of a free space focusing system.
Background
The microwave material is widely applied to the microwave fields of satellite communication, radar navigation, electronic countermeasure, infrared remote sensing and the like, the complex dielectric constant of the material represents the interaction between the material and an electromagnetic field, and the accurate measurement of the complex dielectric constant of the material is the basis of the application of the microwave material. The existing method commonly used for testing the complex dielectric constant of the material comprises a resonant cavity method, a network parameter method and the like, the free space method is one of the network parameter methods, the broadband test can be realized by improving an antenna, and the method has the advantages of no contact and no damage to a sample, so that the method is widely applied to the complex dielectric constant test of the material. The principle of the free space method is that an emission antenna radiates electromagnetic waves to be focused on the surface of a sample to be detected, the electromagnetic waves are reflected and transmitted at the interface between the sample and air due to the discontinuity of the surface of the sample, the reflection coefficient or the transmission coefficient of the sample is measured by using a vector network analyzer, and the complex dielectric constant of the sample to be detected can be obtained through inversion based on a complex dielectric constant inversion model.
The traditional free space method complex dielectric constant inversion model is a plane wave beam model, namely, electromagnetic waves incident to the surface of a plane sample are regarded as uniform plane waves. However, in practical tests, the beam is usually focused by using a point focusing lens antenna or a point focusing reflector antenna, so as to reduce the diffraction effect at the edge of the sample. In practice, therefore, the test antenna does not emit a uniform plane wave with a zero cutoff frequency, but transmits a focused beam with a non-zero cutoff frequency. The propagation constant of the uniform plane wave is different from that of the focused beam, so that when the complex dielectric constant of the sample to be detected is inverted, model errors can be introduced when the focused beam is approximately regarded as the uniform plane wave.
Disclosure of Invention
Aiming at the problem of model error caused by approximately regarding a focused beam as a uniform plane wave at a focal plane in the prior art, the invention aims to provide a complex dielectric constant inversion correction method of a free space focusing system. According to the method, the focusing beam is decomposed into a plurality of uniform plane waves, and a correction formula is obtained by superposing the reflection fields of the components of each uniform plane wave, so that model errors caused by deviation of the focusing beam radiated by an actual focusing system and the uniform plane waves are corrected, and the precision of a complex dielectric constant inversion model of the focusing beam system is improved.
In order to achieve the purpose, the technical scheme of the invention is as follows:
a complex dielectric constant inversion correction method of a free space focusing system comprises the following steps:
step 1: measuring the focal plane position of the focused beam radiated by the focusing antenna and the beam waist radius w at the focal plane by adopting a near-field probe scanning technology 0 ；
Step 2: performing dual-port calibration on the free space focusing system, so that a calibration reference plane is positioned in a focusing beam focal plane;
and step 3: placing a sample to be measured at a focal plane of a focusing system, moving a receiving antenna to enable a calibration reference surface to coincide with planes on two sides of the sample to be measured, and measuring a scattering parameter S of the sample to be measured by using a vector network analyzer 21 ；
And 4, step 4: combining the beam waist radius w measured in the step 1 0 Calculating the relative complex dielectric constant epsilon of the sample to be measured by a sum inversion formula r (ii) a The inversion formula is specifically as follows:
wherein, T ⊥ Fresnel transmission coefficient, k, for vertically polarized waves 0 As the number of free-space waves,
for phase changes caused by propagation of incident waves in the sample to be measured, theta i Is the angle of incidence of a plane wave from air incident on the sample surface.
Further, in the step 1, the near-field probe is a low-disturbance coaxial probe with the diameter smaller than 1.5mm and the outer side coated with the wave-absorbing coating.
Further, the free space focusing system in the step 2 comprises a vector network analyzer, a receiving antenna, a transmitting antenna and a cable; the transmitting antenna and the receiving antenna are respectively connected with the vector network analyzer through cables; the relative positions of the transmitting antenna and the receiving antenna and the focused wave beam generated by the transmitting antenna are positioned on the same plane; the receiving antenna and the transmitting antenna both adopt point focusing antennas.
Further, the point focusing antenna is preferably a point focusing lens antenna or a point focusing reflector antenna.
Further, the two-port calibration uses TRL (Through-Reflect-Line) calibration.
Further, the transverse size of the sample to be tested in step 3 should be larger than 5 times of the beam waist radius to reduce the test error caused by the sample edge diffraction effect, and the sample to be tested needs to be placed perpendicular to the axis of the focused beam.
Further, in step 4,
λ 0 is the free space wavelength, l is the sample thickness.
In summary, due to the adoption of the technical scheme, the invention has the beneficial effects that:
the invention provides a complex dielectric constant inversion correction method of a free space focusing system, which considers the influence of a focusing beam on a complex dielectric constant inversion model, brings the measured waist radius of the focusing beam into a related formula, obtains an inversion formula of the complex dielectric constant 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 the actual focusing system and a uniform plane wave, and improves the precision of the complex dielectric constant inversion model of the focusing beam system.
Drawings
FIG. 1 is a schematic view of a uniform plane wave incident on a sample surface.
Fig. 2 is a schematic view of a focused beam incident on the sample surface.
FIG. 3 is a schematic diagram of a free space method focusing system according to an embodiment of the present invention.
FIG. 4 is a graph of the real part of the inverted relative permittivity as a function of the radius of the beam waist in an embodiment of the present invention.
The device comprises a sample to be detected, a focusing beam waist radius 2, a beam isophase plane 3, a focusing reflecting plane 4, a horn antenna 5, a cable 6 and a vector network analyzer 7.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail with reference to the following embodiments and accompanying drawings.
When the material to be measured is far from the antenna, the electromagnetic wave incident on the surface of the material to be measured is regarded as a uniform plane wave. A schematic diagram of the uniform plane wave incident on the sample surface is shown in fig. 1, where 1 is a sample to be measured, and 3 is a beam equiphase plane of the uniform plane wave. However, due to the limitation of the test space, in the near field measurement, the incident electromagnetic wave is generally a beam with a certain space boundary because the antenna is closer to the material to be measured. As shown in fig. 2, a schematic diagram of an electromagnetic wave radiated by a point focusing antenna commonly used in a test system incident on a sample surface is a typical focused beam, where 1 is a sample to be tested, 2 is a beam waist radius of the focused beam, and 3 is a beam equiphase plane of the focused beam. The propagation constant of the focused beam is different from that of the uniform plane wave, so that the existing inversion model needs to be corrected when the complex dielectric constant of the sample to be detected is inverted.
A complex dielectric constant inversion correction method of a free space focusing system comprises the following steps:
step 1: measuring the focal plane position of the focused beam radiated by the focusing antenna and the beam waist radius w at the focal plane by adopting a near-field probe scanning technology 0 ；
Step 2: performing double-port calibration on the free space focusing system, so that a calibration reference plane is positioned in a focusing beam focal plane; the schematic diagram of the focusing system is shown in fig. 3, and includes a vector network analyzer, a receiving antenna, a transmitting antenna and a cable; the transmitting antenna and the receiving antenna are respectively connected with the vector network analyzer through cables; the relative positions of the transmitting antenna and the receiving antenna and the focused wave beam generated by the transmitting antenna are positioned on the same plane; the receiving antenna and the transmitting antenna both adopt point focusing antennas, preferably horn antennas;
and step 3: placing a sample to be measured at a focal plane of a focusing system, moving a receiving antenna to enable a calibration reference surface to coincide with planes on two sides of the sample to be measured, and measuring a scattering parameter S of the sample to be measured by using a vector network analyzer 21 ；
And 4, step 4: combining the beam waist radius w measured in the step 1 0 Calculating the relative complex dielectric constant epsilon of the sample to be measured by an inversion formula r (ii) a The inversion formula is specifically as follows:
wherein, T ⊥ Fresnel transmission coefficient, k, for vertically polarized waves 0 As the number of free-space waves,
for phase changes caused by propagation of incident waves in the sample to be measured, theta i Is the angle of incidence of a plane wave from air incident on the sample surface.
Example 1
In this example, the free space method focusing system shown in FIG. 3 was used for simulation, and the sample to be measured had a thickness of 2mm and a relative dielectric constant ε' r =3.83, relative permeability μ r Flat fused silica of = 1.
Obtaining beam waist radius w of different focused beams by changing the position of a point focusing antenna and the structural form of the antenna 0 Obtaining scattering parameters S of the focused wave beam acting on the surface of the sample to be measured under different beam waist radiuses 21 Will simulate to obtainS of 21 And respectively carrying out dielectric inversion in the uniform plane wave model and the focused beam model.
Fig. 4 is a curve of relative dielectric constant variation with beam waist radius obtained by respectively using a uniform plane wave model and a focused beam model for inversion in the embodiment of the present invention at a frequency of 110 GHz. It can be seen that the relative dielectric constant inverted by using the focused beam model is basically consistent with the simulation set value, and the deviation is less than 0.01, while the relative dielectric constant inverted by using the uniform plane wave model has larger deviation with the simulation set value, especially when the beam waist radius is smaller; for example, a beam waist radius of 1.3mm, the deviation reaches 0.1. Therefore, when a free space focusing system is used for inverting the complex dielectric constant, if a uniform plane wave model is still adopted, the inversion result has certain error, and the error is larger when the radius of the beam waist of the focused beam is smaller; the complex dielectric constant value obtained by the inversion correction method of the invention has higher precision and is basically not influenced by the change of the beam waist radius of the focused beam.
While the invention has been described with reference to specific embodiments, any feature disclosed in this specification may be replaced by alternative features serving the same, equivalent or similar purpose, unless expressly stated otherwise; all of the disclosed features, or all of the method or process steps, may be combined in any combination, except mutually exclusive features and/or steps.
Claims (7)
1. A complex dielectric constant inversion correction method of a free space focusing system is characterized by comprising the following steps:
step 1: measuring the focal plane position of the focused beam radiated by the focusing antenna and the beam waist radius w at the focal plane by adopting a near-field probe scanning technology 0 ；
Step 2: performing dual-port calibration on the free space focusing system, so that a calibration reference plane is positioned in a focusing beam focal plane;
and step 3: placing the sample to be measured at the focal plane of the focusing system, moving the receiving antenna to make the calibration reference plane coincide with the two side planes of the sample to be measured, and measuring by using a vector network analyzerObtaining scattering parameter S of sample to be measured 21 ；
And 4, step 4: combining the beam waist radius w measured in the step 1 0 Calculating the relative complex dielectric constant epsilon of the sample to be measured by an inversion formula r (ii) a The inversion formula is specifically as follows:
wherein, T ⊥ Fresnel transmission coefficient, k, for vertically polarized waves 0 As the number of free-space waves,
for phase changes caused by propagation of incident waves in the sample to be measured, theta i Is the angle of incidence of a plane wave from air incident on the sample surface.
2. The complex dielectric constant 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 1.5mm and coated with a wave-absorbing coating on the outer side.
3. The complex permittivity inversion correction method of claim 1, wherein 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 with the vector network analyzer through cables; the relative positions of the transmitting antenna and the receiving antenna and the focused wave beam generated by the transmitting antenna are positioned on the same plane; the receiving antenna and the transmitting antenna both adopt 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 method for the inverse modification of complex permittivity as claimed in claim 1, wherein the two-port calibration in step 2 is TRL calibration.
6. The complex dielectric constant inversion correction method of claim 1, wherein in step 3, the lateral dimension of the sample to be measured should be larger than 5 times of the beam waist radius to reduce the measurement error caused by the sample edge diffraction effect, and the sample to be measured should be placed perpendicular to the axis of the focused beam.
7. The complex permittivity inversion correction method of claim 1, wherein, in step 4,
λ 0 is the free space wavelength, and l is the sample thickness.
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