Method for measuring dielectric constant of dielectric and method for verifying validity of the method

Abstract

To provide a dielectric constant measuring method for reducing an analysis error of a dielectric constant in measurement by a free space method.SOLUTION: The method includes a step of preparing a first complex electric field distribution on an incident plane P1 of a dielectric sample 33, a step of preparing a second complex electric field distribution on an emission plane P2 of an electromagnetic wave transmitted from a receiving horn antenna and assumed to be incident on the dielectric sample 33 in a direction opposite to an emission direction of the electromagnetic wave, a step of calculating an angular spectrum distribution on a wave number space by inverse Fourier transformation of the first complex electric field distribution, a step of measuring a thickness of the dielectric sample 33 in a direction along an electromagnetic wave transmission direction, a step of calculating a reference of a complex electric field distribution which is a complex electric field distribution when the electromagnetic wave propagates in a free space by a distance corresponding to the thickness, and a step of obtaining a third complex electric field distribution of the electromagnetic wave propagating in the emission direction on the emission plane P2.SELECTED DRAWING: Figure 2

Description

[Technical Field]

[0001] The present invention relates to a method for measuring the dielectric constant of a dielectric material and a method for verifying the validity of the method. [Background technology]

[0002] When designing lens components used in radio observation systems such as radio telescopes, it is necessary to accurately grasp the dielectric constant of the lens material. Furthermore, when developing devices used in high-speed wireless communication systems, in order to achieve desired performance, it is necessary to measure and evaluate the material constants, particularly the complex dielectric constant, of the materials constituting the device, such as the antenna and circuit board, or the building materials housing the device, against electromagnetic waves. Conventional methods for measuring the dielectric constant of such materials include the resonator method described in Patent Document 1 and the free-space method described in Patent Document 2. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Patent Publication No. 2021-103757 [Patent Document 2] Japanese Patent Application Laid-Open No. 2003-287506 Summary of the Invention [Problem to be solved by the invention]

[0004] However, the measurement by the resonator method described in Patent Document 1 has the problem that the material needs to be processed to a size that can be accommodated in the resonator, and that the dielectric constant can only be measured at a few specific frequencies. The measurement by the free space method described in Patent Document 2 does not have the problems of the measurement by the resonator method described above, but has the problem that the measurement by the free space method uses a plane wave approximation technique, and therefore the measurement error of the dielectric constant due to the plane wave approximation is relatively large.

[0005] The present invention has been made to solve such problems, and has as its object to provide a dielectric constant measurement method that reduces measurement errors of dielectric constant in measurements by the free space method. [Means for solving the problem]

[0006] In order to achieve the above object, a method for measuring the permittivity of a dielectric according to the present invention is provided in a dielectric constant measurement system comprising: a transmitter for transmitting electromagnetic waves; a transmitting antenna connected to the transmitter; a receiver for receiving the electromagnetic waves; a receiving antenna connected to the receiver; a dielectric arranged between the transmitting antenna and the receiving antenna; a measuring device electrically connected to the transmitter and the receiver for measuring the amplitude and phase of the electromagnetic waves transmitted by the transmitter and the electromagnetic waves received by the receiver; and a computing device for calculating the measurement results of the measuring device, wherein the dielectric has an incident surface onto which the electromagnetic waves transmitted from the transmitting antenna are incident and an exit surface from which the electromagnetic waves incident on the dielectric are emitted to the outside of the dielectric, and the electromagnetic waves are transmitted from the transmitting antenna, incident on the incident surface of the dielectric, transmitted through the dielectric, emitted from the exit surface, and received by the receiving antenna, the method comprising: a first step of calculating a measurement value of a transmitted signal in free space including the dielectric between the transmitting antenna and the receiving antenna based on a difference between the amplitude and phase of the electromagnetic wave transmitted by the transmitter and the amplitude and phase of the electromagnetic wave received by the receiver, which are measured by the measuring device; a second step of preparing a first complex electric field distribution on an incident plane of the dielectric of an electromagnetic wave incident on the dielectric in a direction opposite to the direction of emission of the electromagnetic wave; a third step of preparing a second complex electric field distribution on an emission plane of the electromagnetic wave transmitted from the receiving antenna and assumed to be incident on the dielectric in a direction opposite to the direction of emission of the electromagnetic wave; a fourth step of calculating an angular spectrum distribution in wave number space by inverse Fourier transforming the first complex electric field distribution; a fifth step of measuring the thickness of the dielectric in a direction along the transmission direction of the electromagnetic wave; and a fifth step of Fourier transforming the product of the angular spectrum distribution in wave number space and the system transfer function. a sixth step of calculating a reference for the complex electric field distribution, which is the complex electric field distribution when the electromagnetic wave propagates in free space a distance corresponding to the thickness; a seventh step of estimating the complex permittivity of the dielectric and performing a Fourier transform on the product of the first complex electric field distribution and the Fresnel transmission coefficient of the dielectric to obtain a third complex electric field distribution of the electromagnetic wave propagating in the emission direction of the electromagnetic wave on the emission surface of the dielectric, of the electromagnetic wave that passes through the dielectric and is emitted to the outside of the dielectric; an eighth step of calculating a first electric field coupling coefficient between the third complex electric field distribution and the second complex electric field distribution; and a reference for the complex electric field distribution.The method includes a ninth step of calculating a second electric field coupling coefficient between the first and second complex electric field distributions, a tenth step of dividing the first electric field coupling coefficient by the second electric field coupling coefficient to calculate an estimated value of a transmitted signal, an eleventh step of creating an evaluation function for evaluating the difference between the estimated value of the transmitted signal and the measured value of the transmitted signal, and a twelfth step of determining whether the evaluation value obtained by the evaluation function is equal to or greater than a predetermined threshold value, wherein if the evaluation value obtained by the evaluation function is equal to or greater than the predetermined threshold value in the twelfth step, steps seven to twelfth are performed again, and if the evaluation value obtained by the evaluation function is less than the predetermined threshold value in the twelfth step, the estimated value of the complex dielectric constant of the dielectric at that time is taken as the measured value of the complex dielectric constant of the dielectric.

[0007] Furthermore, the first complex electric field distribution and the second complex electric field distribution may be prepared by at least one of estimating the first complex electric field distribution and the second complex electric field distribution through simulation, or measuring the first complex electric field distribution and the second complex electric field distribution in advance.

[0008] A method for verifying the validity of the method for measuring the dielectric constant of a dielectric according to the present invention includes a thirteenth step of preparing model data of an electromagnetic field simulation model used for examining the dielectric constant of a dielectric on software, a fourteenth step of preparing test data of the dielectric constant of the dielectric, a fifteenth step of applying the test data to the model data of the electromagnetic field simulation model, a sixteenth step of applying the test data to the method of claim 1, and a seventeenth step of comparing data of the dielectric constant obtained by the model data of the electromagnetic field simulation model with data of the dielectric constant obtained by the method of claim 1 or 2.

[0009] Another method for verifying validity of the method for measuring the dielectric constant of a dielectric according to the present invention may include an 18th step of preparing model data of an electromagnetic field simulation model used for examining the dielectric constant of a dielectric on software, a 19th step of obtaining a simulated electric field distribution from the model data of the electromagnetic field simulation model, a 20th step of obtaining the dielectric constant of the dielectric when a Gaussian beam is applied to the first complex electric field distribution and the second complex electric field distribution, a 21st step of obtaining the dielectric constant of the dielectric when the simulated electric field distribution is applied to the first complex electric field distribution and the second complex electric field distribution, and a 22nd step of comparing data of the dielectric constant of the dielectric obtained from the model data of the electromagnetic field simulation model, data of the dielectric constant of the dielectric obtained when a Gaussian beam is applied to the first complex electric field distribution and the second complex electric field distribution, and data of the dielectric constant of the dielectric obtained when the simulated electric field distribution is applied to the first complex electric field distribution and the second complex electric field distribution. [Effects of the Invention]

[0010] The method for measuring the dielectric constant of a dielectric according to the present invention includes a first step in which a calculation device calculates a measurement value of a transmission signal in free space including the dielectric between a transmitting antenna and a receiving antenna based on a difference between the amplitude and phase of an electromagnetic wave transmitted by a transmitter and the amplitude and phase of an electromagnetic wave received by a receiver, the difference being measured by a measurement device; a second step in which a first complex electric field distribution is prepared on an incident plane of the dielectric for the electromagnetic wave transmitted from the transmitter and incident on the dielectric via the transmitting antenna; and a second step in which a first complex electric field distribution is prepared on an exit plane of the electromagnetic wave transmitted from the receiving antenna and assumed to be incident on the dielectric in a direction opposite to the exit direction of the electromagnetic wave. a third step of preparing a second complex electric field distribution in the dielectric; a fourth step of calculating an angular spectrum distribution in wave number space by performing an inverse Fourier transform on the first complex electric field distribution; a fifth step of measuring the thickness of the dielectric in the direction along the direction in which the electromagnetic wave transmits; a sixth step of calculating a reference complex electric field distribution, which is the complex electric field distribution when the electromagnetic wave propagates a distance corresponding to the thickness in free space, by performing a Fourier transform on the product of the angular spectrum distribution in wave number space and the system transfer function; and a sixth step of estimating the complex permittivity of the dielectric and calculating the reference complex electric field distribution from the first complex electric field distribution and the Fresnel transmittance of the dielectric. a seventh step of Fourier transforming the product of the transmission coefficient and the third complex electric field distribution of the electromagnetic wave propagating in the direction of emission of the electromagnetic wave at the emission surface of the dielectric, the electromagnetic wave passing through the dielectric and emitting to the outside of the dielectric; an eighth step of calculating a first electric field coupling coefficient between the third complex electric field distribution and the second complex electric field distribution; a ninth step of calculating a second electric field coupling coefficient between a reference complex electric field distribution and the second complex electric field distribution; a tenth step of dividing the first electric field coupling coefficient by the second electric field coupling coefficient to calculate an estimated value of the transmitted signal; and a tenth step of evaluating the difference between the estimated value of the transmitted signal and the measured value of the transmitted signal. and a twelfth step of judging whether the evaluation value obtained by the evaluation function is equal to or greater than a predetermined threshold value in the twelfth step, the seventh step to the twelfth step are executed again when the evaluation value obtained by the evaluation function is equal to or greater than the predetermined threshold value in the twelfth step, and when the evaluation value obtained by the evaluation function is less than the predetermined threshold value in the twelfth step, an estimated value of the complex dielectric constant of the dielectric at that time is set as a measured value of the complex dielectric constant of the dielectric, thereby making it possible to reduce a measurement error of the dielectric constant in the measurement by the free space method.

[0011] The method for verifying the validity of the method for measuring the dielectric constant of a dielectric according to the present invention comprises a thirteenth step of preparing model data of an electromagnetic field simulation model used for examining the dielectric constant of a dielectric on software, a fourteenth step of preparing test data of the dielectric constant of the dielectric, a fifteenth step of applying the test data to the model data of the electromagnetic field simulation model, a sixteenth step of applying the test data to the method according to claim 1, and a seventeenth step of comparing data of the dielectric constant obtained from the model data of the electromagnetic field simulation model with data of the dielectric constant obtained by the method according to claim 1 or 2, thereby making it possible to examine errors due to plane wave approximation and beam shift effects due to a dielectric sample.

[0012] Another method for verifying the validity of the method for measuring the dielectric constant of a dielectric according to the present invention includes an 18th step of preparing model data of an electromagnetic field simulation model used for examining the dielectric constant of a dielectric on software, a 19th step of obtaining a simulated electric field distribution from the model data of the electromagnetic field simulation model, a 20th step of obtaining the dielectric constant of the dielectric when a Gaussian beam is applied to the first complex electric field distribution and the second complex electric field distribution, a 21st step of obtaining the dielectric constant of the dielectric when the simulated electric field distribution is applied to the first complex electric field distribution and the second complex electric field distribution, and a 22nd step of comparing data of the dielectric constant of the dielectric obtained by the model data of the electromagnetic field simulation model, data of the dielectric constant of the dielectric obtained when a Gaussian beam is applied to the first complex electric field distribution and the second complex electric field distribution, and data of the dielectric constant of the dielectric obtained when the simulated electric field distribution is applied to the first complex electric field distribution and the second complex electric field distribution, thereby making it possible to examine the influence of a higher-order mode. [Brief explanation of the drawings]

[0013] [Figure 1] 1 is a schematic diagram of a dielectric constant measurement system in a dielectric constant measurement method according to a first embodiment. [Figure 2] FIG. 2 is a model diagram of the dielectric constant measurement system shown in FIG. [Figure 3] FIG. 3 is a schematic diagram of the optical system of the dielectric constant measurement system shown in FIG. 2 and its design parameters. [Figure 4] 3 is a schematic diagram showing a complex electric field distribution in the dielectric constant measurement system of the first embodiment. FIG. [Figure 5] 5 is a flowchart showing an algorithm for deriving a complex dielectric constant by calculation using the dielectric constant measurement system of the first embodiment. [Figure 6] This is an electromagnetic field simulation model for investigating the effects of errors due to plane wave approximation. [Figure 7] 10 is a graph comparing analytical errors of dielectric constant εr between the dielectric constant measurement method using plane wave approximation and the dielectric constant measurement method of the first embodiment. [Figure 8] 10 is a graph comparing analytical errors of dielectric loss tangent tanδ between the dielectric constant measurement method using plane wave approximation and the dielectric constant measurement method of the first embodiment. [Figure 9] 1 is a graph showing the relationship between Δκ and s for various values ​​of Rerr / Rd. [Figure 10] 10 is a graph showing an analysis error of the dielectric loss tangent due to beam shift in a conventional plane wave model. [Figure 11] 10 is a graph showing an analytical error of the dielectric loss tangent due to beam shift in the model according to the first embodiment of the present invention. [Figure 12] This is an electromagnetic field simulation model for analysis generated using antenna design and analysis software based on an actual optical system design. [Figure 13] 10 is a graph showing the relative error of the complex permittivity εr when a Gaussian beam or a simulated electric field distribution is used for the complex electric field distributions Ep1 and Ep2. [Figure 14] 10 is a graph showing an error in the dielectric loss tangent tanδ when a Gaussian beam or a simulated electric field distribution is used for the complex electric field distributions Ep1 and Ep2. DETAILED DESCRIPTION OF THE INVENTION

[0014] Embodiment 1 (Dielectric constant measurement system) A dielectric constant measurement method according to a first embodiment of the present invention will be described below with reference to the accompanying drawings. FIG. 1 is a schematic diagram of a dielectric constant measurement system in the dielectric constant measurement method of the first embodiment. The dielectric constant measurement system 1 includes a transmitter 21 that transmits an electromagnetic wave beam having a frequency of 67 GHz or more and 500 GHz or less, a transmitting horn antenna 22 connected to the transmitter 21, a receiver 25 that receives the beam, and a receiving horn antenna 26 connected to the receiver 25. A first curved mirror 31, whose curved surface faces the transmitting horn antenna 22, is provided on an extension of the opening of the transmitting horn antenna 22. A second curved mirror 32, whose curved surface faces the receiving horn antenna 26, is provided on an extension of the opening of the receiving horn antenna 26. The first curved mirror 31 and the second curved mirror 32 are ellipsoidal mirrors.

[0015] A dielectric sample 33, the dielectric constant of which is to be measured, is supported by a support member 34 and placed between the curved surface of first curved mirror 31 and the curved surface of second curved mirror 32. Dielectric sample 33 is a thick plate-shaped dielectric material generally called a dielectric slab. Transmitter 21, transmitting horn antenna 22, receiver 25, receiving horn antenna 26, first curved mirror 31, and second curved mirror 32 constitute the optical system of the present invention. The "optical system" used in this embodiment corresponds to the frequency range of millimeter waves and terahertz electromagnetic waves.

[0016] The transmitter 21 and the receiver 25 are connected to a vector network analyzer (VNA) 40 for measuring the amplitude, frequency, phase, etc. of the beams transmitted and received from the transmitter 21 and the receiver 25. The vector network analyzer 40 is connected to a computer 41 for collecting and evaluating measurement data.

[0017] Here, the dielectric constant is generally a physical quantity that represents the propagation of an electric field in a medium, and is expressed as the complex dielectric constant ε r where ε r ' is the real part of the complex permittivity, and ε r '' is the imaginary part of the complex permittivity.

[0018]

number

[0019] Furthermore, the dielectric loss tangent tanδ can be expressed by the following equation (2) from the ratio between the imaginary part and the real part of the complex dielectric constant.

[0020]

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[0021] In addition, in a dielectric material, if c is the propagation speed, it is c / √ε' r The propagation velocity c of the electric field is slowed down depending on the value of . Furthermore, the attenuation of the electric field propagation is characterized by tan δ.

[0022] In this dielectric constant measurement system 1, the components are arranged so that when transmitter 21 transmits a beam, beam A is transmitted from transmitting horn antenna 22, reflected by first curved mirror 31 in a direction approximately 90 degrees, passes through dielectric sample 33, reflected by second curved mirror 32 in a direction approximately 90 degrees, received by receiving horn antenna 26, and then received by receiver 25. Note that beam A shown in FIG. 1 illustrates a typical path of the beam, and is not limited to this path. Beam A is reflected by first curved mirror 31 and second curved mirror 32, and passes through free space B between transmitting horn antenna 22 and receiving horn antenna 26, where dielectric sample 33 is placed.

[0023] Information on the amplitude and phase of beam A transmitted by the transmitter 21 and information on the amplitude and phase of beam A received by the receiver 25 are measured by a vector network analyzer 40. The amplitude and phase of beam A received by the receiver 25, relative to the amplitude and phase of beam A transmitted by the transmitter 21, are affected by the complex permittivity ε of the dielectric sample 33 and change. More specifically, beam A transmitted through the dielectric sample 33 is affected by a phase delay corresponding to the value of the real part ε' of the complex permittivity ε, interfacial reflection at the interface of the dielectric sample 33, and the like, and is affected by attenuation corresponding to the value of the dielectric loss tangent tanδ. Therefore, the amplitude and phase of beam A received by the receiver 25 change relative to beam A transmitted by the transmitter 21. That is, by analyzing the changes in the amplitude and phase of beam A transmitted by the transmitter 21 and beam A received by the receiver 25, measured by the vector network analyzer 40, using a computer 41, the real part ε' of the complex permittivity r The value of the complex dielectric constant ε r can be obtained.

[0024] 2 is a model diagram of the dielectric constant measurement system shown in FIG. 1. In FIG. 2, the first curved mirror 31 onto which the beam transmitted from the transmitting horn antenna 22 is incident is shown as a focusing member equivalent to a lens that focuses the beam. Also, the second curved mirror 32 onto which the beam that has passed through the dielectric sample 33 is incident is shown as a focusing member that focuses the beam. The surface of the dielectric sample 33 onto which the beam is incident is shown as the incident surface P1, and the surface from which the beam exits is shown as the exit surface P2. The beam incident on the incident surface P1 is called the input beam, and the beam exiting from the exit surface P2 is called the output beam.

[0025] Figure 3 is a schematic diagram of the optical system and its design parameters of the dielectric constant measurement system shown in Figure 2. This optical system is designed based on the known theory of frequency independence. The condition for this system with two focusing elements to be frequency independent is expressed by the following equation (3).

[0026]

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[0027] In equation (3), d1 is the distance from the opening of transmitting horn antenna 22 to the center of first curved mirror 31, d3 is the distance from the opening of receiving horn antenna 26 to the center of second curved mirror 32, d2 is the distance from the center of first curved mirror 31 to the center of second curved mirror 32, f1 is the focal length of first curved mirror 31, and f2 is the focal length of second curved mirror 32. Under the frequency-independent condition shown in equation (1), the relationship between the beam parameters of the input beam and the output beam satisfies the frequency-independent conditions of the following equations (4) and (5).

[0028]

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[0029]

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[0030] w in equation (4) in represents the beam size of the input beam, and w out represents the beam size of the output beam. R in Eq. (5) in represents the radius of curvature of the input beam, and R out represents the radius of curvature of the output beam. From the above equations (3), (4), and (5), it can be seen that the design parameters of this optical system satisfy the following conditions (i), (ii), and (iii): (i)w in =w out (ii)R out =-R in (iii) The narrowest point of the beam converged by the first curved mirror 31 and the second curved mirror 32 is equidistant from both mirrors. The design parameters derived in this way are given by equations (6) and (7).

[0031]

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[0032]

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[0033] In equations (6) and (7), f is the parameter value selected in this design. This design allows the optical system to provide excellent frequency-independent beam coupling characteristics and suppress analytical errors due to beam shift to a negligible level.

[0034] (Dielectric constant measurement method) Next, a method for measuring the dielectric constant of the dielectric sample 33 in the dielectric constant measurement system 1 will be described. Fig. 4 is a schematic diagram showing a complex electric field distribution in the dielectric constant measurement system of the present embodiment 1. Hereinafter, the method for measuring the dielectric constant of the dielectric sample 33 will be described with reference to Figs. 2 to 4. First, Cartesian coordinates (x, y, z) are defined for the incident surface P1 and the exit surface P2 of the dielectric sample 33 shown in Fig. 2. In these Cartesian coordinates, z = 0 at the incident surface P1 of the dielectric sample 33, and z = z' at the exit surface P2.

[0035] Next, prepare an actual complex electric field distribution E(x, y, z) on the incident plane P1 of the input beam transmitted from the transmitting horn antenna 22. In FIG. 4, the prepared complex electric field distribution E p1 (x, y, z = 0) is shown as (a). The electric field distribution on the cross section (x, y) propagates from the horn 1 in the positive z-axis direction. The complex electric field distribution E p1 In the optical system shown in Fig. 2, the complex electric field distribution E(x, y) on the incident plane P1 may be actually measured, or may be prepared by electromagnetic field simulation based on the parameters of the actual optical system. In Fig. 4, the electric field strength on the incident plane P1 is shown as concentric circles, with the electric field strength increasing closer to the center of the concentric circles and decreasing as the distance from the periphery increases.

[0036] Next, the complex electric field distribution E at the incident plane P1 p1 (x, y, 0) is subjected to an inverse Fourier transform (IFFT) to obtain the angular spectrum distribution in wave number space. In Figure 4, this inverse Fourier transform is shown as (b), and the angular spectrum distribution in wave number space (k space) obtained by the inverse Fourier transform is shown as (c). By this inverse Fourier transform, the electric field strength distribution E(x, y, 0) is expanded into a series consisting of plane waves of each wave number vector. In other words, the electric field strength distribution E(x, y, 0) is decomposed into plane waves of each wave number vector. Here, E p1 The angular spectrum (c) in wavenumber space is given by equation (8).

[0037]

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[0038] Next, the complex electric field distribution E after propagating a distance z in free space is Ref (x,y,z) is derived as a criterion. This is F p1 (k x ,k y , 0) and the system transfer function H(k x ,k y , z') is obtained by the Fourier transform of the product with

[0039]

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[0040] Here, the system transfer function H(k x ,k y , z') is expressed by equation (10).

[0041]

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[0042] Moreover, the wave vector is expressed by the following equation (11).

[0043]

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[0044] Next, we will explain how to calculate the complex electric field distribution of the beam after the beam has propagated through the dielectric sample 33. In the dielectric sample 33 having an intermediate boundary between z=0 and z=z′, the complex electric field distribution E of the input beam at the incident plane P1 (z=0) is p1 For (x, y, 0), after the beam has propagated through the dielectric sample 33, the complex electric field distribution E of the output beam propagating in the positive Z-axis direction at the exit surface P2 (z=z′) of the boundary of the dielectric sample 33 is MUT (x, y, z) are expressed by equations (12) and (13).

[0045]

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[0046]

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[0047] Here, T(k x ,k y ;z') is the complex Fresnel transmission coefficient. Also, T ⊥ (k x ,k y ;z') is the Fresnel transmission coefficient for vertically polarized light, and T ∥ (k x ,k y ;z') is the Fresnel transmission coefficient of horizontally polarized light. The complex Fresnel transmission coefficient is an equation that describes the amplitude and phase of the transmitted wave when an electromagnetic wave passes through a dielectric interface. In Figure 4, the complex Fresnel transmission coefficient is expressed as (d). As shown in equations (12) and (13), the plane wave F p1 , the complex Fresnel transmission coefficient T(k x ,k y;z'), and by performing a Fourier transform (FFT) on this, the results of multiplying the plane wave of each wave number by the complex Fresnel transmission coefficient (d) are added together to obtain the complex electric field distribution E of the output beam propagating in the positive Z-axis direction at the exit surface P2 after the beam has passed through the dielectric sample 33. MUT We can obtain (x, y, z). In Figure 4, this Fourier transform is shown as (e).

[0048] In this case, the complex Fresnel transmission coefficient of vertically polarized light, T ⊥ (k x ,k y ;z') and the complex Fresnel transmission coefficient T for horizontally polarized light ∥ (k x ,k y ;z') is expressed by equations (14) and (15) in terms of wave number components.

[0049]

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[0050]

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[0051] Also, the wave vector K in vacuum z The component is expressed by equation (16), and the dielectric constant ε r of the wave vector K in the dielectric sample 33 z The components are expressed by equation (17), and the wave number in vacuum is expressed by equation (18).

[0052]

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[0053]

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[0054]

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[0055] where ε r is the relative permittivity, and when deriving the estimated value T of the transmitted signal, the relative permeability ε r Assume =1.

[0056] Next, the relationship between the above-mentioned complex electric field distribution and the electric field coupling coefficient will be explained. a and any other complex electric field distribution E b The electric field coupling coefficient between is defined as shown in equation (19).

[0057]

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[0058] To theoretically determine how electromagnetic waves are transmitted between the transmitting horn antenna 22 and the receiving horn antenna 26, we calculate the electric field coupling constants at any plane of the beams propagating in the positive and negative directions. p1 , the complex electric field distribution of the output beam E MUT , the reference complex electric field distribution E after propagation through a distance z in free space Ref , and the complex electric field distribution E of the beam propagating from the opposite direction p2 By calculating the beam coupling coefficient between , the transmission coefficient for any electric field distribution can be derived. Based on Equation (19), the estimated transmitted signal T n As expressed in equation (20), ε r It can be expressed as a function of

[0059]

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[0060] At this time, the complex electric field distribution E p2 =E p2(x, y, z) is the complex electric field distribution at the exit surface P2 (z=z′) of the dielectric sample 33, propagating in the negative Z-axis direction from the receiving horn antenna 26 shown in FIG. 2. This complex electric field distribution E p2 In the optical system shown in FIG. 2, the complex electric field distribution E(x, y) at the output surface P2 may be actually measured, or may be prepared by electromagnetic field simulation based on the parameters of the actual optical system. The complex electric field distribution E of the output beam at the prepared output surface P2 is p2 (x, y, z = 0) is represented as (f). In Fig. 4, the electric field strength at the output surface P2 is represented as concentric circles, with the electric field strength increasing closer to the center of the concentric circles and decreasing as one moves away from the periphery.

[0061] The complex electric field distribution E of the output beam at the output surface P2 propagating in the positive Z-axis direction in equation (20) is MUT and the complex electric field distribution of the beam at the exit plane P2 propagating in the negative Z-axis direction. <E MUT |E p2 > is the complex electric field distribution E at the exit surface P2 of the beam transmitted through the dielectric sample 33. MUT and the complex electric field distribution E at the exit plane P2 of the beam transmitted from the receiving horn antenna 26 and assumed to be incident on the dielectric sample 33 in the negative Z-axis direction. p2 In addition, the reference complex electric field distribution E after propagation of a distance z in free space in equation (20) is Ref and the complex electric field distribution of the beam at the exit plane P2 propagating in the negative Z-axis direction. <E Ref |E p2 > is the complex electric field distribution E at the beam exit surface P2 when there is no dielectric sample 33. Ref and the complex electric field distribution E on the emission plane P2 of the beam emitted in the negative direction from the receiving horn antenna 26. p2 The electric field coupling coefficient is <E MUT |E p2 >, the electric field coupling coefficient <E Ref |E p2Dividing by , the electric field coupling coefficient without the dielectric sample 33 is <E Ref |E p2 The estimated transmitted signal T, normalized by n can be obtained.

[0062] Next, we will explain the procedure for deriving the dielectric constant of the dielectric sample 33 in the dielectric constant measurement system 1 already explained. The vector network analyzer 40 of the dielectric constant measurement system 1 shown in Fig. 1 actually installs the dielectric sample 33 and measures the changes in the measured values ​​of amplitude and phase of the beam A at the transmitter 21 and the beam A at the receiver 25 before and after they pass through the dielectric sample 33. The computer 41 calculates the measured value T of the transmitted signal from the measured values. Meas Calculate.

[0063] Next, the computer 41 inputs the thickness t and dielectric constant ε of the dielectric sample 33 into the above-mentioned equations (8) to (20). r In the iterative process of substituting the estimated value of , the complex permittivity is derived. n Calculate.

[0064] Next, the computer 41 calculates the complex dielectric constant ε of the dielectric sample 33. r The estimated normalized transmission signal T n and the estimated transmitted signal T calculated from the actual free-space measurement Meas The computer 41 then compares the estimated transmitted signal T n and the measured value of the transmitted signal T Meas The dielectric constant ε of the dielectric sample 33, which has the smallest difference from r By solving the optimization problem to obtain the dielectric constant ε r can be obtained.

[0065] FIG. 5 shows a case where the complex dielectric constant ε is calculated by the computer 41 using the dielectric constant measurement system 1 (see FIG. 1) according to the first embodiment. rThis is a flowchart showing an algorithm for deriving the value T by calculation. This algorithm is explained below. In step S1, the S parameters of the optical system of the dielectric constant measurement system are measured, and unnecessary signal components generated in the optical system are removed by gating in the time domain, and the measured value T of the transmission signal is obtained. Meas In step S2, the complex electric field distribution E of the input beam at the incident plane P1, which is prepared in advance by actually measuring it in the dielectric constant measurement system 1 or by using a simulation, is calculated. p1 and the complex electric field distribution E at the exit surface P2 p2 and are introduced into the calculation.

[0066] Next, in step S3, the thickness t of the dielectric sample 33 in the direction along which the beam A passes is actually measured, and the complex electric field distribution E after the beam A propagates in free space through a distance z=z' corresponding to the thickness t of the dielectric sample is calculated using the above-mentioned equation (9). Ref Next, in step S4, the complex dielectric constant ε r and calculate the complex electric field distribution E of the output beam using the above equation (12). MUT Calculate.

[0067] Next, in step S5, the complex electric field distribution E p1 , complex electric field distribution E p2 , complex electric field distribution E Ref and the complex electric field distribution E MUT Substituting the above, the estimated normalized transmission signal T n Next, in step S6, this estimated value T n and the measured transmitted signal T calculated from the actual free space measurement Meas An evaluation function is created and calculated to evaluate how small the difference is between this estimated value T n and the measured value of the transmitted signal T Meas Since it is desirable that the difference between the estimated complex permittivity and the transmitted signal model formula be minimized, this evaluation function is calculated by substituting the estimated complex permittivity into the transmitted signal model formula. n and the transmission signal T obtained by measurement measThis is a function that evaluates how small the difference between the estimated value T n and the measured value of the transmitted signal T Meas The larger the difference, the higher the value; the smaller the difference, the lower the value.

[0068] Next, in step S7, it is determined whether the evaluation value obtained by this evaluation function is equal to or greater than a predetermined threshold value. If the evaluation value is equal to or greater than the predetermined threshold value, the procedure is repeated from step S4. As a result, the estimated value T n and the estimated transmitted signal T Meas E, which minimizes the difference between MUT , T n , calculate the evaluation function. That is, this calculation is performed to obtain the estimated value T n and the measured value of the transmitted signal T Meas The dielectric constant ε of the dielectric sample 33, which has the smallest difference from r When the evaluation value is less than a predetermined threshold, the theoretical value T n and the measured value of the transmitted signal T Meas The difference between is determined to be minimum, and the algorithm ends. Then, the complex permittivity ε r The estimated value of the complex permittivity ε of the dielectric sample 33 r In this way, the estimated value T n and the measured value of the transmitted signal T Meas The complex permittivity ε where the difference between r The estimated value of the complex permittivity ε of the dielectric sample 33 in the permittivity measurement system 1 is r can be taken as a measurement of

[0069] In conventional dielectric constant measurement methods using the free-space method, the plane wave approximation is used, which assumes that all electromagnetic waves incident on a dielectric sample are single plane waves with uniform amplitude and phase distribution. However, because the electromagnetic waves incident on an actual dielectric sample are not single plane waves, there is a problem that it is difficult to derive an accurate dielectric constant due to systematic errors caused by the plane wave approximation.

[0070] On the other hand, the dielectric constant measurement method of the present embodiment 1 has an advantage that, by introducing each spectral method into a measurement method using the free space method, errors caused by plane wave approximation can be significantly reduced and dielectric constant can be measured more accurately.

[0071] Furthermore, in the conventional dielectric constant measurement method using the free space method, a method is known in which a dielectric constant measurement system in which the incident beam diameter of the electromagnetic wave incident on the dielectric sample is large is used in order to reduce errors due to the plane wave approximation. However, such a dielectric constant measurement system in which the incident beam diameter is large requires an optical design that can accommodate a large beam diameter, and also has the problem that diffraction is likely to occur at the edge of the dielectric sample, so that a large dielectric sample must be used to address this.

[0072] On the other hand, the dielectric constant measurement method of the first embodiment does not require a large-diameter incident beam, and therefore there is no need to adapt the dielectric constant measurement system and the dielectric sample to a large-diameter beam, and the dielectric constant can be measured even with a small dielectric sample, which is advantageous in that the dielectric constant measurement method can be implemented simply and inexpensively.

[0073] As described above, the method for measuring the dielectric constant of a dielectric according to the first embodiment includes the transmitter 21 for transmitting an electromagnetic wave, the transmitting horn antenna 22 connected to the transmitter 21, the receiver 25 for receiving the electromagnetic wave, the receiving horn antenna 26 connected to the receiver 25, the dielectric sample 33 arranged between the transmitting horn antenna 22 and the receiving horn antenna 26, the vector network analyzer 40 electrically connected to the transmitter 21 and the receiver 25 for measuring the amplitude and phase of the electromagnetic wave transmitted by the transmitter 21 and the electromagnetic wave received by the receiver 25, and a measurement unit for measuring the amplitude and phase of the electromagnetic wave transmitted by the transmitter 21 and the electromagnetic wave received by the receiver 25. a computer 41 for calculating the results, and the dielectric sample 33 has an incident surface P1 onto which the electromagnetic wave transmitted from the transmitting horn antenna 22 is incident and an exit surface P2 from which the electromagnetic wave incident on the dielectric sample 33 is emitted to the outside of the dielectric sample 33, and the electromagnetic wave is transmitted from the transmitting horn antenna 22 and incident on the incident surface P1 of the dielectric sample 33, then passes through the dielectric sample 33 and is emitted from the exit surface P2, and is received by the receiving horn antenna 26. The present invention includes a step of calculating a measured value of a transmission signal in free space including a dielectric sample 33 between the transmitting horn antenna 22 and the receiving horn antenna 26 by a computer 41 based on a difference between the amplitude and phase of the electromagnetic wave transmitted by the transmitter 21 and the amplitude and phase of the electromagnetic wave received by the receiver 25; a step of preparing a first complex electric field distribution at an incident plane P1 of the dielectric sample 33 of the electromagnetic wave transmitted from the transmitter 21 and incident on the dielectric sample 33 via the transmitting horn antenna 22; and a step of calculating a first complex electric field distribution of the electromagnetic wave transmitted from the receiving horn antenna 26 and assumed to be incident on the dielectric sample 33 in a direction opposite to the direction of emission of the electromagnetic wave. a step of preparing a second complex electric field distribution at the output surface P2 of the magnetic wave; a step of calculating an angular spectrum distribution in wave number space by performing an inverse Fourier transform on the first complex electric field distribution; a step of measuring the thickness of the dielectric sample 33 in a direction along the transmission direction of the electromagnetic wave; a step of calculating a reference complex electric field distribution, which is a complex electric field distribution when the electromagnetic wave propagates a distance corresponding to the thickness in free space, by performing a Fourier transform on the product of the angular spectrum distribution in wave number space and the system transfer function; a step of estimating an estimated value of the complex permittivity of the dielectric sample 33 and calculating the first complex electric field distribution;the step of calculating a first electric field coupling coefficient between the third complex electric field distribution and the second complex electric field distribution; the step of calculating a second electric field coupling coefficient between a reference complex electric field distribution and the second complex electric field distribution; the step of calculating an estimated value of a transmitted signal by dividing the first electric field coupling coefficient by the second electric field coupling coefficient; the step of creating an evaluation function for evaluating a difference between the estimated value of the transmitted signal and a measured value of the transmitted signal; and the step of determining whether the evaluation value obtained by the evaluation function is equal to or greater than a predetermined threshold value or less, If the evaluation value obtained by the evaluation function is equal to or greater than a predetermined threshold, an estimated value of the complex permittivity of the dielectric sample 33 is estimated, and the product of the first complex electric field distribution and the Fresnel transmission coefficient of the dielectric sample 33 is Fourier transformed to obtain a third complex electric field distribution of the electromagnetic wave propagating in the emission direction of the electromagnetic wave on the emission surface P2 of the dielectric sample 33, of the electromagnetic wave that passes through the dielectric sample 33 and is emitted to the outside of the dielectric sample 33, and the steps up to determining whether the evaluation value obtained by the evaluation function is equal to or greater than a predetermined threshold are performed again, and if the evaluation value obtained by the evaluation function is less than the predetermined threshold in the step of determining whether the evaluation value obtained by the evaluation function is equal to or greater than a predetermined threshold, the estimated value of the complex permittivity of the dielectric sample 33 at that time is used as the measured value of the complex permittivity of the dielectric sample 33, thereby reducing analytical errors in the permittivity in measurements by the free space method.

[0074] Furthermore, since the first complex electric field distribution and the second complex electric field distribution are prepared by estimating the first complex electric field distribution and the second complex electric field distribution through simulation or by measuring the first complex electric field distribution and the second complex electric field distribution in advance, it is possible to reduce an analysis error of the complex dielectric constant of the dielectric sample 33.

[0075] Embodiment 2 (Method for verifying the validity of a dielectric constant measurement method) Next, a second embodiment of the present invention will be described. The second embodiment is a method for verifying the validity of the dielectric constant measurement method of the first embodiment. In the second embodiment, the same reference numerals as those in Figs. 1 to 5 of the first embodiment denote the same or similar components, and therefore detailed description thereof will be omitted. In order to verify the validity of the permittivity measurement method of the first embodiment, a physical optics simulation of an optical system model is performed using known software for designing and analyzing reflector antenna systems. The permittivity measurement method of the first embodiment is applied to test data of electric field distribution to derive an estimated value of complex permittivity, and the derived estimated value of permittivity is compared with an ideal permittivity in a simulation set by the software, thereby verifying the validity of the permittivity measurement method.

[0076] (A. Consideration of errors due to plane wave approximation) Next, we will consider the error caused by the plane wave approximation. In the plane wave model used in the known method of measuring the dielectric constant using the plane wave approximation, the interaction between the dielectric and the incident electromagnetic field is a single plane wave that is incident perpendicularly to the dielectric. However, the actual incident electric field is not a single plane wave, but is a superposition of plane waves with various wave vectors. Therefore, since an error caused by the plane wave approximation always occurs, an analytical method that takes this error into account is required to accurately measure the complex dielectric constant.

[0077] Figure 6 shows an electromagnetic field simulation model for investigating the effects of errors due to plane wave approximation. This model includes two parabolic mirrors, a first parabolic mirror 51 and a second parabolic mirror 52, which are arranged so that the axes of their paraboloids are aligned and their paraboloids face each other, and a dielectric sample 53 is placed between the first and second parabolic mirrors 51 and 52. The beam source of this model is a basic Gaussian beam using the beam parameter design values ​​at the aperture of the horn antenna. In this model, a transmitting horn antenna 54 that transmits the beam is placed between the first parabolic mirror 51 and the dielectric sample 53, and a receiving horn antenna 55 that receives the beam is placed between the dielectric sample 53 and the second parabolic mirror 52.

[0078] The simulation model consists of a parabolic mirror instead of an ellipsoidal mirror to see the purest possible effect of the plane wave approximation, rather than mirror effects such as distortion, polarization, etc. Therefore, the beam source is set up as a basic Gaussian beam with beam parameters equal to the design values ​​of the beam at the horn aperture.

[0079] Next, we will explain how to verify the validity of the dielectric constant measurement method in this simulation model. First, we will explain the radiated electric field distribution E at the opening of the transmitting horn antenna 54. radi Next, by using electromagnetic field simulation such as known physical optics (PO) or method of moments (MoM), the electric field distribution E at the aperture of the receiving horn antenna 55 after the beam has propagated through the optical system in this model is calculated. prop Next, the electric field coupling coefficient c at the opening of receiving horn antenna 55 is calculated using equation (21).

[0080]

number

[0081] Next, the electric field coupling coefficient c is measured using the conventional dielectric constant measurement method based on plane wave approximation and the dielectric constant measurement method of the first embodiment, and the dielectric constant measurement results of both methods are compared with the ideal dielectric constant in a simulation to evaluate the error caused by the dielectric constant measurement. In this way, the conventional dielectric constant measurement method and the dielectric constant measurement method of the first embodiment are compared to consider the error caused by the plane wave approximation.

[0082] FIG. 7 shows the relationship between the dielectric constant ε r The graph shows the analytical error of the dielectric specimen. The horizontal axis of the graph, t / λs, represents the thickness of the dielectric specimen normalized by the wavelength λ of the beam inside the dielectric. The vertical axis of the graph represents the dielectric constant ε r 7(a) is a graph showing the measurement results obtained by the conventional method for measuring dielectric constant using plane wave approximation, and FIG. 7(b) is a graph showing the measurement results obtained by the method for measuring dielectric constant according to the first embodiment. In addition, the left column of the graph shows the dielectric constant ε'. r =2, the middle column is the dielectric constant ε' r =6, the right column is the dielectric constant ε' r = 10. Furthermore, the graph is plotted for the cases where the beam waist size ω0 of the beam is 2 times, 4 times, 6 times, and 8 times the wavelength λ.

[0083] Dielectric constant ε measured by the conventional method using plane wave approximation r The analytical error of the dielectric constant ε is within the range of approximately 0.01% or more and less than 1%. r The analytical error is less than 0.01%, which is a significant reduction compared to conventional dielectric constant measurement methods.

[0084] FIG. 8 is a graph comparing the analytical error of the dielectric loss tangent tanδ between the dielectric constant measurement method using plane wave approximation and the dielectric constant measurement method of embodiment 1. t / λs on the horizontal axis of the graph represents the thickness of the dielectric sample normalized by the wavelength λ of the beam inside the dielectric. The vertical axis of the graph represents the absolute error of the dielectric loss tangent tanδ in percentage. FIG. 8(a) is a graph of the measurement results using the conventional dielectric constant measurement method using plane wave approximation, and FIG. 8(b) is a graph of the measurement results using the dielectric constant measurement method of embodiment 1. In the graph, the left column shows the dielectric constant ε' r =2, the middle column is the dielectric constant ε' r =6, the right column is the dielectric constant ε' r = 10, and the graph is plotted for the cases where the beam waist size ω0 of the beam is 2 times, 4 times, 6 times, and 8 times the wavelength λ.

[0085] The analytical error of the dielectric loss tangent tanδ obtained by the conventional dielectric constant measurement method using plane wave approximation is within the range of approximately 0.0001% or more and less than 0.01%, whereas the analytical error of the dielectric loss tangent tanδ obtained by the dielectric constant measurement method of embodiment 1 is less than 0.001%, which is a significant reduction in analytical error compared to the conventional dielectric constant measurement method.

[0086] (B. Study of beam shift effect due to dielectric sample) Next, we consider the beam shift effect due to a dielectric sample. The plane wave model in the known dielectric constant measurement method using the plane wave approximation assumes that a dielectric sample along the beam path does not affect the beam coupling. However, a dielectric sample shifts the beam along the propagation direction, changing the beam coupling. The change in beam coupling affects the normalization with the reference measurement, resulting in a change in the apparent dielectric loss tangent tanδ.

[0087] When measuring low dielectric loss materials, beam shift causes a large error in the dielectric loss tangent, which is one of the factors that limit the measurable range. rcan be derived based on known quasi-optical calculations and the effect of beam shift in 4f optical systems. In this study, we first estimated the effect of beam shift on the analysis error using quasi-optical calculations. Next, we applied the measurement method of the first embodiment to test data generated by known antenna design and analysis software, and verified the error due to the beam shift effect.

[0088] When the input and output beam parameters are at ideal design values, the beam power coupling coefficient is 1. If the input beam parameters deviate from the design values, the beam power coupling coefficient can be improved by changing the distance d2 from the center of the first curved mirror 31 to the center of the second curved mirror 32 due to the beam shift effect of the dielectric slab, as shown in Figure 3. This means that the measured dielectric loss tangent may have an unphysical value, i.e., a negative dielectric loss tangent. Therefore, to investigate the change in beam power coupling due to beam shift, we consider the error in the input beam parameters using a Gaussian beam model. The radius of curvature R of the output beam that satisfies the above equations (3) and (6) is out d2 and R in It can be expressed as Equation (22), which is a function of

[0089]

number

[0090] In addition, the ideal design value of d2 that satisfies the above-mentioned formula (7) is d2 Thru and an equivalent distance d2 between the two first curved mirror 31 and the second curved mirror 32, taking into account the effect of beam shift due to a dielectric sample in the beam path. DUT The relationship between these can be expressed by the following equation (23).

[0091]

number

[0092] where R dis the design value of the radius of curvature of the input beam, and s is the beam shift in the z-axis direction due to the dielectric sample, expressed by the following equation (24).

[0093]

number

[0094] Since s is always negative, d2 DUT <d2 Thru From the above equations (4) and (6), the relationship between the beam diameters of the input and output beams does not change regardless of d2. Therefore, when a dielectric sample is present, the beam diameter ω of the output beam is out DUT and the beam diameter ω of the output beam when there is no dielectric sample. out Thru can be expressed as the actual input beam diameter with an error, as shown in the following equation (25).

[0095]

number

[0096] In addition, the radius of curvature of the output beam when a dielectric sample is present is R out DUT and the radius of curvature of the output beam without a dielectric sample, R out Thru can be expressed as the following equation (26).

[0097]

number

[0098] where R err is the actual radius of curvature of the input beam, which includes an error. The beam power coupling coefficient between the input and output beams using the Gaussian beam model can be expressed as follows:

[0099]

number

[0100] Moreover, the relative change Δκ of the Gaussian beam power coupling coefficient can be expressed as the following equation (28).

[0101]

number

[0102] Here, α and β are expressed by the following equation (29).

[0103]

number

[0104] Figure 9 shows the results of various R err / R d Δ for the value of κ 1 is a graph showing the relationship between s and s. When the actual input beam radius of curvature at the horn aperture is larger than the design value, i.e., R err / R d > 1, the power coupling coefficient becomes larger than that measured without a dielectric sample due to the beam shift. In other words, the apparent dielectric loss tangent becomes smaller than the true dielectric loss tangent. Conversely, if the actual radius of curvature is smaller than the design value, that is, R err / R d <1, the power coupling coefficient decreases and the apparent dissipation factor increases compared to the true dissipation factor value.

[0105] This tendency is qualitatively consistent with the relationship between the beam diameter position shift and beam coupling in a 4f optical system. In the simulation verification, the dielectric constant is set to 10, the dielectric loss tangent is set to 0, and the thickness t of the dielectric sample is set to 8λ. 0H / √ε r The beam spot size was set to ω0 / λ=8. The R of the simulation model of the antenna design and analysis software errBy substituting various values ​​into , we can obtain model data for the simulation model that includes errors due to beam shift.

[0106] Next, the dielectric constant of a dielectric sample is measured by the conventional dielectric constant measurement method using plane wave approximation and the dielectric constant measurement method of embodiment 1, and the dielectric constant measurement results of both methods are compared with an ideal dielectric constant simulated using model data of a simulation model to evaluate errors caused by the dielectric constant measurement. In this way, the conventional dielectric constant measurement method is compared with the dielectric constant measurement method of embodiment 1, and errors caused by the plane wave approximation are considered.

[0107] Fig. 10 is a graph showing the analytical error of the dielectric loss tangent due to beam shift in the conventional plane wave model. Fig. 11 is a graph showing the analytical error of the dielectric loss tangent due to beam shift in the model according to the first embodiment of the present invention. The horizontal axis in Fig. 10 and Fig. 11 is 1 / λ s The vertical axis shows the analytical error of the dielectric loss tangent tanδ. err / R d =1,R err / R d =2,R err / R d The plots are for R = 0.5. err / R d = 1, the sign of the error in the dielectric loss tangent is reversed, and this qualitatively matches the result obtained by equation (28). This is because the d2 value that maximizes the beam-power coupling coefficient changes due to the error in the radius of curvature of the horn opening. This result suggests that, in the evaluation of ultra-low loss materials, unphysical results such as the dielectric loss tangent falling below zero may occur depending on the optical system. On the other hand, the analysis results using the method of the present invention show that R err / R d This indicates that the method of the present invention suppresses the estimation error of the dielectric loss tangent due to the beam shift.

[0108] (C. Consideration of the influence of higher modes) The permittivity measurement method according to the first embodiment of the present invention utilizes the electric field distribution in an actual optical system model. The guided modes of beam propagation in this optical system model include the fundamental mode and higher-order modes. This differs from a Gaussian beam, which includes only the fundamental mode. Therefore, it is possible to consider the influence of higher-order modes on the permittivity measurement method according to the first embodiment. To investigate the influence of higher-order modes on the analysis error of the permittivity measurement method according to the first embodiment and to verify the effectiveness of the proposed method for suppressing this error, we created model data for an electromagnetic field simulation model for analyzing an actual optical system using known antenna design and analysis software.

[0109] Figure 12 shows an electromagnetic field simulation model for analysis generated by antenna design and analysis software, which has a corrugated horn 61, a first ellipsoidal mirror 62, a second ellipsoidal mirror 63, and a dielectric sample 64, based on the design of an actual optical system. The electric field distribution at the aperture of the corrugated horn 61 is calculated using the method of moments using the actual horn model.

[0110] The complex electric field distribution E of Equation (8) and Equation (20) p1 and the complex electric field distribution E p2 In the case of using a Gaussian beam and the case of using the simulated electric field distribution obtained by the analytical simulation model in Fig. 12, r The results of the analysis of the relative error of the complex electric field distribution E of the Gaussian beam were compared. p1 and E p2 is derived by quasi-optical calculation using the design parameters of the optical system. In this study, the dielectric loss tangent tanδ is set to 0, and the thickness t of the dielectric sample is set to t = 4λ for each value of the relative permittivity. 0H / √ε r It is set to be.

[0111] Figure 13 shows the complex electric field distribution E p1 and E p2 The complex permittivity ε when a Gaussian beam or simulated electric field distribution is used rThe horizontal axis of this graph shows the thickness t of the dielectric sample versus wavelength λ s The vertical axis is the complex permittivity ε r The left column of the graph shows the real part ε' of the dielectric constant. r =2, the real part of the middle column is the permittivity ε' r =6, the real part in the right column is the dielectric constant ε' r This is a graph when the complex electric field distribution E p1 and E p2 When the simulated electric field distribution is used, the complex electric field distribution E p1 and E p2 complex permittivity ε r The relative error is small.

[0112] Figure 14 shows the complex electric field distribution E p1 and E p2 1 is a graph showing the error of the dielectric loss tangent tanδ when a Gaussian beam or a simulated electric field distribution is used. The horizontal axis of this graph is the thickness t of the dielectric sample relative to the wavelength λ. s The vertical axis is the error of the dielectric loss tangent tanδ. Also, in the graph, the real part on the left column is the dielectric constant ε' r =2, the real part of the middle column is the permittivity ε' r =6, the right column is the dielectric constant ε' r This is a graph when the complex electric field distribution E p1 and E p2 When the simulated electric field distribution is used, the complex electric field distribution E p1 and E p2 The relative error of the dielectric loss tangent tanδ is smaller than when a Gaussian beam is used.

[0113] As shown in Figure 14, when higher modes are not considered, that is, when analysis is performed using the fundamental Gaussian beam, the value of the dielectric tangent tanδ is -1×10 -4In contrast, an analysis using the electric field distribution simulated on antenna design and analysis software showed that the error in the dielectric loss tangent tanδ value was close to zero, indicating an improvement in the error. Furthermore, the model optical system shown in Figure 12 is composed of a corrugated horn with a high Gaussianity of over 98%, but errors in the dielectric loss tangent tanδ due to higher-order modes occur, just as in an optical system composed of optical components with low Gaussianity. This result suggests that errors in the dielectric loss tangent tanδ due to higher-order modes may not be negligible when using optical system characteristics, i.e., low-Gaussianity horn antennas or mirrors that significantly distort the beam pattern.

[0114] As described above, as a result of A. examining the error due to plane wave approximation, B. examining the beam shift effect due to a dielectric sample, and C. examining the influence of higher-order modes, it is understood that the dielectric constant measurement method of embodiment 1 of the present application has a smaller error in measuring the dielectric constant of a dielectric sample than the conventional dielectric constant measurement method using plane wave approximation, and is therefore highly valid.

[0115] As described above, the method of verifying the validity of the dielectric constant measurement method of embodiment 1, which is related to A. examination of errors due to plane wave approximation and B. examination of beam shift effect due to dielectric sample in embodiment 2, includes a step of preparing model data for an electromagnetic field simulation model, a step of preparing test data for the dielectric constant of the dielectric sample, a step of applying the test data to the model data, a step of applying the test data to the dielectric constant measurement method of embodiment 1, and comparing the dielectric constant data obtained from the model data with the dielectric constant data obtained by the dielectric constant measurement method of embodiment 1 to verify the validity of the dielectric constant data obtained by the dielectric constant measurement method of embodiment 1. Therefore, it can be understood that the validity of the dielectric constant measurement method of embodiment 1 of the present invention is higher than the validity of conventional dielectric constant measurement methods.

[0116] Furthermore, as described above, the method for verifying the validity of the dielectric constant measurement method of the first embodiment, which is related to C. Consideration of the influence of higher-order modes of the second embodiment, includes the steps of: preparing model data of an electromagnetic field simulation model used to consider the dielectric constant of a dielectric sample on software; obtaining a simulated electric field distribution from the model data of the electromagnetic field simulation model; obtaining the dielectric constant of the dielectric sample when a Gaussian beam is applied to the first complex electric field distribution and the second complex electric field distribution; obtaining the dielectric constant of the dielectric sample when the simulated electric field distribution is applied to the first complex electric field distribution and the second complex electric field distribution; and comparing the data of the dielectric constant of the dielectric sample obtained from the model data of the electromagnetic field simulation model, the data of the dielectric constant of the dielectric sample obtained when a Gaussian beam is applied to the first complex electric field distribution and the second complex electric field distribution, and the data of the dielectric constant of the dielectric sample obtained when the simulated electric field distribution is applied to the first complex electric field distribution and the second complex electric field distribution. Therefore, it is possible to consider the influence of higher-order modes in the dielectric constant measurement method according to the first embodiment of the present invention. [Explanation of symbols]

[0117] 21 transmitter, 22 transmitting horn antenna (transmitting antenna), 25 receiver, 26 receiving horn antenna (receiving antenna), 33 dielectric sample (dielectric), 40 vector network analyzer (measuring device), 41 computer (computing device).

Claims

1. a transmitter for transmitting electromagnetic waves; a transmitting antenna connected to the transmitter; a receiver for receiving electromagnetic waves; a receiving antenna connected to the receiver; a dielectric disposed between the transmitting antenna and the receiving antenna; a measuring device electrically connected to the transmitter and the receiver, for measuring the amplitude and phase of the electromagnetic wave transmitted by the transmitter and the electromagnetic wave received by the receiver; a calculation device for calculating the measurement results of the measurement device; Equipped with the dielectric body has an incident surface onto which the electromagnetic wave transmitted from the transmitting antenna is incident, and an exit surface from which the electromagnetic wave incident on the dielectric body is emitted to the outside of the dielectric body, a dielectric constant measuring method for a dielectric constant measuring system, in which the electromagnetic wave is transmitted from the transmitting antenna, incident on an incident surface of the dielectric, passes through the dielectric, and is emitted from the exit surface, and is received by the receiving antenna, a first step in which the calculation device calculates a measurement value of a transmitted signal in free space including the dielectric between the transmitting antenna and the receiving antenna based on a difference between the amplitude and the phase of the electromagnetic wave transmitted by the transmitter and the amplitude and the phase of the electromagnetic wave received by the receiver, as measured by the measurement device; a second step of preparing a first complex electric field distribution on an incident surface of the dielectric body of an electromagnetic wave transmitted from the transmitter and incident on the dielectric body via the transmitting antenna; a third step of preparing a second complex electric field distribution at the emission plane of an electromagnetic wave that is transmitted from the receiving antenna and is assumed to be incident on the dielectric in a direction opposite to the emission direction of the electromagnetic wave; a fourth step of calculating an angular spectrum distribution in wavenumber space by performing an inverse Fourier transform on the first complex electric field distribution; a fifth step of measuring a thickness of the dielectric in a direction along which the electromagnetic wave passes; a sixth step of calculating a reference complex electric field distribution, which is a complex electric field distribution when the electromagnetic wave propagates a distance corresponding to the thickness in free space, by performing a Fourier transform on the product of the angular spectrum distribution in wave number space and a system transfer function; a seventh step of estimating a complex dielectric constant of the dielectric and performing a Fourier transform on a product of the first complex electric field distribution and a Fresnel transmission coefficient of the dielectric to obtain a third complex electric field distribution of the electromagnetic wave that propagates in the emission direction of the electromagnetic wave on the emission surface of the dielectric, the electromagnetic wave transmitting through the dielectric and being emitted to the outside of the dielectric; an eighth step of calculating a first electric field coupling coefficient between the third complex electric field distribution and the second complex electric field distribution; a ninth step of calculating a second electric field coupling coefficient between the reference complex electric field distribution and the second complex electric field distribution; a tenth step of dividing the first electric field coupling coefficient by the second electric field coupling coefficient to calculate an estimate of the transmitted signal; an eleventh step of creating an evaluation function for evaluating the difference between the estimated value of the transmitted signal and the measured value of the transmitted signal; a twelfth step of determining whether the evaluation value obtained by the evaluation function is equal to or greater than a predetermined threshold value; Including, the seventh step to the twelfth step are performed again when the evaluation value obtained by the evaluation function is equal to or larger than a predetermined threshold value, and the seventh step to the twelfth step are performed again when the evaluation value obtained by the evaluation function is smaller than a predetermined threshold value in the twelfth step, and the estimated value of the complex dielectric constant of the dielectric at that time is set as a measured value of the complex dielectric constant of the dielectric.

2. 2. The method of claim 1, wherein the first complex electric field distribution and the second complex electric field distribution are prepared by at least one of estimating the first complex electric field distribution and the second complex electric field distribution through simulation or measuring the first complex electric field distribution and the second complex electric field distribution in advance.

3. A method for verifying the validity of the method according to claim 1 or 2, comprising: a thirteenth step of preparing model data of an electromagnetic field simulation model used to examine the dielectric constant of the dielectric on software; a fourteenth step of preparing test data for the dielectric constant of the dielectric; a fifteenth step of applying the test data to model data of the electromagnetic field simulation model; a sixteenth step of applying the test data to the method of claim 1 or 2; a seventeenth step of comparing the dielectric constant data obtained from the model data of the electromagnetic field simulation model with the dielectric constant data obtained by the method according to claim 1 or 2; A method comprising:

4. A method for verifying the validity of the method according to claim 1 or 2, comprising: an 18th step of preparing model data of an electromagnetic field simulation model used to examine the dielectric constant of the dielectric on software; a nineteenth step of obtaining a simulated electric field distribution from model data of the electromagnetic field simulation model; a twentieth step of obtaining a dielectric constant of the dielectric when a Gaussian beam is applied to the first complex electric field distribution and the second complex electric field distribution; a 21st step of obtaining a dielectric constant of the dielectric when the simulated electric field distribution is applied to the first complex electric field distribution and the second complex electric field distribution; a 22nd step of comparing data of the dielectric constant of the dielectric obtained from model data of the electromagnetic field simulation model, data of the dielectric constant of the dielectric obtained when a Gaussian beam is applied to the first complex electric field distribution and the second complex electric field distribution, and data of the dielectric constant of the dielectric obtained when the simulated electric field distribution is applied to the first complex electric field distribution and the second complex electric field distribution; A method comprising:

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