Scattering tomography device and scattering tomography method

Abstract

The scattering tomography apparatus (100) comprises: a transmitting antenna element (101) for transmitting radio waves from the outside of an object to the inside of the object; a receiving antenna element (102) for receiving scattered waves of the radio waves transmitted to the inside of the object at the outside of the object; and an information processing circuit (103) for generating an image showing the inside of the object using measurement data showing the scattered waves received by the receiving antenna element (102). The information processing circuit (103) uses the measurement data to derive a relational expression that satisfies an equation with a scattered field function as a solution, uses the relational expression to derive an image function, and uses the image function to generate an image. The image function is a function of a parameter that reflects the corresponding relationship between the frequency change of the radio wave and the dielectric constant change of the object according to Debye relaxation.

Description

Technical Field

[0001] The present disclosure relates to a scattering tomography apparatus and the like that generates an image showing the interior of an object using scattered radio waves. Background Art

[0002] As technologies related to scattering tomography apparatuses and the like that generate images showing the interior of an object using scattered radio waves, there are technologies described in Patent Documents 1, 2, and 3.

[0003] For example, in the technology described in Patent Document 1, a beam emitted from a microwave transmitter is incident on an object to be inspected, and a microwave detector detects the amplitude and phase of the scattered beam. The dielectric constant distribution is then calculated based on the output signal from the microwave detector, allowing for tomographic imaging of the object to be performed.

[0004] (Prior art literature)

[0005] (Patent Document)

[0006] Patent Document 1 Japanese Patent Application Laid-Open No. 62-66145

[0007] Patent Document 2 International Publication No. 2014 / 125815

[0008] Patent Document 3 International Publication No. 2015 / 136936

[0009] However, it is not easy to generate an image showing the interior of an object with high precision using scattered waves of radio waves such as microwaves.

[0010] Specifically, when the internal state of an object is known, determining the measured data, which is the data measured as scattered waves from incident radio waves, is called a forward problem and is easy. However, when the measured data is known, determining the internal state of the object is called an inverse problem and is difficult.

[0011] Furthermore, radio waves incident on an object can contain numerous frequency components. Different frequencies of radio waves cause different dielectric constants within the object, and thus different propagation velocities. In other words, radio waves have multiple propagation velocities corresponding to various frequency components. Because measurement data is affected by these factors, it is difficult to determine the internal state of an object based on these measurements. Summary of the Invention

[0012] Therefore, the present disclosure provides a scattering tomography apparatus and the like that can generate an image showing the interior of an object with high precision using scattered radio waves.

[0013] A scattering tomography apparatus according to one aspect of the present disclosure includes: a transmitting antenna element for transmitting radio waves from the outside of an object to the inside of the object; a receiving antenna element for receiving, at the outside of the object, scattered waves of the radio waves transmitted into the inside of the object; and an information processing circuit for generating an image showing the inside of the object using measurement data showing the scattered waves received by the receiving antenna element. The information processing circuit uses the measurement data to derive a relational expression satisfying an equation whose solution is a scattered field function, wherein the scattered field function is input at a transmission position of the radio waves and a reception position of the scattered waves and outputs the amount of the scattered waves at the reception position. The information processing circuit derives an image function for generating the image using the relational expression, wherein the image function is a function reflecting a parameter showing a correspondence relationship between a change in the frequency of the radio waves and a change in the dielectric constant of the object according to Debye relaxation. The image is generated using the image function.

[0014] In addition, these general or specific forms can be implemented by systems, devices, methods, integrated circuits, computer programs, or non-temporary recording media such as computer-readable CD-ROMs, or by any combination of systems, devices, methods, integrated circuits, computer programs, and recording media.

[0015] According to one aspect of the present disclosure, it is possible to generate an image showing the interior of an object with high precision by utilizing scattered radio waves. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 This is a graph showing the frequency dependency of the dielectric constant of water at 30° C. in the embodiment. Figure 2A Graph showing the relative dielectric constant of breast fat tissue at each frequency in the embodiment.

[0017] Figure 2B Graph showing the effective electrical conductivity of breast fat tissue at each frequency in the embodiment.

[0018] Figure 3 1 is a schematic diagram showing a measuring device for measuring the dielectric constant of a cut sample in an embodiment.

[0019] Figure 4 This is a diagram showing an example in which the array antenna in the embodiment scans a curved surface and measures scattering data.

[0020] Figure 5 This is a schematic diagram showing the relationship between the position of the transmitting antenna element, the position of the receiving antenna element, and the position of the substance in the embodiment.

[0021] Figure 6FIG. 1 is a diagram showing an example in which a monostatic antenna in an embodiment scans a curved surface and measures scattering data.

[0022] Figure 7 This is a schematic diagram showing the relationship between the transmission and reception positions and the positions of substances in the embodiment.

[0023] Figure 8 FIG. 1 is a diagram showing the overall system configuration of a multistatic array radar according to an embodiment.

[0024] Figure 9 This is a diagram showing array antennas arranged in a row on a straight line or a curved line in an embodiment.

[0025] Figure 10 A scanning method performed by the array antenna in the embodiment is shown.

[0026] Figure 11 The diagram shows measurement points in a scanning method performed by the array antenna in the embodiment.

[0027] Figure 12 This is a diagram showing an example of realizing a monostatic antenna capable of measuring radio waves in both polarization directions in the embodiment.

[0028] Figure 13 This is a graph showing the relationship between the relative dielectric constant and the frequency when the dielectric dispersion is large.

[0029] Figure 14A The simulation results of the radio wave at t=0 nanosecond are shown.

[0030] Figure 14B The simulation results of the radio wave at t=0.2 nanosecond are shown.

[0031] Figure 14C The simulation results of the radio wave at t=0.4 nanosecond are shown.

[0032] Figure 14D The simulation results of the radio wave at t=0.6 nanosecond are shown.

[0033] Figure 14E The simulation results of the radio wave at t=0.8 nanosecond are shown.

[0034] Figure 15 Computational model of the reconstructed simulation is shown.

[0035] Figure 16A It is an XY plane diagram showing the simulation results of the first example.

[0036] Figure 16B It is a perspective view showing the results of the simulation of the first example.

[0037] Figure 17A It is an XY plane diagram showing the simulation results of the second example.

[0038] Figure 17B It is a perspective view showing the results of the simulation of the second example.

[0039] Figure 18A It is an XY plane diagram showing the simulation results of the third example.

[0040] Figure 18B It is a perspective view showing the results of the simulation of the third example.

[0041] Figure 19 2 is a block diagram showing a basic configuration of a scattering tomography apparatus according to an embodiment.

[0042] Figure 20 1 is a flowchart illustrating the basic operation of the scattering tomography apparatus in the embodiment. DETAILED DESCRIPTION

[0043] A scattering tomography apparatus according to one aspect of the present disclosure includes: a transmitting antenna element for transmitting radio waves from the outside of an object to the inside of the object; a receiving antenna element for receiving, at the outside of the object, scattered waves of the radio waves transmitted into the inside of the object; and an information processing circuit for generating an image showing the inside of the object using measurement data showing the scattered waves received by the receiving antenna element. The information processing circuit uses the measurement data to derive a relational expression satisfying an equation whose solution is a scattered field function, wherein the scattered field function is input at a transmission position of the radio waves and a reception position of the scattered waves and outputs the amount of the scattered waves at the reception position. The information processing circuit derives an image function for generating the image using the relational expression, wherein the image function is a function reflecting a parameter showing a correspondence relationship between a change in the frequency of the radio waves and a change in the dielectric constant of the object according to Debye relaxation. The image is generated using the image function.

[0044] Based on this, the scattering tomography apparatus can derive a relationship for deriving an image function based on a scattered field function representing the amount of scattered waves based on the transmission and reception positions, and measurement data of scattered waves received by the receiving antenna elements. Furthermore, the image function reflects a parameter representing the correspondence between changes in the frequency of the radio waves and changes in the dielectric constant of the object. Therefore, when generating an image depicting the interior of an object, the scattering tomography apparatus can reflect this correspondence between changes in frequency and changes in dielectric constant.

[0045] That is, the scattering tomography apparatus can generate an image showing the interior of an object with high precision using scattered waves of radio waves.

[0046] In a three-dimensional space composed of X coordinates, Y coordinates, and Z coordinates, the X coordinate of the arrangement position of the transmitting antenna element is the same as the X coordinate of the arrangement position of the receiving antenna element.

[0047] The scattered field function is determined by [Formula 1],

[0048] [Mathematical formula 1]

[0049]

[0050]

[0051]

[0052] x represents the X coordinate of the sending position and the receiving position, y1 represents the Y coordinate of the sending position, y2 represents the Y coordinate of the receiving position, z1 represents the Z coordinate of the sending position, z2 represents the Z coordinate of the receiving position, ω represents the angular frequency of the radio wave, D represents the region including the material that causes the scattered wave to be generated by reflecting the radio wave, ξ represents the X coordinate of the position within the region, η represents the Y coordinate of the position within the region, ζ represents the Z coordinate of the position within the region, ε(ξ, η, ζ) represents the reflectivity, i represents the imaginary unit, and k represents the wave number of the radio wave.

[0053] Thus, the scattering tomography apparatus can accurately derive a relational expression for deriving an image function based on the scattered field function determined based on the X coordinates of the transmitting antenna element and the receiving antenna element being identical.

[0054] The equation is determined by [Mathematical Formula 2],

[0055] [Mathematical formula 2]

[0056]

[0057]

[0058] According to this, the scattering tomography apparatus can accurately derive a relational expression for deriving an image function from the aforementioned partial differential equation determined as an equation having the aforementioned scattered field function as a solution.

[0059] Furthermore, the relationship is determined by [Mathematical Formula 3],

[0060] [Mathematical formula 3]

[0061]

[0062] k xrepresents the wave number of x with respect to the scattered field function, k y1 represents the wave number of y1 with respect to the scattered field function, k y2 represents the wave number of y2 with respect to the scattered field function, a(k x , k y1 , k y2 , k) is determined by [Mathematical Formula 4],

[0063] [Formula 4]

[0064]

[0065] I represents the index of the transmitting position where the transmitting antenna element is located, J represents the index of the receiving position where the receiving antenna element is located, and y I represents the Y coordinate of the transmitting position where the transmitting antenna element is located, y J represents the Y coordinate of the receiving position where the receiving antenna element is located, a I，J (k x , k y1 , k y2 , k) represents the coefficient determined by the measurement data in kx, ky1, ky2 and k, Φ(k x ,y I ,y J , k) represents k x 、y I 、y J and the measurement data in k.

[0066] Therefore, the scattering tomography apparatus can accurately derive the image function based on the above-mentioned relationship determined by the corresponding measurement data of the transmitting position of the transmitting antenna element and the receiving position of the receiving antenna element.

[0067] Furthermore, the image function is determined by [Formula 5],

[0068] [Formula 5]

[0069]

[0070] The x of the image function represents the X coordinate of the image, the y of the image function represents the Y coordinate of the image, and the z of the image function represents the Z coordinate of the image. The variables included in the integrand of the image function are determined by [Mathematical Formula 6],

[0071] [Formula 6]

[0072]

[0073]

[0074]

[0075]

[0076]

[0077] c0 represents the propagation speed of the radio wave in a vacuum, and a, b, and α represent the parameters.

[0078] With this configuration, the scattering tomography apparatus can accurately generate an image using the above-mentioned image function reflecting the parameter showing the correspondence between the change in the frequency of the radio wave and the change in the dielectric constant of the object.

[0079] Furthermore, the information processing circuit utilizes the measurement data obtained at the configuration position of the transmitting antenna element and the configuration position of the receiving antenna element as data obtained by alternating the configuration position of the transmitting antenna element and the configuration position of the receiving antenna element to generate the image.

[0080] According to this, the scattering tomography apparatus can reduce the number of times the arrangement positions of the transmitting antenna elements and the receiving antenna elements are changed to obtain measurement data.

[0081] Furthermore, for example, the scattering tomography apparatus includes a plurality of receiving antenna elements, and the information processing circuit generates the image using the measurement data indicating the scattered waves received by each of the plurality of receiving antenna elements included in the scattering tomography apparatus.

[0082] Thus, the scattering tomography apparatus can obtain measurement data at multiple receiving positions for a single transmission from a single transmission position. Therefore, the scattering tomography apparatus can reduce the number of transmissions and the number of changes to the receiving position.

[0083] Furthermore, for example, the transmitting antenna element and the plurality of receiving antenna elements are arranged in a row, the transmitting antenna element is located at the end of the row formed by the transmitting antenna element and the plurality of receiving antenna elements, and a radio wave absorbing component is arranged between the transmitting antenna element and the plurality of receiving antenna elements.

[0084] This arrangement allows the transmission antenna element and multiple reception antenna elements to be arranged on a straight line or curve. This reduces the complexity of computational processing and scanning. Furthermore, the radio wave absorbing component prevents radio waves from being incident on objects and traveling directly from the transmission antenna element to the reception antenna element.

[0085] Furthermore, for example, in a three-dimensional space consisting of X coordinates, Y coordinates, and Z coordinates, the X coordinates, Y coordinates, and Z coordinates of the configuration position of the transmitting antenna element are respectively the same as the X coordinates, Y coordinates, and Z coordinates of the configuration position of the receiving antenna element.

[0086] The scattered field function is determined by [Equation 7],

[0087] [Formula 7]

[0088]

[0089]

[0090] x represents the X coordinate of the sending position and the receiving position, y represents the Y coordinate of the sending position and the receiving position, z represents the Z coordinate of the sending position and the receiving position, D represents the region including the material that generates the scattered wave by reflecting the radio wave, ξ represents the X coordinate of the position within the region, η represents the Y coordinate of the position within the region, ζ represents the Z coordinate of the position within the region, ε(ξ, η, ζ) represents the reflectivity, i represents the imaginary unit, and k represents the wave number of the radio wave.

[0091] Thus, the scattering tomography apparatus can accurately derive a relational expression for deriving an image function based on the scattered field function determined based on the fact that the arrangement positions of the transmitting antenna elements and the receiving antenna elements are the same.

[0092] And, for example, the equation is determined by [Math. 8],

[0093] [Formula 8]

[0094]

[0095] According to this, the scattering tomography apparatus can accurately derive a relational expression for deriving an image function from the aforementioned partial differential equation determined as an equation having the aforementioned scattered field function as a solution.

[0096] And, for example, the relationship is determined by [Mathematical Formula 9],

[0097] [Formula 9]

[0098]

[0099] k x represents the wave number of x with respect to the scattered field function, k y represents the wave number of y with respect to the scattered field function, a(k x , k y, k) is determined by [Mathematical formula 10],

[0100] [Formula 10]

[0101]

[0102] I represents the index of the transmitting position and the receiving position where the transmitting antenna element and the receiving antenna element are located, and x I represents the X coordinates of the transmitting position and the receiving position where the transmitting antenna element and the receiving antenna element are located, z I and f(x I ) represents the Z coordinates of the transmitting position and the receiving position where the transmitting antenna element and the receiving antenna element are located,

[0103] [Mathematical formula 11]

[0104]

[0105] Represents x I 、k y and the measurement data in k.

[0106] Therefore, the scattering tomography apparatus can accurately derive the image function based on the above-mentioned relationship determined by the measurement data corresponding to the transmitting position of the transmitting antenna element and the receiving position of the receiving antenna element.

[0107] And, for example, the image function is determined by [Mathematical Formula 12],

[0108] [Mathematical formula 12]

[0109]

[0110] The x of the image function represents the X coordinate of the image, the y of the image function represents the Y coordinate of the image, and the z of the image function represents the Z coordinate of the image. The variables included in the integrand of the image function are determined by [Mathematical Formula 13],

[0111] [Mathematical formula 13]

[0112]

[0113]

[0114]

[0115]

[0116]

[0117] c0 represents the propagation speed of the radio wave in a vacuum, and a, b, and α represent the parameters.

[0118] With this configuration, the scattering tomography apparatus can accurately generate an image using the above-mentioned image function reflecting the parameter showing the correspondence between the change in the frequency of the radio wave and the change in the dielectric constant of the object.

[0119] Furthermore, for example, the scattering tomography apparatus includes a plurality of transmitting antenna elements and a plurality of receiving antenna elements. The plurality of transmitting antenna elements included in the scattering tomography apparatus correspond to the plurality of polarization directions of the radio waves, and the plurality of receiving antenna elements included in the scattering tomography apparatus correspond to the plurality of polarization directions of the radio waves.

[0120] According to this, the scattering tomography apparatus can transmit and receive according to multiple polarization directions, and thus can obtain information corresponding to the polarization directions.

[0121] Furthermore, for example, the parameter is determined by measuring a plurality of dielectric constants of objects of the same type as the object at a plurality of frequencies of the radio wave.

[0122] With this configuration, the scattering tomography apparatus can accurately generate an image based on appropriately determined parameters representing the correspondence between changes in the frequency of radio waves and changes in the dielectric constant of an object.

[0123] Furthermore, for example, the radio wave is a pulse wave.

[0124] Thus, the scattering tomography apparatus can generate an image showing the interior of an object with high precision using a pulse wave having a large number of frequency components.

[0125] Moreover, for example, a scatter tomography method according to one aspect of the present disclosure includes the following steps: a step of transmitting an electric wave from the outside of an object to the inside of the object through a transmitting antenna element; a step of receiving a scattered wave of the electric wave transmitted to the inside of the object outside the object through a receiving antenna element; and a step of generating an image showing the inside of the object by using measurement data showing the scattered wave received by the receiving antenna element. In the step of generating the image, the measurement data is used to derive a relational expression that satisfies an equation having a scattered field function as a solution. The scattered field function is input with the transmission position of the electric wave and the reception position of the scattered wave, and outputs the amount of the scattered wave at the reception position. Using the relational expression, an image function for generating the image is derived, and the image function is a function of a parameter that reflects the correspondence between the frequency change of the electric wave and the change in the dielectric constant of the object according to Debye relaxation. The image is generated by using the image function.

[0126] Accordingly, a relational expression for deriving an image function can be derived based on the scattered field function showing the amount of the scattered wave based on the transmission position and the reception position, and the measurement data of the scattered wave received by the receiving antenna element. Moreover, the image function reflects a parameter showing the correspondence between the frequency change of the electric wave and the change in the dielectric constant of the object. Therefore, when generating an image showing the inside of the object, the correspondence between the frequency change and the change in the dielectric constant can be reflected.

[0127] That is, an image showing the inside of the object can be generated with high accuracy by using the scattered wave of the electric wave.

[0128] Hereinafter, embodiments will be described with reference to the drawings. In addition, the embodiments to be described below are all general or specific examples. The numerical values, shapes, materials, constituent elements, arrangement positions and connection manners of the constituent elements, steps, and the order of steps shown in the following embodiments are all examples, and their gist is not to limit the claims.

[0129] (Embodiment)

[0130] The scatter tomography device in the present embodiment generates an image showing the inside of an object by using the scattered wave of an electric wave. Hereinafter, the scatter tomography device in the present embodiment, including the technologies and theories underlying it, will be described in detail. In addition, hereinafter, microwave mammography is mainly assumed, the electric wave uses microwaves, and the object uses a breast as an example. However, the applicable field is not limited to microwave mammography, and electric waves different from microwaves can also be used, and objects different from breasts can also be used.

[0131]

[0132] First, the frequency dependence of the dielectric constant affecting the radio waves used in the scattering tomography apparatus will be described. Maxwell's equations in electromagnetism are expressed by the following equation (1-1).

[0133] [Mathematical formula 14]

[0134]

[0135]

[0136] B=μH

[0137] D=εE

[0138] ···(1-1)

[0139] Here, E represents the electric field, B represents the magnetic flux density, t represents time, H represents the magnetic field, j represents the current, D represents the electric flux density, μ represents the magnetic permeability, and ε represents the dielectric constant. Here, the main focus is on the fluctuations (radio waves) propagating in dielectrics such as biological bodies. Therefore, although the dielectric constant changes, the value of the magnetic permeability in a vacuum is the same. Therefore, the dielectric constant, magnetic permeability, and current can be expressed by the following formula (1-2).

[0140] [Mathematical formula 15]

[0141] ε=ε0ε r

[0142] μ=μ0 (value in vacuum)

[0143] j=0

[0144] ···(1-2)

[0145] Here, ε0 represents the dielectric constant in vacuum. r = is the relative permittivity. μ0 is the magnetic permeability in a vacuum. From the above equations (1-1) and (1-2), the following equation (1-3) can be obtained.

[0146] [Formula 16]

[0147]

[0148] Next, let's consider a one-dimensional wave. Assuming the wave propagation direction is the x-axis and the electric field (E) direction is the y-axis, □·E=0 holds, resulting in equations (1-3) to (1-4).

[0149] [Mathematical formula 17]

[0150]

[0151] When the y-direction component of the electric field (E) is set to When , we can obtain the following equation (1-5) showing the wave equation for one-dimensional waves. That is, based on Maxwell's equations, we can obtain the wave equation.

[0152] [Mathematical formula 18]

[0153]

[0154] For example, the frequency band used in microwave mammography is 1 GHz to 20 GHz, taking into account resolution and transmission distance. However, within this range, water, which accounts for a large proportion of the composition of living organisms, undergoes dielectric dispersion.

[0155] Figure 1 is a graph showing the dependence of the dielectric constant on frequency, showing the Debye relaxation of water at 30°C. Figure 1 In, ε r ' represents the real part of the complex dielectric constant, ε r ” represents the imaginary part of the complex dielectric constant. As the frequency increases, the dielectric constant decreases.

[0156] Figure 2A as well as Figure 2B The dielectric dispersion in the fatty tissue of the breast is shown. Specifically, Figure 2A The relative dielectric constant of breast fat tissue for each frequency is shown. Figure 2B The effective conductivity of breast fat tissue for each frequency is shown.

[0157] For example, the dielectric constant in the 14-20 GHz range is approximately 60% of the value in the 1-5 GHz range. The frequency dependence of the dielectric constant can be expressed by the following equations (1-6), (1-7), (1-8), and (1-9) based on Debye relaxation.

[0158] [Mathematical formula 19]

[0159]

[0160] ε(0)=ε s

[0161] ε(∞)=ε ∞

[0162] ···(1-6)

[0163] [Mathematical formula 20]

[0164]

[0165]

[0166] [Mathematical formula 21]

[0167]

[0168] ω=c(ω)k

[0169] ···(1-8)

[0170] [Mathematical formula 22]

[0171]

[0172] Here, ω represents the angular frequency. ε(ω) represents the complex dielectric constant in ω. i represents the imaginary unit. τ represents the relaxation time. ε r (ω) represents the real part of the complex dielectric constant in ω. a, b, and α represent constants. c(ω) represents the propagation velocity in ω. c0 represents the propagation velocity in a vacuum. k represents the wave number. As shown in Equation (1-8), the propagation velocity depends on the dielectric constant, and the dielectric constant depends on the frequency (angular frequency). Therefore, the propagation velocity depends on the frequency (angular frequency).

[0173] When frequency is represented by f, ω=2πf holds. Solving equation (1-9) for f yields the following equation (1-10).

[0174] [Mathematical formula 23]

[0175]

[0176] When the frequency determined by ω=2πf is fixed, the wave equation is expressed by the following equation (1-11).

[0177] [Mathematical formula 24]

[0178]

[0179] Here, x, y, and z represent coordinate positions. Indicates the displacement of vibration in t, x, y, and z.

[0180] However, in the presence of dielectric dispersion, it's difficult to express fluctuations of non-constant frequency as a solution to a wave equation. This is because the motion of molecules (dipoles), which contribute to dielectric dispersion, must be considered simultaneously. For example, microwave mammography uses pulsed waves with numerous frequency components. To obtain high-precision data, a sharp pulse waveform is typically used. However, since most frequency components propagate at varying speeds, the waveform becomes flat, making it difficult to obtain high-precision data.

[0181] Therefore, Equation (1-10) that expresses the frequency f using the wave number k of space plays an important role in obtaining the solution to the inverse scattering problem in a medium with dielectric dispersion. More specifically, a, b, and α in Equation (1-7) are parameters of the Debye model, which are parameters showing the correspondence between the frequency change and the dielectric constant change. These parameters are determined in advance by measuring the dielectric constant of a specimen of the same type as the object to be inspected at each frequency.

[0182] Figure 3 It is a measuring device for measuring the dielectric constant of the excised specimen. Figure 3 The measuring device 300 shown is a device actually used to measure the dependence of the dielectric constant on the frequency, and includes a vector network analyzer 301, a computer 302, a dielectric constant measurement probe 306, etc.

[0183] The vector network analyzer 301 and the computer 302 are connected by a GPIB (General Purpose Interface Bus) cable 303. The vector network analyzer 301 and the dielectric constant measurement probe 306 are connected by a high-frequency coaxial cable 304.

[0184] For example, for the excised specimen 305 obtained during surgery, a coaxial-type dielectric constant measurement probe 306 is used for measurement. The dielectric constant measurement probe 306 is connected to the S11 port (the port for obtaining forward reflection) of the vector network analyzer 301. Data is stored in the computer 302 via the GPIB cable 303. Based on multiple excised specimens, a, b, and α in Equation (1-7) are determined. These parameters are very important in the following inversion analysis.

[0185] <Inverse Problem of Scattering in a Medium with Dielectric Dispersion>

[0186] The following describes the computational processing for generating an image showing the interior of an object using the scattered waves of radio waves. Additionally, a part of the computational processing described in Patent Document 2 or Patent Document 3 can be appropriately used.

[0187] <II-1 Multistatic Inverse Scattering Theory on a Surface>

[0188] First, as a typical example, multistatic measurements on a surface are adopted to elaborate on the inverse problem of scattering in a medium with dielectric dispersion. Here, it is assumed that an array antenna arranged on a curve with the same X coordinate scans along the surface. This assumption is a relatively realistic assumption in the application of microwave mammography.

[0189] Figure 4An example of an array antenna scanning on a curved surface and measuring scattering data is shown. Figure 4 In FIG, the array antenna 401 is a multistatic antenna including a transmitting antenna element and a receiving antenna element, and is scanned along a curved surface represented by z=f(x, y). In addition, the array antenna 401 may include multiple transmitting antenna elements or multiple receiving antenna elements.

[0190] For example, P1(x, y1, z1) represents the position of the transmitting antenna element, P2(x, y2, z2) represents the position of the receiving antenna element, and P(ξ, η, ζ) represents the position of the material that reflects microwaves. Thus, for example, microwaves are transmitted from P1(x, y1, z1), reflected by P(ξ, η, ζ), and received by P2(x, y2, z2).

[0191] Because of dielectric dispersion, ω = c(ω)k. Here, c(ω) is the propagation velocity and k is the wave number. If the wavelength is λ, then k = 2π / λ. Here, the following scattered field function is introduced:

[0192] [Mathematical formula 25]

[0193]

[0194]

[0195]

[0196] In equation (2-1), the time factor is assumed to be proportional to exp(-iωt). Furthermore, the wave number is expressed as k, and the reflectivity in P(ξ, η, ζ) is expressed as ε(ξ, η, ζ).

[0197] The scattered field function shown in formula (2-1) It can be interpreted as a function that takes as input any transmission position and any reception position on the YZ plane having the same x-coordinate and outputs the amount of scattered waves at the reception position. When the transmission position and reception position input to the scattered field function coincide with the position of the transmission antenna element and the position of the reception antenna element, respectively, the scattered field function The output is consistent with the measurement data obtained by the receiving antenna element.

[0198] Therefore, when the scattered field function is applied to t→0, x→x, y1→y2(=y), and z1→z2(=z), it can be assumed that the scattered field function represents the amount of scattered waves received immediately after transmitting radio waves at (x, y, z), that is, the amount of reflection at (x, y, z). The image function used to generate an image showing the interior of an object is derived as a function representing the following quantities, as shown below.

[0199] In the initial stage, since ε(ξ, η, ζ) is unknown, the scattered field function is unknown. In order to find the scattered field function The specific content of , thus finding the scattered field function as shown below The equation for .

[0200] First, the kernel function in the integrated term of equation (2-1) is expressed by the following equation (2-2).

[0201] [Mathematical formula 26]

[0202]

[0203] In order to obtain the scattered field function that satisfies Equation (2-1) The kernel function in equation (2-2) is obtained The partial differential equation with the solution is . Therefore, 1 / ρ can be calculated by ignoring the higher-order terms among the multiple terms generated by the differentiation. Here, the abbreviated notation of differentiation is defined as shown in the following formula (2-3).

[0204] [Mathematical formula 27]

[0205]

[0206] Kernel Function The differential results of each order can be expressed using formula (2-3) and the following formula (2-4).

[0207] [Mathematical formula 28]

[0208]

[0209]

[0210]

[0211]

[0212]

[0213]

[0214]

[0215]

[0216]

[0217]

[0218] In Equation (2-4), ρ corresponds to ρ1 and ρ2. o is the Landau symbol. If ρ is sufficiently large, then o(ρ-3) is much smaller than ρ-3. Since o(ρ-3) is sufficiently small, the cumbersome term o(ρ-3) will be omitted below. In Equation (2-4), if the sum of the five mathematical expressions related to the second-order differential is obtained, the following Equation (2-5) is obtained.

[0219] [Mathematical formula 29]

[0220]

[0221] Furthermore, the following formula (2-6) is obtained from formula (2-5).

[0222] [Mathematical formula 30]

[0223]

[0224] If the operator on the left side of formula (2-6) is applied twice, the following formula (2-7) is obtained.

[0225] [Mathematical formula 31]

[0226]

[0227] Therefore, the kernel function Satisfy the equation below (2-8).

[0228] [Mathematical formula 32]

[0229]

[0230] If we sort it out, we can get the following equation (2-9).

[0231] [Mathematical formula 33]

[0232]

[0233]

[0234] Formula (2-9) is the kernel function shown in formula (2-2) Become the equation of solution. That is, the kernel function Satisfies formula (2-9). In formula (2-9), the kernel function Can replace the scattered field function shown in formula (2-1) Therefore, Equation (2-9) is also the scattered field function shown in Equation (2-1) The solution is the scattered field function Satisfies formula (2-9).

[0235] Furthermore, since the propagation speed of radio waves varies with frequency, it is not easy to derive a time-dependent wave equation from Equation (2-9). Therefore, the pseudo-differential operator method, described later, is used to derive a time-dependent partial differential equation. In this case, the variables are substituted as shown in Equations (2-10) and (2-11).

[0236] [Mathematical formula 34]

[0237]

[0238] [Mathematical formula 35]

[0239]

[0240] By performing substitutions shown in equations (2-10) and (2-11) on equation (2-9), the following equation (2-12) is obtained as an equation for the scattered field in a medium with dielectric dispersion.

[0241] [Mathematical formula 36]

[0242]

[0243]

[0244] Equations (2-11) and (2-12) employ pseudo-differential operators, described later. Equation (2-12) is a linear partial differential equation, a fundamental equation for the scattered field in the presence of dielectric dispersion. This equation allows for the solution of a fixed-frequency solution that satisfies Equation (2-9) at multiple frequencies to be synthesized, resulting in a general time-dependent function.

[0245] It's not easy to directly solve equation (2-12). Therefore, we fix the frequency and solve the scattered field equation using equation (2-9). If the frequency is fixed, the propagation velocity is fixed, and thus a time-dependent wave equation can be obtained from equation (2-9). Specifically, the variables in equation (2-9) are replaced as shown in equation (2-13). Here, c represents the propagation velocity of the radio wave at a fixed frequency.

[0246] [Mathematical formula 37]

[0247]

[0248] Through the above substitution, equation (2-14) can be obtained as a time-dependent wave equation at a fixed frequency.

[0249] [Mathematical formula 38]

[0250]

[0251] For each wave number k, we solve equation (2-9), and then for equation (2-14) derived from equation (2-9), As shown in the following formula (2-15), multiple Fourier transform is performed on t, x, y1, and y2.

[0252] [Mathematical formula 39]

[0253]

[0254] If the replacement And write D z1 、D z2 , then from equations (2-14) and (2-15) we get the following equation (2-16).

[0255] [Mathematical formula 40]

[0256]

[0257] The basic solution of formula (2-16) is expressed as the following formula (2-17).

[0258] [Mathematical formula 41]

[0259]

[0260] Here, s1 and s2 are functions determined as shown in the following formula (2-18).

[0261] [Mathematical formula 42]

[0262]

[0263]

[0264] Using s1(k x 、k y1 、k y2 ) and s2(k x 、k y1 、k y2 ), the solution of equation (2-9) for each wave number k can be expressed as the following equation (2-19).

[0265] [Mathematical formula 43]

[0266]

[0267] Next, for the function a(k x , k y1 , k y2, k) establish association with measurement data.

[0268] Figure 5 This is a schematic diagram showing the relationship between the position of the transmitting antenna element, the position of the receiving antenna element, and the position of the material. For example, microwaves are transmitted from P, which is the position of the transmitting antenna element. I (x, y I 、z J ) is transmitted, reflected at P(ξ, η, ζ) which is the position of the material, and P which is the position of the receiving antenna element J (x, y J 、z J ) is received. Figure 5 The cross-sectional curve S shown represents Figure 4 The yz cross section of the scanning plane of the array antenna 401 in .

[0269] The equation of the cross-sectional curve S with x fixed is assumed to be, for example, the following equation (2-20). Figure 4 The scanning plane of the array antenna 401 shown is not curved in the x-direction, and the yz cross section of the scanning plane can be assumed by the following equation.

[0270] [Mathematical formula 44]

[0271] z=f(y)

[0272] ···(2-20)

[0273] If it is possible to obtain The value of , then the following differential equation (2-21) can be obtained from equation (2-19).

[0274] [Mathematical formula 45]

[0275]

[0276] Next, find the solution of differential equation (2-21). I 、P J measured The function Φ(kx, y after Fourier transformation I ,y J , k), can be expressed as the following formula (2-22).

[0277] [Mathematical formula 46]

[0278]

[0279] Here, due to z I 、z J On the cross-sectional curve, the following formula (2-23) holds true.

[0280] [Mathematical formula 47]

[0281] z I =f(y I )

[0282] z J =f(z J )

[0283] ···(2-23)

[0284] The following formula (2-24) is obtained from the combination of formula (2-21), formula (2-22) and formula (2-23).

[0285] [Mathematical formula 48]

[0286]

[0287] If we focus on the Y coordinate of the transmitting antenna element, y I , and the Y coordinate of the receiving antenna element, y J , then the formula (2-24) can be transformed into the following formula (2-25). Here, (x, y I , z I )、(x,y J , z J ) is the position of the measurement point in the reference orthogonal coordinate system (the position of the transmitting antenna element and the receiving antenna element), and δ represents the δ function.

[0288] [Mathematical formula 49]

[0289]

[0290] If Fourier transform is performed on both sides of equation (2-25), the following equation (2-26) is obtained.

[0291] [Mathematical formula 50]

[0292]

[0293] As a result of differentiation, equation (2-27) is obtained.

[0294] [Mathematical formula 51]

[0295]

[0296] According to formula (2-27), a I，J It can be calculated by the following formula (2-28).

[0297] [Mathematical formula 52]

[0298]

[0299] For all I and J, if we calculate the sum of formula (2-28), we get the following formula (2-29).

[0300] [Mathematical formula 53]

[0301]

[0302] The relationships expressed in equations (2-19) and (2-29) can be obtained as solutions to equation (2-9). In other words, the relationships expressed in equations (2-19) and (2-29) satisfy equation (2-9) and are solutions to equation (2-9). Although k is used in equation (2-19), k can be converted to ω based on equation (1-9).

[0303] By applying t→0, x→x, y1→y2(=y), and z1→z2(=z) to the relationships expressed in Equations (2-19) and (2-29), a function representing the amount of scattered waves received immediately after radio wave transmission is obtained. The following Equation (2-30) corresponds to this function. The reconstructed image is obtained by integrating Equation (2-30) with respect to k or ω.

[0304] [Mathematical formula 54]

[0305]

[0306] Therefore, as shown in the following formula (2-31), the import becomes k z In addition, the following formula (2-31) also shows the variable k z To express the mathematical formula of k and k z The function differentiated with respect to k.

[0307] [Mathematical formula 55]

[0308]

[0309]

[0310]

[0311] According to formula (1-10), the relationship between wave number k and frequency ω is given by the following formulas (2-32) and (2-33).

[0312] [Mathematical formula 56]

[0313]

[0314] [Mathematical formula 57]

[0315]

[0316] a(k x ,k y1 ,k y2 ,k) in the definition includes measurement data Φ(k x ,y I ,y J ,k) is not given by k but by ω. Therefore, the above k-ω transformation is required. Accordingly, the dielectric dispersion is expressed by Equation (1-9). The reconstructed image obtained by integrating Equation (2-30) with respect to ω is derived as shown in Equation (2-34) below. Equation (2-34) below is also expressed as an image function for generating the reconstructed image.

[0317] [Mathematical formula 58]

[0318]

[0319] If the variables of the integrand in Equation (2-34) are summarized, these variables are expressed by Equation (2-35) below.

[0320] [Mathematical formula 59]

[0321]

[0322]

[0323]

[0324]

[0325]

[0326] The above is the detailed content of the reconstruction theory for measuring scattering data on a surface and obtaining a three-dimensional image inside the region.

[0327] <II-2 Monostatic Inverse Scattering Theory on a Surface>

[0328] Figure 6 An example of a monostatic antenna scanning on a surface and measuring scattering data is shown. In this example, the monostatic antenna 601 combines the transmitting antenna element and the receiving antenna element and scans along the surface. Also, it is assumed that the transmitting antenna element and the receiving antenna element of the monostatic antenna 601 are located at the same point. That is, the monostatic antenna 601 transmits and receives at the same point.

[0329] Monostatic antenna 601 scans along the curve in the x-axis direction, then shifts in the y-axis direction and scans again along the curve in the x-axis direction. By repeating this process, monostatic antenna 601 scans along the curved surface. As an example, data is acquired on a straight line in the y-axis direction and on the curve z = f(x) in the x-axis direction. Thus, the boundary conditions are given on the curved surface.

[0330] The above theory about the array antenna 401 is basically applicable to the monostatic antenna 601. However, since the monostatic antenna 601 transmits and receives at the same point, the calculation formula is different.

[0331] Figure 7 This is a schematic diagram showing the relationship between the transmission and reception positions and the positions of substances. Figure 7 The cross-sectional curve S shown represents Figure 6 The xz cross section of the scanning plane of the monostatic antenna 601 in the image is shown in FIG. The monostatic antenna 601 scans in the x-axis direction along the curve S determined by z = f(x). In other words, the position where transmission and reception are performed is the position of the measurement point P. I (x I ,y,z I ) moves on the cross-sectional curve S.

[0332] Consider a point P on the curve S I radiate, and after reflection at point P, it is reflected again by point P I For example, microwaves from P I (x I ,y,z I ) radiates, reflects at P(ξ, η, ζ), and I (x I ,y,z I ) is received. The scattered field function showing the scattered intensity It can be written as the following formula (3-1).

[0333] [Mathematical formula 60]

[0334]

[0335]

[0336] Furthermore, the scattered field function of the formula (3-1) satisfies the equation expressed by the following formula (3-2). That is, the scattered field function of the formula (3-1) satisfies the following formula (3-2).

[0337] [Mathematical formula 61]

[0338]

[0339] The relationship between k and ω is given by the following formula (3-3).

[0340] [Mathematical formula 62]

[0341]

[0342] The equation of the time-dependent scattered field is expressed by the following equation (3-4).

[0343] [Mathematical formula 63]

[0344]

[0345] The general solution of the scattered field equation with a fixed frequency is given by the following equation (3-5). x It is about the scattered field function The wave number of x, k y It is about the scattered field function The wave number of y.

[0346] [Mathematical formula 64]

[0347]

[0348] The equation of the curved surface corresponding to the scanning surface is expressed by the following equation (3-6).

[0349] [Mathematical formula 65]

[0350] z=f(x)

[0351] ···(3-6)

[0352] Here, a(k x , k y , k) is obtained by using the measured values ​​on the surface as boundary conditions using the following formula (3-7).

[0353] [Mathematical formula 66]

[0354]

[0355] Here,

[0356] [Mathematical formula 67]

[0357]

[0358] is x I 、k y and the measured values ​​of the scattering data in k.

[0359] When Φ(x, y, ω) is Fourier imaging of the scattering data with respect to time, an imaging function expressed by the following equation (3-8) can be obtained.

[0360] [Mathematical formula 68]

[0361]

[0362] Here, there is a relationship of the following formula (3-9). The dispersion of the dielectric constant occurs when ω and k are correlated.

[0363] [Mathematical formula 69]

[0364]

[0365]

[0366]

[0367]

[0368]

[0369] <Summary of the III UWB microwave radar device>

[0370] Next, the summary of the system of the multistatic array radar will be described.

[0371] Figure 8 The overall system configuration of the multistatic array radar is shown.

[0372] The microwave signal is a pseudo-random code sequence signal (PN code: PseudoNoise Code) having frequency components from DC to 20 GHz. This signal is output from the FPGA board 1002 for PN code generation. More specifically, there are two such signals. One of the signals (LO signal: local oscillator signal) is sent to the RF detection circuit (RF detection board 1007) through the delay circuit (digital control board 1003). <I

[0373] The other signal (RF signal: Radio Frequency Signal) is sent to the transmitting microwave UWB antenna of the multistatic array antenna 1008 and is radiated. The scattered microwave signal is received by the receiving UWB antenna of the multistatic array antenna 1008 and is sent to the RF detection circuit (RF detection board 1007). Here, the transceiver signals pass through the antenna element selection switch (UWB antenna RF switch 1004).

[0374] [[ID=II0001032]]And the delayed signal (LO signal) changes at 1 / 2 of the time when the value of each PN code changes nThe detected signal is delayed by a time factor of 1 (n is an integer greater than 2). The detected signal is converted into an IF signal (Intermediate Frequency Signal) and stored in the signal processing computer 1005. Information indicating the detected signal can also be displayed on the signal monitoring device 1006.

[0375] The timing of this series of operations is controlled by the microprocessor in the digital control board 1003 in synchronization with the signal (distance signal or free oscillation signal) from the rangefinder 1001. For example, the microprocessor in the digital control board 1003 sends switch switching signals and PN code scanning triggers.

[0376] The signal processing computer 1005 then uses the A / D-converted and stored signals to perform three-dimensional reconstruction and display a three-dimensional image. Furthermore, the signal processing computer 1005 can perform signal correction and display the original waveform.

[0377] Next, the UWB antenna will be described.

[0378] Figure 9 Array antennas are arranged in a row on a straight line or a curve. Figure 9 In , the array antenna is a linear array antenna having n+1 antenna elements arranged on a line, and among the n+1 antenna elements, one is a transmitting antenna and n are receiving antennas. Figure 9 In FIG. 1 , one antenna element for transmission is labeled with a T, and n antenna elements for reception are labeled with R ( R1 , R2 , . . . Rn).

[0379] exist Figure 9 In the figure, the portion marked with an A corresponds to the radio wave absorbing element. By placing the radio wave absorbing element between the transmitting and receiving antenna elements, UWB antenna performance is improved. T and R can be interchanged, meaning that n of the n+1 antenna elements can be used for transmission and one for reception. Even with T and R interchanged, equivalent scattering data can be obtained.

[0380] The value of n can be changed depending on the object being inspected. The scanning direction is the direction of the arrow in the diagram. For example, projecting onto the plane z = 0, the direction in which the multiple antenna elements constituting the array antenna are arranged is defined as the y-axis direction, and the scanning direction is defined as the x-axis direction. In this case, the lines scanned by the array antenna are gradually offset (for example, by shifting in the y-axis direction by half the size of the antenna element) to measure scattering data. Although this requires measurement time, it can improve resolution.

[0381] Figure 10 Shown by Figure 9 The scanning method performed by the array antenna in the embodiment of the present invention is as follows: Figure 10 The array antenna in FIG includes one transmitting antenna element and three receiving antenna elements. The array antenna scans by shifting the scan line 1, scan line 2, scan line 3, ..., scan line n in the y-axis direction by half the size of the antenna element.

[0382] Figure 11 Shown Figure 10 The measurement points in the scanning method shown. Specifically, by shifting the scan line of an array antenna consisting of one transmitting antenna element and three receiving antenna elements in the y direction by half the size of each antenna element, the Y coordinates of the transmission and reception positions where scattered data was measured are represented by diagonal lines. The Y coordinate of the transmission position is represented by y1, and the Y coordinate of the reception position is represented by y2.

[0383] The length of one side of a block corresponds to 1 / 2 the size of the antenna element. The values ​​of y1 and y2 are expressed in units of 1 / 2 the size of the antenna element. Therefore, for example, if the Y coordinate of the transmitting antenna element is 1, the Y coordinates of the three receiving antenna elements are 5, 7, and 9. Similarly, if the Y coordinate of the transmitting antenna element is 2, the Y coordinates of the three receiving antenna elements are 6, 8, and 10.

[0384] Furthermore, even if the positions of the transmitting and receiving antenna elements are swapped, the same scattering data is obtained. Therefore, the matrix (y1, y2) is symmetrical. Measurement points are also embedded to the left of the diagonal. The resulting scattering data is used for image reconstruction.

[0385] Figure 12 This is an example of realizing a monostatic antenna capable of measuring radio waves in both of two orthogonal polarization directions.

[0386] exist Figure 12 In the figure, a common radio wave absorbing member, labeled A, is placed between the transmitting antenna element labeled T1 and the receiving antenna element labeled R1, and between the transmitting antenna element labeled T2 and the receiving antenna element labeled R2. Therefore, the combination of T1 and R1, and the combination of T2 and R2, were used for scattering data measurement.

[0387] The above configuration enables measurement of scattering data corresponding to two polarization directions. For example, information about substances that react to a specific polarization direction can be obtained. This configuration also enables the realization of a monostatic antenna with a one-to-one correspondence between multiple transmitting antenna elements and multiple receiving antenna elements.

[0388] In addition, the scanning direction can correspond to two orthogonal directions as shown by the arrows in the figure.

[0389] <IV Pseudo-differential operator>

[0390] Next, the pseudo-differential operator in the theory of partial differential equations will be described. Functions in the n-dimensional Euclidean space R n are used here. Therefore, the notation shown in the following formula (4-1) is adopted.

[0391] [Mathematical formula 70]

[0392] x = (x1, x2,..., x n )

[0393] y = (y1, y2,..., y n )

[0394] ξ = (ξ1, ξ2,..., ξ n )

[0395] α = (α1, α2,..., α n )<00杯1085>

[0396]

[0397] Assume the linear differential operator with constant coefficients as shown in the following formula (4-2).

[0398] [Mathematical formula 71]

[0399]

[0400] By applying the linear differential operator of formula (4-2) to the smooth function u with compact support on R n , formula (4-3) is obtained. [[ID=杯2]]

[0401] [[ID=5杯]][Mathematical formula 72]

[0402]

[0403] If formula (4-3) is Fourier-transformed, it becomes well-known that it is a simple multiplication operation by a polynomial called the symbol.

[0404] The following formula (4-4) shows this polynomial.

[0405] [Mathematical formula 73]

[0406]

[0407] If the inverse Fourier transform of formula (4-4) is performed, formula (4-5) is obtained.

[0408] [Mathematical formula 74]

[0409]

[0410] By generalizing Formula (4-5), an operator P(x, D) applicable even to a general polynomial including x in symbol can be defined as shown in the following Formula (4-6).

[0411] [Mathematical formula 75]

[0412]

[0413] P(x, D) in equation (4-6) is called a pseudo differential operator. Furthermore, the partial differential equation represented by equation (4-7) below is solved for u(x).

[0414] [Mathematical formula 76]

[0415] P1(D)u(x)=P2(D)f(x)

[0416] ···(4-7)

[0417] If Fourier transform is performed on both sides of equation (4-7), the following equation (4-8) is obtained.

[0418] [Mathematical formula 77]

[0419]

[0420] From formula (4-8), we can obtain the relationship shown in formula (4-9).

[0421] [Mathematical formula 78]

[0422]

[0423] If the inverse Fourier transform of equation (4-9) is written, it can be expressed as the following equation (4-10).

[0424] [Mathematical formula 79]

[0425]

[0426] P(D) in formula (4-10) is also a pseudo-differential operator and can be described as shown in the following formula (4-11).

[0427] [Mathematical formula 80]

[0428]

[0429] As described above, concepts such as rational polynomials and non-integer exponentiation of ordinary differential operators can be introduced through pseudo differential operators.

[0430] <Simulation of Dielectric Dispersion>

[0431] Next, simulations related to the effects of dielectric dispersion are shown.

[0432] <Wave Equation in a V-1 Dispersive Medium>

[0433] In the simulation, the case where the dispersion of the medium is described by the Debye model is considered.

[0434] The case of a single station is taken as the object for simulation. The propagation of electromagnetic waves (radio waves) in a one-dimensional space with dispersion in the dielectric constant can be described by the pseudo-differential equation shown in the following equation (5-1).

[0435] [Mathematical Formula 81]

[0436]

[0437] Here, c0 is the speed of electromagnetic waves (radio waves) in vacuum. Regarding the factor 4 of the term for time differentiation, in the case of considering single-station inverse scattering, it passes through the same path for the wave twice.

[0438] Figure 13 The relationship between the relative dielectric constant and the frequency in the case of large dielectric dispersion is shown. Figure 13 The relationship between the relative dielectric constant and the frequency shown is based on a = 1, b = 7, and α = 0.0001.

[0439] Figure 14A 、 Figure 14B 、 Figure 14C 、 Figure 14D and <000119​​​​​​​​​​​​​​​​​​​​​​​​​The relationship between wave number k and angular frequency ω is given by the following formula (6-2).

[0445] [Mathematical formula 83]

[0446]

[0447] The following shows what happens when an inversion analysis is performed, ignoring dielectric dispersion, based on the results of emitting radio waves and measuring scattered data in a medium with dielectric dispersion.

[0448] Figure 15 The calculation model is shown. The analysis target model included in the calculation model is three points separated by 0.8 cm on a plane with a depth of 1 cm in 3D space. In this calculation model, the number of measurement points in the x-axis direction is NX = 128, the number of measurement points in the y-axis direction is NY = 64, the interval between the measurement points in the x-axis direction is dx = 0.1 cm, and the interval between the measurement points in the y-axis direction is dy = 0.1 cm.

[0449] Figure 16A is an XY plane diagram at z (depth) = 1 cm showing the results of the simulation of the first example, Figure 16B : is a perspective view showing the results of the simulation of the first example. Specifically, Figure 16A as well as Figure 16B The simulation results are shown when the relative permittivity is 7.5 at 5 GHz and 5.0 at 14 GHz.

[0450] Figure 17A is an XY plane diagram at z (depth) = 1 cm showing the results of the simulation of the second example, Figure 17B : is a perspective view showing the results of the simulation of the second example. Specifically, Figure 17A as well as Figure 17B The simulation results are shown when the relative permittivity is 6.5 at 5 GHz and when the relative permittivity is 5.5 at 14 GHz.

[0451] Figure 18A is an XY plane diagram at z (depth) = 1 cm showing the results of the simulation of the third example, Figure 18B : is a perspective view showing the results of the simulation of the third example. Specifically, Figure 18A as well as Figure 18B The simulation results are shown when the relative permittivity is 6 at 5 GHz and when the relative permittivity is 6 at 14 GHz.

[0452] The simulation results for the third example correspond to the results of backscattering analysis in a medium without dielectric dispersion. The results of dielectric constant measurements of normal biological tissue (breast) are close to the dispersion observed in the second example. Ignoring dielectric dispersion significantly reduces image resolution.

[0453] The above analysis corresponds to the single - station scattered field analysis. However, the same content can also be applied to the multi - station scattered field analysis. Therefore, it is important to consider dielectric dispersion in the scattered field analysis.

[0454] <VI Summary>

[0455] Based on the above content, the composition and operation of a scatter tomography device that uses the scattered waves of radio waves to generate an image showing the interior of an object will be briefly described below.

[0456] Figure 19 This is the basic configuration diagram of the scatter tomography device in this embodiment. Figure 19 The shown scatter tomography device 100 includes a transmitting antenna element 101, a receiving antenna element 102, and an information processing circuit 103.

[0457] The transmitting antenna element 101 is a circuit that transmits radio waves. Specifically, the transmitting antenna element 101 transmits radio waves from the outside of the object to the inside of the object. The radio waves can be microwaves, millimeter waves, terahertz waves, etc. The object can be a living body, a manufactured object, or a natural material, etc. In particular, the object can be a breast. The scatter tomography device 100 can also include multiple transmitting antenna elements 101.

[0458] The receiving antenna element 102 is a circuit that receives radio waves such as scattered waves of radio waves. Specifically, the receiving antenna element 102 receives the scattered waves of the radio waves transmitted to the inside of the object outside the object. The scatter tomography device 100 can also include multiple receiving antenna elements 102. And, the receiving antenna element 102 can be substantially arranged at the same position as the transmitting antenna element 101, or can be arranged at a position different from the transmitting antenna element 101.

[0459] Moreover, the transmitting antenna element 101 and the receiving antenna element 102 can form a multi - station antenna or a single - station antenna.

[0460] The information processing circuit 103 is a circuit that performs information processing. Specifically, the information processing circuit 103 uses the measurement data showing the scattered waves received by the receiving antenna element 102 to generate an image showing the interior of the object. The information processing circuit 103 can be a computer or a processor of a computer. The information processing circuit 103 can read a program from a memory and perform information processing by executing the program. And, the information processing circuit 103 can also be a dedicated circuit that uses the measurement data to generate an image showing the interior of the object.

[0461] For example, the information processing circuit 103 can be connected to Figure 8Specifically, for example, the information processing circuit 103 may correspond to the signal processing computer 1005. Furthermore, the information processing circuit 103 may display the generated image on a display device such as a liquid crystal display device.

[0462] Figure 20 It shows Figure 19 The flowchart of the basic operation of the scattering tomography apparatus 100 is shown in FIG. Figure 19 The scattering tomography apparatus 100 shown in FIG. 1 is provided with a transmitting antenna element 101, a receiving antenna element 102, and an information processing circuit 103. Figure 20 Work shown.

[0463] First, transmitting antenna element 101 transmits radio waves from the outside of an object to its interior (S201). Next, receiving antenna element 102 receives scattered waves from the outside of the object, which were transmitted toward the interior of the object (S202). Information processing circuit 103 then generates an image showing the interior of the object using measurement data representing the scattered waves received by receiving antenna element 102 (S203).

[0464] When the information processing circuit 103 generates an image using the measurement data, it first uses the measurement data to derive a relationship that satisfies an equation whose solution is a scattered field function. The scattered field function is a function that takes as input the transmission position of a radio wave and the reception position of the scattered wave, and outputs the amount of scattered waves at the reception position. In other words, the scattered field function is a function that indicates the amount of scattered waves at the reception position for arbitrarily determined transmission and reception positions.

[0465] The information processing circuit 103 then uses the derived relationship to derive an image function. The image function is a function used to generate an image and is a function that reflects parameters that indicate the relationship between changes in the frequency of radio waves and changes in the dielectric constant of an object based on Debye relaxation. The information processing circuit 103 then uses the image function to generate an image showing the interior of the object.

[0466] Thus, the scattering tomography apparatus 100 can derive a relational expression for deriving an image function based on a scattered field function representing the amount of scattered waves at the transmission and reception positions, and measurement data of scattered waves received by the receiving antenna element 102. Furthermore, the image function reflects a parameter representing the correspondence between changes in the frequency of radio waves and changes in the dielectric constant of an object. Therefore, the scattering tomography apparatus 100 can reflect this correspondence between changes in frequency and changes in dielectric constant when generating an image representing the interior of an object.

[0467] That is, the scattering tomography apparatus 100 can generate an image showing the interior of an object with high precision using scattered waves of radio waves.

[0468] For example, the components, mathematical expressions, and variables described in this embodiment can be appropriately applied to the transmitting antenna element 101, receiving antenna element 102, information processing circuit 103, scattered field functions, equations, relationships, image functions, and parameters shown in the above-described basic configuration and basic operation.

[0469] Furthermore, the scattered field functions, equations, relationships, and image functions described in this embodiment may be modified as appropriate for application. For example, for substantially the same content as the above-described mathematical formula, a mathematical formula expressed in another manner may be used, or another mathematical formula derived based on the above-described theory may be used.

[0470] Furthermore, for example, radio waves have multiple frequency components and may or may not be pulse waves.

[0471] (Replenish)

[0472] The above description of the form of a scattering tomography apparatus is based on the embodiments. However, the form of the scattering tomography apparatus is not limited to the embodiments. The embodiments may be modified as would be conceivable to those skilled in the art, and the various components of the embodiments may be arbitrarily combined. For example, in the embodiments, a process performed by a specific component may be replaced by another component. Furthermore, the order of multiple processes may be changed, and multiple processes may be performed in parallel.

[0473] Furthermore, the scattering tomography method, including the steps executed by the various components of the scattering tomography apparatus, can be performed by any device or system. For example, part or all of the scattering tomography method can be performed by a computer equipped with a processor, memory, and input / output circuits. In this case, the scattering tomography method is performed by executing a program on the computer that causes the computer to execute the scattering tomography method.

[0474] Furthermore, the above-mentioned program can be recorded on a non-transitory computer-readable recording medium.

[0475] Furthermore, the various components of the scattering tomography apparatus may be comprised of dedicated hardware, general-purpose hardware that executes the aforementioned programs, or a combination of these hardware components. Furthermore, the general-purpose hardware may be comprised of a memory storing programs and a general-purpose processor that reads and executes the programs from the memory. The memory may be a semiconductor memory or a hard disk, and the general-purpose processor may be a CPU.

[0476] Furthermore, the dedicated hardware may be composed of a memory and a dedicated processor, etc. For example, the dedicated processor may refer to the memory for recording measurement data to execute the above-mentioned scattering tomography method.

[0477] Furthermore, each component of the scattering tomography apparatus may be a circuit. These circuits may constitute a single circuit as a whole, or may constitute individual circuits. Furthermore, these circuits may correspond to dedicated hardware or general-purpose hardware that executes the aforementioned program, etc.

[0478] One aspect of the present invention can be effectively applied to a scattering tomography apparatus that generates an image showing the interior of an object using scattered radio waves, and can be applied to physical exploration, medical diagnosis, and the like.

[0479] Explanation of symbols

[0480] 100 Scattering Tomography Device

[0481] 101 Transmitting Antenna Element

[0482] 102 receiving antenna elements

[0483] 103 Information Processing Circuit

[0484] 300 measuring devices

[0485] 301 Vector Network Analyzer

[0486] 302 Computer

[0487] 303 GPIB cable

[0488] 304 high frequency coaxial cable

[0489] 305 Removal of specimen

[0490] 306 Dielectric Constant Measurement Probe

[0491] 401 Array Antenna

[0492] 601 Monostatic Antenna

[0493] 1001 Rangefinder

[0494] 1002 PN code generation FPGA substrate

[0495] 1003 Digital Control Board

[0496] 1004 UWB Antenna RF Switch

[0497] 1005 Signal Processing Computer

[0498] 1006 Signal Monitoring Device

[0499] 1007 RF detection substrate

[0500] 1008 Multistatic Array Antenna

Claims

1. A scattering tomography device, The scattering tomography imaging device comprises: a transmitting antenna element for transmitting radio waves from the outside of the object to the inside of the object; a receiving antenna element that receives, outside the object, a scattered wave of the radio wave transmitted to the inside of the object; and an information processing circuit that generates an image showing the interior of the object using measurement data showing the scattered waves received by the receiving antenna element, the information processing circuit, deriving a relational expression satisfying an equation having a scattered field function as a solution, using the measurement data, in which a transmission position of the radio wave and a reception position of the scattered wave are input and an amount of the scattered wave at the reception position is output, An image function for generating the image is derived using the relationship, wherein the image function is a function reflecting a parameter showing the correspondence between a change in the frequency of the radio wave and a change in the dielectric constant of the object according to Debye relaxation, the parameter being determined by measuring the dielectric constant of a sample of the same type as the object at each frequency. The image is generated using the image function.

2. The scattering tomography apparatus according to claim 1, In a three-dimensional space composed of X coordinates, Y coordinates, and Z coordinates, the X coordinate of the arrangement position of the transmitting antenna element is the same as the X coordinate of the arrangement position of the receiving antenna element. The scattered field function is determined by [Formula 1], [Mathematical formula 1] x represents the X coordinate of the sending position and the receiving position, y1 represents the Y coordinate of the sending position, y2 represents the Y coordinate of the receiving position, z1 represents the Z coordinate of the sending position, z2 represents the Z coordinate of the receiving position, ω represents the angular frequency of the radio wave, D represents the region including the material that causes the scattered wave to be generated by reflecting the radio wave, ξ represents the X coordinate of the position within the region, η represents the Y coordinate of the position within the region, ζ represents the Z coordinate of the position within the region, ε(ξ, η, ζ) represents the reflectivity, i represents the imaginary unit, and k represents the wave number of the radio wave.

3. The scattering tomography apparatus according to claim 2, The correspondence between the change in the frequency of the radio wave and the change in the dielectric constant of the object is expressed by [Equation 2] to [Equation 5] according to Debye relaxation. [Mathematical formula 2] e(0)=e s ε(∞)=ε ∞ [Mathematical formula 3] [Formula 4] ω=c(ω)k [Formula 5] ε(ω) represents the complex dielectric constant in ω, τ represents the relaxation time, and ε r (ω) represents the real part of the complex dielectric constant in ω, a, b, and α represent the parameters, c(ω) represents the propagation velocity in ω, and c0 represents the propagation velocity in vacuum.

4. The scattering tomography apparatus according to claim 3, The equation is determined by [Mathematical Formula 6], [Formula 6] 5. The scattering tomography apparatus according to claim 4, The relationship is determined by [Mathematical Formula 7], [Formula 7] k x represents the wave number of x with respect to the scattered field function, k y1 represents the wave number of y1 with respect to the scattered field function, k y2 represents the wave number of y2 with respect to the scattered field function, s1(k x , k y1 , k y2 ) and s2(k x , k y1 , k y2 ) is determined by [Mathematical Formula 8], [Formula 8] a(k x , k y1 , k y2 , k) is determined by [Mathematical Formula 9], [Formula 9] I represents the index of the transmitting position where the transmitting antenna element is located, J represents the index of the receiving position where the receiving antenna element is located, and y I represents the Y coordinate of the transmitting position where the transmitting antenna element is located, y J represents the Y coordinate of the receiving position where the receiving antenna element is located, and Z I represents the Z coordinate of the transmitting position where the transmitting antenna element is located, Z J represents the Z coordinate of the receiving position where the receiving antenna element is located, a I，J (k x , k y1 , k y2 , k) represents k x 、k y1 、k y2 and the coefficients determined by the measurement data in k, Φ(k x ,y I ,y J , k) represents k x 、y I 、y J and the measurement data in k.

6. The scattering tomography apparatus according to claim 5, The image function is determined by [Mathematical Formula 10], [Formula 10] The x of the image function represents the X coordinate of the image, the y of the image function represents the Y coordinate of the image, and the z of the image function represents the Z coordinate of the image. The variables included in the integrand of the image function are determined by [Mathematical Formula 11], [Formula 11] 7. The scattering tomography apparatus according to any one of claims 1 to 6, The information processing circuit generates the image by utilizing the measurement data obtained at the configuration positions of the transmitting antenna element and the receiving antenna element as data obtained by alternating the configuration positions of the transmitting antenna element and the receiving antenna element.

8. The scattering tomography apparatus according to any one of claims 1 to 6, The scattering tomography apparatus includes a plurality of the receiving antenna elements. The information processing circuit generates the image using the measurement data indicating the scattered waves received by each of the plurality of receiving antenna elements included in the scattering tomography apparatus.

9. The scattering tomography apparatus according to claim 8, The transmitting antenna element and the plurality of receiving antenna elements are arranged in a row, The transmitting antenna element is located at an end of the row formed by the transmitting antenna element and the plurality of receiving antenna elements. A radio wave absorbing member is arranged between the transmitting antenna element and the plurality of receiving antenna elements.

10. The scattering tomography apparatus according to claim 1, In a three-dimensional space consisting of X coordinates, Y coordinates, and Z coordinates, the X coordinates, Y coordinates, and Z coordinates of the configuration position of the transmitting antenna element are respectively the same as the X coordinates, Y coordinates, and Z coordinates of the configuration position of the receiving antenna element. The scattered field function is determined by [Equation 12], [Mathematical formula 12] x represents the X coordinate of the sending position and the receiving position, y represents the Y coordinate of the sending position and the receiving position, z represents the Z coordinate of the sending position and the receiving position, D represents the region including the material that generates the scattered wave by reflecting the radio wave, ξ represents the X coordinate of the position within the region, η represents the Y coordinate of the position within the region, ζ represents the Z coordinate of the position within the region, ε(ξ, η, ζ) represents the reflectivity, i represents the imaginary unit, and k represents the wave number of the radio wave.

11. The scattering tomography apparatus according to claim 10, The equation is determined by [Mathematical Formula 13], [Mathematical formula 13] 12. The scattering tomography apparatus according to claim 11, The relationship is determined by [Mathematical Formula 14], [Mathematical formula 14] k x represents the wave number of x with respect to the scattered field function, k y represents the wave number of y with respect to the scattered field function, a(k x , k y , k) is determined by [Mathematical Formula 15], [Mathematical formula 15] I represents the index of the transmitting position and the receiving position where the transmitting antenna element and the receiving antenna element are located, and x I represents the X coordinates of the transmitting position and the receiving position where the transmitting antenna element and the receiving antenna element are located, z I and f(x I ) represents the Z coordinates of the transmitting position and the receiving position where the transmitting antenna element and the receiving antenna element are located, [Formula 16] Represents x I 、k y and the measurement data in k.

13. The scattering tomography apparatus according to claim 12, The image function is determined by [Equation 17], [Mathematical formula 17] The x of the image function represents the X coordinate of the image, the y of the image function represents the Y coordinate of the image, and the z of the image function represents the Z coordinate of the image. The variables included in the integrand of the image function are determined by [Mathematical Formula 18], [Mathematical formula 18] c0 represents the propagation speed of the radio wave in a vacuum, and a, b, and α represent the parameters.

14. The scattering tomography apparatus according to claim 1, The scattering tomography apparatus includes a plurality of the transmitting antenna elements and a plurality of the receiving antenna elements. The plurality of transmitting antenna elements provided in the scattering tomography apparatus correspond to the plurality of polarization directions of the radio waves, respectively. The plurality of receiving antenna elements included in the scattering tomography apparatus correspond to the plurality of polarization directions of the radio waves, respectively.

15. The scattering tomography apparatus according to any one of claims 1 to 6, The electric wave is a pulse wave.

16. A scattering tomography method, The scattering tomography method comprises the following steps: a step of transmitting radio waves from the outside of the object to the inside of the object through a transmitting antenna element; a step of receiving, outside the object, a scattered wave of the radio wave transmitted to the inside of the object by a receiving antenna element; and a step of generating an image showing the interior of the object using measurement data showing the scattered waves received by the receiving antenna elements, In the step of generating the image, deriving a relational expression satisfying an equation having a scattered field function as a solution, using the measurement data, in which the transmission position of the radio wave and the reception position of the scattered wave are input and the amount of the scattered wave at the reception position is output, An image function for generating the image is derived using the relationship, wherein the image function is a function reflecting a parameter showing the correspondence between a change in the frequency of the radio wave and a change in the dielectric constant of the object according to Debye relaxation, the parameter being determined by measuring the dielectric constant of a sample of the same type as the object at each frequency. The image is generated using the image function.

Images