Visualization device and imaging method

Abstract

This video-capturing device (100) comprises: a transmitter row (101) including a plurality of transmitters (111) arranged on a straight line, the plurality of transmitters (111) transmitting waves to a region; a receiver row (102) including a plurality of receivers (112) arranged on a separate straight line parallel to the straight line on which the plurality of transmitters (111) are arranged, the plurality of receivers (112) receiving the waves from the region, and the receiver row (102) being provided with a gap from the transmitter row (101); and an information processing circuit (103) for deriving a video-forming function that corresponds to a scattering location function relating to scattering of the waves in accordance with measurement data obtained by combining some or all of the plurality of transmitters (111) and plurality of receivers (112) and with the distance between the straight line on which the plurality of transmitters (111) are arranged and the straight line on which the plurality of receivers (112) are arranged, and visualizing the structure of a scatterer included among objects within the region by using the video-forming function.

Description

[Technical Field]

[0001] The present disclosure relates to an imaging device and the like that uses waves to visualize the structure of scatterers contained in objects within a region. [Background technology]

[0002] Patent Documents 1, 2, 3, 4 and 5 disclose techniques relating to imaging devices that use waves to visualize the structure of scattering bodies contained in objects within a region.

[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 the amplitude and phase of the scattered beam are detected by a microwave detector. Then, the distribution of dielectric constant is calculated from the output signal of the microwave detector, and a cross-sectional image of the object to be inspected is displayed. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Japanese Patent Application Publication No. 62-66145 [Patent Document 2] International Publication No. 2014 / 125815 [Patent Document 3] International Publication No. 2015 / 136936 [Patent Document 4] International Publication No. 2021 / 020387 [Patent Document 5] International Publication No. 2021 / 053971 Summary of the Invention [Problem to be solved by the invention]

[0005] However, it is not easy to visualize the structure of scatterers contained in objects within a region using waves. Specifically, when the state within a region is known, it is easy to obtain data on scattered waves emitted from the region in response to a wave incident on the region, which is called a forward problem. On the other hand, when the data on scattered waves is known, it is not easy to obtain the state within the region, which is called an inverse problem.

[0006] Furthermore, for example, various arrangements of transmitting elements and receiving elements can provide a variety of measurement data. This is expected to improve the spatial resolution in visualizing the structure of the scattering object. However, various arrangements of transmitting elements and receiving elements complicate the calculation process and increase the processing delay. Therefore, it is difficult to improve the spatial resolution in visualizing the structure of the scattering object.

[0007] Therefore, the present disclosure provides an imaging device, etc., that can use waves to visualize the structure of scatterers contained in objects within a region, and can increase the spatial resolution in visualizing the structure of scatterers while suppressing the complexity of calculation processing. [Means for solving the problem]

[0008] An imaging device according to one aspect of the present disclosure comprises a transmitter array including a plurality of transmitters arranged in a straight line and transmitting waves to an area to be measured; a receiver array arranged on another straight line parallel to the straight line on which the plurality of transmitters are arranged and including a plurality of receivers that receive the waves from the area, the receiver array being spaced apart from the transmitter array; and an information processing circuit that derives a visualization function corresponding to a scattering field function related to the scattering of the waves according to measurement data obtained by combining all or part of the plurality of transmitters and the plurality of receivers and the distance between the straight line on which the plurality of transmitters are arranged and the straight line on which the plurality of receivers are arranged, and uses the visualization function to visualize the structure of scatterers contained in objects within the area.

[0009] These comprehensive or specific aspects may be realized as a system, an apparatus, a method, an integrated circuit, a computer program, or a non-transitory recording medium such as a computer-readable CD-ROM, or may be realized as any combination of a system, an apparatus, a method, an integrated circuit, a computer program, and a recording medium. [Effects of the Invention]

[0010] According to one aspect of the present disclosure, it is possible to use waves to visualize the structure of scatterers contained in objects within a region, thereby increasing the spatial resolution in visualizing the structure of scatterers while suppressing the complexity of computational processing. [Brief explanation of the drawings]

[0011] [Figure 1] FIG. 1 is a diagram showing a multistatic antenna according to a reference example. [Figure 2] FIG. 2 is a diagram showing an example of an S-array multistatic antenna according to the embodiment. [Figure 3] FIG. 3 is a diagram showing an example of each coordinate regarding the S-Array in the embodiment. [Figure 4] FIG. 4 is an external view of the S-Array according to the embodiment. [Figure 5] FIG. 5 is a conceptual diagram showing a one-dimensional multistatic array antenna. [Figure 6] FIG. 6 is a conceptual diagram showing the relationship between the transmitting point and the receiving point. [Figure 7] FIG. 7 is a conceptual diagram showing the coordinates of the transmission point and the reception point. [Figure 8] FIG. 8 is a conceptual diagram showing the relationship between the transmitting point and the receiving point in forward scattering. [Figure 9] FIG. 9 is a conceptual diagram showing the relationship between transmitting points and receiving points on a plane. [Figure 10] FIG. 10 is a conceptual diagram showing the relationship between transmission points and reception points on a curved surface. [Figure 11]FIG. 11 is a diagram showing a multi-row linear array antenna. [Figure 12] FIG. 12 is a conceptual diagram showing combinations of transmitting and receiving positions of a multistatic array antenna. [Figure 13] FIG. 13 is a diagram showing a quasi-two-dimensional array antenna on a curved surface. [Figure 14] FIG. 14 is a block diagram showing the basic configuration of an imaging device according to an embodiment. [Figure 15] FIG. 15 is a flowchart showing the basic operation of the imaging device according to the embodiment. [Figure 16] FIG. 16 is a block diagram showing a specific configuration of the imaging device according to the embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0012] An imaging device according to one aspect of the present disclosure comprises a transmitter array including a plurality of transmitters arranged in a straight line and transmitting waves to an area to be measured; a receiver array arranged on another straight line parallel to the straight line on which the plurality of transmitters are arranged and including a plurality of receivers that receive the waves from the area, the receiver array being spaced apart from the transmitter array; and an information processing circuit that derives a visualization function corresponding to a scattering field function related to the scattering of the waves according to measurement data obtained by combining all or part of the plurality of transmitters and the plurality of receivers and the distance between the straight line on which the plurality of transmitters are arranged and the straight line on which the plurality of receivers are arranged, and uses the visualization function to visualize the structure of scatterers contained in objects within the area.

[0013] This allows the imaging device to acquire sufficient information as measurement data according to various combinations of the multiple transmitters in the transmitter array and the multiple receivers in the receiver array. Furthermore, since the imaging device has a distance between the transmitter array and the receiver array, it can appropriately transmit waves to and receive waves from the area. The imaging device can then appropriately visualize the structure of the scattering object using an imaging function derived according to the wave measurement data and the distance between the transmitter array and the receiver array.

[0014] Furthermore, since the arrangement of the transmitters and receivers in the imaging device is constrained to two straight lines, the computational processing can be simplified compared to when the transmitters and receivers are arbitrarily arranged. Therefore, the imaging device can suppress the complexity of the computational processing. In other words, the imaging device can visualize the structure of scatterers contained in objects within the area using waves, and can increase the spatial resolution in visualizing the structure of scatterers while suppressing the complexity of the computational processing.

[0015] For example, the information processing circuit derives the scattered field function according to the measurement data and the distance, and derives the visualization function according to the scattered field function, and the scattered field function is

number

number

[0016] This allows the imaging device to derive a scattered field function that is determined on the assumption that the transmitting position and the receiving position have the same z coordinate, and to derive an imaging function according to the scattered field function. Therefore, the imaging device can appropriately derive the scattered field function and the imaging function according to measurement data obtained along the planar boundary of the region using multiple transmitters of the transmitter array and multiple receivers of the receiver array.

[0017] For example, the information processing circuit derives the scattered field function by solving an equation that the scattered field function satisfies, the equation being

number

number

[0018] This allows the imaging device to analytically derive the solution of the equation satisfied by the scattered field function as the scattered field function, and therefore the imaging device can efficiently derive an appropriate scattered field function.

[0019] Also, for example, the visualization function is

number

[0020] This allows the imaging device to derive an imaging function according to the limit operation of the scattered field function, thereby enabling the imaging device to visualize the scattering state within the region and appropriately visualize the structure of scatterers contained in the object within the region.

[0021] Furthermore, for example, the information processing circuit

number

number

number

[0022] This allows the imaging device to properly reflect the wave measurement data and the distance between the transmitter array and the receiver array in the scattered field function, and therefore the imaging device can derive a scattered field function that properly represents the scattering state.

[0023] Furthermore, for example, the information processing circuit

number

number

number

number

[0024] This allows the imaging device to appropriately reflect the wave measurement data and the distance between the transmitter array and the receiver array in the imaging function, and the imaging device can derive an imaging function that appropriately represents the scattering state.

[0025] Also, for example, the imaging device comprises a plurality of transmitter arrays as the transmitter array, a plurality of receiver arrays as the receiver array, or a plurality of transmitter arrays and a plurality of receiver arrays as the transmitter array and the receiver array.

[0026] This allows the imaging device to acquire sufficient information as measurement data according to multiple combinations of the transmitter array and the receiver array. Furthermore, the imaging device can establish a multistatic relationship with respect to two directions, parallel and perpendicular to the transmitter array and the receiver array. Therefore, the imaging device can properly visualize the structure of scatterers contained in objects within the area.

[0027] Furthermore, for example, the information processing circuit may perform the following with respect to one transmitter array and n receiver arrays that the imaging device includes as the transmitter array and the receiver array:

number

number

number

number

[0028] This allows the imaging device to appropriately reflect the wave measurement data and the distance between the transmitter array and the receiver array in the imaging function. Specifically, the imaging device can derive an imaging function that appropriately represents the scattering state by performing linear addition corresponding to the distance between the transmitter array and the receiver array on the measurement data obtained according to multiple combinations of the transmitter array and the receiver array.

[0029] Furthermore, for example, when the dielectric constant corresponding to the reflectance in the region has frequency dependency, the information processing circuit

number

number

number

number

[0030] This allows the imaging device to derive an imaging function that reflects parameters related to Debye relaxation, thereby suppressing deterioration in accuracy that occurs depending on the wave frequency.

[0031] Furthermore, for example, the information processing circuit derives the scattered field function according to the measurement data and the distance, and derives the visualization function according to the scattered field function, and the scattered field function is

number

number

[0032] This allows the imaging device to derive a scattered field function that is determined on the assumption that the transmitting position and the receiving position may have different z coordinates, and to derive an imaging function according to the scattered field function. Therefore, the imaging device can appropriately derive the scattered field function and imaging function according to measurement data obtained using multiple transmitters in the transmitter array and multiple receivers in the receiver array along a tangent plane of a region having a curved boundary.

[0033] For example, the information processing circuit derives the scattered field function by solving an equation that the scattered field function satisfies, the equation being

number

number

[0034] This allows the imaging device to analytically derive the solution of the equation satisfied by the scattered field function as the scattered field function, and therefore the imaging device can efficiently derive an appropriate scattered field function.

[0035] Also, for example, the visualization function is

number

[0036] This allows the imaging device to derive an imaging function using the scattering field function to which the imaging target position is input, thereby enabling the imaging device to visualize the scattering state within the region and appropriately visualize the structure of scatterers contained in objects within the region.

[0037] Furthermore, for example, the information processing circuit

number

number

[0038] This allows the imaging device to properly reflect the wave measurement data and the distance between the transmitter array and the receiver array in the scattered field function, and therefore the imaging device can derive a scattered field function that properly represents the scattering state.

[0039] Furthermore, for example, the information processing circuit

number

number

[0040] This allows the imaging device to appropriately reflect the wave measurement data and the distance between the transmitter array and the receiver array in the imaging function, and the imaging device can derive an imaging function that appropriately represents the scattering state.

[0041] Furthermore, for example, the information processing circuit derives the imaging function using a synthesis of a plurality of scattered field functions for a plurality of combinations of the transmitter array and the receiver array, each of the plurality of scattered field functions corresponding to the scattered field function;

number

number

[0042] This allows the imaging device to derive an imaging function that appropriately represents the scattering state by combining multiple scattering field functions that reflect the wave measurement data and the distance between the transmitter array and the receiver array.

[0043] Furthermore, for example, when the dielectric constant corresponding to the reflectance in the region has frequency dependency, the information processing circuit

number

number

number

[0044] This allows the imaging device to derive an imaging function that reflects parameters related to Debye relaxation, thereby suppressing deterioration in accuracy that occurs depending on the wave frequency.

[0045] Furthermore, a visualization method according to one aspect of the present disclosure includes the steps of: transmitting waves to an area to be measured using a plurality of transmitters in a transmitter array including a plurality of transmitters arranged in a straight line; receiving the waves from the area using a plurality of receivers in a receiver array including a plurality of receivers arranged on another straight line parallel to the straight line on which the plurality of transmitters are arranged, the plurality of receivers being spaced apart from the transmitter array; and deriving a visualization function corresponding to a scattering field function related to the scattering of the waves according to measurement data obtained by combining all or part of the plurality of transmitters and the plurality of receivers and the distance between the straight line on which the plurality of transmitters are arranged and the straight line on which the plurality of receivers are arranged, and visualizing the structure of scatterers contained in objects within the area using the visualization function.

[0046] This allows sufficient information to be obtained as measurement data according to various combinations of multiple transmitters in the transmitter array and multiple receivers in the receiver array. Furthermore, the spacing between the transmitter array and the receiver array allows waves to be appropriately transmitted to and received from the area. Using the wave measurement data and an imaging function derived according to the distance between the transmitter array and the receiver array, the structure of the scattering object can be appropriately visualized.

[0047] Furthermore, since the transmitter and receiver are constrained to be located on two straight lines, the calculation process can be simplified compared to when the transmitter and receiver are located arbitrarily. Therefore, the complexity of the calculation process can be suppressed. In other words, the structure of scatterers contained in objects within the region can be visualized using waves, and the spatial resolution in visualizing the structure of scatterers can be increased while suppressing the complexity of the calculation process.

[0048] Hereinafter, embodiments will be described with reference to the drawings. Note that the embodiments described below are all comprehensive or specific examples. The numerical values, shapes, materials, components, the arrangement and connection of the components, steps, the order of steps, and the like shown in the following embodiments are merely examples and are not intended to limit the scope of the claims.

[0049] In the following description, the technologies described in Patent Documents 2, 3, 4, and 5 may be particularly referred to as existing technologies. In the following description, radio waves such as microwaves are primarily assumed as waves, but waves are not limited to radio waves such as microwaves. Visualization based on scattering may be expressed as scattering tomography. Therefore, the imaging device and imaging method in the following description may also be expressed as a scattering tomography device and a scattering tomography method, respectively.

[0050] (Embodiment) The imaging device of this embodiment uses waves to visualize the structure of scatterers contained in objects within a region. The imaging device of this embodiment will be described in detail below, including the underlying technology and theory.

[0051] <i 概要> This disclosure describes a microwave imaging technique based on S-Array (super-array) scattering field theory.

[0052] 1 is a diagram showing a multistatic (MS) antenna according to a reference example. In the multistatic antenna, multiple transmitting antenna elements T and multiple receiving antenna elements R are arranged alternately in a row. The transmitting antenna elements T and receiving antenna elements R may also be simply referred to as transmitting elements and receiving elements.

[0053] Each antenna element is half a wavelength (λ / 2) in size. Therefore, the resolution in the y-axis direction is half a wavelength (λ / 2). This does not satisfy the Nyquist sampling condition, and a phenomenon called aliasing occurs. To solve this problem, it is possible to shift the antenna array by λ / 4 in the y direction and scan it in the x direction. Alternatively, two independent array antenna systems can be bundled together and scanned together.

[0054] However, with this type of array antenna, the number of data points obtained is very small compared to the length in the y direction.

[0055] For example, the data obtained from the multistatic antenna in Figure 1 is 9 pairs each at positions I and II of the multistatic antenna, for a total of 18 pairs. Furthermore, if coupling due to electromagnetic induction between adjacent transmitting and receiving elements is eliminated, the data obtained is only 4 pairs each at positions I and II, for a total of 8 pairs. No matter what antenna element arrangement is considered, it is difficult to realize a single array antenna system that satisfies the Nyquist sampling theorem.

[0056] FIG. 2 is a diagram showing an example of an S-array multistatic antenna according to this embodiment. The S-array multistatic antenna may be simply referred to as an S-array. In this example, the S-array multistatic array antenna includes two array antennas: a transmitting array antenna TA and a receiving array antenna RA. The S-array multistatic array antenna can obtain 36 pairs of data during transmission and reception.

[0057] However, until now, there has been virtually no inverse scattering analysis technology that can obtain accurate images of targets from such data. Building a theory that correctly incorporates the phase based on the distance between the transmitting and receiving array antennas has been an extremely difficult task.

[0058] The S-array scattering field theory in this disclosure solves this problem and realizes a virtual high-density S-array as shown in the lower part of Figure 2, which satisfies the Nyquist sampling condition. In other words, the S-array scattering field theory theoretically converts two rows of array antennas, a transmitting array antenna TA and a receiving array antenna RA, into a single row of transmitting and receiving array antennas. Therefore, a resolution of λ / 4 can be obtained in the y direction. Furthermore, scanning in the x direction can obtain any desired resolution in the x direction.

[0059] The S-Array scattering field theory in this disclosure differs crucially from existing scattering field theories related to two-dimensional array antennas in the following respects.

[0060] In existing methods, a two-dimensional array antenna is scanned in the x direction to satisfy the sampling condition. This results in multiple integrals in the scattering inversion algorithm being one-dimensionally larger than with an S-Array. As a result, the time required for analysis takes n times or more. Here, n is the number of samples in the x direction, and n is, for example, 128 to 256. Therefore, it is difficult to put existing scattering field analysis methods for two-dimensional array antennas into practical use with current computer capabilities.

[0061] For example, in an existing two-dimensional method, a signal is transmitted from any element in a two-dimensional array antenna in a planar lattice pattern, and the signal is received by any other element in the two-dimensional array antenna. 4 The data obtained is a set of n (n is the number of elements on one side of a square lattice). Each set of data is time-series data with a bandwidth of 10 GHz or more. Reconstruction theory has already been derived for an algorithm that reconstructs an image of an object from such two-dimensional multistatic data.

[0062] However, as mentioned above, imaging using this two-dimensional array antenna is not necessarily practical due to the complexity of the equipment and the difficulty of obtaining effective resolution. Furthermore, there are issues with resolution unless scanning is performed in the x-direction. In contrast, the S-Array scattering field theory is highly sophisticated, as described below, and the scattering inversion algorithm can be obtained with only minor modifications from existing one-dimensional algorithms, making it highly feasible.

[0063] Fig. 3 is a diagram showing an example of each coordinate related to the S-Array in this embodiment. The S-Array is a quasi-two-dimensional array antenna consisting of two linear array antennas, namely, one row of transmitting array antennas TA and one row of receiving array antennas RA, as shown in Fig. 3.

[0064] Specifically, the transmitting array antenna TA includes n transmitting antenna elements T. The receiving array antenna RA includes n receiving antenna elements R. The x coordinate of the transmitting array antenna TA is represented by x1, the x coordinate of the receiving array antenna RA is represented by x2, and the distance in the x direction between the transmitting array antenna TA and the receiving array antenna RA is represented by d. In this configuration, n of any combinations of n transmitting elements and n receiving elements can be obtained at each point x in the scanning direction. 2 pieces of time series data are obtained.

[0065] Figure 4 is an external view of the S-Array in the present embodiment. A transmission array antenna TA including a plurality of transmission antenna elements T and a reception array antenna RA including a plurality of reception antenna elements R are configured separately. That is, the plurality of transmission antenna elements T and the plurality of reception antenna elements R are arranged quasi-two-dimensionally.

[0066] When applying the reconstruction theory for an existing two-dimensional array antenna to such a quasi-two-dimensional array antenna arrangement, since the dimension becomes one higher, it takes a great deal of calculation time. Therefore, it is still difficult to put into practical use. An efficient calculation method is desired, such as the reconstruction using an analytical solution in the case of a linear array antenna in which a plurality of transmission antenna elements T and a plurality of reception antenna elements R are arranged on one line. The efficient calculation method is useful for the practical application of the quasi-two-dimensional array antenna.

[0067] Surprisingly, recently, the inventors have obtained an analytical solution for the reconstruction in the case of this quasi-two-dimensional array. That is, a method of bridging the theory of one-dimensional arrays and the theory of two-dimensional arrays has been discovered, and a reconstruction formula for the case of a quasi-two-dimensional array has been obtained analytically. According to this theory (S-Array scattering field theory), when the transmission array antenna TA and the reception array antenna RA are linear antennas spatially separated, it becomes possible to construct a practical inverse scattering theory. Hereinafter, the content of this theory and its application will be described in detail.

[0068] <II Preparation from Existing Theories> <II-1 One-Dimensional Array MS Inverse Scattering Theory for a Plane Boundary> The method used for imaging an object in an imaging device using a one-dimensional array antenna is extremely simple and only involves solving the wave equation of the following formula (2-1-1).

[0069]

Equation

[0070] Here,

number

[0071] This method is called monostatic. In this method, paired elements, each consisting of a transmitting element and a receiving element, are arranged along the y-axis. If there are n pairs of transmitting and receiving elements, n sets of data can be obtained. However, the accuracy obtained with this method is basically twice the size of each transmitting and receiving antenna element. Therefore, it is difficult to obtain high-resolution images.

[0072] Figure 5 is a conceptual diagram showing a one-dimensional multistatic array antenna. When any two elements out of n are selected as the transmitting and receiving elements, as shown in Figure 5, the spatial resolution is doubled. Furthermore, signals can be received with a high S / N ratio from short to long distances. This significantly improves the quality of the final image. Naturally, the amount of data increases n-fold, but the time required for reconstruction is also dramatically reduced thanks to the theory described below.

[0073] As shown in Figure 5, we consider a situation in which a radio wave emitted from point P1 (x, y1, z) is reflected at point P (ξ, η, ζ) and received at point P2 (x, y2, z). When point P moves across the entire area D, the signal received at P2 is expressed by the following equation (2-1-2).

[0074]

number

[0075] Here, ε(ξ, η, ζ) is a function of the dielectric constant at point P(ξ, η, ζ) and corresponds to the reflectance at point P(ξ, η, ζ). Point P(ξ, η, ζ) corresponds to the reflection point. Note that ε(ξ, η, ζ) is unknown. It is also assumed that the time factor is proportional to exp(-iωt). The kernel function in the integrand term of the above equation is expressed by φ in the following equation (2-1-3).

[0076]

number

[0077] Next, we consider partial differential equations for which equation (2-1-3) is an asymptotic solution. Therefore, calculations are performed ignoring higher-order terms related to 1 / ρ that appear in the differential results. Here, a shorthand notation for differentiation is defined as equation (2-1-4).

[0078]

number

[0079] Here, we consider a partial differential equation in which equation (2-1-3) has an asymptotic solution at short wavelengths (high frequencies or large k). The solution of such a partial differential equation can be considered to be almost an exact solution for microwave imaging. First, the differential results of each order of φ are expressed as shown in equation (2-1-5) below.

[0080]

number

[0081] In the following, the complicated o(*) term is omitted. By adding up the four equations related to the second derivative, we obtain the following equation (2-1-6).

[0082]

number

[0083] Therefore, the following equation (2-1-7) is obtained from equation (2-1-6).

[0084]

number

[0085] By applying the operator on the right side of equation (2-1-7) twice, the following equation (2-1-8) is obtained.

[0086]

number

[0087] By rearranging equation (2-1-8), we obtain the following equation (2-1-9).

[0088]

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[0089] This formula (2-1-9) was derived assuming a steady state, but it is easy to extend this formula (2-1-9) to a non-steady state. Therefore, ∂ t , and c, which indicates the propagation speed of radio waves, are used to replace variables as in the following equation (2-1-10).

[0090]

number

[0091] Through the above process, we finally obtain the following equation (2-1-11).

[0092]

number

[0093] The above equation (2-1-11) is a partial differential equation whose solution is φ in equation (2-1-3). By applying differentiation to the integral kernel of equation (2-1-2),

number

[0094] This equation is then solved using a Fourier transform.

number

[0095]

number

[0096] The derivative with respect to z is D z When this is expressed as follows, the following equation (2-1-13) is obtained from equations (2-1-11) and (2-1-12).

[0097]

number

[0098] Here, the relationship ω=ck is used. The four fundamental solutions of this equation are expressed as follows (2-1-14).

[0099]

number

[0100] The time factor is e -iωt Considering that the phase is added along the path of the radiated radio wave, and that the radio wave reflected by the object bounces back toward the measurement surface, E1 is the only meaningful solution. Therefore, the following equation (2-1-15) is obtained.

[0101]

number

[0102] By substituting z=0 into this equation (2-1-15), a(k x , k y1 , k y2 , k) is obtained as in the following equation (2-1-16).

[0103]

Equation

[0104] Finally,

Equation

[0105]

Equation

[0106] Under the condition that k and z are fixed, applying the limit operation (y2 → y1 = y) to equation (2-1-17) and integrating the result with respect to k, the imaging function is obtained as in the following equation (2-1-18).

[0107]

Equation

[0108] As described above, it is possible to analytically solve the multi-static inverse scattering problem in a one-dimensional array. However, there are significant constraints such as arranging the transmitting and receiving elements in a one-dimensional array. There are also hardware issues such as the need to provide a gap to avoid inductive coupling between the transmitting and receiving elements, and the inability to switch the transmitting and receiving roles when an active balun is adopted. Furthermore, there is also an issue that the data acquisition time becomes long because it is difficult to parallelize the measurement.

[0109] <II-2 Backscattering and 1D Array MS Inverse Scattering Theory for Curved Boundaries> The inverse scattering theory for the case where the boundary surface of the region is a curved surface is described.

[0110] Figure 6 is a conceptual diagram showing the relationship between the transmitting and receiving points. Figure 6 shows a situation in which a wave emitted from r1 is reflected at point ξ (ξ1, ξ2, ...) and returns to point r2.

[0111] For example, under the condition that the angular frequency ω (= 2πf) is constant, the wave transmission point r1 and reception point r2 move freely and independently within the x-section D while satisfying certain constraints. If the data obtained at this time is expressed as a function G(r1, r2, ω), this function G(r1, r2, ω) should be related to the distribution of reflection points within the area.

[0112] Here, G(r1, r2, ω) is the sum of the reflected signals from all points ξ. Also, since there are many reflection points within the region, G(r1, r2, ω) can be expressed as the following equation (2-2-1).

[0113]

number

[0114] where:

number

[0115] Furthermore, the constraint imposed on the wave transmission point r1 and reception point r2 is that the x coordinates of r1 and r2 are always equal.

[0116] Below, we will explain the theoretical structure of the inverse problem of scattering using this function G(r1, r2, ω). Also, here, a partial region of three-dimensional space is expressed as D, and its boundary is expressed as ∂D. In this case, the function G(r1, r2, ω) becomes the solution of the differential equation shown in the following equation (2-2-2) inside the region D.

[0117]

number

[0118] where:

number

[0119]

number

[0120] Here, Tr denotes the trace operation. This ρ(r) is a function related to the gradient of the dielectric constant in the domain D that we are trying to find. In reality, it is difficult to find the differential operator L(∂ / ∂t, ∂ / ∂r1, ∂ / ∂r2) that appears here.

[0121] Below, we will explain how to find this differential operator. On an arbitrary curve, r1 and r2 are not necessarily equal in terms of the y and z coordinates. Specifically, r1 and r2 are expressed as r1 = (x, y1, z1) and r2 = (x, y2, z2). Then, the function G is defined as follows:

[0122]

number

[0123] Next, the equation satisfied by the function G(r1, r2, ω) is considered, where ω = ck. c is the propagation velocity and k is the wave number. If the wavelength is λ, then the relationship k = 2π / λ holds.

[0124] Figure 7 is a conceptual diagram showing the coordinates of the transmitting point and the receiving point. In Figure 7, the transmitting point is located at P1 (x, y1, z1), and the receiving point is located at P2 (x, y2, z2). A wave emitted from the transmitting point P1 is reflected at point P (ξ, η, ζ) and reaches the receiving point P2.

[0125] For example, z1 and z2 are arbitrary. Measurement points corresponding to transmitting point P1 and receiving point P2 move on a cross-sectional curve S. The cross-sectional curve S can be expressed as z = f(y). Therefore, z1 = f(y1) and z2 = f(y2) hold. Furthermore, the distance between P1 and P is expressed as ρ1, and the distance between P2 and P is expressed as ρ2.

[0126] In the above case, a function φ as shown in the following equation (2-2-5) is introduced as the scattered field function.

[0127]

number

[0128] Here, ε(ξ, η, ζ) is a function of the dielectric constant at point (ξ, η, ζ) and corresponds to the reflectance at point (ξ, η, ζ). Point (ξ, η, ζ) corresponds to the reflection point. Note that ε(ξ, η, ζ) is unknown. Furthermore, k indicates the wave number. It is also assumed that the time factor is proportional to exp(-iωt). The function in the integral term of the above equation (2-2-5) is the same as that of equation (2-2-1).

number

[0129]

number

[0130] Next, we consider a partial differential equation for which equation (2-2-6) is an asymptotic solution at high frequencies. Therefore, calculations are performed ignoring higher-order terms related to 1 / ρ that appear in the differential result. Here, a shorthand notation for differentiation is defined as follows:

[0131]

number

[0132] As a result of the calculation, it is found that φ satisfies the following equation (2-2-8).

[0133]

number

[0134] This equation (2-2-8) was derived assuming a steady state, but it is easy to extend this equation (2-2-8) to a non-steady state. To do this, the variables are replaced as in the following equation (2-2-9).

[0135]

number

[0136] Finally, the following equation (2-2-10) is obtained.

[0137]

number

[0138] Next, assuming that the time factor of φ is proportional to exp(-iωt), the solution of equation (2-2-10) is examined. First, by performing a multiple Fourier transform of φ with respect to t, x, y1, and y2, the following equation (2-2-11) is obtained.

[0139]

number

[0140] The partial differentials with respect to z1 and z2 are D z1 , D z2 By expressing it as such, the following equation (2-2-12) is obtained.

[0141]

number

[0142] Next, we consider solving the equation (2-2-12). However, there are two variables, z1 and z2. Therefore, we can solve the equation (2-2-12) by using the fixed (x, y1, y2) or (k x , k y1 , k y2 ), it is difficult to solve equation (2-2-12) unless the boundary conditions are given in a one-dimensional region with degrees of freedom in the (z1, z2) space. However, the boundary conditions obtained by radar measurements are only given at one point (f(y1), f(y2)) in the (z1, z2) space.

[0143] To solve this problem, we will utilize the consistency between the theory in this section and the theory in the case where z1 = z and z2 = z. In other words, the solution derived from the theory in this section, in which z1 and z2 are independent, includes the solution for the special case where z1 = z and z2 = z. Therefore, first, the solution to equation (2-2-12) is assumed to be as follows: (2-2-13).

[0144]

number

[0145] When z1=z2=z, the following equation (2-2-14) is obtained.

[0146]

number

[0147] Furthermore, by substituting equation (2-2-14) into equation (2-2-12), the following equation (2-2-15) is obtained.

[0148]

number

[0149] Furthermore, one more equation is used. Specifically, the following equation (2-2-16) is obtained from equation (2-1-15) in the previous section, following the consistency mentioned above.

[0150]

Number

[0151] From equations (2-2-15) and (2-2-16), s1(k x , k y1 , k y2 ), s2(k x , k y1 , k y2 ) are determined as in the following equation (2-2-17).

[0152]

Number

[0153] Using the above s1(k x , k y1 , k y2 , k) and s2(k x , k y1 , k y2 , k), the solution of the equation in equation (2-2-10) is derived as in the following equation (2-2-18).

[0154]

Number

[0155] <II-3 Forward Scattering and 1D Array MS Inverse Scattering Theory for Planar Boundaries> Figure 8 is a conceptual diagram showing the relationship between the transmission point and the reception point in forward scattering. The difference between forward scattering and backscattering (II-2) is that the z-coordinates of all scattering points are included between the z-coordinate of the transmission point r1 and the z-coordinate of the reception point r2. r1 and r2 move freely under the constraint that they are located at the same x-coordinate on ∂D1 and ∂D2, respectively, and scattering data is measured. The scattering field function in this system is defined as in the following equation (2-3-1).

[0156]

Number

[0157] The difference from equation (2-2-5) for the backscattering example is that the phase factor of exp(-ikρ2) / ρ2 in the integral sign is negative. However, the scattered field function satisfies the following partial differential equation, equation (2-3-2), which is the same as equation (2-2-10) for the backscattering example.

[0158]

number

[0159] Next, assuming that the time factor of φ is proportional to exp(-iωt), the solution of equation (2-3-2) is examined. First, by performing a multiple Fourier transform of φ with respect to t, x, y1, and y2, the following equation is obtained:

[0160]

number

[0161] The partial differentials with respect to z1 and z2 are D z1 , D z2 By expressing it as follows, the following equation (2-3-4) is obtained.

[0162]

number

[0163] Next, we consider solving the equation (2-3-4). However, there are two variables, z1 and z2. To solve this problem, we utilize the consistency between the theory in this section and the theory in which z1 = z and z2 = z. In other words, the solution derived from the theory in this section, in which z1 and z2 are independent, includes the solution for the special case where z1 = z and z2 = z. Therefore, first, the solution to equation (2-3-4) is assumed to be as shown in the following equation (2-3-5).

[0164]

number

[0165] Furthermore, the following equation (2-3-6) is obtained from equation (2-3-4).

[0166]

number

[0167] When z1=z2=z, equation (2-3-5) can be expressed as the following equation (2-3-7).

[0168]

number

[0169] Then, similar to equation (2-2-16), the following equation (2-3-8) is obtained.

[0170]

number

[0171] From equations (2-3-6) and (2-3-8), s1(k x , k y1 , k y2 ) and s2(k x , k y1 , k y2 ) is determined as shown in the following equation (2-3-9).

[0172]

number

[0173] Therefore, the scattering field function is obtained as shown in the following equation (2-3-10).

[0174]

number

[0175] Next, the z - coordinate of ∂D1 is set to z = 0, and the z - coordinate of ∂D2 is set to z = h. When the scattered data measured at the boundary surface is expressed as Φ(x, y1, y2, k), the following equation (2 - 3 - 11) holds.

[0176]

Number

[0177] Then, by performing the Fourier transform of both sides of equation (2 - 3 - 11) with respect to (x, y1, y2), the following equation (2 - 3 - 12) is obtained.

[0178]

Number

[0179] The function a is obtained as in the following equation (2 - 3 - 13) from the above equation (2 - 3 - 12).

[0180]

Number

[0181] By substituting the above equation (2 - 3 - 13) into equation (2 - 3 - 10), the scattered - field function is obtained as in the following equation (2 - 3 - 14).

[0182]

Number

[0183] <II - 4 Two - Dimensional Array MS Inverse Scattering Theory for Plane Boundaries> First, the theory for the case of an existing two - dimensional array is explained.

[0184] Figure 9 is a conceptual diagram showing the relationship between transmitting and receiving points on a plane. As shown in Figure 9, microwaves emitted from point P1 are reflected at point P on the target and received at point P2. Points P1 and P2 move to arbitrary points on a lattice point (two-dimensional antenna array) in the plane. Under this assumption, the microwave path passing through point P on the target is n 4 This number of passes contributes greatly to improving the quality of the final image. The method for processing such complex data to obtain an image is described below.

[0185] For example, as shown in Figure 9, radio waves emitted from point P1 (x1, y1, z) are reflected at point P (ξ, η, ζ) and received at point P2 (x2, y2, z). When point P moves across the entire area D, the signal received at P2 is expressed as follows:

[0186]

number

[0187] Here, the time factor is assumed to be proportional to exp(-iωt). The kernel function of the integrand term in the above equation is expressed by the following equation (2-4-2).

[0188]

number

[0189] Next, we consider partial differential equations for which equation (2-4-2) is an asymptotic solution at short wavelengths. Therefore, calculations are performed ignoring higher-order terms with respect to 1 / ρ that appear in the differential results. Here, a shorthand notation for differentiation is defined as equation (2-4-3).

[0190]

number

[0191] Using equation (2-4-3), the derivative of each order of the kernel function is expressed as in equation (2-4-4) below.

[0192]

number

[0193] In the following, the complicated o(*) term is omitted. By adding up the five equations related to second-order derivatives, we obtain the following equation (2-4-5).

[0194]

number

[0195] Therefore, the following equation (2-4-6) is obtained from equation (2-4-5).

[0196]

number

[0197] By applying the operator on the right side above twice, the following equation (2-4-7) is obtained.

[0198]

number

[0199] By rearranging equation (2-4-7), we obtain the following equation (2-4-8).

[0200]

number

[0201] Although this equation (2-4-8) was derived assuming a steady state, it is easy to extend this equation (2-4-8) to a non-steady state. To do so, the variables are replaced as in the following equation (2-4-9).

[0202]

number

[0203] By this substitution, equation (2-4-8) is transformed into equation (2-4-10) including time as follows:

[0204]

number

[0205] The above equation (2-4-10) is a partial differential equation whose solution is the kernel function shown in equation (2-4-2), and by applying differentiation to the integral kernel of equation (2-4-2), φ also satisfies the above partial differential equation. This equation is a five-dimensional pseudo-wave equation consisting of six variables (t, x1, y1, x2, y2, z).

[0206] Next, this equation is solved using a Fourier transform. First, φ is subjected to a multiple Fourier transform with respect to t, x1, y1, x2, and y2, as shown in the following equation (2-4-11).

[0207]

number

[0208] The derivative with respect to z is D z When this is expressed as: the following equation (2-4-12) is obtained from equations (2-4-10) and (2-4-11).

[0209]

number

[0210] Here, the relationship ω=ck is used. The four fundamental solutions of this equation are expressed as follows (2-4-13).

[0211]

number

[0212] The time factor is e -iωt Considering that the phase is added along the path of the radiated radio wave, and that the radio wave reflected by the object bounces back towards the measurement surface, E1 is the only meaningful solution. Therefore, the following equation (2-4-14) is obtained.

[0213]

number

[0214] By substituting z=0 into equation (2-4-14), a(k x1 , k y1 , k x2 , k y2 , k) can be calculated using the following equation (2-4-15).

[0215]

number

[0216] From the above, φ can be calculated as follows:

[0217]

number

[0218] Next, by applying the limit operation (y1 → y and y2 → y) to equation (2-4-16) under the condition that k and z are fixed, we obtain the following equation (2-4-17).

[0219]

number

[0220] Next, by integrating equation (2-4-17) with respect to k, the following equation (2-4-18) is obtained as the visualization function.

[0221]

number

[0222] In equation (2-4-18), k x1 , k y1 , k x2 , k y2 The integral with respect to is in Fourier transform form, which is suitable for computer processing. On the other hand, the term exp(iz···) in the integrand is not in Fourier transform form. Therefore, for example, a normal integral with respect to k is performed while specifying the value of z. Alternatively, to reduce calculation time, equation (2-4-18) can be transformed so that the entire equation is expressed using only the Fourier transform.

[0223] For example, the coefficient of iz in exp(iz···) in equation (2-4-17) is expressed as the following equation (2-4-19) using the new variable u.

[0224]

number

[0225] By rationalizing the right-hand side of equation (2-4-19), we obtain the following equation (2-4-20).

[0226]

number

[0227] By solving each square root from the two equations (2-4-19) and (2-4-20), we obtain the following equation (2-4-21).

[0228]

number

[0229] Therefore, k is expressed as in the following equation (2-4-22).

[0230]

number

[0231] Next, by differentiating both sides of Equation (2-4-19) with respect to k and u, the following Equation (2-4-23) is obtained.

[0232]

Equation

[0233] By solving Equation (2-4-23) for dk, the following Equation (2-4-24) is obtained.

[0234]

Equation

[0235] Finally, summarizing, Equation (2-4-18) is transformed as follows: Equation (2-4-25).

[0236]

Equation

[0237] When this result is applied to the quasi-two-dimensional array antenna array described in the overview, the dimension of the integration increases by the amount related to dk x2 Therefore, with the current computing power of computers, it takes a computationally intensive time far from real-time.

[0238] <II-5 Two-Dimensional Array MS Inverse Scattering Theory for Curved Surfaces> Figure 10 is a conceptual diagram showing the relationship between the transmission point and the reception point on the curved surface. Assuming that the z coordinates of the transmission point and the reception point are different in order to use the boundary conditions of the curved surface, the scattered field function is expressed as follows: Equation (2-5-1).

[0239]

Equation

[0240] Here, k indicates the wave number. The time factor is assumed to be proportional to exp(-iωt). D indicates the domain, which corresponds to D3 in Figure 10. The kernel function of the integrand term in the above equation is expressed by the following equation (2-5-2).

[0241]

number

[0242] Next, we consider a partial differential equation for which equation (2-5-2) is a solution except for the region very close to the transmitting and receiving points. Therefore, calculations are performed ignoring higher-order terms with respect to 1 / ρ that appear in the differential result. Here, a shorthand notation for differentiation is defined as follows: (2-5-3)

[0243]

number

[0244] In this case, by performing the same calculation as in the previous section, it is derived that the kernel function satisfies the following equation (2-5-4).

[0245]

number

[0246] Assuming that the time factor is proportional to exp(-iωt), the solution to the above equation (2-5-4) is examined. First, the kernel function is subjected to a multiple Fourier transform with respect to t, x1, x2, y1, and y2 to obtain the following equation:

[0247]

number

[0248] As with equation (2-4-12) in the previous section, the following equation (2-5-6) can be obtained from equation (2-5-4).

[0249]

number

[0250] Next, we consider solving this equation. However, there are two variables, z1 and z2. Therefore, we can solve the equation by using fixed (x1, x2, y1, y2) or (k x1 , k x2 , k y1 , k y2 ), it is difficult to solve equation (2-5-6) unless the boundary conditions are given in a one-dimensional region with degrees of freedom in the (z1, z2) space. However, the boundary conditions obtained by radar measurements are only given at one point {f(x1, y1), f(x2, y2)} in the (z1, z2) space.

[0251] To solve this problem, we utilize the consistency between the theory in this section and the theory in the case where z1 = z and z2 = z. In other words, the solution derived from the theory in this section, in which z1 and z2 are independent, includes the solution for the special case where z1 = z and z2 = z. Therefore, first, the solution to equation (2-5-6) is assumed to be as follows: (2-5-7)

[0252]

number

[0253] According to equations (2-5-6), (2-5-7) and the consistency described above, the following equations (2-5-8) and (2-5-9) are obtained.

[0254]

number

[0255]

number

[0256] From these, s1 and s2 are obtained as shown in the following equation (2-5-10).

[0257]

number

[0258] As above, s1(k x , k y1 , k y2 ) and s2(k x , k y1 , k y2 ), the solution to the equation is expressed as follows (2-5-11).

[0259]

number

[0260] Furthermore, the equation of the surface S is assumed to be, for example, the following equation (2-5-12).

[0261]

number

[0262] The boundary condition given on the surface S is expressed as the following equation (2-5-13).

[0263]

number

[0264] The equation in (2-5-13) is a(k x1 , k x2 , k y1 , k y2 ) is used to determine the following. In the following, the following shorthand notation is used:

[0265]

number

[0266] Using the simplified notation of Equation (2-5-14), an integral equation for a(k) as shown in the following Equation (2-5-15) is derived.

[0267]

Number

[0268] If a(k) is obtained from the above Equation (2-5-15), the scattered field function can be expressed as shown in the following Equation (2-5-16).

[0269]

Number

[0270] In the above Equation (2-5-16), when z1 = z2 = z is applied and then a Fourier transform is performed with respect to k, the imaging function is obtained as shown in the following Equation (2-5-17).

[0271]

Number

[0272] Through the above process, the final imaging function ρ(r) is obtained.

[0273] <III S-Array Scattered Field Theory> <III-1 S-Array Scattered Field Theory of Plane Boundary and Quasi-2D Array> Here, the configuration shown in Figure 3 is used. Also, Equation (2-4-10) for the 2D array is used as the starting point of the study. The following Equation (3-1-1) is the same as Equation (2-4-10).

[0274]

Number

[0275] Also,

Number

[0276]

number

[0277] In the following, the variable x2 may be expressed as u. By Fourier transforming both sides of equation (3-1-1) with respect to t, x1, y1, and y2, the following equation (3-1-3) is obtained.

[0278]

number

[0279] The solution of the above equation (3-1-3), which is a two-dimensional partial differential equation for u and z, is assumed to be as shown in the following equation (3-1-4).

[0280]

number

[0281] Here, s3 and s4 are k x1 , k y1 , k y2 and k. In other words, s3 and s4 are functions of k x1 , k y1 , k y2 and k is a constant determined by

[0282]

number

[0283] By substituting equation (3-1-4) into equation (3-1-3), the following equation (3-1-6) is obtained.

[0284]

number

[0285] This algebraic equation alone does not determine s3 and s4. Next, equation (3-1-4) is changed to the following equation (3-1-7).

[0286]

number

[0287] Equation (3-1-7) is k x1 , k y1 and k y2 By performing an inverse Fourier transform on u → x2 and applying the result to u → x2, we obtain the following equation (3-1-8).

[0288]

number

[0289] By applying x2=x1=x to equation (3-1-8), the following equation (3-1-9) is obtained.

[0290]

number

[0291] where k x is expressed by the following equation (3-1-10).

[0292]

number

[0293] The above equation (3-1-9) is the same as the solution to the scattering field equation for a one-dimensional array, so it should be the same as equation (2-1-17). The following equation (3-1-11) is the same as equation (2-1-17).

[0294]

number

[0295] By comparing equation (3-1-9) with equation (3-1-11), the following equation (3-1-12) is obtained.

[0296]

number

[0297] By squaring the second equation of equation (3-1-12), the following equation (3-1-13) is obtained.

[0298]

number

[0299] By substituting equation (3-1-13) into equation (3-1-6), the following equation (3-1-14) is obtained.

[0300]

number

[0301] By rearranging equation (3-1-14), we obtain the following equation (3-1-15).

[0302]

number

[0303] Since the solution to this equation is a multiple root, the solution expressed by the following equation (3-1-16) can be obtained uniquely.

[0304]

number

[0305] According to the equations (3-1-12) and (3-1-16) obtained in the above process, s3 and s4 are analytically determined. Then, the scattering field function is obtained from equation (3-1-8) as shown in the following equation (3-1-17).

[0306]

number

[0307] Next, the measurement data Φ(x1, y1, y2, k) and a(k x1 , k y1 , k y2 , k) is considered. x =k x1 By setting z = 0 and x2 = x1 + d into equation (3-1-17), the following equation (3-1-18) is established: where Φ(x1, y1, y2, k) is the measurement data for the transmitting point (x1, y1, 0), the receiving point (x1 + d, y2, 0), and the wave number k.

[0308]

number

[0309] Hereafter, k defined by the following equation (3-1-19) x and s3 are used.

[0310]

number

[0311] By Fourier transforming both sides of equation (3-1-18) with respect to x1, y1, and y2, we obtain the following equation (3-1-20).

[0312]

number

[0313] From equation (3-1-20), the function a(k x , k y1 , k y2 , k) is obtained as in the following equation (3-1-21).

[0314]

Equation

[0315] Therefore, the scattering field function of equation (3-1-17) is obtained in the complete form as in the following equation (3-1-22).

[0316]

Equation

[0317] And the imaging function is obtained as in the following equation (3-1-23).

[0318]

Equation

[0319] In the quasi-two-dimensional array, it becomes possible to acquire information on the substance included between the x coordinate of the transmission position and the x coordinate of the reception position. In particular, even if there is an obstacle with a high dielectric constant in front, it becomes possible to wrap around in the x direction, transmit radio waves, and receive waves. Therefore, it becomes possible to acquire information that is difficult to acquire with a one-dimensional array in the y direction. Therefore, it becomes possible to reconstruct a more appropriate image.

[0320]

[0321] <III-2 Plane Boundary and S-Array Scattering Field Theory of Two-Dimensional Array> Figure 11 is a diagram showing a plurality of linear array antennas. The plurality of linear array antennas shown in Figure 11 includes a single row of transmission array antenna TA and n rows of reception array antennas RA1, RA2, RA3, ···, RA n The polarization direction of each antenna element can be either the x-direction or the y-direction. TA and RA can also be interchanged. The quasi-two-dimensional array MS inverse scattering method described in Section III-1 is applied to this type of array.

[0322] Multiple receiving array antennas RA1, RA2, RA3, . . . RA n There are (TA, RA1), (TA, RA2), (TA, RA3), ···, (TA, RA n ) are measured independently of each other. The scattered field function is obtained by linear addition of these data. Therefore, the imaging function is also obtained by linear addition. j The distance between j and each measurement data is Φ j When (x1, y1, y2, k), the following equation (3-2-1) is obtained from equation (3-1-23).

[0323]

number

[0324] Next, the difference between the case where an S-Array two-dimensional array to which the quasi-two-dimensional array of the present disclosure is applied is used and the case where an existing two-dimensional array is used will be described.

[0325] In the case of the S-Array, the two-dimensional array is limited to one-dimensional arrays for the TA and RA. A scanning probe using this array may be able to acquire high-quality images and may be able to shorten the scanning time while maintaining image quality. Alternatively, scanning may be omitted.

[0326] On the other hand, when an existing two-dimensional array is used, there are no restrictions on the arrangement of transmitting and receiving elements. 4 There are many combinations of transmission and reception on the order of , and the dimension becomes large. Therefore, when n is a practical value (such as 100), the system becomes large-scale, and the measurement time and calculation time become enormous. Therefore, existing two-dimensional arrays are not practical for medical diagnosis and infrastructure diagnosis.

[0327] FIG. 12 is a conceptual diagram showing the combination of transmitting and receiving positions of a multistatic array antenna. FIG. 12 shows an S-Array two-dimensional array as a multistatic array antenna. With an S-Array two-dimensional array, measurement data is acquired at multiple receiving positions in both the x and y directions without scanning. In other words, the S-Array two-dimensional array has multistatic characteristics in both the x and y directions. Therefore, sufficient information can be acquired, and scanning can be omitted or reduced.

[0328] As described above, transmission and reception may be interchanged. In this case, multiple transmitting array antennas transmit radio waves in sequence. More specifically, multiple transmitting elements transmit radio waves in sequence. It is assumed that the amount of received scattering remains the same even if the transmitting and receiving positions are interchanged. Therefore, even if transmission and reception are interchanged, substantially the same results can be obtained. Furthermore, when multiple transmitting array antennas are used, linear addition may be performed in the same way as when multiple receiving array antennas are used.

[0329] Alternatively, a plurality of transmitting array antennas and a plurality of receiving array antennas may be used, and the plurality of transmitting array antennas and the plurality of receiving array antennas may be arranged alternately.

[0330] Scanning may also be performed using an S-Array two-dimensional array, which provides information over a wider range.

[0331] As described above, an imaging function can be derived by synthesizing a plurality of scattering field functions for a plurality of combinations related to the transmitting array antenna and the receiving array antenna. For example, a plurality of scattering field functions are synthesized into one scattering field function, and the imaging function is derived by performing a limiting operation on the scattering field function. Each of the plurality of scattering field functions may be a scattering field function expressed by Expression (3-1-23), and the synthesis may be linear addition.

[0332] <III-3 S-Array Scattering Field Theory for Curved Surface Boundaries> Hereinafter, the S-Array scattering field theory in the case where the boundary of the region, that is, the boundary surface for measuring the scattering data, is a curved surface with a small curvature will be described.

[0333] FIG. 13 is a diagram showing a quasi-two-dimensional array antenna on a curved surface. FIG. 13 shows a quasi-two-dimensional array antenna projected onto the x-y plane of the plane z = 0. When the curvature of the curved surface is large, the inclination of the array antenna cannot be ignored, and it is not allowed to ignore that the distance in the x-y plane between the antenna elements changes depending on the location. However, on a curved surface with a small curvature, the distance in the x-y plane between the elements can be approximately regarded as constant.

[0334] Here, based on the theory of II-5, the inverse scattering theory for the case of a quasi-two-dimensional array is constructed. The scattering field function is a function as shown in the following Expression (3-3-1).

[0335]

Equation

[0336] The equation satisfied by the scattering field function of Expression (3-3-1) is Expression (2-5-4), which is expressed as the following Expression (3-3-2).

[0337]

Equation

[0338] Here, the Fourier transform as shown in the following equation (3-3-3) is used.

[0339]

number

[0340] From equations (3-3-2) and (3-3-3), the following equation (3-3-4) is obtained.

[0341]

number

[0342] The following equation (3-3-5) is assumed as the solution to equation (3-3-4).

[0343]

number

[0344] By substituting equation (3-3-5) into equation (3-3-4), the following equation (3-3-6) is obtained.

[0345]

number

[0346] next,

number

[0347]

number

[0348] In the transition from x2 to x1, equation (3-3-7) is equal to equation (2-2-18). In the transition from x2 to x1, equation (3-3-7) can be expressed as the following equation (3-3-8).

[0349]

number

[0350] Furthermore, the same equation as equation (2-2-18) can be expressed as the following equation (3-3-9).

[0351]

number

[0352] Since equation (3-3-8) and equation (3-3-9) coincide, the following equation (3-3-10) is obtained.

[0353]

number

[0354] Next, from equations (3-3-6), (3-3-9), and (3-3-10), an algebraic equation for s3 is obtained as shown in the following equation (3-3-11).

[0355]

number

[0356] By expanding and simplifying the squared terms in equation (3-3-11), we obtain the following equation (3-3-12).

[0357]

number

[0358] Furthermore, by rearranging equation (3-3-12), we obtain the following equation (3-3-13).

[0359]

number

[0360] There are two solutions to equation (3-3-13). However, the solution to equation (3-3-13) should be the same as the case of a plane boundary in Section III-1. Therefore, according to equation (3-1-16), the following equation (3-3-14) should be selected as the solution.

[0361]

number

[0362] Summarizing the above, the scattering field function is obtained as shown in the following equation (3-3-15).

[0363]

number

[0364] Also, in equation (3-3-15), k x1 From k x By converting the variables to, the following equation (3-3-16) is obtained.

[0365]

number

[0366] Next, the measurement data Φ(x1, y1, y2, k) and b(k x1 , k y1 , k y2 , k) is considered. I , P J The measured data Φ(x I , y I , x I +d, y J , t) is expressed as the following equation (3-3-17).

[0367]

number

[0368] The shape of the boundary surface, which is the measurement surface, is expressed as the following equation (3-3-18).

[0369]

number

[0370] where (x, y) are coordinates on the plane at z=0. P I , P J The z coordinate at is expressed as in the following equation (3-3-19).

[0371]

number

[0372] By substituting x2 = x1 + d into equation (3-3-15), the following equation (3-3-20) is obtained.

[0373]

number

[0374] The above equation (3-3-20) can be expressed as the following equation (3-3-21) using data Φ obtained by measuring on the boundary.

[0375]

number

[0376] Φ(x I , y I , y J , z I , z J , k) is the transmission point (x I , y I , z I ), receiving point (x I +d, y J , z J ) and wave number k. By Fourier transforming both sides of equation (3-3-21), we obtain the following equation (3-3-22).

[0377]

number

[0378] Then, as a result of integrating equation (3-3-22) with respect to x1, y1, and y2, the following equation (3-3-23) is obtained.

[0379]

number

[0380] By rearranging the result of equation (3-3-23), we obtain the following equation (3-3-24).

[0381]

number

[0382] By summing all pairs of I and J in equation (3-3-24), the following equation (3-3-25) is obtained.

[0383]

number

[0384] From equations (3-3-15) and (3-3-25), the scattering field function is obtained as shown in the following equation (3-3-26).

[0385]

number

[0386] Applying x2 = x1 = x, y1 = y2 = y, and z1 = z2 = z to equation (3-3-26) and integrating with respect to k, we obtain the visualization function. Next, we consider improving the visualization function formula so that the result can be obtained by Fourier transform, which allows for fast calculations. The basic variables are k x , k y1 , k y2 , k z The other variables are expressed explicitly using these. The visualization function is obtained by the following procedure.

[0387] First, by applying x2 = x1 = x, y1 = y2 = y, and z1 = z2 = z to equation (3-3-26), the following equation (3-3-27) is obtained.

[0388]

number

[0389] The visualization function ρ is obtained by integrating with respect to k as shown in the following equation (3-3-28).

[0390]

number

[0391] For this calculation, the following equation (3-3-29) is used.

[0392]

number

[0393] In the above description, a quasi-two-dimensional array is used, but a two-dimensional array such as that shown in FIG. 11 may also be used. In this case, the imaging function may be derived by combining multiple scattered field functions for multiple combinations of transmitting array antennas and receiving array antennas. For example, multiple scattered field functions are combined into one scattered field function, and the imaging function is derived by limit operations on the scattered field function. Here, each of the multiple scattered field functions may be the scattered field function expressed by equation (3-3-26), and the combination may be linear addition.

[0394] Also, in FIG. 13, a cylindrical surface is shown as the curved surface boundary of the region, but the curved surface boundary of the region may not be a cylindrical surface. The above process may be applied not only to the tangent plane of the cylindrical surface but also to the tangent planes of other curved surface boundaries.

[0395] <IV Frequency Dependence of Dielectric Constant> <IV-1 Basic Theory> When using the reconstruction formula obtained in Chapter III, the presence or absence of the dispersion of the dielectric constant may be considered. When there is no dispersion of the dielectric constant, the frequency f and the wave number k have a simple relationship as shown in the following equation (4-1-1). Here, ε r is the relative dielectric constant, and c0 is the speed of electromagnetic waves in vacuum.

[0396]

Equation

[0397] The variable conversion from f to k in the case where there is no dispersion of the dielectric constant is easy. However, in applications to living bodies, etc., it should be considered that the dielectric constant changes depending on the frequency. Hereinafter, it is considered that the dielectric constant has frequency dependence.

[0398] In the region of 14 to 20 GHz, the dielectric constant becomes about 60% compared to the region of 1 to 5 GHz. The Debye equations for the frequency dependence of the dielectric constant are shown in the following equations (4-1-2) and (4-1-3).

[0399]

Equation

[0400]

Equation

[0401] Here, ω represents the angular frequency. ε(ω) represents the complex dielectric constant at ω. i represents the imaginary unit. τ represents the relaxation time. ε r ε(ω) represents the real part of the complex dielectric constant at ω. a, b, and α represent constants. Specifically, a, b, and α are parameters indicating the correspondence between the frequency change and the dielectric constant change according to the Debye relaxation.

[0402] Also, the relationships among the velocity, frequency, and wavenumber of an electromagnetic wave are expressed as the following equations (4-1-4) and (4-1-5).

[0403] [Number]

[0404] [Number]

[0405] Here, c(ω) represents the propagation velocity at ω. ω and f have the relationship ω = 2πf. Also, the following equation (4-1-6) is obtained from equation (4-1-5).

[0406] [Number]

[0407] Furthermore, the following equation (4-1-7) is also obtained from equation (4-1-6).

[0408] [Number]

[0409] [IV-2 S-Array Scattering Field Theory for Planar Boundary and Dispersive Media] Here, a visualization function for generating an image of the interior of a dielectric dispersive medium by measuring data with an S-Array at a planar boundary is considered. The time factor is e -iωt Therefore, when considering that the permittivity has frequency dependence, the integration is performed with frequency ω instead of k in Equation (3-2-1). As a result, visualization functions are obtained as shown in the following Equations (4-2-1) and (4-2-2).

[0410]

Number

[0411]

Number

[0412] <IV-3 S-Array Scattering Field Theory for Curved Surfaces and Dispersive Media> Here, the visualization function for generating an image of the interior of a dielectric dispersive medium by measuring data with an S-Array at a curved surface boundary is considered. Since the factor of time is e -iωt Therefore, when considering that the permittivity has frequency dependence, the integration is performed with frequency ω instead of k in Equation (3-3-28). As a result, visualization functions are obtained as shown in the following Equations (4-3-1) and (4-3-2).

[0413]

Number

[0414]

Number

[0415] <V Configuration and Operation of Visualization Device> Based on the above-described content, the configuration and operation of a visualization device for visualizing the structure of a scatterer included in an object in a region using waves are shown below.

[0416] Here, the wave may be, for example, a radio wave, a microwave, a millimeter wave, or a terahertz wave. Furthermore, light or sound may be used as the wave. The object within the region may be a living body, a manufactured product, a natural material, or the like. In particular, the imaging device may be used for mammography, and the object may be a breast.

[0417] Furthermore, scatterers contained in an object within the region correspond to portions having physical properties different from those of the surrounding medium. Specifically, this physical property is a physical property corresponding to the reflectivity of the wave. When radio waves are used as the wave, the physical property may be the dielectric constant. Furthermore, scatterers contained in the object may be rebar contained in reinforced concrete, a tumor contained in a breast, or the like. Furthermore, the region to be measured may be the same as the region of the object.

[0418] Fig. 14 is a diagram showing the basic configuration of an imaging device according to this embodiment. The imaging device 100 shown in Fig. 14 includes a transmitter array 101, a receiver array 102, and an information processing circuit 103. The imaging device 100 may also include a display 104.

[0419] The transmitter array 101 is a circuit that transmits waves. Specifically, the transmitter array 101 includes a plurality of transmitters 111 arranged in a line. Each transmitter 111 transmits a wave. The imaging device 100 may include a plurality of transmitter arrays 101 arranged in parallel with each other.

[0420] The receiver array 102 is a circuit that receives waves. Specifically, the receiver array 102 includes a plurality of receivers 112 arranged on a line parallel to the line on which the plurality of transmitters 111 are arranged. Each receiver 112 receives waves. The receiver array 102 is also arranged at an interval from the transmitter array 101. In other words, the receiver array 102 is spaced apart from the transmitter array 101. The imaging device 100 may also include a plurality of receiver arrays 102 that are parallel to one another.

[0421] The information processing circuit 103 is a circuit that performs information processing. Specifically, the information processing circuit 103 visualizes the structure of scatterers contained in objects within the area based on the measurement data obtained by the transmitter array 101 and the receiver array 102. For example, when visualizing the structure of scatterers based on the measurement data, the information processing circuit 103 performs arithmetic processing as shown in the above-mentioned theory.

[0422] The information processing circuit 103 may be a computer or a computer processor. The information processing circuit 103 may read a program from a memory and execute the program to process information. The information processing circuit 103 may be a dedicated circuit for visualizing the structure of a scatterer based on measurement data.

[0423] Furthermore, the information processing circuitry 103 may generate an image showing the structure of the scatterer in order to visualize the structure of the scatterer.

[0424] The information processing circuitry 103 may then visualize the structure of the scatterer by outputting an image showing the structure of the scatterer to a display 104 or the like. Alternatively, the information processing circuitry 103 may visualize the structure of the scatterer by outputting an image showing the structure of the scatterer to a printer (not shown). Alternatively, the information processing circuitry 103 may visualize the structure of the scatterer by transmitting the image as electronic data to another device (not shown) via wired or wireless communication.

[0425] The display 104 is a display device such as a liquid crystal display. The display 104 is an optional component and is not an essential component. The display 104 may also be an external device that is not part of the imaging device 100.

[0426] Fig. 15 is a flowchart showing the basic operation of the imaging device 100 shown in Fig. 14. Specifically, the transmitter array 101, receiver array 102, information processing circuit 103, etc. of the imaging device 100 shown in Fig. 14 perform the operations shown in Fig. 15.

[0427] First, the multiple transmitters 111 of the transmitter array 101 transmit waves to a region to be measured (S101). For example, the multiple transmitters 111 transmit the waves sequentially. Furthermore, the multiple receivers 112 of the receiver array 102 receive the waves from the region (S102). For example, the multiple receivers 112 receive the waves in parallel. The received waves can also be expressed as scattered waves. Then, the information processing circuit 103 visualizes the structure of scatterers contained in objects within the region using measurement data obtained by the multiple transmitter arrays 101 and the multiple receiver arrays 102 (S103).

[0428] When visualizing the structure of a scatterer, the information processing circuit 103 first derives an imaging function corresponding to a scattering field function related to wave scattering according to the measurement data and the distance. Here, the measurement data is measurement data obtained by combining all or part of the multiple transmitters 111 and the multiple receivers 112. The distance is the distance between the line on which the multiple transmitters 111 are arranged and the line on which the multiple receivers 112 are arranged. Then, the information processing circuit 103 visualizes the structure of the scatterer included in the object within the region using the imaging function.

[0429] This allows the imaging device 100 to acquire sufficient information as measurement data according to various combinations of the multiple transmitters 111 in the transmitter array 101 and the multiple receivers 112 in the receiver array 102. Furthermore, since the imaging device 100 has a gap between the transmitter array 101 and the receiver array 102, it can appropriately transmit waves to an area and appropriately receive waves from the area.

[0430] The imaging device 100 can then properly visualize the structure of the scatterer using the wave measurement data and an imaging function derived according to the distance between the transmitter array 101 and the receiver array 102.

[0431] Furthermore, in the imaging device 100, the arrangement of the transmitter 111 and the receiver 112 is constrained to two straight lines, and therefore the computational processing can be simplified compared to when the transmitter 111 and the receiver 112 are arbitrarily arranged. Therefore, the imaging device 100 can suppress the complexity of the computational processing. In other words, the imaging device 100 can visualize the structure of scatterers contained in objects within the area using waves, and can increase the spatial resolution in visualizing the structure of scatterers while suppressing the complexity of the computational processing.

[0432] For example, the information processing circuitry 103 may derive a scattering field function according to the measurement data and the distance, and then derive an imaging function according to the scattering field function.

[0433] where the scattered field function is

number

number

[0434] Also, (x1, y1, z) indicates the transmitting position of the wave. (x2, y2, z) indicates the receiving position of the wave. k indicates the wave number of the wave. D indicates the area. (ξ, η, ζ) corresponds to the reflected position of the wave. ε corresponds to the unknown reflectivity at the reflected position.

[0435] This allows the imaging device 100 to derive a scattered field function that is determined on the assumption that the transmitting position and the receiving position have the same z coordinate, and to derive an imaging function according to the scattered field function. Therefore, the imaging device 100 can appropriately derive the scattered field function and the imaging function according to measurement data obtained along the planar boundary of the region using the multiple transmitters 111 of the transmitter array 101 and the multiple receivers 112 of the receiver array 102.

[0436] For example, the information processing circuitry 103 may derive the scattered field function by solving an equation that the scattered field function satisfies.

[0437] Here, the equation satisfied by the scattered field function is

number

number

[0438] Furthermore, c indicates the propagation speed of the wave, and t indicates the time from transmission to reception of the wave.

[0439] This allows the imaging device 100 to analytically derive the solution of the equation satisfied by the scattered field function as the scattered field function, and therefore the imaging device 100 can efficiently derive an appropriate scattered field function.

[0440] Also, for example, the visualization function is

number

[0441] This allows the imaging device 100 to derive the imaging function according to the limit operation of the scattered field function, thereby enabling the imaging device 100 to visualize the scattering state within the region and appropriately visualize the structure of the scatterers contained in the object within the region.

[0442] Furthermore, for example, the information processing circuit 103

number

[0443] where k x , s3 and s4 are

number

[0444] Also, k x1 , k y1 and k y2 denotes the wave numbers for x1, y1, and y2 of the scattered field function. d denotes the distance.

[0445] Also,

number

[0446] This allows the imaging device 100 to appropriately reflect the wave measurement data and the distance between the transmitter array 101 and the receiver array 102 in the scattered field function, and therefore the imaging device 100 can derive a scattered field function that appropriately represents the scattering state.

[0447] Furthermore, for example, the information processing circuit 103

number

[0448] where k x , k z , k, dk / dk z and s4 is

number

[0449] Also, s3 is

number

[0450] Also, (x, y, z) indicates the position of the object to be visualized. x1 , k y1 and k y2 denotes the wave numbers for x1, y1, and y2 of the scattered field function. d denotes the distance.

[0451] Also,

number

[0452] This allows the imaging device 100 to appropriately reflect the wave measurement data and the distance between the transmitter array 101 and the receiver array 102 in the imaging function. The imaging device 100 can derive an imaging function that appropriately represents the scattering state.

[0453] Also, for example, the imaging device 100 may include a plurality of transmitter arrays 101 as the transmitter array 101, a plurality of receiver arrays 102 as the receiver array 102, or a plurality of transmitter arrays 101 and a plurality of receiver arrays 102 as the transmitter array 101 and the receiver array 102.

[0454] This allows imaging device 100 to acquire sufficient information as measurement data according to multiple combinations of transmitter array 101 and receiver array 102. Furthermore, imaging device 100 can establish a multistatic relationship with respect to two directions, that is, a direction parallel to and a direction perpendicular to transmitter array 101 and receiver array 102. Therefore, imaging device 100 can appropriately visualize the structure of scatterers contained in objects within the area.

[0455] Furthermore, for example, the information processing circuit 103 may perform the following with respect to the one transmitter array 101 and the n receiver arrays 102 provided in the imaging device 100:

number

[0456] Also, k x , k z , k, dk / dk z and s4 is

number

[0457] Also, s3 is

number

[0458] Also, (x, y, z) indicates the position of the object to be visualized. x1 , k y1 and k y2 denotes the wave numbers for x1, y1, and y2 of the scattered field function. d j indicates the distance.

[0459] Also,

number

[0460] This allows the imaging device 100 to appropriately reflect the wave measurement data and the distance between the transmitter array 101 and the receiver array 102 in the imaging function. Specifically, the imaging device 100 performs linear addition corresponding to the distance between the transmitter array 101 and the receiver array 102 on the measurement data obtained according to multiple combinations of the transmitter array 101 and the receiver array 102, thereby deriving an imaging function that appropriately represents the scattering state.

[0461] Furthermore, for example, when the dielectric constant corresponding to the reflectance in the region has frequency dependency, the information processing circuit 103

number

[0462] Also, k x , k z , k, dk / dk z , dω / dk and s4 are

number

[0463] Also, s3 is

number

[0464] Also, (x, y, z) indicates the position of the object to be visualized. x1 , k y1 and k y2 denotes the wave numbers for x1, y1, and y2 of the scattered field function. d denotes the distance. ω denotes the angular frequency of the wave. c0 denotes the propagation velocity of the wave in vacuum. a, b, and α denote parameters related to Debye relaxation.

[0465] Also,

number

[0466] This allows the imaging device 100 to derive an imaging function that reflects parameters related to Debye relaxation, thereby suppressing deterioration in accuracy that occurs depending on the frequency of the wave.

[0467] Furthermore, for example, the information processing circuitry 103 may derive a scattering field function according to the measurement data and the distance, and then derive an imaging function according to the scattering field function.

[0468] where the scattered field function is

number

[0469] In addition, ρ1 and ρ2 are

number

[0470] Also, (x1, y1, z1) indicates the transmitting position of the wave. (x2, y2, z2) indicates the receiving position of the wave. k indicates the wave number of the wave. D indicates the area, and (ξ, η, ζ) corresponds to the reflected position of the wave. ε corresponds to the unknown reflectivity at the reflected position.

[0471] This allows the imaging device 100 to derive a scattered field function that is determined on the assumption that the transmitting position and the receiving position may have different z coordinates, and to derive an imaging function according to the scattered field function. Therefore, the imaging device 100 can appropriately derive the scattered field function and the imaging function according to measurement data obtained using the multiple transmitters 111 of the transmitter array 101 and the multiple receivers 112 of the receiver array 102 along the tangent plane of a region having a curved boundary.

[0472] For example, the information processing circuitry 103 may derive the scattered field function by solving an equation that the scattered field function satisfies.

[0473] Here, the equation satisfied by the scattered field function is

number

[0474] Also, Δ6 is

number

[0475] This allows the imaging device 100 to analytically derive the solution of the equation satisfied by the scattered field function as the scattered field function, and therefore the imaging device 100 can efficiently derive an appropriate scattered field function.

[0476] Also, for example, the visualization function is

number

[0477] This allows the imaging device 100 to derive an imaging function using the scattering field function to which the imaging target position is input, thereby enabling the imaging device 100 to visualize the scattering state within the region and appropriately visualize the structure of scatterers contained in objects within the region.

[0478] Furthermore, for example, the information processing circuit 103

number

[0479] where k x , s3, s4 and s5 are

number

[0480] Also, k x1 , k y1 and k y2 denotes the wave numbers for x1, y1, and y2 of the scattered field function. d denotes the distance. Φ(x I , y I , y J , z I , z J , k) is the transmission position (x I , y I , z I ) and the receiving position is (x I +d, y J , z J ) shows the measurement data.

[0481] This allows the imaging device 100 to appropriately reflect the wave measurement data and the distance between the transmitter array 101 and the receiver array 102 in the scattered field function, and therefore the imaging device 100 can derive a scattered field function that appropriately represents the scattering state.

[0482] Furthermore, for example, the information processing circuit 103

number

[0483] where k x , k z , k, dk / dk z , s3, s4 and s5 are

number

[0484] Also, (x, y, z) indicates the position of the object to be visualized. x1 , k y1 and k y2 indicates the wave numbers of the scattered field function for x1, y1, and y2. d indicates the distance. Also, Φ(x I , y I , y J , z I , z J , k) is the transmission position (x I , y I , z I ) and the receiving position is (x I +d, y J , z J ) shows the measurement data.

[0485] This allows the imaging device 100 to appropriately reflect the wave measurement data and the distance between the transmitter array 101 and the receiver array 102 in the imaging function. The imaging device 100 can derive an imaging function that appropriately represents the scattering state.

[0486] Also, for example, the information processing circuitry 103 may derive the imaging function using a synthesis of multiple scattered field functions for multiple combinations of the transmitter array 101 and the receiver array 102 .

[0487] where each of the multiple scattered field functions is

number

[0488] Also, k x , s3, s4 and s5 are

number

[0489] Also, k x1 , k y1 and k y2 indicates the wave numbers of the scattered field function for x1, y1, and y2. d indicates the distance. Also, Φ(x I , y I , y J , z I , z J , k) is the transmission position (x I , y I , z I ) and the receiving position is (x I +d, y J , z J ) shows the measurement data.

[0490] This allows the visualization device 100 to derive a visualization function that appropriately represents the scattering state by combining multiple scattering field functions that reflect the wave measurement data and the distance between the transmitter array 101 and the receiver array 102.

[0491] Furthermore, for example, when the dielectric constant corresponding to the reflectance in the region has frequency dependency, the information processing circuit 103

number

[0492] where k x , k z , k, dk / dk z , dω / dk, s3, s4 and s5 are

number

[0493] Also, (x, y, z) indicates the position of the object to be visualized. x1 , k y1 and k y2 denotes the wave numbers for x1, y1, and y2 of the scattered field function. d denotes the distance. ω denotes the angular frequency of the wave. c0 denotes the propagation velocity of the wave in vacuum. a, b, and α denote parameters related to Debye relaxation.

[0494] Also,

number

[0495] This allows the imaging device 100 to derive an imaging function that reflects parameters related to Debye relaxation, thereby suppressing deterioration in accuracy that occurs depending on the frequency of the wave.

[0496] Furthermore, for example, the scattered field function may be determined as a function that inputs a wave transmission position and a wave reception position and outputs a value indicating the wave at the reception position. Furthermore, the imaging function may be determined based on a value output from the scattered field function by inputting the imaging target position as the transmission position and the reception position into the scattered field function.

[0497] The information processing circuitry 103 may then use the measurement data as boundary conditions to derive a scattered field function, and may use the scattered field function to derive an imaging function. Here, the scattered field function and the imaging function may reflect the distance between the line on which the multiple transmitters 111 are arranged and the line on which the multiple receivers 112 are arranged.

[0498] Furthermore, for example, other components, equations, variables, etc. shown in this embodiment can be applied as appropriate to the transmitter array 101, receiver array 102, information processing circuit 103, scattered field function, and imaging function shown in the above basic configuration and basic operation.

[0499] Furthermore, the scattering field function, imaging function, etc. shown in this embodiment may be modified as appropriate and applied. For example, a mathematical expression that expresses substantially the same content as the above mathematical expression in a different way may be used, or another mathematical expression derived based on the above theory may be used.

[0500] FIG. 16 is a block diagram showing a specific configuration of the imaging device 100 shown in FIG.

[0501] The transmitter array 101 and the receiver array 102 of the imaging device 100 shown in Fig. 14 may be included in a multistatic array antenna 1008. The information processing circuit 103 of the imaging device 100 shown in Fig. 14 may correspond to one or more of the components shown in Fig. 16. Specifically, for example, the information processing circuit 103 may correspond to the signal processing computer 1005. Furthermore, the display 104 shown in Fig. 14 may correspond to the signal monitoring device 1006.

[0502] The microwave signal used in the imaging device 100 is a pseudorandom time-series signal (PN code: Pseudo Noise Code) having frequency components from DC to 20 GHz. This signal is output from a PN code generation FPGA board 1002. More specifically, there are two types of this signal. One type of signal (LO signal: local oscillator signal) is sent to an RF detection circuit (RF detection board 1007) through a delay circuit (digital control board 1003).

[0503] The other type of signal (RF signal: Radio Frequency Signal) is sent to and radiated from the transmitting microwave UWB antenna of the multistatic array antenna 1008. The scattered microwave signal is received by the receiving UWB antenna of the multistatic array antenna 1008 and sent to the RF detection circuit (RF detection board 1007), where the transmitted and received signals pass through the antenna element selection switch (UWB antenna RF switch 1004).

[0504] In addition, the delayed signal (LO signal) is 1 / 2 the time it takes for the value of the PN code to change. n The detected signal is delayed by a time of n times (n is an integer greater than 2). The detected signal is A / D converted and stored as an IF signal (Intermediate Frequency Signal) by signal processing computer 1005. Information indicating the detected signal may also be displayed on signal monitoring device 1006.

[0505] The timing of this series of operations is controlled by a microprocessor in the digital control board 1003 so as to be synchronized with a signal (distance signal or free-run signal) from the rangefinder 1001. For example, the microprocessor in the digital control board 1003 transmits a switch switching signal, a PN code sweep trigger, etc.

[0506] Furthermore, the signal processing computer 1005 performs three-dimensional reconstruction using the A / D converted and stored signals, and displays a three-dimensional image. The signal processing computer 1005 may also perform signal calibration. The signal processing computer 1005 may also display raw waveforms. For example, the signal processing computer 1005 may also store three-dimensional images, etc. in the memory 1009.

[0507] The configuration shown in Fig. 16 is an example, and the configuration of imaging device 100 is not limited to the configuration shown in Fig. 16. Part of the configuration shown in Fig. 16 may be omitted or changed.

[0508] (supplement) Although the above describes aspects of the imaging device based on the embodiments, the aspects of the imaging device are not limited to the embodiments. Modifications conceivable by those skilled in the art may be made to the embodiments, and multiple components in the embodiments may be combined in any manner. For example, a process performed by a specific component in the embodiments may be performed by another component instead of the specific component. Furthermore, the order of multiple processes may be changed, and multiple processes may be performed in parallel.

[0509] Furthermore, the imaging method including the steps performed by each component of the imaging device may be executed by any device or system. For example, a part or all of the imaging method may be executed by a computer including a processor, a memory, an input / output circuit, etc. In this case, the imaging method may be executed by the computer executing a program for causing the computer to execute the imaging method.

[0510] The above program may also be recorded on a non-transitory computer-readable recording medium.

[0511] Furthermore, each component of the imaging device may be configured with dedicated hardware, general-purpose hardware that executes the above-mentioned programs, or a combination of these. The general-purpose hardware may be configured with a memory in which the programs are recorded and a general-purpose processor that reads and executes the programs from the memory. Here, the memory may be a semiconductor memory or a hard disk, and the general-purpose processor may be a CPU.

[0512] Furthermore, the dedicated hardware may be configured with a memory, a dedicated processor, etc. For example, the dedicated processor may execute the visualization method described above by referring to a memory for recording measurement data.

[0513] Furthermore, each component of the imaging device may be an electric circuit. These electric circuits may form a single electric circuit as a whole, or each may be a separate electric circuit. These electric circuits may correspond to dedicated hardware, or may correspond to general-purpose hardware that executes the above-mentioned programs, etc. [Industrial Applicability]

[0514] One aspect of the present disclosure is useful for an imaging device that uses waves to visualize the structure of scatterers contained in objects within a region, and is applicable to geophysical exploration, medical diagnosis, and the like. [Explanation of symbols]

[0515] 100 Imaging Device 101 Transmitter Row 102 Receiver Row 103 Information Processing Circuit 104 Display 111 Transmitter 112 Receiver 1001 Distance meter 1002 FPGA board for PN code generation 1003 Digital Control Board 1004 UWB Antenna RF Switch 1005 Signal Processing Computer 1006 Signal monitoring device 1007 RF detector board 1008 Multistatic Array Antenna 1009 Memory

Claims

1. a transmitter array including a plurality of transmitters arranged in a line and transmitting waves to a region to be measured; a receiver array spaced apart from the transmitter array, the receiver array including a plurality of receivers arranged on another line parallel to the line on which the plurality of transmitters are arranged and configured to receive the waves from the region; an information processing circuit that derives a visualization function corresponding to a scattering field function related to scattering of the wave according to measurement data obtained by combining all or part of the plurality of transmitters and the plurality of receivers and the distance between the line on which the plurality of transmitters are arranged and the line on which the plurality of receivers are arranged, and visualizes the structure of scatterers included in objects within the area using the visualization function; Imaging device.

2. the information processing circuit derives the scattered field function according to the measurement data and the distance, and derives the visualization function according to the scattered field function; The scattered field function is [Equation 1] is a function expressed as ρ １ and ρ ２ teeth, [Equation 2] It is defined in (x １ , y １ , z) indicates the transmitting position of the wave, and (x ２ , y ２ , z) denotes the receiving position of the wave, k denotes the wave number of the wave, D denotes the area, (ξ, η, ζ) corresponds to the reflection position of the wave, and ε corresponds to the unknown reflectivity at the reflection position. The imaging device of claim 1 .

3. the information processing circuit derives the scattered field function by solving an equation satisfied by the scattered field function; The equation is: [Equation 3] It is expressed as Δ ５ teeth, [Equation 4] It is defined in c indicates the propagation speed of the wave, and t indicates the time from transmission to reception of the wave.

3. The imaging device of claim 2.

4. The visualization function is [Equation 5] It is expressed as (x, y, z) indicates the position of the object to be visualized 4. The imaging device according to claim 2 or 3.

5. The information processing circuit [Equation 6] is derived as the scattered field function, k ｘ , s ３ and s ４ teeth, [Equation 7] It is defined in k ｘ１ , k ｙ１ and k ｙ２ is the x of the scattered field function １ , y １ and y ２ d indicates the distance, [Equation 8] is x １ , y １ and y ２ The measurement data is Fourier transformed with respect to 4. The imaging device according to claim 2 or 3.

6. The information processing circuit [Equation 9] is derived as the visualization function, k ｘ , k ｚ , k, dk / dk ｚ and s ４ teeth, [Equation 10] is determined by s ３ teeth, [0011] It is defined in (x, y, z) indicates the position of the object to be visualized, and k ｘ１ , k ｙ１ and k ｙ２ is the x of the scattered field function １ , y １ and y ２ d indicates the distance, [0012] is x １ , y １ and y ２ The measurement data is Fourier transformed with respect to 4. The imaging device according to claim 2 or 3.

7. The imaging device may comprise a plurality of transmitter arrays as the transmitter array, a plurality of receiver arrays as the receiver array, or a plurality of transmitter arrays and a plurality of receiver arrays as the transmitter array and the receiver array. The imaging device of claim 1 .

8. The imaging device may comprise a plurality of transmitter arrays as the transmitter array, a plurality of receiver arrays as the receiver array, or a plurality of transmitter arrays and a plurality of receiver arrays as the transmitter array and the receiver array.

4. The imaging device according to claim 2 or 3.

9. The information processing circuit [0013] is derived as the scattered field function, k ｘ , s ３ and s ４ teeth, [0014] It is defined in k ｘ１ , k ｙ１ and k ｙ２ is the x of the scattered field function １ , y １ and y ２ d indicates the distance, [Equation 15] is x １ , y １ and y ２ The measurement data is Fourier transformed with respect to 9. The imaging device of claim 8.

10. The information processing circuit, for one transmitter array and n receiver arrays provided in the imaging device as the transmitter array and the receiver array, [0016] is derived as the visualization function, k ｘ , k ｚ , k, dk / dk ｚ and s ４ teeth, [Equation 17] is determined by s ３ teeth, [Equation 18] It is defined in (x, y, z) indicates the position of the object to be visualized, and k ｘ１ , k ｙ１ and k ｙ２ is the x of the scattered field function １ , y １ and y ２ indicates the wave number for ｊ denotes the distance, [Equation 19] is x １ , y １ and y ２ The measurement data is Fourier transformed with respect to 9. The imaging device of claim 8.

11. When the dielectric constant corresponding to the reflectance in the region has frequency dependency, the information processing circuit [Equation 20] is derived as the visualization function, k ｘ , k ｚ , k, dk / dk ｚ , dω / dk and s ４ teeth, [0000] It is defined in s ３ teeth, [Equation 22] It is defined in (x, y, z) indicates the position of the object to be visualized, and k ｘ１ , k ｙ１ and k ｙ２ is the x of the scattered field function １ , y １ and y ２ where d denotes the distance, ω denotes the angular frequency of the wave, and c ０ denotes the propagation velocity of the wave in vacuum, a, b, and α denote parameters related to Debye relaxation, [Equation 23] is x １ , y １ and y ２ The measurement data is Fourier transformed with respect to 4. The imaging device according to claim 2 or 3.

12. the information processing circuit derives the scattered field function according to the measurement data and the distance, and derives the visualization function according to the scattered field function; The scattered field function is [0000] is a function expressed as ρ １ and ρ ２ teeth, [Equation 25] It is defined in (x １ , y １ , z １ ) indicates the transmitting position of the wave, and (x ２ , y ２ , z ２ ) denotes the receiving position of the wave, k denotes the wave number of the wave, D denotes the area, (ξ, η, ζ) corresponds to the reflection position of the wave, and ε corresponds to the unknown reflectivity at the reflection position. The imaging device of claim 1 .

13. the information processing circuit derives the scattered field function by solving an equation satisfied by the scattered field function; The equation is: [Equation 26] It is expressed as Δ ６ teeth, [0000] It is determined by 13. The imaging device of claim 12.

14. The visualization function is [0000] It is expressed as (x, y, z) indicates the position of the object to be visualized 14. The imaging device according to claim 12 or 13.

15. The information processing circuit [0000] is derived as the scattered field function, k ｘ , s ３ , s ４ and s ５ teeth, [Equation 30] It is defined in k ｘ１ , k ｙ１ and k ｙ２ is the x of the scattered field function １ , y １ and y ２ , d denotes the distance, and Φ(x Ｉ , y Ｉ , y Ｊ , z Ｉ , z Ｊ , k) is the transmission position (x Ｉ , y Ｉ , z Ｉ ) and the receiving position is (x Ｉ +d, y Ｊ , z Ｊ ) The measurement data in the case 14. The imaging device according to claim 12 or 13.

16. The information processing circuit [Equation 31] is derived as the visualization function, k ｘ , k ｚ , k, dk / dk ｚ , s ３ , s ４ and s ５ teeth, [Equation 32] It is defined in (x, y, z) indicates the position of the object to be visualized, and k ｘ１ , k ｙ１ and k ｙ２ is the x of the scattered field function １ , y １ and y ２ , d denotes the distance, and Φ(x Ｉ , y Ｉ , y Ｊ , z Ｉ , z Ｊ , k) is the transmission position (x Ｉ , y Ｉ , z Ｉ ) and the receiving position is (x Ｉ +d, y Ｊ , z Ｊ ) The measurement data in the case 14. The imaging device according to claim 12 or 13.

17. The imaging device may comprise a plurality of transmitter arrays as the transmitter array, a plurality of receiver arrays as the receiver array, or a plurality of transmitter arrays and a plurality of receiver arrays as the transmitter array and the receiver array.

14. The imaging device according to claim 12 or 13.

18. The information processing circuit [Equation 33] is derived as the scattered field function, k ｘ , s ３ , s ４ and s ５ teeth, [Equation 34] It is defined in k ｘ１ , k ｙ１ and k ｙ２ is the x of the scattered field function １ , y １ and y ２ , d denotes the distance, and Φ(x Ｉ , y Ｉ , y Ｊ , z Ｉ , z Ｊ , k) is the transmission position (x Ｉ , y Ｉ , z Ｉ ) and the receiving position is (x Ｉ +d, y Ｊ , z Ｊ ) The measurement data in the case 18. The imaging device of claim 17.

19. the information processing circuitry derives the imaging function using a combination of a plurality of scattered field functions for a plurality of combinations of the transmitter array and the receiver array; each of the plurality of scattered field functions corresponds to the scattered field function; [Equation 35] It is expressed as k ｘ , s ３ , s ４ and s ５ teeth, [Equation 36] It is defined in k ｘ１ , k ｙ１ and k ｙ２ is the x of the scattered field function １ , y １ and y ２ , d denotes the distance, and Φ(x Ｉ , y Ｉ , y Ｊ , z Ｉ , z Ｊ , k) is the transmission position (x Ｉ , y Ｉ , z Ｉ ) and the receiving position is (x Ｉ +d, y Ｊ , z Ｊ ) The measurement data in the case 18. The imaging device of claim 17.

20. When the dielectric constant corresponding to the reflectance in the region has frequency dependency, the information processing circuit [Equation 37] is derived as the visualization function, k ｘ , k ｚ , k, dk / dk ｚ , dω / dk, s ３ , s ４ and s ５ teeth, [Equation 38] It is defined in (x, y, z) indicates the position of the object to be visualized, and k ｘ１ , k ｙ１ and k ｙ２ is the x of the scattered field function １ , y １ and y ２ where d denotes the distance, ω denotes the angular frequency of the wave, and c ０ denotes the propagation velocity of the wave in vacuum, a, b, and α denote parameters related to Debye relaxation, [0.39] is x １ , y １ and y ２ The measurement data is Fourier transformed with respect to 14. The imaging device according to claim 12 or 13.

21. transmitting waves to a region to be measured by a plurality of transmitters of a transmitter array including a plurality of transmitters arranged in a line; receiving the waves from the area by a plurality of receivers in a receiver array spaced apart from the transmitter array, the receivers including a plurality of receivers arranged on another line parallel to the line on which the plurality of transmitters are arranged; and deriving an imaging function corresponding to a scattering field function relating to scattering of the wave according to measurement data obtained by a combination of all or part of the plurality of transmitters and the plurality of receivers and the distance between the line on which the plurality of transmitters are arranged and the line on which the plurality of receivers are arranged, and visualizing a structure of scatterers included in an object within the region using the imaging function. Visualization method.

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