Imaging device and imaging method

Abstract

The present disclosure provides an imaging device and the like capable of imaging a distant object in a wide range of measurement regions with high precision. A video device (100) is provided with: a plurality of transmitters (101) that transmit fluctuations from respective transmission regions to a measurement region; a plurality of receivers (102) that receive fluctuating scattered waves from the measurement region in respective reception regions; and an information processing circuit (103) that images an object in the measurement region, the transmission region and the reception region each having a finite size, and that derives a scattered field function reflecting the finite size using the measurement data. A video function determined on the basis of the amount output from the scattered field function by inputting the position to be video as the transmission position and the reception position into the scattered field function is derived, and the object is video by using the video function.

Description

Technical Field

[0001] The present disclosure relates to an imaging device and the like that uses measurement data of scattered waves to image an object in a measurement area. Background Art

[0002] As technologies related to imaging devices, there are known technologies described in Patent Documents 1, 2, 3, 4 and 5. The above-mentioned imaging devices are devices that use measurement data of scattered waves to image objects in a measurement area.

[0003] For example, in the technology described in Patent Document 1, a beam transmitted from a microwave transmitter is incident on an inspection object, and the amplitude and phase of the scattered beam are detected by a microwave detector. Furthermore, the distribution of the dielectric constant is calculated based on the output signal of the microwave detector, and an image of the section in the inspection object is displayed.

[0004] (Prior art literature)

[0005] (Patent Document)

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

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

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

[0009] Patent Document 4: International Publication No. 2021 / 020387

[0010] Patent Document 5: International Publication No. 2021 / 053971 Summary of the invention

[0011] Problems to be solved by the invention

[0012] However, it is not easy to image the objects in the measurement area using the measurement data of scattered waves. Specifically, when the state in the measurement area is known, obtaining the data of scattered waves radiated from the area for the waves incident on the measurement area is called a forward problem, which is easy. On the other hand, when the data of scattered waves is known, obtaining the state in the area is called an inversion problem, which is not easy.

[0013] Furthermore, it is difficult to transmit a wave to a distant object and receive a scattered wave from the distant object. Therefore, it is not easy to image a distant object in a wide measurement area with high accuracy.

[0014] Therefore, the present disclosure provides an imaging device and the like that can image a distant object in a wide measurement area with high accuracy.

[0015] Means for solving problems

[0016] An imaging device according to one embodiment of the present disclosure includes: a plurality of transmitters, each of which has a transmission area and transmits a wave from the respective transmission area to a measurement area; a plurality of receivers, each of which has a reception area and receives a scattered wave of the wave from the measurement area in the respective reception area; and an information processing circuit, which uses measurement data of the scattered wave to image an object in the measurement area, wherein the transmission area and the reception area each have a finite size, and the information processing circuit uses the measurement data to derive a scattering field function, which is a scattering field function reflecting the finite size, and the scattering field function is input to a transmission position of the wave and a reception position of the scattered wave and outputs an amount of the scattered wave at the reception position, and derives an imaging function, the imaging function being determined based on an amount output from the scattering field function by inputting an imaging target position as the transmission position and the reception position into the scattering field function, and the imaging function is input to the imaging target position and outputs an image intensity of the imaging target position, and the object in the measurement area is imaged using the imaging function.

[0017] In addition, these general or specific methods can be implemented through systems, devices, methods, integrated circuits, computer programs, or non-temporary recording media such as computer-readable CD-ROMs, or through any combination of systems, devices, methods, integrated circuits, computer programs, and recording media.

[0018] Effects of the Invention

[0019] According to the present disclosure, it is possible to image a distant object in a wide measurement area with high accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 is a conceptual diagram showing a one-dimensional multistatic array antenna.

[0021] Figure 2 This is a conceptual diagram showing the relationship between a transmission point and a reception point.

[0022] Figure 3 It is a conceptual diagram showing the coordinates of the transmission point and the reception point.

[0023] Figure 4This is a conceptual diagram showing the relationship between transmission points and reception points on a plane.

[0024] Figure 5 This is a conceptual diagram showing the relationship between transmission points and reception points on a curved surface.

[0025] Figure 6 : is a conceptual diagram showing an example of each coordinate related to a quasi-two-dimensional array antenna.

[0026] Figure 7 is a conceptual diagram showing a quasi-two-dimensional array antenna on a curved surface.

[0027] Figure 8 This is a conceptual diagram showing a quasi-two-dimensional array antenna composed of a plurality of directional antennas arranged on a plane.

[0028] Fig. 9 is a conceptual diagram showing a transmitting antenna and a receiving antenna having finite sizes.

[0029] Fig.10 This is a conceptual diagram showing a quasi-two-dimensional array antenna composed of a plurality of directional antennas arranged on an inclined surface.

[0030] Fig.11 is a conceptual diagram showing the rotation of the antenna.

[0031] Fig.12 is a conceptual diagram showing a matrix display rotated around the X-axis.

[0032] Fig.13 is a conceptual diagram showing a matrix display rotated about the y-axis.

[0033] Fig.14 is a conceptual diagram showing rotation scanning.

[0034] Fig.15 This is a block diagram showing the basic structure of the imaging device.

[0035] Fig.16 This is a flowchart showing the basic operation of the imaging device. DETAILED DESCRIPTION

[0036] An imaging device according to one embodiment of the present disclosure includes: a plurality of transmitters, each of which has a transmission area and transmits a wave from the respective transmission area to a measurement area; a plurality of receivers, each of which has a reception area and receives a scattered wave of the wave from the measurement area in the respective reception area; and an information processing circuit, which uses measurement data of the scattered wave to image an object in the measurement area, wherein the transmission area and the reception area each have a finite size, and the information processing circuit uses the measurement data to derive a scattering field function, which is a scattering field function reflecting the finite size, and the scattering field function is input to a transmission position of the wave and a reception position of the scattered wave and outputs an amount of the scattered wave at the reception position, and derives an imaging function, the imaging function being determined based on an amount output from the scattering field function by inputting an imaging target position as the transmission position and the reception position into the scattering field function, and the imaging function is input to the imaging target position and outputs an image intensity of the imaging target position, and the object in the measurement area is imaged using the imaging function.

[0037] According to this, the imaging device can use the measurement data to derive the state of scattering in the measurement area. Therefore, the imaging device can image the objects in the measurement area with high precision. In addition, the imaging device can send waves to distant objects and receive scattered waves from distant objects according to the directivity of the transmission area and the receiving area with limited size. Therefore, the imaging device can image distant objects in a wide range of measurement areas with high precision.

[0038] For example, the finite size is the same in the plurality of transmitters and the plurality of receivers.

[0039] According to this, the imaging device can apply the same calculation process to a plurality of transmitters and a plurality of receivers. Therefore, the imaging device can suppress the complexity of the calculation process.

[0040] Furthermore, for example, the transmission area and the reception area are each a rectangular area.

[0041] According to this, the imaging device can perform arithmetic processing corresponding to a simple shape. Therefore, the imaging device can suppress the complication of arithmetic processing.

[0042] In addition, for example, the multiple transmitters are arranged on a straight line, the multiple receivers are arranged on another straight line parallel to the straight line on which the multiple transmitters are arranged, and the distance between the straight line on which the multiple transmitters are arranged and the straight line on which the multiple receivers are arranged is reflected in the scattered field function.

[0043] According to this, the imaging device can obtain sufficient information as measurement data according to various combinations of multiple transmitters and multiple receivers arranged in quasi-two dimensions. In addition, since intervals are provided between the multiple transmitters and the multiple receivers, the imaging device can efficiently transmit waves to the measurement area and efficiently receive scattered waves from the measurement area.

[0044] Furthermore, the imaging device can image the object with high accuracy by using the measurement data of the scattered waves and the scattered field function derived according to the distances between the plurality of transmitters and the plurality of receivers.

[0045] In addition, for example, the scattered field function is expressed by [Mathematical Formula 1],

[0046] [Mathematical formula 1]

[0047]

[0048] x1 and y1 represent the x-coordinate and y-coordinate of the sending position, x2 and y2 represent the x-coordinate and y-coordinate of the receiving position, z represents the z-coordinate of the sending position and the receiving position, k represents the wave number of the wave, x , k y1 and k y2 represents the integral variable, d represents the distance,

[0049] [Mathematical formula 2] represents the measurement data after Fourier transformation of y1 and y2,

[0050] [Mathematical formula 2]

[0051]

[0052] k x1 , k x2 and k z It is defined by [Mathematical formula 3],

[0053] [Mathematical formula 3]

[0054]

[0055] a represents 1 / 2 of the finite size in the x-axis direction, and b represents 1 / 2 of the finite size in the y-axis direction.

[0056] According to this, the imaging device can image the object with high accuracy by using the scattered field function when the transmission position and the reception position have the same z coordinate.

[0057] In addition, for example, the imaging function is expressed by [Formula 4],

[0058] [Formula 4]

[0059]

[0060] The x, y, and z input to the imaging function represent the x-coordinate, y-coordinate, and z-coordinate of the imaging object position.

[0061] According to this, the imaging device can image the object with high accuracy using the imaging function when the transmission position and the reception position have the same z coordinate.

[0062] In addition, for example, the scattered field function is expressed by [Mathematical Formula 5],

[0063] [Formula 5]

[0064]

[0065] x1, y1 and z1 represent the x-coordinate, y-coordinate and z-coordinate of the sending position, x2, y2 and z2 represent the x-coordinate, y-coordinate and z-coordinate of the receiving position, k represents the wave number of the wave, k x , k y1 and k y2 represents an integral variable, d represents the distance in the x-axis direction, h1 represents the z-coordinate of the sending position corresponding to the measurement data, h2 represents the z-coordinate of the receiving position corresponding to the measurement data,

[0066] [Mathematical formula 6] represents the measurement data after Fourier transformation of y1 and y2,

[0067] [Mathematical formula 6]

[0068]

[0069] k x1 , k x2 , k z1 and k z2 It is defined by [Formula 7],

[0070] [Formula 7]

[0071]

[0072] a represents 1 / 2 of the finite size in the x-axis direction, and b represents 1 / 2 of the finite size in the y-axis direction.

[0073] According to this, the imaging device can image the object with high accuracy by using the scattered field function when the transmission position and the reception position may have different z-coordinates.

[0074] In addition, for example, the imaging function is expressed by [Mathematical Formula 8],

[0075] [Mathematical formula 8]

[0076]

[0077] The x, y, and z input to the imaging function represent the x-coordinate, y-coordinate, and z-coordinate of the imaging object position.

[0078] According to this, the imaging device can image the object with high accuracy using the imaging function when the transmission position and the reception position may have different z coordinates.

[0079] In addition, for example, each of the multiple transmitters changes the normal direction of the surface of the sending area by mechanically or electrically rotating the sending area, and each of the multiple receivers changes the normal direction of the surface of the receiving area by mechanically or electrically rotating the receiving area, and the information processing circuit uses the measurement data after the rotation of the sending area and the receiving area to image the object in the measurement area.

[0080] According to this, the imaging device can change the normal direction of the surface of each of the sending area and the receiving area. Thus, the imaging device can change the direction of the directivity of each of the sending area and the receiving area. Therefore, the imaging device changes the direction of the directivity and can image a distant object in that direction.

[0081] In addition, for example, the scattered field function is expressed by [Mathematical Formula 9],

[0082] [Mathematical formula 9]

[0083]

[0084] x1, y1 and z1 represent the x-coordinate, y-coordinate and z-coordinate of the sending position, x2, y2 and z2 represent the x-coordinate, y-coordinate and z-coordinate of the receiving position, k represents the wave number of the wave, k x , k y1 and k y2 represents an integral variable, d represents the distance in the x-axis direction, h1 represents the z-coordinate of the sending position corresponding to the measurement data, h2 represents the z-coordinate of the receiving position corresponding to the measurement data,

[0085] [Equation 10] represents the measurement data after Fourier transformation of y1 and y2,

[0086] [Formula 10]

[0087]

[0088] k x1 , k x2 , k z1 and k z2 It is defined by [Formula 11],

[0089] [Mathematical formula 11]

[0090]

[0091] f1 and f2 are defined by [Formula 12],

[0092] [Mathematical formula 12]

[0093]

[0094] a represents 1 / 2 of the finite size in the x-axis direction, b represents 1 / 2 of the finite size in the y-axis direction, α represents the rotation angle of the sending area and the receiving area around the x-axis by mechanical rotation or electrical rotation, β represents the rotation angle of the sending area and the receiving area around the y-axis by mechanical rotation or electrical rotation.

[0095] According to this, the imaging device can image the object with high accuracy by using the scattered field function when the direction of directivity can be changed.

[0096] In addition, for example, the imaging function is expressed by [Mathematical Formula 13],

[0097] [Mathematical formula 13]

[0098]

[0099] The x, y, and z input to the imaging function represent the x-coordinate, y-coordinate, and z-coordinate of the imaging object position.

[0100] According to this, the imaging device can image the object with high accuracy using an imaging function in which the direction of directivity can be changed.

[0101] In addition, for example, each of the multiple transmitters changes the normal direction of the surface of the transmitting area to multiple directions by causing the transmitting area to be mechanically rotated or electrically rotated at multiple rotation angles, and each of the multiple receivers changes the normal direction of the surface of the receiving area to be mechanically rotated or electrically rotated at the multiple rotation angles, and the information processing circuit uses the measurement data obtained for the multiple rotation angles of mechanical rotation or electrical rotation to image the object in the measurement area.

[0102] According to this, the imaging device can change the normal direction of the surface of the sending area and the receiving area in multiple directions. Therefore, the imaging device can change the direction of the directivity of the sending area and the receiving area in multiple directions. Therefore, the imaging device changes the direction of the directivity in multiple directions and can image distant objects in multiple directions.

[0103] In addition, for example, the scattered field function is expressed by [Equation 14],

[0104] [Formula 14]

[0105]

[0106] x1, y1 and z1 represent the x-coordinate, y-coordinate and z-coordinate of the sending position, x2, y2 and z2 represent the x-coordinate, y-coordinate and z-coordinate of the receiving position, k represents the wave number of the wave, k x , k y1 and k y2 represents an integral variable, d represents the distance in the x-axis direction, h1 represents the z-coordinate of the sending position corresponding to the measurement data, h2 represents the z-coordinate of the receiving position corresponding to the measurement data,

[0107] [Equation 15] represents the measurement data after Fourier transformation of y1 and y2,

[0108] [Mathematical formula 15]

[0109]

[0110] k x1 , k x2 , k z1 and k z2 It is defined by [Formula 16],

[0111] [Formula 16]

[0112]

[0113] f1 and f2 are defined by [Formula 17],

[0114] [Mathematical formula 17]

[0115]

[0116] a represents 1 / 2 of the finite size in the x-axis direction, b represents 1 / 2 of the finite size in the y-axis direction, α represents the rotation angle of the sending area and the receiving area around the x-axis by mechanical rotation or electrical rotation, β represents the rotation angle of the sending area and the receiving area around the y-axis by mechanical rotation or electrical rotation.

[0117] According to this, the imaging device can image the object with high accuracy by using the scattered field function when the direction of directivity can be changed in a plurality of directions.

[0118] In addition, for example, the imaging function is expressed by [Mathematical Formula 18],

[0119] [Mathematical formula 18]

[0120]

[0121] The x, y, and z input to the imaging function represent the x-coordinate, y-coordinate, and z-coordinate of the imaging object position.

[0122] According to this, the imaging device can image the object with high accuracy using an imaging function in which the direction of directivity can be changed to a plurality of directions.

[0123] In addition, an imaging method according to one embodiment of the present disclosure includes: a step of transmitting a wave from each of the transmitting regions to a measurement region by a plurality of transmitters each having a transmitting region; a step of receiving scattered waves of the wave from the measurement region in each of the receiving regions by a plurality of receivers each having a receiving region; and a step of imaging an object in the measurement region using measurement data of the scattered waves, wherein the transmitting region and the receiving region each have a finite size, and in the step of imaging the object in the measurement region, a scattering field function is derived using the measurement data, the scattering field function is a scattering field function that reflects the finite size, and the scattering field function is input to a transmitting position of the wave and a receiving position of the scattered wave and outputs an amount of the scattered wave at the receiving position, and an imaging function is derived, the imaging function is determined based on an amount output from the scattering field function by inputting an imaging target position as the transmitting position and the receiving position into the scattering field function, and the imaging function is input to the imaging target position and outputs an image intensity of the imaging target position, and the object in the measurement region is imaged using the imaging function.

[0124] According to this, the state of scattering in the measurement area can be derived using the measurement data. Thus, the objects in the measurement area can be imaged with high precision. Furthermore, according to the directivity of the transmission area and the receiving area with limited size, the wave can be sent to the distant object and the scattered wave can be received from the distant object. Therefore, the distant object in the wide range of the measurement area can be imaged with high precision.

[0125] The following embodiments are described using the accompanying drawings. In addition, the embodiments to be described below are all general or specific examples. The values, shapes, materials, components, configuration positions of components, connection methods, steps, and the order of steps shown in the following embodiments are all examples, and their purpose is not to limit the technical solution.

[0126] In addition, in the following description, in particular, the technologies described in the above-mentioned Patent Documents 2, 3, 4, and 5 can be referred to as prior art. In addition, in the following description, radio waves such as microwaves are mainly assumed to be waves, but waves are not limited to radio waves such as microwaves. In addition, imaging based on scattering can be expressed as scattering tomography. Therefore, the imaging device and the imaging method in the following description can be expressed as a scattering tomography device and a scattering tomography method, respectively.

[0127] (Implementation Method)

[0128] The imaging device in this embodiment uses the measurement data of the scattered waves to image the object in the measurement area. Hereinafter, the imaging device in this embodiment will be described in detail including the underlying technology and theory.

[0129] <1 Summary>

[0130] In the present disclosure, the scattered field theory using directional antennas is shown. For example, the scattered field theory using non-directional antennas is used for imaging the interior of a dielectric. For example, in imaging the interior of a dielectric, the surface of the dielectric is scanned and a three-dimensional image of the interior of the dielectric is reconstructed. The scattered field theory using directional antennas is used for imaging objects in the air.

[0131] For example, the area in the air cannot be scanned as the antenna moves because it is vast. Instead, an antenna with high directivity is used to image the object. As examples of using directional antennas in imaging objects, laser radar and millimeter wave radar can be cited. These devices are easy to implement. On the other hand, these devices have short wavelengths and strong beam properties compared to the properties of waves. From the perspective of the frequency of electromagnetic waves, the signal attenuation is large due to the influence of moisture in the air. Therefore, these devices cannot be used except at close range.

[0132] This disclosure shows imaging technology using microwaves that have both the properties of a beam (in other words, directivity) and the properties of a wave. In particular, Chapter 3 shows the theory of scattered fields using directional antennas. In addition, a specific mathematical formula for generating an image representing an object in a measurement area based on measurement data is shown when the transmitting antenna and the receiving antenna are fixed.

[0133] <2 Case of non-directional antenna>

[0134] First, in this chapter, the scattered field theory using omnidirectional antennas is explained.

[0135] <2-1 One-dimensional arrangement and plane boundary case>

[0136] In the method of arranging antenna elements for transmission and reception in one row, there is a limit to the spatial resolution.

[0137] Figure 1 is a conceptual diagram showing a one-dimensional multi-base array antenna. Figure 1As shown, when any two of the n elements are selected as the transmitting element and the receiving element, the above-mentioned double resolution can be obtained. Furthermore, the signal can be received with a high signal-to-noise ratio (S / N ratio) from short distance to long distance. Therefore, the quality of the final image is greatly improved. Of course, the amount of data increases n times, but according to the theory described below, the time required for reconstruction is also greatly shortened.

[0138] like Figure 1 As shown, what will be discussed here is the situation where the radio wave radiated 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 throughout the entire area D, the signal received at P2 is as shown in the following formula (2-1-1).

[0139] [Mathematical formula 19]

[0140]

[0141] Here, ε(ξ, η, ζ) represents a function of the dielectric constant of point P(ξ, η, ζ), corresponding to the reflectivity at point P(ξ, η, ζ). And point P(ξ, η, ζ) corresponds to the reflection point. In addition, ε(ξ, η, ζ) is unknown. And it is assumed that the time factor is proportional to exp(-iωt). The kernel function of the integrand in the above equation is expressed by φ in the following equation (2-1-2).

[0142] [Mathematical formula 20]

[0143]

[0144] Next, we will investigate the partial differential equation for which this equation (2-1-2) has an asymptotic solution. Therefore, we will calculate 1 / ρ generated in the differential result while ignoring the higher-order terms. Here, the abbreviated notation of the differential is defined as in equation (2-1-3).

[0145] [Mathematical formula 21]

[0146]

[0147] In addition, the partial differential equation (2-1-2) is considered to be an asymptotic solution in the case of short wavelength (high frequency or large k). The solution of this partial differential equation can be roughly regarded as an exact solution in the visualization using microwaves. First, the differential results of each order of φ are expressed as the following formula (2-1-4).

[0148] [Mathematical formula 22]

[0149]

[0150] The complicated terms of o(*) are omitted below. The following equation (2-1-5) is obtained by summing the four equations related to the second-order differential.

[0151] [Mathematical formula 23]

[0152]

[0153] Therefore, according to formula (2-1-5), the following formula (2-1-6) is obtained.

[0154] [Mathematical formula 24]

[0155]

[0156] By performing the operation of formula (2-1-6) twice, the following formula (2-1-7) is obtained.

[0157] [Mathematical formula 25]

[0158]

[0159] Arranging equation (2-1-7) yields the following equation (2-1-8).

[0160] [Mathematical formula 26]

[0161]

[0162] This equation (2-1-8) is derived assuming a steady state, but it is easy to extend this equation (2-1-8) to an unstable state. Therefore, we use the partial differential with respect to time t. And c, which represents the propagation speed of radio waves, replace the variables as shown in the following formula (2-1-9).

[0163] [Mathematical formula 27]

[0164]

[0165] Through the above process, the following equation (2-1-10) is finally obtained.

[0166] [Mathematical formula 28]

[0167]

[0168] The above equation (2-1-10) is a partial differential equation with φ as the solution of equation (2-1-2). By applying differentiation to the integral kernel of equation (2-1-1), [Mathematical Formula 29] of equation (2-1-1)

[0169]

[0170] The above partial differential equation is also satisfied. This equation is a four-dimensional simulated wave equation consisting of five variables (t, x, y1, y2, z).

[0171] Next, we use the Fourier transform to solve the equation. First,

[0172] [Math 30]

[0173]

[0174] As shown in the following formula (2-1-11), multiple Fourier transform is performed on t, x, y1, and y2.

[0175] [Mathematical formula 31]

[0176]

[0177] When expressing the differential with respect to z as D z In the case of , the following formula (2-1-12) is obtained according to formula (2-1-10) and formula (2-1-11).

[0178] [Math 32]

[0179]

[0180] Here, the relationship of ω=ck is used. The four basic solutions of this equation are expressed as shown in the following equation (2-1-13).

[0181] [Mathematical formula 33]

[0182]

[0183] When the time factor is considered to be e -iωt , when the phase is added to the path of the radiated radio wave, and when the radio wave reflected by the object bounces back toward the measurement surface (measurement surface), E1 is the only meaningful solution. Therefore, the following equation (2-1-14) is obtained.

[0184] [Math 34]

[0185]

[0186] By substituting z=0 into the formula (2-1-14), a(k x , k y1 , k y2 , k).

[0187] [Mathematical formula 35]

[0188]

[0189] final,

[0190] [Mathematical formula 36]

[0191]

[0192] It can be calculated as shown in the following formula (2-1-16).

[0193] [Mathematical formula 37]

[0194]

[0195] Under the condition that k and z are fixed, the limit operation (y2→y1=y) is applied to equation (2-1-16), and the result is integrated with respect to k to obtain the visualization function as shown in equation (2-1-17).

[0196] [Math 38]

[0197]

[0198] As described above, the multi-base backscattering problem in a one-dimensional array can be solved analytically. However, there is a big restriction that the transmitting element and the receiving element are arranged in a one-dimensional array. In addition, there are hardware issues, such as the need to set a gap to avoid inductive coupling between the transmitting element and the receiving element, and the inability to switch the role of transmitting and receiving when an active balun is used. Furthermore, due to the difficulty in parallelizing the measurement, there is also the issue of longer data acquisition time.

[0199] <2-2 One-dimensional arrangement and curved surface boundary case>

[0200] The inverse scattering theory is described below when the boundary surface of the region is a curved surface.

[0201] Figure 2 This is a conceptual diagram showing the relationship between a transmission point and a reception point. Figure 2 The diagram shows a situation in which a wave emitted from point r1 is reflected at points ξ (ξ1, ξ2, ...) and returns to point r2.

[0202] For example, under the condition that the angular frequency ω (= 2πf) is constant, the transmitting point r1 and the receiving point r2 of the wave move freely and independently inside the x-section D while satisfying a certain constraint condition. When the data obtained at this time is represented by the function G (r1, r2, ω), the function G (r1, r2, ω) should be related to the distribution of the reflection points in the area.

[0203] Here, G(r1, r2, ω) is the sum of the reflection signals from all points ξ. In addition, since there are a large number of reflection points in the area, G(r1, r2, ω) can be expressed as shown in the following equation (2-2-1).

[0204] [Math 39]

[0205]

[0206] Here,

[0207] [Math 40]

[0208]

[0209] It represents the signal strength of the fluctuation that is emitted from point r1, reflected at point ξ and returned to point r2.

[0210] Furthermore, a constraint is imposed on the fluctuating transmitting point r1 and receiving point r2 that the x-coordinates of r1 and r2 are always equal.

[0211] The following uses this function G(r1, r2, ω) to explain the theoretical construction of the inverse problem of scattering. Here, a partial region of the three-dimensional space is represented by D, and its boundary is represented by In this case, the function G(r1, r2, ω) inside the region D becomes a solution of the differential equation shown in the following equation (2-2-2).

[0212] [Mathematical formula 41]

[0213]

[0214] Here,

[0215] [Mathematical formula 42]

[0216]

[0217] is the function obtained by Fourier transforming the function G(r1, r2, ω) with respect to ω. The value of G(r1, r2, ω) at is based on the measured value of the receiving element. The above equation is solved under this boundary condition. Based on the result, ρ(r) is defined as follows in equation (2-2-3).

[0218] [Mathematical formula 43]

[0219]

[0220] Here, Tr represents a tracking operation. This ρ(r) is a function related to the gradient of the dielectric constant in the region D to be determined. In practice, it is difficult to determine the differential operator that appears here.

[0221] The following describes a method for finding the differential operator. The y coordinates and z coordinates of r1 and r2 on an arbitrary curve are not necessarily equal. Specifically, r1 and r2 can be expressed as r1 = (x, y1, z1) and r2 = (x, y2, z2). Furthermore, the function G is defined as follows.

[0222] [Mathematical formula 44]

[0223]

[0224] Next, we will consider an equation that satisfies the function G(r1, r2, ω). Here, ω=ck. c is the propagation velocity, and k is the wave number. When the wavelength is λ, the relationship k=2π / λ holds.

[0225] Figure 3 is a conceptual diagram showing the coordinates of the transmission point and the reception point. Figure 3 In the example, the transmitting point is located at P1 (x, y1, z1) and the receiving point is located at P2 (x, y2, z2). The wave radiated from the transmitting point P1 is reflected at the point P (ξ, η, ζ) and reaches the receiving point P2.

[0226] For example, z1 and z2 are arbitrary. The measurement points corresponding to the transmission point P1 and the reception point P2 move on the 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. In addition, the distance between P1 and P is expressed by ρ1, and the distance between P2 and P is expressed by ρ2.

[0227] In the above case, a function φ such as the following equation (2-2-5) is introduced as a scattered field function.

[0228] [Mathematical formula 45]

[0229]

[0230] Here, ε(ξ, η, ζ) represents a function of the dielectric constant of the point (ξ, η, ζ), corresponding to the reflectivity of the point (ξ, η, ζ). And, the point (ξ, η, ζ) corresponds to the reflection point. In addition, ε(ξ, η, ζ) is unknown. And, k represents the wave number. And, it is assumed that the time factor is proportional to exp(-iωt). The function in the integrated term of the above formula (2-2-5) is [Mathematical Formula 46] of the formula (2-2-1).

[0231] [Mathematical formula 46]

[0232]

[0233] That is, the following formula (2-2-6) holds.

[0234] [Mathematical formula 47]

[0235]

[0236] Next, we will discuss the partial differential equation for which equation (2-2-6) becomes an asymptotic solution at high frequencies. Therefore, we calculate 1 / ρ generated in the differential result by ignoring the higher-order terms. Here, the simplified notation of the differential is defined as in the following equation (2-2-7).

[0237] [Mathematical formula 48]

[0238]

[0239] As a result of the calculation, an equation was derived in which φ satisfies the following equation (2-2-8).

[0240] [Math 49]

[0241]

[0242] This equation (2-2-8) is derived assuming a stable state, but it is easy to extend this equation (2-2-8) to an unstable state. To do this, variables are replaced as in the following equation (2-2-9).

[0243] [Mathematical formula 50]

[0244]

[0245] Finally, the following formula (2-2-10) is obtained.

[0246] [Mathematical formula 51]

[0247]

[0248] Next, assuming that the time factor φ is proportional to exp(-iωt), we will explore the solution of equation (2-2-10). First, by performing multiple Fourier transforms on φ with respect to t, x, y1, and y2, we obtain the following equation (2-2-11).

[0249] [Mathematical formula 52]

[0250]

[0251] By expressing the partial differentials with respect to z1 and z2 as D z1 , D z2 , and obtain the following formula (2-2-12).

[0252] [Mathematical formula 53]

[0253]

[0254] Next, let's consider the solution to equation (2-2-12). However, there are two variables z1 and z2. Therefore, for fixed (x, y1, y2) or (k x , k y1 , k y2 ), it is difficult to solve equation (2-2-12) if boundary conditions are not given for the region with one degree of freedom in the (z1, z2) space. However, the boundary conditions obtained by radar measurement are given only at one point (f(y1), f(y2)) in the (z1, z2) space.

[0255] In order to solve this problem, we use the integration of the theory in the case of z1=z and z2=z and the theory in this section. That is, the solution derived from the theory in this section where z1 and z2 are independent includes the solution in the special case where z1=z and z2=z. Therefore, we first assume that the solution of equation (2-2-12) is as shown in equation (2-2-13).

[0256] [Mathematical formula 54]

[0257]

[0258] When z1=z2=z, the following formula (2-2-14) is obtained.

[0259] [Mathematical formula 55]

[0260]

[0261] Furthermore, by substituting formula (2-2-13) into formula (2-2-12), the following formula (2-2-15) is obtained.

[0262] [Mathematical formula 56]

[0263]

[0264] Furthermore, another equation is used. Specifically, based on the equation (2-1-15) in the previous section, according to the above integration, the following equation (2-2-16) is obtained.

[0265] [Mathematical formula 57]

[0266]

[0267] According to equations (2-2-15) and (2-2-16), s1(k x , k y1 , k y2 , k) and s2(k x, k y1 , k y2 , k).

[0268] [Mathematical formula 58]

[0269]

[0270] Using the above s1(k x , k y1 , k y2 , k) and s2(k x , k y1 , k y2 , k), derive the solution of equation (2-2-10) as shown in equation (2-2-18).

[0271] [Math 59]

[0272]

[0273] <2-3 Two-dimensional arrangement and plane boundaries>

[0274] In this section, the theory is explained in the case of two-dimensional arrays and planar boundaries.

[0275] Figure 4 is a conceptual diagram showing the relationship between the transmission point and the reception point in a plane. Figure 4 As shown in the figure, the microwave radiated from point P1 is reflected at point P on the target and received at point P2. Points P1 and P2 move to any point on the grid point (two-dimensional array antenna) in the plane. Under this assumption, the path of the microwave passing through point P on the target has n 4 These numerous paths contribute greatly to improving the quality of the final image. The following describes a method for processing such complex data and obtaining an image.

[0276] For example Figure 4 As shown, the radio wave radiated from point P1 (x1, y1, z) is reflected at point P (ξ, η, ζ) and received at point P2 (x2, y2, z). When point P moves in the entire area D, the signal received at point P2 is expressed as follows.

[0277] [Math 60]

[0278]

[0279] Here, it is assumed that the time factor is proportional to exp(-iωt). The kernel function of the integrand in the above equation is expressed by the following equation (2-3-2).

[0280] [Mathematical formula 61]

[0281]

[0282] Next, we will investigate the partial differential equation that this equation (2-3-2) becomes an asymptotic solution in the case of short wavelengths. Therefore, regarding 1 / ρ generated in the differential result, the calculation is performed while ignoring the higher-order terms. Here, the simplified notation of the differential is defined as in equation (2-3-3).

[0283] [Mathematical formula 62]

[0284]

[0285] Using formula (2-3-3), the differentials of the kernel function at each order are expressed as shown in the following formula (2-3-4).

[0286] [Mathematical formula 63]

[0287]

[0288] In the following, the complicated o(*) term is omitted. According to the sum of the five equations about the second-order differential, the following equation (2-3-5) is obtained.

[0289] [Mathematical formula 64]

[0290]

[0291] Therefore, according to formula (2-3-5), the following formula (2-3-6) is obtained.

[0292] [Mathematical formula 65]

[0293]

[0294] By performing the operation of formula (2-3-6) twice, the following formula (2-3-7) is obtained.

[0295] [Mathematical formula 66]

[0296]

[0297] Arranging formula (2-3-7) yields the following formula (2-3-8).

[0298] [Mathematical formula 67]

[0299]

[0300] This equation (2-3-8) is derived assuming a stable state, but it is easy to extend this equation (2-3-8) to an unstable state. To this end, variables are replaced as shown in the following equation (2-3-9).

[0301] [Mathematical formula 68]

[0302]

[0303] Through this replacement, equation (2-3-8) is transformed into the following equation (2-3-10) including time.

[0304] [Math 69]

[0305]

[0306] The above equation (2-3-10) is a partial differential equation with the kernel function shown in equation (2-3-2) as a solution. By applying differentiation to the integral kernel of equation (2-3-1), φ also satisfies the above partial differential equation. This equation is a five-dimensional simulated wave equation consisting of six variables (t, x1, y1, x2, y2, z).

[0307] Next, the equation is solved using Fourier transform. First, φ is multi-Fourier transformed with respect to t, x1, y1, x2, and y2 as shown in the following equation (2-3-11).

[0308] [Mathematical formula 70]

[0309]

[0310] When expressing the differential with respect to z as D z In the case of , the following formula (2-3-12) is obtained according to formulas (2-3-10) and (2-3-11).

[0311] [Mathematical formula 71]

[0312]

[0313] Here, the relationship of ω=ck is used. The four basic solutions of this equation are expressed as shown in the following equation (2-3-13).

[0314] [Mathematical formula 72]

[0315]

[0316] When the time factor is considered to be e -iωt , adding a phase to the path of the radiated radio wave, and when the radio wave reflected by the object bounces back toward the measurement surface, E1 is the only meaningful solution. Therefore, the following equation (2-3-14) is obtained.

[0317] [Mathematical formula 73]

[0318]

[0319] By substituting z=0 into the formula (2-3-14), a(k x1 , ky1 , k x2 , k y2 , k).

[0320] [Mathematical formula 74]

[0321]

[0322] Based on the above, φ is calculated as shown in the following formula (2-3-16).

[0323] [Mathematical formula 75]

[0324]

[0325] Next, by applying the limit operation (y1→y and y2→y) to equation (2-3-16) under the condition that k and z are fixed, the following equation (2-3-17) is obtained.

[0326] [Mathematical formula 76]

[0327]

[0328] Next, by integrating equation (2-3-17) with respect to k, the following equation (2-3-18) is obtained as a visualization function.

[0329] [Mathematical formula 77]

[0330]

[0331] In formula (2-3-18), with k x1 , k y1 , k x2 , k y2 The relevant integral becomes a Fourier transform form, which is suitable for computer processing. On the other hand, in the integrand, the term exp(iz...) does not become a Fourier transform form. Therefore, for example, the normal integration is performed with respect to k while specifying the value of z. Alternatively, in order to reduce the calculation time, the formula (2-3-18) can be deformed so that the whole is represented only by the Fourier transform.

[0332] For example, the coefficient of iz in exp(iz...) in equation (2-3-17) is expressed as in the following equation (2-4-19) using a new variable u.

[0333] [Mathematical formula 78]

[0334]

[0335] By rationalizing the right side of equation (2-3-19), we obtain the following equation (2-3-20).

[0336] [Mathematical formula 79]

[0337]

[0338] By solving each square root according to equations (2-3-19) and (2-3-20), the following equation (2-3-21) is obtained.

[0339] [Math 80]

[0340]

[0341] Therefore, k is expressed as shown in the following formula (2-3-22).

[0342] [Mathematical formula 81]

[0343]

[0344] Furthermore, by differentiating k and u on both sides of equation (2-3-19), the following equation (2-3-23) is obtained.

[0345] [Mathematical formula 82]

[0346]

[0347] By solving dk according to formula (2-3-23), we can obtain the following formula (2-3-24).

[0348] [Mathematical formula 83]

[0349]

[0350] Finally, to summarize, formula (2-3-18) is transformed into the following formula (2-3-25).

[0351] [Mathematical formula 84]

[0352]

[0353] In the case of applying this result to the quasi-two-dimensional array antenna arrangement described later, the dimension of the integration will only increase by the value of dk x2 Therefore, with the computing power of existing computers, it takes time to calculate, which is far from real time.

[0354] <2-4 Two-dimensional arrangement and curved surface boundary case>

[0355] Figure 5 This is a conceptual diagram showing the relationship between the transmission point and the reception point on the curved surface. Since the boundary condition of the curved surface is used, it is assumed that the z coordinates of the transmission point and the reception point are different. Therefore, the scattered field function is expressed as shown in the following equation (2-4-1).

[0356] [Mathematical formula 85]

[0357]

[0358] Here, k represents the wave number. And, it is assumed that the time factor is proportional to exp(-iωt). And, D represents the area, corresponding to Figure 5 D3 in the above equation. The kernel function of the integrand is expressed by the following equation (2-4-2).

[0359] [Mathematical formula 86]

[0360]

[0361] Next, we will explore the partial differential equations that can be solved by equation (2-4-2) except for the area very close to the transmission and reception point. Therefore, for 1 / ρ generated in the differential result, the higher-order terms are ignored and the calculation is performed. Here, the simplified notation of the differential is defined as in the following equation (2-4-3).

[0362] [Mathematical formula 87]

[0363]

[0364] In this case, through the same calculation as in the previous section, the kernel function is derived to satisfy the following equation (2-4-4).

[0365] [Mathematical formula 88]

[0366]

[0367] Assuming that the time factor is proportional to exp(-iωt), we explore the solution of the above equation (2-4-4). First, by performing multiple Fourier transforms on the kernel function with respect to t, x1, x2, y1, and y2, we obtain the following equation.

[0368] [Mathematical formula 89]

[0369]

[0370] Similar to formula (2-3-12) in the previous section, the following formula (2-4-6) is obtained based on formula (2-4-4).

[0371] [Mathematical formula 90]

[0372]

[0373] Next, let's consider solving this equation. However, there are two variables z1 and z2. Therefore, for a fixed (x1, x2, y1, y2) or (k x1 , k x2 , ky1 , k y2 ), it is difficult to solve the equation of formula (2-4-6) without giving boundary conditions to the region with one-dimensional freedom in the (z1, z2) space. However, the boundary conditions obtained by radar measurement are given only at one point {f(x1, y1), f(x2, y2)} in the (z1, z2) space.

[0374] To solve this problem, we use the integration of the theory in the case of z1=z and z2=z and the theory in this section. That is, the solution derived from the theory in this section based on z1 and z2 being independent includes the solution in the special case of z1=z and z2=z. So, first, assume that the solution of equation (2-4-6) is as shown in equation (2-4-7).

[0375] [Mathematical formula 91]

[0376]

[0377] Based on formula (2-4-6), formula (2-4-7) and the above integration, the following formula (2-4-8) and formula (2-4-9) are obtained.

[0378] [Mathematical formula 92]

[0379]

[0380] [Mathematical formula 93]

[0381]

[0382] Thus, s1 and s2 are obtained as shown in the following formula (2-4-10).

[0383] [Mathematical formula 94]

[0384]

[0385] Using s1 and s2 as described above, the solution of the equation is expressed as shown in the following equation (2-4-11).

[0386] [Mathematical formula 95]

[0387]

[0388] In addition, the equation of the curved surface S is assumed to be, for example, the following equation (2-4-12).

[0389] [Mathematical formula 96]

[0390] z=f(x,y)

[0391] …(2-4-12)

[0392] The boundary conditions given on the curved surface S are expressed as follows (2-4-13).

[0393] [Mathematical formula 97]

[0394]

[0395] The equation (2-4-13) is used to determine a(k x1 , k x2 , k y1 , k y2 ). In the following text, a simplified notation such as the following formula (2-4-14) is used.

[0396] [Mathematical formula 98]

[0397]

[0398] Using the abbreviated notation of formula (2-4-14), an integral equation related to a(k) as shown in the following formula (2-4-15) is derived.

[0399] [Mathematical formula 99]

[0400]

[0401] If a(k) is calculated according to the above formula (2-4-15), the scattered field function can be expressed as shown in the following formula (2-4-16).

[0402] [Mathematical formula 100]

[0403]

[0404] In the above formula (2-4-16), z1=z2=z is applied, and then Fourier transform is performed on k, thereby obtaining the imaging function as shown in the following formula (2-4-17).

[0405] [Math 101]

[0406]

[0407] Through the above process, the final visualization function ρ(r) is obtained.

[0408] <2-5 Quasi-two-dimensional arrangement and plane boundary case>

[0409] Figure 61 is a conceptual diagram showing an example of coordinates related to a quasi-two-dimensional array antenna. In this example, the quasi-two-dimensional array antenna is composed of two columns of linear array antennas, one column of transmission array antennas TA and one column of reception array antennas RA. Such a quasi-two-dimensional array antenna is expressed as an S-Array (super-array) or an S-Array multi-base antenna.

[0410] The transmission array antenna TA includes n transmission antenna elements T. The reception array antenna RA includes n reception antenna elements R. The x coordinate of the transmission array antenna TA is represented by x1, the x coordinate of the reception array antenna RA is represented by x2, and the distance between the transmission array antenna TA and the reception array antenna RA in the x-axis direction is represented by d. In this configuration, n arbitrary combinations of n transmission elements and n reception elements are obtained at each point x in the scanning direction. 2 time series data.

[0411] In this section, the following are described: Figure 6 The theory of imaging an object using data obtained from a quasi-two-dimensional array antenna as shown. First, as a starting point for discussion, we use equation (2-3-10) related to two-dimensional arrangement. The following equation (2-5-1) is the same as equation (2-3-10).

[0412] [Mathematical formula 102]

[0413]

[0414] also,

[0415] [Mathematical formula 103]

[0416]

[0417] The Fourier transform of t, x1, y1, y2 is expressed as the following formula (2-5-2).

[0418] [Mathematical formula 104]

[0419]

[0420] The variable x2 is expressed as u below. By Fourier transforming both sides of equation (2-5-1) with respect to t, x1, y1, and y2, the following equation (2-5-3) is obtained.

[0421] [Mathematical formula 105]

[0422]

[0423] The solution of the above-mentioned formula (2-5-3) as a two-dimensional partial differential equation for u and z is assumed to be the following formula (2-5-4).

[0424] [Mathematical formula 106]

[0425]

[0426] Here, s3 and s4 are related to k as shown in the following formula (2-5-5): x1 , k y1 , k y2 and k. In other words, s3 and s4 are determined by k x1 , k y1 , k y2 and k are constants defined by the equation

[0427] [Mathematical formula 107]

[0428]

[0429] By substituting formula (2-5-4) into formula (2-5-3), the following formula (2-5-6) is obtained.

[0430] [Mathematical formula 108]

[0431]

[0432] s3 and s4 cannot be determined by only this algebraic equation. Next, the equation (2-5-4) is changed to the following equation (2-5-7).

[0433] [Mathematical formula 109]

[0434]

[0435] By converting equation (2-5-7) about k x1 , k y1 and k y2 Perform an inverse Fourier transform and apply u→x2 to the result to obtain the following equation (2-5-8).

[0436] [Mathematical formula 110]

[0437]

[0438] By applying x2=x1=x to equation (2-5-8), the following equation (2-5-9) is obtained.

[0439] [Mathematical formula 111]

[0440]

[0441] Here, k x It is expressed by the following formula (2-5-10).

[0442] [Mathematical formula 112]

[0443]

[0444] The above equation (2-5-9) is consistent with the solution of the scattered field equation of the one-dimensional array, and therefore should be consistent with equation (2-1-16). The following equation (2-5-11) is the same as equation (2-1-16).

[0445] [Mathematical formula 113]

[0446]

[0447] By comparing formula (2-5-9) with formula (2-5-11), the following formula (2-5-12) can be obtained.

[0448] [Mathematical formula 114]

[0449]

[0450] By squaring the second part of equation (2-5-12), we obtain the following equation (2-5-13).

[0451] [Mathematical formula 115]

[0452]

[0453] By substituting formula (2-5-13) into formula (2-5-6), the following formula (2-5-14) is obtained.

[0454] [Mathematical formula 116]

[0455]

[0456] By rearranging formula (2-5-14), we obtain the following formula (2-5-15).

[0457] [Mathematical formula 117]

[0458]

[0459] Since the solution of this equation is a repeated root, the solution expressed by the following equation (2-5-16) is uniquely obtained.

[0460] [Mathematical formula 118]

[0461]

[0462] According to equations (2-5-12) and (2-5-16) obtained in the above process, s3 and s4 are analytically calculated. Furthermore, according to equation (2-5-8), the scattered field function is obtained as shown in equation (2-5-17).

[0463] [Mathematical formula 119]

[0464]

[0465] Next, we will discuss the relationship between the measured data Φ(x1, y1, y2, k) and a(k x1 , k y1 , k y2 , k) are connected. Therefore, by determining k x =k x1 +is3, substitute z=0 and x2=x1+d into equation (2-5-17), and the following equation (2-5-18) is established. Here, Φ(x1, y1, y2, k) is the measurement data of the transmission point (x1, y1, 0), the receiving point (x1+d, y2, 0) and the wave number k.

[0466] [Mathematical formula 120]

[0467]

[0468] Hereinafter, k defined by the following formula (2-5-19) is used x and s3.

[0469] [Mathematical formula 121]

[0470]

[0471] By performing Fourier transform on both sides of equation (2-5-18) with respect to x1, y1, and y2, we obtain the following equation (2-5-20).

[0472] [Mathematical formula 122]

[0473]

[0474] According to formula (2-5-20), the function a(k x , k y1 , k y2 , k).

[0475] [Mathematical formula 123]

[0476]

[0477] Therefore, equation (2-5-17) as a scattered field function is obtained in a complete form as shown in the following equation (2-5-22).

[0478] [Mathematical formula 124]

[0479]

[0480] Then, the visualization function is obtained as shown in the following formula (2-5-23).

[0481] [Mathematical formula 125]

[0482]

[0483] Furthermore, compared with a one-dimensional array, a larger number of transmitting elements and a larger number of receiving elements can be arranged in a quasi-two-dimensional array, so that information can be obtained more efficiently.

[0484] <2-6 Quasi-two-dimensional arrangement and curved surface boundary case>

[0485] The following describes a theory in the case where the boundary of a region, that is, the boundary surface where the scattered data is measured is a curved surface.

[0486] Figure 7 This is a conceptual diagram showing a quasi-two-dimensional array antenna on a curved surface. Here, the shape of the curved surface is a simple shape represented by z=f(x). A plurality of transmitting antennas are arranged on a straight line where x=x1 and z=z1. Furthermore, a plurality of receiving antennas are arranged on a plurality of columns defined by a straight line where x=x2 and z=z2, and a straight line where x=x3 and z=z3, etc. A receiving array antenna in one column of a plurality of columns of receiving array antennas may also be used. Furthermore, scanning may also be performed by moving the quasi-two-dimensional array antenna in the x-axis direction along the curved surface.

[0487] The inverse scattering theory for the case of a quasi-two-dimensional array is constructed based on the theory of Section 4. The scattered field function is a function such as the following equation (2-6-1).

[0488] [Mathematical formula 126]

[0489]

[0490] The equation satisfied by the scattered field function of formula (2-6-1) is formula (2-4-4) and is expressed as shown in the following formula (2-6-2).

[0491] [Mathematical formula 127]

[0492]

[0493] Here, a Fourier transform such as the following equation (2-6-3) is used.

[0494] [Mathematical formula 128]

[0495]

[0496] Based on formula (2-6-2) and formula (2-6-3), the following formula (2-6-4) is obtained.

[0497] [Mathematical formula 129]

[0498]

[0499] As a solution to the equation of formula (2-6-4), assume the following formula (2-6-5).

[0500] [Mathematical formula 130]

[0501]

[0502] By substituting formula (2-6-5) into formula (2-6-4), the following formula (2-6-6) is obtained.

[0503] [Mathematical formula 131]

[0504]

[0505] then,

[0506] [Mathematical formula 132]

[0507]

[0508] It is expressed as the following formula (2-6-7).

[0509] [Mathematical formula 133]

[0510]

[0511] In the case of x2→x1, equation (2-6-7) is consistent with equation (2-2-18). In the case of x2→x1, equation (2-6-7) is expressed as follows: equation (2-6-8).

[0512] [Mathematical formula 134]

[0513]

[0514] In addition, the same formula as formula (2-2-18) is expressed as the following formula (2-6-9).

[0515] [Mathematical formula 135]

[0516]

[0517] Since formula (2-6-8) is consistent with formula (2-6-9), the following formula (2-6-10) is obtained.

[0518] [Mathematical formula 136]

[0519]

[0520] Next, based on equations (2-6-6), (2-6-9) and (2-6-10), an algebraic equation for s3 is obtained as shown in equation (2-6-11).

[0521] [Mathematical formula 137]

[0522]

[0523] Regarding formula (2-6-11), by expanding the quadratic term and simplifying it, we obtain the following formula (2-6-12).

[0524] [Mathematical formula 138]

[0525]

[0526] Furthermore, by rearranging formula (2-6-12), we obtain the following formula (2-6-13).

[0527] [Mathematical formula 139]

[0528]

[0529] There are two solutions in equation (2-6-13). However, the solution of equation (2-6-13) should be consistent with the case of the plane boundary in the previous section. Therefore, according to equation (2-5-16), the following equation (2-6-14) should be selected as the solution.

[0530] [Mathematical formula 140]

[0531]

[0532] Summarizing the above, the scattered field function is obtained as shown in the following formula (2-6-15).

[0533] [Mathematical formula 141]

[0534]

[0535] In addition, in formula (2-6-15), by changing the variable from k x1 Transform to k x , thus obtaining the following formula (2-6-16).

[0536] [Mathematical formula 142]

[0537]

[0538] Next, we will discuss the relationship between the measured data Φ(x1, y1, y2, k) and b(k x1 , k y1 , k y2 , k) connected. By the point P on the surface I and PJ The measured data Φ(x I ,y I , x I +d,y J , t) is Fourier transformed and the function obtained is expressed as follows (2-6-17).

[0539] [Mathematical formula 143]

[0540]

[0541] The shape of the boundary curved surface serving as the measurement surface is expressed as shown in the following formula (2-6-18).

[0542] [Mathematical formula 144]

[0543] z=f(x,y)

[0544] …(2-6-18)

[0545] Here, (x, y) is the coordinate on the plane when z = 0. I , P J The z coordinate of is expressed as shown in the following formula (2-6-19).

[0546] [Mathematical formula 145]

[0547] z1=f(x1,y1)

[0548] z J =f(x J ,y J )

[0549] …(2-6-19)

[0550] By substituting x2=x1+d into formula (2-6-15), the following equation (2-6-20) is established.

[0551] [Mathematical formula 146]

[0552]

[0553] The above formula (2-6-20) uses the data Φ obtained by measurement on the boundary and is expressed as follows in the formula (2-6-21).

[0554] [Mathematical formula 147]

[0555]

[0556] Φ(x I ,y I ,y J , z I , zJ , k) is the sending point (x I ,y I , z I ), receiving point (x I +d,y J , z J ) and the measurement data of wave number k. By Fourier transforming both sides of equation (2-6-21), we get the following equation (2-6-22).

[0557] [Mathematical formula 148]

[0558]

[0559] And, as a result of the integration related to x1, y1, and y2 in formula (2-6-22), the following formula (2-6-23) is obtained.

[0560] [Mathematical formula 149]

[0561]

[0562] By arranging the results of formula (2-6-23), we obtain the following formula (2-6-24).

[0563] [Mathematical formula 150]

[0564]

[0565] By summing up all the sets of I and J related to formula (2-6-24), the following formula (2-6-25) is obtained.

[0566] [Mathematical formula 151]

[0567]

[0568] Based on equations (2-6-15) and (2-6-25), the scattered field function is calculated as shown in equation (2-6-26).

[0569] [Mathematical formula 152]

[0570]

[0571] Apply x2=x1=x, y1=y2=y, and z1=z2=z to equation (2-6-26), integrate k, and get the visualization function. Next, we will explore the mathematical formula of the improved visualization function and get the result through the Fourier transform that can be calculated at high speed. The basic variable is k. x , k y1 , k y2 , k z, other variables are explicitly expressed using these. The visualization function is obtained by the following steps.

[0572] First, by applying x2=x1=x, y1=y2=y, and z1=z2=z to equation (2-6-26), the following equation (2-6-27) is obtained.

[0573] [Mathematical formula 153]

[0574]

[0575] By integrating with respect to k, the visualization function ρ is obtained as shown in the following formula (2-6-28).

[0576] [Mathematical formula 154]

[0577]

[0578] The following formula (2-6-29) is used in this calculation.

[0579] [Mathematical formula 155]

[0580]

[0581] When a plurality of columns of receiving array antennas are used, the imaging function can be derived by synthesizing a plurality of scattered field functions corresponding to the plurality of columns of receiving array antennas. For example, a plurality of scattered field functions are synthesized into one scattered field function, and the imaging function is derived by the limit operation of the scattered field function. Here, the plurality of scattered field functions can be scattered field functions represented by equation (2-6-26), and the synthesis can also be linear addition.

[0582] <3 Directional Antenna Case>

[0583] In this chapter, the scattered field theory using directional antennas is explained.

[0584] <3-1 Case where array antenna is arranged on a plane>

[0585] In Chapter 2, as shown in formula (2-1-1), non-directional antennas are used both in radiation and reception. On the other hand, directional antennas can also be used for radars targeting objects in the air. For example, a directional antenna is composed of multiple antenna elements, and the multiple antenna elements operate with essentially the same phase. Regarding phased arrays, the phases are also essentially uniform. Therefore, directional antennas are designed to have a large opening surface, so that the directivity becomes better.

[0586] By introducing such a directional antenna into the scattered field theory, it is possible to identify the state of distant scattering with high accuracy. Below, we will use the example in Section 5 of Chapter 2 as a basis to explore the introduction of directional antennas into the scattered field theory.

[0587] Figure 8 : is a conceptual diagram showing a quasi-two-dimensional array antenna composed of a plurality of directional antennas arranged on a plane. In this example, the quasi-two-dimensional array antenna is composed of two columns of linear array antennas, one column of transmitting array antennas TA and one column of receiving array antennas RA. 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 between the transmitting array antenna TA and the receiving array antenna RA in the x-axis direction is represented by d.

[0588] The transmitting array antenna TA includes n transmitting antennas T1, ..., T n The receiving array antenna RA includes n receiving antennas R1, .., R n . n transmitting antennas T1, .., T n Each may include multiple transmitting antenna elements. n Each may include multiple receiving antenna elements. n Each of them can also be represented as a transmitter. n Each can also behave as a receiver.

[0589] In Section 5 of Chapter 2, according to equation (2-5-17), the scattered field function is expressed as follows: equation (3-1-1).

[0590] [Mathematical formula 156]

[0591]

[0592] Here, it is assumed that the kernel function b(k x1 , k y1 , k y2 , k) is determined based on the measurement results. When the above formula is used as it is, the same scattered field function and imaging function as those in Section 5 of Chapter 2, which assumes an omnidirectional antenna, are obtained. However, the measurement results when a directional antenna is used are different from those when an omnidirectional antenna is used. Regarding the same scattered field function and imaging function as those in Section 5 of Chapter 2, which assumes an omnidirectional antenna, correct information cannot be obtained from the measurement results of the directional antenna.

[0593] The size of a directional antenna is large enough compared to the wavelength of a commonly used electromagnetic wave. Therefore, a directional antenna is not considered to be an infinitely small point, but has a finite size. For simplicity, a rectangle (2a×2b) is used as the shape of the antenna. In addition, the size and shape of the antenna here correspond to the size and shape of the transmitting area or receiving area of ​​the antenna. Here, scattering data measured by an antenna with a finite size is discussed. In addition, in the scattered field theory of Chapter 2, it is assumed that the antenna is a non-directional point antenna.

[0594] Fig. 9 is a conceptual diagram showing a transmitting antenna and a receiving antenna having a finite size. Fig. 9 As shown, the transmitting antenna and the receiving antenna have limited dimensions and are rectangular in shape. The transmitting antenna transmits radio waves in the z-axis direction, and the receiving antenna receives radio waves in the z-axis direction. Fig. 9 In the equation (x, η), (ξ, η) corresponds to the displacement vector of the sending position (x1, y1). Similarly, (u, v) corresponds to the displacement vector of the receiving position (x2, y2).

[0595] In formula (3-1-1), the variables regarding the transmission position and the reception position are replaced as in the following formula (3-1-2).

[0596] [Mathematical formula 157]

[0597] x1→x1+ξ y1→y1+η

[0598] x2→x2+u y2→y2+v

[0599] …(3-1-2)

[0600] By replacing the variables, the scattered field function is replaced from equation (3-1-1) to the following equation (3-1-3).

[0601] [Mathematical formula 158]

[0602]

[0603] Integrate both sides of equation (3-1-3) inside the transmitting antenna and the receiving antenna to obtain equation (3-1-4).

[0604] [Mathematical formula 159]

[0605]

[0606] The integration range T is -a≤ξ≤a and -b≤η≤b, and the integration range R is -a≤u≤a and -b≤v≤b. The integration result is obtained as shown in the following formula (3-1-5).

[0607] [Mathematical formula 160]

[0608]

[0609] Here, the integrand function includes a function f representing the directivity of the antenna as shown in the following equation (3-1-6).

[0610] [Mathematical formula 161]

[0611]

[0612] The above function f is affected by constants a and b representing the size of the antenna. x1 , k y1 , k x1 and k y1 The integral result of the function f is that when the constants a and b representing the size of the antenna are larger, even if k x1 , k y1 , k x1 and k y1 The smaller the integral range, the easier it is to approach 0. In other words, when the constants a and b representing the size of the antenna are larger, the greater the directivity.

[0613] Next, we explore how to find the kernel function b(k x1 , k y1 , k y2 , k). This kernel function is a function related to an omnidirectional antenna, and cannot be strictly obtained from the result measured by a directional antenna with a finite size. Here, the result measured by a directional antenna with a finite size is used as an approximation of the result obtained by the omnidirectional antenna. Specifically, the result measured by a directional antenna with a finite size is used as an approximation of the result obtained when ξ, η, u, and v are 0.

[0614] In this case, assuming that the transmission position of the array antenna is fixed to x1 = 0 and the reception position is fixed to x2 = x1 + d, the measurement data Φ(y1, y2, k) is obtained by x1 = 0 and z = 0, and the following equation (3-1-7) is satisfied.

[0615] [Mathematical formula 162]

[0616]

[0617] By changing the variable from k x1 Transform to k x , and obtain the following formula (3-1-8).

[0618] [Mathematical formula 163]

[0619]

[0620] By performing an inverse Fourier transform on both sides of equation (3-1-8), we obtain the following equation (3-1-9).

[0621] [Mathematical formula 164]

[0622]

[0623] By removing the symbol (') from formula (3-1-9), the following formula (3-1-10) is obtained.

[0624] [Mathematical formula 165]

[0625]

[0626] The scattered field function taking directivity into consideration is derived as shown in the following equation (3-1-11).

[0627] [Mathematical formula 166]

[0628]

[0629] By applying x2→x1=x and y2→y1=y to the formula (3-1-11) and integrating k, a visualization function is obtained as shown in the following formula (3-1-12).

[0630] [Mathematical formula 167]

[0631]

[0632] When a directional antenna is used, waves can be sent to a distant object, and scattered waves can be received from the distant object. Furthermore, according to the scattered field function and imaging function described above, the distant object can be imaged with high precision.

[0633] For example, a plurality of directional antennas can be arranged on the ground in a fixed quasi-two-dimensional arrangement. Furthermore, it is also possible to image flying objects above the plurality of directional antennas. For example, in this case, a wide range of spatial cross sections along the direction directly above the plurality of directional antennas can be imaged with high precision. Furthermore, through the above, it is possible to image distant flying objects passing through such spatial cross sections.

[0634] <3-2 Array antenna configuration on an inclined surface>

[0635] Next, it is assumed that the array antenna is arranged on an inclined surface, and each antenna constituting the array antenna is oriented in the z-axis direction. In this regard, an example using an omnidirectional antenna is described in Section 6 of Chapter 2.

[0636] Fig.101 is a conceptual diagram showing a quasi-two-dimensional array antenna composed of a plurality of directional antennas arranged on an inclined surface. In this example, the quasi-two-dimensional array antenna is composed of two linear array antennas, one row of transmission array antennas TA and one row of reception array antennas RA.

[0637] 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 between the transmitting array antenna TA and the receiving array antenna RA in the x-axis direction is represented by d. The z coordinate of the transmitting array antenna TA is represented by z1, and the z coordinate of the receiving array antenna RA is represented by z2. Fig.10 In the example of , the coordinates are defined as x1=0, x2=d, z1=h1, and z2=h2.

[0638] The transmitting array antenna TA includes n transmitting antennas T1, ..., T n The receiving array antenna RA includes n receiving antennas R1, .., R n . n transmitting antennas T1, .., T n Each may include multiple transmitting antenna elements. n Each may include multiple receiving antenna elements. n Each of them can also be represented as a transmitter. n Each can also behave as a receiver.

[0639] In Section 6 of Chapter 2, according to equation (2-6-15), the scattered field function is expressed as follows: equation (3-2-1).

[0640] [Mathematical formula 168]

[0641]

[0642] Here, it is assumed that the kernel function b(k x1 , k y1 , k y2 , k) is determined based on the measurement results. When the above formula is used as it is, the same scattered field function and imaging function as those in Section 6 of Chapter 2 assuming an omnidirectional antenna are obtained. However, the measurement results when a directional antenna is used are different from those when an omnidirectional antenna is used. Regarding the same scattered field function and imaging function as those in Section 6 of Chapter 2 assuming an omnidirectional antenna, correct information cannot be obtained from the measurement results of the directional antenna.

[0643] The size of a directional antenna is large enough compared to the wavelength of a commonly used electromagnetic wave. Therefore, a directional antenna is not considered to be an infinitely small point, but has a finite size. For simplicity, a rectangle (2a×2b) is used as the shape of the antenna. In addition, the size and shape of the antenna here correspond to the size and shape of the transmitting area or receiving area of ​​the antenna. Here, scattering data measured by an antenna with a finite size is discussed. In addition, in the scattered field theory of Chapter 2, it is assumed that the antenna is a non-directional point antenna.

[0644] As used in the previous section Fig. 9 In the example described here, the transmitting antenna and the receiving antenna have limited dimensions and are rectangular in shape. The transmitting antenna transmits radio waves in the z-axis direction, and the receiving antenna receives radio waves in the z-axis direction.

[0645] In formula (3-2-1), the variables regarding the transmission position and the reception position are replaced as in the following formula (3-2-2).

[0646] [Mathematical formula 169]

[0647] x1→x1+ξ y1→y1+η

[0648] x2→x2+u y2→y2+v

[0649] …(3-2-2)

[0650] By replacing the variables, the scattered field function is replaced from equation (3-2-1) to the following equation (3-2-3).

[0651] [Mathematical formula 170]

[0652]

[0653] Integrate both sides of equation (3-2-3) inside the transmitting antenna and the receiving antenna to obtain equation (3-2-4).

[0654] [Mathematical formula 171]

[0655]

[0656] The integration range T is -a≤ξ≤a and -b≤η≤b, and the integration range R is -a≤u≤a and -b≤v≤b. The integration result is obtained as shown in the following formula (3-2-5).

[0657] [Mathematical formula 172]

[0658]

[0659] Here, the integrand function includes a function f representing the directivity of the antenna as shown in the following equation (3-2-6).

[0660] [Mathematical formula 173]

[0661]

[0662] Next, we explore how to find the kernel function b(k x1 , k y1 , k y2 , k). This kernel function is a function related to an omnidirectional antenna, and cannot be strictly obtained from the result measured by a directional antenna with a finite size. Here, the result measured by a directional antenna with a finite size is used as an approximation of the result obtained by the omnidirectional antenna. Specifically, the result measured by a directional antenna with a finite size is used as an approximation of the result obtained when ξ, η, u, and v are 0.

[0663] In this case, it is assumed that the transmission position of the array antenna is fixed to x1 = 0 and the reception position is fixed to x2 = x1 + d. The measurement data Φ(y1, y2, k) is obtained by x1 = 0 and satisfies the following equation (3-2-7).

[0664] [Mathematical formula 174]

[0665]

[0666] By changing the variable from k x1 Transform to k x , and obtain the following formula (3-2-8).

[0667] [Mathematical formula 175]

[0668]

[0669] By performing an inverse Fourier transform on both sides of equation (3-2-8), we obtain the following equation (3-2-9).

[0670] [Mathematical formula 176]

[0671]

[0672] By removing the symbol (') from formula (3-2-9), the following formula (3-2-10) is obtained.

[0673] [Mathematical formula 177]

[0674]

[0675] The scattered field function taking directivity into consideration is derived as shown in the following equation (3-2-11).

[0676] [Mathematical formula 178]

[0677]

[0678] By applying x2→x1=x, y2→y1=y, and z1→z2=z to equation (3-2-11) and integrating k, a visualization function is obtained as shown in the following equation (3-2-12).

[0679] [Mathematical formula 179]

[0680]

[0681] According to this, even when it is difficult to arrange a plurality of directional antennas on a flat surface, it is possible to use a plurality of directional antennas arranged on a curved surface, thereby imaging an object with high accuracy.

[0682] <3-3 Directional Antenna Rotation Case>

[0683] In this section, the scattered field theory is further described when the directional antenna described in the previous section is mechanically rotated or electrically rotated and the direction of directivity related to transmission and reception is changed.

[0684] For example, mechanical rotation of a directional antenna corresponds to the directional antenna physically rotating as a solid object. And, for example, electrical rotation of a directional antenna corresponds to the directional antenna operating as a phased array antenna, controlling the timing of transmission or reception, thereby changing the direction of directivity as if the directional antenna rotates.

[0685] Fig.11 is a conceptual diagram showing the rotation of the antenna. Specifically, Fig.11 The figure shows the mechanical rotation or electrical rotation of the antenna around the x-axis. The antenna is mechanically rotated or electrically rotated so that the transmitting position and the receiving position are changed.

[0686] Fig.12 This is a conceptual diagram showing a matrix display that is mechanically or electrically rotated around the x-axis. When the antenna is mechanically or electrically rotated around the x-axis at an angle α, the point (ξ, η, 0) on the antenna surface is transformed into the following equation (3-3-1).

[0687] [Mathematical formula 180]

[0688]

[0689] Therefore, in this case, the integrated term of the scattered field function changes as shown in the following formula (3-3-2).

[0690] [Mathematical formula 181]

[0691]

[0692] According to formula (3-3-2), a function representing directivity is obtained as shown in the following formula (3-3-3).

[0693] [Mathematical formula 182]

[0694]

[0695] Fig.13 This is a conceptual diagram showing a matrix display that is mechanically or electrically rotated around the y-axis. When the antenna is mechanically or electrically rotated around the y-axis at an angle β, the point (ξ, η, 0) on the antenna surface is transformed into the following equation (3-3-4).

[0696] [Mathematical formula 183]

[0697]

[0698] Therefore, in this case, the integrated term of the scattered field function changes as shown in the following formula (3-3-5).

[0699] [Mathematical formula 184]

[0700]

[0701] According to formula (3-3-5), a function representing directivity is obtained as shown in the following formula (3-3-6).

[0702] [Mathematical formula 185]

[0703]

[0704] The synthesis of mechanical rotation or electrical rotation at an angle α around the x-axis and mechanical rotation or electrical rotation at an angle β around the y-axis is expressed as the following formula (3-3-7).

[0705] [Mathematical formula 186]

[0706]

[0707] Through the above synthesis, the point (ξ, η, 0) within the antenna plane is transformed into the following formula (3-3-8).

[0708] [Mathematical formula 187]

[0709]

[0710] Therefore, the integrated term of the scattered field function changes as shown in the following equation (3-3-9).

[0711] [Mathematical formula 188]

[0712]

[0713] According to formula (3-3-9), a function representing directivity is obtained as shown in the following formula (3-3-10).

[0714] [Mathematical formula 189]

[0715]

[0716] Regardless of the configuration of the array antenna in the previous section, whether the antenna is mechanically rotated or electrically rotated, the scattered field function is expressed as the following equation (3-3-11).

[0717] [Mathematical formula 190]

[0718]

[0719] Moreover, the imaging function is expressed as the following formula (3-3-12).

[0720] [Mathematical formula 191]

[0721]

[0722] The directional antenna can transmit waves to a distant object and receive scattered waves from the distant object in a direction adaptively defined by mechanical or electrical rotation. Therefore, the distant object can be imaged with high precision in the adaptively defined direction.

[0723] <3-4 Case of Rotational Scanning by Mechanical Rotation or Electrical Rotation>

[0724] Fig.14 This is a conceptual diagram showing rotational scanning by mechanical rotation or electrical rotation. For example, a directional array antenna scans space by mechanically rotating or electrically rotating each antenna.

[0725] When the rotation angle of the antenna is (α, β), the scattered data is expressed as Φ(y1, y2, k, α, β). And the Fourier transform of y1 and y2 is expressed as follows.

[0726] [Mathematical formula 192]

[0727]

[0728] Moreover, the directivity function of the antenna angle is expressed as f1(k x1 , k y1 , k z1 , α, β) and f2(kx2 , k y2 , k z2 , α, β). When these symbols are used, the scattered field function is expressed as the following equation (3-4-1).

[0729] [Mathematical formula 193]

[0730]

[0731] Moreover, the image function is expressed as the following formula (3-4-2).

[0732] [Mathematical formula 194]

[0733]

[0734] By mechanically rotating or electrically rotating the rotational scanning, it is possible to send a wave to a distant object in any direction and receive a scattered wave from the distant object. Therefore, it is possible to image the distant object with high precision in any direction.

[0735] <3-5 Modification Example>

[0736] In this chapter, the plurality of transmitting antennas and the plurality of receiving antennas have the same size. However, the plurality of transmitting antennas and the plurality of receiving antennas may have sizes different from each other.

[0737] In addition, in this chapter, the multiple transmitting antennas and the multiple receiving antennas have a rectangular shape. However, the multiple transmitting antennas and the multiple receiving antennas may have a shape different from the rectangular shape. Furthermore, the multiple transmitting antennas and the multiple receiving antennas may have shapes different from each other.

[0738] In addition, in this chapter, the positions of the multiple transmitting antennas and the multiple receiving antennas are fixed, but they can also be moved, thereby obtaining data corresponding to various positions.

[0739] In addition, in this chapter, the plurality of transmitting antennas and the plurality of receiving antennas are arranged in a quasi-two-dimensional arrangement. However, the plurality of transmitting antennas and the plurality of receiving antennas may also be arranged in an arrangement different from the quasi-two-dimensional arrangement.

[0740] In addition, in this chapter, multiple transmitting antennas are configured as a column, and multiple receiving antennas are configured as a column. However, multiple transmitting antennas may be configured as multiple columns, and multiple receiving antennas may be configured as multiple columns. For example, multiple receiving antenna columns may be configured for one transmitting antenna column, and multiple transmitting antenna columns may be configured for one receiving antenna column.

[0741] In this case, the imaging function can be derived by synthesizing multiple scattered field functions for multiple combinations of the transmitting array antenna and the receiving array antenna. For example, multiple scattered field functions are synthesized into one scattered field function, and the imaging function is derived by the limit operation of the scattered field function. Here, each of the multiple scattered field functions can be any of the scattered field functions shown in this chapter, and the synthesis can also be linear addition.

[0742] Alternatively, a plurality of transmission antenna columns and a plurality of reception antenna columns may be arranged alternately. Furthermore, data corresponding to various positions can be obtained without moving the antennas in a direction perpendicular to the columns (x-axis direction).

[0743] In addition, in this chapter, the number of transmit antennas included in one transmit antenna column is the same as the number of receive antennas included in one receive antenna column. However, the number of transmit antennas included in one transmit antenna column may be different from the number of receive antennas included in one receive antenna column.

[0744] In Sections 3 and 4 of this chapter, the plurality of transmitting antennas and the plurality of receiving antennas are mechanically or electrically rotated at the same rotation angle. However, the plurality of transmitting antennas and the plurality of receiving antennas may be mechanically or electrically rotated at different rotation angles.

[0745] In the above-mentioned modification examples, the scattered field function and the imaging function may also be derived based on the same kind of theory as the above-mentioned theory.

[0746] <4 Composition and Operation of Imaging Device>

[0747] Based on the above contents, the configuration and operation of an imaging device for imaging an object in a measurement area using measurement data of scattered waves will be described below.

[0748] Here, the wave used for measuring the scattered wave may be, for example, an electric wave, or may be a microwave, a millimeter wave, or a terahertz wave. In addition, light or sound may be used as the wave. Furthermore, the measurement area may be an area in the air, and the object may be a flying object. The object in the measurement area has a physical property different from the physical property of the surrounding medium. Specifically, the physical property is a physical property corresponding to the reflectivity of the wave. When an electric wave is used as the wave, the physical property may also be a dielectric constant.

[0749] Fig.15 This is a diagram showing the basic structure of the imaging device in this embodiment. Fig.15 The imaging device 100 shown includes a plurality of transmitters 101 , a plurality of receivers 102 , and an information processing circuit 103 . The imaging device 100 may also include a display 104 .

[0750] Each transmitter 101 is a circuit that transmits a wave. Specifically, each transmitter 101 has a transmission area, and transmits a wave from the transmission area to the measurement area. Furthermore, each transmitter 101 may be a transmission antenna, or may be composed of a plurality of transmission elements such as a plurality of transmission antenna elements.

[0751] Each receiver 102 is a circuit for receiving the scattered waves of the fluctuations. Specifically, each receiver 102 has a receiving area, and receives the scattered waves of the fluctuations from the transmitting area in the receiving area. In addition, each receiver 102 can be a receiving antenna, or can be composed of multiple receiving elements such as multiple receiving antenna elements.

[0752] The transmission area and the receiving area each have a finite size. The finite size may be the same in the plurality of transmitters 101 and the plurality of receivers 102. The transmission area and the receiving area each may be a rectangular shape. The plurality of transmitters 101 and the plurality of receivers 102 may be arranged in a quasi-two-dimensional arrangement.

[0753] The information processing circuit 103 is a circuit for performing information processing. Specifically, the information processing circuit 103 obtains the measurement data of the scattered waves, and uses the measurement data of the scattered waves to image the object in the measurement area. For example, when the information processing circuit 103 uses the measurement data to image the object, it performs the calculation processing shown in the above theory.

[0754] In addition, the information processing circuit 103 may also be a computer or a processor of a computer. The information processing circuit 103 may perform information processing by reading a program from a memory and executing the program. Furthermore, the information processing circuit 103 may also be a dedicated circuit for imaging an object in a measurement area based on measurement data.

[0755] In addition, the information processing circuit 103 may be able to communicate with multiple transmitters 101 and multiple receivers 102. Furthermore, the information processing circuit 103 may control the operations of the multiple transmitters 101 and multiple receivers 102. Furthermore, the information processing circuit 103 may obtain position information and measurement data from the multiple transmitters 101 and multiple receivers 102.

[0756] In addition, the information processing circuit 103 may generate an image showing the object in the process of imaging the object. Furthermore, the information processing circuit 103 may output the image showing the object to the display 104 or the like. Alternatively, the information processing circuit 103 may output the image showing the object to a printer (not shown). Alternatively, the information processing circuit 103 may send the image as electronic data to another device (not shown) through wired or wireless communication.

[0757] The display 104 is a display device such as a liquid crystal display. The display 104 is an arbitrary component and is not an essential component. Furthermore, the display 104 may be a device external to the imaging device 100 and may not constitute the imaging device 100 .

[0758] Fig.16 It is shown Fig.15 The flowchart of the basic operation of the imaging device 100 is shown in FIG. Fig.15 The imaging device 100 shown in the figure includes a plurality of transmitters 101, a plurality of receivers 102, and an information processing circuit 103. Fig.16 Work shown.

[0759] First, each transmitter 101 transmits a wave from a transmission area to a measurement area (S101), and each receiver 102 receives a scattered wave of the wave from the measurement area in a reception area (S102).

[0760] Next, the information processing circuit 103 uses the measurement data to derive a scattered field function (S103). Here, the scattered field function is a function that reflects the finite size of each of the transmission area and the reception area, and the scattered field function is input to the transmission position of the wave and the reception position of the scattered wave and outputs the amount of the scattered wave at the reception position.

[0761] Then, the information processing circuit 103 derives an imaging function using the scattering field function (S104). The imaging function is a function determined based on the amount output from the scattering field function by inputting the imaging target position as the transmission position and the reception position into the scattering field function, and the imaging function is input with the imaging target position and outputs the image intensity of the imaging target position.

[0762] Finally, the information processing circuit 103 uses an imaging function to image the object in the measurement area ( S105 ).

[0763] Based on this, the imaging device 100 can use the measurement data to derive the state of scattering in the measurement area. Therefore, the imaging device 100 can image the objects in the measurement area with high precision. In addition, the imaging device 100 can send waves to distant objects and receive scattered waves from distant objects according to the directivity of the transmission area and the receiving area with limited size. Therefore, the imaging device 100 can image distant objects in a wide range of measurement areas with high precision.

[0764] For example, the above-mentioned limited size may be the same in the plurality of transmitters 101 and the plurality of receivers 102. Thus, the imaging device 100 can apply the same calculation process to the plurality of transmitters 101 and the plurality of receivers 102. Therefore, the imaging device 100 can suppress the complexity of the calculation process.

[0765] In addition, for example, the transmission area and the reception area may be rectangular areas. In this way, the imaging device 100 can perform calculation processing corresponding to a simple shape. Therefore, the imaging device 100 can suppress the complexity of calculation processing.

[0766] In addition, for example, the plurality of transmitters 101 may be arranged on a straight line, and the plurality of receivers 102 may be arranged on another straight line parallel to the straight line on which the plurality of transmitters 101 are arranged. Furthermore, the distance between the straight line on which the plurality of transmitters 101 are arranged and the straight line on which the plurality of receivers 102 are arranged may be reflected in the scattered field function.

[0767] Thus, the imaging device 100 can obtain sufficient information as measurement data according to various combinations of the plurality of transmitters 101 and the plurality of receivers 102 arranged in quasi-two dimensions. In addition, since intervals are provided between the plurality of transmitters 101 and the plurality of receivers 102, the imaging device 100 can efficiently transmit waves to the measurement area and efficiently receive scattered waves from the measurement area.

[0768] Furthermore, the imaging device 100 can image the object with high accuracy by using the measurement data of the scattered waves and the scattered field function derived according to the distances between the plurality of transmitters 101 and the plurality of receivers 102 .

[0769] In addition, for example, the scattered field function may be expressed by [Formula 195].

[0770] [Mathematical formula 195]

[0771]

[0772] Here, x1 and y1 represent the x-coordinate and y-coordinate of the transmission position. Also, x2 and y2 represent the x-coordinate and y-coordinate of the reception position. Also, z represents the z-coordinate of the transmission position and the reception position. Also, k represents the wave number of the wave. Also, k x , k y1 and k y2 represents an integral variable, and d represents the above-mentioned distance.

[0773] In addition, [Equation 196] represents the measurement data after Fourier transform of y1 and y2.

[0774] [Mathematical formula 196]

[0775]

[0776] In addition, k x1 , k x2 and k z It is defined by [Mathematical Formula 197].

[0777] [Mathematical formula 197]

[0778]

[0779] Furthermore, a represents 1 / 2 of the above-mentioned finite size in the x-axis direction, and b represents 1 / 2 of the above-mentioned finite size in the y-axis direction.

[0780] According to this, the imaging device 100 can image the object with high accuracy by using the scattered field function when the transmission position and the reception position have the same z coordinate.

[0781] In addition, for example, the visualization function may be expressed by [Formula 198].

[0782] [Mathematical formula 198]

[0783]

[0784] Here, x, y, and z input to the imaging function represent the x-coordinate, y-coordinate, and z-coordinate of the imaging target position.

[0785] According to this, the imaging device 100 can image the object with high accuracy using the imaging function when the transmission position and the reception position have the same z coordinate.

[0786] In addition, for example, the scattered field function may be expressed by [Formula 199].

[0787] [Mathematical formula 199]

[0788]

[0789] Here, x1, y1, and z1 represent the x-coordinate, y-coordinate, and z-coordinate of the transmission position. Also, x2, y2, and z2 represent the x-coordinate, y-coordinate, and z-coordinate of the reception position. Also, k represents the wave number of the wave. Also, k x , k y1 and k y2 represents an integral variable. And, d represents the above-mentioned distance in the x-axis direction. And, h1 represents the z-coordinate of the transmission position corresponding to the measurement data. And, h2 represents the z-coordinate of the reception position corresponding to the measurement data.

[0790] In addition, [Equation 200] represents the measurement data after Fourier transform is performed on y1 and y2.

[0791] [Mathematical formula 200]

[0792]

[0793] In addition, k x1 , k x2 , k z1 and k z2 It is defined by [Mathematical Formula 201].

[0794] [Mathematical formula 201]

[0795]

[0796] In addition, a represents 1 / 2 of the above-mentioned finite size in the x-axis direction, and b represents 1 / 2 of the above-mentioned finite size in the y-axis direction.

[0797] According to this, the imaging device 100 can image the object with high accuracy by using the scattered field function when the transmission position and the reception position may have different z-coordinates.

[0798] In addition, for example, the visualization function may be expressed by [Formula 202].

[0799] [Mathematical formula 202]

[0800]

[0801] Here, x, y, and z input to the imaging function represent the x-coordinate, y-coordinate, and z-coordinate of the imaging target position.

[0802] According to this, the imaging device 100 can image the object with high accuracy by using the imaging function when the transmission position and the reception position may have different z coordinates.

[0803] In addition, for example, each transmitter 101 may change the normal direction of the surface of the transmission area by mechanically or electrically rotating the transmission area. Each receiver 102 may change the normal direction of the surface of the receiving area by mechanically or electrically rotating the receiving area. Furthermore, the information processing circuit 103 may image the object in the measurement area using the measurement data after the rotation of the transmission area and the receiving area.

[0804] According to this, the imaging device 100 can change the normal direction of the surface of each of the sending area and the receiving area. Thus, the imaging device 100 can change the direction of the directivity of each of the sending area and the receiving area. Therefore, the imaging device 100 changes the direction of the directivity and can image a distant object in that direction.

[0805] In addition, for example, the scattered field function may be expressed by [Formula 203].

[0806] [Mathematical formula 203]

[0807]

[0808] Here, x1, y1, and z1 represent the x-coordinate, y-coordinate, and z-coordinate of the transmission position. Also, x2, y2, and z2 represent the x-coordinate, y-coordinate, and z-coordinate of the reception position. Also, k represents the wave number of the wave. Also, k x , k y1 and k y2 represents an integral variable. And, d represents the above-mentioned distance in the x-axis direction. And, h1 represents the z-coordinate of the transmission position corresponding to the measurement data. And, h2 represents the z-coordinate of the reception position corresponding to the measurement data.

[0809] In addition, [Equation 204] represents the measurement data after Fourier transform of y1 and y2.

[0810] [Mathematical formula 204]

[0811]

[0812] In addition, k x1 , k x2 , k z1 and k z2 It is defined by [Mathematical Formula 205].

[0813] [Mathematical formula 205]

[0814]

[0815] In addition, f1 and f2 are defined by [Formula 206].

[0816] [Mathematical formula 206]

[0817]

[0818] In addition, a represents 1 / 2 of the above-mentioned finite size in the x-axis direction. And, b represents 1 / 2 of the above-mentioned finite size in the y-axis direction. And, α represents the rotation angle of the transmission area and the receiving area around the x-axis for mechanical rotation or electrical rotation. And, β represents the rotation angle of the transmission area and the receiving area around the y-axis for mechanical rotation or electrical rotation.

[0819] According to this, the imaging device 100 can image the object with high accuracy by using the scattered field function when the direction of directivity can be changed.

[0820] In addition, for example, the visualization function may be expressed by [Formula 207].

[0821] [Mathematical formula 207]

[0822]

[0823] Here, x, y, and z input to the imaging function represent the x-coordinate, y-coordinate, and z-coordinate of the imaging target position.

[0824] According to this, the imaging device 100 can image the object with high accuracy using the imaging function in the case where the direction of directivity can be changed.

[0825] In addition, for example, each transmitter 101 may mechanically or electrically rotate the transmission area at a plurality of rotation angles, thereby changing the normal direction of the surface of the transmission area to a plurality of directions. Each receiver 102 may mechanically or electrically rotate the receiving area at a plurality of rotation angles, thereby changing the normal direction of the surface of the receiving area to a plurality of directions. Furthermore, the information processing circuit 103 may image the object in the measurement area using the measurement data obtained for the plurality of rotation angles of mechanical rotation or electrical rotation.

[0826] According to this, the imaging device 100 can change the normal direction of the surface of each of the sending area and the receiving area to multiple directions. Therefore, the imaging device 100 can change the direction of the directivity of each of the sending area and the receiving area to multiple directions. Therefore, the imaging device 100 changes the direction of the directivity to multiple directions and can image a distant object in multiple directions.

[0827] In addition, for example, the scattered field function may be expressed by [Formula 208].

[0828] [Mathematical formula 208]

[0829]

[0830] Here, x1, y1, and z1 represent the x-coordinate, y-coordinate, and z-coordinate of the transmission position. Also, x2, y2, and z2 represent the x-coordinate, y-coordinate, and z-coordinate of the reception position. Also, k represents the wave number of the wave. Also, k x , k y1 and k y2 represents an integral variable. And, d represents the above-mentioned distance in the x-axis direction. And, h1 represents the z-coordinate of the transmission position corresponding to the measurement data. And, h2 represents the z-coordinate of the reception position corresponding to the measurement data.

[0831] In addition, [Equation 209] represents the measurement data after Fourier transform of y1 and y2.

[0832] [Mathematical formula 209]

[0833]

[0834] In addition, k x1 , k x2 , k z1 and k z2 It is defined by [Mathematical Formula 210].

[0835] [Mathematical formula 210]

[0836]

[0837] In addition, f1 and f2 are defined by [Mathematical Formula 211].

[0838] [Mathematical formula 211]

[0839]

[0840] In addition, a represents 1 / 2 of the above-mentioned finite size in the x-axis direction. And, b represents 1 / 2 of the above-mentioned finite size in the y-axis direction. And, α represents the rotation angle of the transmission area and the receiving area around the x-axis for mechanical rotation or electrical rotation. And, β represents the rotation angle of the transmission area and the receiving area around the y-axis for mechanical rotation or electrical rotation.

[0841] According to this, the imaging device 100 can image the object with high accuracy by using the scattered field function when the direction of directivity can be changed to a plurality of directions.

[0842] In addition, for example, the visualization function may be expressed by [Formula 212].

[0843] [Mathematical formula 212]

[0844]

[0845] Here, x, y, and z input to the imaging function represent the x-coordinate, y-coordinate, and z-coordinate of the imaging target position.

[0846] According to this, the imaging device 100 can image the object with high accuracy using an imaging function in which the direction of directivity can be changed to a plurality of directions.

[0847] In addition, for example, the wave may be a microwave. According to this, the imaging device 100 can suppress the attenuation of the wave caused by the moisture in the measurement area.

[0848] In addition, for example, in the multiple transmitters 101, multiple receivers 102, information processing circuit 103, scattered field function, and imaging function shown in the above basic configuration and basic operation, other components, formulas, variables, and the like shown in this embodiment can be appropriately applied. In addition, the scattered field function and the imaging function shown in this embodiment can be appropriately modified and applied. For example, a mathematical formula that expresses substantially the same content as the above mathematical formula in other expressions can be used, and other mathematical formulas derived based on the above theory can also be used.

[0849] (Replenish)

[0850] The above describes the form of the imaging device based on the embodiment, but the form of the imaging device is not limited to the embodiment. The embodiment can be modified as expected by a person skilled in the art, and multiple components in the embodiment can be arbitrarily combined. For example, in the embodiment, the processing performed by a specific component can be performed by another component instead of a specific component. In addition, the order of multiple processing can be changed, and multiple processing can be performed in parallel.

[0851] In addition, the imaging method including the steps performed by the components of the imaging device can be executed by any device or system. For example, a part or all of the imaging method can be executed by a computer having a processor, a memory, and an input / output circuit. In this case, the imaging method can also be executed by executing a program for causing the computer to execute the imaging method.

[0852] Furthermore, the above-mentioned program may be recorded in a non-transitory computer-readable recording medium.

[0853] In addition, each component of the imaging device may be composed of dedicated hardware, general-purpose hardware that executes the above-mentioned program, etc., or a combination thereof. In addition, the general-purpose hardware may be composed of a memory that records the program, and a general-purpose processor that reads the program from the memory and executes it. Here, the memory may be a semiconductor memory or a hard disk, etc., and the general-purpose processor may be a CPU, etc.

[0854] In addition, the dedicated hardware may be composed of a memory and a dedicated processor, etc. For example, the dedicated processor may refer to the memory for recording the measurement data to execute the above-mentioned imaging method.

[0855] In addition, each component of the imaging device may also be a circuit. These circuits may constitute a circuit as a whole, or they may be different circuits. In addition, these circuits may correspond to dedicated hardware, or they may correspond to general hardware that executes the above-mentioned program, etc.

[0856] Furthermore, the imaging device is not limited to a physically integrated device, but may include a plurality of sub-devices that are dispersedly arranged. Furthermore, the imaging device may also be expressed as an imaging system.

[0857] Industrial Applicability

[0858] One aspect of the present disclosure is useful in an imaging device that images an object in a measurement area using measurement data of scattered waves, and can be applied to a detection system that detects a distant object in a wide measurement area.

[0859] Description of Reference Numerals

[0860] 100 Imaging Installation

[0861] 101 Transmitter

[0862] 102 Receiver

[0863] 103 Information Processing Circuit

[0864] 104 Display

Claims

1. An imaging device, The imaging device comprises: a plurality of transmitters, each of the plurality of transmitters having a transmission area and transmitting the wave motion from the respective transmission area to the measurement area; a plurality of receivers, each of the plurality of receivers having a receiving area and receiving scattered waves of the fluctuation from the measurement area in the respective receiving areas; and The information processing circuit uses the measurement data of the scattered wave to image the object in the measurement area. The sending area and the receiving area each have a finite size, The information processing circuit, deriving a scattered field function using the measurement data, the scattered field function being a scattered field function reflecting the finite size, and inputting the scattered field function into a sending position of the wave and a receiving position of the scattered wave, and outputting the amount of the scattered wave at the receiving position, deriving an imaging function, the imaging function being determined based on a quantity output from the scattering field function by inputting an imaging target position as the transmission position and the reception position into the scattering field function, and wherein the imaging function is input with the imaging target position and outputs an image intensity of the imaging target position, The object in the measurement area is imaged using the imaging function.

2. The imaging device according to claim 1, The finite size is the same in the plurality of transmitters and the plurality of receivers.

3. The imaging device according to claim 1 or 2, The sending area and the receiving area are each a rectangular area.

4. The imaging device according to claim 1 or 2, The plurality of transmitters are arranged in a straight line, The plurality of receivers are arranged on another straight line parallel to the straight line on which the plurality of transmitters are arranged, The distance between the straight line where the plurality of transmitters are arranged and the straight line where the plurality of receivers are arranged is reflected in the scattered field function.

5. The imaging device according to claim 4, The scattered field function is expressed by [Formula 1]: [Mathematical formula 1] x1 and y1 represent the x-coordinate and y-coordinate of the sending position, x2 and y2 represent the x-coordinate and y-coordinate of the receiving position, z represents the z-coordinate of the sending position and the receiving position, k represents the wave number of the wave, x , k y1 and k y2 represents the integral variable, d represents the distance, [Mathematical formula 2] represents the measurement data after Fourier transformation of y1 and y2, [Mathematical formula 2] k x1 , k x2 and k z It is defined by [Mathematical formula 3], [Mathematical formula 3] a represents 1 / 2 of the finite size in the x-axis direction, and b represents 1 / 2 of the finite size in the y-axis direction.

6. The imaging device according to claim 5, The imaging function is expressed by [Formula 4]: [Formula 4] The x, y, and z input to the imaging function represent the x-coordinate, y-coordinate, and z-coordinate of the imaging object position.

7. The imaging device according to claim 4, The scattered field function is expressed by [Formula 5], [Formula 5] x1, y1 and z1 represent the x-coordinate, y-coordinate and z-coordinate of the sending position, x2, y2 and z2 represent the x-coordinate, y-coordinate and z-coordinate of the receiving position, k represents the wave number of the wave, k x , k y1 and k y2 represents an integral variable, d represents the distance in the x-axis direction, h1 represents the z-coordinate of the sending position corresponding to the measurement data, h2 represents the z-coordinate of the receiving position corresponding to the measurement data, [Mathematical formula 6] represents the measurement data after Fourier transformation of y1 and y2, [Mathematical formula 6] k x1 , k x2 , k z1 and k z2 It is defined by [Formula 7], [Formula 7] a represents 1 / 2 of the finite size in the x-axis direction, and b represents 1 / 2 of the finite size in the y-axis direction.

8. The imaging device according to claim 7, The visualization function is expressed by [Formula 8]: [Mathematical formula 8] The x, y, and z input to the imaging function represent the x-coordinate, y-coordinate, and z-coordinate of the imaging object position.

9. The imaging device according to claim 4, Each of the plurality of transmitters changes the normal direction of the surface of the transmission area by mechanically or electrically rotating the transmission area. Each of the plurality of receivers changes the normal direction of the surface of the receiving area by mechanically or electrically rotating the receiving area. The information processing circuit uses the measurement data after the rotation of the transmission area and the reception area to image the object in the measurement area.

10. The imaging device according to claim 9, The scattered field function is expressed by [Equation 9]: [Mathematical formula 9] x1, y1 and z1 represent the x-coordinate, y-coordinate and z-coordinate of the sending position, x2, y2 and z2 represent the x-coordinate, y-coordinate and z-coordinate of the receiving position, k represents the wave number of the wave, k x , k y1 and k y2 represents an integral variable, d represents the distance in the x-axis direction, h1 represents the z-coordinate of the sending position corresponding to the measurement data, h2 represents the z-coordinate of the receiving position corresponding to the measurement data, [Equation 10] represents the measurement data after Fourier transformation of y1 and y2. [Equation 10] k x1 , k x2 , k z1 and k z2 It is defined by [Formula 11], [Mathematical formula 11] f1 and f2 are defined by [Formula 12], [Mathematical formula 12] a represents 1 / 2 of the finite size in the x-axis direction, b represents 1 / 2 of the finite size in the y-axis direction, α represents the rotation angle of the sending area and the receiving area around the x-axis by mechanical rotation or electrical rotation, β represents the rotation angle of the sending area and the receiving area around the y-axis by mechanical rotation or electrical rotation.

11. The imaging device according to claim 10, The imaging function is expressed by [Formula 13], [Mathematical formula 13] The x, y, and z input to the imaging function represent the x-coordinate, y-coordinate, and z-coordinate of the imaging object position.

12. The imaging device according to claim 4, Each of the plurality of transmitters mechanically or electrically rotates the transmission area at a plurality of rotation angles, thereby changing the normal direction of the surface of the transmission area to a plurality of directions. Each of the plurality of receivers mechanically or electrically rotates the receiving area at the plurality of rotation angles, thereby changing the normal direction of the surface of the receiving area to the plurality of directions. The information processing circuit visualizes the object in the measurement area using the measurement data obtained for the plurality of rotation angles of mechanical rotation or electrical rotation.

13. The imaging device according to claim 12, The scattered field function is expressed by [Equation 14]: [Mathematical formula 14] x1, y1 and z1 represent the x-coordinate, y-coordinate and z-coordinate of the sending position, x2, y2 and z2 represent the x-coordinate, y-coordinate and z-coordinate of the receiving position, k represents the wave number of the wave, k x , k y1 and k y2 represents an integral variable, d represents the distance in the x-axis direction, h1 represents the z-coordinate of the sending position corresponding to the measurement data, h2 represents the z-coordinate of the receiving position corresponding to the measurement data, [Equation 15] represents the measurement data after Fourier transformation of y1 and y2. [Equation 15] k x1 , k x2 , k z1 and k z2 It is defined by [Formula 16], [Formula 16] f1 and f2 are defined by [Formula 17], [Mathematical formula 17] a represents 1 / 2 of the finite size in the x-axis direction, b represents 1 / 2 of the finite size in the y-axis direction, α represents the rotation angle of the sending area and the receiving area around the x-axis by mechanical rotation or electrical rotation, β represents the rotation angle of the sending area and the receiving area around the y-axis by mechanical rotation or electrical rotation.

14. The imaging device according to claim 13, The imaging function is expressed by [Formula 18], [Mathematical formula 18] The x, y, and z input to the imaging function represent the x-coordinate, y-coordinate, and z-coordinate of the imaging object position.

15. An imaging method, The imaging method includes: The step of transmitting the wave motion from the respective transmission areas to the measurement area by a plurality of transmitters each having a transmission area; A step of receiving the scattered waves of the fluctuations from the measurement area in respective receiving areas by a plurality of receivers each having a receiving area; as well as The step of imaging the object in the measurement area using the measurement data of the scattered waves, The sending area and the receiving area each have a finite size, In the step of imaging the object in the measurement area, deriving a scattered field function using the measurement data, the scattered field function being a scattered field function reflecting the finite size, and inputting the scattered field function into a sending position of the wave and a receiving position of the scattered wave, and outputting the amount of the scattered wave at the receiving position, deriving an imaging function, the imaging function being determined based on a quantity output from the scattering field function by inputting an imaging target position as the transmission position and the reception position into the scattering field function, and wherein the imaging function is input with the imaging target position and outputs an image intensity of the imaging target position, The object in the measurement area is imaged using the imaging function.

Images