Imaging device and imaging method

Abstract

A video device (100) is provided with: a plurality of transmitters (101) that each transmit fluctuations to a measurement region; a plurality of receivers (102) each receiving fluctuating scattered waves from the measurement region; and an information processing circuit (103) that uses the measurement data of the scattered waves to image the object in the measurement region, the information processing circuit (103) derives a scattered field function using the measurement data and the velocity vector of the object, derives an image function, and outputs the image function. The information processing circuit (103) derives a scattered field function from the measurement data using a coordinate system in which the position of an object to be imaged is fixed, the image function being determined using an amount output from the scattered field function by inputting the position of the object to be imaged into the scattered field function, the image function being used to image the object in the measurement region, and the information processing circuit (103) deriving the scattered field function from the measurement data using the coordinate system in which the position of the object is fixed.

Description

Technical Field

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

[0002] As technologies related to imaging devices, the technologies described in Patent Documents 1, 2, 3, 4, and 5 are known. 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 cross-section of 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, using scattered wave measurement data to visualize objects within the measurement area is not easy. Specifically, when the state within the measurement area is known, estimating the measurement data of scattered waves emanating from the measurement area based on the waves incident on the measurement area is called a forward modeling problem, which is easy. On the other hand, when the scattered wave measurement data is known, determining the state within the measurement area is called an inversion problem, which is not easy.

[0013] Furthermore, when an object moves in the measurement area, the position of the object becomes uncertain, making it difficult to image the object with high precision.

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

[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 transmits a wave motion to a measurement area; a plurality of receivers, each of which receives scattered waves of the wave motion from the measurement area; and an information processing circuit, which uses measurement data of the scattered waves to image an object in the measurement area. In imaging the object, the information processing circuit uses the measurement data and a velocity vector of the object to derive a scattered field function, the scattered field function being a function that receives as input a transmission position of the wave motion and a reception position of the scattered wave and outputs an amount of the scattered wave at the reception position, and deriving an imaging function. An imaging function is a function that receives an imaging target position as input and outputs an image intensity of the imaging target position. The imaging function is determined using a quantity 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. The object in the measurement area is imaged using the imaging function. The information processing circuit derives the scattering field function from the measurement data using a coordinate system determined using the velocity vector and fixing the position of the object in at least two directions.

[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, an object moving in a measurement area can be imaged with high precision. 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 transmission points and reception points on a plane.

[0022] Figure 3 This is a conceptual diagram showing an example of coordinates related to a quasi-two-dimensional array antenna.

[0023] Figure 4 This is a conceptual diagram showing the relationship between multiple transmitters, multiple receivers, and an aircraft.

[0024] Figure 5 This is a conceptual diagram showing two coordinate systems when using a one-dimensionally arranged transmission and reception array antenna.

[0025] Figure 6 1 is a conceptual diagram showing two coordinate systems when using a quasi-two-dimensionally arranged transmission array antenna and a reception array antenna.

[0026] Figure 7 This is a conceptual diagram showing an analysis area far from the antenna installation position.

[0027] Figure 8 This is a block diagram showing the basic structure of an imaging device.

[0028] Figure 9 This is a flowchart showing the basic operation of the imaging device. DETAILED DESCRIPTION

[0029] An imaging device according to one embodiment of the present disclosure includes: a plurality of transmitters, each of which transmits a wave motion to a measurement area; a plurality of receivers, each of which receives scattered waves of the wave motion from the measurement area; and an information processing circuit, which uses measurement data of the scattered waves to image an object in the measurement area. In imaging the object, the information processing circuit uses the measurement data and a velocity vector of the object to derive a scattered field function, the scattered field function being a function that receives as input a transmission position of the wave motion and a reception position of the scattered wave and outputs an amount of the scattered wave at the reception position, and deriving an imaging function. An imaging function is a function that receives an imaging target position as input and outputs an image intensity of the imaging target position. The imaging function is determined using a quantity 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. The object in the measurement area is imaged using the imaging function. The information processing circuit derives the scattering field function from the measurement data using a coordinate system determined using the velocity vector and fixing the position of the object in at least two directions.

[0030] This allows the imaging device to fix the position of an object and image it. Therefore, the imaging device can image an object moving within the measurement area with high precision. Furthermore, without having to move the multiple transmitters and receivers, the imaging device can transmit waves toward the object from various directions and receive scattered waves. Therefore, even with a small number of transmitters and receivers, the imaging device can obtain sufficient information and image the object with high precision.

[0031] For example, the plurality of transmitters and the plurality of receivers are arranged on a straight line parallel to the y-axis, and the scattered field function is expressed by [Formula 1]:

[0032] [Mathematical formula 1]

[0033]

[0034] The x and z of the scattering field function represent the x coordinate and z coordinate of the sending position and the receiving position, the y1 of the scattering field function represents the y coordinate of the sending position, the y2 of the scattering field function represents the y coordinate of the receiving position, k represents the wave number of the fluctuation, and k x 、k y1 and k y2 represents the variables corresponding to the wave numbers of x, y1, and y2 with respect to the scattered field function,

[0035] [Mathematical formula 2] represents the measurement data after Fourier transformation,

[0036] [Mathematical formula 2]

[0037]

[0038] u and w are determined by [Formula 3],

[0039] [Mathematical formula 3]

[0040]

[0041] v x and v y represents the x-component and y-component of the velocity vector.

[0042] With this configuration, the imaging device can image an object moving in a measurement area with high accuracy using a scattered field function derived from measurement data obtained using a plurality of transmitters and a plurality of receivers arranged on a straight line.

[0043] In addition, for example, the imaging function is expressed by [Formula 4],

[0044] [Formula 4]

[0045]

[0046] x, y, and z in the imaging function represent the x-coordinate, y-coordinate, and z-coordinate of the imaging object position, k z and dk / dk z It is determined by [Formula 5].

[0047] [Formula 5]

[0048]

[0049] With this configuration, the imaging device can image an object moving in a measurement area with high accuracy using an imaging function derived from measurement data obtained using a plurality of transmitters and a plurality of receivers arranged on a straight line.

[0050] Furthermore, for example, the plurality of transmitters are arranged on a first straight line parallel to the y-axis, and the plurality of receivers are arranged on a second straight line parallel to the y-axis. The scattered field function is expressed by [Equation 6]:

[0051] [Formula 6]

[0052]

[0053] The z of the scattering field function represents the z coordinates of the sending position and the receiving position, the x1 and y1 of the scattering field function represent the x coordinate and y coordinate of the sending position, the x2 and y2 of the scattering field function represent the x coordinate and y coordinate of the receiving position, k represents the wave number of the fluctuation, and k x 、k y1 and k y2 represents a variable corresponding to the wave number of x, y1, and y2 with respect to the scattered field function, d represents the distance between the first straight line and the second straight line,

[0054] [Mathematical formula 7] represents the measurement data after Fourier transformation,

[0055] [Formula 7]

[0056]

[0057] s3 and s4 are determined by [Formula 8],

[0058] [Formula 8]

[0059]

[0060] u and w are determined by [Formula 9],

[0061] [Formula 9]

[0062]

[0063] v x and v y represents the x-component and y-component of the velocity vector.

[0064] Thus, the imaging device can image an object moving in the measurement area with high accuracy using a scattered field function derived from measurement data obtained by multiple transmitters arranged on the first straight line and multiple receivers arranged on the second straight line.

[0065] In addition, for example, the imaging function is expressed by [Mathematical Formula 10],

[0066] [Formula 10]

[0067]

[0068] x, y, and z in the imaging function represent the x-coordinate, y-coordinate, and z-coordinate of the imaging object position.

[0069] Thus, the imaging device can image an object moving in the measurement area with high accuracy using an imaging function derived from measurement data obtained by multiple transmitters arranged on the first straight line and multiple receivers arranged on the second straight line.

[0070] Furthermore, for example, the information processing circuit uses the imaging function after the x-coordinate is shifted according to x=L+ξ to image the object. The imaging function after the x-coordinate is shifted is expressed by [Mathematical Formula 11],

[0071] [Formula 11]

[0072]

[0073] L represents the offset of the x-coordinate, and ξ represents the x-coordinate offset by L.

[0074] This allows the imaging device to shift the imaging target area. Therefore, the imaging device can efficiently image a distant object using multiple transmitters and multiple receivers.

[0075] Furthermore, for example, the information processing circuit uses the measurement data instead of the velocity vector to derive a tentative scattered field function, uses the tentative scattered field function to derive a tentative imaging function, and uses the tentative imaging function to derive the velocity vector.

[0076] Thus, the imaging device can derive the velocity vector of the object using a provisional scattered field function and a provisional imaging function, which are derived without using the object's velocity vector. Furthermore, the imaging device can use the scattered field function and imaging function derived using the velocity vector to image the object moving within the measurement area with high precision.

[0077] Furthermore, for example, the information processing circuit derives the velocity vector using the operation expression represented by [Equation 12] in deriving the velocity vector.

[0078] [Mathematical formula 12]

[0079]

[0080] The a, b, c, e, f, g, h, m, and n of the above operation expression are determined by [Mathematical Formula 13],

[0081] [Mathematical formula 13]

[0082]

[0083] v x 、v y and v z represents the x component, y component and z component of the velocity vector, ε represents a positive value, and ρ k With τ as one of the input variables, and ρ k represents the tentative imaging function after Fourier transform of x, y, and z, and k in the calculation expression x 、k y and k z represents the x, y, and z wave numbers for the tentative imaging function,

[0084] [Mathematical formula 14] represents the k of the above operation expression x 、k y and k z The wave number vector is formed,

[0085] [Formula 14]

[0086] k

[0087] τ represents a time unit equivalent to the number of times data is acquired, cc. represents the conjugate complex number of the term immediately preceding cc.,

[0088] [Formula 15] represents ρ k The complex conjugate of .

[0089]

[0090] According to this, the imaging device can use the calculation expression to derive the velocity vector of the object according to the provisional imaging function.

[0091] Furthermore, an imaging method according to one embodiment of the present disclosure includes: a step of transmitting a wave motion from each of a plurality of transmitters to a measurement area; a step of receiving scattered waves of the wave motion from the measurement area at each of a plurality of receivers; and a step of imaging an object in the measurement area using measurement data of the scattered waves, wherein the step of imaging the object includes: a step of deriving a scattered field function using the measurement data and a velocity vector of the object, the scattered field function being a function that receives as input a transmission position of the wave motion and a reception position of the scattered waves and outputs an amount of the scattered waves at the reception position; and a step of deriving an imaging function, wherein the imaging function A function is inputted with an imaging target position and outputs an image intensity of the imaging target position, wherein the imaging function is determined using a quantity outputted from the scattered field function by inputting the imaging target position as the transmitting position and the receiving position into the scattered field function; and a step of imaging the object in the measurement area using the imaging function, wherein in the step of deriving the scattered field function, the scattered field function is derived from the measurement data using a coordinate system determined using the velocity vector and fixing the position of the object in at least two directions.

[0092] This allows the position of an object to be fixed and imaged. This allows for highly accurate imaging of objects moving within the measurement area. Furthermore, without the need to move multiple transmitters and receivers, waves can be transmitted from various directions toward the object and scattered waves received. Therefore, even with a small number of transmitters and receivers, sufficient information can be obtained, enabling highly accurate imaging of the object.

[0093] The following embodiments are described using the accompanying drawings. The embodiments described below are generally or specifically examples. The numerical values, shapes, materials, components, component configurations, connection methods, steps, and step sequences shown in the following embodiments are merely examples and are not intended to limit the technical solutions.

[0094] In the following description, in particular, the technologies described in Patent Documents 2, 3, 4, and 5 mentioned above may be referenced as prior art. Furthermore, in the following description, radio waves such as microwaves or electromagnetic waves are primarily considered as waves, but waves are not limited to microwaves or electromagnetic waves and may also be elastic waves. Furthermore, imaging based on scattering can be expressed as scattering tomography. Therefore, the imaging device and imaging method described below may be expressed as a scattering tomography device and a scattering tomography method, respectively.

[0095] (Implementation Method)

[0096] The imaging device in this embodiment uses scattered wave measurement data to image an object in a measurement area. The imaging device in this embodiment will be described in detail below, including its underlying technology and theory.

[0097] <1 Summary>

[0098] Scattering field theory is used to visualize objects within a measurement area. For example, a wave is transmitted from each of multiple transmission locations into the measurement area, and scattered waves from the wave are received at each of multiple reception locations. Measurement data for the scattered waves is obtained for each combination of transmission and reception locations. The measurement data is then used to visualize the object within the measurement area. Using this measurement data, the scattered field theory calculates the state of scattering within the measurement area, and based on this state, the object is imaged with high precision.

[0099] However, when an object moves in a measurement area, the position of the object becomes uncertain, making it difficult to image the object with high precision.

[0100] Therefore, this disclosure describes a scattered field theory for accurately imaging an object moving in a measurement region. Specifically, the scattered field theory without considering the object's movement is first described, followed by a scattered field theory that takes the object's movement into account.

[0101] <2 Scattering field theory that does not take into account the movement of objects>

[0102] In this chapter, the scattered field theory without considering the movement of the object is explained.

[0103] <2-1 One-dimensional arrangement>

[0104] Figure 1 : is a conceptual diagram showing a one-dimensional multi-base array antenna. Figure 1As shown, by using any two of the n elements as both transmitting and receiving elements, the resolution can be doubled compared to a monostatic environment where the pairing of transmitting and receiving elements is fixed. Furthermore, signals can be received with a high signal-to-noise ratio from short to long distances. This significantly improves the quality of the resulting image. While the amount of data increases by a factor of n, the time required for reconstruction is also dramatically reduced, based on the theory described below.

[0105] like Figure 1 As shown, here we will discuss the situation where a 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). As point P moves throughout area D, the signal received at P2 is expressed as shown in the following equation (2-1-1).

[0106] [Mathematical formula 16]

[0107]

[0108] Here, ε(ξ, η, ζ) represents a function of the dielectric constant at point P(ξ, η, ζ), corresponding to the reflectivity at point P(ξ, η, ζ). Furthermore, point P(ξ, η, ζ) corresponds to the reflection point. Furthermore, ε(ξ, η, ζ) is unknown. The time factor is assumed to be proportional to exp(-iωt). The kernel function in the integrand above is represented by φ in the following equation (2-1-2).

[0109] [Mathematical formula 17]

[0110]

[0111] Next, let's consider the partial differential equation for which this equation (2-1-2) has an asymptotic solution. Therefore, we will calculate 1 / ρ, which is generated by the differentiation result, while ignoring the higher-order terms. Here, the abbreviated notation for differentiation is defined as in equation (2-1-3).

[0112] [Mathematical formula 18]

[0113]

[0114] Furthermore, we will examine the partial differential equation (2-1-2) that has an asymptotic solution at short wavelengths (high frequencies or large k). The solution to this partial differential equation can be roughly considered an exact solution when visualized using microwaves. First, the results of differentiating φ at various degrees are expressed as shown in the following equation (2-1-4).

[0115] [Mathematical formula 19]

[0116]

[0117] The complicated terms of o(*) are omitted below. The sum of the four equations related to the second-order differential gives the following equation (2-1-5).

[0118] [Mathematical formula 20]

[0119]

[0120] Therefore, according to formula (2-1-5), the following formula (2-1-6) is obtained.

[0121] [Mathematical formula 21]

[0122]

[0123] By performing the operation of formula (2-1-6) twice, the following formula (2-1-7) is obtained.

[0124] [Mathematical formula 22]

[0125]

[0126] Arranging formula (2-1-7) yields the following formula (2-1-8).

[0127] [Mathematical formula 23]

[0128]

[0129] Although the equation (2-1-8) is derived assuming a steady state, it is easy to extend the equation (2-1-8) to an unsteady state. Therefore, the partial differential with respect to time t can be expressed using And c, which represents the propagation speed of radio waves, performs variable substitution as shown in the following formula (2-1-9).

[0130] [Mathematical formula 24]

[0131]

[0132] Through the above process, we can finally obtain the following equation (2-1-10).

[0133] [Mathematical formula 25]

[0134]

[0135] The above equation (2-1-10) is a partial differential equation for which the φ of equation (2-1-2) is a solution. By applying differentiation to the integral kernel of equation (2-1-1), the equation (2-1-1) [Mathematical Equation 26]

[0136]

[0137] The above partial differential equation is also satisfied. This equation is a four-dimensional wave equation consisting of five variables (t, x, y1, y2, z).

[0138] Next, use the Fourier transform to solve the equation. First,

[0139] [Mathematical formula 27]

[0140]

[0141] As shown in the following formula (2-1-11), multiple Fourier transform is performed on t, x, y1, and y2.

[0142] [Mathematical formula 28]

[0143]

[0144] 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).

[0145] [Mathematical formula 29]

[0146]

[0147] 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).

[0148] [Mathematical formula 30]

[0149]

[0150] When the time factor is considered to be e -iωt When the phases of the radiated radio waves are added together along the path, and the radio waves reflected by the object bounce back toward the measurement surface (measurement surface), E1 is the only meaningful solution. Therefore, the following equation (2-1-14) is obtained.

[0151] [Mathematical formula 31]

[0152]

[0153] By substituting z=0 into the formula (2-1-14), a(k x , k y1 , k y2 , k).

[0154] [Mathematical formula 32]

[0155]

[0156] Finally, the

[0157] [Mathematical formula 33]

[0158]

[0159] It is calculated as shown in the following formula (2-1-16).

[0160] [Mathematical formula 34]

[0161]

[0162] 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).

[0163] [Mathematical formula 35]

[0164]

[0165] As described above, the multistatic inverse scattering problem in a one-dimensional array can be solved analytically.

[0166] <2-2 Two-dimensional arrangement>

[0167] In this section, the theory in the case of a two-dimensional arrangement is explained.

[0168] Figure 2 This is a conceptual diagram showing the relationship between the transmission point and the reception point in a plane. Figure 2 As shown, the microwave radiated from point P1 is reflected by point P on the target and received by point P2. Points P1 and P2 are moved to arbitrary points on the grid points in the plane (two-dimensional array antenna). Under this assumption, the path of the microwave passing through point P on the target is n 4 These numerous paths contribute significantly to improving the quality of the final image. The following describes how to process this complex data to obtain an image.

[0169] For example Figure 2 As shown, a 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). As point P moves throughout area D, the signal received at point P2 is expressed as follows.

[0170] [Mathematical formula 36]

[0171]

[0172] Here, we assume 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 (2-2-2).

[0173] [Mathematical formula 37]

[0174]

[0175] Next, we will examine the partial differential equation that asymptotically solves Equation (2-2-2) at short wavelengths. Therefore, we will calculate 1 / ρ, which is generated by the differentiation, while ignoring the higher-order terms. Here, the abbreviated notation for differentiation is defined as in Equation (2-2-3).

[0176] [Mathematical formula 38]

[0177]

[0178] Using formula (2-2-3), the differentials of the kernel function at each order are expressed as shown in the following formula (2-2-4).

[0179] [Mathematical formula 39]

[0180]

[0181] In the following text, the complicated o(*) term is omitted. The sum of the five equations for second-order differentials yields the following equation (2-2-5).

[0182] [Mathematical formula 40]

[0183]

[0184] Therefore, according to formula (2-2-5), the following formula (2-2-6) is obtained.

[0185] [Mathematical formula 41]

[0186]

[0187] By performing the operation of formula (2-2-6) twice, the following formula (2-2-7) is obtained.

[0188] [Mathematical formula 42]

[0189]

[0190] Arranging formula (2-2-7) yields the following formula (2-2-8).

[0191] [Mathematical formula 43]

[0192]

[0193] Although this equation (2-2-8) is derived assuming a steady state, it is easy to extend this equation (2-2-8) to an unsteady state. Therefore, the variables are replaced as shown in the following equation (2-2-9).

[0194] [Mathematical formula 44]

[0195]

[0196] By this substitution, the formula (2-2-8) is transformed into the following formula (2-2-10) including time.

[0197] [Mathematical formula 45]

[0198]

[0199] Equation (2-2-10) above is the partial differential equation for which the kernel function shown in Equation (2-2-2) is the solution. By differentiating the integral kernel of Equation (2-2-1), φ also satisfies the above partial differential equation. This equation is a five-dimensional wave equation consisting of six variables (t, x1, y1, x2, y2, z).

[0200] 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 (2-2-11).

[0201] [Mathematical formula 46]

[0202]

[0203] When expressing the differential with respect to z as D z In the case of , the following formula (2-2-12) is obtained according to formulas (2-2-10) and (2-2-11).

[0204] [Mathematical formula 47]

[0205]

[0206] Here, the relationship of ω=ck is used. The four basic solutions of this equation are expressed as shown in the following equation (2-2-13).

[0207] [Mathematical formula 48]

[0208]

[0209] When the time factor is considered to be e -iωt When the phases are added along the path of the radiated radio waves, and the radio waves reflected by the object bounce back toward the measurement surface, E1 is the only meaningful solution. Therefore, the following equation (2-2-14) is obtained.

[0210] [Mathematical formula 49]

[0211]

[0212] By substituting z=0 into the formula (2-2-14), a(k x1 , k y1 , k x2 , k y2 , k).

[0213] [Mathematical formula 50]

[0214]

[0215] Based on the above, φ is calculated as shown in the following formula (2-2-16).

[0216] [Mathematical formula 51]

[0217]

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

[0219] [Mathematical formula 52]

[0220]

[0221] Next, by integrating the equation (2-2-17) with respect to k, the following equation (2-2-18) is obtained as a visualization function.

[0222] [Mathematical formula 53]

[0223]

[0224] In formula (2-2-18), with k x1 、k y1 、k x2 、k y2 The relevant integrals are in Fourier transform form, making them suitable for computer processing. On the other hand, the terms in the integrand, exp(iz...), are not in Fourier transform form. Therefore, for example, a normal integral with respect to k can be performed while specifying the value of z. Alternatively, to reduce computation time, equation (2-2-18) can be modified so that the entire equation is expressed solely in Fourier transform form.

[0225] For example, the coefficient of iz in exp(iz...) in Formula (2-2-17) is expressed as in the following Formula (2-2-19) using a new variable u.

[0226] [Mathematical formula 54]

[0227]

[0228] By rationalizing the right side of formula (2-2-19), we obtain the following formula (2-2-20).

[0229] [Mathematical formula 55]

[0230]

[0231] By solving each square root according to equations (2-2-19) and (2-2-20), the following equation (2-2-21) is obtained.

[0232] [Mathematical formula 56]

[0233]

[0234] Therefore, k is expressed as shown in the following formula (2-2-22).

[0235] [Mathematical formula 57]

[0236]

[0237] Furthermore, by differentiating k and u on both sides of formula (2-2-19), the following formula (2-2-23) is obtained.

[0238] [Mathematical formula 58]

[0239]

[0240] By solving dk according to formula (2-2-23), we can obtain the following formula (2-2-24).

[0241] [Mathematical formula 59]

[0242]

[0243] Finally, to summarize, formula (2-2-18) is transformed into the following formula (2-2-25).

[0244] [Mathematical formula 60]

[0245]

[0246] <2-3 Quasi-two-dimensional arrangement>

[0247] Figure 3This is a conceptual diagram showing an example of coordinates related to a quasi-2D array antenna. In this example, the quasi-2D array antenna consists of two linear array antennas: one array of transmit array antennas TA and one array of receive array antennas RA. This quasi-2D array antenna can be expressed as an S-array (super-array) or an S-array multistatic antenna.

[0248] The transmitting array antenna TA includes n transmitting antenna elements T. The receiving array antenna RA includes n receiving antenna elements R. The x-coordinate of the transmitting array antenna TA is represented by x1, the x-coordinate of the receiving array antenna RA is represented by x2, and the distance between the transmitting array antenna TA and the receiving array antenna RA in the x-axis direction is represented by d. In this configuration, at each point x in the scanning direction, n arbitrary combinations of n transmitting elements and n receiving elements are obtained. 2 time series data.

[0249] In this section, the Figure 3 This paper explains the theory of imaging objects using data obtained using the quasi-two-dimensional array antenna shown. First, as a starting point for this discussion, we'll use equation (2-2-10) related to two-dimensional arrays. The following equation (2-3-1) is identical to equation (2-2-10).

[0250] [Mathematical formula 61]

[0251]

[0252] also,

[0253] [Mathematical formula 62]

[0254]

[0255] The Fourier transform of t, x1, y1, and y2 is expressed as the following formula (2-3-2).

[0256] [Mathematical formula 63]

[0257]

[0258] The variable x2 is expressed as u below. By Fourier transforming both sides of equation (2-3-1) with respect to t, x1, y1, and y2, the following equation (2-3-3) is obtained.

[0259] [Mathematical formula 64]

[0260]

[0261] The solution of the above-mentioned formula (2-3-3), which is a two-dimensional partial differential equation for u and z, is assumed to be the following formula (2-3-4).

[0262] [Mathematical formula 65]

[0263]

[0264] Here, s3 and s4 are related to k as shown in the following formula (2-3-5): x1 、k y1 、k y2 And a function of k. In other words, s3 and s4 are based on k x1 、k y1 、k y2 and a constant determined by k.

[0265] [Mathematical formula 66]

[0266] s3=s3(k x1 ,k y1 ,k y2 ,k)

[0267] s4=s4(k x1 ,k y1 ,k y2 ,k)

[0268] ···(2-3-5)

[0269] By substituting formula (2-3-4) into formula (2-3-3), the following formula (2-3-6) is obtained.

[0270] [Mathematical formula 67]

[0271]

[0272] s3 and s4 cannot be determined by this algebraic equation alone. Next, Formula (2-3-4) is changed to the following Formula (2-3-7).

[0273] [Mathematical formula 68]

[0274]

[0275] By converting Equation (2-3-7) about k x1 、k y1 and k y2 Perform an inverse Fourier transform and apply u→x2 to the result to obtain the following formula (2-3-8).

[0276] [Mathematical formula 69]

[0277]

[0278] By applying x2=x1=x to Formula (2-3-8), the following Formula (2-3-9) is obtained.

[0279] [Mathematical formula 70]

[0280]

[0281] Here, k x It is expressed by the following formula (2-3-10).

[0282] [Mathematical formula 71]

[0283]

[0284] The above equation (2-3-9) agrees with the solution of the scattered field equation for a one-dimensional array, and therefore should agree with equation (2-1-16). The following equation (2-3-11) is the same as equation (2-1-16).

[0285] [Mathematical formula 72]

[0286]

[0287] By comparing formula (2-3-9) with formula (2-3-11), the following formula (2-3-12) can be obtained.

[0288] [Mathematical formula 73]

[0289]

[0290] By squaring the second equation of equation (2-3-12), we obtain the following equation (2-3-13).

[0291] [Mathematical formula 74]

[0292]

[0293] By substituting formula (2-3-13) into formula (2-3-6), the following formula (2-3-14) is obtained.

[0294] [Mathematical formula 75]

[0295]

[0296] By rearranging formula (2-3-14), we obtain the following formula (2-3-15).

[0297] [Mathematical formula 76]

[0298]

[0299] Since the solution of this equation is a repeated root, the solution expressed by the following equation (2-3-16) is uniquely obtained.

[0300] [Mathematical formula 77]

[0301]

[0302] Using equations (2-3-12) and (2-3-16) obtained in the above process, s3 and s4 are analytically determined. Furthermore, the scattered field function is obtained as shown in equation (2-3-17) based on equation (2-3-8).

[0303] [Mathematical formula 78]

[0304]

[0305] Next, we will discuss the relationship between the measured data Φ(x1, y1, y2, k) and a(k x1 , k y1 , k y2 Therefore, by determining k x =k x1 Substituting z = 0 and x2 = x1 + d into equation (2-3-17), the following equation (2-3-18) holds. Here, Φ(x1, y1, y2, k) represents the measurement data for the transmission point (x1, y1, 0), the reception point (x1 + d, y2, 0), and the wave number k.

[0306] [Mathematical formula 79]

[0307]

[0308] Hereinafter, k defined by the following formula (2-3-19) is used x and s3.

[0309] [Mathematical formula 80]

[0310]

[0311] By performing Fourier transform on both sides of equation (2-3-18) with respect to x1, y1, and y2, the following equation (2-3-20) is obtained.

[0312] [Mathematical formula 81]

[0313]

[0314] According to formula (2-3-20), the function a(k x , k y1 , k y2 , k).

[0315] [Mathematical formula 82]

[0316]

[0317] Therefore, the scattered field function of equation (2-3-17) is obtained in a complete form as shown in the following equation (2-3-22).

[0318] [Mathematical formula 83]

[0319]

[0320] Then, the visualization function is obtained as shown in the following formula (2-3-23).

[0321] [Mathematical formula 84]

[0322]

[0323] Compared to a one-dimensional array, a quasi-two-dimensional array can accommodate more transmitting elements and more receiving elements, thereby enabling more efficient acquisition of information.

[0324] <3 Scattering Field Theory Considering Object Movement>

[0325] This chapter explains the scattering field theory that takes the motion of objects into account. In particular, it explains the scattering field theory used to image flying objects moving in the atmosphere.

[0326] For example, a tentative visualization function is first derived at constant time intervals based on scattered field theory that does not account for object motion. The velocity of the object is then derived based on the tentative visualization function derived at constant time intervals. Furthermore, the visualization function is derived based on scattered field theory that accounts for object motion, specifically, the velocity of the object.

[0327] <3-1 Velocity Analysis of Flying Objects>

[0328] Figure 4 This is a conceptual diagram showing the relationship between multiple transmitters, multiple receivers, and a flying object. The x-axis and y-axis directions correspond to the horizontal direction, and the z-axis direction corresponds to the vertical direction. N ) and multiple receivers (R0, ···, R N ) and the obtained measurement data are shown as follows.

[0329] [Mathematical formula 85]

[0330]

[0331] Here, t represents real time. τ is a time unit equivalent to the number of times data is acquired. Specifically, when the fluctuating transmission and reception time is expressed as Δt, t = τΔt holds true. Therefore, τ can represent time. Furthermore, in this section, the distance d between the transmit and receive arrays is assumed to be 0 (d = 0). The transmit and receive array antennas are arranged along the y-axis and do not move, so the measurement data does not depend on x.

[0332] Then, the measurement data is re-expressed as follows.

[0333] [Mathematical formula 86]

[0334]

[0335] By substituting the above-mentioned τ into the visualization function of formula (2-1-17), the visualization function of the following formula (3-1-1) is obtained.

[0336] [Mathematical formula 87]

[0337]

[0338] The visualization function of the above-mentioned formula (3-1-1) is a visualization function obtained by the scattered field theory without considering the movement of the object, and this visualization function depends on τ.

[0339] The velocity of an object is calculated from ρ(τ, x, y, z), so the Lagrange differential is used. The Lagrange differential is defined as the following formula (3-1-2).

[0340] [Mathematical formula 88]

[0341]

[0342] In formula (3-1-2), V represents the velocity vector (v) of the incompressible flow field in the (x, y, z) space. x , v y , v z V can be considered a function of (x, y, z). However, since only flying objects have velocity, when there is only one flying object, V is assumed to be constant in space and dependent on time τ. When there are multiple flying objects, V is not constant in space but is constant near the flying object. Based on these conditions, the following equation (3-1-3) is added to the visualization function.

[0343] [Mathematical formula 89]

[0344]

[0345] When V=(v x , vy , v z ) is constant, the speed of the flying object is (v x , v y , v z ) is derived. However, when ρ(τ, x, y, z) is 0, in formula (3-1-3), (v x , v y , v z ) cannot be determined. Therefore, the speed of the flying object is calculated based on formula (3-1-4).

[0346] [Mathematical formula 90]

[0347]

[0348] Here, ε is a positive number. Formula (3-1-4) is about (v x , v y , v z ) is a quadratic form with positive coefficients, so the minimum value must exist. Furthermore, a term of ε is set to prevent the following situation, that is, when ρ(τ, x, y, z) is 0 (v x , v y , v z ) is an arbitrary value and reaches the minimum value. When ρ(τ, x, y, z) is 0, (v x , v y , v z ) is derived as (0, 0, 0). In order to avoid errors caused by the term of ε, the value of ε is preferably small.

[0349] In order to derive (v x , v y , v z ), first perform Fourier transform on ρ(τ, x, y, z) to obtain the following formula (3-1-5).

[0350] [Mathematical formula 91]

[0351]

[0352] By substituting formula (3-1-5) into formula (3-1-3), the following formula (3-1-6) is obtained.

[0353] [Mathematical formula 92]

[0354]

[0355] For convenience, the function appearing on the right side of formula (3-1-6) is written as follows.

[0356] [Mathematical formula 93]

[0357]

[0358] Using the symbols of formula (3-1-7), formula (3-1-6) can be expressed as follows: formula (3-1-8).

[0359] [Mathematical formula 94]

[0360]

[0361] In order to actually calculate the formula (3-1-4), the formula (3-1-8) is evaluated as the formula in the absolute value symbol of the formula (3-1-4), thereby obtaining the formula (3-1-9).

[0362] [Mathematical formula 95]

[0363]

[0364] Here, cc. represents the complex conjugate of the immediately preceding term. Variables with a horizontal bar above them represent the complex conjugate of that variable. The integral calculation on the right side of this equation (3-1-9) can be greatly simplified to the following equation (3-1-10).

[0365] [Mathematical formula 96]

[0366]

[0367] Formula (3-1-9) is expressed as the following formula (3-1-11) using formula (3-1-10).

[0368] [Mathematical formula 97]

[0369]

[0370] Moreover, formula (3-1-4) can be expressed as the following formula (3-1-12).

[0371] [Mathematical formula 98]

[0372]

[0373] The following formula (3-1-13) is derived based on formula (3-1-12).

[0374] [Mathematical formula 99]

[0375]

[0376] Furthermore, the following formula (3-1-14) is derived from formula (3-1-13).

[0377] [Mathematical Formula 100]

[0378]

[0379] The elements of the matrix can be easily calculated using formula (3-1-10). Therefore, the velocity vector can be calculated.

[0380] Here, the integration area of ​​formula (3-1-10) is explained. For example, by integrating in the area near a flying object, the speed of the flying object is obtained. And, for example, by integrating in an area including multiple flying objects moving in a queue, the average speed of the multiple flying objects as a whole is obtained. And, in the case where there is no flying object, a, b, c, .., m, n are infinitely close to 0. In this case, it can be clearly seen from formula (3-1-13) that by the introduced ε, v x 、v y 、v z is exported as 0.

[0381] <3-2 One-dimensional arrangement>

[0382] After the velocity of the flying object is determined, a coordinate system in which the flying object is fixed in the (x, y) plane is introduced.

[0383] Figure 5 This is a conceptual diagram showing a coordinate system (x, y) in which a flying object is not fixed and a coordinate system (ξ, η) in which the flying object is fixed when a one-dimensional multistatic array antenna is used.

[0384] In the coordinate system (x, y), the one-dimensional multistatic array antenna is arranged on the y-axis. Figure 5 The same method is used to calculate the projection velocity (v) of the flying object on the two-dimensional plane (x, y) x , v y ) in the coordinate system (ξ, η). In the coordinate system (ξ, η), the position of the flying object is virtually maintained and does not change, while the position of the one-dimensional multistatic array antenna is virtually changed. Moreover, the measurement data Φ at time τ τ (x, y1, y2, t) can be regarded as data acquired at locations with different ξ values.

[0385] Thus, it can be viewed as a one-dimensional multistatic array antenna scanning in the ξ-axis direction. Furthermore, information in the x-axis direction (ξ-axis direction) can be obtained. In other words, information in the x-axis direction (ξ-axis direction) can be constructed from time-series information. Ultimately, this improves the resolution in all directions of the flying object image.

[0386] Here, the relationship between the coordinate system (x, y) and the coordinate system (ξ, η) is expressed by the following formula (3-2-1). The coordinate system (ξ, η) can also be expressed as an oblique coordinate system.

[0387] [Math 101]

[0388] x=ξcos(θ)

[0389] y=ξsin(θ)+η

[0390]

[0391] The scattered field function based on the one-dimensional multistatic array antenna is given by equation (2-1-16). The following equation (3-2-2) is the same as equation (2-1-16).

[0392] [Mathematical Formula 102]

[0393]

[0394] Using u=cos(θ) and w=sin(θ), the following formula (3-2-3) is obtained from formula (3-2-1).

[0395] [Mathematical formula 103]

[0396] x=uξ

[0397] y1=wξ+η1

[0398] y2=wξ+η2

[0399] ···(3-2-3)

[0400] Using formula (3-2-3), the following formula (3-2-4) is obtained according to formula (3-2-2).

[0401] [Mathematical formula 104]

[0402]

[0403] Furthermore, for formula (3-2-4), the variable transformation of the following formula (3-2-5) is applied.

[0404] [Mathematical formula 105]

[0405]

[0406] Thus, the following formula (3-2-6) is obtained.

[0407] [Mathematical formula 106]

[0408]

[0409] 1 / u in equation (3-2-6) corresponds to the Jacobian. Furthermore, in equation (3-2-6), permutation is applied as shown in equation (3-2-7).

[0410] [Mathematical formula 107]

[0411]

[0412] Next, we will discuss how to use the measured data to find α(k ξ , k η1 , k η2 , k). The measurement data is obtained from Figure 5 By substituting z=0 into equation (3-2-7), the measurement data Φ(ξ, η1, η2, k) is expressed as follows (3-2-8).

[0413] [Mathematical formula 108]

[0414]

[0415] Through the inverse Fourier transform of formula (3-2-8), α(k ξ , k η1 , k η2 , k) is calculated as shown in the following formula (3-2-9).

[0416] [Mathematical formula 109]

[0417]

[0418] Therefore, the scattered field function is obtained as shown in the following formula (3-2-10).

[0419] [Mathematical Formula 110]

[0420]

[0421] The scattering field function of formula (3-2-10) based on the coordinate system (ξ, η) is restored to the scattering field function based on the original coordinate system (x, y), thereby obtaining the following formula (3-2-11).

[0422] [Mathematical Formula 111]

[0423]

[0424] The visualization function is obtained as shown in the following formula (3-2-12) by setting y1=y2=y.

[0425] [Mathematical formula 112]

[0426]

[0427] <3-3 Quasi-two-dimensional arrangement>

[0428] In this section, the scattered field theory in the previous section is extended to the scattered field theory of a quasi-two-dimensional arrangement in which the transmitting array antenna and the receiving array antenna are far away from each other.

[0429] Figure 6 A conceptual diagram showing a coordinate system (x, y) where the flying object is not fixed and a coordinate system (ξ, η) where the flying object is fixed when using a quasi-two-dimensional array antenna. The distance between the transmitting array antenna and the receiving array antenna is d.

[0430] In the coordinate system (x, y), the transmit array antenna is arranged along the y-axis at x=0, and the receive array antenna is arranged along the y-axis at x=d. Figure 6 As shown, the projection velocity (v x , v y ) in the coordinate system (ξ, η). The position of the flying object in the coordinate system (ξ, η) does not change, but the positions of the transmitting array antenna and the receiving array antenna change. τ (x, y1, y2, t) can be regarded as data acquired at locations with different ξ values.

[0431] Thus, the transmitting and receiving array antennas can be considered to be scanning in the ξ-axis direction. Furthermore, information in the x-axis direction (ξ-axis direction) can be obtained. In other words, information in the x-axis direction (ξ-axis direction) can be constructed from time-series information. This ultimately improves the resolution in all directions of the flying object image.

[0432] Here, the relationship between (x1, y1, y2) and (ξ1, η1, η2) is expressed by the following formula (3-3-1).

[0433] [Mathematical formula 113]

[0434] x1=ξ1cos(θ)

[0435] y1=ξ1sin(θ)+η1

[0436] y2=ξ1sin(θ)+η2

[0437]

[0438] Through formula (2-3-17), the scattered field function of the quasi-two-dimensional arrangement is expressed as the following formula (3-3-2).

[0439] [Mathematical formula 114]

[0440]

[0441] In order to find the function b(k x1 , k y1 , k y2 , k), using the measurement data in z=0.

[0442] Substituting x2=x1+d and z=0 into the right side of equation (3-3-2) yields the following equation (3-3-3): Here, Φ(x1, y1, y2, k) is measurement data.

[0443] [Mathematical formula 115]

[0444]

[0445] Substitute the following formula (3-3-4) into formula (3-3-3).

[0446] [Mathematical formula 116]

[0447] x1=ξ1cos(θ)

[0448] y1=ξ1sin(θ)+η1

[0449] y2=ξ1sin(θ)+η2

[0450]

[0451] u=cos(θ)w=sin(θ)

[0452] ···(3-3-4)

[0453] Thus, the following formula (3-3-5) is obtained.

[0454] [Mathematical formula 117]

[0455]

[0456] Furthermore, substitution is applied to Formula (3-3-5) as shown in Formula (3-3-6).

[0457] [Mathematical formula 118]

[0458]

[0459] Thus, we obtain formula (3-3-7).

[0460] [Mathematical formula 119]

[0461]

[0462] Perform an inverse Fourier transform on both sides of equation (3-3-7) to obtain the following equation (3-3-8).

[0463] [Mathematical formula 120]

[0464]

[0465] Therefore, b(k x1 , k y1 , k y2 , k) is obtained as follows.

[0466] [Mathematical formula 121]

[0467]

[0468] Then, the scattered field function is obtained as shown in the following formula (3-3-10).

[0469] [Mathematical formula 122]

[0470]

[0471] Then, the imaging function for wave number k is obtained as shown in the following formula (3-3-11) from the scattered field function.

[0472] [Mathematical formula 123]

[0473]

[0474] Furthermore, by integrating all the values ​​of k, the final visualization function is obtained as shown in the following formula (3-3-12).

[0475] [Mathematical formula 124]

[0476]

[0477] Figure 7 This is a conceptual diagram showing the analysis area far from the antenna installation location. When an aircraft is located very far from the antenna installation location, visualizing the entire area from the antenna installation location to the aircraft in three dimensions is not only inefficient but also difficult to display. Therefore, Equation (3-3-12) can be offset in the x-axis direction. Specifically, when the offset in the x-axis direction is L, the variables in Equation (3-3-12) can be permuted according to x = L + ξ. This yields the following Equation (3-3-13).

[0478] [Mathematical formula 125]

[0479]

[0480] Here, the Fourier transformed measurement data corresponding to the new analysis area can be expressed by the following formula (3-3-14).

[0481] [Mathematical formula 126]

[0482]

[0483] <3-4 Modification>

[0484] In this chapter, the velocities used are derived using a provisional visualization function. However, velocities determined by other methods can also be used. For example, if the object's velocity is known, that known velocity can be used. Alternatively, velocities measured by other velocity sensors, such as Doppler sensors, can be used. Furthermore, velocities estimated based on the object's properties can also be used.

[0485] In this chapter, the scattered field theory considering the movement of objects is applied to the examples of one-dimensional and quasi-two-dimensional arrays. However, the scattered field theory considering the movement of objects can be further applied to the example of two-dimensional arrays.

[0486] In this chapter, a coordinate system in which the position of an object is fixed about the x-axis and the y-axis is used. However, a coordinate system in which the position of an object is fixed about the z-axis can also be used.

[0487] <4. Composition and Operation of Imaging Device>

[0488] Based on the above, 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.

[0489] Here, the wave used to measure scattered waves can be, for example, radio waves, but can also be microwaves, millimeter waves, or terahertz waves. Furthermore, the wave can be light or sound. Furthermore, the measurement area can be an aerial region, and the object can be a flying object. The object in the measurement area has physical properties that differ from those of the surrounding medium. Specifically, these physical properties correspond to the reflectivity of the wave. When using radio waves as the wave, the physical property can be the dielectric constant.

[0490] Figure 8 This is a diagram showing the basic structure of the imaging device in this embodiment. Figure 8 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.

[0491] Each transmitter 101 is a circuit that transmits a wave. Specifically, each transmitter 101 transmits a wave to a measurement area. Furthermore, each transmitter 101 may be a transmitting antenna or may be composed of multiple transmitting elements such as multiple transmitting antenna elements.

[0492] Each receiver 102 is a circuit that receives scattered waves of the wave. Specifically, each receiver 102 receives scattered waves of the wave from the measurement area. Furthermore, each receiver 102 may be a receiving antenna or may be composed of multiple receiving elements such as multiple receiving antenna elements.

[0493] The multiple transmitters 101 and the multiple receivers 102 may be configured as a one-dimensional arrangement, a two-dimensional arrangement, or a quasi-two-dimensional arrangement.

[0494] The information processing circuit 103 performs information processing. Specifically, the information processing circuit 103 obtains scattered wave measurement data and uses this scattered wave measurement data to visualize the object within the measurement area. For example, when using the measurement data to visualize the object, the information processing circuit 103 performs the computational processing described in the aforementioned theory.

[0495] Alternatively, the information processing circuit 103 may be a computer or a computer processor. The information processing circuit 103 may process information by reading a program from a memory and executing the program. Furthermore, the information processing circuit 103 may be a dedicated circuit that images objects within the measurement area based on measurement data.

[0496] Furthermore, the information processing circuit 103 may be capable of communicating 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.

[0497] Furthermore, the information processing circuit 103 can generate an image showing the object during the visualization of the object. Furthermore, the information processing circuit 103 can output the image showing the object to a display 104 or the like. Alternatively, the information processing circuit 103 can output the image showing the object to a printer (not shown). Alternatively, the information processing circuit 103 can transmit the image as electronic data to another device (not shown) via wired or wireless communication.

[0498] The display 104 is a display device such as a liquid crystal display. The display 104 is an optional component and is not an essential component. Furthermore, the display 104 may not be an external device that constitutes the imaging device 100.

[0499] Figure 9 It shows Figure 8 The flowchart of the basic operation of the imaging device 100 is shown in FIG. Figure 8 The imaging device 100 shown in FIG. 1 includes a plurality of transmitters 101, a plurality of receivers 102, and an information processing circuit 103. Figure 9 Work shown.

[0500] First, each transmitter 101 transmits a wave to the measurement area (S101). Each receiver 102 then receives the scattered wave from the measurement area (S102). The information processing circuit 103 then uses the measurement data from the scattered wave to visualize the object in the measurement area (S103, S104, and S105).

[0501] Specifically, to visualize the object, the information processing circuit 103 first derives a scattered field function using the measurement data and the object's velocity vector (S103). The scattered field function is a function that takes as input the transmission position of a wave and the reception position of the scattered wave, and outputs the amount of the scattered wave at the reception position. Specifically, to derive the scattered field function, the information processing circuit 103 uses a coordinate system determined by the object's velocity vector and fixing the object's position in at least two directions.

[0502] Next, the information processing circuit 103 derives an imaging function using the scattered field function (S104). Here, the imaging function is a function that receives an imaging target position as input and outputs the image intensity of the imaging target position. The imaging function is determined using the quantity output from the scattered field function by inputting the imaging target position as the transmission position and the reception position into the scattered field function.

[0503] Finally, the information processing circuit 103 uses an imaging function to image the object in the measurement area ( S105 ).

[0504] Thus, the imaging device 100 can fix the position of the object and image the object. Therefore, the imaging device 100 can image the object moving in the measurement area with high accuracy.

[0505] Furthermore, imaging device 100 can transmit waves to an object from various directions and receive scattered waves without moving multiple transmitters 101 and multiple receivers 102. Therefore, imaging device 100 can obtain sufficient information even with a small number of transmitters 101 and multiple receivers 102, and can image the object with high precision.

[0506] For example, the plurality of transmitters 101 and the plurality of receivers 102 may be arranged on a straight line parallel to the y-axis.

[0507] Furthermore, the scattered field function can be expressed by [Formula 127].

[0508] [Mathematical formula 127]

[0509]

[0510] Here, x and z of the scattered field function represent the x-coordinate and z-coordinate of the transmitting position and the receiving position, respectively. y1 of the scattered field function represents the y-coordinate of the transmitting position. y2 of the scattered field function represents the y-coordinate of the receiving position. k represents the wave number of the wave. x 、k y1 and k y2 represents a variable corresponding to the wave number of x, y1, and y2 with respect to the scattered field function.

[0511] In addition, [Equation 128] represents the measurement data after Fourier transformation.

[0512] [Mathematical formula 128]

[0513]

[0514] In addition, u and w are determined by [Mathematical Formula 129].

[0515] [Mathematical formula 129]

[0516]

[0517] v x and v y Represents the x-component and y-component of the velocity vector.

[0518] Thus, the imaging device 100 can image an object moving in a measurement area with high accuracy using a scattered field function derived from measurement data obtained by a plurality of transmitters 101 and a plurality of receivers 102 arranged in a straight line.

[0519] In addition, for example, the visualization function can be expressed by [Equation 130].

[0520] [Mathematical formula 130]

[0521]

[0522] Here, x, y, and z in the visualization function represent the x-coordinate, y-coordinate, and z-coordinate of the visualization target position.

[0523] In addition, k z and dk / dkz Determined by [Mathematical Formula 131].

[0524] [Mathematical formula 131]

[0525]

[0526] Thus, the imaging device 100 can image an object moving in a measurement area with high accuracy using an imaging function derived from measurement data obtained by the plurality of transmitters 101 and the plurality of receivers 102 arranged on a straight line.

[0527] Furthermore, for example, the plurality of transmitters 101 may be arranged on a first straight line parallel to the y-axis, and the plurality of receivers 102 may be arranged on a second straight line parallel to the y-axis.

[0528] In addition, the scattered field function can be expressed by [Equation 132].

[0529] [Mathematical formula 132]

[0530]

[0531] Here, z of the scattered field function represents the z coordinates of the transmitting and receiving positions. x1 and y1 of the scattered field function represent the x coordinates and y coordinates of the transmitting and receiving positions. x2 and y2 of the scattered field function represent the x coordinates and y coordinates of the receiving position. k represents the wave number of the wave. x 、k y1 and k y2 represents a variable corresponding to the wave number of x, y1, and y2 with respect to the scattered field function, and d represents the distance between the first straight line and the second straight line.

[0532] In addition, [Equation 133] represents the measurement data after Fourier transformation.

[0533] [Mathematical formula 133]

[0534]

[0535] In addition, s3 and s4 are determined by [Mathematical Formula 134].

[0536] [Mathematical formula 134]

[0537]

[0538] In addition, u and w are determined by [Mathematical Formula 135].

[0539] [Mathematical formula 135]

[0540]

[0541] In addition, v x and v y Represents the x-component and y-component of the velocity vector.

[0542] Thus, the imaging device 100 can image an object moving in the measurement area with high accuracy using a scattered field function derived from measurement data obtained by the plurality of transmitters 101 arranged on the first straight line and the plurality of receivers 102 arranged on the second straight line.

[0543] In addition, for example, the visualization function is expressed by [Mathematical Formula 136].

[0544] [Mathematical formula 136]

[0545]

[0546] Here, x, y, and z in the visualization function represent the x-coordinate, y-coordinate, and z-coordinate of the visualization target position.

[0547] Thus, the imaging device 100 can image an object moving in the measurement area with high accuracy using an imaging function derived from measurement data obtained by the plurality of transmitters 101 arranged on the first straight line and the plurality of receivers 102 arranged on the second straight line.

[0548] Furthermore, for example, the information processing circuit 103 can visualize the object using a visualization function after the x-coordinate is shifted according to x=L+ξ. The visualization function after the x-coordinate is shifted can be expressed by [Equation 137].

[0549] [Mathematical formula 137]

[0550]

[0551] Here, L represents the offset amount of the x-coordinate, and ξ represents the x-coordinate offset by L.

[0552] Thus, the imaging device 100 can shift the imaging target area. Therefore, the imaging device 100 can efficiently image a distant object using the plurality of transmitters 101 and the plurality of receivers 102.

[0553] Furthermore, for example, the information processing circuit 103 may derive a tentative scattered field function using measurement data instead of the velocity vector. Furthermore, the information processing circuit 103 may derive a tentative imaging function using the tentative scattered field function. Furthermore, the information processing circuit 103 may derive a velocity vector using the tentative imaging function.

[0554] Thus, the imaging device 100 can derive the velocity vector of the object using a provisional scattered field function and a provisional imaging function, which are derived without using the object's velocity vector. Furthermore, the imaging device 100 can use the scattered field function and imaging function derived using the velocity vector to image an object moving within the measurement area with high precision.

[0555] In addition, for example, the information processing circuit 103 can derive the velocity vector using the operation expression represented by [Mathematical Formula 138].

[0556] [Mathematical formula 138]

[0557]

[0558] Here, a, b, c, e, f, g, h, m, and n in the operation expression are determined by [Mathematical Formula 139].

[0559] [Mathematical formula 139]

[0560]

[0561] In addition, v x 、v y and v z represents the x-component, y-component, and z-component of the velocity vector. ε represents a positive value. ρ k With τ as one of the input variables, and ρ k represents a tentative visualization function after Fourier transform of x, y, and z. x 、k y and k z Indicates the x, y, and z wave numbers for a tentative imaging function.

[0562] In addition, [Mathematical formula 140] represents the k of the operation expression x 、k y and k z The wave number vector.

[0563] [Mathematical formula 140]

[0564] k

[0565] τ represents a time unit corresponding to the number of times data is acquired, and cc. represents the conjugate complex number of the term immediately preceding cc.

[0566] In addition, [Equation 141] represents ρ k The complex conjugate of .

[0567] [Mathematical formula 141]

[0568]

[0569] Thus, the imaging device 100 can use the calculation expression to derive the velocity vector of the object according to the provisional imaging function.

[0570] Furthermore, the wave may be, for example, a microwave. In this way, the imaging device 100 can suppress the attenuation of the wave caused by moisture in the measurement area more than short-wavelength electromagnetic waves.

[0571] Furthermore, for example, in the basic configuration and basic operation described above, other components, equations, and variables described in this embodiment can be appropriately applied to the multiple transmitters 101, multiple receivers 102, information processing circuit 103, scattered field functions, and visualization functions. Furthermore, the scattered field functions and visualization functions described in this embodiment can be appropriately modified and applied. For example, mathematical equations expressing substantially the same content as the above-described mathematical equations in other expressions can be used, or other mathematical equations derived based on the above-described theory can be used.

[0572] (Replenish)

[0573] The above description of the imaging device is based on the embodiment, but the imaging device is not limited to the embodiment. The embodiment can be modified as would be expected by a person skilled in the art, and multiple components of the embodiment can be arbitrarily combined. For example, in the embodiment, a process performed by a specific component can be replaced by another component. In addition, the order of multiple processes can be changed, and multiple processes can be performed in parallel.

[0574] Furthermore, the imaging method, including the steps performed by the various components of the imaging device, can be executed by any device or system. For example, a computer equipped with a processor, memory, and input / output circuits can execute part or all of the imaging method. Alternatively, the imaging method can be executed by the computer executing a program that causes the computer to execute the imaging method.

[0575] Furthermore, the above-mentioned program may be recorded in a non-transitory computer-readable recording medium.

[0576] Furthermore, the various components of the imaging device may be composed of dedicated hardware, general-purpose hardware that executes the aforementioned programs, or a combination thereof. Furthermore, the general-purpose hardware may be composed of a memory that stores programs and a general-purpose processor that reads and executes the programs from the memory. The memory may be a semiconductor memory or a hard disk, and the general-purpose processor may be a CPU.

[0577] Furthermore, the dedicated hardware may be composed of a memory and a dedicated processor, etc. For example, the dedicated processor may refer to the memory for recording the measurement data to execute the above-mentioned imaging method.

[0578] Furthermore, each component of the imaging device may be a circuit. These circuits may constitute a single circuit as a whole, or they may be separate circuits. Furthermore, these circuits may correspond to dedicated hardware or general-purpose hardware that executes the aforementioned program, etc.

[0579] Furthermore, the imaging device is not limited to a physically integrated device, but may include a plurality of sub-devices that are distributed. Furthermore, the imaging device may also be expressed as an imaging system.

[0580] Industrial applicability

[0581] One embodiment 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 is applicable to, for example, an exploration system that explores an object moving in the measurement area.

[0582] Description of Reference Numerals

[0583] 100 Imaging Installation

[0584] 101 Transmitter

[0585] 102 Receiver

[0586] 103 Information Processing Circuit

[0587] 104 Display

Claims

1. An imaging device, The imaging device comprises: a plurality of transmitters, each of the plurality of transmitters transmitting a wave motion to a measurement area; a plurality of receivers, each of the plurality of receivers receiving the fluctuating scattered waves from the measurement region; and The information processing circuit uses the measurement data of the scattered wave to image the object in the measurement area. The information processing circuit, in imaging the object, deriving a scattered field function using the measurement data and the velocity vector of the object, the scattered field function being a function that receives as inputs 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, deriving an imaging function, the imaging function being a function that receives an imaging target position as an input and outputs an image intensity of the imaging target position, and the imaging function being a function determined using a quantity 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, imaging the object in the measurement area using the imaging function, The information processing circuit derives the scattering field function from the measurement data using a coordinate system in deriving the scattering field function, wherein the coordinate system is a coordinate system determined using the velocity vector and is a coordinate system that fixes the position of the object in at least two directions.

2. The imaging device according to claim 1, The plurality of transmitters and the plurality of receivers are arranged on a straight line parallel to the y-axis, The scattered field function is expressed by [Formula 1], [Mathematical formula 1] x and z of the scattering field function represent the x-coordinate and z-coordinate of the sending position and the receiving position, y1 of the scattering field function represents the y-coordinate of the sending position, y2 of the scattering field function represents the y-coordinate of the receiving position, k represents the wave number of the wave, k x , k y1 and k y2 represents the variable corresponding to the wavenumbers of x, y1 and y2 with respect to the scattered field function, [Mathematical formula 2] represents the measurement data after Fourier transformation, [Mathematical formula 2] u and w are determined by [Formula 3], [Mathematical formula 3] v x and v y represents the x-component and y-component of the velocity vector.

3. The imaging device according to claim 2, The imaging function is expressed by [Formula 4]: [Formula 4] x, y and z of the imaging function represent the x-coordinate, y-coordinate and z-coordinate of the imaging object position, k z and dk / dk z Determined by [Formula 5], [Mathematical formula 5] 4. The imaging device according to claim 1, The plurality of transmitters are arranged on a first straight line parallel to the y-axis, The plurality of receivers are arranged on a second straight line parallel to the y-axis, The scattered field function is expressed by [Equation 6]: [Mathematical formula 6] The z of the scattering field function represents the z coordinates of the sending position and the receiving position, the x1 and y1 of the scattering field function represent the x coordinate and y coordinate of the sending position, the x2 and y2 of the scattering field function represent the x coordinate and y coordinate of the receiving position, k represents the wave number of the wave, k x , k y1 and k y2 represents a variable corresponding to the wave numbers of x, y1 and y2 with respect to the scattered field function, d represents the distance between the first straight line and the second straight line, [Mathematical formula 7] represents the measurement data after Fourier transformation, [Formula 7] s3 and s4 are determined by [Formula 8], [Mathematical formula 8] u and w are determined by [Formula 9], [Mathematical formula 9] v x and v y represents the x-component and y-component of the velocity vector.

5. The imaging device according to claim 4, The imaging function is expressed by [Formula 10], [Formula 10] The x, y, and z of the imaging function represent the x-coordinate, y-coordinate, and z-coordinate of the imaging object position.

6. The imaging device according to claim 5, The information processing circuit uses the imaging function after the x-coordinate is shifted according to x=L+ξ to image the object. The imaging function after x-coordinate shift is expressed by [Formula 11]: [Mathematical formula 11] L represents the shift amount of the x-coordinate, and ξ represents the x-coordinate shifted by L.

7. The imaging device according to any one of claims 1 to 6, The information processing circuit, deriving a tentative scattered field function using the measurement data instead of the velocity vector, Using the tentative scattered field function to derive a tentative imaging function, The velocity vector is derived using the tentative imaging function.

8. The imaging device according to claim 7, The information processing circuit, in deriving the velocity vector, The velocity vector is derived using the calculation expression represented by [Mathematical Formula 12], [Mathematical formula 12] a, b, c, e, f, g, h, m and n of the above operation expression are determined by [Mathematical formula 13], [Mathematical formula 13] v x 、v y and v z represents the x component, y component and z component of the velocity vector, ε represents a positive value, ρ k With τ as one of the input variables, and ρ k represents the tentative imaging function after Fourier transformation of x, y, and z, and k in the calculation expression x , k y and k z represents the x, y and z wave numbers for the tentative imaging function, [Mathematical formula 14] represents k of the above operation expression x , k y and k z The wave number vector is composed of [Mathematical formula 14] k τ represents a time unit equivalent to the number of times data is acquired, cc. represents the conjugate complex number of the term immediately preceding cc., [Formula 15] represents ρ k The complex conjugate of [Mathematical formula 15] 9. An imaging method, The imaging method comprises: The step of transmitting the wave motion from each of the plurality of transmitters to the measurement area; The step of receiving the fluctuating scattered waves from the measurement area at each of a plurality of receivers; as well as The step of imaging the object in the measurement area using the measurement data of the scattered waves, The step of imaging the object comprises: A step of deriving a scattered field function using the measurement data and a velocity vector of the object, the scattered field function being a function that receives as inputs 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; a step of deriving an imaging function, the imaging function being a function that receives an imaging target position as an input and outputs an image intensity of the imaging target position, and the imaging function being a function determined using a quantity 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; as well as The step of imaging the object in the measurement area using the imaging function, In the step of deriving the scattered field function, a coordinate system is used to derive the scattered field function according to the measured data. The scattering field function is derived, the coordinate system is a coordinate system determined by using the velocity vector, And it is a coordinate system that fixes the position of the object in at least two directions.

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