Imaging device and imaging method

Abstract

A video device (100) is provided with: a plurality of transmitters (101) for transmitting fluctuations to measurement regions in the atmosphere; a plurality of receivers (102) that receive fluctuating scattered waves from the measurement region; and an information processing circuit (103) that uses the measurement data of the scattered waves to image an object in the measurement region, the information processing circuit (103) derives a scattered field function using the measurement data, derives an image function determined using the amount output from the scattered field function by inputting the position of the object to be imaged into the scattered field function, and outputs the image function from the scattered field function. An object in a measurement region is imaged using an imaging function, and an information processing circuit (103) reflects a scattered field function that reflects that the wavenumber of the fluctuation varies as the refractive index in the atmosphere varies according to the height in the atmosphere.

Description

Technical Field

[0001] This disclosure relates to an imaging apparatus, etc., that uses measurement data of scattered waves to image objects in a measurement area. Background Technology

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

[0003] For example, in the technology described in Patent Document 1, a beam transmitted from a microwave transmitter is incident on the object being inspected, 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 tomography in the object being inspected is displayed.

[0004] Existing technical documents Patent documents Patent Document 1: Japanese Patent Application Publication No. 62-66145 Patent Document 2: International Publication No. 2014 / 125815 Patent Document 3: International Publication No. 2015 / 136936 Patent Document 4: International Publication No. 2021 / 020387 Patent Document 5: International Publication No. 2021 / 053971 Summary of the Invention

[0005] The problem that the invention aims to solve However, imagering objects within a measurement area using measurement data of scattered waves is not easy. Specifically, when the state within the measurement area is known, estimating the measurement data of the scattered waves emitted from the measurement area for the wave incident on the measurement area is called a forward modeling problem, which is easy. On the other hand, when the measurement data of the scattered waves is known, determining the state within the measurement area is called an inversion problem, which is not easy.

[0006] Furthermore, when the measurement area is in the atmosphere, the concentration of the atmosphere varies with altitude, so the wave incident on the measurement area may not travel in a straight line. Therefore, when the measurement area is in the atmosphere, it is not easy to image an object using waves and scattered waves.

[0007] Therefore, this disclosure provides an imaging device and the like that can image objects in a measurement area in the atmosphere with high precision.

[0008] Methods for solving problems An imaging apparatus according to one aspect of this disclosure comprises: a plurality of transmitters that transmit waves to a measurement area in the atmosphere; a plurality of receivers that receive scattered waves from the measurement area; and an information processing circuit that uses measurement data of the scattered waves to image an object in the measurement area. In the imagery of the object, the information processing circuit derives a scattering field function using the measurement data. This scattering field function is a function that outputs the amount of the scattered wave at the receiving position when the transmission position of the wave and the receiving position of the scattered wave are input. It also derives an imaging function that outputs the image intensity at the imaged object position when the imaged object position is input. This imaging function is determined using the amount output from the scattering field function by inputting the imaged object position as the transmission position and the receiving position. The imaging function is used to image the object in the measurement area. In the derivation of the scattering field function, the information processing circuit ensures that the scattering field function reflects the change in wavenumber of the wave as the refractive index in the atmosphere changes with altitude in the atmosphere.

[0009] Furthermore, these general or specific methods can be implemented by non-transitory recording media such as systems, devices, methods, integrated circuits, computer programs, or computer-readable CD-ROMs, or by any combination of systems, devices, methods, integrated circuits, computer programs, and recording media.

[0010] Invention Effects This disclosure enables the high-precision imaging of objects in a measurement area within the atmosphere. Attached Figure Description

[0011] Figure 1 This is a conceptual diagram representing a one-dimensional multi-base array antenna.

[0012] Figure 2 It is a conceptual diagram representing the relationship between the sending point and the receiving point in a plane.

[0013] Figure 3 This is a conceptual diagram representing an example of the coordinates associated with a quasi-two-dimensional array antenna.

[0014] Figure 4 It is a simulation diagram representing the trajectory of a 1 GHz electromagnetic wave emitted from the Earth's surface at a radiation angle of 1°.

[0015] Figure 5 It is a simulation diagram representing the trajectory of a 1 GHz electromagnetic wave emitted from the Earth's surface at a radiation angle of 2.56°.

[0016] Figure 6This is a conceptual diagram representing a multi-layered medium.

[0017] Figure 7 It is a block diagram showing the basic structure of an imaging device.

[0018] Figure 8 This is a flowchart illustrating the basic operations of the imaging device. Detailed Implementation

[0019] One aspect of this disclosure relates to an imaging apparatus comprising: a plurality of transmitters, each transmitting a wave into a measurement area in the atmosphere; a plurality of receivers, each receiving a scattered wave from the measurement area; and an information processing circuit that uses measurement data of the scattered waves to image an object in the measurement area. In the imagery of the object, the information processing circuit derives a scattering field function using the measurement data. This scattering field function is a function that takes the transmission position of the wave and the reception position of the scattered wave as input and outputs the amount of the scattered wave at the reception position. The imagery function is... The image processing circuit is a function that outputs the image intensity of the imaged object location when the imaged object location is input, and is a function that outputs a quantity from the scattering field function by inputting the imaged object location as the sending location and the receiving location into the scattering field function. The image function is used to image the object in the measurement area. In the derivation of the scattering field function, the information processing circuit makes the scattering field function reflect the wavenumber change of the wave as the refractive index in the atmosphere changes with the altitude in the atmosphere.

[0020] Therefore, the imaging device can derive a scattering field function and an imaging function that reflect the atmospheric refractive index as it varies with altitude. Consequently, the imaging device can image objects in a measurement area within the atmosphere with high precision.

[0021] For example, the plurality of transmitters and the plurality of receivers are arranged on a straight line parallel to the y-axis, the measurement region in the atmosphere is divided into multiple layers, and the scattering field function of the nth layer of the plurality of layers is represented by [Mathematical Formula 1].

[0022] [Mathematical Formula 1] The x and z values ​​of the scattering field function represent the x and z coordinates of the transmitting and receiving positions, respectively. The y1 value of the scattering field function represents the y coordinate of the transmitting position, and the y2 value of the scattering field function represents the y coordinate of the receiving position. k1 and k... j and k nh represents the wave number of the fluctuations in the 1st, jth, and nth layers of the plurality of layers. j Let k represent the height of the j-th floor. x k y1 and k y2 The variable represents the wavenumber corresponding to x, y1, and y2 of the scattering field function. [Mathematical Formula 2] This represents the measurement data after Fourier transform.

[0023] Thus, the imaging device can image objects in a measurement area of ​​the atmosphere with high precision using measurement data obtained from multiple transmitters and multiple receivers arranged in a straight line, according to the scattering field function derived for each layer.

[0024] Additionally, for example, the imaging function of the nth layer among the plurality of layers is represented by [Mathematical Formula 3]. [Mathematical Formula 3] The x, y, and z values ​​in the imaging function represent the x, y, and z coordinates of the imaged object's position, respectively; ω represents the angular frequency of the wave; and k... zn Determined by [Mathematical Formula 4].

[0025] [Mathematical Formula 4] Thus, the imaging device can image objects in a measurement area in the atmosphere with high precision using measurement data obtained from multiple transmitters and multiple receivers arranged in a straight line, according to an imaging function derived for each layer.

[0026] Additionally, for example, the plurality of transmitters and the plurality of receivers are arranged on a straight line parallel to the y-axis, and the scattering field function is expressed by [Mathematical Equation 5]. [Mathematical Formula 5] The x and z of the scattering field function represent the x and z coordinates of the transmitting and receiving positions, respectively; y1 of the scattering field function represents the y coordinate of the transmitting position; y2 of the scattering field function represents the y coordinate of the receiving position; k represents the wavenumber of the wave at the z-coordinate position; k1 represents the wavenumber of the wave at the z-coordinate position; k(z) a ) indicates that the z-coordinate is z a The wave number of the fluctuation at the location, z a k represents the variable corresponding to the z-coordinate. x ky1 and k y2 The variable represents the wavenumber corresponding to x, y1, and y2 of the scattering field function. [Mathematical Formula 6] This represents the measurement data after Fourier transform.

[0027] Thus, the imaging device can image objects in a measurement area in the atmosphere with high precision using a scattering field function derived from measurement data obtained from multiple transmitters and multiple receivers arranged in a straight line.

[0028] Additionally, for example, the imaging function is expressed by [Mathematical Formula 7], [Mathematical Expression 7] The x, y, and z values ​​of the imaging function represent the x, y, and z coordinates of the imaged object's position, and ω represents the variable corresponding to the angular frequency of the fluctuation.

[0029] Thus, the imaging device can image objects in a measurement area in the atmosphere with high precision using an imaging function derived from measurement data obtained from multiple transmitters and multiple receivers arranged in a straight line.

[0030] Additionally, one aspect of the imaging method disclosed herein includes the following steps: transmitting waves from multiple transmitters to a measurement area in the atmosphere; receiving scattered waves from the measurement area from multiple receivers; and imaging an object in the measurement area using measurement data of the scattered waves. The imaging step includes: deriving a scattering field function using the measurement data, the scattering field function being input to the transmission location of the wave and the reception location of the scattered wave and outputting the amount of the scattered wave at the reception location; and deriving an imaging function, which is an imaging function input to the imaged object location and outputting the image intensity of the imaged object location, the imaging function being determined using the amount output from the scattering field function by inputting the imaged object location as the transmission location and the reception location; and imaging the object in the measurement area using the imaging function. In the step of deriving the scattering field function, the scattering field function reflects the wavenumber change of the wave as the refractive index in the atmosphere changes with altitude in the atmosphere.

[0031] Therefore, a scattering field function reflecting the atmospheric refractive index varying with altitude and an imaging function can be derived. Consequently, the imaging device can image objects in a measurement area in the atmosphere with high precision.

[0032] The embodiments are described below with reference to the accompanying drawings. Furthermore, the embodiments described below are all general or specific examples. The numerical values, shapes, materials, constituent elements, the arrangement and position of constituent elements, connection methods, steps, and the order of steps shown in the following embodiments are all examples and are not intended to limit the technical solution.

[0033] Furthermore, in the following description, particularly the technologies described in Patent Documents 2, 3, 4, and 5, can be referred to as prior art. Also, in the following description, microwaves and other radio waves or electromagnetic waves are primarily conceived as waves, but waves are not limited to microwaves or other radio waves or electromagnetic waves; they can also be elastic waves, etc. Furthermore, scattering-based imaging can be represented as scattering tomography. Therefore, the imaging apparatus and imaging method described below can be respectively represented as a scattering tomography apparatus and a scattering tomography method.

[0034] (Implementation Method) The imaging device in this embodiment uses measurement data of scattered waves to image objects in the measurement area. The imaging device of this embodiment, including the underlying technologies and theories, will be described in detail below.

[0035] <1 Summary> Scattering field theory is a theory used for image representation of objects in a measurement area. For example, waves are transmitted into the measurement area from multiple transmitting positions, and the scattered waves are received from the measurement area from multiple receiving positions. Measurement data of the scattered waves is obtained for each combination of transmitting and receiving positions. Then, using this measurement data, the objects in the measurement area are imaged. In this case, by using scattering field theory, the scattering state in the measurement area is calculated based on the measurement data, and the objects are imaged with high precision based on the scattering state.

[0036] However, when the measurement area is in the atmosphere, the atmospheric concentration varies with altitude, so the waves sent to the measurement area may not travel in a straight line. This phenomenon is also known as atmospheric refraction. Therefore, when the measurement area is in the atmosphere, it is not easy to image an object using waves and scattered waves.

[0037] Therefore, this disclosure describes a scattering field theory for imaging objects in a measurement area in the atmosphere. Specifically, first, a scattering field theory without considering the atmospheric refractive index is described, and then a scattering field theory considering the atmospheric refractive index is described.

[0038] <2 Scattering field theory without considering atmospheric refraction> This chapter explains the theory of scattering fields without considering atmospheric refraction.

[0039] <2-1 One-Dimensional Arrangement> Figure 1 This is a conceptual diagram representing a one-dimensional multi-base array antenna. For example... Figure 1 As shown, by using any two elements from n elements as both the transmitting and receiving elements, a high signal-to-noise ratio (S / N ratio) can be achieved from near to far distances, compared to a monostatic environment where the pairing of transmitting and receiving elements is fixed. Therefore, the quality of the final image can be significantly improved. While the amount of data increases by n times, according to the theory described below, the reconstruction time is also dramatically reduced.

[0040] like Figure 1 As shown, this discussion addresses the situation where an electromagnetic wave emitted from point P1 (x, y1, z) is reflected at point P (ξ, η, ζ) and received at point P2 (x, y2, z). The signal received at P2 as point P moves throughout the region D is shown in equation (2-1-1).

[0041] [Mathematical Formula 8] 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). Point P(ξ, η, ζ) corresponds to the reflection point. Furthermore, ε(ξ, η, ζ) is unknown and is assumed to be proportional to the time factor exp(-iωt). The kernel function in the integrand of the above equation is represented by φ in equation (2-1-2).

[0042] [Mathematical Expression 9] Next, we will explore the partial differential equation for which equation (2-1-2) becomes an asymptotic solution. Therefore, we will neglect higher-order terms when calculating 1 / ρ generated in the differential result. Here, the simplified notation of the differential is defined as in equation (2-1-3).

[0043] [Mathematical Formula 10] Furthermore, this paper explores the partial differential equation (2-1-2) as an asymptotic solution at short wavelengths (high frequency, or large k). The solution of such a partial differential equation can be roughly regarded as an exact solution in microwave imaging. First, the differential results of φ are expressed as shown in the following equation (2-1-4).

[0044] [Mathematical Formula 11] The following omits the complex "o" ( The terms of the second-order differential are summed according to the four equations related to the second-order differential, resulting in equation (2-1-5).

[0045] [Mathematical Formula 12] Therefore, according to equation (2-1-5), we obtain equation (2-1-6).

[0046] [Mathematical Formula 13] By applying the operation of equation (2-1-6) twice, we obtain the following equation (2-1-7).

[0047] [Mathematical Formula 14] Rearranging equation (2-1-7) yields equation (2-1-8).

[0048] [Mathematical Formula 15] Although equation (2-1-8) is derived assuming a steady state, it is easy to extend it to an unsteady state. Therefore, ∂²⁻¹ can be used to represent the partial derivative with respect to time t. t And the variable c, which represents the propagation speed of radio waves, is replaced as shown in equation (2-1-9).

[0049] [Mathematical Expression 16] Through the above process, the equation (2-1-10) can be obtained.

[0050] [Mathematical Expression 17] Equation (2-1-10) above is a partial differential equation in which φ becomes the solution of equation (2-1-2). By applying differentiation to the integral kernel of equation (2-1-1), [Mathematical Expression 18] of equation (2-1-1) also satisfies the above partial differential equation.

[0051] [Mathematical Formula 18] The equation is a four-dimensional pseudo-wave equation consisting of five variables (t, x, y1, y2, z).

[0052] Next, the Fourier transform is used to solve the equation. First, [Mathematical Formula 19] As shown in equation (2-1-11), multiple Fourier transforms are performed on t, x, y1, and y2.

[0053] [Mathematical Formula 20] When the differential with respect to z is expressed as D z In the case of equation (2-1-10) and equation (2-1-11), we obtain the following equation (2-1-12).

[0054] [Mathematical Formula 21] Here, we use the relationship ω = ck. The four fundamental solutions of this equation are expressed as shown in equation (2-1-13).

[0055] [Mathematical Expression 22] If we consider the time factor as e -iωt Considering the addition of phases along the path of the radiated radio wave and the bounce of the reflected radio wave towards the measuring surface (determining surface), E1 is the only meaningful solution. Therefore, we obtain the following equation (2-1-14).

[0056] [Mathematical Formula 23] By substituting z = 0 into equation (2-1-14), we can obtain a(k) from equation (2-1-15). x k y1 k y2 ,k).

[0057] [Mathematical Formula 24] Ultimately, it can be [Mathematical Formula 25] The answer is obtained from the following equation (2-1-16).

[0058] [Mathematical Formula 26] With k and z fixed, apply the limit operation (y2→y1=y) to equation (2-1-16) and integrate the result with respect to k. The image function is then obtained as shown in equation (2-1-17).

[0059] [Mathematical Expression 27] As mentioned above, the multibase inverse scattering problem in one-dimensional arrangements can be solved analytically.

[0060] <2-2 Two-Dimensional Arrangement> This section explains the theory for the two-dimensional arrangement.

[0061] Figure 2 It is a conceptual diagram representing the relationship between sending and receiving points in a plane. For example... Figure 2 As shown, microwaves emitted from point P1 are reflected at point P on the target and received at point P2. Points P1 and P2 can be moved to arbitrary points on a grid within a plane (two-dimensional array antenna). Under this assumption, the microwave path through point P on the target has n paths. 4 These numerous paths greatly contribute to improving the quality of the final image. The following describes a method for processing such complex data to obtain an image.

[0062] For example, such as Figure 2 As shown, the radio wave emitted from point P1 (x1, y1, z) is reflected at point P (ξ, η, ζ) and received at point P2 (x2, y2, z). The signal received at point P2 as point P moves throughout the entire region D is shown in the following equation.

[0063] [Mathematical Formula 28] 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 (2-2-2).

[0064] [Mathematical Formula 29] Next, we explore the partial differential equation for which equation (2-2-2) becomes an asymptotic solution at short wavelengths. Therefore, we neglect higher-order terms when calculating 1 / ρ in the differential result. Here, the simplified notation of the differential is defined as in equation (2-2-3).

[0065] [Mathematical Formula 30] Using equation (2-2-3), the differentials of the kernel function are expressed as shown in equation (2-2-4).

[0066] [Mathematical Formula 31] The following will omit the complicated o ( The term is given by summing the five equations concerning the second differential, which yields equation (2-2-5).

[0067] [Mathematical Formula 32] Therefore, according to equation (2-2-5), we obtain equation (2-2-6).

[0068] [Mathematical Formula 33] By applying the operation of equation (2-2-6) twice, we obtain the following equation (2-2-7).

[0069] [Mathematical Formula 34] Arrange equation (2-2-7) to obtain equation (2-2-8).

[0070] [Mathematical Formula 35] Although equation (2-2-8) is derived assuming a steady state, it is easy to extend it to an unstable state. Therefore, we can perform a variable substitution as shown in equation (2-2-9).

[0071] [Mathematical Formula 36] Through this substitution, equation (2-2-8) is transformed into equation (2-2-10) which includes time.

[0072] [Mathematical Formula 37] Equation (2-2-10) above is the partial differential equation for which the kernel function shown in equation (2-2-2) becomes the solution. By applying differentiation to the integral kernel of equation (2-2-1), [Mathematical Equation 38] also satisfies the above partial differential equation.

[0073] [Mathematical Formula 38] The equation is a five-dimensional pseudo-wave equation consisting of six variables (t, x1, y1, x2, y2, z).

[0074] Next, the Fourier transform is used to solve the equation. First, [Mathematical Formula 39] As shown in equation (2-2-11), multiple Fourier transforms are performed on t, x1, y1, x2, and y2.

[0075] [Mathematical Formula 40] When the differential with respect to z is expressed as D z In the case of (2-2-10) and (2-2-11), we obtain the following equation (2-2-12).

[0076] [Mathematical Formula 41] Here, we use the relationship ω = ck. The four fundamental solutions to this equation are expressed as shown in equation (2-2-13).

[0077] [Mathematical Formula 42] If we consider the time factor as e -iωt Considering the addition of phases along the path of the emitted radio wave and the bounce of the reflected wave towards the measurement surface, E1 is the only meaningful solution. Therefore, we obtain the following equation (2-2-14).

[0078] [Mathematical Formula 43] By substituting z = 0 into equation (2-2-14), we can obtain a(k) from equation (2-2-15). x1 k y1 k x2 k y2 ,k).

[0079] [Mathematical Formula 44] Based on the above, [Mathematical Formula 45] The result is obtained as shown in equation (2-2-16).

[0080] [Mathematical Formula 46] Next, by applying the limit operation (y1→y and y2→y) to equation (2-2-16) with k and z fixed, we obtain equation (2-2-17).

[0081] [Mathematical Formula 47] Next, by integrating equation (2-2-17) with respect to k, we obtain equation (2-2-18) as a visualization function.

[0082] [Mathematical Formula 48] In equation (2-2-18), with k x1 k y1 k x2 k y2 The relevant integral becomes a Fourier transform, suitable for computer processing. On the other hand, the terms in the integrand, exp(iz…), do not become Fourier transforms. Therefore, for example, the usual integration is performed with respect to k while specifying the value of z. Alternatively, to reduce computation time, equation (2-2-18) can also be transformed into an integral expression consisting solely of Fourier transforms.

[0083] For example, the coefficient of iz in exp(iz…) of equation (2-2-17) is expressed using a new variable u, as in equation (2-2-19) below.

[0084] [Mathematical Formula 49] By rationalizing the right side of equation (2-2-19), we obtain equation (2-2-20).

[0085] [Mathematical Formula 50] By solving for each square root according to equations (2-2-19) and (2-2-20), we obtain equation (2-2-21).

[0086] [Mathematical Formula 51] Therefore, k is expressed as shown in equation (2-2-22).

[0087] [Mathematical Formula 52] Furthermore, by differentiating k and u on both sides of equation (2-2-19), we obtain equation (2-2-23).

[0088] [Mathematical Formula 53] By solving dk according to equation (2-2-23), we obtain equation (2-2-24).

[0089] [Mathematical Formula 54] In conclusion, equation (2-2-18) is transformed into equation (2-2-25).

[0090] [Mathematical Expression 55] <2-3 Quasi-two-dimensional arrangement> Figure 3 This is a conceptual diagram illustrating an example of the coordinates associated with a quasi-two-dimensional array antenna. In this example, the quasi-two-dimensional array antenna consists of two linear array antennas: a transmit array antenna TA and a receive array antenna RA. Such a quasi-two-dimensional array antenna can be represented as an S-Array (super-array) or, alternatively, as an S-Array multibase antenna.

[0091] The transmitting array antenna TA comprises n transmitting antenna elements T. The receiving array antenna RA comprises n receiving antenna elements R. The x-coordinate of the transmitting array antenna TA is represented by x1, the x-coordinate of the receiving array antenna RA is represented by x2, and the distance in the x-axis direction between the transmitting array antenna TA and the receiving array antenna RA is represented by d. In this configuration, at each point x along the scanning direction, n is obtained from any combination of n transmitting elements and n receiving elements. 2 Time series data.

[0092] In this section, for those used according to, as Figure 3 The theory of imagery of objects based on data obtained from the quasi-two-dimensional array antenna is explained. First, as a starting point for the discussion, equation (2-2-10) related to two-dimensional arrangement is used. The following equation (2-3-1) uses the same operator as equation (2-2-10).

[0093] [Mathematical Formula 56] also, [Mathematical Formula 57] The Fourier transform of t, x1, y1, y2 is expressed as shown in equation (2-3-2).

[0094] [Mathematical Formula 58] The variable x2 will be represented as u. By performing a Fourier transform on both sides of equation (2-3-1) with respect to t, x1, y1, and y2, we obtain equation (2-3-3).

[0095] [Mathematical Formula 59] The solution to the above equation (2-3-3) for the two-dimensional partial differential equations in terms of u and z is assumed to be the following equation (2-3-4).

[0096] [Mathematical Formula 60] Here, s3 and s4 are related to k as in equation (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.

[0097] [Mathematical Formula 61] By substituting equation (2-3-4) into equation (2-3-3), we obtain the following equation (2-3-6).

[0098] [Mathematical Formula 62] The algebraic equation alone cannot determine s3 and s4. Next, we change equation (2-3-4) to equation (2-3-7).

[0099] [Mathematical Formula 63] By applying equation (2-3-7) with respect to k x1 k y1 and k y2 Performing an inverse Fourier transform and applying u→x2 to the result, we obtain the following equation (2-3-8).

[0100] [Mathematical Formula 64] By applying x2=x1=x to equation (2-3-8), we obtain the following equation (2-3-9).

[0101] [Mathematical Formula 65] Here, k x It can be represented by the following formula (2-3-10).

[0102] [Mathematical Expression 66] Equation (2-3-9) above is consistent with the solution of the scattering field equation for a one-dimensional arrangement, and therefore should be consistent with equation (2-1-16). Equation (2-3-11) below is the same as equation (2-1-16).

[0103] [Mathematical Formula 67] By comparing equation (2-3-9) with equation (2-3-11), we can obtain equation (2-3-12).

[0104] [Mathematical Formula 68] By squaring the second equation of equation (2-3-12), we obtain the following equation (2-3-13).

[0105] [Mathematical Formula 69] By substituting equation (2-3-13) into equation (2-3-6), we obtain the following equation (2-3-14).

[0106] [Mathematical Formula 70] By rearranging equation (2-3-14), we obtain equation (2-3-15).

[0107] [Mathematical Formula 71] Since the solution to this equation is a repeated root, the solution uniquely expressed by the following equation (2-3-16) is obtained.

[0108] [Mathematical Formula 72] Based on equations (2-3-12) and (2-3-16) obtained in the above process, s3 and s4 are analytically determined. Furthermore, the scattering field function is obtained according to equation (2-3-8) as shown in equation (2-3-17).

[0109] [Mathematical Formula 73] Next, we will explore the relationship between the measured data Φ(x1, y1, y2, k) and a(k). x1 k y1 k y2 The case of connection k). Therefore, by determining k as k x =k x1 Substituting z = 0 and x2 = x1 + d into equation (2-3-17), we obtain the equation (2-3-18) as shown below. Here, Φ(x1, y1, y2, k) represents the measured data of the transmitting point (x1, y1, 0), the receiving point (x1 + d, y2, 0), and the wavenumber k.

[0110] [Mathematical Expression 74] Hereafter, we will use k as defined by the following equation (2-3-19). x And s3.

[0111] [Mathematical Expression 75] By performing a Fourier transform on both sides of equation (2-3-18) with respect to x1, y1, and y2, we obtain equation (2-3-20).

[0112] [Mathematical Expression 76] Based on equation (2-3-20), the function a(k) can be obtained as shown in equation (2-3-21). x k y1 k y2 ,k).

[0113] [Mathematical Expression 77] Therefore, equation (2-3-17), which is the scattering field function, is obtained in its complete form as shown in equation (2-3-22).

[0114] [Mathematical Formula 78] Moreover, the image function is obtained as shown in equation (2-3-23).

[0115] [Mathematical Expression 79] Compared to one-dimensional arrangements, quasi-two-dimensional arrangements allow for the configuration of more transmitting and receiving elements. Therefore, information can be acquired more efficiently.

[0116] <3 Scattering field theory considering atmospheric refraction> This chapter explains the theory of scattering fields that takes into account atmospheric refraction.

[0117] <3-1 Model of Atmospheric Refractive Index> As altitude increases, the atmosphere becomes thinner. Furthermore, space above the stratosphere is a vacuum. The concentration of this atmosphere is directly related to its refractive index. At the Earth's surface, the refractive index is approximately n≈1.0003, extremely close to the vacuum value. However, as radio waves travel longer distances, their propagation axes gradually refract. The dependence of atmospheric refractive index on altitude is given by equation (3-1-1).

[0118] [Mathematical Formula 80] Here, z represents altitude, and n(z) represents the refractive index at altitude z. n0 represents the refractive index at the Earth's surface (h=0). Additionally, c... e It is a coefficient that represents the rate of change of refractive index relative to the change of height.

[0119] n0 and c e Based on measured values ​​within the United States, this constant is published as the Exponential Reference Atmosphere (CRPL) constant. Specifically, n0 is a constant relative to N, which is known as the Earth's surface refractive index. s It has the following relationship (3-1-2).

[0120] [Mathematical Formula 81] As a standard model, these constants are given as in equation (3-1-3).

[0121] [Mathematical Formula 82] Therefore, the following equation (3-1-4) holds true.

[0122] [Mathematical Formula 83] c0 represents the speed of electromagnetic waves in a vacuum, and c(z) represents the speed of electromagnetic waves at height z.

[0123] <3-2 Propagation and Refraction of Plane Waves> For example, radar electromagnetic waves propagate through a vast space where the refractive index changes slowly. The trajectory of such radar electromagnetic waves can be represented using geometrical optics. Specifically, firstly, the electromagnetic field is represented as shown in equation (3-2-1).

[0124] [Mathematical Formula 84] In equation (3-2-1), a represents the amplitude, and φ represents the phase, which is called the eikonal. φ is represented by dividing the time factor as shown in equation (3-2-2).

[0125] [Mathematical Formula 85] In equation (3-2-2), ω represents the angular frequency, t represents time, and φ0(x, y, z) represents the initial phase of (x, y, z). Equation (3-2-3) holds.

[0126] [Mathematical Formula 86] In equation (3-2-3), k represents the wavenumber vector and r represents the position vector. The functional equation is expressed as shown in equation (3-2-4).

[0127] [Mathematical Formula 87] In equation (3-2-4), c represents the phase velocity. The wavefront is the set of surfaces (equiphase surfaces) with the same value of φ0(x, y, z). Furthermore, the functional equation is expressed as shown in equation (3-2-5).

[0128] [Mathematical Formula 88] In the (x, z) plane, which is independent of the y-axis direction, the trajectory of the electromagnetic wave is determined as follows. First, in the x-axis direction, k represents the wave number. x Under constant conditions, we get the following equation (3-2-6).

[0129] [Mathematical Formula 89] In equation (3-2-6), k z (z) represents the wave number along the z-axis, which depends on z. According to equation (3-2-6), k z (z) is expressed as shown in equation (3-2-7).

[0130] [Mathematical Expression 90] The solutions in equation (3-2-7) below are used as positive solutions. The direction of wave propagation (the direction of the wave number vector) is expressed as shown in equation (3-2-8).

[0131] [Mathematical Formula 91] Furthermore, the tangent of the orbit is expressed as shown in equation (3-2-9).

[0132] [Mathematical Formula 92] Therefore, the propagation trajectory of the radio wave is given by the following equation (3-2-10).

[0133] [Mathematical Formula 93] Figure 4 This is a simulation diagram representing the trajectory of a 1 GHz electromagnetic wave emitted from the Earth's surface at a radiation angle of 1°. Figure 4The diagram shows orbitals with and without refractive index consideration. The orbital with refractive index consideration is derived based on equation (3-2-10) and is envisioned as a close approximation of the actual orbital.

[0134] Figure 5 This is a simulation diagram showing the trajectory of a 1 GHz electromagnetic wave emitted from the Earth's surface at a radiation angle of 2.56°. Figure 5 In, with Figure 4 The same shows orbitals with and without considering the refractive index. The orbital considering the refractive index is derived based on equation (3-2-10) and is envisioned as a close approximation of the actual orbital.

[0135] like Figure 4 and Figure 5 As shown, different orbits are envisioned depending on whether atmospheric refractive index is considered. These differences can potentially introduce errors in the visualization of objects.

[0136] <3-3 Scattering Field Theory Considering Atmospheric Refraction> In layered media, refraction makes it difficult to visualize objects within the medium. However, by neglecting multiple scattering, objects in the medium can be visualized relatively easily using scattering field theory, as follows.

[0137] Figure 6 This is a conceptual diagram representing a multilayered medium. For example, in Figure 6 In the diagram, the z-axis corresponds to the vertical direction, and the x-axis corresponds to the horizontal direction.

[0138] The medium has n layers along the z-axis, from layer 1 to layer n. Layers 1, 2, ..., n have h1, h2, ..., h... n The height. Additionally, the 1st layer, the 2nd layer, ..., the nth layer have ε1, ε2, ..., ε... n The dielectric constant of . In the 1st, 2nd, ..., nth layers, the propagation speed of the wave is c1, c2, ..., c. n Relative to a wave with angular frequency ω, the wave numbers of the wave are k1, k2, ..., k n .

[0139] According to equation (2-1-16), the scattering field function in the first layer is expressed as shown in equation (3-3-1).

[0140] [Mathematical Expression 94] Here, [Mathematical Formula 95] This represents the measurement data when z=0.

[0141] The scattering field function in the second layer is expressed as shown in equation (3-3-2).

[0142] [Mathematical Formula 96] The unknown function a2(k) in equation (3-3-2) x k y1 k y2 The following steps are used to calculate k1 and k2.

[0143] Specifically, the two scattering field functions in equations (3-3-1) and (3-3-2) consist of components parallel to the layer interface of the electromagnetic field. Furthermore, if the decrease in the intensity of the electromagnetic field entering the second layer due to reflection at the layer interface can be ignored, Maxwell's equations derive that the output values ​​of the two scattering field functions on both sides of the discontinuity are equal. Therefore, with respect to the interlayer boundary, equation (3-3-3) holds.

[0144] [Mathematical Formula 97] By performing the inverse Fourier transform on both sides of equation (3-3-3), we obtain equation (3-3-4).

[0145] [Mathematical Formula 98] By following the same steps, the following equation (3-3-5) generally holds true.

[0146] [Mathematical Expression 99] Therefore, the scattering field function in the nth layer is expressed as shown in equation (3-3-6).

[0147] [Mathematical formula 100] The image function is expressed as shown in equation (3-3-7).

[0148] [Mathematical Formula 101] Here, assuming that the medium has no dielectric dispersion, the following equation (3-3-8) holds.

[0149] [Mathematical Formula 102] The exponential function portion of Π in equations (3-3-6) and (3-3-7) is passed through h. jThe limit operation of →0 is expressed as an integral. Therefore, the scattering field function considering atmospheric refraction is expressed as shown in the following equation (3-3-9).

[0150] [Mathematical Formula 103] Here, k corresponds to the wave number of the oscillation when z=z, k(z) a ) corresponds to z=z a The wavenumber of the oscillation at time z=0, k1 corresponds to the wavenumber of the oscillation at z=0. That is, k, k(z) a ) and k1 can be expressed as shown in equation (3-3-10).

[0151] [Mathematical expression 104] In addition, the imaging function of atmospheric refraction is considered as shown in the following equation (3-3-11).

[0152] [Mathematical expression 105] <3-4 Variations> In this chapter, the scattering field theory considering atmospheric refraction was applied in the example of a one-dimensional arrangement. However, the scattering field theory considering atmospheric refraction can also be applied in the examples of two-dimensional and quasi-two-dimensional arrangements.

[0153] Additionally, a model of atmospheric refractive index is shown in this chapter. However, atmospheric refractive index determined differently from the model shown in this chapter can also be used. For example, atmospheric refractive index measured at various altitudes in actual installation locations can also be used.

[0154] <4. Composition and Operation of the Imaging Device> Based on the above, the following describes the structure and operation of an imaging device that uses measurement data from scattered waves to image objects in a measurement area.

[0155] Here, the wave used for measuring the scattered wave is, for example, an electromagnetic wave, or a microwave, millimeter wave, or terahertz wave. Furthermore, light or sound can be used as the wave. The measurement area can be a region in the air, and the object can be a flying object. The object in the measurement area has physical properties that differ from the physical properties of the surrounding medium. Specifically, this physical property corresponds to the reflectivity of the wave. When using an electromagnetic wave as the wave, the physical property can be the dielectric constant.

[0156] Figure 7 This is a basic structural diagram of the imaging device in this embodiment. Figure 7The imaging device 100 shown includes multiple transmitters 101, multiple receivers 102, and information processing circuitry 103. Furthermore, the imaging device 100 may also include a display 104.

[0157] Each transmitter 101 is a circuit that transmits waves. Specifically, each transmitter 101 transmits waves to the measurement area. Furthermore, each transmitter 101 may also be a transmitting antenna, or may be composed of multiple transmitting elements such as multiple transmitting antenna elements.

[0158] Each receiver 102 is a circuit that receives the scattered waves of the wave. Specifically, each receiver 102 receives the scattered waves of the wave from the measurement area. Furthermore, each receiver 102 may also be a receiving antenna, or may be composed of multiple receiving elements such as multiple receiving antenna elements.

[0159] The multiple transmitters 101 and multiple receivers 102 can be configured in a one-dimensional arrangement, a two-dimensional arrangement, or a quasi-two-dimensional arrangement.

[0160] The information processing circuit 103 is a circuit that performs information processing. Specifically, the information processing circuit 103 acquires measurement data of the scattered waves and uses the measurement data 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 computational processing described in the theory above.

[0161] Furthermore, the information processing circuit 103 can also be a computer or a computer processor. The information processing circuit 103 can perform information processing by reading a program from memory and executing that program. Additionally, the information processing circuit 103 can also be a dedicated circuit that images objects in a measurement area based on measurement data.

[0162] Alternatively, the information processing circuit 103 can communicate with multiple transmitters 101 and multiple receivers 102. Furthermore, the information processing circuit 103 can control the operation of the multiple transmitters 101 and multiple receivers 102. Additionally, the information processing circuit 103 can obtain position information and measurement data from the multiple transmitters 101 and multiple receivers 102.

[0163] Furthermore, the information processing circuit 103 can also generate an image representing the object during the object imaging process. The information processing circuit 103 can also output the image representing the object to a display 104 or the like. Alternatively, the information processing circuit 103 can output the image representing the object to a printer (not shown). Alternatively, the information processing circuit 103 can also transmit the image as electronic data to other devices (not shown) via wired or wireless communication.

[0164] The display 104 is a display device such as a liquid crystal display. Furthermore, the display 104 is an optional component, not a necessary one. Also, the display 104 may be an external device that is not part of the imaging device 100.

[0165] Figure 8 It means Figure 7 A flowchart illustrating the basic operation of the imaging device 100. Specifically, by... Figure 7 The imaging device 100 shown includes multiple transmitters 101, multiple receivers 102, and information processing circuitry 103, etc. Figure 8 The actions shown.

[0166] First, each transmitter 101 transmits a wave to the measurement area in the atmosphere (S101). Then, each receiver 102 receives the scattered wave from the measurement area (S102). Finally, the information processing circuit 103 uses the measurement data from the scattered wave to image the objects in the measurement area (S103, S104, S105).

[0167] Specifically, in the imaging of an object, the information processing circuit 103 first derives a scattering field function using measurement data (S103). Here, the scattering field function is a function of the amount of scattered wave at the receiving position, which is input as the sending position of the wave and the receiving position of the scattered wave. In deriving the scattering field function, the information processing circuit 103 makes the scattering field function reflect the change in wavenumber of the wave as the refractive index in the atmosphere changes with the altitude in the atmosphere.

[0168] Next, the information processing circuit 103 derives the imaging function using the scattering field function (S104). Here, the imaging function is a function that outputs the image intensity of the imaged object position when the imaged object position is input, and it is a function determined by the quantity output from the scattering field function when the imaged object position is input as the sending position and the receiving position.

[0169] Finally, the information processing circuit 103 uses an imaging function to image the objects in the measurement area (S105).

[0170] Therefore, the imaging device 100 can derive a scattering field function and an imaging function that reflect the atmospheric refractive index as it varies with altitude. Consequently, the imaging device 100 can image objects in the measurement area of ​​the atmosphere with high precision.

[0171] For example, multiple transmitters 101 and multiple receivers 102 can also be configured on a straight line parallel to the y-axis. Additionally, the measurement area in the atmosphere can be divided into multiple layers.

[0172] Furthermore, the scattering field function of the nth layer in the multiple layers is represented by [Mathematical Formula 106].

[0173] [Mathematical expression 106] Here, x and z represent the x-coordinates and z-coordinates of the transmitting and receiving positions, respectively. y1 represents the y-coordinate of the transmitting position. y2 represents the y-coordinate of the receiving position. k1, k j and k n h represents the wave number of the fluctuations in the 1st, jth, and nth layers of a multi-layer system. j k represents the height of the j-th floor. x k y1 and k y2 The variable represents the wavenumber corresponding to x, y1, and y2 of the scattering field function.

[0174] in addition, [Mathematical expression 107] This represents the measurement data after Fourier transform.

[0175] Thus, the imaging device 100 can image objects in the measurement area of ​​the atmosphere with high precision using measurement data obtained from multiple transmitters 101 and multiple receivers 102 arranged in a straight line, according to the scattering field function derived for each layer.

[0176] Additionally, for example, the image function of the nth layer in a plurality of layers can also be represented by [Mathematical Formula 108].

[0177] [Mathematical expression 108] Here, x, y, and z in the imaging function represent the x, y, and z coordinates of the imaged object's position. ω represents the angular frequency of the wave.

[0178] In addition, k zn Determined by [Mathematical Formula 109].

[0179] [Mathematical expression 109] Thus, the imaging device 100 can image objects in the measurement area of ​​the atmosphere with high precision using measurement data obtained from multiple transmitters 101 and multiple receivers 102 arranged in a straight line, according to an imaging function derived for each layer.

[0180] Alternatively, for example, multiple transmitters 101 and multiple receivers 102 can also be configured on a straight line parallel to the y-axis.

[0181] Furthermore, the scattering field function can also be expressed by [Mathematical Formula 110].

[0182] [Mathematical expression 110] Here, x and z in the scattered field function represent the x-coordinates and z-coordinates of the transmitting and receiving positions, respectively. y1 in the scattered field function represents the y-coordinate of the transmitting position. y2 in the scattered field function represents the y-coordinate of the receiving position. k represents the wavenumber of the wave at the z-coordinate position. k1 represents the wavenumber of the wave at the z-coordinate position. k(z) a ) indicates that the z-coordinate is z a The wave number of the fluctuation at the location. a This represents the variable corresponding to the z-coordinate. k x k y1 and k y2 The variable represents the wavenumber corresponding to x, y1, and y2 of the scattering field function.

[0183] in addition, [Mathematical Expression 111] This represents the measurement data after Fourier transform.

[0184] Thus, the imaging device 100 can image objects in the measurement area of ​​the atmosphere with high precision using a scattering field function derived from measurement data obtained from a plurality of transmitters 101 and a plurality of receivers 102 arranged in a straight line.

[0185] Alternatively, for example, the image function can also be represented by [Mathematical Formula 112].

[0186] [Mathematical expression 112] Here, x, y, and z in the imaging function represent the x, y, and z coordinates of the imaged object's position. ω represents the variable corresponding to the angular frequency of the fluctuation.

[0187] Thus, the imaging device 100 can image objects in the measurement area of ​​the atmosphere with high precision using an imaging function derived from measurement data obtained by a plurality of transmitters 101 and a plurality of receivers 102 arranged in a straight line.

[0188] Alternatively, the wave could be a microwave. Therefore, compared to electromagnetic waves with shorter wavelengths, the imaging device 100 can suppress the attenuation of the wave due to moisture in the measurement area.

[0189] Furthermore, for example, other constituent elements, formulas, and variables shown in this embodiment can be appropriately applied to the plurality of transmitters 101, plurality of receivers 102, information processing circuit 103, scattering field function, and imaging function shown in the basic configuration and basic operation described above. Moreover, the scattering field function and imaging function shown in this embodiment can be appropriately modified for application. For example, mathematical formulas that express substantially the same content as the mathematical formulas described above can be used, or other mathematical formulas derived based on the above theory can be used.

[0190] (Replenish) The imaging apparatus has been described above based on the embodiments, but the imaging apparatus is not limited to the embodiments described above. Modifications conceivable to those skilled in the art can be made to the embodiments, and multiple components in the embodiments can be combined arbitrarily. For example, in an embodiment, a process performed by a specific component can be performed by another component instead of the specific component. Furthermore, the order of multiple processes can be changed, or multiple processes can be executed in parallel.

[0191] Furthermore, the imaging method, which includes steps performed by the various components of the imaging apparatus, can be executed by any device or system. For example, a part or all of the imaging method can be executed by a computer equipped with a processor, memory, and input / output circuits. In this case, the imaging method can also be executed by the computer executing a program for causing the computer to perform the imaging method.

[0192] Furthermore, the aforementioned procedures can be recorded in a non-transitory computer-readable recording medium.

[0193] Furthermore, the components of the imaging device can be composed of dedicated hardware, general-purpose hardware that executes the aforementioned programs, or a combination of these. Additionally, the general-purpose hardware can consist 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 can be a semiconductor memory or a hard disk, and the general-purpose processor can be a CPU.

[0194] Furthermore, dedicated hardware can also consist of a memory and a dedicated processor. For example, the dedicated processor can also execute the imaging method described above, referring to the memory used to record measurement data.

[0195] Furthermore, the components of the imaging device can also be circuits. These circuits can be integrated as a whole or they can be separate circuits. Additionally, these circuits can correspond to dedicated hardware or general-purpose hardware that executes the aforementioned programs.

[0196] Furthermore, the imaging device is not limited to a physically integrated device, but can also have multiple sub-devices arranged in a distributed manner. In addition, the imaging device can also be manifested as an imaging system.

[0197] Industrial applicability One aspect of this disclosure is useful in imaging devices that image objects in a measurement area using measurement data of scattered waves, and can be applied to detection systems that detect objects in a measurement area in the atmosphere.

[0198] Explanation of reference numerals in the attached figures 100 Imaging Devices 101 transmitter 102 Receiver 103 Information Processing Circuit 104 monitor

Claims

1. An imaging device, wherein, have: Multiple transmitters send waves to the measurement area in the atmosphere, respectively. Multiple receivers, each receiving the scattered waves of the wave from the measurement area; as well as The information processing circuit uses the measurement data of the scattered waves to image the objects in the measurement area. The information processing circuit, in the imaging of the object, The measurement data is used to derive a scattering field function, which is a function that takes the emission location of the wave and the receiving location of the scattered wave as input, and outputs the amount of the scattered wave at the receiving location. A derived imager function is defined as a function that takes the imager object location as input and outputs the image intensity at that location. This function is determined by using a quantity output from the scattering field function by inputting the imager object location as both the transmitting and receiving locations. The object in the measurement area is imaged using the imager function. In deriving the scattering field function, the information processing circuit ensures that the scattering field function reflects the wavenumber change of the wave as the refractive index in the atmosphere changes with the altitude in the atmosphere.

2. The imaging apparatus according to claim 1, wherein, The plurality of transmitters and the plurality of receivers are arranged on a straight line parallel to the y-axis. The measurement area in the atmosphere is divided into multiple layers. The scattering field function of the nth layer among the plurality of layers is expressed by [Mathematical Formula 1]. [Mathematical Formula 1] The x and z values ​​of the scattering field function represent the x and z coordinates of the transmitting and receiving positions, respectively. The y1 value of the scattering field function represents the y coordinate of the transmitting position, and the y2 value of the scattering field function represents the y coordinate of the receiving position. k1 and k... j and k n h represents the wave number of the fluctuation in the 1st, jth, and nth layers of the plurality of layers. j Let k represent the height of the j-th floor. x k y1 and k y2 The variable represents the wavenumber corresponding to x, y1, and y2 of the scattering field function. [Mathematical Formula 2] This represents the measurement data after Fourier transform.

3. The imaging apparatus according to claim 2, wherein, The image function of the nth layer among the plurality of layers is expressed by [Mathematical Formula 3]. [Mathematical Formula 3] The x, y, and z values ​​in the imaging function represent the x, y, and z coordinates of the imaged object's position, respectively; ω represents the angular frequency of the wave; and k... zn Determined by [Mathematical Formula 4], [Mathematical Formula 4] 。 4. The imaging apparatus according to claim 1, wherein, The plurality of transmitters and the plurality of receivers are arranged on a straight line parallel to the y-axis. The scattering field function is expressed by [Mathematical Equation 5]. [Mathematical Formula 5] The x and z of the scattering field function represent the x and z coordinates of the transmitting and receiving positions, respectively; y1 of the scattering field function represents the y coordinate of the transmitting position; y2 of the scattering field function represents the y coordinate of the receiving position; k represents the wavenumber of the wave at the z-coordinate position; k1 represents the wavenumber of the wave at the z-coordinate position; k(z) a ) indicates that the z-coordinate is z a The wave number of the fluctuation at the location, z a k represents the variable corresponding to the z-coordinate. x k y1 and k y2 The variable represents the wavenumber corresponding to x, y1, and y2 of the scattering field function. [Mathematical Formula 6] This represents the measurement data after Fourier transform.

5. The imaging apparatus according to claim 4, wherein, The image rendering function is represented by [Mathematical Expression 7]. [Mathematical Expression 7] The x, y, and z values ​​of the imaging function represent the x, y, and z coordinates of the imaged object's position, and ω represents the variable corresponding to the angular frequency of the fluctuation.

6. An imaging method, wherein, include: The steps of transmitting waves from multiple transmitters to the measurement area in the atmosphere; The step of receiving the scattered waves of the wave from the measurement area by multiple receivers respectively; as well as The step of imagering the objects in the measurement area using the measurement data of the scattered waves. The steps for imagering the object include: The step of deriving a scattering field function using the measurement data is a function that takes the sending position of the wave and the receiving position of the scattered wave as input and outputs the amount of the scattered wave at the receiving position. The step of deriving the image function, wherein the image function is a function that outputs the image intensity of the image object location when the image object location is input, and is a function determined by using the quantity output from the scattering field function by inputting the image object location as the sending location and the receiving location into the scattering field function; as well as The step of using the imaging function to image the object in the measurement area. In the step of deriving the scattering field function, the scattering field function is made to reflect the wavenumber change of the wave as the refractive index in the atmosphere changes with the altitude in the atmosphere.

Images