Visualization device and imaging method

Abstract

An imaging device (100) comprises: a plurality of transmitters (101) that are disposed on both sides of a region, and that transmit wave motions to the region; a plurality of receivers (102) that are disposed on both sides of the region, and that receive wave motions from the region; and an information processing circuit (103) that derives, in accordance with the correspondence between measurement data obtained by the plurality of transmitters (101) and the plurality of receivers (102) and a composite of multiple functions related to a plurality of primary scatterings which constitute a multiple scattering, an imaging function corresponding to a scattered field function related to scattering of the wave motions, and that uses the imaging function to visualize a three-dimensional structure of a scattering body included in an object within the region.

Description

[Technical Field]

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

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

[0003] For example, in the technology described in Patent Document 1, a beam emitted from a microwave transmitter is incident on an object to be inspected, and the amplitude and phase of the scattered beam are detected by a microwave detector. Then, the distribution of dielectric constant is calculated from the output signal of the microwave detector, and a cross-sectional image of the object to be inspected is displayed. [Prior art documents] [Patent documents]

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

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

[0006] Furthermore, multiple scattering (reflection) may occur within a region for a single wave transmission. In other words, not only primary scattering corresponding to one scattering, but also secondary scattering corresponding to two scatterings, tertiary scattering corresponding to three scatterings, etc. may occur. Scattering more than two times is also called multiple scattering. Data on scattered waves associated with multiple scattering may be obtained by measurement. Analysis methods that do not consider multiple scattering and only primary scattering cannot accurately determine the state within the region.

[0007] Therefore, the present disclosure provides an imaging device and the like that can visualize the three-dimensional structure of scatterers contained in objects within a region with high accuracy using waves. [Means for solving the problem]

[0008] An imaging device according to one aspect of the present disclosure includes a plurality of transmitters arranged on both sides of a region to be measured and transmitting waves to the region, a plurality of receivers arranged on both sides and receiving the waves from the region, and an information processing circuit that derives an imaging function corresponding to a scattering field function related to the scattering of the waves in accordance with a correspondence between measurement data obtained by the plurality of transmitters and the plurality of receivers and a combination of a plurality of functions related to a plurality of first-order scatterings that constitute multiple scattering, and uses the imaging function to visualize the three-dimensional structure of scatterers contained in an object within the region.

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

[0010] According to the present disclosure, it is possible to use waves to visualize with high accuracy the three-dimensional structure of scatterers contained in objects within a region. [Brief explanation of the drawings]

[0011] [Figure 1] FIG. 1 is a conceptual diagram showing an example of the orders of multiple scattering in the embodiment. [Figure 2] FIG. 2 is a diagram showing four types of scattering regimes corresponding to four types of fundamental solutions of the scattered field equation. [Figure 3] FIG. 3 is a conceptual diagram regarding the definition of the Green's function. [Figure 4] FIG. 4 is a conceptual diagram showing an example of application of the fundamental solution of the scattered field. [Figure 5] FIG. 5 is a diagram showing the propagation path of a wave. [Figure 6] FIG. 6 is a conceptual diagram showing an example of application of the fundamental solution of the scattered field for second-order scattering. [Figure 7] FIG. 7 is a diagram showing four types of scattering models for third-order scattering. [Figure 8] FIG. 8 is a diagram showing definitions of four types of measurement data. [Figure 9] FIG. 9 is a block diagram showing the basic configuration of an imaging device according to an embodiment. [Figure 10] FIG. 10 is a conceptual diagram showing an example of the relationship between a plurality of transmitters, a plurality of receivers, and an area. [Figure 11] FIG. 11 is a conceptual diagram showing a modified example of the relationship between a plurality of transmitters, a plurality of receivers, and an area. [Figure 12]FIG. 12 is a flowchart showing the basic operation of the imaging device according to the embodiment. [Figure 13] FIG. 13 is a block diagram showing a specific configuration of the imaging device according to the embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0012] An imaging device according to one aspect of the present disclosure includes a plurality of transmitters arranged on both sides of a region to be measured and transmitting waves to the region, a plurality of receivers arranged on both sides and receiving the waves from the region, and an information processing circuit that derives an imaging function corresponding to a scattering field function related to the scattering of the waves in accordance with a correspondence between measurement data obtained by the plurality of transmitters and the plurality of receivers and a combination of a plurality of functions related to a plurality of first-order scatterings that constitute multiple scattering, and uses the imaging function to visualize the three-dimensional structure of scatterers contained in an object within the region.

[0013] This allows the imaging device to apply the correspondence between the measurement data and a combination of multiple functions related to multiple first-order scattering to derive an imaging function for visualizing the three-dimensional structure of scatterers contained in objects within the region. Multiple scattering is assumed to be a combination of multiple first-order scattering. Therefore, the imaging device can analytically solve the inverse problem of scattering, including multiple scattering, according to this correspondence. Therefore, the imaging device can visualize the three-dimensional structure of scatterers contained in objects within the region with high accuracy.

[0014] For example, the information processing circuit derives the visualization function corresponding to the scattered field function by solving an equation of the scattered field function based on the measurement data, and the scattered field function is expressed as

[0015]

number

[0016]

number

[0017] This allows the imaging device to visualize with high accuracy the three-dimensional structure of scatterers contained in objects within the region according to the scattered field function associated with the scattering phenomenon and the equation satisfied by the scattered field function.

[0018] Further, for example, the information processing circuit derives an analytical solution of the equation based on the measurement data, and derives the visualization function based on the analytical solution, and the analytical solution is

[0019]

number

[0020] This allows the imaging device to visualize with high accuracy the three-dimensional structure of scatterers contained in objects within the region according to the analytical solution of the equation satisfied by the scattered field function associated with the scattering phenomenon.

[0021] Also, for example, the visualization function is

[0022]

number

[0023] This allows the imaging device to visualize with high accuracy the three-dimensional structure of scatterers contained in objects within the region in accordance with an imaging function that is appropriately associated with the scattered field function.

[0024] Also, for example, the multiple scattering is expressed using four functions in spectral space corresponding to four fundamental solutions of the equation for the scattered field function, the relationship between the measurement data and the four functions is expressed by a nonlinear integral equation, and the information processing circuit derives the four functions from the measurement data in accordance with the nonlinear integral equation, and derives the visualization function corresponding to the scattered field function using the four functions.

[0025] This allows the imaging device to visualize with high accuracy the three-dimensional structure of scatterers contained in objects within the region, in accordance with the relational equation that expresses multiple scattering.

[0026] Furthermore, for example, the measurement data is

[0027]

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[0028]

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[0029]

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[0030]

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[0031]

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[0032]

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[0033] This allows the imaging device to visualize with high accuracy the three-dimensional structure of scatterers contained in objects within the region, according to a formula based on the theory of multiple scattering.

[0034] Furthermore, for example, the measurement data is

[0035]

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[0036]

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[0037]

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[0038]

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[0039]

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[0040]

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[0041] This allows the imaging device to visualize with high accuracy the three-dimensional structure of scatterers contained in objects within the region according to an equation that appropriately corresponds to the measurement data based on the theory of multiple scattering.

[0042] Furthermore, for example, the measurement data is

[0043]

number

[0044]

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[0045]

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[0046]

number

[0047] This allows the imaging device to visualize with high accuracy the three-dimensional structure of scatterers contained in objects within the region, according to an equation that specifically expresses the scattering phenomenon based on the theory of multiple scattering.

[0048] Furthermore, for example, the measurement data is

[0049]

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[0050]

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[0051]

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[0052]

number

[0053] This allows the imaging device to specifically express the scattering phenomenon based on the theory of multiple scattering, and to visualize with high accuracy the three-dimensional structure of scatterers contained in objects within the region according to an equation to which the measurement data is appropriately associated.

[0054] Furthermore, for example, the measurement data is

[0055]

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[0056]

number

[0057]

number

[0058]

number

[0059] This allows the imaging device to visualize with high accuracy the three-dimensional structure of scatterers contained in objects within the region, according to an equation organized based on the theory of multiple scattering.

[0060] Furthermore, for example, a visualization method according to one aspect of the present disclosure includes the steps of transmitting waves to a region to be measured by a plurality of transmitters arranged on both sides of the region, receiving the waves from the region by a plurality of receivers arranged on both sides, deriving a visualization function corresponding to a scattering field function related to the scattering of the waves in accordance with a correspondence between measurement data obtained by the plurality of transmitters and the plurality of receivers and a combination of a plurality of functions related to a plurality of first-order scatterings that constitute multiple scattering, and visualizing the three-dimensional structure of scatterers included in an object within the region using the visualization function.

[0061] This makes it possible to apply the correspondence between measurement data and a composite of multiple functions related to multiple first-order scattering to derive an imaging function for visualizing the three-dimensional structure of scatterers contained in objects within a region. Multiple scattering is assumed to be a combination of multiple first-order scattering. Therefore, according to this correspondence, it is possible to analytically solve the inverse problem of scattering, including multiple scattering. Therefore, it is possible to visualize the three-dimensional structure of scatterers contained in objects within a region with high accuracy.

[0062] Hereinafter, embodiments will be described with reference to the drawings. Note that the embodiments described below are all comprehensive or specific examples. The numerical values, shapes, materials, components, the arrangement and connection of the components, steps, the order of steps, and the like shown in the following embodiments are merely examples and are not intended to limit the scope of the claims.

[0063] In the following description, the technologies described in Patent Documents 2, 3, 4, and 5 may be particularly referred to as existing technologies. In the following description, radio waves such as microwaves are primarily assumed as waves, but waves are not limited to radio waves such as microwaves. Visualization based on scattering may be expressed as scattering tomography. Therefore, the imaging device and imaging method in the following description may also be expressed as a scattering tomography device and a scattering tomography method, respectively.

[0064] (Embodiment) The imaging device of this embodiment uses waves to visualize the three-dimensional structure of scatterers contained in objects within a region. The imaging device of this embodiment will be described in detail below, including the underlying technology and theory.

[0065] <i 概要> Scattered field theory has been developed to visualize the inside of an object using waves such as microwaves. Scattered field theory is not only theoretically novel but also useful in practice. It is expected to be applied to fields such as diagnostic imaging, since it allows accurate three-dimensional reconstructed images to be calculated instantly from measurement data. This disclosure develops the scattered field theory to solve the difficult problem of inverse scattering of multiple scattering (multiple reflection), and presents an imaging device and imaging method that use the developed scattered field theory.

[0066] For example, in the inverse scattering reconstruction theory where the measurement surface on which the transmitting points and receiving points are arranged is a curved surface, a function φ as shown in the following equation (1-1) is defined.

[0067]

number

[0068] Here, (x, y1, z1) indicate the coordinates of the wave emission point, and (x, y2, z2) indicate the coordinates of the wave reception point. Radiation is sometimes expressed as transmission. k indicates the wave number of the wave. D indicates the area to be measured. ε(ξ, η, ζ) indicates the function of the permittivity at the position (ξ, η, ζ) and corresponds to the reflectivity of the wave at the position (ξ, η, ζ). (ξ, η, ζ) correspond to the reflection point of the wave. ρ1 indicates the distance from the transmission point to the reflection point, and ρ2 indicates the distance from the reflection point to the reception point. Note that ε(ξ, η, ζ) is unknown.

[0069] The phenomenon of wave scattering where the value of the dielectric constant function ε (ξ, η, ζ) is large can be understood as a function of the wave emission and reception points. By defining the emission and reception points within the entire region, the above φ is used as the scattered field function that indicates the scattered field. The scattered field function satisfies the partial differential equation shown in the following equation (1-2).

[0070]

number

[0071] Here, Δ5 denotes the five-dimensional Laplace operator with respect to x, y1, y2, z1, and z2. ∂ denotes the partial derivative of the variable indicated by the suffix. c denotes the wave propagation speed. t denotes time. Also, the general solution of the differential equation in equation (1-2) is expressed as the following equation (1-3).

[0072]

number

[0073] where k x , k y1 and k y2 indicates the wave numbers of the scattered field function in terms of x, y1, and y2. The solution of a fourth-order partial differential equation is completely determined by the measurements (radar reflection data) at the boundary of the domain, so the kernel function of this general solution, a(k x , k y1 , k y2 , k) can also be obtained by Fourier transform. Then, by applying the limit values ​​of y2 → y1 and t → 0 to φ, the visualization function ρ can be obtained. For example, the visualization function ρ can be expressed as in the following equation (1-4).

[0074]

number

[0075] In the above process, based on the assumption that there is no multiple scattering, the scattered field function φ(x, y1, y2, z1, z2, k) is directly linked to the measured values ​​(radar reflection data) at the boundary of the region. For example, the shape of the boundary surface is defined by the curve z = f(y) on the zy plane. The data obtained by Fourier transforming the radar reflection data measured at that boundary surface with respect to (x, t) is Φ(k x , y I , y J , k). Assuming that there is no multiple scattering, the following equation (1-5) is assumed to hold.

[0076]

number

[0077] However, when it is not allowed to ignore multiple scattering, as shown in FIG. 1, there may be second-order, third-order, and fourth-order scatterings.

[0078] FIG. 1 is a conceptual diagram showing an example of the order of multiple scattering (multiple reflection) in an embodiment. In FIG. 1, P1 indicates a transmission point, and P2 indicates a reception point. A signal is transmitted from P1 and received at P2 through reflections corresponding to the order within the region. Multiple reflections are called multiple reflection or multiple scattering.

[0079] In the present disclosure, a method for solving an inverse problem of scattering including multiple scattering as described above, and an imaging device and an imaging method using the method will be described.

[0080] To perform inverse analysis of multiple scattering, radar reflection data over the entire boundary of the region is used. Multiple scattering of second order or higher is expressed by a combination (synthesis) of four fundamental solutions E1, E2, E3, and E4 of the partial differential equation of the scattering field.

[0081] FIG. 2 is a diagram showing four types of scattering forms corresponding to four types of fundamental solutions of the equation of the scattering field. The scattering form can also be expressed as a scattering model. Multiple scattering is expressed by the synthesis of these four types of fundamental solutions (E1, E2, E3, and E4). Functions a1, a2, a3, and a4 in the spectral space are introduced corresponding to E1, E2, E3, and E4. To determine these from the measurement data, two backscatterings and a forward scattering measurement are performed.

[0082] Inverse scattering analysis of multiple scattering in a three-dimensional region is a difficult problem. However, the present disclosure provides a solution to the inverse scattering problem using scattering field theory.

[0083] <II Theory of Scattering Field> <II-1 Simple Propagation Function> The Helmholtz equation for wave propagation is expressed by the following equation (2-1).

[0084]

Number

[0085] Here, φ is an unknown function representing the displacement of vibration at the position (x, y, z). Δ3 represents the three-dimensional Laplace operator. k represents the wave number. (ξ, η, ζ) represents the position of the wave source.

[0086] The equation obtained by performing a Fourier transform of φ with respect to (x, y, t) is expressed as the following equation (2-2).

[0087]

Number

[0093]

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[0094] This integral kernel function indicates the signal strength of a wave that originates from r1, reflects at point ξ, and returns to point r2. ω is the angular frequency. This Green's function is embodied using a new function name as shown in the following equation (2-6). Here, ε is a function of the dielectric constant.

[0095]

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[0096] The above φ(x, y1, y2, z1, z2) is the solution of the partial differential equation for the scattered field as shown in the following equation (2-7).

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[0098] Next, the solution of equation (2-7) is examined. First, φ is subjected to a multiple Fourier transform with respect to t, x, y1, and y2, and equation (2-7) is transformed to obtain equation (2-8) below. Here, D z1 , D z2 indicate partial derivatives with respect to z1 and z2, respectively.

[0099]

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[0100] Equation (2-8) has four solutions, which are expressed as the following equation (2-9).

[0101] [Number]

[0102] Here, s1 and s2 are expressed as in the following equation (2-10).

[0103] [Number]

[0104] The scattering corresponding to the four fundamental solutions of equation (2-9) is as shown in Figure 2. Among these four fundamental solutions, E3 and E4 have a time-reversed relationship with each other and are not independent. Therefore, E1, E2, and E3 are independent fundamental solutions. The four general solutions of equation (2-7) corresponding to the four fundamental solutions are expressed as in the following equation (2-11).

[0105] [Number]

[0106] The four general solutions of equation (2-11) shown above can be regarded as the four scattering field functions corresponding to the four first-order scattering models shown in Figure 2. The scattering field function corresponding to multiple scattering is derived based on the synthesis of these four scattering field functions.

[0107] <III Multiple Scattering> <III-1 Degree of Multiple Scattering> The degree of multiple scattering is as shown in Figure 1. In the multiple scattering of each degree shown in Figure 1, there are also various geometric varieties that vary depending on the location where the scattering occurs. And the characteristics are different depending on the signs of the z-coordinate components of the incident and scattered direction vectors at the location where the scattering occurs. The fact that the characteristics are different depending on the signs of the z-coordinate components of the incident and scattered direction vectors is explained in the fundamental solution of the scattering field in Chapter II.

[0108] <III-2 Outline of the Approach Using the Scattering Field Theory of Multiple Scattering> Fig. 4 is a conceptual diagram showing an example of application of the fundamental solution of the scattered field. Specifically, Fig. 4 shows a third-order scattering model to which multiple fundamental solutions are applied. For example, in the third-order scattering model shown in Fig. 4, the fundamental solutions E1 and E2 of the scattered field are used in the regions inside the dashed lines. The following equation (3-1) shows the relationship between the path and the fundamental solution.

[0109]

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[0110] Although scattering points S1, S2, and S3 are arbitrary points within the region, the condition that they must adhere to geometric rules is imposed on scattering points S1, S2, S3, etc. Specifically, the sign of the z-coordinate component of the directional vector indicated by the arrow representing the wave propagation in Figure 4 is maintained. Furthermore, P1, P2, S2, and S3 move within the measurement plane under the condition that their x-coordinates are equal. Furthermore, P1 and P2 have the same z-coordinate. However, it is assumed that there are no restrictions on the x-coordinate of S1.

[0111] Fig. 5 is a diagram showing wave propagation paths. Specifically, Fig. 5 shows multiple propagation paths for a common transmitting point P1 and a common receiving point P2 when basic solutions E1 and E2 are used. These multiple propagation paths correspond to the above-mentioned geometric rules.

[0112] The backscattering amplitude measured on the y-axis is expressed as follows:

[0113]

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[0114] Here, G (specifically, G1 and G2) is a Green's function and is defined as in the following equation (3-3).

[0115]

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[0116] where:

[0117]

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[0118]

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[0119] a1(k x , k y1 , k y2 , k) can be obtained from this equation by Fourier transform. By substituting the approximate function thus obtained into the integral symbol on the right side of equation (3-3), G1(P1, P2, k) that takes multiple scattering into account can be obtained, and a1(k x , k y1 , k y2 , k) is obtained.

[0120] By the way, the right side of equation (3-2) contains G2(S 2- , S 3- , k). Since this is determined by measurement, the measurement results for a surface with a different z value from the previous one are used. When Φ2(P1, P2, k) indicates the measurement results for a surface with a different z value, the following equation (3-5) holds.

[0121]

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[0122] This allows us to obtain a more accurate a1(k x , k y1 , k y2 , k) can be found.

[0123] <Formulation of the inverse scattering problem in III-3 multiple scattering> (1) Second-order scattering FIG. 6 is a conceptual diagram showing an application example of the fundamental solution of the scattering field for second-order scattering. As shown in FIG. 6, second-order scattering corresponds to a form in which the fundamental solutions E1 and E4 of the scattering field equation are connected by S 2- S 2- is assumed to be infinitely close to S2. In the fundamental solutions E3 and E4, the condition that the direct wave directly propagating from S 2- to P2 is not included is satisfied.

[0124] The path of second-order scattering is limited to the path shown in FIG. 6 and the path (symmetrically transformed path) in which P1 and P2 in FIG. 6 are interchanged. The fundamental solutions E1 and E4 are applied as shown in FIG. 6 and are named as functions as in the following equation (3-6).

[0125]

Equation

[0126] Here, (x, y1, z) corresponds to the position of P1, (x, y2, z) corresponds to the position of P2, and (x, η 2- , ζ 2- ) corresponds to the position of S 2- . The specific equation of equation (3-6) is expressed as the following equation (3-7) according to equation (2-11).

[0127]

Equation

[0128] The synthesis of the above functions corresponding to the path of second-order multiple scattering P1→S1→S 2- →S2→P2 is expressed as the following equation (3-8).

[0129]

Equation

[0130] In equation (3-8), η 2- →η and ζ 2- Applying →ζ and integrating with respect to the coordinates (η, ζ) of point S2, we obtain the following equation (3-9).

[0131]

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[0132] By substituting equation (3-7) into equation (3-9), we obtain the following equation (3-10): Note that to avoid confusion, suffixes such as a, b, +, and - are added to variables in equation (3-10) as appropriate.

[0133]

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[0134] Here, δ represents the delta function. δ(k η- +k η+ ) and δ(s2(k xa , k y1 , k η- )-s1(k xb , k η+ , k y2 )) is the connection point S 2- This corresponds to the input and output matching at z=0. By Fourier transforming equation (3-10) with respect to (x, y1, y2) at z=0, the following equation (3-11) is obtained.

[0135]

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[0136] (2) Third-order scattering An example in which the fundamental solution of the scattered field is applied to third-order scattering is shown in Figure 4. With reference to Figure 4, the scattered field function is defined as in the following equation (3-12). The suffixes 2- and 3- for η and ζ correspond to immediately before point S2 and immediately before point S3, respectively.

[0137]

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[0138] The function on the right side of equation (3-12) corresponds to the general solution of the scattered field of first-order scattering, and is a function such as the following equation (3-13).

[0139]

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[0140] The synthesis of the above equations corresponds to the third-order multiple scattering path P1 → S1 → S2 → S3 → P2, and is expressed as the following equation (3-14).

[0141]

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[0142] In equation (3-14), η 2- →η2, η 3- →η3, ζ 2- →ζ2 and ζ 3- By applying →ζ3 and integrating with respect to the coordinates (η2, ζ2) and (η3, ζ3) of points S2 and S3, the following equation (3-15) is obtained.

[0143]

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[0144] The function obtained by the above process represents the third-order scattering amplitude as seen from P1 and P2. Substituting equation (3-13) into equation (3-15) gives the following equation (3-16). In equation (3-16), + and - are added to the suffix of the wave number k as appropriate to avoid confusion with the integral symbol.

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[0146] In the theory of scattered fields, there is a relationship such as the following equation (3-17).

[0147]

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[0148] By performing integration of equation (3-16) with respect to η and ζ, the following equation (3-18) is obtained.

[0149]

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[0150] Here, δ represents a delta function, which corresponds to the input and output matching at the connection point. By Fourier transforming equation (3-18) with respect to (x, y1, y2) at z=0, the following equation (3-19) is obtained.

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[0152] When multiple scattering is taken into consideration, the scattered field function Ψ(x, y1, y2, z, k) is expressed as the following equation (3-20).

[0153]

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[0154] Here, Ψ1 is a scattered field function corresponding to first-order scattering, Ψ2 is a scattered field function corresponding to second-order scattering, and Ψ3 is a scattered field function corresponding to third-order scattering. Based on equation (2-11) etc., the following equation (3-21) holds.

[0155]

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[0156] For example, when the second term and the terms after the fourth term on the right side in Equation (3-20) can be ignored, by performing a Fourier transform on the entire Equation (3-20), the following Equation (3-22) can be obtained.

[0157]

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[0158] Using the measurement data Φ1(k) at z = 0, the left side of Equation (3-22) can be expressed as follows in Equation (3-23).

[0159]

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[0160] The right side of Equation (3-23) is the measurement data on the boundary surface. Therefore, the left side of Equation (3-22) is determined. Thus, Equation (3-22) is an ordinary non-linear integral equation regarding a1(k x , k y1 , k y2 , k) and a2(k x , k y1 , k y2 , k).

[0161] A similar equation can be obtained for another boundary surface expressed by z = h. Although this integral equation is non-linear, its solution can be obtained very easily using the Neumann series expansion. The inverse problem of scattering can be solved as if solving the forward problem of scattering.

[0162] <III-4 Fundamental Equation of Inverse Scattering Problem Considering All Models> Fig. 7 is a diagram showing four types of scattering models related to third-order scattering. Specifically, D1, D2, D3, and D4 in Fig. 7 correspond to the four types of scattering models related to third-order scattering. The scattering models can also be expressed as scattering diagrams. In Fig. 7, the regions to which the fundamental solutions E1 to E4 apply are indicated by dashed lines. The following equations (3-24), (3-25), (3-26), (3-27), and (3-28) show the scattering field functions of D1 to D4.

[0163]

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[0168] In the above equation, (η 2- , ζ 2- ) and (η 3- , ζ 3- ) represent the coordinates of the point immediately before point S2 and the point immediately before point S3, respectively.

[0169] The composition of the above functions corresponds to the third-order multiple scattering path P1 → S1 → S2 → S3 → P2, and is expressed as the following equation (3-29).

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[0171] Apply η in Equation (3-29) 2- → η2, η 3- → η3, ζ 2- → ζ2 and ζ 3- Apply → ζ3 and integrate with respect to the coordinates (η2, ζ2), (η3, ζ3) of points S2 and S3, and the following Equation (3-30) is obtained.

[0172]

Equation

[0173] Perform the integration of Equation (3-30) with respect to (η2, ζ2), (η3, ζ3), and perform Fourier transform of the result with respect to (x, y1, y2) at z = 0, and Equations (3-31), Equation (3-32), Equation (3-33) and Equation (3-34) are obtained.

[0174]

Equation

[0175]

Equation

[0176]

Equation

[0177]

Equation

[0178] <III-5 Integral Equation for Inverse Scattering Problem in Multiple Scattering> When multiple scattering is considered, the scattered field function Ψ(x, y1, y2, z, k) is expressed as the following Equation (3-35).

[0179]

Equation

[0180] By performing a Fourier transform on the entire expression of Equation (3-35) at z = 0, Equation (3-36) and Equation (3-37) are obtained.

[0181]

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[0182]

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[0183] Here,

[0184] <X

Number

[0185] To solve this integral equation including the multiple scattering term, the measured values in two z = const planes are used. Solving this integral equation based on the measured values is extremely easy. The result is obtained in the form of a Neumann series. Note that O(a 4 ) in Equation (3-37) is a term corresponding to scattering of the fourth order or higher, and may be omitted.

[0186] <III-6 Solution of the Integral Equation for the Inverse Scattering Problem in Multiple Scattering> Figure 8 is a diagram showing the definitions of the four types of measurement data. That is, the four types of measurement data of multistatic scattering tomography are defined as shown in Figure 8. From equations (3-31), (3-32), (3-33), and (3-34), the following equation (3-38) holds.

[0187]

number

[0188] The right-hand sides of the four equations in equation (3-38) represent four types of functions obtained by Fourier transforming the four types of scattering field functions of multiple scattering corresponding to the four types of measurement methods.

[0189] From equation (3-37), when multiple scattering is not taken into account, a1(k x , k y1 , k y2 , k) are found. In the following, the suffix "0" is added to solutions that do not take multiple scattering into consideration. The results shown in the following equation (3-39) are obtained for the four types of measurement data in Figure 8.

[0190]

number

[0191] By expanding a1, a2, a3, and a4 into a series corresponding to the scattering orders, we obtain the following equation (3-40): Note that a1, a2, a3, and a4 have suffixes related to the scattering orders.

[0192]

number

[0193] By substituting the measurement data expressed by equation (3-38) into equation (3-37), the following equation (3-41) is obtained.

[0194]

number

[0195] From this equation (3-41), the a related to second-order scattering 1、1 (k x , k y1 , k y2 , k) can be expressed using only measurement data. 2、1 , a 3、1 , a 4、1 A similar equation can be found for

[0196] Substituting equation (3-40) into equation (3-41) and leaving only the zeroth-order term in the integral symbol, we obtain the following equation (3-42).

[0197]

number

[0198] Note that the "+···" in equation (3-42) represents a term corresponding to fourth-order or higher scattering and may be omitted. Rearranging equation (3-42) yields the following equation (3-43).

[0199]

number

[0200] In equation (3-43), a1 corresponds to first-order scattering, second-order scattering, and third-order scattering. Specifically, a1 is derived by removing the effects of second-order scattering and third-order scattering from the measurement data. Using a similar procedure, a1 corresponding to higher-order scattering may be derived. Furthermore, a2, a3, and a4 may also be derived using a similar procedure. The general solution of the scattered field equation is expressed using a1 as in the following equation (3-44):

[0201]

number

[0202] The visualization function ρ(x, y, z) is expressed as in the following equation (3-45) using φ1 in the above equation (3-44).

[0203]

number

[0204] This imaging function is a function from which the influence of multiple scattering has been removed, and is a function that explicitly provides a solution to the inverse problem of scattering in the case of nonlinearity.

[0205] Equation (3-41) may be generalized as follows: Equation (3-46) may then be used as equation (3-41).

[0206]

number

[0207] where a m1 , a m2 , a m3 , , a mL a1, a2, a3 and a4, which are expressed as x , k y1 , k y2 , k). Also, f2, f3, . . ., f L denotes the product of 2, 3, . . . , and L variables in parentheses, corresponding to 2, 3, . . . , and L scatterings, respectively.

[0208] Also,

[0209]

number

[0210] Furthermore, equation (3-42) may be generalized as in equation (3-47) below: Then, equation (3-47) may be used as equation (3-42).

[0211]

number

[0212] where a m a1, a2, a3 and a4, which are expressed as x , k y1 , k y2 , k). Also, Φ m1n1 , Φ m2n2 , Φ m3n3 , , Φ mLnL Φ expressed as 11 , Φ 12 , Φ 21 and Φ 22 corresponds to the measurement data for the four scattering modes. Also, g2, g3, . . ., g L denotes the product of 2, 3, . . . , and L variables in parentheses, corresponding to 2, 3, . . . , and L scatterings applied from transmission to reception of the wave, respectively.

[0213] Also,

[0214]

number

[0215] The scattered field function may also be generalized as in the following equation (3-48):

[0216]

number

[0217] Also, the imaging function may be generalized as in the following equation (3-49).

[0218]

Equation

[0219] <Configuration and Operation of the Imaging Device> Based on the above-described content, the configuration and operation of an imaging device that visualizes the three-dimensional structure of scatterers included in an object within a region using waves are shown below.

[0220] Here, the wave is, for example, a radio wave, and may be a microwave, millimeter wave, terahertz wave, or the like. Also, light, sound, or the like may be used as the wave. The object within the region may be a living body, a manufactured product, or a natural material. In particular, the imaging device may be used for mammography, and the object may be a breast.

[0221] Also, the scatterers included in the object within the region correspond to portions having physical characteristics different from those of the surrounding medium. Specifically, this physical characteristic is a physical characteristic corresponding to the reflectivity of the wave. When a radio wave is used as the wave, the physical characteristic may be the dielectric constant. And the scatterers included in the object may be steel bars included in reinforced concrete, tumors included in the breast, or the like. Also, the region to be measured may be equivalent to the region of the object.

[0222] FIG. 9 is a basic configuration diagram of the imaging device in the present embodiment. The imaging device 100 shown in FIG. 9 includes a plurality of transmitters 101, a plurality of receivers 102, and an information processing circuit 103. Also, the imaging device 100 may include a display 104.

[0223] Each of the plurality of transmitters 101 is a circuit that transmits a wave. Specifically, the plurality of transmitters 101 sequentially transmit waves. The plurality of transmitters 101 are arranged on both sides of the region to be measured.

[0224] Each of the multiple receivers 102 is a circuit that receives waves. The multiple receivers 102 may receive waves simultaneously in parallel. The multiple receivers 102, like the multiple transmitters 101, are arranged on both sides of the area to be measured. Furthermore, the multiple receivers 102 may be arranged in substantially the same position as the multiple transmitters 101, or may be arranged in a different position from the multiple transmitters 101.

[0225] Furthermore, the transmitter 101 and the receiver 102 may form a multistatic antenna or a monostatic antenna.

[0226] The information processing circuit 103 is a circuit that performs information processing. Specifically, the information processing circuit 103 visualizes the three-dimensional structure of scatterers contained in objects within the area based on measurement data obtained by the multiple transmitters 101 and the multiple receivers 102. For example, when visualizing the three-dimensional structure of scatterers based on the measurement data, the information processing circuit 103 performs arithmetic processing shown in the above-mentioned theory.

[0227] The information processing circuit 103 may be a computer or a computer processor. The information processing circuit 103 may read a program from a memory and execute the program to process information. The information processing circuit 103 may be a dedicated circuit for visualizing the three-dimensional structure of a scatterer based on measurement data.

[0228] Furthermore, the information processing circuitry 103 may generate an image showing the three-dimensional structure of the scatterer in order to visualize the three-dimensional structure of the scatterer.

[0229] The information processing circuit 103 may then visualize the three-dimensional structure of the scatterer by outputting an image showing the three-dimensional structure of the scatterer to a display 104 or the like. Alternatively, the information processing circuit 103 may visualize the three-dimensional structure of the scatterer by outputting an image showing the three-dimensional structure of the scatterer to a printer (not shown). Alternatively, the information processing circuit 103 may visualize the three-dimensional structure of the scatterer by transmitting the image as electronic data to another device (not shown) via wired or wireless communication.

[0230] The display 104 is a display device such as a liquid crystal display. The display 104 is an optional component and is not an essential component. The display 104 may also be an external device that is not part of the imaging device 100.

[0231] 10 is a conceptual diagram showing an example of the relationship between multiple transmitters 101, multiple receivers 102, and an area. As shown in FIG. 10, multiple transmitters 101 are arranged on both sides of the area to be measured. Similarly, multiple receivers 102 are arranged on both sides of the area to be measured. The multiple transmitters 101 and multiple receivers 102 may be arranged two-dimensionally on each of two measurement planes. Alternatively, the transmitters 101 and receivers 102 arranged on each of the two measurement planes may move, thereby performing transmission and reception at multiple transmission positions and multiple reception positions.

[0232] Fig. 11 is a conceptual diagram showing a modified example of the relationship between the area and the multiple transmitters 101 and the multiple receivers 102. As shown in Fig. 11, the multiple transmitters 101 and the multiple receivers 102 may be arranged on a curved surface on each side of the area.

[0233] Fig. 12 is a flowchart showing the basic operation of the imaging device 100 shown in Fig. 9. Specifically, the multiple transmitters 101, multiple receivers 102, and information processing circuit 103 of the imaging device 100 shown in Fig. 9 perform the operation shown in Fig. 10.

[0234] First, multiple transmitters 101 transmit waves to a region to be measured (S101). For example, the multiple transmitters 101 transmit the waves sequentially. Furthermore, multiple receivers 102 receive the waves from the region to be measured (S102). For example, the multiple receivers 102 receive the waves in parallel. The received waves can also be expressed as scattered waves. Then, the information processing circuit 103 visualizes the three-dimensional structure of scatterers included in objects within the region using measurement data obtained by the multiple transmitters 101 and the multiple receivers 102 (S103).

[0235] Specifically, the information processing circuit 103 derives a visualization function corresponding to the scattering field function related to the scattering of the wave in accordance with the correspondence between the measurement data and a combination of multiple functions related to multiple first-order scatterings that constitute multiple scattering, and then visualizes the three-dimensional structure of the scatterers contained in the object within the region using the visualization function.

[0236] This allows the imaging device 100 to apply a correspondence between the measurement data and a combination of multiple functions related to multiple first-order scattering to derive an imaging function for visualizing the three-dimensional structure of scatterers contained in objects within the region. Multiple scattering is assumed to be a combination of multiple first-order scattering. Therefore, the imaging device 100 can analytically solve the inverse problem of scattering, including multiple scattering, according to this correspondence. Therefore, the imaging device 100 can visualize the three-dimensional structure of scatterers contained in objects within the region with high accuracy.

[0237] For example, the information processing circuitry 103 may derive an imaging function corresponding to the scattered field function by solving an equation of the scattered field function based on the measurement data.

[0238]

number

[0239] where (x, y1, z1) indicates the transmitting position of the wave, (x, y2, z2) indicates the receiving position of the wave, k indicates the wave number of the wave, D indicates the area, (ξ, η, ζ) corresponds to the reflecting position of the wave, and ε corresponds to the unknown reflectivity at the reflecting position. Also, ρ1 indicates the distance from the transmitting position to the reflecting position, and ρ2 indicates the distance from the reflecting position to the receiving position.

[0240] Also, the equation for the scattered field function is

[0241]

number

[0242] This allows the imaging device 100 to visualize with high accuracy the three-dimensional structure of scatterers contained in objects within the region in accordance with the scattered field function associated with the scattering phenomenon and the equation satisfied by the scattered field function.

[0243] Furthermore, for example, the information processing circuitry 103 may derive an analytical solution to the equation based on the measurement data. Then, the information processing circuitry 103 may derive a visualization function based on the analytical solution. The analytical solution is given by

[0244]

number

[0245] where k x , k y1 and k y2 indicates the wave numbers of the scattered field function for x, y1, and y2. Also, a(k x , k y1 , k y2 , k) is k x , k y1 , k y2 and k, and s1(k x , k y1 , k y2 ) is k x , k y1 and k y2 Denote the function based on s2(k x , k y1 , k y2 ) is k x , k y1 and k y2 Here we show a function based on

[0246] This allows the imaging device 100 to visualize with high accuracy the three-dimensional structure of scatterers contained in objects within the region according to the analytical solution of the equation satisfied by the scattered field function associated with the scattering phenomenon.

[0247] Also, for example, the visualization function is

[0248]

number

[0249] This allows the imaging device 100 to visualize with high accuracy the three-dimensional structure of scatterers contained in objects within the region, in accordance with an imaging function that is appropriately associated with the scattered field function.

[0250] Furthermore, for example, multiple scattering may be expressed using four functions in spectral space corresponding to four fundamental solutions of the equation for the scattered field function. Furthermore, the relationship between the measurement data and the four functions may be expressed by a nonlinear integral equation. Then, the information processing circuitry 103 may derive the four functions from the measurement data according to the nonlinear integral equation. Then, the information processing circuitry 103 may derive an imaging function corresponding to the scattered field function using the four functions.

[0251] This allows the imaging device 100 to visualize with high accuracy the three-dimensional structure of scatterers contained in objects within the region, in accordance with the relational expressions that express multiple scattering.

[0252] For example, the measurement data is

[0253]

number

[0254] Then, the information processing circuit 103:

[0255]

number

[0256]

number

[0257] where a m1 , a m2 , a m3 , , a mL a1, a2, a3 and a4, which are expressed as x , k y1 , k y2 , k). Also, f2, f3, . . ., f L denotes the product of 2, 3, . . . , and L variables in parentheses, which correspond to 2, 3, . . . , and L scatterings applied from the transmission to the reception of the wave, respectively.

[0258]

number

[0259] Then, the information processing circuit 103:

[0260]

number

[0261]

number

[0262] This allows the imaging device 100 to visualize with high accuracy the three-dimensional structure of scatterers contained in objects within the region, in accordance with an equation based on the theory of multiple scattering.

[0263] For example, the measurement data is

[0264]

number

[0265] Then, the information processing circuit 103:

[0266]

number

[0267]

number

[0268] where a m a1, a2, a3 and a4, which are expressed as x , k y1 , k y2 , k). Also, Φ m1n1 , Φ m2n2 , Φ m3n3 , , Φ mLnL Φ expressed as 11 , Φ 12 , Φ 21 and Φ 22 corresponds to the measurement data for the four scattering modes. Also, g2, g3, . . ., g L denotes the product of 2, 3, . . . , and L variables in parentheses, corresponding to 2, 3, . . . , and L scatterings applied from transmission to reception of the wave, respectively.

[0269] Also,

[0270]

number

[0271] Then, the information processing circuit 103:

[0272]

number

[0273]

number

[0274] This allows the imaging device 100 to visualize with high accuracy the three-dimensional structure of scatterers contained in objects within the region, in accordance with an equation in which the measurement data is appropriately associated based on the theory of multiple scattering.

[0275] For example, the measurement data is

[0276]

number

[0277] Then, the information processing circuit 103:

[0278]

number

[0279] where δ denotes the delta function and k xa , k xb , k xc is k x is the variable corresponding to k η and k η2 is k y1 is the variable corresponding to k η3 is k y2 is a variable corresponding to O(a 4 ) is a term corresponding to fourth-order or higher scattering.

[0280] Then, the information processing circuit 103:

[0281]

number

[0282]

number

[0283] This allows the imaging device 100 to visualize with high accuracy the three-dimensional structure of scatterers contained in objects within the region according to an equation that specifically expresses the scattering phenomenon based on the theory of multiple scattering.

[0284] For example, the measurement data is

[0285]

number

[0286] Then, the information processing circuit 103:

[0287]

number

[0288] where δ denotes the delta function and k xa , k xb , k xc is k x is the variable corresponding to k η and k η2 is k y1 is the variable corresponding to k η3 is k y2 is the variable corresponding to

[0289] Then, the information processing circuit 103:

[0290]

number

[0291]

number

[0292] As a result, the visualization device 100 can visualize the three-dimensional structure of scatterers contained in objects within the region with high accuracy, according to an equation that specifically expresses the scattering phenomenon based on the theory of multiple scattering and appropriately corresponds to the measurement data.

[0293] For example, the measurement data is

[0294]

number

[0295] Then, the information processing circuit 103:

[0296]

number

[0297] Then, the information processing circuit 103:

[0298]

number

[0299]

number

[0300] This allows the imaging device 100 to visualize with high accuracy the three-dimensional structure of scatterers contained in objects within the region, in accordance with an equation arranged based on the theory of multiple scattering.

[0301] Furthermore, for example, the scattered field function may be determined as a function that inputs a wave transmission position and a wave reception position and outputs a value indicating the wave at the reception position. Furthermore, the imaging function may be determined based on a value output from the scattered field function by inputting the imaging target position as the transmission position and the reception position into the scattered field function. The information processing circuitry 103 may derive the scattered field function using the measurement data as a boundary condition, and may derive the imaging function using the scattered field function.

[0302] Furthermore, for example, other components, equations, variables, etc. shown in this embodiment can be applied as appropriate to the multiple transmitters 101, multiple receivers 102, information processing circuit 103, scattered field function, and visualization function shown in the above basic configuration and basic operation.

[0303] Furthermore, the scattering field function, imaging function, etc. shown in this embodiment may be modified as appropriate and applied. For example, a mathematical expression that expresses substantially the same content as the above mathematical expression in a different way may be used, or another mathematical expression derived based on the above theory may be used.

[0304] In addition, in the above description, expressions of fundamental solutions and expressions of analytical solutions may be interpreted interchangeably.

[0305] FIG. 13 is a block diagram showing a specific configuration of the imaging device 100 shown in FIG.

[0306] The transmitter 101 and the receiver 102 of the imaging device 100 shown in Fig. 9 may be included in a multistatic array antenna 1008. The information processing circuit 103 of the imaging device 100 shown in Fig. 9 may correspond to one or more of the components shown in Fig. 13. Specifically, for example, the information processing circuit 103 may correspond to the signal processing computer 1005. Furthermore, the display 104 shown in Fig. 9 may correspond to the signal monitoring device 1006.

[0307] The microwave signal used in the imaging device 100 is a pseudorandom time-series signal (PN code: Pseudo Noise Code) having frequency components from DC to 20 GHz. This signal is output from a PN code generation FPGA board 1002. More specifically, there are two types of this signal. One type of signal (LO signal: local oscillator signal) is sent to an RF detection circuit (RF detection board 1007) through a delay circuit (digital control board 1003).

[0308] The other type of signal (RF signal: Radio Frequency Signal) is sent to and radiated from the transmitting microwave UWB antenna of the multistatic array antenna 1008. The scattered microwave signal is received by the receiving UWB antenna of the multistatic array antenna 1008 and sent to the RF detection circuit (RF detection board 1007), where the transmitted and received signals pass through the antenna element selection switch (UWB antenna RF switch 1004).

[0309] In addition, the delayed signal (LO signal) is 1 / 2 the time it takes for the value of the PN code to change. n The detected signal is delayed by a time of n times (n is an integer greater than 2). The detected signal is A / D converted and stored as an IF signal (Intermediate Frequency Signal) by signal processing computer 1005. Information indicating the detected signal may also be displayed on signal monitoring device 1006.

[0310] The timing of this series of operations is controlled by a microprocessor in the digital control board 1003 so as to be synchronized with a signal (distance signal or free-run signal) from the rangefinder 1001. For example, the microprocessor in the digital control board 1003 transmits a switch switching signal, a PN code sweep trigger, etc.

[0311] Furthermore, the signal processing computer 1005 performs three-dimensional reconstruction using the A / D converted and stored signals, and displays a three-dimensional image. The signal processing computer 1005 may also perform signal calibration. The signal processing computer 1005 may also display raw waveforms. For example, the signal processing computer 1005 may also store three-dimensional images, etc. in the memory 1009.

[0312] The configuration shown in Fig. 13 is an example, and the configuration of imaging device 100 is not limited to the configuration shown in Fig. 13. Part of the configuration shown in Fig. 13 may be omitted or changed.

[0313] (supplement) Although the above describes aspects of the imaging device based on the embodiments, the aspects of the imaging device are not limited to the embodiments. Modifications conceivable by those skilled in the art may be made to the embodiments, and multiple components in the embodiments may be combined in any manner. For example, a process performed by a specific component in the embodiments may be performed by another component instead of the specific component. Furthermore, the order of multiple processes may be changed, and multiple processes may be performed in parallel.

[0314] Furthermore, the imaging method including the steps performed by each component of the imaging device may be executed by any device or system. For example, a part or all of the imaging method may be executed by a computer including a processor, a memory, an input / output circuit, etc. In this case, the imaging method may be executed by the computer executing a program for causing the computer to execute the imaging method.

[0315] The above program may also be recorded on a non-transitory computer-readable recording medium.

[0316] Furthermore, each component of the imaging device may be configured with dedicated hardware, general-purpose hardware that executes the above-mentioned programs, or a combination of these. The general-purpose hardware may be configured with a memory in which the programs are recorded and a general-purpose processor that reads and executes the programs from the memory. Here, the memory may be a semiconductor memory or a hard disk, and the general-purpose processor may be a CPU.

[0317] Furthermore, the dedicated hardware may be configured with a memory, a dedicated processor, etc. For example, the dedicated processor may execute the visualization method described above by referring to a memory for recording measurement data.

[0318] Furthermore, each component of the imaging device may be an electric circuit. These electric circuits may form a single electric circuit as a whole, or each may be a separate electric circuit. These electric circuits may correspond to dedicated hardware, or may correspond to general-purpose hardware that executes the above-mentioned programs, etc. [Industrial Applicability]

[0319] One aspect of the present disclosure is useful for an imaging device that uses waves to visualize the three-dimensional structure of scatterers contained in objects within a region, and is applicable to geophysical exploration, medical diagnosis, and the like. [Explanation of symbols]

[0320] 100 Imaging Device 101 Transmitter 102 Receiver 103 Information Processing Circuit 104 Display 1001 Distance meter 1002 FPGA board for PN code generation 1003 Digital Control Board 1004 UWB Antenna RF Switch 1005 Signal Processing Computer 1006 Signal monitoring device 1007 RF detector board 1008 Multistatic Array Antenna 1009 Memory

Claims

1. a plurality of transmitters arranged on both sides of a region to be measured and transmitting waves to the region; a plurality of receivers disposed on both sides and receiving the waves from the region; an information processing circuit that derives a visualization function corresponding to a scattering field function related to the scattering of the wave in accordance with correspondence between measurement data obtained by the plurality of transmitters and the plurality of receivers and a synthesis of a plurality of functions related to a plurality of first-order scatterings that constitute multiple scattering, and visualizes a three-dimensional structure of a scatterer included in an object within the region using the visualization function; Imaging device.

2. the information processing circuit derives the imaging function corresponding to the scattered field function by solving an equation of the scattered field function based on the measurement data; The scattered field function is [Equation 1] (x, y １ , z １ ) indicates the transmitting position of the wave, and (x, y ２ , z ２ ) denotes the receiving position of the wave, k denotes the wave number of the wave, D denotes the area, (ξ, η, ζ) corresponds to the reflection position of the wave, ε corresponds to the unknown reflectivity at the reflection position, and ρ １ denotes the distance from the transmitting position to the reflecting position, and ρ ２ indicates the distance from the reflection position to the reception position, The equation is: [Equation 2] and Δ ５ is x, y １ , y ２ , z １ and z ２ where c denotes the propagation speed of the wave, and t denotes the time from transmission to reception of the wave. The imaging device of claim 1 .

3. the information processing circuit derives an analytical solution of the equation based on the measurement data, and derives the visualization function based on the analytical solution; The analytical solution is [Equation 3] and k ｘ , k ｙ１ and k ｙ２ are the x, y values ​​of the scattered field function １ and y ２ indicates the wave number for a(k ｘ , k ｙ１ , k ｙ２ , k) is k ｘ , k ｙ１ , k ｙ２ and k, and s １ (k ｘ , k ｙ１ , k ｙ２ ) is k ｘ , k ｙ１ and k ｙ２ denotes a function based on s ２ (k ｘ , k ｙ１ , k ｙ２ ) is k ｘ , k ｙ１ and k ｙ２ Show functions based on 3. The imaging device of claim 2.

4. the information processing circuit derives the visualization function based on the analytical solution; The visualization function is [Equation 4] where (x, y, z) indicates the position of the object to be visualized.

4. The imaging device of claim 3.

5. the multiple scattering is expressed using four functions in spectral space corresponding to four fundamental solutions of an equation for the scattered field function; The relationship between the measurement data and the four functions is expressed by a nonlinear integral equation, The information processing circuit deriving the four functions from the measurement data according to the nonlinear integral equation; Derive the imaging function corresponding to the scattered field function using the four functions. The imaging device of claim 1 .

6. The measurement data is [Equation 5] and Φ ｉｊ Φ expressed as １１ , Φ １２ , Φ ２１ and Φ ２２ corresponds to the measurement data for four scattering modes, two forward scattering modes corresponding to two directions and two backward scattering modes corresponding to two directions; The information processing circuit [Equation 6] The effect of multiple scattering was removed using [Equation 7] Derive a ｍ１ , a ｍ２ , a ｍ３ , ..., a ｍＬ a expressed as １ , a ２ , a ３ and a ４ is the a(k ｘ , k ｙ１ , k ｙ２ , k), and f ２ , f ３ , ..., f Ｌ denotes a product of 2, 3, ..., L variables in parentheses corresponding to 2, 3, ..., L scatterings applied from transmission to reception of the wave, respectively, [Equation 8] is f ２ , f ３ , ..., f Ｌ denotes a wave vector with respect to coordinate variables contained in two, three, ..., L variables in the brackets, The information processing circuit [Equation 9] as the scattered field function, [Equation 10] is derived as the visualization function.

5. The imaging device of claim 4.

7. The measurement data is [0011] and Φ ｉｊ Φ expressed as １１ , Φ １２ , Φ ２１ and Φ ２２ corresponds to the measurement data for four scattering modes, two forward scattering modes corresponding to two directions and two backward scattering modes corresponding to two directions; The information processing circuit [0012] The effect of multiple scattering was removed using [0013] Derive a ｍ a expressed as １ , a ２ , a ３ and a ４ is the a(k ｘ , k ｙ１ , k ｙ２ , k), and Φ ｍ１ｎ１ , Φ ｍ２ｎ２ , Φ ｍ３ｎ３ , ..., Φ ｍＬｎＬ Φ expressed as １１ , Φ １２ , Φ ２１ and Φ ２２ corresponds to the measurement data for the four scattering modes, and g ２ , g ３ , ..., g Ｌ denotes a product of 2, 3, ..., L variables in parentheses corresponding to 2, 3, ..., L scatterings applied from transmission to reception of the wave, respectively, [0014] is g ２ , g ３ , ..., g Ｌ denotes a wave vector with respect to coordinate variables contained in two, three, ..., L variables in the brackets, The information processing circuit [Equation 15] as the scattered field function, [0016] is derived as the visualization function.

5. The imaging device of claim 4.

8. The measurement data is [Equation 17] and Φ ｉｊ Φ expressed as １１ , Φ １２ , Φ ２１ and Φ ２２ corresponds to the measurement data for four scattering modes, two forward scattering modes corresponding to two directions and two backward scattering modes corresponding to two directions; The information processing circuit [Equation 18] The effect of multiple scattering is removed using １ Derive δ denotes the delta function, and k ｘａ , k ｘｂ , k ｘｃ is k ｘ is a variable corresponding to k η and k η２ is k ｙ１ is a variable corresponding to k η３ is k ｙ２ is a variable corresponding to O(a ４ ) is a term corresponding to fourth-order or higher scattering, The information processing circuit [Equation 19] as the scattered field function, [Equation 20] is derived as the visualization function.

5. The imaging device of claim 4.

9. The measurement data is [Equation 21] and Φ ｉｊ Φ expressed as １１ , Φ １２ , Φ ２１ and Φ ２２ corresponds to the measurement data for four scattering modes, two forward scattering modes corresponding to two directions and two backward scattering modes corresponding to two directions; The information processing circuit [Equation 22] The effect of multiple scattering is removed using １ Derive δ denotes the delta function, and k ｘａ , k ｘｂ , k ｘｃ is k ｘ is a variable corresponding to k η and k η２ is k ｙ１ is a variable corresponding to k η３ is k ｙ２ is the variable corresponding to The information processing circuit [Equation 23] as the scattered field function, [0000] is derived as the visualization function.

5. The imaging device of claim 4.

10. The measurement data is [Equation 25] and Φ ｉｊ Φ expressed as １１ , Φ １２ , Φ ２１ and Φ ２２ corresponds to the measurement data for four scattering modes, two forward scattering modes corresponding to two directions and two backward scattering modes corresponding to two directions; The information processing circuit [Equation 26] The effect of multiple scattering is removed using １ Derive δ denotes the delta function, and k ｘａ , k ｘｂ , k ｘｃ is k ｘ is a variable corresponding to k η and k η２ is k ｙ１ is a variable corresponding to k η３ is k ｙ２ is the variable corresponding to The information processing circuit [0000] as the scattered field function, [0000] is derived as the visualization function.

5. The imaging device of claim 4.

11. transmitting waves into the area to be measured by a plurality of transmitters positioned on either side of the area; receiving the waves from the region by a plurality of receivers disposed on both sides; and a step of deriving an imaging function corresponding to a scattering field function related to the scattering of the wave according to correspondence between measurement data obtained by the plurality of transmitters and the plurality of receivers and a synthesis of a plurality of functions related to a plurality of first-order scatterings that constitute multiple scattering, and visualizing a three-dimensional structure of a scatterer included in an object within the region using the imaging function. Visualization method.

Images