Imaging 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

Visualization device and imaging method

[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.

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

[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 tomographic image of the object to be inspected is displayed.

[0004] Japanese Patent Application Laid-Open No. 62-66145 International Publication No. 2014 / 125815 International Publication No. 2015 / 136936 International Publication No. 2021 / 020387 International Publication No. 2021 / 053971

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

[0006] Furthermore, multiple scatterings (reflections) may occur within a region for a single wave transmission. That is, 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. An analysis method that does 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.

[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.

[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.

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

[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] and (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 denotes the distance from the reflection location to the reception location, and the equation is:

[0016] 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.

[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] 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 Here we show a function based on

[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] where (x, y, z) indicates the position of the object to be visualized.

[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 a relational expression that expresses multiple scattering.

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

[0027] and Φ ｉｊΦ expressed as １１ , Φ １２ , Φ ２１ and Φ ２２ corresponds to the measurement data relating to four scattering forms, namely, two forward scatterings corresponding to two directions and two backward scatterings corresponding to two directions, and the information processing circuit is

[0028] The effect of multiple scattering was removed using

[0029] 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,

[0030] is f ２ , f ３ , ..., f Ｌ represents a wave vector related to coordinate variables included in two, three, ..., L variables in the parentheses, and the information processing circuit is

[0031] as the scattered field function,

[0032] is derived as the visualization function.

[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] and Φ ｉｊ Φ expressed as １１ , Φ １２ , Φ ２１ and Φ ２２ corresponds to the measurement data relating to four scattering forms, namely, two forward scatterings corresponding to two directions and two backward scatterings corresponding to two directions, and the information processing circuit is

[0036] The effect of multiple scattering was removed using

[0037] 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,

[0038] is g ２ , g ３ , ..., g Ｌ represents a wave vector related to coordinate variables included in two, three, ..., L variables in the parentheses, and the information processing circuit is

[0039] as the scattered field function,

[0040] is derived as the visualization function.

[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] and Φ ｉｊ Φ expressed as １１ , Φ １２ , Φ ２１ and Φ ２２ corresponds to the measurement data relating to four scattering forms, namely, two forward scatterings corresponding to two directions and two backward scatterings corresponding to two directions, and the information processing circuit is

[0044] The effect of multiple scattering is removed using １ is derived, 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 or higher order scattering, and the information processing circuit

[0045] as the scattered field function,

[0046] is derived as the visualization function.

[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] and Φ ｉｊ Φ expressed as １１ , Φ １２ , Φ２１ and Φ ２２ corresponds to the measurement data relating to four scattering forms, namely, two forward scatterings corresponding to two directions and two backward scatterings corresponding to two directions, and the information processing circuit is

[0050] The effect of multiple scattering is removed using １ is derived, 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 and the information processing circuit is a variable corresponding to

[0051] as the scattered field function,

[0052] is derived as the visualization function.

[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] and Φ ｉｊ Φ expressed as １１ , Φ １２ , Φ ２１ and Φ ２２ corresponds to the measurement data relating to four scattering forms, namely, two forward scatterings corresponding to two directions and two backward scatterings corresponding to two directions, and the information processing circuit is

[0056] The effect of multiple scattering is removed using １ is derived, δ denotes the delta function, and k ｘａ , k ｘｂ , k ｘｃ is k ｘis a variable corresponding to k η and k η２ is k ｙ１ is a variable corresponding to k η３ is k ｙ２ and the information processing circuit is a variable corresponding to

[0057] as the scattered field function,

[0058] is derived as the visualization function.

[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 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, 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 the 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] Furthermore, in the following description, the technologies described in Patent Documents 2, 3, 4, and 5 may be particularly referred to as existing technologies. Furthermore, 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. Furthermore, imaging 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) An imaging device according to this embodiment uses waves to visualize the three-dimensional structure of scatterers contained in objects within a region. The imaging device according to this embodiment will be described in detail below, including the underlying technology and theory.

[0065] <I. Overview> 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. Because it allows accurate three-dimensional reconstructed images to be calculated instantaneously from measurement data, it is expected to be applied to fields such as diagnostic imaging. In this disclosure, the scattered field theory has been developed to solve the difficult problem of the inverse scattering problem of multiple scattering (multiple reflection), and an imaging device and imaging method using the developed scattered field theory are presented.

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

[0067]

[0068] Here, (x, y １ , z １ ) indicates the coordinates of the radiation point of the wave, and (x, y ２ , z ２) indicates the coordinates of the receiving point of the wave. 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) corresponds to the reflection point of the wave. ρ １ denotes the distance from the transmitting point to the reflecting point, and ρ ２ indicates the distance from the reflection point to the reception point, where 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 point and reception point. By defining the emission point and reception point within the entire region, the above φ is used as a 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]

[0071] Here, Δ ５ is x, y １ , y ２ , z １ and z ２ represents the five-dimensional Laplace operator with respect to . ∂ represents the partial derivative of the variable indicated by the suffix. c represents the wave propagation speed. t represents time. Furthermore, the general solution of the differential equation in equation (1-2) is expressed as the following equation (1-3).

[0072]

[0073] Here, k ｘ , k ｙ１ and k ｙ２ are the x and y scattering field functions １ , y ２ Since the solution of a fourth-order partial differential equation is completely determined by measurements (radar reflection data) at the boundary of the domain, the kernel function of this general solution, a(k ｘ , k ｙ１ , k ｙ２ , k) can also be obtained by Fourier transform. ２ →y １The visualization function ρ is obtained by applying the limit value of t→0. For example, the visualization function ρ is expressed as in the following equation (1-4).

[0074]

[0075] In the above process, based on the assumption that there is no multiple scattering, the scattered field function φ(x, y １ , y ２ , z １ , z ２ , k) is directly linked to the measurement values ​​(radar reflection data) at the boundary of the region. For example, the shape of the boundary surface is defined by a curve z = f(y) on the zy plane. The data obtained by Fourier transforming the radar reflection data measured at the boundary surface with respect to (x, t) is Φ(k ｘ , y Ｉ , y Ｊ , k). If it is assumed that there is no multiple scattering, the following equation (1-5) is assumed to hold.

[0076]

[0077] However, if multiple scattering cannot be ignored, second, third and fourth order scattering may be present, as shown in FIG.

[0078] FIG. 1 is a conceptual diagram showing an example of the order of multiple scattering (multiple reflection) in the embodiment. １ indicates the transmitting point, and P ２ indicates the receiving point. １ is transmitted from P through a number of reflections corresponding to the order in the region. ２ The multiple reflections are called multiple reflections or multiple scattering.

[0079] This disclosure describes a method for solving the inverse problem of scattering, including multiple scattering, as described above, and an imaging device and imaging method that use the method.

[0080] To perform the inverse analysis of multiple scattering, radar reflection data from the entire domain boundary is used. Second-order and higher multiple scattering can be solved by four fundamental solutions of the partial differential equation of the scattering field, E １ , E ２ , E３ , E ４ It is expressed by a combination (synthesis) of the above.

[0081] FIG. 2 shows four types of scattering forms corresponding to four types of fundamental solutions of the scattering field equation. The scattering forms can also be expressed as scattering models. Multiple scattering occurs in these four types of fundamental solutions (E １ , E ２ , E ３ , E ４ ) is expressed by the synthesis of E １ , E ２ , E ３ and E ４ Corresponding to a １ , a ２ , a ３ and a ４ To determine these from the measurement data, two backscattering and forward scattering measurements are performed.

[0082] Inverse scattering analysis of multiple scattering in a three-dimensional domain is a challenging problem, but the present disclosure provides a solution to the inverse scattering problem using scattered field theory.

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

[0084]

[0085] where φ is an unknown function that indicates the displacement of the vibration at the position (x, y, z). ３ denotes the three-dimensional Laplace operator. k denotes the wave number. (ξ, η, ζ) denotes the position of the wave source.

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

[0087]

[0088] Here, k ｘ indicates the wave number with respect to x. ｙ denotes the wave number related to y. Equation (2-1) is transformed into equations (2-3) and (2-4).

[0089]

[0090]

[0091] where ∂ ｚ ２ indicates the second partial differential with respect to z. a(k ｘ , k ｙ , k) is (k ｘ , k ｙ , k).

[0092] <II-2 Fundamental Solution of Scattered Field> Figure 3 is a conceptual diagram regarding the definition of the Green's function. Unless otherwise specified below, the transmitting point and the receiving point have the same x coordinate. １ = (x, y １ , z １ ) and r ２ = (x, y ２ , z ２ ), the Green's function is defined as the following equation (2-5).

[0093]

[0094] The kernel function is r １ It comes out from the point ξ and reflects at point r ２ where ε is a function of the dielectric constant.

[0095]

[0096] The above φ(x, y １ , y ２ , z １ , z ２ ) is the solution of the partial differential equation of the scattered field as shown in the following equation (2-7).

[0097]

[0098] Next, the solution of equation (2-7) is examined. First, let φ be the vector of t, x, y. １ , y ２ By performing a multiple Fourier transform on D and transforming equation (2-7), the following equation (2-8) is obtained.ｚ１ , D ｚ２ are respectively z １ , z ２ Show the partial derivative with respect to

[0099]

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

[0101]

[0102] Here, s １ , s ２ is expressed as the following equation (2-10).

[0103]

[0104] The scattering corresponding to the four fundamental solutions of Equation (2-9) is as shown in Figure 2. Among these four fundamental solutions, E ３ and E ４ and have a time-reverse relationship with each other and are not independent. １ , E ２ , E ３ 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]

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

[0107] <III Multiple Scattering> <III-1 Order of Multiple Scattering> The order of multiple scattering is as shown in Figure 1. Even for each order of multiple scattering shown in Figure 1, there are many different geometric variations at the location where scattering occurs. The characteristics differ depending on whether the z-coordinate component of each directional vector of incidence and scattering at the location where scattering occurs. The fact that the characteristics differ depending on whether the z-coordinate component of each directional vector of incidence and scattering is positive or negative is explained in the fundamental solution of the scattered field in Chapter II.

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

[0109]

[0110] Scattered point S １ , S ２ , S ３ is an arbitrary point in the region, but the condition of observing the geometric rules is the scattered point S １ , S ２ , S ３ Specifically, the sign of the z-coordinate component of the directional vector indicated by the arrow representing the wave propagation in FIG. 4 is maintained. Furthermore, P １ , P ２ , S ２ and S ３ move within the measurement plane under the condition that their x coordinates are equal. １ and P ２ The z coordinates are equal. １ It is assumed that there are no restrictions on the x coordinate for

[0111] FIG. 5 is a diagram showing the propagation path of the wave. Specifically, FIG. 5 shows the fundamental solution E １ and E ２ When a common transmission point P １ and a common receiving point P ２ These multiple propagation paths correspond to the geometric rules above.

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

[0113]

[0114] Here, G (specifically, G １ and G ２) is a Green's function and is defined as the following equation (3-3).

[0115]

[0116] where:

[0117] is r １ It comes out from the point ξ and reflects at point r ２ The suffixes 1 and 2 on the Green's function indicate the signal strength of the wave returning to the fundamental solution E １ , E ２ In a theory that does not consider multiple scattering, the second and subsequent terms on the right side of equation (3-2) can be ignored to obtain the following equation (3-4).

[0118]

[0119] a in formula (2-11) １ (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), G １ (P １ , P ２ , k) is obtained, and a more accurate １ (k ｘ , k ｙ１ , k ｙ２ , k) is obtained.

[0120] By the way, the right side of equation (3-2) contains G ２ (S ２－ , S ３－ , k) is included. In order to obtain this by measurement, the measurement results for a surface with a different z value from the above are used. Φ ２ (P １ , P ２ , k) indicate the measurement results on a surface with different z values, the following equation (3-5) holds.

[0121]

[0122] This allows us to obtain a more accurate a １ (k ｘ , kｙ１ , k ｙ２ , k) can be found.

[0123] <III-3 Formulation of the inverse scattering problem in multiple scattering> (1) Second-order scattering Figure 6 is a conceptual diagram showing an example of application of the fundamental solution of the scattering field for second-order scattering. As shown in Figure 6, second-order scattering is １ and E ４ Toga S ２－ It corresponds to the connected form. ２－ is as S as possible ２ It is assumed that the basic solution E ３ , E ４ Well then, S. ２－ From P ２ The condition that no direct waves propagating directly to the

[0124] The path of the second-order scattering is shown in FIG. 6 and the path P in FIG. １ and P ２ The solution is limited to the path where the and are interchanged (path that has been symmetrically transformed). １ and E ４ are applied as shown in FIG. 6, and the function name is given as in the following equation (3-6).

[0125]

[0126] Here, (x, y １ , z) is P １ corresponds to the position of (x, y ２ , z) is P ２ corresponds to the position of (x, η ２－ , ζ ２－ ) is S ２－ A specific expression of the formula (3-6) is expressed as the following formula (3-7) according to the formula (2-11).

[0127]

[0128] Second-order multiple scattering path P １ →S １ →S ２－ →S ２ →P ２ The synthesis of the above functions corresponding to is expressed as the following equation (3-8).

[0129]

[0130] In equation (3-8), η ２－ →η and ζ ２－ → Apply ζ to point S ２ By integrating with respect to the coordinates (η, ζ), the following equation (3-9) is obtained.

[0131]

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

[0133]

[0134] Here, δ represents a delta function. 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－ At z=0, the input and output are the same. １ , y ２ ), the following equation (3-11) is obtained.

[0135]

[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 FIG. 4. With reference to FIG. 4, the scattered field function is defined as in the following equation (3-12). The suffixes 2- and 3- for η and ζ respectively represent the scattering field function of the point S ２ Just before, point S ３ It corresponds to the character immediately before .

[0137]

[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]

[0140] The synthesis of the above equations gives the third-order multiple scattering path P １ →S １ →S ２ →S ３ →P ２ and is expressed as the following equation (3-14).

[0141]

[0142] In equation (3-14), η ２－ →η ２ , η ３－ →η ３ , ζ ２－ →ζ ２ and ζ ３－ →ζ ３ Applying S ２ , S ３ The coordinates of the point (η ２ , ζ ２ ), (η ３ , ζ ３ ), the following equation (3-15) is obtained.

[0143]

[0144] The function obtained by the above process is P １ , P ２ This shows the third-order scattering amplitude as seen from the plane of the wave number k. 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 needed to avoid confusion with integral symbols.

[0145]

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

[0147]

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

[0149]

[0150] Here, δ represents a delta function, which corresponds to the input and output being equal at the connection point. At z=0, we convert equation (3-18) into (x, y １ , y ２ ), the following equation (3-19) is obtained.

[0151]

[0152] The scattered field function Ψ(x, y １ , y ２ , z, k) is expressed as in the following equation (3-20) when multiple scattering is taken into consideration.

[0153]

[0154] where Ψ １ is the scattered field function corresponding to the first scattering, and Ψ ２ is the scattered field function corresponding to the second scattering, and Ψ ３ is a scattered field function corresponding to third-order scattering. Based on equation (2-11) etc., the following equation (3-21) holds.

[0155]

[0156] For example, if the second and fourth terms onwards on the right hand side of equation (3-20) can be ignored, the following equation (3-22) can be obtained by Fourier transforming the entire equation (3-20).

[0157]

[0158] Measurement data Φ at z = 0 １ Using (k), the left side of equation (3-22) can be expressed as the following equation (3-23).

[0159]

[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. Therefore, equation (3-22) is a １ (k ｘ , k ｙ１ , k ｙ２ , k) and a ２ (k ｘ , k ｙ１ , k ｙ２, k) is a general nonlinear integral equation.

[0161] A similar equation is obtained for the other boundary surface, expressed as z = h. Although this integral equation is nonlinear, it can be solved very easily using a Neumann series expansion. The inverse scattering problem can be solved just like the forward scattering problem.

[0162] <III-4 Fundamental equations for the inverse scattering problem considering all models> Figure 7 is a diagram showing four types of scattering models related to third-order scattering. Specifically, D1, D2, D3, and D4 in Figure 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 Figure 7, the fundamental solution E １ ~E ４ The region to which is applied is indicated by a dashed line. The following equations (3-24), (3-25), (3-26), (3-27) and (3-28) show the scattered field functions of D1 to D4.

[0163]

[0164]

[0165]

[0166]

[0167]

[0168] In the above equation, (η ２－ , ζ ２－ ) and (η ３－ , ζ ３－ ) are the points S ２ Just before and point S ３ represents the coordinates of the point immediately before .

[0169] The composition of the above functions is the third-order multiple scattering path P １ →S １ →S ２ →S ３ →P ２ and is expressed as the following equation (3-29).

[0170]

[0171] In equation (3-29), η ２－ →η ２ , η ３－ →η ３ , ζ ２－ →ζ ２ and ζ ３－ →ζ ３ Applying this, point S ２ , S ３ The coordinates of (η ２ , ζ ２ ), (η ３ , ζ ３ ), the following equation (3-30) is obtained.

[0172]

[0173] (η ２ , ζ ２ ), (η ３ , ζ ３ ) and integrate the result with respect to (x, y １ , y ２ ), equations (3-31), (3-32), (3-33) and (3-34) are obtained.

[0174]

[0175]

[0176]

[0177]

[0178] <III-5 Integral equation for inverse scattering problem in multiple scattering> Scattered field function Ψ(x, y １ , y ２ , z, k) is expressed as in the following equation (3-35) when multiple scattering is taken into consideration.

[0179]

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

[0181]

[0182]

[0183] where:

[0184] is the measurement value of the multistatic radar at z = 0. Therefore, this equation (3-37) is １ (k ｘ , k ｙ１ , k ｙ２ , k), a ２ (k ｘ , k ｙ１ , k ｙ２ , k), a ３ (k ｘ , k ｙ１ , k ｙ２ , k), and a ４ (k ｘ , k ｙ１ , k ｙ２ , k).

[0185] To solve this integral equation including the multiple scattering term, two measurements on the z = const plane are used. It is very easy to solve this integral equation based on the measurements. The result is obtained in the form of a Neumann series. Note that O(a ４ ) is a term corresponding to fourth or higher order scattering 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 four types of measurement data. That is, the four types of measurement data for 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]

[0188] The right-hand sides of the four equations in equation (3-38) represent four types of functions obtained by Fourier transforming 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 consideration, １ (k ｘ , k ｙ１ , k ｙ２, k) are found. In the following, the suffix "0" is attached 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 FIG.

[0190]

[0191] a １ , a ２ , a ３ and a ４ By expanding into a series corresponding to the order of scattering, the following equation (3-40) is obtained. １ , a ２ , a ３ and a ４ with a suffix related to the order of scattering.

[0192]

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

[0194]

[0195] From this equation (3-41), 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 sign, we obtain the following equation (3-42).

[0197]

[0198] In addition, the "+..." in equation (3-42) represents a term corresponding to fourth-order or higher scattering and may be omitted. By rearranging equation (3-42), the following equation (3-43) is obtained.

[0199]

[0200] a in formula (3-43) １ corresponds to the first, second and third scattering. Specifically, the influence of the second and third scattering is removed from the measurement data, and a １ By using a similar procedure, the a corresponding to higher order scattering is derived. １ may be derived. ２ , a ３ and a ４ can be derived in a similar manner. The general solution of the scattered field equation is a １ Using this, it is expressed as the following equation (3-44).

[0201]

[0202] The visualization function ρ(x, y, z) is expressed by φ in the above equation (3-44). １ Using this, it is expressed as the following equation (3-45).

[0203]

[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 in the following equation (3-46): Then, equation (3-46) may be used as equation (3-41).

[0206]

[0207] Here, a ｍ１ , a ｍ２ , a ｍ３ , ..., a ｍＬ a expressed as １ , a ２ , a ３ and a ４ is the analytical solution for the four scattering modes, a(k ｘ , k ｙ１ , k ｙ２ , k). ２ , f ３ , ..., f Ｌ denotes the product of 2, 3, . . . , L variables in parentheses corresponding to 2, 3, . . . , L scatterings, respectively.

[0208] Also,

[0209] is f ２ , f ３ , ..., f Ｌ denotes a wave vector related to coordinate variables contained in two, three, ..., L variables in the parentheses.

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

[0211]

[0212] Here, a ｍ a expressed as １ , a ２ , a ３ and a ４ is the analytical solution for the four scattering modes, a(k 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. ２ , g ３ , ..., g Ｌ denotes the product of 2, 3, . . . , L variables in parentheses corresponding to 2, 3, . . . , L scatterings applied from transmission to reception of a wave, respectively.

[0213] Also,

[0214] is g ２ , g ３ , ..., g Ｌ denotes a wave vector related to coordinate variables contained in two, three, ..., L variables in the parentheses.

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

[0216]

[0217] The visualization function may also be generalized as in the following equation (3-49).

[0218]

[0219] <IV. Configuration and Operation of Imaging Apparatus> Based on the above, the configuration and operation of an imaging apparatus that uses waves to visualize the three-dimensional structure of scatterers contained in an object within a region will be described below.

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

[0221] Furthermore, scatterers contained in an object within the region correspond to portions having physical properties different from those of the surrounding medium. Specifically, this physical property is a physical property corresponding to the reflectivity of the wave. When radio waves are used as the wave, the physical property may be the dielectric constant. Furthermore, scatterers contained in the object may be rebar contained in reinforced concrete, a tumor contained in a breast, or the like. Furthermore, the region to be measured may be the same as the region of the object.

[0222] 9 is a diagram showing the basic configuration of an imaging device according to this 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. The imaging device 100 may also include a display 104.

[0223] Each of the multiple transmitters 101 is a circuit that transmits waves. Specifically, the multiple transmitters 101 transmit waves in sequence. The multiple transmitters 101 are arranged on both sides of the area 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 circuitry 103 may then visualize the three-dimensional structure of the scatterer by outputting an image showing the three-dimensional structure of the scatterer to the display 104 or the like. Alternatively, the information processing circuitry 103 may visualize the three-dimensional structure of the scatterer by outputting the image showing the three-dimensional structure of the scatterer to a printer (not shown). Alternatively, the information processing circuitry 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, transmission and reception may be performed at multiple transmission positions and multiple reception positions by moving the transmitters 101 and receivers 102 arranged on each of the two measurement planes.

[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 contained 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 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 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] It may be expressed as:

[0239] Here, (x, y １ , z １ ) indicates the transmitting position of the wave, and (x, y ２ , z ２ ) 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. 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.

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

[0241] Here, Δ ５ is x, y １ , y ２ , z １ and z２ where c denotes the propagation speed of the wave, and t denotes the time from transmission to reception of the wave.

[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 of 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] It may be expressed as:

[0245] Here, k ｘ , k ｙ１ and k ｙ２ are the x and y scattering field functions １ and y ２ Also, 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 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] Here, (x, y, z) indicate the position of the object to be visualized.

[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 scattering 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 equation that expresses multiple scattering.

[0252] For example, the measurement data is

[0253] where Φ ｉｊ Φ expressed as １１ , Φ １２ , Φ ２１ and Φ ２２ corresponds to measurement data for four scattering modes: two forward scattering modes corresponding to two directions and two backward scattering modes corresponding to two directions.

[0254] Then, the information processing circuit 103

[0255] The effect of multiple scattering was removed using

[0256] may be derived.

[0257] Here, a ｍ１ , a ｍ２ , a ｍ３ , ..., a ｍＬ a expressed as １ , a２ , a ３ and a ４ is the analytical solution for the four scattering modes, a(k ｘ , k ｙ１ , k ｙ２ , k). ２ , f ３ , ..., f Ｌ denotes the product of 2, 3, ..., L variables in parentheses corresponding to 2, 3, ..., L scattering times applied from transmission to reception of a wave, respectively.

[0258] is f ２ , f ３ , ..., f Ｌ denotes a wave vector related to coordinate variables contained in two, three, ..., L variables in the parentheses.

[0259] Then, the information processing circuit 103

[0260] as the scattering field function,

[0261] may be derived as a visualization function.

[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] where Φ ｉｊ Φ expressed as １１ , Φ １２ , Φ ２１ and Φ ２２ corresponds to measurement data for four scattering modes: two forward scattering modes corresponding to two directions and two backward scattering modes corresponding to two directions.

[0265] Then, the information processing circuit 103

[0266] The effect of multiple scattering was removed using

[0267] may be derived.

[0268] Here, a ｍ a expressed as １ , a ２ , a ３ and a ４ is the analytical solution for the four scattering modes, a(k 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. ２ , g ３ , ..., g Ｌ denotes the product of 2, 3, . . . , L variables in parentheses corresponding to 2, 3, . . . , L scatterings applied from transmission to reception of a wave, respectively.

[0269] Also,

[0270] is g ２ , g ３ , ..., g Ｌ denotes a wave vector related to coordinate variables contained in two, three, ..., L variables in the parentheses.

[0271] Then, the information processing circuit 103

[0272] as the scattering field function,

[0273] may be derived as a visualization function.

[0274] 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 in which the measurement data is appropriately matched based on the theory of multiple scattering.

[0275] For example, the measurement data is

[0276] where Φｉｊ Φ expressed as １１ , Φ １２ , Φ ２１ and Φ ２２ corresponds to measurement data for four scattering modes: two forward scattering modes corresponding to two directions and two backward scattering modes corresponding to two directions.

[0277] Then, the information processing circuit 103

[0278] The effect of multiple scattering is removed using １ may be derived.

[0279] where 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 or higher order scattering.

[0280] Then, the information processing circuit 103

[0281] as the scattering field function,

[0282] may be derived as a visualization function.

[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] where Φ ｉｊ Φ expressed as １１ , Φ １２ , Φ ２１ and Φ ２２corresponds to measurement data for four scattering modes: two forward scattering modes corresponding to two directions and two backward scattering modes corresponding to two directions.

[0286] Then, the information processing circuit 103

[0287] The effect of multiple scattering is removed using １ may be derived.

[0288] where 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

[0289] Then, the information processing circuit 103

[0290] as the scattering field function,

[0291] may be derived as a visualization function.

[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, in accordance with 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] where Φ ｉｊ Φ expressed as １１ , Φ １２ , Φ ２１ and Φ ２２ corresponds to measurement data for four scattering modes: two forward scattering modes corresponding to two directions and two backward scattering modes corresponding to two directions.

[0295] Then, the information processing circuit 103

[0296] The effect of multiple scattering is removed using １ 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

[0297] Then, the information processing circuit 103

[0298] as the scattering field function,

[0299] may be derived as a visualization function.

[0300] 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 organized 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, scattering 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 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 the 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 the 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] The signal to be delayed (LO signal) is 1 / 2 the time it takes for the value of the PN code to change. ｎThe 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 the signal processing computer 1005. Information indicating the detected signal may be displayed on the 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, and the like.

[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 the 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] (Supplementary Information) Although the above has described 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] Each component of the imaging device may be an electric circuit. These electric circuits may form a single electric circuit as a whole, or may be separate electric circuits. These electric circuits may correspond to dedicated hardware or general-purpose hardware that executes the above-mentioned programs, etc.

[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.

[0320] 100 Imaging device 101 Transmitter 102 Receiver 103 Information processing circuit 104 Display 1001 Rangefinder 1002 FPGA board for PN code generation 1003 Digital control board 1004 UWB antenna RF switch 1005 Signal processing computer 1006 Signal monitor device 1007 RF detection board 1008 Multistatic array antenna 1009 Memory

Claims

1. An imaging device comprising: a plurality of transmitters arranged on both sides of a measurement target area for transmitting waves to said area; a plurality of receivers arranged on both sides for receiving the waves from said area; 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 said plurality of transmitters and said plurality of receivers and a combination of a plurality of functions related to a plurality of primary scatterings that constitute multiple scattering, and uses said imaging function to visualize the three-dimensional structure of scatterers contained in an object within said area.

2. The information processing circuit derives the visualization function corresponding to the scattering field function by solving an equation of the scattering field function based on the measurement data, and the scattering field function is It is expressed as Δ ５ is x, y １ , y ２ , z １ and z ２ 2. The imaging device according to claim 1, wherein c denotes a propagation speed of the wave, and t denotes a time from transmission to reception of the wave.

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 being: and k ｘ , k ｙ１ and k ｙ２ are the x, y scattering field functions 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 Denote a function based on s ２ (k ｘ , k ｙ１ , k ｙ２ ) is k ｘ , k ｙ１ and k ｙ２ The imaging device of claim 2 , wherein the imaging device exhibits a function based on 4. The information processing circuit derives the visualization function based on the analytical solution, and the visualization function is 4. The imaging device of claim 3, wherein (x, y, z) indicates a position of an object to be imaged.

5. The imaging device of claim 1, wherein 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, and the information processing circuit derives the four functions from the measurement data in accordance with the nonlinear integral equation, and derives the imaging function corresponding to the scattered field function using the four functions.

6. The measurement data is The imaging device according to claim 4 , wherein the imaging function is derived as follows:

7. The measurement data is The imaging device according to claim 4 , wherein the imaging function is derived as follows:

8. The measurement data is The imaging device according to claim 4 , wherein the imaging function is derived as follows:

9. The measurement data is The imaging device according to claim 4 , wherein the imaging function is derived as follows:

10. The measurement data is The imaging device according to claim 4 , wherein the imaging function is derived as follows:

11. An imaging method comprising the steps of: transmitting waves to a measurement target area by a plurality of transmitters arranged on both sides of the area; receiving the waves from the area by a plurality of receivers arranged on both sides; deriving 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 primary scatterings that constitute multiple scattering, and visualizing a three-dimensional structure of a scatterer included in an object within the area using the imaging function.

Images