Data processing method, measurement system, and program

Abstract

Provided is a simple data processing method offering excellent calculation speed, even for structures that have a curved shape, in synthetic aperture processing using Fourier transform. This data processing method for analyzing scattered waves from waves emitted at an object includes: emitting waves at an object from a plurality of transmitting / receiving points p(x', y', z') arrayed over a curve of a single-valued function z'=g(x', y') pertaining to (x', y') in a plane parallel to the yz-plane; receiving scattered waves reflected with a reflectance f(x, y, z) at reflection points (x, y, x) on the object as measured values sa(x', y', k) at the transmitting / receiving points p(x', y', z') from which the waves were emitted; running the measured values sa(x', y', k) through double Fourier transform to find Sa(kx, ky, k); defining an operator having the eigenvalue (x', y') with respect to Sa(kx, ky, k); and running through a triple inverse Fourier transform to find the reflectance f(x, y, z).

Description

[Technical Field]

[0001] The present invention relates to a data processing method, a measurement system, and a program for processing, using a computer, measurement data of waves whose values ​​are determined by the frequency of waves such as electromagnetic waves generated in space and the spatial coordinates of the space. [Background technology]

[0002] Conventionally, radar devices have been known that nondestructively inspect the interior of nonmetallic structures such as concrete and wood. Conventional radar devices have an array antenna in which multiple antennas are arranged on a flat surface. The array antenna has, for example, a configuration in which antennas such as planar antennas are aligned in one direction, with a transmitting array antenna and a receiving array antenna arranged closely to each other. Furthermore, in order to accurately measure the interior of a structure, the radar device measures the object to be measured using a wide frequency band while changing the frequency of electromagnetic waves at set frequency intervals.

[0003] Regarding radar devices having array antennas, for example, a radar device in which a transmitting array antenna and a receiving array antenna each composed of a plurality of planar antennas are formed on a common dielectric substrate is known (JP 2015-095840 A, hereinafter referred to as "Patent Document 1"). In conventional radar devices, the arrangement direction of the planar antennas of the transmitting array antenna is parallel to the arrangement direction of the planar antennas of the receiving array antenna. The position of the planar antennas of the receiving array antenna in the arrangement direction is midway between the positions of two adjacent planar antennas of the transmitting array antenna.

[0004] Also, a scattering tomography method is known that can quickly and generally analyze an inverse problem and easily visualize information about the inside of an object (Japanese Patent No. 6557747, hereinafter referred to as "Patent Document 2").

[0005] Synthetic aperture processing is used to visualize the interior of structures from the measured data. There are two main types of synthetic aperture processing: additive methods such as the diffraction stacking method, and methods that use Fourier transforms such as the FK migration method. To achieve a practical calculation time, synthetic aperture processing using Fourier transform is practical. Here, synthetic aperture processing using Fourier transform requires measurements on an equally spaced plane.

[0006] However, when measuring on a curved surface such as the surface of a tunnel, it is difficult to measure on a flat surface, and it is necessary to perform calculations using a planar approximation. The greater the curvature of the curved surface, the greater the error caused by the planar approximation, resulting in a problem of blurring of the processed 3D image. Summary of the Invention [Problem to be solved by the invention]

[0007] In a radar device having an array antenna in which planar antennas are arranged in one direction, as shown in Patent Document 1, it may be difficult to place each array antenna close to a structure having a curved surface. Furthermore, in the scattering tomography method disclosed in Patent Document 2, the calculations required to visualize information about the inside of an object are complicated, resulting in a long calculation time.

[0008] An object of the present invention is to provide a data processing method, measurement system, and program that are simple and have excellent calculation speed, even for structures with curved surfaces, in synthetic aperture processing using Fourier transform. [Means for solving the problem]

[0009] A first aspect of the present invention is A data processing method for analyzing scattered waves of waves radiated to an object, comprising: The wave is emitted to the object from a plurality of transmitting and receiving points p(x', y', z') arranged on a curve of a single-valued function z'=g(x', y') with respect to (x', y') in a plane parallel to the yz plane; The scattered wave reflected at the reflection point (x, y, z) on the object with reflectivity f(x, y, z) is measured at the transmitting / receiving point p(x', y', z') where the wave was emitted. a Received as (x', y', k), The measured value s a (x', y', k) is double Fourier transformed using equation (1) to obtain S a (k x , k y , k) and JPEG0007808129000001.jpg862 S a (k x , k y , k), define the operator shown in equation (2) with eigenvalues ​​(x', y'), JPEG0007808129000002.jpg2331 The reflectance f(x, y, z) is calculated by triple inverse Fourier transform using equation (3). JPEG0007808129000003.jpg1481 It is a data processing method. however, k is the wave number of the propagating wave, k x , k y , k z is a component of the wave vector of the round-trip spherical wave of the wave propagating between the transmitting and receiving point p(x', y', z') and the reflecting point (x, y, z), is.

[0010] A second aspect of the present invention is A measurement system for analyzing scattered waves of waves radiated to an object, comprising: A transmitting / receiving unit having a plurality of transmitting / receiving points p(x', y', z') arranged on a curve of a single-valued function z'=g(x', y') with respect to (x', y') in a plane parallel to the yz plane, radiating the wave to the object, and measuring the scattered wave reflected at a reflection point (x, y, z) on the object with a reflectivity f(x, y, z) at the transmitting / receiving point p(x', y', z') from which the wave was radiated. a a transmitter / receiver that receives the signal as (x', y', k); A processing device, The measured value s a (x', y', k) is double Fourier transformed using equation (1) to obtain S a (k x , k y , k) and JPEG0007808129000004.jpg862 S a (k x , k y , k), and define the operator shown in equation (2) with eigenvalues ​​(x', y'). JPEG0007808129000005.jpg2331 A procedure of calculating the reflectance f(x, y, z) by triple inverse Fourier transform using equation (3); JPEG0007808129000006.jpg1481 a processing unit for executing the The measurement system has the following features: k is the wave number of the propagating wave, k x , k y , k z is a component of the wave vector of the round-trip spherical wave of the wave propagating between the transmitting and receiving point p(x', y', z') and the reflecting point (x, y, z), is.

[0011] A third aspect of the present invention is A program for analyzing scattered waves of waves radiated to an object, Measurement values a(x', y', k) is double Fourier transformed using equation (1) to obtain S a (k x , k y , k) and JPEG0007808129000007.jpg862 S a (k x , k y , k), and define the operator shown in equation (2) with eigenvalues ​​(x', y'). JPEG0007808129000008.jpg2331 The procedure for calculating the reflectance f(x, y, z) by triple inverse Fourier transform using equation (3) is as follows: JPEG0007808129000009.jpg1481 It is a program that causes a computer to execute the above. however, k is the wave number of the propagating wave, k x , k y , k z is the component of the wave vector of the round-trip spherical wave of the wave propagating between the transmitting and receiving point p(x', y', z') and the reflecting point (x, y, z), is.

[0012] A fourth aspect of the present invention is A data processing method for analyzing scattered waves of waves radiated to an object, comprising: The wave is emitted to the object from a plurality of transmission points p1(x', y'1, z'1) arranged on the y axis; The scattered wave reflected at the reflection point (x, y, z) on the object with reflectivity f(x, y, z) is measured at multiple receiving points p2(x', y'2, z'2) arranged on the y axis. a Received as (x', y'1, y'2, k), The plurality of transmission points p1(x', y'1, z'1) and the plurality of reception points p2(x', y'2, z'2) arranged on the y-axis are moved on a curved surface of a single-valued function z'=g(x') with respect to x'; The measured value s a(x', y'1, y'2, k) is triple Fourier transformed using equation (1) to obtain S a (k' x , k' y1 , k' y2 , k) and JPEG0007808129000010.jpg680 S a (k' x1 , k' x2 , k' y1 , k' y2 , k), define the operator shown in equation (2) with eigenvalue x', JPEG0007808129000011.jpg926 The reflectance f(x, y, z) is calculated by triple inverse Fourier transform using equation (3). JPEG0007808129000012.jpg18101 It is a data processing method. however, x' = x'1= x'2 z' = z'1= z'2 k is the wave number of the propagating wave, k' x1 , k' y1 , k' z1 is a component of the wave vector of the spherical wave of the wave propagating between the transmission point p1 (x'1, y'1, z'1) and the reflection point (x, y, z), k' x2 , k' y2 , k' z2 is a component of the wave vector of the spherical wave of the wave propagating between the reflection point (x, y, z) and the reception point p2 (x'2, y'2, z'2), k y = k' y1 + k' y2 , v = k' y1 - k' y2 is.

[0013] A fifth aspect of the present invention is A measurement system for analyzing scattered waves of waves radiated to an object, comprising: A transceiver unit, a transmitting unit that radiates the wave to the object from a plurality of transmitting points p1(x', y'1, z'1) arranged on the y-axis; The scattered wave reflected at the reflection point (x, y, z) on the object with reflectivity f(x, y, z) is measured at multiple receiving points p2(x', y'2, z'2) arranged on the y axis. a a receiving unit that receives the data as (x', y'1, y'2, k); and a transmitting / receiving unit that moves the plurality of transmission points p1(x', y'1, z'1) and the plurality of reception points p2(x', y'2, z'2) arranged on the y-axis on a curved surface of a single-valued function z'=g(x') with respect to x'; A processing device, The measured value s a (x', y'1, y'2, k) is triple Fourier transformed using equation (1) to obtain S a (k' x , k' y1 , k' y2 , k) and JPEG0007808129000013.jpg680 S a (k' x1 , k' x2 , k' y1 , k' y2 , k), defining the operator shown in equation (2) with eigenvalue x'; JPEG0007808129000014.jpg926 A procedure of calculating the reflectance f(x, y, z) by triple inverse Fourier transform using equation (3); JPEG0007808129000015.jpg18101 a processing unit for executing the The measurement system has the following features: however, x' = x'1= x'2 z' = z'1= z'2 k is the wave number of the propagating wave, k' x1 , k'y1 , k' z1 is a component of the wave vector of the spherical wave of the wave propagating between the transmission point p1 (x'1, y'1, z'1) and the reflection point (x, y, z), k' x2 , k' y2 , k' z2 is a component of the wave vector of the spherical wave of the wave propagating between the reflection point (x, y, z) and the reception point p2 (x'2, y'2, z'2), k y = k' y1 + k' y2 , v = k' y1 - k' y2 is.

[0014] A sixth aspect of the present invention is A program for analyzing scattered waves of waves radiated to an object, Measurement values a (x', y'1, y'2, k) is triple Fourier transformed using equation (1) to obtain S a (k' x , k' y1 , k' y2 , k) and JPEG0007808129000016.jpg680 S a (k' x1 , k' x2 , k' y1 , k' y2 , k), defining the operator shown in equation (2) with eigenvalue x'; JPEG0007808129000017.jpg926 The procedure for calculating the reflectance f(x, y, z) by triple inverse Fourier transform using equation (3) is as follows: JPEG0007808129000018.jpg18101 It is a program that causes a computer to execute the above. however, x' = x'1= x'2 z' = z'1= z'2 k is the wave number of the propagating wave, k' x1 , k' y1 , k' z1 is the component of the wave vector of the spherical wave of the wave propagating between the transmitting point p1 (x'1, y'1, z'1) and the reflecting point (x, y, z), k' x2 , k' y2 , k' z2 is the component of the wave vector of the spherical wave of the wave propagating between the reflection point (x, y, z) and the reception point p2 (x'2, y'2, z'2), k y = k' y1 + k' y2 , v = k' y1 - k' y2 is.

[0015] A seventh aspect of the present invention is A data processing method for analyzing scattered waves of waves radiated to an object, comprising: The wave is emitted to the object from a plurality of transmission points p1 (x'1, y'1, z'1) arranged two-dimensionally on the xy plane; The scattered waves reflected with reflectivity f(x, y, z) at a reflection point (x, y, z) on the object are received as measurement values ​​s(x'1, x'2, y'1, y'2, z'1, z'2, k) at a plurality of reception points p2(x'2, y'2, z'2) arranged two-dimensionally on the xy plane, The measured value s(x'1, x'2, y'1, y'2, z'1, z'2, k) is subjected to a quadruple Fourier transform using equation (1) to obtain S(k' x1 , k' x2 , k' y1 , k' y2 , z'1, z'2, k) and JPEG0007808129000019.jpg6105 The reflectance f(x, y, z) is calculated by performing a triple inverse Fourier transform using equation (2). JPEG0007808129000020.jpg1396 It is a data processing method. however, z'1= z'2= 0 k is the wave number of the propagating wave, k' x1 , k' y1 , k' z1 is a component of the wave vector of the spherical wave of the wave propagating between the transmission point p1 (x'1, y'1, z'1) and the reflection point (x, y, z), k' x2 , k' y2 , k' z2 is a component of the wave vector of the spherical wave of the wave propagating between the reflection point (x, y, z) and the reception point p2 (x'2, y'2, z'2), k x = k' x1 + k' x2 , u = k' x1 - k' x2 , k y = k' y1 + k' y2 , v = k' y1 - k' y2 is.

[0016] An eighth aspect of the present invention is A measurement system for analyzing scattered waves of waves radiated to an object, comprising: A transceiver unit, a transmitting unit that radiates the wave to the object from a plurality of transmitting points p1 (x'1, y'1, z'1) that are two-dimensionally arranged on an xy plane; a receiving unit that receives the scattered waves reflected at a reflection point (x, y, z) on the object with a reflectivity f(x, y, z) as measurement values ​​s(x'1, x'2, y'1, y'2, z'1, z'2, k) at a plurality of receiving points p2(x'2, y'2, z'2) that are two-dimensionally arranged on the xy plane; a transceiver unit having A processing device, The measured value s(x'1, x'2, y'1, y'2, z'1, z'2, k) is subjected to a quadruple Fourier transform using equation (1) to obtain S(k' x1 , k'x2 , k' y1 , k' y2 , z'1, z'2, k) and JPEG0007808129000021.jpg6105 A procedure of calculating the reflectance f(x, y, z) by triple inverse Fourier transform using equation (2); JPEG0007808129000022.jpg1396 a processing unit for executing the The measurement system has the following features: however, z'1= z'2= 0 k is the wave number of the propagating wave, k' x1 , k' y1 , k' z1 is a component of the wave vector of the spherical wave of the wave propagating between the transmission point p1 (x'1, y'1, z'1) and the reflection point (x, y, z), k' x2 , k' y2 , k' z2 is a component of the wave vector of the spherical wave of the wave propagating between the reflection point (x, y, z) and the reception point p2 (x'2, y'2, z'2), k x = k' x1 + k' x2 , u = k' x1 - k' x2 , k y = k' y1 + k' y2 , v = k' y1 - k' y2 is.

[0017] A ninth aspect of the present invention is A program for analyzing scattered waves of waves radiated to an object, The measured value s(x'1, x'2, y'1, y'2, z'1, z'2, k) is quadruple Fourier transformed using equation (1) to obtain S(k' x1 , k' x2 , k' y1 , k'y2 , z'1, z'2, k) and JPEG0007808129000023.jpg6105 The procedure for calculating the reflectance f(x, y, z) by triple inverse Fourier transform using equation (2) is as follows: JPEG0007808129000024.jpg1396 It is a program that causes a computer to execute the above. however, z'1= z'2= 0 k is the wave number of the propagating wave, k' x1 , k' y1 , k' z1 is the component of the wave vector of the spherical wave of the wave propagating between the transmitting point p1 (x'1, y'1, z'1) and the reflecting point (x, y, z), k' x2 , k' y2 , k' z2 is the component of the wave vector of the spherical wave of the wave propagating between the reflection point (x, y, z) and the reception point p2 (x'2, y'2, z'2), k x = k' x1 + k' x2 , u = k' x1 - k' x2 , k y = k' y1 + k' y2 , v = k' y1 - k' y2 is.

[0018] A tenth aspect of the present invention is A data processing method for analyzing scattered waves of waves radiated to an object, comprising: The wave is emitted to the object from a plurality of transmission points p1 (x'1, y'1, z'1) arranged on the y-axis; The scattered waves reflected at a reflection point (x, y, z) on the object with a reflectivity f(x, y, z) are received as measurement values ​​s(x'1, x'2, y'1, y'2, z'1, z'2, k) at a plurality of reception points p2(x'2, y'2, z'2) arranged on the y axis, The measured value s(x'1, x'2, y'1, y'2, z'1, z'2, k) is triple Fourier transformed using equation (1) to obtain S(k' x1 , k' x2 , k' y1 , k' y2 , z'1, z'2, k) and JPEG0007808129000025.jpg690 The reflectance f(x, y, z) is calculated by performing a triple inverse Fourier transform using equation (2). JPEG0007808129000026.jpg1282 It is a data processing method. however, x' = x'1= x'2 z'1= z'2= 0 k is the wave number of the propagating wave, k' x1 , k' y1 , k' z1 is a component of the wave vector of the spherical wave of the wave propagating between the transmission point p1 (x'1, y'1, z'1) and the reflection point (x, y, z), k' x2 , k' y2 , k' z2 is a component of the wave vector of the spherical wave of the wave propagating between the reflection point (x, y, z) and the reception point p2 (x'2, y'2, z'2), k x = k' x1 + k' x2 , u = k' x1 - k' x2 , k y = k' y1 + k' y2 , v = k' y1 - k' y2 is.

[0019] An eleventh aspect of the present invention is A measurement system for analyzing scattered waves of waves radiated to an object, comprising: A transceiver unit, a transmitting unit that radiates the wave to the object from a plurality of transmitting points p1 (x'1, y'1, z'1) arranged on the y-axis; a receiving unit that receives the scattered waves reflected at a reflection point (x, y, z) on the object with a reflectivity f(x, y, z) as measurement values ​​s(x'1, x'2, y'1, y'2, z'1, z'2, k) at a plurality of receiving points p2(x'2, y'2, z'2) arranged on the y axis; a transceiver unit having A processing device, The measured value s(x'1, x'2, y'1, y'2, z'1, z'2, k) is triple Fourier transformed using equation (1) to obtain S(k' x1 , k' x2 , k' y1 , k' y2 , z'1, z'2, k) and JPEG0007808129000027.jpg690 A procedure of calculating the reflectance f(x, y, z) by triple inverse Fourier transform using equation (2); JPEG0007808129000028.jpg1282 a processing unit for executing the The measurement system has the following features: however, x' = x'1= x'2 z'1= z'2= 0 k is the wave number of the propagating wave, k' x1 , k' y1 , k' z1 is a component of the wave vector of the spherical wave of the wave propagating between the transmission point p1 (x'1, y'1, z'1) and the reflection point (x, y, z), k' x2 , k' y2 , k' z2is a component of the wave vector of the spherical wave of the wave propagating between the reflection point (x, y, z) and the reception point p2 (x'2, y'2, z'2), k x = k' x1 + k' x2 , u = k' x1 - k' x2 , k y = k' y1 + k' y2 , v = k' y1 - k' y2 is.

[0020] A twelfth aspect of the present invention is A program for analyzing scattered waves of waves radiated to an object, The measured value s(x'1, x'2, y'1, y'2, z'1, z'2, k) is triple Fourier transformed using equation (1) to obtain S(k' x1 , k' x2 , k' y1 , k' y2 , z'1, z'2, k) and JPEG0007808129000029.jpg690 The procedure for calculating the reflectance f(x, y, z) by triple inverse Fourier transform using equation (2) is as follows: JPEG0007808129000030.jpg1282 It is a program that causes a computer to execute the above. however, x' = x'1= x'2 z'1= z'2= 0 k is the wave number of the propagating wave, k' x1 , k' y1 , k' z1 is a component of the wave vector of the spherical wave of the wave propagating between the transmission point p1 (x'1, y'1, z'1) and the reflection point (x, y, z), k' x2 , k' y2 , k' z2is a component of the wave vector of the spherical wave of the wave propagating between the reflection point (x, y, z) and the reception point p2 (x'2, y'2, z'2), k x = k' x1 + k' x2 , u = k' x1 - k' x2 , k y = k' y1 + k' y2 , v = k' y1 - k' y2 is.

[0021] A thirteenth aspect of the present invention is A data processing method for analyzing scattered waves of waves radiated to an object, comprising: The wave is emitted to the object from a plurality of transmitting points p1(x'1, y'1, z'1) arranged on a curve of a first single-valued function z'1=g1(x'1, y'1) with respect to (x'1, y'1) in a plane parallel to the yz plane; The scattered wave reflected at the reflection point (x, y, z) on the object with reflectivity f(x, y, z) is measured at a plurality of receiving points p2(x'2, y'2, z'2) arranged on the curve of a second single-valued function z'2 = g2(x'2, y'2) with respect to (x'2, y'2) in a plane parallel to the yz plane. a Received as (x'1, x'2, y'1, y'2, k), The measured value s a (x'1, x'2, y'1, y'2, k) is transformed by the quadruple Fourier transform using equation (1) to obtain S a (k' x1 , k' x2 , k' y1 , k' y2 , k) and JPEG0007808129000031.jpg7122 S a (k' x1 , k' x2 , k' y1 , k' y2, k), define operators shown in equations (2) and (3) having eigenvalues ​​(x'1, y'1, x'2, y'2), JPEG0007808129000032.jpg2583 The reflectance f(x, y, z) is calculated by triple inverse Fourier transform using equation (4). JPEG0007808129000033.jpg23137 It is a data processing method. however, k is the wave number of the propagating wave, k' x1 , k' y1 , k' z1 is a component of the wave vector of the spherical wave of the wave propagating between the transmission point p1 (x'1, y'1, z'1) and the reflection point (x, y, z), k' x2 , k' y2 , k' z2 is a component of the wave vector of the spherical wave of the wave propagating between the reflection point (x, y, z) and the reception point p2 (x'2, y'2, z'2), k x = k' x1 + k' x2 , u = k' x1 - k' x2 , k y = k' y1 + k' y2 , v = k' y1 - k' y2 is.

[0022] A fourteenth aspect of the present invention is A measurement system for analyzing scattered waves of waves radiated to an object, comprising: A transceiver unit, a transmitting unit that radiates the wave to the object from a plurality of transmitting points p1(x'1, y'1, z'1) arranged on a curve of a first single-valued function z'1=g1(x'1, y'1) with respect to (x'1, y'1) in a plane parallel to the yz plane; The scattered wave reflected at the reflection point (x, y, z) on the object with reflectivity f(x, y, z) is measured at a plurality of receiving points p2(x'2, y'2, z'2) arranged on the curve of a second single-valued function z'2 = g2(x'2, y'2) with respect to (x'2, y'2) in a plane parallel to the yz plane. a a receiving unit that receives the data as (x'1, x'2, y'1, y'2, k); a transceiver unit having A processing device, The measured value s a (x'1, x'2, y'1, y'2, k) is transformed by the quadruple Fourier transform using equation (1) to obtain S a (k' x1 , k' x2 , k' y1 , k' y2 , k) and JPEG0007808129000034.jpg7122 S a (k' x1 , k' x2 , k' y1 , k' y2 , k), defining the operators shown in equations (2) and (3) with eigenvalues ​​(x'1, y'1, x'2, y'2); JPEG0007808129000035.jpg2583 A procedure of calculating the reflectance f(x, y, z) by triple inverse Fourier transform using equation (4); JPEG0007808129000036.jpg23137 a processing unit for executing the The measurement system has the following features: however, k is the wave number of the propagating wave, k' x1 , k' y1 , k' z1 is a component of the wave vector of the spherical wave of the wave propagating between the transmission point p1 (x'1, y'1, z'1) and the reflection point (x, y, z), k' x2 , k' y2 , k'z2 is a component of the wave vector of the spherical wave of the wave propagating between the reflection point (x, y, z) and the reception point p2 (x'2, y'2, z'2), k x = k' x1 + k' x2 , u = k' x1 - k' x2 , k y = k' y1 + k' y2 , v = k' y1 - k' y2 is.

[0023] A fifteenth aspect of the present invention is A program for analyzing scattered waves of waves radiated to an object, Measurement values a (x'1, x'2, y'1, y'2, k) is transformed by the quadruple Fourier transform using equation (1) to obtain S a (k' x1 , k' x2 , k' y1 , k' y2 , k) and JPEG0007808129000037.jpg7122 S a (k' x1 , k' x2 , k' y1 , k' y2 , k), defining the operators shown in equations (2) and (3) with eigenvalues ​​(x'1, y'1, x'2, y'2); JPEG0007808129000038.jpg2583 A procedure of calculating the reflectance f(x, y, z) by triple inverse Fourier transform using equation (4); JPEG0007808129000039.jpg23137 It is a program that causes a computer to execute the above. however, k is the wave number of the propagating wave, k' x1 , k' y1 , k'z1 is the component of the wave vector of the spherical wave of the wave propagating between the transmitting point p1 (x'1, y'1, z'1) and the reflecting point (x, y, z), k' x2 , k' y2 , k' z2 is the component of the wave vector of the spherical wave of the wave propagating between the reflection point (x, y, z) and the reception point p2 (x'2, y'2, z'2), k x = k' x1 + k' x2 , u = k' x1 - k' x2 , k y = k' y1 + k' y2 , v = k' y1 - k' y2 is.

[0024] A sixteenth aspect of the present invention is A data processing method for analyzing scattered waves of waves radiated to an object, comprising: The wave is emitted to the object from a plurality of transmitting points p1(x'1, y'1, z'1) arranged on a curve of a first single-valued function z'1=g1(x'1, y'1) with respect to (x'1, y'1) in a plane parallel to the yz plane; The scattered wave reflected at the reflection point (x, y, z) on the object with reflectivity f(x, y, z) is measured at a plurality of receiving points p2(x'2, y'2, z'2) arranged on the curve of a second single-valued function z'2 = g2(x'2, y'2) with respect to (x'2, y'2) in a plane parallel to the yz plane. a Received as (x', y'1, y'2, k), The measured value s a (x', y'1, y'2, k) is triple Fourier transformed using equation (1) to obtain S a (k' x , k' y1 , k' y2 , k) and JPEG0007808129000040.jpg784 S a(k' x , k' y1 , k' y2 , k), define operators shown in equations (2) and (3) with eigenvalues ​​(x', y'1, y'2), JPEG0007808129000041.jpg2269 The reflectance f(x, y, z) is calculated by triple inverse Fourier transform using equation (4). JPEG0007808129000042.jpg19102 It is a data processing method. however, x' = x'1= x'2 k is the wave number of the propagating wave, k' x1 , k' y1 , k' z1 is a component of the wave vector of the spherical wave of the wave propagating between the transmission point p1 (x'1, y'1, z'1) and the reflection point (x, y, z), k' x2 , k' y2 , k' z2 is a component of the wave vector of the spherical wave of the wave propagating between the reflection point (x, y, z) and the reception point p2 (x'2, y'2, z'2), k y = k' y1 + k' y2 , v = k' y1 - k' y2 is.

[0025] A seventeenth aspect of the present invention is A measurement system for analyzing scattered waves of waves radiated to an object, comprising: A transceiver unit, a transmitting unit that radiates the wave to the object from a plurality of transmitting points p1(x'1, y'1, z'1) arranged on a curve of a first single-valued function z'1=g1(x'1, y'1) with respect to (x'1, y'1) in a plane parallel to the yz plane; The scattered wave reflected at the reflection point (x, y, z) on the object with reflectivity f(x, y, z) is measured at a plurality of receiving points p2(x'2, y'2, z'2) arranged on the curve of a second single-valued function z'2 = g2(x'2, y'2) with respect to (x'2, y'2) in a plane parallel to the yz plane. a a receiving unit that receives the data as (x', y'1, y'2, k); a transceiver unit having A processing device, The measured value s a (x', y'1, y'2, k) is triple Fourier transformed using equation (1) to obtain S a (k' x , k' y1 , k' y2 , k) and JPEG0007808129000043.jpg784 S a (k' x , k' y1 , k' y2 , k), defining the operators shown in equations (2) and (3) with eigenvalues ​​(x', y'1, y'2); JPEG0007808129000044.jpg2269 A procedure of calculating the reflectance f(x, y, z) by triple inverse Fourier transform using equation (4); JPEG0007808129000045.jpg19102 a processing unit for executing the The measurement system has the following features: however, x' = x'1= x'2 k is the wave number of the propagating wave, k' x1 , k' y1 , k' z1 is a component of the wave vector of the spherical wave of the wave propagating between the transmission point p1 (x'1, y'1, z'1) and the reflection point (x, y, z), k' x2 , k' y2 , k' z2is a component of the wave vector of the spherical wave of the wave propagating between the reflection point (x, y, z) and the reception point p2 (x'2, y'2, z'2), k y = k' y1 + k' y2 , v = k' y1 - k' y2 is.

[0026] An eighteenth aspect of the present invention is A program for analyzing scattered waves of waves radiated to an object, Measurement values a (x', y'1, y'2, k) is triple Fourier transformed using equation (1) to obtain S a (k' x , k' y1 , k' y2 , k) and JPEG0007808129000046.jpg784 S a (k' x , k' y1 , k' y2 , k), defining the operators shown in equations (2) and (3) with eigenvalues ​​(x', y'1, y'2); JPEG0007808129000047.jpg2269 A procedure of calculating the reflectance f(x, y, z) by triple inverse Fourier transform using equation (4); JPEG0007808129000048.jpg19102 It is a program that causes a computer to execute the above. however, x' = x'1= x'2 k is the wave number of the propagating wave, k' x1 , k' y1 , k' z1 is the component of the wave vector of the spherical wave of the wave propagating between the transmitting point p1 (x'1, y'1, z'1) and the reflecting point (x, y, z), k' x2 , k' y2, k' z2 is the component of the wave vector of the spherical wave of the wave propagating between the reflection point (x, y, z) and the receiving point p2 (x'2, y'2, z'2), k y = k' y1 + k' y2 , v = k' y1 - k' y2 is. [Effects of the Invention]

[0027] According to the data processing method, measurement system, and program of the present invention, synthetic aperture processing using Fourier transform can be performed simply and in a short calculation time, even for structures having curved surfaces. [Brief explanation of the drawings]

[0028] [Figure 1] FIG. 1 is a diagram showing a configuration of a radar device according to a first embodiment; [Figure 2] A diagram showing the configuration of the array antenna shown in Figure 1. [Figure 3] FIG. 1 is a diagram illustrating the positional relationship between the array antenna and the object to be measured in the first embodiment. [Figure 4] 1 is a flowchart illustrating a data processing method according to a first embodiment. [Figure 5] FIG. 10 is a diagram illustrating the positional relationship between the array antenna and the object to be measured in the second embodiment. [Figure 6] 10 is a flowchart showing a data processing method according to a second embodiment. [Figure 7] (a) is the measurement layout diagram for horizontal surface measurement, (b) is the measurement layout diagram for curved surface measurement 1, and (c) is the measurement layout diagram for curved surface measurement 2. [Figure 8] Point target simulated by the data processing method of the first embodiment based on the measurement layout of the horizontal plane measurement [Figure 9](a) is a point target simulated by the data processing method of the first embodiment using the measurement layout of curved surface measurement 1, and (b) is a point target simulated by the data processing method of the second embodiment using the measurement layout of curved surface measurement 1. [Figure 10] (a) is a point target simulated by the data processing method of the first embodiment using the measurement layout of curved surface measurement 2, and (b) is a point target simulated by the data processing method of the second embodiment using the measurement layout of curved surface measurement 2. [Figure 11] FIG. 10 is a diagram illustrating the positional relationship between the array antenna and the object to be measured in the third embodiment. [Figure 12] 10 is a flowchart showing a data processing method according to a third embodiment. [Figure 13] FIG. 10 is a diagram illustrating the positional relationship between the array antenna and the object to be measured in the fourth embodiment. [Figure 14] 10 is a flowchart showing a data processing method according to a fourth embodiment. [Figure 15] FIG. 11 is a diagram illustrating the positional relationship between the array antenna and the object to be measured according to the fifth embodiment. [Figure 16] 10 is a flowchart showing a data processing method according to a fifth embodiment. [Figure 17] FIG. 13 is a diagram illustrating the positional relationship between the array antenna of the sixth embodiment and the object to be measured. [Figure 18] Flowchart showing a data processing method according to the sixth embodiment [Figure 19] (a) is the measurement layout diagram for horizontal surface measurement, (b) is the measurement layout diagram for curved surface measurement 1, and (c) is the measurement layout diagram for curved surface measurement 2. [Figure 20] Point target simulated by the data processing method of the fifth embodiment based on the measurement layout of the horizontal plane measurement [Figure 21] (a) is a point target simulated by the data processing method of the fifth embodiment using the measurement layout of curved surface measurement 1, and (b) is a point target simulated by the data processing method of the sixth embodiment using the measurement layout of curved surface measurement 1. [Figure 22](a) is a point target simulated by the data processing method of the fifth embodiment using the measurement layout of curved surface measurement 2, and (b) is a point target simulated by the data processing method of the sixth embodiment using the measurement layout of curved surface measurement 2. [Figure 23] FIG. 13 is a diagram illustrating the positional relationship between the array antenna of the seventh embodiment and an object to be measured. [Figure 24] Flowchart showing a data processing method according to the seventh embodiment DETAILED DESCRIPTION OF THE INVENTION

[0029] First Embodiment The data processing method, measurement system, and program of the first embodiment will be described in detail below. Fig. 1 shows the configuration of a radar device of this embodiment. Fig. 2 shows the configuration of the array antenna shown in Fig. 1. Fig. 3 is a diagram explaining the positional relationship between the array antenna of this embodiment and an object to be measured. In this embodiment, electromagnetic waves are described as waves that are radiated into space, but waves that propagate through space, such as X-rays or ultrasound, may also be used instead of electromagnetic waves.

[0030] The measurement system 1 of this embodiment includes a transceiver and a processing device. The processing device may be provided integrally with the transceiver, or may be provided in a separate location connected to the transceiver via a network. In the following embodiment, an example in which the processing device is provided integrally with the transceiver will be described.

[0031] 1 uses a transmitting array antenna and a receiving array antenna (transmitter / receiver) to emit electromagnetic waves from the transmitting antenna while sweeping the frequency of the electromagnetic waves. The radar device 60 then receives the waves reflected from the object to be measured with the receiving antenna to obtain measurement data s(x', y', z', k). The measurement data s(x', y', z', k) is data whose variables are the x-coordinate component, the y-coordinate component, the z-coordinate component, and the frequency of the electromagnetic waves.

[0032] The radar device 60 has a measurement unit 61, a data processing unit (processing device) 66, and an image display unit 68. The measurement unit 61 has a transmitting array antenna 50, a receiving array antenna 52, high-frequency switches 58 and 59, a high-frequency circuit 62, and a system control circuit 64. The radar device 60 emits electromagnetic waves of 10 MHz or higher, for example, 10 to 20 GHz, but the frequency of the electromagnetic waves is not particularly limited.

[0033] As shown in Fig. 2, the transmitting array antenna 50 has multiple transmitting antennas 10a arranged in one direction. Each transmitting antenna 10a radiates electromagnetic waves toward the object to be measured. The receiving array antenna 52 has multiple receiving antennas 10b arranged in the same direction as the transmitting antennas 10a. Each receiving antenna 10b receives electromagnetic waves reflected from the object to be measured. The transmitting antennas 10a of the transmitting array antenna 50 and the receiving antennas 10b of the receiving array antenna 52 are arranged on the same plane. The transmitting array antenna 50 and the receiving array antenna 52 are arranged so that the object to be measured faces this plane.

[0034] The data processing unit 66 processes a plurality of measurement data obtained by transmission to the measurement object by the plurality of transmitting antennas 10a and reception by the plurality of receiving antennas 10b, and calculates image data relating to the measurement object. The transmitting antenna 10a and the receiving antenna 10b in this embodiment are planar antennas in which an antenna pattern is formed in a plane on a substrate, but are not limited to planar antennas.

[0035] The transmitting array antenna 50 and the receiving array antenna 52 move parallel to the surface of the object to be measured. That is, the transmitting array antenna 50 and the receiving array antenna 52 perform measurements while scanning along the surface of the object to be measured. When the transmitting array antenna 50 and the receiving array antenna 52 move, the system control circuit 64 controls the operation of the high-frequency circuit 62. Specifically, the system control circuit 64 controls the operation of the high-frequency circuit 62 so that the transmitting antenna 10a is switched by the high-frequency switch 58 and electromagnetic waves are radiated for each unit length of the movement distance of the transmitting array antenna 50 and the receiving array antenna 52.

[0036] The radar device 60 has an encoder 69. The encoder 69 generates a pulse signal every time a certain distance is moved. The encoder 69 detects the movement of the transmitting array antenna 50 and the receiving array antenna 52. At this time, every time an electromagnetic wave is radiated from each of the transmitting antennas 10a, the high frequency switch 59 sequentially switches among the plurality of receiving antennas 10b, causing each receiving antenna 10b to receive the wave.

[0037] The frequency of the electromagnetic waves radiated from the transmitting array antenna 50 is swept at set frequency intervals within a range of, for example, 10 to 20 GHz for a fixed period of time, and the electromagnetic waves are radiated. Therefore, the measurement data obtained from the high-frequency circuit 62 is data whose value is determined by the position from which the transmitting antenna 10a transmits, the position from which the receiving antenna 10b receives, the frequency, and the position of the target. At this time, the operation of the high-frequency switch 59 is controlled so that when an electromagnetic wave radiated from the transmitting antenna 10a is reflected by the object to be measured, the reflected wave of the electromagnetic wave is received by the receiving antenna 10b closest to the transmitting antenna 10a that radiated the electromagnetic wave. The receiving microwave amplifier (RF amplifier) ​​may be set to change the gain for each pair of the transmitting antenna 10a that transmits and the receiving antenna 10b that receives the electromagnetic wave. In this case, the high-frequency circuit 62 has a variable gain amplification function that switches the gain depending on the selected pair of the transmitting antenna 10a and the receiving antenna 10b. This makes it possible to increase the depth at which defects, etc., can be inspected in the object to be measured.

[0038] In this embodiment, the arrangement directions of the transmitting antennas 10a and the receiving antennas 10b are parallel, and as shown in Fig. 2, the arrangement direction is defined as the y direction. Meanwhile, the movement direction (scanning direction) of the transmitting array antenna 50 and the receiving array antenna 52 is defined as the x direction. The direction toward the object to be measured (the direction of transmission of electromagnetic waves) as viewed from the transmitting array antenna 50 and the receiving array antenna 52 is defined as the z direction.

[0039] The movement direction (scanning direction) of the transmitting array antenna 50 and the receiving array antenna 52 may be the y direction. That is, they may move (scan) in the same direction as the arrangement direction of the transmitting antennas 10a and the receiving antennas 10b. Alternatively, the transmitting array antenna 50 may have only one transmitting antenna 10a, and the receiving array antenna 52 may have multiple receiving antennas 10b. In this case, the movement direction (scanning direction) of the transmitting array antenna 50 and the receiving array antenna 52 may also be the y direction. In other words, they may move (scan) in the same direction as the arrangement direction of the receiving antennas 10b.

[0040] The data processing unit 66 processes the measurement data s(x', y', z', k) obtained by transmitting and receiving electromagnetic waves using the transmitting array antenna 50 and the receiving array antenna 52, and creates image data representing the interior of the object to be measured. The data processing unit 66 is configured, for example, by a computer, and invokes and starts a program stored in the storage unit 66a. This enables the functions of the data processing unit 66 to be fulfilled. In other words, the data processing unit 66 is configured by software modules. The image display unit 68 displays an image of the interior of the object to be measured using the created image data.

[0041] 2 shows a schematic diagram of a transmitting array antenna 50 and a receiving array antenna 52. The transmitting antenna 10a and the receiving antenna 10b are offset in the x direction by ΔL, but in the following explanation, the x direction positions of the transmitting antenna 10a and the receiving antenna 10b are assumed to be at a circular point midway between the transmitting antenna 10a and the receiving antenna 10b. This circular point is called the transmitting / receiving point. Note that there may be no misalignment in the y direction between the transmitting antenna 10a and the receiving antenna 10b. That is, Δy = 0. There may also be cases where the transmitting antenna 10a and the receiving antenna 10b are shared. That is, Δy = 0 and ΔL = 0.

[0042] Therefore, the positional relationship between the object to be measured, the transmitting array antenna 50, and the receiving array antenna 52 can be expressed as shown in FIG. Here, the coordinates of the transmitting and receiving points are p(x',y',z'). The reflectance at the reflection point (x,y,z) of the object to be measured is f(x,y,z). The measurement data at the transmitting and receiving point p(x',y',z') is s(x',y',z',k). The propagation wavelength of the electromagnetic wave in a vacuum is λ0. The relative permittivity of the medium is ε r Let k be the wave number of the propagating electromagnetic wave.

[0043] In this case, the measurement data s(x', y', z', k) at the transmitting and receiving point p(x', y', z') can be expressed by the following equation. JPEG0007808129000049.jpg17124 however, JPEG0007808129000050.jpg1338 is.

[0044] In equation (1-1), electromagnetic waves are expressed as spherical waves, and distance attenuation is omitted. This distance attenuation is omitted because it has little effect on subsequent processing. If the exponent part of the integrand function in the second equation in equation (1-1) is expressed in Fourier transform notation, it becomes the following equation. This is equivalent to decomposing the round-trip spherical wave in equation (1-1) into a three-dimensional plane wave. JPEG0007808129000051.jpg17115 where (k x ,k y ,k z ) are the components of the wave vector of the round-trip spherical wave of the wave propagating between the transmitting and receiving point p(x', y', z') and the reflecting point (x, y, z). JPEG0007808129000052.jpg751 Meet the following.

[0045] Hereinafter, the reflectance f(x, y, z) is derived from the measurement data s(x', y', z', k) based on the formula (1-3). First, the formula (1-3) is rearranged as follows: JPEG0007808129000053.jpg17121

[0046] Here, the integral inside {} is the triple Fourier transform with respect to (x,y,z). Also, the integral inside [ ] is (k x ,k y ) is a double inverse Fourier transform with respect to (x', y'). Therefore, a double Fourier transform is performed on both sides of equation (1-5) with respect to (x', y'). The function after triple Fourier transform of function f(x, y, z) is F(k x ,k y ,k z ) The function after double Fourier transform of the measurement data s(x', y', z', k) is S(k x ,k y ,z',k). In this case, equation (1-5) can be expressed as follows: JPEG0007808129000054.jpg1580

[0047] Change both sides of the second line of equation (1-6) to (k x ,k y ,k z ), the reflectance f(x,y,z) is obtained as follows: JPEG0007808129000055.jpg12122

[0048] In this embodiment, as shown in FIG. 3, the transmitting and receiving point p(x', y', z') is arranged on the xy plane, and z'=0, so that equation (1-7) can be expressed as follows. JPEG0007808129000056.jpg18121 JPEG0007808129000057.jpg9117

[0049] As described above, the data processing unit 66 obtains the reflectance f(x, y, z) based on the measurement data s(x', y', z', k).

[0050] The data processing method and program of this embodiment will be described below with reference to Fig. 4. Fig. 4 is a flowchart showing the data processing method of this embodiment. First, the measurement unit 61 acquires the measurement data s(x', y', 0, k) (step S1-1). Then, the data processing unit 66 performs a Hilbert transform on the measurement data s(x', y', 0, k) (step S1-2). This obtains the imaginary component of the frequency data at each transmitting and receiving point.

[0051] Next, the data processing unit 66 performs a double Fourier transform of the measurement data s(x', y', 0, k) with respect to (x', y') (step S1-3). As a result, as shown in equation (1-6), S(k x ,k y ,0,k) is obtained. Next, the data processing unit 66 calculates S(k x ,k y , 0, k), variable substitution is performed (step S1-4). Specifically, using equation (1-4), x ,k y ,k) function (k x ,k y ,k z ) function. This makes S(k x ,k y ,k z ) is obtained. Next, the data processing unit 66 calculates S(k x ,ky ,k z ), (k x ,k y ,k z ) is subjected to a triple inverse Fourier transform (step S1-5). As a result, the reflectance f(x, y, z) is obtained as shown in equation (1-8).

[0052] The storage unit 66a stores a program for executing the data processing method of this embodiment. The program stored in the storage unit 66a causes the data processing unit 66 to execute the data processing method of this embodiment.

[0053] Second Embodiment The data processing method, measurement system, and program of the second embodiment will be described in detail below. The transmitting array antenna 50 and receiving array antenna 52 of the first embodiment are arranged in one direction (the y direction in FIG. 3), but the arrangement of the transmitting array antenna 50 and receiving array antenna 52 of this embodiment is different. The transmitting array antenna 50 and receiving array antenna 52 of this embodiment are arranged in a curved shape. Specifically, the transmitting and receiving points p(x', y', z') are arranged on the curve of a single-valued function z'=g(x', y') of (x', y') in a plane parallel to the yz plane.

[0054] In this embodiment, as shown in FIG. 5, a function expressed by the following equation representing a semi-cylindrical measurement surface with a radius R0 will be used for explanation. JPEG0007808129000058.jpg984 The function g(x', y') may be any single-valued function of (x', y').

[0055] The equation (1-5) in the first embodiment is an equation relating to an arbitrary transmitting / receiving point p(x', y', z'). JPEG0007808129000059.jpg17121 Therefore, if we start by substituting equation (2-1) into equation (1-5), we obtain the following equation. JPEG0007808129000060.jpg16122

[0056] Since the left side of equation (2-2) is a function of (x', y', k), it can be rewritten as follows: JPEG0007808129000061.jpg22119

[0057] Here, the integral inside {} is the triple Fourier transform with respect to (x,y,z). Also, the integral inside [ ] is (k x ,k y ) is a double inverse Fourier transform with respect to (x', y'). Therefore, a double Fourier transform is performed on both sides of equation (2-3) with respect to (x', y'). The function after triple Fourier transform of function f(x, y, z) is F(k x ,k y ,k z ) Measurement data s a The double Fourier transform function of (x', y', k) is S a (k x ,k y , k). In this case, equation (2-3) can be expressed as follows: JPEG0007808129000062.jpg1789

[0058] Change both sides of the second line of equation (2-4) to (k x ,k y ,k z ), the reflectance f(x,y,z) is obtained as follows: JPEG0007808129000063.jpg7118

[0059] Here, the following operators are defined for (x', y'): JPEG0007808129000064.jpg2440 The operator in equation (2-6) is S a (k x ,k y ,k), for (k x ,k y ,k z ) space has eigenvalues ​​of (x',y').

[0060] By substituting equation (2-6) into equation (2-5), the reflectance f(x,y,z) is obtained as follows: JPEG0007808129000065.jpg17118 JPEG0007808129000066.jpg9110

[0061] As described above, the data processing unit 66 obtains the reflectance f(x, y, z) based on the measurement data s(x', y', z', k).

[0062] The data processing method and program of this embodiment will be described below with reference to Fig. 6. Fig. 6 is a flowchart showing the data processing method of this embodiment. First, the measurement unit 61 acquires the measurement data s(x', y', z', k) (step S2-1). Then, the data processing unit 66 organizes the measurement data s(x', y', z', k) (step S2-2). As a result, the measurement data s a (x',y',k) is obtained. The data processing unit 66 then processes the measurement data s a A Hilbert transform is performed on (x', y', k) (step S2-3), thereby obtaining the imaginary component of the frequency data at each transmitting and receiving point.

[0063] Next, the data processing unit 66 processes the measurement data s a A double Fourier transform is performed on (x', y', k) with respect to (x', y') (step S2-4). As a result, as shown in equation (2-4), S a (k x ,k y ,k) is obtained. Next, the data processing unit 66 processes the measurement data s a (x',y',k) and S a (k x ,k y , k), the operator expressed by equation (2-6) is obtained (step S2-5).

[0064] Next, the data processing unit 66 performs variable substitution on the following equation (step S2-6). JPEG0007808129000067.jpg1338 This allows S a (k x ,k y ,k) is obtained.

[0065] Next, the data processing unit 66 calculates S a (k x ,k y ,k), for (k x ,k y ,k z ) is then subjected to a triple inverse Fourier transform (step S2-7). As a result, the reflectance f(x, y, z) is obtained as shown in equation (2-7).

[0066] The storage unit 66a stores a program for executing the data processing method of this embodiment. The program stored in the storage unit 66a causes the data processing unit 66 to execute the data processing method of this embodiment.

[0067] (Simulation results) The results of computer simulations of the data processing method of the first embodiment and the data processing method of the second embodiment will be described below. The simulation conditions are as follows:

[0068] Frequency band used f min ~f max :DC~20GHz ·Center frequency fc (wavelength λc): 10GHz (30mm) Measurement interval in scanning direction Δx: 4 mm Number of measurement points in the scanning direction: 256 Measurement width in scanning direction x max :1024mm(4mm×256) Measurement interval Δy in the array antenna direction (same transmitting and receiving point): 3.75 mm Number of measurement points in the array antenna direction: 128 Measurement width y in the direction of the array antennamax :480mm(3.75mm×128) Maximum depth z max :476mm - Relative permittivity ε of the medium r :1 Point target coordinates (unit: mm): (512, 240, 50), (512, 240, 100), (512, 240, 200), (512, 240, 400) Horizontal plane measurement: z'=0 Curved surface measurement 1 (unit: m): JPEG0007808129000068.jpg959 Curved surface measurement 2 (unit: m): JPEG0007808129000069.jpg861

[0069] FIG. 7(a) shows a measurement layout diagram for horizontal surface measurement. FIG. 7(b) shows a measurement layout diagram for curved surface measurement 1. FIG. 7(c) shows a measurement layout diagram for curved surface measurement 2. FIG. 8 shows point targets simulated using the data processing method of the first embodiment based on the measurement layout for horizontal surface measurement. FIG. 9(a) shows point targets simulated using the data processing method of the first embodiment based on the measurement layout for curved surface measurement 1. FIG. 9(b) shows point targets simulated using the data processing method of the second embodiment based on the measurement layout for curved surface measurement 1. FIG. 10(a) shows point targets simulated using the data processing method of the first embodiment based on the measurement layout for curved surface measurement 2. FIG. 10(b) shows point targets simulated using the data processing method of the second embodiment based on the measurement layout for curved surface measurement 2.

[0070] Using the measurement layout for horizontal plane measurement shown in Fig. 7(a), a simulation was performed on four point targets using equation (1-8) of the data processing method of the first embodiment. The results are shown in Fig. 8. In Fig. 8, a 3D image on which the four point targets converge can be confirmed. From the results in Fig. 8, it can be seen that a good 3D image can be obtained from the measurement layout for horizontal plane measurement using equation (1-8).

[0071] Next, using the measurement layout for curved surface measurement 1 shown in FIG. 7(b), a simulation was performed using four point targets with equation (1-8) of the data processing method of the first embodiment. The results are shown in FIG. 9(a). In FIG. 9(a), a three-dimensional image can be seen in which the four point targets extend in the same direction as the measurement layout for curved surface measurement 1 shown in FIG. 7(b). From the results in FIG. 9(a), it can be seen that equation (1-8) does not provide a good three-dimensional image for the measurement layout for curved surface measurement 1. Next, using the measurement layout for curved surface measurement 1 shown in FIG. 7(b), a simulation was performed using four point targets and equation (2-7) of the data processing method of the second embodiment. The results are shown in FIG. 9(b). In FIG. 9(b), a 3D image where the four point targets converge can be confirmed. From the results in FIG. 9(b), it can be seen that a good 3D image can be obtained from the measurement layout for curved surface measurement 1 using equation (2-7).

[0072] Next, using the measurement layout for curved surface measurement 2 shown in Figure 7(c), a simulation was performed using four point targets with equation (1-8) of the data processing method of the first embodiment. The results are shown in Figure 10(a). In Figure 10(a), a three-dimensional image can be seen in which the four point targets extend in the same direction as the measurement layout for curved surface measurement 2 shown in Figure 7(c). From the results in Figure 10(a), it can be seen that equation (1-8) does not provide a good three-dimensional image for the measurement layout for curved surface measurement 2. Next, using the measurement layout of curved surface measurement 2 shown in Figure 7(c), a simulation was performed using four point targets and equation (2-7) of the data processing method of the second embodiment. The results are shown in Figure 10(b). In Figure 10(b), a 3D image where the four point targets converge can be confirmed. From the results of Figure 10(b), it can be seen that a good 3D image can be obtained from the measurement layout of curved surface measurement 2 using equation (2-7).

[0073] From the results of Figures 9(a) and 9(b) and the results of Figures 10(a) and 10(b), it was confirmed that by inserting the operator defined in equation (2-6) into the exponent part of equation (2-7), it is possible to obtain the reflectance f(x, y, z) corresponding to the measurement layout of curved surface measurement 1.

[0074] Third Embodiment The data processing method, measurement system, and program of the third embodiment will be described in detail below. The transmitting array antenna 50 and receiving array antenna 52 of the first embodiment are arranged in one direction (the y direction in FIG. 3), but the arrangement of the transmitting array antenna 50 and receiving array antenna 52 of this embodiment is different. The transmitting array antenna 50 and receiving array antenna 52 of this embodiment are arranged in a plane. In addition, in the first embodiment, the coordinates of both the transmission point and the reception point are p(x', y', z'), but in this embodiment, the coordinates of the transmission point and the reception point are different. In this embodiment, as shown in Fig. 11, a transmission point p1 (x'1, y'1, z'1) and a reception point p2 (x'2, y'2, z'2) are arranged on the xy plane.

[0075] Here, the reflectivity at the reflection point (x, y, z) of the object to be measured is defined as f(x, y, z). The measurement data at the transmission point p1 (x'1, y'1, z'1) and the reception point p2 (x'2, y'2, z'2) is defined as s(x'1, x'2, y'1, y'2, z'1, z'2, k). The propagation wavelength of the electromagnetic wave in a vacuum is defined as λ0. The relative permittivity of the medium is defined as ε r Let k be the wave number of the propagating electromagnetic wave.

[0076] In this case, the measurement data s(x'1, x'2, y'1, y'2, z'1, z'2, k) can be expressed by the following formula. JPEG0007808129000070.jpg14109 however, JPEG0007808129000071.jpg1337 is.

[0077] In equation (3-1), electromagnetic waves are expressed as spherical waves, and distance attenuation is omitted. This distance attenuation is omitted because it has little effect on subsequent processing. When the exponential part of the integrand in equation (3-1) is expressed in Fourier transform notation, it becomes the following equation. This is equivalent to decomposing the spherical wave in equation (3-1) into three-dimensional plane waves.

[0078] JPEG0007808129000072.jpg44110 Here, (k' x1 ,k' y1 ,k' z1 ) is the component of the wave vector of the spherical wave of the wave propagating from the transmitting point to the reflecting point. x2 ,k' y2 ,k' z2 ) is the component of the wave vector of the spherical wave of the wave propagating from the reflection point to the receiving point. JPEG0007808129000073.jpg1758 Meet the following.

[0079] Below, based on equation (3-3), the reflectance f(x, y, z) is derived from s(x'1, x'2, y'1, y'2, z'1, z'2, k). First, a quadruple Fourier transform is performed on both sides of equation (3-3) with respect to (x'1, x'2, y'1, y'2). JPEG0007808129000074.jpg14101

[0080] The left side of equation (3-5) is rewritten and rearranged as equation (3-6) below. JPEG0007808129000075.jpg13104 Then, equation (3-5) can be expressed as equation (3-7). JPEG0007808129000076.jpg1699

[0081] Perform the following integral on both sides of equation (3-7). JPEG0007808129000077.jpg20105

[0082] Here, the following variable substitutions are made: JPEG0007808129000078.jpg1443 JPEG0007808129000079.jpg1545 JPEG0007808129000080.jpg844

[0083] Here, the following equation is obtained from equations (3-9) and (3-10). JPEG0007808129000081.jpg2345 JPEG0007808129000082.jpg2445

[0084] The absolute value of the Jacobian |J| in this variable substitution is given by the following equations from equations (3-12) and (3-13): JPEG0007808129000083.jpg2468 JPEG0007808129000084.jpg2367

[0085] Substituting equations (3-9), (3-10), (3-14), and (3-15) into equation (3-8) and performing variable substitution, we obtain the following equation. JPEG0007808129000085.jpg6493

[0086] Here, the integral for (u, v) on the right side of the second line of equation (3-16) is a constant, so it has been omitted. x ,k y ,k z ), the reflectance f(x,y,z) is obtained as follows: JPEG0007808129000086.jpg13109

[0087] To solve equation (3-17), (k' z1 ,k' z2 ,k) to (k' x1 ,k' x2 ,k' y1 ,k' y2 ,k z ) or (kx ,u,k y ,v,k z ) must be expressed as By rearranging using equations (3-4) and (3-11), and if the transmitting and receiving points are both located on the xy plane passing through the origin, z'1 = z'2 = 0, so equation (3-17) can be expressed as follows. JPEG0007808129000087.jpg14108 JPEG0007808129000088.jpg23104

[0088] As described above, the data processing unit 66 obtains the reflectance f(x, y, z) based on the measurement data s(x'1, x'2, y'1, y'2, z'1, z'2, k).

[0089] The data processing method and program of this embodiment will be described below with reference to Fig. 12. Fig. 12 is a flowchart showing the data processing method of this embodiment. First, the measurement unit 61 acquires the measurement data s(x'1, x'2, y'1, y'2, z'1, z'2, k) (step S3-1). Then, the data processing unit 66 performs a Hilbert transform on the measurement data s(x'1, x'2, y'1, y'2, z'1, z'2, k) (step S3-2). This obtains the imaginary component of the frequency data at each measurement point.

[0090] Next, the data processing unit 66 performs a quadruple Fourier transform of the measurement data s(x'1, x'2, y'1, y'2, z'1, z'2, k) with respect to (x'1, x'2, y'1, y'2) (step S3-3). As a result, as shown in equation (3-6), S(k' x1 ,k' x2 ,k' y1 ,k' y2 ,0,0,k) is obtained. Next, the data processing unit 66 calculates S(k' x1 ,k' x2 ,k' y1 ,k' y2,0,0,k) is subjected to variable substitution (step S3-4). Specifically, using equations (3-9), (3-10), (3-14), and (3-15), (k' x1 ,k' x2 ,k' y1 ,k' y2 ,k) function (k x ,k y ,k z ) function. This makes S(k x ,k y ,k z ) is obtained. Next, the data processing unit 66 calculates S(k x ,k y ,k z ), (k x ,k y ,k z ) is subjected to a triple inverse Fourier transform (step S3-5). As a result, the reflectance f(x, y, z) is obtained as shown in equation (3-18).

[0091] The storage unit 66a stores a program for executing the data processing method of this embodiment. The program stored in the storage unit 66a causes the data processing unit 66 to execute the data processing method of this embodiment.

[0092] <Fourth embodiment> The data processing method, measurement system, and program of the fourth embodiment will be described in detail below. While the transmitting array antenna 50 and receiving array antenna 52 of the third embodiment are arranged on a plane, the arrangement of the transmitting array antenna 50 and receiving array antenna 52 of this embodiment is different. The transmitting array antenna 50 and receiving array antenna 52 of this embodiment are arranged on a curved surface. Specifically, the transmitting point p1(x'1, y'1, z'1) is arranged on a curve of a single-valued function z'1=g1(x'1, y'1) related to (x'1, y'1). The receiving point p2(x'2, y'2, z'2) is arranged on a curve of a single-valued function z'2=g2(x'2, y'2) related to (x'2, y'2).

[0093] In this embodiment, as shown in FIG. 13, a function expressed by the following equation representing a semi-cylindrical measurement surface with a radius R0 will be used for explanation. JPEG0007808129000089.jpg1675 Note that the function g1(x'1, y'1) may be any single-valued function related to (x'1, y'1), and the function g2(x'2, y'2) may be any single-valued function related to (x'2, y'2).

[0094] The equation (3-3) in the third embodiment is an equation for an arbitrary transmission point p1 (x'1, y'1, z'1) and a reception point p2 (x'2, y'2, z'2). Therefore, by substituting the equation (4-1) into the equation (3-3), the following equation is obtained. JPEG0007808129000090.jpg7105 Since the right-hand side of equation (4-2) is a function of (x'1, x'2, y'1, y'2, k), it can be rearranged and expressed as equation (4-3) below. JPEG0007808129000091.jpg7101

[0095] where s a The function after the quadruple Fourier transform of (x'1, x'2, y'1, y'2, k) is S a (k' x1 ,k' x2 ,k' y1 ,k' y2 ,k'). In this case, equation (4-3) can be expressed as follows: JPEG0007808129000092.jpg21101

[0096] Here, by substituting equations (4-1) to (4-4) into equation (3-17), the reflectance f(x, y, z) is obtained as follows: JPEG0007808129000093.jpg18105

[0097] Here, the following operators are defined for (x'1, y'1) and (x'2, y'2). JPEG0007808129000094.jpg2539 JPEG0007808129000095.jpg2539

[0098] The operators in equations (4-6) and (4-7) are S a (k' x1 ,k' x2 ,k' y1 ,k' y2 ,k'), for (k' x1 ,k' x2 ,k' y1 ,k' y2 ,k') space has eigenvalues ​​of (x'1,x'2,y'1,y'2).

[0099] By substituting equations (4-6) and (4-7) into equation (4-5), the reflectance f(x, y, z) is obtained as follows: JPEG0007808129000096.jpg18109

[0100] As described above, the data processing unit 66 obtains the reflectance f(x, y, z) based on the measurement data s(x'1, x'2, y'1, y'2, z'1, z'2, k).

[0101] The data processing method and program of this embodiment will be described below with reference to Fig. 14. Fig. 14 is a flowchart showing the data processing method of this embodiment. First, the measurement unit 61 acquires the measurement data s(x'1, x'2, y'1, y'2, z'1, z'2, k) (step S4-1). Then, the data processing unit 66 organizes the measurement data s(x'1, x'2, y'1, y'2, z'1, z'2, k) (step S4-2). As a result, the measurement data s a (x'1,x'2,y'1,y'2,k) is obtained. The data processing unit 66 then processes the measurement data s a A Hilbert transform is performed on (x'1, x'2, y'1, y'2, k) (step S4-3), thereby obtaining the imaginary component of the frequency data at each measurement point.

[0102] Next, the data processing unit 66 processes the measurement data s a A quadruple Fourier transform is performed on (x'1, x'2, y'1, y'2, k) with respect to (x'1, x'2, y'1, y'2) (step S4-4). As a result, as shown in equation (4-4), S a (k' x1 ,k' x2 ,k' y1 ,k' y2 ,k') is obtained. Next, the data processing unit 66 processes the measurement data s a (x'1,x'2,y'1,y'2,k) and S a (k' x1 ,k' x2 ,k' y1 ,k' y2 , k'), operators expressed by equations (4-6) and (4-7) are obtained (step S4-5).

[0103] Next, the data processing unit 66 performs variable substitution on the following equation (step S4-6). JPEG0007808129000097.jpg1380 This allows S a (k x ,k y ,k z ) is obtained.

[0104] Next, the data processing unit 66 calculates S a (k x ,k y ,k z ), (k x ,k y ,k z ) is subjected to a triple inverse Fourier transform (step S4-7). As a result, the reflectance f(x, y, z) is obtained as shown in equation (4-8).

[0105] The storage unit 66a stores a program for executing the data processing method of this embodiment. The program stored in the storage unit 66a causes the data processing unit 66 to execute the data processing method of this embodiment.

[0106] Fifth Embodiment The data processing method, measurement system, and program of the fifth embodiment will be described in detail below. In the third embodiment, the transmitting array antenna 50 and the receiving array antenna 52 are arranged in a plane, but in this embodiment, the arrangement of the transmitting array antenna 50 and the receiving array antenna 52 is different. In this embodiment, the transmitting array antenna 50 and the receiving array antenna 52 are arranged in a straight line. Specifically, in this embodiment, the transmitting antennas 10a and receiving antennas 10b are arranged in the y direction, as shown in Fig. 15. The movement direction (scanning direction) of the transmitting array antenna 50 and receiving array antenna 52 is defined as the x direction. The direction toward the object to be measured (the transmission direction of electromagnetic waves) as viewed from the transmitting array antenna 50 and receiving array antenna 52 is defined as the z direction. The movement direction (scanning direction) of the transmitting array antenna 50 and the receiving array antenna 52 may be the y direction.

[0107] Therefore, the positional relationship between the object to be measured, the transmitting array antenna 50, and the receiving array antenna 52 can be expressed as shown in FIG. Here, the coordinates of the transmitting point are p1(x'1,y'1,z'1), and the coordinates of the receiving point are p2(x'2,y'2,z'2). The reflectivity at the reflection point (x,y,z) of the object to be measured is f(x,y,z). The measurement data at p2(x'2,y'2,z'2) is s(x'1,x'2,y'1,y'2,z'1,z'2,k). The propagation wavelength of the electromagnetic wave in a vacuum is λ0. The relative dielectric constant of the medium is ε r Let k be the wave number of the propagating electromagnetic wave.

[0108] In this case, the measurement data s(x'1, x'2, y'1, y'2, z'1, z'2, k) can be expressed by the following formula. JPEG0007808129000098.jpg13112 however JPEG0007808129000099.jpg1337 is.

[0109] In equation (5-1), electromagnetic waves are represented as spherical waves, and distance attenuation is omitted. This distance attenuation is omitted because it has little effect on subsequent processing. If the exponent part of the integrand function in the second equation in equation (5-1) is expressed in Fourier transform notation, it becomes the following equation. This is equivalent to decomposing the spherical wave in equation (5-1) into three-dimensional plane waves.

[0110] JPEG0007808129000100.jpg45112 Here, (k' x1 ,k' y1 ,k' z1 ) is the component of the wave vector of the spherical wave of the wave propagating from the transmitting point to the reflecting point. x2 ,k' y2 ,k' z2 ) is the component of the wave vector of the spherical wave of the wave propagating from the reflection point to the receiving point. JPEG0007808129000101.jpg1760 Meet the following.

[0111] Here, since the x coordinates of the transmitting point p1 (x'1, y'1, z'1) and the receiving point p2 (x'2, y'2, z'2) are equal, if we set x' = x'1 = x'2, equation (5-3) can be expressed as follows: JPEG0007808129000102.jpg21110

[0112] Here, the following variable substitutions are made: JPEG0007808129000103.jpg1643 The following equation is obtained from equation (5-6): JPEG0007808129000104.jpg2142

[0113] Calculating the absolute value of the Jacobian from equation (5-7) gives the following equation: JPEG0007808129000105.jpg2181

[0114] Substituting equations (5-6) and (5-8) into equation (5-5) and performing variable substitution, we obtain the following equation. JPEG0007808129000106.jpg41113

[0115] Here, the integral with respect to u in the second line of equation (5-9) is omitted because it is a constant. If we perform a triple inverse Fourier transform on both sides of equation (5-9) with respect to (x, y1, y2), we obtain the following equation. JPEG0007808129000107.jpg17114

[0116] Rewrite and rearrange the left side of equation (5-10) as follows: JPEG0007808129000108.jpg17115 Then, equation (5-10) can be expressed as follows: JPEG0007808129000109.jpg21115

[0117] By performing the following integral on both sides of equation (5-12), we obtain the following equation. JPEG0007808129000110.jpg16115

[0118] Here, (k' y1 ,k' y2 ), (k' z1 ,k' z2 ), we define the following variable substitutions: JPEG0007808129000111.jpg1547 JPEG0007808129000112.jpg848

[0119] Here, the following equation is obtained from equation (5-14): JPEG0007808129000113.jpg2447 The absolute value of the Jacobian under this variable substitution is given by the following formula: JPEG0007808129000114.jpg2671

[0120] Substituting equations (5-1), (5-15), and (5-17) into equation (5-13) and performing variable substitution, we obtain the following equation. JPEG0007808129000115.jpg81113

[0121] Here, the integral of v on the right side of the second line of equation (5-18) is omitted because it is a constant. x ,k y ,k z ), the reflectance f(x,y,z) is obtained as follows: JPEG0007808129000116.jpg14115 Here, in order to align the measurement surface with the x'-y' plane passing through the origin, if z'=0 is set, equation (5-19) can be expressed as follows: JPEG0007808129000117.jpg16115

[0122] To solve equation (5-20), let k be (k' y1 ,k' y2 ,k z ) or (k y ,v,k z ) must be expressed as The four simultaneous equations, Equation (5-4), Equation (5-6), Equation (5-15), and Equation (5-21) obtained from the assumption, are solved. JPEG0007808129000118.jpg1953

[0123] From this, k is expressed by the following formula. JPEG0007808129000119.jpg3298

[0124] As described above, the data processing unit 66 obtains the reflectance f(x, y, z) based on the measurement data s(x'1, x'2, y'1, y'2, z'1, z'2, k).

[0125] The data processing method and program of this embodiment will be described below with reference to Fig. 16. Fig. 16 is a flowchart showing the data processing method of this embodiment. First, the measurement unit 61 acquires the measurement data s(x', y'1, y'2, 0, 0, k) (step S5-1). Then, the data processing unit 66 performs a Hilbert transform on the measurement data s(x', y'1, y'2, 0, 0, k) (step S5-2). This obtains the imaginary component of the frequency data at each measurement point.

[0126] Next, the data processing unit 66 performs a triple Fourier transform of the measurement data s(x', y'1, y'2, 0, 0, k) with respect to (x', y'1, y'2) (step S5-3). As a result, as shown in equation (5-11), S(k x ,k' y1 ,k' y2 ,0,0,k) is obtained. Next, the data processing unit 66 calculates S(k x ,k' y1 ,k' y2 ,0,0,k) is subjected to variable substitution (step S5-4). Specifically, using equations (5-14) and (5-15), x ,k' y1 ,k' y2 ,k) function (k x ,k y ,v,k) function. This makes S(k x ,k y ,v,0,0,k) is obtained. Next, the data processing unit 66 calculates S(k x ,k y ,v,0,0,k), for (k x ,k y ,k z ) is subjected to a triple inverse Fourier transform (step S5-5). As a result, the reflectance f(x, y, z) is obtained as shown in equation (5-20).

[0127] Sixth Embodiment The data processing method, measurement system, and program of the sixth embodiment will be described in detail below. The transmitting array antenna 50 and receiving array antenna 52 of this embodiment are arranged linearly. Specifically, the transmitting array antenna 50 and receiving array antenna 52 are arranged in one direction (the y direction in FIG. 17). Furthermore, the transmitting array antenna 50 and receiving array antenna 52 are moved (scanned) along a curved surface.

[0128] The positional relationship between the object to be measured, the transmitting array antenna 50, and the receiving array antenna 52 can be expressed as shown in FIG. Here, the coordinates of the transmitting point are p1 (x'1, y'1, z'1) and the coordinates of the receiving point are p2 (x'2, y'2, z'2). The reflectivity at the reflection point (x, y, z) of the object to be measured is f(x, y, z). The measurement data at the receiving point p2 (x'2, y'2, z'2) is s(x'1, x'2, y'1, y'2, z'1, z'2, k). The propagation wavelength of the electromagnetic wave in a vacuum is λ0. The relative permittivity of the medium is ε r Let k be the wave number of the propagating electromagnetic wave.

[0129] Furthermore, the transmission point p1 (x'1, y'1, z'1) and the reception point p2 (x'2, y'2, z'2) scan on the curve of a single-valued function z'=g(x') for x'=x'1=x'2. In this embodiment, as shown in FIG. 17, a function expressed by the following equation representing a semi-cylindrical measurement surface with a radius R0 will be used for explanation. JPEG0007808129000120.jpg984 The function g(x') may be any single-valued function of x'.

[0130] Equation (5-5) of the fifth embodiment is an equation relating to an arbitrary transmission point p1 (x'1, y'1, z'1) and reception point p2 (x'2, y'2, z'2). JPEG0007808129000121.jpg21110 Therefore, if we start by substituting equation (6-1) into equation (5-5), we obtain the following equation. JPEG0007808129000122.jpg8113

[0131] The right-hand side of equation (6-2) is a function of (x', y'1, y'2, k), so it can be rearranged to be expressed as the following equation. JPEG0007808129000123.jpg9108 s a The triple Fourier transform function of (x', y'1, y'2, k) is S a (k x ,k' y1 ,k' y2 ,k), the following equation is obtained: JPEG0007808129000124.jpg2497

[0132] Here, by substituting equations (6-1) to (6-4) into equation (5-19), the following equation is obtained. JPEG0007808129000125.jpg14113 Since equation (5-21) also holds true in this embodiment, equation (5-22) can also be used as is in this embodiment.

[0133] Here, the following operators are defined for x': JPEG0007808129000126.jpg1238 The operator in equation (6-6) is S a (k x ,k' y1 ,k' y2 ,k), for (k x ,k' y1 ,k' y2 , k) space.

[0134] By substituting equation (6-6) into equation (6-5), the reflectance f(x,y,z) is obtained as follows: JPEG0007808129000127.jpg23126

[0135] As described above, the data processing unit 66 obtains the reflectance f(x, y, z) based on the measurement data s(x', y'1, y'2, z'1, z'2, k).

[0136] The data processing method and program of this embodiment will be described below with reference to Fig. 18. Fig. 18 is a flowchart showing the data processing method of this embodiment. First, the measurement unit 61 acquires the measurement data s(x', y'1, y'2, z'1, z'2, k) (step S6-1). Then, the data processing unit 66 organizes the measurement data s(x', y'1, y'2, z'1, z'2, k) (step S6-2). As a result, the measurement data s a (x', y'1, y'2, k) is obtained. The data processing unit 66 then processes the measurement data s a A Hilbert transform is performed on (x', y'1, y'2, k) (step S6-3), thereby obtaining the imaginary component of the frequency data at each measurement point.

[0137] Next, the data processing unit 66 processes the measurement data s a A triple Fourier transform is performed on (x', y'1, y'2, k) with respect to (x', y'1, y'2) (step S6-4). As a result, as shown in equation (6-4), S a (k' x ,k' y1 ,k' y2 ,k') is obtained. Next, the data processing unit 66 obtains the operator expressed by equation (6-6) (step S6-5).

[0138] Next, the data processing unit 66 performs variable substitution on the following equation (step S6-6). JPEG0007808129000128.jpg1259 This allows S a (k x ,k y ,k z ) is obtained.

[0139] Next, the data processing unit 66 calculates S a (k x ,k y ,k z ), (k x ,k y ,k z ) is subjected to a triple inverse Fourier transform (step S6-7). As a result, the reflectance f(x, y, z) is obtained as shown in equation (6-7).

[0140] The storage unit 66a stores a program for executing the data processing method of this embodiment. The program stored in the storage unit 66a causes the data processing unit 66 to execute the data processing method of this embodiment.

[0141] (Simulation results) The results of computer simulations of the data processing method of the fifth embodiment and the data processing method of the sixth embodiment will be described below. The simulation conditions are as follows:

[0142] Frequency band used f min ~f max : DC to 4.5 GHz ·Center frequency fc (wavelength λc): 2.25GHz (133mm) Measurement interval in scanning direction Δx: 10 mm Number of measurement points in the scanning direction: 128 Measurement width in scanning direction x max :1280mm(10mm×128) Measurement interval Δy in the array antenna direction (same transmitting and receiving point): 38.5 mm Number of measurement points in the direction of the transmitting array antenna: 16 Number of measurement points in the direction of the receiving array antenna: 16 Measurement width y in the direction of the array antenna max :616mm(38.5mm×16) Maximum depth z max :958mm - Relative permittivity ε of the medium r :5 Point target coordinates (unit: mm): (640, 308, 50), (640, 308, 100), (640, 308, 200), (640, 308, 400) Horizontal plane measurement: z'=0 Curved surface measurement 1 (unit: m): JPEG0007808129000129.jpg960 Curved surface measurement 2 (unit: m): JPEG0007808129000130.jpg863

[0143] FIG. 19(a) shows a measurement layout diagram for horizontal surface measurement. FIG. 19(b) shows a measurement layout diagram for curved surface measurement 1. FIG. 19(c) shows a measurement layout diagram for curved surface measurement 2. FIG. 20 shows point targets simulated using the data processing method of the fifth embodiment based on the measurement layout for horizontal surface measurement. FIG. 21(a) shows point targets simulated using the data processing method of the fifth embodiment based on the measurement layout for curved surface measurement 1. FIG. 21(b) shows point targets simulated using the data processing method of the sixth embodiment based on the measurement layout for curved surface measurement 1. FIG. 22(a) shows point targets simulated using the data processing method of the fifth embodiment based on the measurement layout for curved surface measurement 2. FIG. 22(b) shows point targets simulated using the data processing method of the sixth embodiment based on the measurement layout for curved surface measurement 2.

[0144] Using the measurement layout for horizontal plane measurement shown in Fig. 19(a), a simulation was performed on four point targets using equation (5-20) of the data processing method of the fifth embodiment. The results are shown in Fig. 20. In Fig. 20, a three-dimensional image on which the four point targets converge can be confirmed. From the results in Fig. 20, it can be seen that a good three-dimensional image can be obtained from the measurement layout for horizontal plane measurement using equation (5-20).

[0145] Next, using the measurement layout for curved surface measurement 1 shown in Figure 19(b), a simulation was performed using four point targets with equation (5-20) of the data processing method of the fifth embodiment. The results are shown in Figure 21(a). In Figure 21(a), a three-dimensional image can be seen in which the four point targets extend in the same direction as the measurement layout for curved surface measurement 1 shown in Figure 19(b). From the results in Figure 21(a), it can be seen that equation (5-20) does not provide a good three-dimensional image for the measurement layout for curved surface measurement 1. Next, using the measurement layout for curved surface measurement 1 shown in FIG. 19(b), a simulation was performed using four point targets and equation (6-7) of the data processing method of the sixth embodiment. The results are shown in FIG. 21(b). In FIG. 21(b), a 3D image where the four point targets converge can be confirmed. From the results in FIG. 21(b), it can be seen that a good 3D image can be obtained from the measurement layout for curved surface measurement 1 using equation (6-7).

[0146] Next, using the measurement layout for curved surface measurement 2 shown in Figure 19(c), a simulation was performed on four point targets using equation (5-20) of the data processing method of the fifth embodiment. The results are shown in Figure 22(a). In Figure 22(a), a three-dimensional image can be seen in which the four point targets extend in the same direction as the measurement layout for curved surface measurement 2 shown in Figure 19(c). The results in Figure 22(a) show that equation (5-20) does not provide a good three-dimensional image for the measurement layout for curved surface measurement 2. Next, using the measurement layout for curved surface measurement 2 shown in Figure 19(c), a simulation was performed using four point targets and equation (6-7) of the data processing method of the sixth embodiment. The results are shown in Figure 22(b). In Figure 22(b), a 3D image where the four point targets converge can be confirmed. From the results in Figure 22(b), it can be seen that a good 3D image can be obtained from the measurement layout for curved surface measurement 2 using equation (6-7).

[0147] From the results of Figures 21(a) and 21(b) and the results of Figures 22(a) and 22(b), it was confirmed that by inserting the operator defined in equation (6-6) into the exponent part of equation (6-7), it is possible to obtain the reflectance f(x, y, z) corresponding to the measurement layout of curved surface measurement 1.

[0148] Seventh Embodiment The data processing method, measurement system, and program of the seventh embodiment will be described in detail below. While the transmitting array antenna 50 and receiving array antenna 52 of the sixth embodiment are arranged in one direction (the y direction in FIG. 17), the arrangement of the transmitting array antenna 50 and receiving array antenna 52 of this embodiment is different. The transmitting array antenna 50 and receiving array antenna 52 of this embodiment are arranged in a curved shape. Furthermore, the transmitting array antenna 50 and receiving array antenna 52 are moved (scanned) along the curved surface.

[0149] The positional relationship between the object to be measured, the transmitting array antenna 50, and the receiving array antenna 52 can be expressed as shown in FIG. Here, the coordinates of the transmitting point are p1 (x'1, y'1, z'1) and the coordinates of the receiving point are p2 (x'2, y'2, z'2). The reflectivity at the reflection point (x, y, z) of the object to be measured is f(x, y, z). The measurement data at the receiving point p2 (x'2, y'2, z'2) is s(x'1, x'2, y'1, y'2, z'1, z'2, k). The propagation wavelength of the electromagnetic wave in a vacuum is λ0. The relative permittivity of the medium is ε r Let k be the wave number of the propagating electromagnetic wave.

[0150] Furthermore, the transmission point p1 (x'1, y'1, z'1) and the reception point p2 (x'2, y'2, z'2) satisfy x'=x'1=x'2. In this embodiment, as shown in FIG. 23, a function expressed by the following equation representing a semi-cylindrical measurement surface with a radius R0 will be used for explanation. JPEG0007808129000131.jpg1694 Note that the function g1(x', y'1) may be any single-valued function related to (x', y'1), and the function g2(x', y'2) may be any single-valued function related to (x', y'2).

[0151] Equation (5-5) of the fifth embodiment is an equation relating to an arbitrary transmission point p1 (x'1, y'1, z'1) and reception point p2 (x'2, y'2, z'2). JPEG0007808129000132.jpg21110 Therefore, if we start by substituting equation (7-1) into equation (5-5), we obtain the following equation. JPEG0007808129000133.jpg8104

[0152] The right-hand side of equation (7-2) is a function of (x', y'1, y'2, k), so it can be rearranged to be expressed as the following equation. JPEG0007808129000134.jpg7102 s a The triple Fourier transform function of (x', y'1, y'2, k) is S a (k x ,k' y1 ,k' y2 ,k), the following equation is obtained: JPEG0007808129000135.jpg2291

[0153] Here, by substituting equations (7-1) to (7-4) into equation (5-19), the following equation is obtained. JPEG0007808129000136.jpg13103 In this embodiment, the formula (5-22) can also be used approximately.

[0154] Here, the following operators are defined for (x', y'1, y'2). JPEG0007808129000137.jpg1135 JPEG0007808129000138.jpg2236 The operators in equations (7-6) and (7-7) are S a(k x ,k' y1 ,k' y2 ,k), for (k x ,k' y1 ,k' y2 , k) space.

[0155] By substituting equations (7-6) and (7-7) into equation (7-5), the reflectance f(x, y, z) is obtained as follows: JPEG0007808129000139.jpg19105

[0156] As described above, the data processing unit 66 obtains the reflectance f(x, y, z) based on the measurement data s(x', y'1, y'2, z'1, z'2, k).

[0157] The data processing method and program of this embodiment will be described below with reference to Fig. 24. Fig. 24 is a flowchart showing the data processing method of this embodiment. First, the measurement unit 61 acquires the measurement data s(x', y'1, y'2, z'1, z'2, k) (step S7-1). Then, the data processing unit 66 organizes the measurement data s(x', y'1, y'2, z'1, z'2, k) (step S7-2). As a result, the measurement data s a (x', y'1, y'2, k) is obtained. The data processing unit 66 then processes the measurement data s a A Hilbert transform is performed on (x', y'1, y'2, k) (step S7-3), thereby obtaining the imaginary component of the frequency data at each measurement point.

[0158] Next, the data processing unit 66 processes the measurement data s a A triple Fourier transform is performed on (x', y'1, y'2, k) with respect to (x', y'1, y'2) (step S7-4). As a result, as shown in equation (7-4), S a (k' x ,k' y1 ,k' y2,k') is obtained. Next, the data processing unit 66 obtains the operators expressed by equations (7-6) and (7-7) (step S7-5).

[0159] Next, the data processing unit 66 performs variable substitution on the following equation (step S7-6). JPEG0007808129000140.jpg1275 This allows S a (k x ,k y ,k z ) is obtained.

[0160] Next, the data processing unit 66 calculates S a (k x ,k y ,k z ), (k x ,k y ,k z ) is subjected to a triple inverse Fourier transform (step S7-7). As a result, the reflectance f(x, y, z) is obtained as shown in equation (7-7).

[0161] The storage unit 66a stores a program for executing the data processing method of this embodiment. The program stored in the storage unit 66a causes the data processing unit 66 to execute the data processing method of this embodiment. [Explanation of symbols]

[0162] 10a Transmitting antenna 10b Receiving antenna 50 Transmitting array antenna 52 Receiving array antenna 60 Radar equipment 61 Measurement Unit 64 System Control Circuit 66 Data Processing Unit 68 Image display unit 58, 59 High frequency switches 62 High-frequency circuits 69 Encoder

Claims

1. A data processing method for analyzing scattered waves of waves radiated to an object, comprising: The wave is emitted to the object from a plurality of transmitting and receiving points p(x', y', z') arranged on a curve of a single-valued function z'=g(x', y') with respect to (x', y') in a plane parallel to the yz plane; The scattered wave reflected at the reflection point (x, y, z) on the object with reflectivity f(x, y, z) is measured at the transmitting / receiving point p(x', y', z') where the wave was emitted. a Received as (x', y', k), The measured value s a (x', y', k) is double Fourier transformed using equation (1) to obtain S a (k x , k y , k) and S a (k x , k y , k), define an operator shown in equation (2) having eigenvalues ​​(x', y'), The reflectance f(x, y, z) is calculated by performing a triple inverse Fourier transform using equation (3). Data processing methods. however, k is the wave number of the propagating wave, k x , k y , k z is a component of the wave vector of the round-trip spherical wave of the wave propagating between the transmitting and receiving point p(x', y', z') and the reflecting point (x, y, z), is.

2. The plurality of transmitting and receiving points p(x', y', z') move in the x direction. The data processing method according to claim 1 .

3. The plurality of transmitting and receiving points p(x', y', z') move in the y direction. The data processing method according to claim 1 .

4. The wave number and wave vector components of the wave satisfy the formula (4). The data processing method according to any one of claims 1 to 3.

5. A measurement system for analyzing scattered waves of waves radiated to an object, comprising: A transmitting / receiving unit having a plurality of transmitting / receiving points p(x', y', z') arranged on a curve of a single-valued function z'=g(x', y') with respect to (x', y') in a plane parallel to the yz plane, radiating the wave to the object, and measuring the scattered wave reflected at a reflection point (x, y, z) on the object with a reflectivity f(x, y, z) at the transmitting / receiving point p(x', y', z') from which the wave was radiated. a a transmitter / receiver that receives the signal as (x', y', k); A processing device, The measured value s a (x', y', k) is double Fourier transformed using equation (1) to obtain S a (k x , k y , k) and S a (k x , k y , k), defining an operator shown in equation (2) with eigenvalues ​​(x', y'); A procedure of calculating the reflectance f(x, y, z) by triple inverse Fourier transform using equation (3); a processing unit for executing the A measurement system having: k is the wave number of the propagating wave, k x , k y , k z is a component of the wave vector of the round-trip spherical wave of the wave propagating between the transmitting and receiving point p(x', y', z') and the reflecting point (x, y, z), is.

6. The transceiver moves in the x direction. The measurement system according to claim 5 .

7. The transceiver moves in the y direction. The measurement system according to claim 5 .

8. The wave number and wave vector components of the wave satisfy the formula (4). The measurement system according to any one of claims 5 to 7.

9. A program for analyzing scattered waves of waves radiated to an object, A wave is emitted to the object from a plurality of transmitting and receiving points p(x', y', z') arranged on a curve of a single-valued function z' = g(x', y') with respect to (x', y') in a plane parallel to the yz plane. The scattered wave is reflected at a reflection point (x, y, z) on the object with a reflectivity f(x, y, z). The measured value s is the value received at the transmitting and receiving point p(x', y', z') from which the wave was emitted. a (x', y', k) is double Fourier transformed using equation (1) to obtain S a (k x , k y , k) and S a (k x , k y , k), defining an operator shown in equation (2) with eigenvalues ​​(x', y'); A procedure of calculating the reflectance f(x, y, z) by triple inverse Fourier transform using equation (3); A program that causes a computer to execute the following. however, k is the wave number of the propagating wave, k x , k y , k z is the component of the wave vector of the round-trip spherical wave of the wave propagating between the transmitting and receiving point p(x', y', z') and the reflecting point (x, y, z), is.

10. The wave number and wave vector components of the wave satisfy the formula (4). The program according to claim 9.

11. A data processing method for analyzing scattered waves of waves radiated to an object, comprising: Multiple transmitting points p arranged on the y-axis 1 (x', y' 1 , z' 1 ) to emit the wave to the object, The scattered wave reflected at the reflection point (x, y, z) on the object with reflectivity f(x, y, z) is received by a plurality of receiving points p arranged on the y axis. 2 (x', y' 2 , z' 2 ) and the measured value s a (x', y' 1 , y' 2 , k) and The plurality of transmission points p arranged on the y-axis 1 (x', y' 1 , z' 1 ) and the plurality of receiving points p 2 (x', y' 2 , z' 2 ) on the surface of a single-valued function z'=g(x') with respect to x', The measured value s a (x', y' 1 , y' 2 , k) is triple Fourier transformed using equation (1) to obtain S a (k' x , k' y1 , k' y2 , k) and S a (k' x, k' y1 , k' y2 , k), define an operator shown in equation (2) with eigenvalue x', The reflectance f(x, y, z) is calculated by performing a triple inverse Fourier transform using equation (3). Data processing methods. however, x’ = x’ 1 = x’ 2 z' = z' 1 = with' 2 k is the wave number of the propagating wave, k' x1 , k' y1 , k' z1 is the transmission point p 1 (x' 1 , y' 1 , z' 1 ) to the reflection point (x, y, z), the components of the wave vector of the spherical wave of the wave propagating between k' x2 , k' y2 , k' z2 is the distance from the reflection point (x, y, z) to the reception point p 2 (x' 2 , y' 2 , z' 2 ) the components of the wave vector of the spherical wave of the wave propagating between to y = k' y1 + k' y2 , v = k' y1 - to y2 is.

12. The wave number and wave vector components of the wave satisfy the formula (4). The data processing method according to claim 11.

13. A measurement system for analyzing scattered waves of waves radiated to an object, comprising: A transceiver unit, Multiple transmitting points p arranged on the y-axis 1 (x', y' 1 , z' 1 a transmitting unit that radiates the wave from the object to the object; The scattered wave reflected at the reflection point (x, y, z) on the object with reflectivity f(x, y, z) is received by a plurality of receiving points p arranged on the y axis. 2 (x', y' 2 , z' 2 ) and the measured value s a (x', y' 1 , y' 2 , k) as a receiving unit; and The plurality of transmission points p arranged on the y-axis 1 (x', y' 1 , z' 1 ) and the plurality of receiving points p 2 (x', y' 2 , z' 2 ) on the surface of a single-valued function z'=g(x') with respect to x'; A processing device, The measured value s a (x', y' 1 , y' 2 , k) is triple Fourier transformed using equation (1) to obtain S a (k' x , k' y1 , k' y2 , k) and S a (k' x, k' y1 , k' y2 , k), defining the operator shown in equation (2) with eigenvalue x'; A procedure of calculating the reflectance f(x, y, z) by triple inverse Fourier transform using equation (3); a processing unit for executing the A measurement system having: however, x’ = x’ 1 = x’ 2 z' = z' 1 = with' 2 k is the wave number of the propagating wave, k' x1 , k' y1 , k' z1 is the transmission point p 1 (x' 1 , y' 1 , z' 1 ) to the reflection point (x, y, z), the components of the wave vector of the spherical wave of the wave propagating between k' x2 , k' y2 , k' z2 is the distance from the reflection point (x, y, z) to the reception point p 2 (x' 2 , y' 2 , z' 2 ) the components of the wave vector of the spherical wave of the wave propagating between to y = k' y1 + k' y2 , v = k' y1 - to y2 is.

14. The wave number and wave vector components of the wave satisfy the formula (4). The measurement system of claim 13.

15. A program for analyzing scattered waves of waves radiated to an object, Multiple transmitting points p arranged on the y-axis 1 (x', y' 1 , z' 1 ) to the object, the wave is reflected at a reflection point (x, y, z) on the object with a reflectivity f(x, y, z), and the scattered wave is received by a plurality of receiving points p 2 (x', y' 2 , z' 2 ) and the measured value s is the value received by moving on the surface of a single-valued function z' = g(x') related to x'. a (x', y' 1 , y' 2 , k) is triple Fourier transformed using equation (1) to obtain S a (k' x , k' y1 , k' y2 , k) and S a (k' x, k' y1 , k' y2 , k), defining the operator shown in equation (2) with eigenvalue x'; A procedure of calculating the reflectance f(x, y, z) by triple inverse Fourier transform using equation (3); A program that causes a computer to execute the following. however, x’ = x’ 1 = x’ 2 z' = z' 1 = with' 2 k is the wave number of the propagating wave, k' x1 , k' y1 , k' z1 is the transmitting point p 1 (x' 1 , y' 1 , z' 1 ) to the reflection point (x, y, z), the components of the wave vector of the spherical wave of the wave, k' x2 , k' y2 , k' z2 is the distance from the reflection point (x, y, z) to the receiving point p 2 (x' 2 , y' 2 , z' 2 ) the components of the wave vector of the spherical wave of the wave propagating between to y = k' y1 + k' y2 , v = k' y1 - to y2 is.

16. The wave number and wave vector components of the wave satisfy the formula (4). The program according to claim 15.

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