WO2023119371A1 - Procédé de traitement de données, système de mesure et programme - Google Patents

Procédé de traitement de données, système de mesure et programme Download PDF

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WO2023119371A1
WO2023119371A1 PCT/JP2021/047054 JP2021047054W WO2023119371A1 WO 2023119371 A1 WO2023119371 A1 WO 2023119371A1 JP 2021047054 W JP2021047054 W JP 2021047054W WO 2023119371 A1 WO2023119371 A1 WO 2023119371A1
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wave
equation
point
waves
data processing
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PCT/JP2021/047054
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Japanese (ja)
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康成 森
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株式会社三井Ｅ＆Ｓマシナリー
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Priority to JP2022571838A priority Critical patent/JP7300077B1/ja
Priority to PCT/JP2021/047054 priority patent/WO2023119371A1/fr
Publication of WO2023119371A1 publication Critical patent/WO2023119371A1/fr

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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N22/00—Investigating or analysing materials by the use of microwaves or radio waves, i.e. electromagnetic waves with a wavelength of one millimetre or more
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N22/00—Investigating or analysing materials by the use of microwaves or radio waves, i.e. electromagnetic waves with a wavelength of one millimetre or more
    • G01N22/02—Investigating the presence of flaws

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  • 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 frequencies of waves such as electromagnetic waves generated in space and the spatial coordinates of the space.
  • a radar device that non-destructively inspects the inside of non-metallic structures such as concrete and wood.
  • a conventional radar device has an array antenna in which a plurality of antennas are arranged on a plane.
  • An array antenna has, for example, a structure in which antennas such as planar antennas are arranged in one direction, and a transmitting array antenna and a receiving array antenna are arranged close to each other. Further, in order to accurately measure the inside of a structure, the radar device measures the object to be measured at wideband frequencies while changing the frequency of electromagnetic waves at set frequency intervals.
  • Patent Document 1 Japanese Patent Laid-Open No. 2015-095840. No. 1, hereinafter referred to as “Patent Document 1”.
  • the array direction of the planar antennas of the transmitting array antenna is parallel to the arraying direction of the planar antennas of the receiving array antenna.
  • the position of the receiving array antenna in the array direction of the planar antennas is between two positions of the adjacent planar antennas of the transmitting array antenna.
  • Patent Document 2 Japanese Patent No. 6557747, hereinafter referred to as “Patent Document 2”.
  • Synthetic aperture processing is used to visualize the interior of the structure from the measured data.
  • Synthetic aperture processing is broadly classified into addition methods such as the diffraction stacking method and methods using Fourier transform such as the FK migration method.
  • Synthetic aperture processing using Fourier transform is realistic for achieving a practical computation time.
  • synthetic aperture processing using Fourier transform measurements on a plane with equal intervals are required.
  • Patent Document 1 In a radar apparatus having an array antenna in which planar antennas are arranged in one direction, as disclosed in Patent Document 1, it is sometimes difficult to bring each array antenna close to a structure having a curved surface shape. Further, in the scattering tomography method as disclosed in Patent Document 2, the computation for visualizing the information inside the object is complicated, and the computation time is long.
  • the measured value s a (x ', y', k) is double Fourier transformed from equation (1) to obtain S a (k x , ky , k), Defining an operator shown in equation (2) with eigenvalues (x', y ') for S a (k x , k y , k), Perform triple inverse Fourier transform from equation (3) to obtain the reflectance f (x, y, z), Data processing method.
  • k is the wave number of said wave propagating;
  • k x , k y , k z are the wave vectors of round-trip spherical waves of the wave propagating between the transmitting/receiving point p(x', y', z') and the reflecting point (x, y, z); component, is.
  • a third aspect of the present invention is A program for analyzing scattered waves of waves radiated to an object, A procedure for obtaining S a (k x , k y , k) by double Fourier transforming the measured value S a ( x ' , y ' , k) from equation (1); Defining the operator shown in equation (2) with eigenvalues (x', y ') for S a (k x , k y , k); A procedure for obtaining the reflectance f (x, y, z) by performing a triple inverse Fourier transform from Equation (3); is a program that causes a computer to execute however, k is the wave number of said wave propagating; k x , k y , k z are the components of the round-trip spherical wave vector of said wave propagating between the transmitting/receiving point p(x', y', z') and the reflecting point (x, y, z
  • a fourth aspect of the present invention is A data processing method for analyzing scattered waves of waves radiated to an object, radiating the waves to the object from a plurality of transmission points p 1 (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 the reflectance f(x, y, z) is received at a plurality of reception points p 2 (x', y ' 2 , z' 2 ) as measured value s a (x', y' 1 , y' 2 , k),
  • Let the plurality of transmission points p 1 (x', y' 1 , z' 1 ) and the plurality of reception points p 2 (x', y' 2 , z' 2 ) arranged on the y-axis be x' Move on the surface of the single-valued function z' g(x') with respect to The
  • k' x1 , k' y1 , k' z1 are values of the waves propagating between the transmitting point p 1 (x' 1 , y' 1 , z' 1 ) and the reflecting point (x, y, z).
  • the components of the wave vector of the spherical wave, k' x2 , k' y2 , k' z2 are the values of the waves propagating between the reflecting point (x, y, z) and the receiving point p 2 (x' 2 , y' 2 , z' 2 ).
  • a fifth aspect of the present invention is A measurement system for analyzing scattered waves of waves radiated to an object, a transmitting/receiving unit, a transmitter that radiates the waves to the object from a plurality of transmission points p 1 (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 the reflectance f(x, y, z) is received at a plurality of reception points p 2 (x', y ' 2 , z' 2 ) as measured value s a (x', y' 1 , y' 2 , k); has Let the plurality of transmission points p 1 (x', y' 1 , z' 1 ) and the plurality of reception points p 2 (x', y' 2 , z' 2 ) arranged on the y-axis be x' a transmitting/receiving
  • the components of the wave vector of the spherical wave, k' x2 , k' y2 , k' z2 are the values of the waves propagating between the reflecting point (x, y, z) and the receiving point p 2 (x' 2 , y' 2 , z' 2 ).
  • a seventh aspect of the present invention is A data processing method for analyzing scattered waves of waves radiated to an object, radiating the waves to the object from a plurality of transmission points p 1 (x' 1 , y' 1 , z' 1 ) arranged two-dimensionally on the xy plane;
  • the scattered wave reflected at the reflection point (x, y, z) on the object with the reflectance f(x, y, z) is received at a plurality of receiving points p 2 (x ' 2 , y' 2 , z' 2 ) as measurements s(x' 1 , x' 2 , y' 1 , y' 2 , z' 1 , z' 2 , k) and
  • the measured value s ( x'1 , x'2 , y'1, y'2 , z'1 , z'2 , k) is quadruple Fourier transformed by Equation (1) to obtain S( k'x
  • the components of the wave vector of the spherical wave, k' x2 , k' y2 , k' z2 are the values of the waves propagating between the reflecting point (x, y, z) and the receiving point p 2 (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
  • An eighth aspect of the present invention is A measurement system for analyzing scattered waves of waves radiated to an object, a transmitting/receiving unit, a transmitting unit that radiates the waves to the object from a plurality of transmitting points p 1 (x' 1 , y' 1 , z' 1 ) arranged two-dimensionally on the xy plane;
  • the scattered wave reflected at the reflection point (x, y, z) on the object with the reflectance f(x, y, z) is received at a plurality of receiving points p 2 (x ' 2 , y' 2 , z' 2 ) as measured values s (x' 1 , x' 2 , y' 1 , y' 2 , z' 1 , z' 2 , k);
  • a transceiver having A processing device, The measured value s ( x'1 , x'2 , y'1, y'2 , z'1 ,
  • the components of the wave vector of the spherical wave, k' x2 , k' y2 , k' z2 are the values of the waves propagating between the reflecting point (x, y, z) and the receiving point p 2 (x' 2 , y' 2 , z' 2 ).
  • a ninth aspect of the present invention is A program for analyzing scattered waves of waves radiated to an object, Measured values s( x'1 , x'2 , y'1 , y'2 , z'1 , z'2 , k) are quadruple Fourier transformed by formula (1) to obtain S( k'x1 , k' x2 , k' y1 , k' y2 , z' 1 , z' 2 , k);
  • a tenth aspect of the present invention is A data processing method for analyzing scattered waves of waves radiated to an object, radiating the waves to the object from a plurality of transmission points p 1 (x' 1 , y' 1 , z' 1 ) arranged on the y-axis;
  • the scattered wave reflected at the reflection point (x, y, z) on the object with the reflectance f(x, y, z) is received at a plurality of reception points p 2 (x′ 2 , y' 2 , z' 2 ) as measurements s(x' 1 , x' 2 , y' 1 , y' 2 , z' 1 , z' 2 , k) and
  • the measured value s ( x'1 , x'2 , y'1, y'2 , z'1 , z'2 , k) is triple Fourier transformed by Equation (1) to obtain S( k'x1 , k
  • k' x1 , k' y1 , k' z1 are values of the waves propagating between the transmitting point p 1 (x' 1 , y' 1 , z' 1 ) and the reflecting point (x, y, z).
  • the components of the wave vector of the spherical wave, k' x2 , k' y2 , k' z2 are the values of the waves propagating between the reflecting point (x, y, z) and the receiving point p 2 (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
  • An eleventh aspect of the present invention is A measurement system for analyzing scattered waves of waves radiated to an object, a transmitting/receiving unit, a transmitter that radiates the waves to the object from a plurality of transmission points p 1 (x' 1 , y' 1 , z' 1 ) arranged on the y-axis;
  • the scattered wave reflected at the reflection point (x, y, z) on the object with the reflectance f(x, y, z) is received at a plurality of reception points p 2 (x′ 2 , y'2 , z'2 ) as measured values s(x'1, x'2 , y'1 , y'2 , z'1 , z'2 , k);
  • a transceiver having A processing device,
  • the components of the wave vector of the spherical wave, k' x2 , k' y2 , k' z2 are the values of the waves propagating between the reflecting point (x, y, z) and the receiving point p 2 (x' 2 , y' 2 , z' 2 ).
  • 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 from Equation (1) to obtain S( k'x1 , k' x2 , k' y1 , k' y2 , z' 1 , z' 2 , k);
  • k' x1 , k' y1 , k' z1 are values of the waves propagating between the transmit
  • the components of the wave vector of the spherical wave, k' x2 , k' y2 , k' z2 are the values of the waves propagating between the reflecting point (x, y, z) and the receiving point p 2 (x' 2 , y' 2 , z' 2 ).
  • the scattered wave reflected at the reflection point (x, y, z) on the object with the reflectance f(x, y, z) is expressed as (x' 2 , y' 2 ) in a plane parallel to the yz plane
  • Measured values at a plurality of receiving points p 2 ( x' 2 , y' 2 , z' 2 ) arranged on the curve of the second single-valued function z' 2 g 2 (x' 2 , y' 2 ) received as s
  • k is the wave number of said wave propagating;
  • k' x1 , k' y1 , k' z1 are values of the waves propagating between the transmitting point p 1 (x' 1 , y' 1 , z' 1 ) and the reflecting point (x, y, z).
  • the components of the wave vector of the spherical wave, k' x2 , k' y2 , k' z2 are the values of the waves propagating between the reflecting point (x, y, z) and the receiving point p 2 (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
  • the scattered wave reflected at the reflection point (x, y, z) on the object with the reflectance f(x, y, z) is expressed as (x' 2 , y' 2 ) in a plane parallel to the yz plane
  • Measured values at a plurality of receiving points p 2 (x' 2 , y' 2 , z ' 2 ) arranged on the curve of the second single-valued function z' 2 g 2 (
  • the components of the wave vector of the spherical wave, k' x2 , k' y2 , k' z2 are the values of the waves propagating between the reflecting point (x, y, z) and the receiving point p 2 (x' 2 , y' 2 , z' 2 ).
  • a fifteenth aspect of the present invention is A program for analyzing scattered waves of waves radiated to an object,
  • the measured value s a (x' 1 , x' 2 , y' 1 , y' 2 , k) is quadruple Fourier transformed from the equation (1) to obtain S a (k' x1 , k' x2 , k' y1 , a procedure for obtaining k' y2 , k); Equation (2) with eigenvalues ( x'1 , y'1 , x'2 , y'2 ) for Sa( k'x1 , k'x2 , k'y1, k'y2 , k ) and equation A procedure for defining the operator indicated by (3);
  • a procedure for obtaining the reflectance f (x, y, z) by performing a triple inverse Fourier transform from Equation (4); is a program that causes a computer to execute however, k is the wave
  • the scattered wave reflected at the reflection point (x, y, z) on the object with the reflectance f(x, y, z) is expressed as (x' 2 , y' 2 ) in a plane parallel to the yz plane
  • Measured values at a plurality of receiving points p 2 (x' 2 , y' 2 , z ' 2 ) arranged on the curve of the second single-valued function z' 2 g 2 (x' 2 , y' 2 ) received as s
  • k' x1 , k' y1 , k' z1 are values of the waves propagating between the transmitting point p 1 (x' 1 , y' 1 , z' 1 ) and the reflecting point (x, y, z).
  • the components of the wave vector of the spherical wave, k' x2 , k' y2 , k' z2 are the values of the waves propagating between the reflecting point (x, y, z) and the receiving point p 2 (x' 2 , y' 2 , z' 2 ).
  • the scattered wave reflected at the reflection point (x, y, z) on the object with the reflectance f(x, y, z) is expressed as (x' 2 , y' 2 ) in a plane parallel to the yz plane
  • Measured values at a plurality of receiving points p 2 ( x' 2 , y' 2 , z' 2 ) arranged on the curve of the second single-valued function z' 2 g 2 (
  • the components of the wave vector of the spherical wave, k' x2 , k' y2 , k' z2 are the values of the waves propagating between the reflecting point (x, y, z) and the receiving point p 2 (x' 2 , y' 2 , z' 2 ).
  • FIG. 4 A diagram showing the configuration of the array antenna shown in FIG. FIG. 4 is a diagram for explaining the positional relationship between the array antenna of the first embodiment and the object to be measured;
  • Flowchart showing the data processing method of the first embodiment A diagram for explaining the positional relationship between the array antenna of the second embodiment and an object to be measured.
  • Flowchart showing the data processing method of the second embodiment (a) is a measurement layout diagram for horizontal surface measurement, (b) is a measurement layout diagram for curved surface measurement 1, and (c) is a measurement layout diagram for curved surface measurement 2.
  • a point target simulated by the data processing method of the first embodiment using a measurement layout for horizontal surface measurement.
  • point target (a) is a point target simulated by the data processing method of the first embodiment using the measurement layout of curved surface measurement 1
  • point target (b) is the measurement layout of curved surface measurement 1 simulated by the data processing method of the second embodiment.
  • point target (a) is a point target simulated by the data processing method of the first embodiment based on the measurement layout of the curved surface measurement 2
  • (b) is simulated by the data processing method of the second embodiment based on the measurement layout of the curved surface measurement 2.
  • point target A diagram for explaining the positional relationship between the array antenna of the third embodiment and an object to be measured. Flowchart showing the data processing method of the third embodiment FIG.
  • FIG. 11 is a diagram for explaining the positional relationship between the array antenna of the fourth embodiment and the object to be measured; Flowchart showing the data processing method of the fourth embodiment FIG. 11 is a diagram for explaining the positional relationship between the array antenna of the fifth embodiment and the object to be measured; Flowchart showing the data processing method of the fifth embodiment A diagram for explaining the positional relationship between the array antenna of the sixth embodiment and an object to be measured.
  • Flowchart showing a data processing method of the sixth embodiment (a) is a measurement layout diagram for horizontal surface measurement, (b) is a measurement layout diagram for curved surface measurement 1, and (c) is a measurement layout diagram for curved surface measurement 2.
  • a point target simulated by the data processing method of the fifth embodiment using a measurement layout for horizontal surface measurement.
  • point target (a) is a point target simulated by the data processing method of the fifth embodiment using the measurement layout of curved surface measurement 1
  • point target (b) is the measurement layout of curved surface measurement 1 simulated by the data processing method of the sixth embodiment.
  • point target (a) is a point target simulated by the data processing method of the fifth embodiment based on the measurement layout of the curved surface measurement 2
  • (b) is simulated by the data processing method of the sixth embodiment based on the measurement layout of the curved surface measurement 2.
  • point target A diagram for explaining the positional relationship between the array antenna of the seventh embodiment and an object to be measured. Flowchart showing the data processing method of the seventh embodiment
  • FIG. 1 shows the configuration of a radar device according to this embodiment.
  • FIG. 2 shows the configuration of the array antenna shown in FIG.
  • FIG. 3 is a diagram for explaining the positional relationship between the array antenna of this embodiment and the object to be measured.
  • waves that radiate electromagnetic waves into space are described, but waves that propagate in space, such as X-rays and ultrasonic waves, may be used instead of electromagnetic waves.
  • the measurement system 1 of this embodiment has a transmitting/receiving section and a processing device.
  • the processing device may be provided integrally with the transmitting/receiving unit, or may be provided at a separate location connected to the transmitting/receiving unit via a network.
  • a processing device is provided integrally with a transmission/reception unit will be described.
  • the radar device 60 of the present embodiment shown in FIG. 1 uses a transmitting array antenna and a receiving array antenna (transmitting/receiving unit) to radiate electromagnetic waves from the transmitting antenna while sweeping the frequency of the electromagnetic waves. Then, the radar device 60 receives the reflected wave of the object to be measured by the receiving antenna and obtains the 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 wave.
  • 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 transmission array antenna 50 , a reception array antenna 52 , high frequency switches 58 and 59 , a high frequency circuit 62 and a system control circuit 64 .
  • the radar device 60 radiates electromagnetic waves of 10 MHz or more, for example 10 to 20 GHz, but the frequency of the electromagnetic waves is not particularly limited.
  • the transmitting array antenna 50 has a plurality of transmitting antennas 10a arranged in one direction. Each transmitting antenna 10a radiates electromagnetic waves toward the object to be measured.
  • the reception array antenna 52 has a plurality of reception antennas 10b arranged along the arrangement direction of the transmission antennas 10a. Each receiving antenna 10b receives electromagnetic waves reflected from the object to be measured.
  • the transmitting antenna 10a of the transmitting array antenna 50 and the receiving antenna 10b of the receiving array antenna 52 are arranged on one plane.
  • a transmitting array antenna 50 and a receiving array antenna 52 are arranged so that the object to be measured faces this plane.
  • the data processing unit 66 processes a plurality of measurement data obtained by transmission toward the measurement object by the plurality of transmission antennas 10a and reception by the plurality of reception antennas 10b, and calculates image data regarding the measurement object.
  • the transmitting antenna 10a and the receiving antenna 10b of this embodiment are planar antennas in which an antenna pattern is formed planarly on a substrate, but are not limited to planar antennas.
  • 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 measurement while scanning along the surface of the object to be measured.
  • the system control circuit 64 controls the operation of the high frequency circuit 62 when the transmitting array antenna 50 and the receiving array antenna 52 move. Specifically, the system control circuit 64 radiates electromagnetic waves while switching the transmitting antenna 10a by the high-frequency switch 58 for each unit length of the moving distance of the transmitting array antenna 50 and the receiving array antenna 52. It controls the operation of the high frequency circuit 62 .
  • the radar device 60 has an encoder 69 .
  • the encoder 69 generates a pulse signal every fixed moving distance.
  • Encoder 69 senses the movement of transmitting array antenna 50 and receiving array antenna 52 .
  • the high-frequency switch 59 sequentially switches the plurality of receiving antennas 10b to allow each receiving antenna 10b to receive the electromagnetic wave.
  • the frequency of the electromagnetic waves radiated from the transmitting array antenna 50 is swept at predetermined frequency intervals, for example, in the range of 10 to 20 GHz, 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 transmitted by the transmitting antenna 10a, the position received by the receiving antenna 10b, the frequency, and the position of the target.
  • the high-frequency switch 59 operates so that the reflected wave of the electromagnetic wave when the electromagnetic wave radiated from the transmitting antenna 10a is reflected by the object to be measured is received by the receiving antenna 10b closest to the transmitting antenna 10a that radiated the electromagnetic wave. is controlled.
  • the receiving microwave amplifier may be set to change the gain for each pair of transmitting transmitting antenna 10a and receiving receiving antenna 10b.
  • the high-frequency circuit 62 has a variable gain amplification function that switches the gain according to the selection of the pair of the transmitting antenna 10a and the receiving antenna 10b. As a result, it is possible to increase the inspectable depth of defects, etc. in the object to be measured.
  • the arrangement direction of the transmitting antenna 10a and the receiving antenna 10b is parallel, and as shown in FIG. 2, the arrangement direction is the y direction.
  • the moving direction (scanning direction) of the transmitting array antenna 50 and the receiving array antenna 52 is assumed to be the x direction.
  • the direction in which the object to be measured is the z-direction.
  • the moving direction (scanning direction) of the transmitting array antenna 50 and the receiving array antenna 52 may be the y direction. That is, it may move (scan) in the same direction as the arrangement direction of the transmitting antenna 10a and the receiving antenna 10b.
  • the transmitting array antenna 50 may have only one transmitting antenna 10a, and the receiving array antenna 52 may have a plurality of receiving antennas 10b.
  • the moving direction (scanning direction) of the transmitting array antenna 50 and the receiving array antenna 52 may be the y direction. That is, it may move (scan) in the same direction as the arrangement direction of the receiving antennas 10b.
  • the data processing unit 66 processes the measurement data s (x', y', z', k) obtained by transmission and reception of electromagnetic waves by the transmission array antenna 50 and the reception array antenna 52, and analyzes the inside of the object to be measured. Create image data to represent.
  • the data processing unit 66 is configured by, for example, a computer, and starts by calling a program stored in the storage section 66a. Thereby, the function of the data processing unit 66 can be exhibited. That is, the data processing unit 66 is composed of software modules.
  • the image display unit 68 uses the created image data to display an image of the interior of the object to be measured.
  • FIG. 2 schematically shows a transmitting array antenna 50 and a receiving array antenna 52.
  • the positions of the transmitting antenna 10a and the receiving antenna 10b are shifted by ⁇ L in the x direction. Do the one at the middle circled point. This circled point is called a transmission/reception point.
  • ⁇ y 0 in some cases.
  • 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.
  • f(x, y, z) be the reflectance at the reflection point (x, y, z) of the object to be measured.
  • Let s(x', y', z', k) be the measurement data at the transmission/reception point p(x', y', z').
  • ⁇ 0 be the propagation wavelength of an electromagnetic wave in vacuum.
  • Let ⁇ r be the dielectric constant of the medium.
  • Let k be the wave number of the propagating electromagnetic wave.
  • the measurement data s(x', y', z', k) at the transmission/reception point p(x', y', z') can be expressed by the following equation. however, is.
  • equation (1-1) electromagnetic waves are represented by spherical waves, and distance attenuation is omitted. This distance attenuation is omitted because it has little effect on subsequent processing.
  • the exponent part of the integrand function in the second-level equation in equation (1-1) is expressed in Fourier transform notation as follows. This is equivalent to decomposing the reciprocating spherical wave of equation (1-1) into three-dimensional plane waves.
  • (k x , k y , k z ) is the wavenumber of the round-trip spherical wave propagating between the transmitting/receiving point p(x', y', z') and the reflecting point (x, y, z) are the components of the vector. however, meet.
  • the reflectance f(x, y, z) is derived from the measurement data s(x', y', z', k) based on equation (1-3).
  • formula (1-3) is rearranged as follows.
  • the data processing unit 66 obtains the reflectance f (x, y, z) based on the measurement data s (x', y', z', k).
  • FIG. 4 is a flow chart showing the data processing method of this embodiment.
  • the measurement unit 61 acquires measurement data s (x', y', 0, k) (step S1-1).
  • the data processing unit 66 performs Hilbert transform on the measurement data s (x', y', 0, k) (step S1-2). As a result, the imaginary component of the frequency data at each transmission/reception point is obtained.
  • the data processing unit 66 performs a double Fourier transform of (x', y') on the measurement data s (x', y', 0, k) (step S1-3). This yields S(k x , k y , 0, k) as shown in equation (1-6).
  • the data processing unit 66 performs variable substitution on S(k x , k y , 0, k) (step S1-4). Specifically, the function (k x , k y , k) is converted to the function (k x , k y , k z ) using equation (1-4). This gives S(k x , k y , k z ).
  • the data processing unit 66 performs a triple inverse Fourier transform on (k x , ky , k z ) for S(k x , ky , k z ) (step S1-5). .
  • the storage unit 66a stores a program for executing the data processing method of this embodiment.
  • the program stored in the storage section 66a causes the data processing unit 66 to execute the data processing method of this embodiment.
  • the transmitting array antenna 50 and the receiving array antenna 52 of the first embodiment are arranged in one direction (the y direction in FIG. 3). Arrays are different.
  • the transmitting array antenna 50 and the receiving array antenna 52 of this embodiment are arranged in a curved line.
  • Equation (1-5) of the first embodiment relates to an arbitrary transmitting/receiving point p(x', y', z'). Therefore, starting from substituting equation (2-1) into equation (1-5), the following equation is obtained.
  • equation (2-2) Since the left side of equation (2-2) is a function of (x', y', k), it can be rewritten as the following equation.
  • Equation (2-6) has the eigenvalues of (x ' , y') in the (k x , k y , k z ) space for S a (k x , k y , k).
  • the data processing unit 66 obtains the reflectance f (x, y, z) based on the measurement data s (x', y', z', k).
  • FIG. 6 is a flow chart showing the data processing method of this embodiment.
  • the measurement unit 61 acquires measurement data s (x', y', z', k) (step S2-1).
  • the data processing unit 66 organizes the measurement data s(x', y', z', k) (step S2-2). Thereby, measurement data s a (x', y', k) are obtained.
  • the data processing unit 66 performs Hilbert transform on the measurement data s a (x', y', k) (step S2-3). As a result, the imaginary component of the frequency data at each transmission/reception point is obtained.
  • the data processing unit 66 performs a double Fourier transform of (x', y') on the measurement data s a (x', y', k) (step S2-4). This yields S a (k x , k y , k) as shown in equation (2-4).
  • the data processing unit 66 obtains the operator represented by the formula (2-6) from the measurement data s a (x', y', k) and S a (k x , k y , k) (Step S2-5).
  • Data processing unit 66 then performs variable substitution on the following equation (step S2-6). This yields S a (k x , ky , k).
  • the data processing unit 66 performs a triple inverse Fourier transform with respect to (k x , ky , k z ) on S a (k x , ky , k) (step S2-7). This gives the reflectance f(x, y, z) as shown in equation (2-7).
  • the storage unit 66a stores a program for executing the data processing method of this embodiment.
  • the program stored in the storage section 66a causes the data processing unit 66 to execute the data processing method of this embodiment.
  • Simulation result The results of computer simulation of the data processing method of the first embodiment and the data processing method of the second embodiment will be described below. Simulation conditions are as follows.
  • ⁇ Frequency band used f min to f max DC to 20 GHz ⁇ Center frequency fc (wavelength ⁇ c): 10 GHz (30 mm) ⁇ Measurement interval ⁇ x in the scanning direction: 4 mm ⁇ Number of measurement points in the scanning direction: 256 ⁇ Measurement width x max in scanning direction: 1024 mm (4 mm x 256) ⁇ Measurement interval ⁇ y in the direction of the array antenna (same transmitting and receiving points): 3.75 mm ⁇ Number of measurement points in the direction of the array antenna: 128 ⁇ Measurement width y max in the array antenna direction: 480 mm (3.75 mm ⁇ 128) ⁇ Maximum depth zmax : 476mm ⁇ Relative permittivity of medium ⁇ r : 1 ⁇ Point target coordinates (unit: mm): (512, 240, 50), (512, 240, 100), (512, 240, 200), (
  • FIG. 7(a) shows a measurement layout diagram for horizontal plane measurement.
  • FIG. 7(b) shows a measurement layout diagram of curved surface measurement 1.
  • FIG. 7(c) shows a measurement layout diagram of curved surface measurement 2.
  • FIG. 8 shows point targets simulated by the data processing method of the first embodiment using a measurement layout for horizontal surface measurement.
  • FIG. 9A shows a point target simulated by the data processing method of the first embodiment using the measurement layout of curved surface measurement 1.
  • FIG. FIG. 9B shows point targets simulated by the data processing method of the second embodiment using the measurement layout of curved surface measurement 1 .
  • FIG. 10A shows a point target simulated by the data processing method of the first embodiment using the measurement layout of curved surface measurement 2.
  • FIG. 10B shows point targets simulated by the data processing method of the second embodiment using the measurement layout of curved surface measurement 2 .
  • FIG. 9(a) a simulation was performed for four point targets according to formula (1-8) of the data processing method of the first embodiment.
  • the results are shown in FIG. 9(a).
  • FIG. 9(a) a three-dimensional image in which four point targets are spread in the same direction as the measurement layout of curved surface measurement 1 shown in FIG. 7(b) can be confirmed. From the result of FIG. 9A, it can be seen that the formula (1-8) cannot obtain a good three-dimensional image for the measurement layout of the curved surface measurement 1.
  • FIG. 7B a simulation was performed for four point targets according to formula (2-7) of the data processing method of the second embodiment.
  • FIG. 9(b) The results are shown in FIG. 9(b).
  • FIG. 9B a three-dimensional image in which four point targets converge can be confirmed. From the result of FIG. 9(b), it can be seen that a good three-dimensional image can be obtained from the measurement layout of the curved surface measurement 1 by the formula (2-7).
  • FIG. 10(a) a simulation was performed for four point targets using equation (1-8) of the data processing method of the first embodiment.
  • the results are shown in FIG. 10(a).
  • FIG. 10(a) a three-dimensional image in which four point targets are spread in the same direction as the measurement layout of the curved surface measurement 2 shown in FIG. 7(c) can be confirmed. From the result of FIG. 10(a), it can be seen that the formula (1-8) cannot obtain a good three-dimensional image for the measurement layout of the curved surface measurement 2.
  • FIG. 7(c) a simulation was performed for four point targets using equation (2-7) of the data processing method of the second embodiment.
  • FIG. 10(b) The results are shown in FIG. 10(b).
  • FIG. 10B a three-dimensional image in which four point targets converge can be confirmed. From the result of FIG. 10(b), it can be seen that a good three-dimensional image can be obtained from the measurement layout of the curved surface measurement 2 by the formula (2-7).
  • the transmitting array antenna 50 and the receiving array antenna 52 of the first embodiment are arranged in one direction (the y direction in FIG. 3). Arrays are different.
  • the transmitting array antenna 50 and the receiving array antenna 52 of this embodiment are arranged in a plane. Also, in the first embodiment, the coordinates of the transmission point and the reception point are both p(x', y', z'), but in the present embodiment, the coordinates of the transmission point and the reception point are different. In this embodiment, as shown in FIG.
  • a transmission point p 1 (x' 1 , y' 1 , z' 1 ) and a reception point p 2 (x' 2 , y' 2 , z' 2 ) are xy Arranged in a plane.
  • f(x, y, z) be the reflectance at the reflection point (x, y, z) of the object to be measured.
  • ⁇ 0 be the propagation wavelength of an electromagnetic wave in vacuum.
  • ⁇ r be the dielectric constant of the medium.
  • k be the wave number of the propagating electromagnetic wave.
  • the measurement data s (x' 1 , x' 2 , y' 1 , y' 2 , z' 1 , z' 2 , k) can be represented by the following formula. however, is.
  • (k' x1 , k' y1 , k' z1 ) are the components of the spherical wave vector of the wave propagating from the transmission point to the reflection point.
  • (k' x2 , k' y2 , k' z2 ) are the components of the wave vector of the spherical wave of the wave propagating from the reflecting point to the receiving point. however, meet.
  • equation (3-5) The left side of equation (3-5) is rewritten and arranged as in equation (3-6) below. Then, equation (3-5) is expressed by equation (3-7).
  • equation (3-17) (k' z1 , k' z2 , k) are replaced by (k' x1 , k' x2 , k' y1 , k' y2 , k z ) or (k x , u, k y , v, k z ).
  • equation (3-17) can be expressed as follows.
  • the data processing unit 66 calculates the reflectance f ( x , y, z).
  • FIG. 12 is a flow chart showing the data processing method of this embodiment.
  • the measurement unit 61 acquires measurement data s (x' 1 , x' 2 , y' 1 , y' 2 , z' 1 , z' 2 , k) (step S3-1).
  • the data processing unit 66 performs Hilbert transform on the measurement data s (x' 1 , x' 2 , y' 1 , y' 2 , z' 1 , z' 2 , k) (step S3- 2).
  • the imaginary component of the frequency data at each measurement point is obtained.
  • step S3-3 the data processing unit 66 performs ( x ' 1 , x' 2 , y' 1 , y' 2 ) is subjected to quadruple Fourier transform (step S3-3). This yields S(k' x1 , k' x2 , k' y1 , k' y2 , 0, 0, k) as shown in equation (3-6).
  • step S3-4 the data processing unit 66 performs variable substitution on S(k' x1 , k' x2 , k' y1 , k' y2 , 0, 0, k) (step S3-4).
  • the storage unit 66a stores a program for executing the data processing method of this embodiment.
  • the program stored in the storage section 66a causes the data processing unit 66 to execute the data processing method of this embodiment.
  • the transmitting array antenna 50 and the receiving array antenna 52 of the third embodiment are arranged in a plane, 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 of this embodiment are arranged in a curved surface.
  • the function g 1 (x' 1 , y' 1 ) may be any univalent function on (x' 1 , y' 1 ).
  • the function g 2 (x' 2 , y' 2 ) may be any univalent function on (x' 2 , y' 2 ).
  • Equation (3-3) of the third embodiment is an arbitrary transmission point p 1 (x' 1 , y' 1 , z' 1 ) and reception point p 2 (x' 2 , y' 2 , z' 2 ) is an expression for Therefore, substituting equation (4-1) into equation (3-3) yields the following equation. Since the right side of equation (4-2) is a function related to (x' 1 , x' 2 , y' 1 , y' 2 , k), it is organized and represented by equation (4-3) below.
  • the function after the quadruple Fourier transform of s a is S a (k' x1 , k' x2 , k' y1 , k' y2 , k').
  • the formula (4-3) is represented by the following formula.
  • Equation ( 4-6 ) and (4-7) are ( k' x1 , k has eigenvalues of (x ' 1 , x' 2 , y' 1 , y' 2 ) in the ' x2 , k' y1 , k' y2 , k' ) space.
  • the data processing unit 66 calculates the reflectance f ( x , y, z).
  • FIG. 14 is a flow chart showing the data processing method of this embodiment.
  • the measurement unit 61 acquires measurement data s (x' 1 , x' 2 , y' 1 , y' 2 , z' 1 , z' 2 , k) (step S4-1).
  • 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).
  • measurement data s a (x' 1 , x' 2 , y' 1 , y' 2 , k) are obtained.
  • the data processing unit 66 performs Hilbert transform on the measurement data s a (x' 1 , x' 2 , y' 1 , y' 2 , k) (step S4-3).
  • the imaginary component of the frequency data at each measurement point is obtained.
  • step S4-4 the data processing unit 66 performs (x' 1 , x ' 2 , y' 1 , y ' 2 ) is subjected to quadruple Fourier transform (step S4-4). This yields S a (k' x1 , k' x2 , k' y1 , k' y2 , k') as shown in equation (4-4).
  • 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' the operators represented by equations (4-6) and (4-7) are obtained (step S4-5).
  • step S4-6 the data processing unit 66 performs variable substitution on the following formula (step S4-6). This gives S a (k x , k y , k z ).
  • the data processing unit 66 performs a triple inverse Fourier transform on (k x , ky , k z ) for S a (k x , ky , k z ) (step S4-7 ). This gives the reflectance f(x, y, z) as shown in equation (4-8).
  • the storage unit 66a stores a program for executing the data processing method of this embodiment.
  • the program stored in the storage section 66a causes the data processing unit 66 to execute the data processing method of this embodiment.
  • the transmitting array antenna 50 and the receiving array antenna 52 are arranged in a plane, but this embodiment differs in the arrangement of the transmitting array antenna 50 and the receiving array antenna 52 .
  • the transmitting array antenna 50 and the receiving array antenna 52 of this embodiment are arranged linearly.
  • the transmitting antenna 10a and the receiving antenna 10b are arranged in the y direction as shown in FIG. Let the moving direction (scanning direction) of the transmitting array antenna 50 and the receiving array antenna 52 be the x direction.
  • the direction in which the object to be measured is located is defined as the z direction.
  • the moving direction (scanning direction) of the transmitting array antenna 50 and the receiving array antenna 52 may be the y direction.
  • 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.
  • the coordinates of the transmission point are p 1 (x' 1 , y' 1 , z' 1 )
  • the coordinates of the reception point are p 2 (x' 2 , y' 2 , z' 2 ).
  • f(x, y, z) be the reflectance at the reflection point (x, y, z) of the object to be measured.
  • s(x' 1 , x ' 2 , y' 1 , y' 2 , z ' 1 , z' 2 , k) be the measurement data at p 2 (x' 2 , y' 2 , z' 2 ).
  • ⁇ 0 be the propagation wavelength of an electromagnetic wave in vacuum.
  • ⁇ r be the dielectric constant of the medium.
  • k be the wave number of the propagating electromagnetic wave.
  • the measurement data s (x' 1 , x' 2 , y' 1 , y' 2 , z' 1 , z' 2 , k) can be represented by the following formula. however is.
  • electromagnetic waves are represented by spherical waves, and distance attenuation is omitted. This distance attenuation is omitted because it has little effect on subsequent processing.
  • the exponent part of the integrand function in the second stage of the equation (5-1) is expressed in Fourier transform notation as follows. This is equivalent to decomposing the spherical wave of equation (5-1) into three-dimensional plane waves.
  • (k' x1 , k' y1 , k' z1 ) are the components of the spherical wave vector of the wave propagating from the transmission point to the reflection point.
  • (k' x2 , k' y2 , k' z2 ) are the components of the wave vector of the spherical wave of the wave propagating from the reflecting point to the receiving point. however, meet.
  • equation (5-3) is represented by the following equation.
  • equations (5-6) and (5-8) By substituting equations (5-6) and (5-8) into equation (5-5) and performing variable substitution, the following equation is obtained.
  • equation (5-10) is represented by the following formula.
  • variable substitutions are defined for (k' y1 , k' y2 ) and (k' z1 , k' z2 ).
  • equations (5-1), (5-15), and (5-17) By substituting equations (5-17), and (5-17) into equation (5-13) and performing variable substitution, the following equation is obtained.
  • Equation (5-18) the integral with respect to v on the right side of the second line of Equation (5-18) is omitted because it is a constant.
  • Equation (5-18) Performing a triple inverse Fourier transform on both sides of equation (5-18) with respect to (k x , k y , k z ) yields the reflectance f(x, y, z) as follows.
  • equation (5-19) is expressed as follows.
  • Equation (5-20) To solve equation (5-20), we need to represent k by (k' y1 , k' y2 , k z ) or (k y , v, k z ). Solve the four simultaneous equations of equations (5-4), (5-6), (5-15), and the following equation (5-21) obtained from the assumption.
  • k is represented by the following formula.
  • the data processing unit 66 calculates the reflectance f ( x , y, z).
  • FIG. 16 is a flow chart showing the data processing method of this embodiment.
  • the measurement unit 61 acquires measurement data s (x', y' 1 , y' 2 , 0, 0, k) (step S5-1).
  • the data processing unit 66 performs Hilbert transform on the measurement data s (x', y' 1 , y' 2 , 0, 0, k) (step S5-2). As a result, the imaginary component of the frequency data at each measurement point is obtained.
  • the data processing unit 66 performs a triple Fourier transform on (x', y' 1 , y' 2 ) for the measurement data s(x', y' 1 , y' 2 , 0, 0, k). Conversion is performed (step S5-3). This yields S(k x , k' y1 , k' y2 , 0, 0, k) as shown in equation (5-11). Next, the data processing unit 66 performs variable substitution on S(k x , k' y1 , k' y2 , 0, 0, k) (step S5-4).
  • Equation (5-14) and (5-15) the function (k x , k′ y1 , k′ y2 , k) is converted to (k x , k y , v, k) be a function of This yields S(k x , ky , v, 0, 0, k).
  • Data processing unit 66 then performs a triple inverse Fourier transform on (k x , k y , k z ) on S(k x , k y , v, 0, 0, k) ( step S5-5). This gives the reflectance f(x, y, z) as shown in equation (5-20).
  • the transmitting array antenna 50 and the receiving array antenna 52 of this embodiment are arranged linearly. Specifically, the transmitting array antenna 50 and the receiving array antenna 52 are arranged in one direction (the y direction in FIG. 17). Also, the transmitting array antenna 50 and the receiving array antenna 52 are moved (scanned) along the curved surface.
  • 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.
  • the coordinates of the transmission point are p 1 (x' 1 , y' 1 , z' 1 )
  • the coordinates of the reception point are p 2 (x' 2 , y' 2 , z' 2 ).
  • f(x, y, z) be the reflectance at the reflection point (x, y, z) of the object to be measured.
  • the measurement data at the receiving point p 2 (x' 2 , y' 2 , z' 2 ) be s (x' 1 , x' 2 , y' 1 , y' 2 , z' 1 , z' 2 , k) do.
  • ⁇ 0 be the propagation wavelength of an electromagnetic wave in vacuum.
  • ⁇ r be the dielectric constant of the medium.
  • k be the wave number of the propagating electromagnetic wave.
  • a function expressed by the following equation representing a semi-cylindrical measurement curved surface with a radius of R0 will be described. It should be noted that the function g(x') may be any univalent function regarding x'.
  • Equation (5-5) of the fifth embodiment is an arbitrary transmission point p 1 (x' 1 , y' 1 , z' 1 ) and reception point p 2 (x' 2 , y' 2 , z' 2 ) is an expression for Therefore, starting from substituting equation (6-1) into equation (5-5), the following equation is obtained.
  • Equation (6-2) Since the right side of equation (6-2) is a function related to (x', y' 1 , y' 2 , k), it can be expressed by the following equation when organized. If the function after the triple Fourier transform of s a (x′, y′ 1 , y′ 2 , k) is S a (k x , k′ y1 , k′ y2 , k), the following equation is obtained .
  • equations (6-1) to (6-4) into equation (5-19) yields the following equation. Since the formula (5-21) holds true in this embodiment as well, the formula (5-22) can be used as it is in the present embodiment.
  • Equation (6-6) The operator of equation (6-6) is given by, for S a (k x , k' y1 , k' y2 , k), x' in (k x , k' y1 , k' y2 , k) space have eigenvalues.
  • the data processing unit 66 calculates the reflectance f (x, y, z) based on the measurement data s (x', y' 1 , y' 2 , z' 1 , z' 2 , k) Ask for
  • FIG. 18 is a flow chart showing the data processing method of this embodiment.
  • the measurement unit 61 acquires measurement data s (x', y' 1 , y' 2 , z' 1 , z' 2 , k) (step S6-1).
  • the data processing unit 66 organizes the measurement data s(x', y' 1 , y' 2 , z' 1 , z' 2 , k) (step S6-2). Thereby, measurement data s a (x', y' 1 , y' 2 , k) is obtained.
  • the data processing unit 66 performs Hilbert transform on the measurement data s a (x', y' 1 , y' 2 , k) (step S6-3). As a result, the imaginary component of the frequency data at each measurement point is obtained.
  • the data processing unit 66 performs a triple Fourier transform of (x', y' 1 , y' 2 ) on the measurement data s a (x', y' 1 , y' 2 , k). (Step S6-4). This yields S a (k' x , k' y1 , k' y2 , k') as shown in equation (6-4).
  • data processing unit 66 obtains the operator represented by equation (6-6) (step S6-5).
  • step S6-6 the data processing unit 66 performs variable substitution on the following formula (step S6-6). This gives S a (k x , k y , k z ).
  • the data processing unit 66 performs a triple inverse Fourier transform on (k x , ky , k z ) for S a (k x , ky , k z ) (step S6-7 ). This gives the reflectance f(x, y, z) as shown in equation (6-7).
  • the storage unit 66a stores a program for executing the data processing method of this embodiment.
  • the program stored in the storage section 66a causes the data processing unit 66 to execute the data processing method of this embodiment.
  • Simulation result The results of computer simulation of the data processing method of the fifth embodiment and the data processing method of the sixth embodiment will be described below. Simulation conditions are as follows.
  • ⁇ Frequency band used f min to f max DC to 4.5 GHz ⁇ Center frequency fc (wavelength ⁇ c): 2.25 GHz (133 mm) ⁇ Measurement interval ⁇ x in the scanning direction: 10 mm ⁇ Number of measurement points in the scanning direction: 128 ⁇ Measurement width x max in the scanning direction: 1280 mm (10 mm x 128) ⁇ Measurement interval ⁇ y in the direction of the array antenna (same transmitting and receiving points): 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 max in the array antenna direction: 616 mm (38.5 mm x 16) ⁇ Maximum depth zmax : 958 mm ⁇ Relative permittivity of medium ⁇ r : 5 ⁇ Point target coordinates (unit: mm): (640,
  • FIG. 19(a) shows a measurement layout diagram for horizontal plane measurement.
  • FIG. 19(b) shows a measurement layout diagram of curved surface measurement 1.
  • FIG. 19(c) shows a measurement layout diagram of curved surface measurement 2.
  • FIG. 20 shows point targets simulated by the data processing method of the fifth embodiment using a measurement layout for horizontal plane measurement.
  • FIG. 21( a ) shows point targets simulated by the data processing method of the fifth embodiment using the measurement layout of curved surface measurement 1 .
  • FIG. 21(b) shows a point target simulated by the data processing method of the sixth embodiment using the measurement layout of curved surface measurement 1.
  • FIG. FIG. 22A shows a point target simulated by the data processing method of the fifth embodiment using the measurement layout of curved surface measurement 2.
  • FIG. 22B shows point targets simulated by the data processing method of the sixth embodiment using the measurement layout of curved surface measurement 2 .
  • FIG. 21(a) a simulation was performed for four point targets using the formula (5-20) of the data processing method of the fifth embodiment.
  • the results are shown in FIG. 21(a).
  • FIG. 21(a) a three-dimensional image in which four point targets are spread in the same direction as the measurement layout of curved surface measurement 1 shown in FIG. 19(b) can be confirmed. From the result of FIG. 21(a), it can be seen that the formula (5-20) cannot obtain a good three-dimensional image for the measurement layout of the curved surface measurement 1.
  • FIG. 21(b) The results are shown in FIG. 21(b).
  • FIG. 21(b) a three-dimensional image in which four point targets converge can be confirmed. From the result of FIG. 21(b), it can be seen that a good three-dimensional image can be obtained from the measurement layout of the curved surface measurement 1 by the formula (6-7).
  • FIG. 22(a) a simulation was performed for four point targets according to formula (5-20) of the data processing method of the fifth embodiment.
  • the results are shown in FIG. 22(a).
  • FIG. 22(a) a three-dimensional image in which four point targets are spread in the same direction as the measurement layout of curved surface measurement 2 shown in FIG. 19(c) can be confirmed. From the result of FIG. 22(a), it can be seen that the expression (5-20) cannot obtain a good three-dimensional image for the measurement layout of the curved surface measurement 2.
  • a simulation was performed for four point targets according to formula (6-7) of the data processing method of the sixth embodiment.
  • FIG. 22(b) The results are shown in FIG. 22(b).
  • FIG. 22(b) a three-dimensional image in which four point targets converge can be confirmed. From the result of FIG. 22(b), it can be seen that a good three-dimensional image can be obtained from the measurement layout of curved surface measurement 2 according to equation (6-7).
  • the data processing method, measurement system, and program of the seventh embodiment will be described in detail below.
  • the transmitting array antenna 50 and the receiving array antenna 52 of the sixth embodiment are arranged in one direction (the y direction in FIG. 17). Arrays are different.
  • the transmitting array antenna 50 and the receiving array antenna 52 of this embodiment are arranged in a curved line. Also, the transmitting array antenna 50 and the receiving array antenna 52 are moved (scanned) along the curved surface.
  • 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.
  • the coordinates of the transmission point are p 1 (x' 1 , y' 1 , z' 1 )
  • the coordinates of the reception point are p 2 (x' 2 , y' 2 , z' 2 ).
  • f(x, y, z) be the reflectance at the reflection point (x, y, z) of the object to be measured.
  • the measurement data at the receiving point p 2 (x' 2 , y' 2 , z' 2 ) be s (x' 1 , x' 2 , y' 1 , y' 2 , z' 1 , z' 2 , k) do.
  • ⁇ 0 be the propagation wavelength of an electromagnetic wave in vacuum.
  • ⁇ r be the dielectric constant of the medium.
  • k be the wave number of the propagating electromagnetic wave.
  • a function expressed by the following equation representing a semi-cylindrical measurement curved surface with a radius of R0 will be described.
  • the function g 1 (x', y' 1 ) may be any univalent function on (x', y' 1 ).
  • the function g 2 (x', y' 2 ) may be any univalent function on (x', y' 2 ).
  • Equation (5-5) of the fifth embodiment is an arbitrary transmission point p 1 (x' 1 , y' 1 , z' 1 ) and reception point p 2 (x' 2 , y' 2 , z' 2 ) is an expression for Therefore, starting from substituting equation (7-1) into equation (5-5), the following equation is obtained.
  • Equation (7-2) Since the right side of equation (7-2) is a function related to (x', y' 1 , y' 2 , k), it can be expressed by the following equation when rearranged. If the function after the triple Fourier transform of s a (x′, y′ 1 , y′ 2 , k) is S a (k x , k′ y1 , k′ y2 , k), the following equation is obtained .
  • Equation (5-22) can be used approximately in this embodiment as well.
  • the data processing unit 66 calculates the reflectance f (x, y, z) based on the measurement data s (x', y' 1 , y' 2 , z' 1 , z' 2 , k) Ask for
  • FIG. 24 is a flow chart showing the data processing method of this embodiment.
  • the measurement unit 61 acquires measurement data s (x', y' 1 , y' 2 , z' 1 , z' 2 , k) (step S7-1).
  • the data processing unit 66 organizes the measurement data s(x', y' 1 , y' 2 , z' 1 , z' 2 , k) (step S7-2). Thereby, measurement data s a (x', y' 1 , y' 2 , k) is obtained.
  • the data processing unit 66 performs Hilbert transform on the measurement data s a (x', y' 1 , y' 2 , k) (step S7-3). As a result, the imaginary component of the frequency data at each measurement point is obtained.
  • the data processing unit 66 performs a triple Fourier transform of (x', y' 1 , y' 2 ) on the measurement data s a (x', y' 1 , y' 2 , k). (Step S7-4). This yields S a (k' x , k' y1 , k' y2 , k') as shown in equation (7-4).
  • the data processing unit 66 obtains operators represented by equations (7-6) and (7-7) (step S7-5).
  • step S7-6 the data processing unit 66 performs variable substitution on the following formula (step S7-6). This yields S a (k x , k y , k z ).
  • the data processing unit 66 performs a triple inverse Fourier transform on (k x , ky , k z ) for S a (k x , ky , k z ) (step S7-7 ). This gives the reflectance f(x, y, z) as shown in equation (7-7).
  • the storage unit 66a stores a program for executing the data processing method of this embodiment.
  • the program stored in the storage section 66a causes the data processing unit 66 to execute the data processing method of this embodiment.

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Abstract

La présente invention concerne un procédé de traitement de données qui, dans un traitement d'ouverture synthétique à l'aide d'une transformée de Fourier, est simple et présente une excellente vitesse de calcul, même par rapport à une structure qui présente une forme de surface incurvée. L'invention concerne un procédé de traitement de données destiné à analyser des ondes diffusées d'ondes émises vers un objet : des ondes étant émises vers un objet à partir d'une pluralité de points de transmission p1(x'1, y'1, z'1) agencés sur la courbe d'une première fonction uniforme z'1 = g1(x'1, y'1) relative à (x'1, y'1) dans un plan parallèle au plan yz ; des ondes diffusées réfléchies selon une réflectivité f (x, y, z) à un point de réflexion (x, y, z) sur l'objet étant reçues en tant que valeurs de mesure sa(x'1, x'2, y'1, y'2, k) à une pluralité de points de réception p2(x'2, y'2, z'2) agencés sur la courbe d'une seconde fonction uniforme z'2 = g2(x'2, y'2) relative à (x'2, y'2) dans un plan parallèle au plan yz ; une transformée de Fourier quadruple étant appliquée aux valeurs de mesure sa(x'1, x'2, y'1, y'2, k) pour trouver Sa(k'x1, k'x2, et k'y1, k'y2, k) ; un opérateur présentant une valeur propre (x'1, y'1, x'2, y'2) relativement à Sa(k'x1, k'x2, k'y1, k'y2, k) étant défini ; et une transformée de Fourier inverse triple étant appliquée pour trouver la réflectivité f (x, y, z).
PCT/JP2021/047054 2021-12-20 2021-12-20 Procédé de traitement de données, système de mesure et programme WO2023119371A1 (fr)

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Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH03188391A (ja) * 1989-09-04 1991-08-16 Ricoh Co Ltd ３次元物体認識方式
WO2017149582A1 (fr) * 2016-02-29 2017-09-08 三井造船株式会社 Procédé de traitement de données et dispositif de mesure
JP2018138880A (ja) * 2017-02-24 2018-09-06 株式会社三井Ｅ＆Ｓホールディングス データ処理方法及び計測装置
WO2021020387A1 (fr) * 2019-08-01 2021-02-04 株式会社 Ｉｎｔｅｇｒａｌ Ｇｅｏｍｅｔｒｙ Ｓｃｉｅｎｃｅ Dispositif de tomographie à diffusion et procédé de tomographie à diffusion

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH03188391A (ja) * 1989-09-04 1991-08-16 Ricoh Co Ltd ３次元物体認識方式
WO2017149582A1 (fr) * 2016-02-29 2017-09-08 三井造船株式会社 Procédé de traitement de données et dispositif de mesure
JP2018138880A (ja) * 2017-02-24 2018-09-06 株式会社三井Ｅ＆Ｓホールディングス データ処理方法及び計測装置
WO2021020387A1 (fr) * 2019-08-01 2021-02-04 株式会社 Ｉｎｔｅｇｒａｌ Ｇｅｏｍｅｔｒｙ Ｓｃｉｅｎｃｅ Dispositif de tomographie à diffusion et procédé de tomographie à diffusion

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