WO2023119371A1 - Data processing method , measurement system, and program - Google Patents

Abstract

The present invention provides a data processing method that, in synthetic aperture processing using a Fourier transform, is simple and has excellent calculation speed, even with respect to a structure that has a curved surface shape. Provided is a data processing method for analyzing scattered waves of waves emitted toward an object, wherein: waves are emitted toward an object from a plurality of transmission points p₁(x'₁, y'₁, z'₁) arranged on the curve of a first single-valued function z'₁=g₁(x'₁, y'₁) relating to (x'₁, y'₁) in a plane parallel to the yz plane; scattered waves reflected with a reflectivity f (x, y, z) at a reflection point (x, y, z) on the object are received as measurement values s_a(x'₁, x'₂, y'₁, y'₂, k) at a plurality of reception 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) relating to (x'₂, y'₂) in a plane parallel to the yz plane; a quadruple Fourier transform is applied to the measurement values s_a(x'₁, x'₂, y'₁, y'₂, k) to find S_a(k'_x1, k'_x2, and k'_y1, k'_y2, k); an operator having an eigenvalue (x'₁, y'₁, x'₂, y'₂) with respect to S_a(k'_x1, k'_x2, k'_y1, k'_y2, k) is defined; and a triple inverse Fourier transform is applied to find reflectivity f (x, y, z).

Description

DATA PROCESSING METHOD, MEASUREMENT SYSTEM AND PROGRAM

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.

　Conventionally, there is known 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.

Regarding a radar device having an array antenna, for example, there is known a radar device in which a transmitting array antenna and a receiving array antenna each including a plurality of planar antennas are formed on a common dielectric substrate (Japanese Patent Laid-Open No. 2015-095840. No. 1, hereinafter referred to as “Patent Document 1”). In the conventional radar apparatus, 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.

In addition, there is known a scattering tomography method that can perform analysis of inverse problems at high speed for general purposes and can easily visualize information inside an object (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. Here, in synthetic aperture processing using Fourier transform, measurements on a plane with equal intervals are required.

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 flat approximation and perform calculations. As the curvature of the curved surface increases, the error due to plane approximation increases, resulting in a problem that the 3D image after processing is blurred.

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.

SUMMARY OF THE INVENTION It is an object of the present invention to provide a data processing method, a measurement system, and a program which are simple and excellent in calculation speed even for a structure having a curved surface shape in synthetic aperture processing using Fourier transform. .

A first aspect of the present invention is
A data processing method for analyzing scattered waves of waves radiated to an object,
A plurality of transmitting/receiving points p(x', y', z arranged on the curve of the univalent function z'=g(x', y') with respect to (x', y') in the plane parallel to the yz plane '), radiating said wave to said object,
The scattered wave reflected at the reflection point (x, y, z) on the object with the reflectance f(x, y, z) is transferred to the transmitting/receiving point p(x', y', z' that radiated the wave. ) as the measured value s _a (x', y', k),
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.
however,
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 second aspect of the present invention is
A measurement system for analyzing scattered waves of waves radiated to an object,
A plurality of transmitting/receiving points p(x', y', z arranged on the curve of the univalent function z'=g(x', y') with respect to (x', y') in the plane parallel to the yz plane '), which radiates the wave to the object and reflects the scattered wave reflected at a reflection point (x, y, z) on the object with a reflectance f(x, y, z) , a transmitting/receiving unit that receives as a measured value s _a (x', y', k) at the transmitting/receiving point p(x', y', z') that radiated the wave;
A processing device,
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);

a processor for performing
A measurement system having
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);
is.

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 measured value s _a (x', y' ₁ , y' ₂ , k) is subjected to a triple Fourier transform from equation (1) to obtain S _a (k' _x , k' _y1 , k' _y2 , k) ,

define an operator shown in equation (2) with eigenvalues x' for S _a (k' _x1 , k' _x2 , k' _y1 , k' _y2 , k),

Perform triple inverse Fourier transform from equation (3) to obtain the reflectance f (x, y, z),

Data processing method.
however,
x' = x' ₁ = x' ₂
z' = z' ₁ = z' ₂
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 ). the components of the wave vector of the spherical wave,
k _y = k' _y1 + k' _y2 , v = k' _y1 - k' _y2
is.

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 unit that moves on a curved surface of a single-valued function z'=g(x') for
A processing device,
The measured value s _a (x', y' ₁ , y' ₂ , k) is subjected to a triple Fourier transform from equation (1) to obtain S _a (k' _x , k' _y1 , k' _y2 , k) a procedure;

Defining the operator shown in equation (2) with eigenvalues x' for S _a (k' _x1 , k' _x2 , k' _y1 , k' _y2 , k);

A procedure for obtaining the reflectance f (x, y, z) by performing a triple inverse Fourier transform from Equation (3);

a processor for performing
A measurement system having
however,
x' = x' ₁ = x' ₂
z' = z' ₁ = z' ₂
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 ). the components of the wave vector of the spherical wave,
k _y = k' _y1 + k' _y2 , v = k' _y1 - k' _y2
is.

A sixth 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' _y1 , k' _y2 , k) by performing a triple Fourier transform on the measured value s a ( _x ', y' ₁ , y' ₂ , k) from the formula (1) and,

Defining the operator shown in equation (2) with eigenvalues x' for S _a (k' _x1 , k' _x2 , k' _y1 , k' _y2 , 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,
x' = x' ₁ = x' ₂
z' = z' ₁ = z' ₂
k is the wave number of said wave propagating;
k' _x1 , k' _y1 , k' _z1 are the spherical waves of said wave 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 ,
k' _x2 , k' _y2 , k' _z2 are the spherical surfaces of the waves propagating between the reflecting point (x, y, z) and the receiving point p ₂ (x' ₂ , y' ₂ , z' ₂ ) the components of the wavenumber vector of the wave,
k _y = k' _y1 + k' _y2 , v = k' _y1 - k' _y2
is.

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'x1 , k ' _x2 , k' _y1 , k' _y2 , z' ₁ , z' ₂ , k),

Perform triple inverse Fourier transform from equation (2) to obtain the reflectance f (x, y, z),

Data processing method.
however,
_z'1 = _z'2 = 0
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 ). the components of the wave vector of the spherical wave,
k _x = k' _x1 + k' _x2 , u = k' _x1 - k' _x2 , k _y = k' _y1 + k' _y2 , v = k' _y1 - k' _y2
is.

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 , _{z'2 ,} k) is quadruple Fourier transformed by Equation (1) to obtain S( _k'x1 , k ' _x2 , k' _y1 , k' _y2 , z' ₁ , z' ₂ , k);

A procedure for obtaining the reflectance f (x, y, z) by performing a triple inverse Fourier transform from Equation (2);

a processor for performing
A measurement system having
however,
_z'1 = _z'2 = 0
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 ). the components of the wave vector of the spherical wave,
k _x = k' _x1 + k' _x2 , u = k' _x1 - k' _x2 , k _y = k' _y1 + k' _y2 , v = k' _y1 - k' _y2
is.

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 procedure for obtaining the reflectance f (x, y, z) by performing a triple inverse Fourier transform from Equation (2);

is a program that causes a computer to execute
however,
_z'1 = _z'2 = 0
k is the wave number of said wave propagating;
k' _x1 , k' _y1 , k' _z1 are the spherical waves of said wave 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 ,
k' _x2 , k' _y2 , k' _z2 are the spherical surfaces of the waves propagating between the reflecting point (x, y, z) and the receiving point p ₂ (x' ₂ , y' ₂ , z' ₂ ) the components of the wavenumber vector of the wave,
k _x = k' _x1 + k' _x2 , u = k' _x1 - k' _x2 , k _y = k' _y1 + k' _y2 , v = k' _y1 - k' _y2
is.

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 ' _x2 , k' _y1 , k' _y2 , z' ₁ , z' ₂ , k),

Perform triple inverse Fourier transform from equation (2) to obtain the reflectance f (x, y, z),

Data processing method.
however,
x' = x' ₁ = x' _2
z'1 = _z'2 = 0
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 ). the components of the wave vector of the spherical wave,
k _x = k' _x1 + k' _x2 , u = k' _x1 - k' _x2 , k _y = k' _y1 + k' _y2 , v = k' _y1 - k' _y2
is.

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 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 ' _x2 , k' _y1 , k' _y2 , z' ₁ , z' ₂ , k);

A procedure for obtaining the reflectance f (x, y, z) by performing a triple inverse Fourier transform from Equation (2);

a processor for performing
A measurement system having
however,
x' = x' ₁ = x' _2
z'1 = _z'2 = 0
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 ). the components of the wave vector of the spherical wave,
k _x = k' _x1 + k' _x2 , u = k' _x1 - k' _x2 , k _y = k' _y1 + k' _y2 , v = k' _y1 - k' _y2
is.

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);

A procedure for obtaining the reflectance f (x, y, z) by performing a triple inverse Fourier transform from Equation (2);

is a program that causes a computer to execute
however,
x' = x' ₁ = x' _2
z'1 = _z'2 = 0
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 ). the components of the wave vector of the spherical wave,
k _x = k' _x1 + k' _x2 , u = k' _x1 - k' _x2 , k _y = k' _y1 + k' _y2 , v = k' _y1 - k' _y2
is.

A thirteenth aspect of the present invention is
A data processing method for analyzing scattered waves of waves radiated to an object,
A plurality of transmitting points arranged on the curve of the first univalent function z' ₁ =g ₁ (x' ₁ , y' ₁ ) with respect to (x' ₁ , y' ₁ ) in a plane parallel to the yz plane radiating said wave to said object from p ₁ (x' ₁ , y' ₁ , z' ₁ );
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 _a (x' ₁ , x' ₂ , y' ₁ , y' ₂ , k) and
The measured values s _a (x' ₁ , x' ₂ , y' ₁ , y' ₂ , k) are quadruple Fourier transformed by Equation (1) to S _a (k' _x1 , k' _x2 , k' _y1 , 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 Define the operator indicated by (3),

Perform triple inverse Fourier transform from equation (4) to obtain the reflectance f (x, y, z),

Data processing method.
however,
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 ). the components of the wave vector of the spherical wave,
k _x = k' _x1 + k' _x2 , u = k' _x1 - k' _x2 , k _y = k' _y1 + k' _y2 , v = k' _y1 - k' _y2
is.

A fourteenth aspect of the present invention is
A measurement system for analyzing scattered waves of waves radiated to an object,
a transmitting/receiving unit,
A plurality of transmitting points arranged on the curve of the first univalent function z' ₁ =g ₁ (x' ₁ , y' ₁ ) with respect to (x' ₁ , y' ₁ ) in a plane parallel to the yz plane a transmitter that radiates the wave to the object from p ₁ (x' ₁ , y' ₁ , z' ₁ );
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 ) a receiver for receiving as s _a (x' ₁ , x' ₂ , y' ₁ , y' ₂ , k);
a transceiver having
A processing device,
The measured values s _a (x' ₁ , x' ₂ , y' ₁ , y' ₂ , k) are quadruple Fourier transformed by Equation (1) to S _a (k' _x1 , k' _x2 , k' _y1 , 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);

a processor for performing
A measurement system having
however,
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 ). the components of the wave vector of the spherical wave,
k _x = k' _x1 + k' _x2 , u = k' _x1 - k' _x2 , k _y = k' _y1 + k' _y2 , v = k' _y1 - k' _y2
is.

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 number of said wave propagating;
k' _x1 , k' _y1 , k' _z1 are the spherical waves of said wave 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 ,
k' _x2 , k' _y2 , k' _z2 are the spherical surfaces of the waves propagating between the reflecting point (x, y, z) and the receiving point p ₂ (x' ₂ , y' ₂ , z' ₂ ) the components of the wavenumber vector of the wave,
k _x = k' _x1 + k' _x2 , u = k' _x1 - k' _x2 , k _y = k' _y1 + k' _y2 , v = k' _y1 - k' _y2
is.

A sixteenth aspect of the present invention is
A data processing method for analyzing scattered waves of waves radiated to an object,
A plurality of transmitting points arranged on the curve of the first univalent function z' ₁ =g ₁ (x' ₁ , y' ₁ ) with respect to (x' ₁ , y' ₁ ) in a plane parallel to the yz plane radiating said wave to said object from p ₁ (x' ₁ , y' ₁ , z' ₁ );
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 _a (x', y' ₁ , y' ₂ , k),
The measured value s _a (x', y' ₁ , y' ₂ , k) is subjected to a triple Fourier transform from equation (1) to obtain S _a (k' _x , k' _y1 , k' _y2 , k) ,

Let the operators shown in equations (2) and (3) with eigenvalues (x', y' ₁ , y' ₂ ) for S _a ( _k ' x , k' _y1 , k' y2 , _k ) be define and

Perform triple inverse Fourier transform from equation (4) to obtain the reflectance f (x, y, z),

Data processing method.
however,
x' = x' ₁ = x' ₂
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 ). the components of the wave vector of the spherical wave,
k _y = k' _y1 + k' _y2 , v = k' _y1 - k' _y2
is.

A seventeenth aspect of the present invention is
A measurement system for analyzing scattered waves of waves radiated to an object,
a transmitting/receiving unit,
A plurality of transmitting points arranged on the curve of the first univalent function z' ₁ =g ₁ (x' ₁ , y' ₁ ) with respect to (x' ₁ , y' ₁ ) in a plane parallel to the yz plane a transmitter that radiates the wave to the object from p ₁ (x' ₁ , y' ₁ , z' ₁ );
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 ) a receiver for receiving as s _a (x', y' ₁ , y' ₂ , k);
a transceiver having
A processing device,
The measured value s _a (x', y' ₁ , y' ₂ , k) is subjected to a triple Fourier transform from equation (1) to obtain S _a (k' _x , k' _y1 , k' _y2 , k) a procedure;

Let the operators shown in equations (2) and (3) with eigenvalues (x', y' ₁ , y' ₂ ) for S _a ( _k ' x , k' _y1 , k' y2 , _k ) be a procedure that defines

A procedure for obtaining the reflectance f (x, y, z) by performing a triple inverse Fourier transform from Equation (4);

a processor for performing
A measurement system having
however,
x' = x' ₁ = x' ₂
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 ). the components of the wave vector of the spherical wave,
k _y = k' _y1 + k' _y2 , v = k' _y1 - k' _y2
is.

An eighteenth aspect of the present invention is
A program for analyzing scattered waves of waves radiated to an object,
Procedure for obtaining S _a (k' x, k' _y1 , k' _y2 , k) by performing a triple Fourier transform on the measured value _{s a} ( _x ', y' ₁ , y' ₂ , k) from the formula (1) and,

Let the operators shown in equations (2) and (3) with eigenvalues (x', y _{' 1 ,} y' ₂ ) for S _a ( _k ' x , k' _y1 , k' y2 , k) be a procedure that defines

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,
x' = x' ₁ = x' ₂
k is the wave number of said wave propagating;
k' _x1 , k' _y1 , k' _z1 are the spherical waves of said wave 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 ,
k' _x2 , k' _y2 , k' _z2 are the spherical surfaces of the waves propagating from the reflecting point (x, y, z) to the receiving point p ₂ (x' ₂ , y' ₂ , z' ₂ ) the components of the wavenumber vector of the wave,
k _y = k' _y1 + k' _y2 , v = k' _y1 - k' _y2
is.

According to the data processing method, measurement system, and program of the present invention, in synthetic aperture processing using Fourier transform, it is possible to simplify and shorten the calculation time even for a structure having a curved surface shape.

The figure which shows the structure of the radar apparatus of 1st Embodiment. 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. (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 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, and (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. 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. (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 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, and (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

<First Embodiment>
Hereinafter, the data processing method, measurement system, and program of the first embodiment will be described in detail. 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. In this embodiment, 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. In the following embodiments, an example in which 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.

As shown in FIG. 2, 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 .
At this time, each time an electromagnetic wave is radiated from each transmitting antenna 10a, 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.
At this time, 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 (RF amplifier) may be set to change the gain for each pair of transmitting transmitting antenna 10a and receiving receiving antenna 10b. At this time, 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.

In this embodiment, 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. On the other hand, the moving direction (scanning direction) of the transmitting array antenna 50 and the receiving array antenna 52 is assumed to be the x direction. When viewed from the transmitting array antenna 50 and the receiving array antenna 52, the direction in which the object to be measured (the transmitting direction of electromagnetic waves) is the z-direction.

Note that 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.
Alternatively, 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. Also in this case, 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. As shown in FIG. The positions of the transmitting antenna 10a and the receiving antenna 10b are shifted by ΔL in the x direction. Do the one at the middle circled point. This circled point is called a transmission/reception point.
In some cases, there is no deviation in the y direction between the transmitting antenna 10a and the receiving antenna 10b. That is, Δy=0 in some cases. In some cases, the transmitting antenna 10a and the receiving antenna 10b are shared. That is, Δy=0 and ΔL=0 in some cases.

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.
Let p(x', y', z') be the coordinates of the transmission/reception point. Let 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'). Let λ ₀ be the propagation wavelength of an electromagnetic wave in vacuum. Let ε _r be the dielectric constant of the medium. Let k be the wave number of the propagating electromagnetic wave.

At this time, 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.

In 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.

where (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.

Below, the reflectance f(x, y, z) is derived from the measurement data s(x', y', z', k) based on equation (1-3). First, formula (1-3) is rearranged as follows.

where the integral inside { } is the triple Fourier transform with respect to (x, y, z). Also, the integral inside [ ] is the double inverse Fourier transform with respect to (k _x , _ky ). Therefore, both sides of equation (1-5) are subjected to double Fourier transform with respect to (x', y'). Let F(k x , ky , k z ) be the function after the triple Fourier transform of the function f( _x , _y , _z ). Let S(k x , k y , z', k) be a function after the double Fourier transform of the measurement data s ( _x ', y _' , z', k). At this time, the formula (1-5) is represented by the following formula.

If both sides of the second line of equation (1-6) are subjected to a triple inverse Fourier transform with respect to (k _x , k _y , k _z ), the reflectance f(x, y, z) is obtained as follows. .

Here, in the present embodiment, as shown in FIG. 3, the transmitting/receiving points p(x', y', z') are placed on the xy plane, and z'=0, so equation (1-7) is It can be expressed as follows.

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).

The data processing method and program of this embodiment will be described below with reference to FIG. FIG. 4 is a flow chart showing the data processing method of this embodiment.
First, the measurement unit 61 acquires measurement data s (x', y', 0, k) (step S1-1). Then, 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.

Next, 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).
Next, 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 ).
Next, 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). . This gives the reflectance f(x, y, z) as shown in equation (1-8).

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.

<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 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. Specifically, the transmission/reception point p(x', y', z') is a univalent function z'=g(x', y') on (x', y') in a plane parallel to the yz plane. are arranged on the curve of

In the present embodiment, as shown in FIG. 5, 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', y') may be any univalent function on (x', y').

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.

Since the left side of equation (2-2) is a function of (x', y', k), it can be rewritten as the following equation.

where the integral inside { } is the triple Fourier transform with respect to (x, y, z). Also, the integral inside [ ] is the double inverse Fourier transform with respect to (k _x , _ky ). Therefore, both sides of equation (2-3) are subjected to double Fourier transform with respect to (x', y'). Let F(k x , ky , k z ) be the function after the triple Fourier transform of the function f( _x , _y , _z ). Let S _a (k x , k y , k) be a function after the double Fourier transform of the measurement data s _a (x _′ , _y′ , k). At this time, the formula (2-3) is represented by the following formula.

If both sides of the second line of equation (2-4) are triple inverse Fourier transformed with respect to (k _x , k _y , k _z ), the reflectance f (x, y, z) is obtained as follows .

Here, the following operators are defined for (x', y').

The operator of 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).

By substituting equation (2-6) into equation (2-5), reflectance f(x, y, z) is obtained as follows.

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).

A data processing method and a program according to the present embodiment will be described below with reference to FIG. FIG. 6 is a flow chart showing the data processing method of this embodiment.
First, the measurement unit 61 acquires 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). Thereby, measurement data s _a (x', y', k) are obtained.
Then, 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.

Next, 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).
Next, 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).

Next, 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 λc): 10 GHz (30 mm)
・Measurement interval Δx 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 Δy 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 ε _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):

・Curved surface measurement 2 (unit: m):

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. As shown in FIG. FIG. 7(c) shows a measurement layout diagram of curved surface measurement 2. As shown in FIG. 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. FIG. 10B shows point targets simulated by the data processing method of the second embodiment using the measurement layout of curved surface measurement 2 .

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

Next, using the measurement layout of curved surface measurement 1 shown in FIG. 7B, 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). In 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.
Next, using the measurement layout of curved surface measurement 1 shown in FIG. 7B, a simulation was performed for four point targets according to formula (2-7) of the data processing method of the second embodiment. The results are shown in FIG. 9(b). In 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).

Next, using the measurement layout of curved surface measurement 2 shown in FIG. 7(c), 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). In 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.
Next, using the measurement layout of curved surface measurement 2 shown in FIG. 7(c), a simulation was performed for four point targets using equation (2-7) of the data processing method of the second embodiment. The results are shown in FIG. 10(b). In 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).

From the results of FIGS. 9A and 9B and the results of FIGS. It was confirmed that the reflectance f(x, y, z) corresponding to the measurement layout of the curved surface measurement 1 was obtained by inserting into the exponent part of .

<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 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. 11, 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.

Let f(x, y, z) be the reflectance at the reflection point (x, y, z) of the object to be measured. _{Let s (} x _{' 1 , x ' 2 , y} ' ₁ , y' ₂ , z' ₁ , z' ₂ , k). Let λ ₀ be the propagation wavelength of an electromagnetic wave in vacuum. Let ε _r be the dielectric constant of the medium. Let k be the wave number of the propagating electromagnetic wave.

At this time, 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.

In formula (3-1), 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. When the exponent part of the integrand in the formula (3-1) is expressed in Fourier transform notation, the following formula is obtained. This is equivalent to decomposing the spherical wave of equation (3-1) into three-dimensional plane waves.

Here, (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. Also, (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.

_Below , based on _{the formula} (3-3) _, reflectance f ₍ x, y, _z ). First, both sides of equation (3-3) are subjected to quadruple Fourier transform with respect to (x' ₁ , x' ₂ , y' ₁ , y' ₂ ).

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).

Both sides of equation (3-7) are integrated as follows.

Here, the following variable substitution is performed.

Here, the following equations are obtained from equations (3-9) and (3-10).

The absolute value |J| of the Jacobian in this variable substitution is given by the following formulas from formulas (3-12) and (3-13).

By substituting equation (3-9), equation (3-10), equation (3-14), and equation (3-15) into equation (3-8) and performing variable substitution, the following equation is obtained .

Here, since the integral regarding (u, v) on the right side of the second line of equation (3-16) is a constant, it is omitted. Performing a triple inverse Fourier transform on both sides of equation (3-16) with respect to (k _x , k _y , k _z ) yields the reflectance f(x, y, z) as follows.

To solve 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 ).
Arranged using equations (3-4) and (3-11), and when both the transmission point and the reception point are located on the xy plane passing through the origin, z′ ₁ =z′ ₂ =0 Therefore, equation (3-17) can be expressed as follows.

As described above, _{the data} processing _unit 66 calculates _the reflectance _f ( _x , y, z).

A data processing method and a program according to this embodiment will be described below with reference to FIG. FIG. 12 is a flow chart showing the data processing method of this embodiment.
First, the measurement unit 61 acquires 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 Hilbert transform on the measurement data s (x' ₁ , x' ₂ , y' ₁ , y' ₂ , z' ₁ , z' ₂ , k) (step S3- 2). As a result, the imaginary component of the frequency data at each measurement point is obtained.

Next, _{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).
Next, the data processing unit 66 performs variable substitution on S(k' _x1 , k' _x2 , k' _y1 , k' _y2 , 0, 0, k) (step S3-4). Specifically, using equations (3-9), (3-10), (3-14), and (3-15), (k′ _x1 , k′ _x2 , k′ _y1 , k ' Let the function of _y2 , k) be a function of (k _x , k _y , k _z ). This gives S(k _x , k _y , k _z ).
Next, 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 S3-5). . This gives the reflectance f(x, y, z) as shown in equation (3-18).

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.

<Fourth Embodiment>
The data processing method, measurement system, and program of the fourth embodiment will be described in detail below. Although 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. Specifically, the transmission point p ₁ (x′ ₁ , y′ ₁ , z′ ₁ ) is a univalent function z′ ₁ =g ₁ (x′ 1 , y′) on (x′ ₁ , y _{′ 1} ) ₁ ) are arranged on the curve. The receiving point p ₂ (x' ₂ , y' ₂ , z' ₂ ) is on the curve of the univalent function z' ₂ =g ₂ (x' ₂ , y' ₂ ) with respect to (x' ₂ , y' ₂ ) are arranged in

In the present embodiment, as shown in FIG. 13, 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 ₁ (x' ₁ , y' ₁ ) may be any univalent function on (x' ₁ , y' ₁ ). Also, 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.

Here, the function after the quadruple Fourier transform of s _a (x' ₁ , x' ₂ , y' ₁ , y' ₂ , k) is S _a (k' _x1 , k' _x2 , k' _y1 , k' _y2 , k'). At this time, the formula (4-3) is represented by the following formula.

Here, by substituting equations (4-1) to (4-4) into equation (3-17), reflectance f(x, y, z) is obtained as follows.

Here, the following operators are defined for (x' ₁ , y' ₁ ) and (x' ₂ , y' ₂ ).

The operators _of equations _{( 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.

By substituting equations (4-6) and (4-7) into equation (4-5), reflectance f(x, y, z) is obtained as follows.

As described _above , _{the data} processing unit 66 calculates _the reflectance _f ( _x , y, z).

A data processing method and a program according to this embodiment will be described below with reference to FIG. FIG. 14 is a flow chart showing the data processing method of this embodiment.
First, 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). Thereby, measurement data s _a (x' ₁ , x' ₂ , y' ₁ , y' ₂ , k) are obtained.
Then, 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). As a result, the imaginary component of the frequency data at each measurement point is obtained.

Next, _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).
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'), the operators represented by equations (4-6) and (4-7) are obtained (step S4-5).

Next, 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 ).

Next, 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.

<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 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.
Specifically, in this embodiment, 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. When viewed from the transmitting array antenna 50 and the receiving array antenna 52, the direction in which the object to be measured is located (direction in which electromagnetic waves are transmitted) is defined as the z direction.
Note that the moving direction (scanning direction) of the transmitting array antenna 50 and the receiving array antenna 52 may be the y direction.

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 transmission point are p ₁ (x' ₁ , y' ₁ , z' ₁ ), and the coordinates of the reception point are p ₂ (x' ₂ , y' ₂ , z' ₂ ). Let f(x, y, z) be the reflectance at the reflection point (x, y, z) of the object to be measured. Let 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 ). Let λ ₀ be the propagation wavelength of an electromagnetic wave in vacuum. Let ε _r be the dielectric constant of the medium. Let k be the wave number of the propagating electromagnetic wave.

At this time, 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.

In formula (5-1), 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 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.

Here, (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. Also, (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.

_{Here , x ' = x _ _} Assuming that ' ₁ =x' ₂ , equation (5-3) is represented by the following equation.

Here, the following variable substitutions are performed.

The following equation is obtained from equation (5-6).

Calculating the absolute value of the Jacobian from equation (5-7) yields the following equation.

By substituting equations (5-6) and (5-8) into equation (5-5) and performing variable substitution, the following equation is obtained.

Here, the integral regarding u on the second line of equation (5-9) is omitted because it is a constant. The following equation is obtained by subjecting both sides of equation (5-9) to triple inverse Fourier transform for (x, y ₁ , y ₂ ).

The left side of equation (5-10) is rewritten and arranged as in the following equation.

Then, formula (5-10) is represented by the following formula.

The following equation is obtained by performing the following integration on both sides of the equation (5-12).

Here, the following variable substitutions are defined for (k' _y1 , k' _y2 ) and (k' _z1 , k' _z2 ).

Here, the following equation is obtained from equation (5-14).

The absolute value of the Jacobian for this variable substitution is given by

By substituting equations (5-1), (5-15), and (5-17) into equation (5-13) and performing variable substitution, the following equation is obtained.

Here, 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. 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.

Here, assuming that z'=0 in order to align the measurement plane with the x'-y' plane passing through the origin, equation (5-19) is expressed as follows.

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.

From this, k is represented by the following formula.

As described _above , _{the data} processing unit 66 calculates _the reflectance _f ( _x , y, z).

A data processing method and a program according to this embodiment will be described below with reference to FIG. FIG. 16 is a flow chart showing the data processing method of this embodiment.
First, the measurement unit 61 acquires measurement data s (x', y' ₁ , y' ₂ , 0, 0, k) (step S5-1). Then, 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.

Next, 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). Specifically, using equations (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).

<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 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.
Here, the coordinates of the transmission point are p ₁ (x' ₁ , y' ₁ , z' ₁ ), and the coordinates of the reception point are p ₂ (x' ₂ , y' ₂ , z' ₂ ). Let f(x, y, z) be the reflectance at the reflection point (x, y, z) of the object to be measured. Let 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. Let λ ₀ be the propagation wavelength of an electromagnetic wave in vacuum. Let ε _r be the dielectric constant of the medium. Let k be the wave number of the propagating electromagnetic wave.

Also, the transmitting point p ₁ (x' ₁ , y' ₁ , z' ₁ ) and the receiving point p ₂ (x' ₂ , y' ₂ , z' ₂ ) are related to x'=x' ₁ =x' ₂ Scan on the curve of the univalent function z'=g(x').
In the present embodiment, as shown in FIG. 17, 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.

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 .

Substituting 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.

Here, we define the following operators for x'.

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.

By substituting equation (6-6) into equation (6-5), the reflectance f(x, y, z) is obtained as follows.

As described above, 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

A data processing method and a program according to this embodiment will be described below with reference to FIG. FIG. 18 is a flow chart showing the data processing method of this embodiment.
First, the measurement unit 61 acquires 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). Thereby, measurement data s _a (x', y' ₁ , y' ₂ , k) is obtained.
Then, 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.

Next, 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).
Next, data processing unit 66 obtains the operator represented by equation (6-6) (step S6-5).

Next, 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 ).

Next, 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 λc): 2.25 GHz (133 mm)
・Measurement interval Δx 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 Δy 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 ε _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):

・Curved surface measurement 2 (unit: m):

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. As shown in FIG. FIG. 19(c) shows a measurement layout diagram of curved surface measurement 2. As shown in FIG. 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. FIG. 22B shows point targets simulated by the data processing method of the sixth embodiment using the measurement layout of curved surface measurement 2 .

Using the measurement layout for horizontal plane measurement shown in FIG. 19(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. In FIG. 20, a three-dimensional image in which four point targets converge can be confirmed. From the results of 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).

Next, using the measurement layout of curved surface measurement 1 shown in FIG. 19B, 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). In 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.
Next, using the measurement layout of curved surface measurement 1 shown in FIG. 19B, a simulation was performed for four point targets according to formula (6-7) of the data processing method of the sixth embodiment. The results are shown in FIG. 21(b). In 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).

Next, using the measurement layout of curved surface measurement 2 shown in FIG. 19(c), 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). In 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.
Next, using the measurement layout of curved surface measurement 2 shown in FIG. 19(c), a simulation was performed for four point targets according to formula (6-7) of the data processing method of the sixth embodiment. The results are shown in FIG. 22(b). In 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).

From the results of FIGS. 21A and 21B and the results of FIGS. It was confirmed that the reflectance f(x, y, z) corresponding to the measurement layout of the curved surface measurement 1 was obtained by inserting into the exponent part of .

<Seventh Embodiment>
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.
Here, the coordinates of the transmission point are p ₁ (x' ₁ , y' ₁ , z' ₁ ), and the coordinates of the reception point are p ₂ (x' ₂ , y' ₂ , z' ₂ ). Let f(x, y, z) be the reflectance at the reflection point (x, y, z) of the object to be measured. Let 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. Let λ ₀ be the propagation wavelength of an electromagnetic wave in vacuum. Let ε _r be the dielectric constant of the medium. Let k be the wave number of the propagating electromagnetic wave.

Also, the transmitting point p ₁ (x' ₁ , y' ₁ , z' ₁ ) and the receiving point p ₂ (x' ₂ , y' ₂ , z' ₂ ) are x'=x' ₁ =x' ₂ Fulfill.
In the present embodiment, as shown in FIG. 23, a function expressed by the following equation representing a semi-cylindrical measurement curved surface with a radius of _R0 will be described.

Note that the function g ₁ (x', y' ₁ ) may be any univalent function on (x', y' ₁ ). Also, 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.

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 .

Substituting equations (7-1) to (7-4) into equation (5-19) yields the following equation.

Equation (5-22) can be used approximately in this embodiment as well.

Here, the following operators are defined for (x', y' ₁ , y' ₂ ).

The operators of equations (7-6) and (7-7) are (k _x , k' _y1 , k' _y2 , k' y2 , for S _a (k _x , k' _y1 , k' _y2 , k) k) have eigenvalues of (x', y' ₁ , y' ₂ ) in space.

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

As described above, 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

A data processing method and a program according to this embodiment will be described below with reference to FIG. FIG. 24 is a flow chart showing the data processing method of this embodiment.
First, the measurement unit 61 acquires 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). Thereby, measurement data s _a (x', y' ₁ , y' ₂ , k) is obtained.
Then, 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.

Next, 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).
Next, the data processing unit 66 obtains operators represented by equations (7-6) and (7-7) (step S7-5).

Next, 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 ).

Next, 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.

10a transmitting antenna 10b receiving antenna 50 transmitting array antenna 52 receiving array antenna 60 radar device 61 measurement unit 64 system control circuit 66 data processing unit 68 image display units 58, 59 high frequency switch 62 high frequency circuit 69 encoder

Claims (14)

1. A data processing method for analyzing scattered waves of waves radiated to an object,
   A plurality of transmitting points arranged on the curve of the first univalent function z' ₁ =g ₁ (x' ₁ , y' ₁ ) with respect to (x' ₁ , y' ₁ ) in a plane parallel to the yz plane radiating said wave to said object from p ₁ (x' ₁ , y' ₁ , z' ₁ );
   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 _a (x' ₁ , x' ₂ , y' ₁ , y' ₂ , k) and
   The measured values s _a (x' ₁ , x' ₂ , y' ₁ , y' ₂ , k) are quadruple Fourier transformed by Equation (1) to S _a (k' _x1 , k' _x2 , k' _y1 , 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 Define the operator indicated by (3),
   

   

   
   Perform triple inverse Fourier transform from equation (4) to obtain the reflectance f (x, y, z),
   

   

   
   Data processing method.
   however,
   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 ). the components of the wave vector of the spherical wave,
   k _x = k' _x1 + k' _x2 , u = k' _x1 - k' _x2 , k _y = k' _y1 + k' _y2 , v = k' _y1 - k' _y2
   is.
2. The wavenumber and wavevector components of the wave satisfy equation (5),
   The data processing method according to claim 1.
   

   
3. A measurement system for analyzing scattered waves of waves radiated to an object,
   a transmitting/receiving unit,
   A plurality of transmitting points arranged on the curve of the first univalent function z' ₁ =g ₁ (x' ₁ , y' ₁ ) with respect to (x' ₁ , y' ₁ ) in a plane parallel to the yz plane a transmitter that radiates the wave to the object from p ₁ (x' ₁ , y' ₁ , z' ₁ );
   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 ) a receiver for receiving as s _a (x' ₁ , x' ₂ , y' ₁ , y' ₂ , k);
   a transceiver having
   A processing device,
   The measured values s _a (x' ₁ , x' ₂ , y' ₁ , y' ₂ , k) are quadruple Fourier transformed by Equation (1) to S _a (k' _x1 , k' _x2 , k' _y1 , 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);
   

   

   
   a processor for performing
   A measurement system.
   however,
   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 ). the components of the wave vector of the spherical wave,
   k _x = k' _x1 + k' _x2 , u = k' _x1 - k' _x2 , k _y = k' _y1 + k' _y2 , v = k' _y1 - k' _y2
   is.
4. The wavenumber and wavevector components of the wave satisfy equation (5),
   The measurement system according to claim 3.
   

   
5. 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);
   

   

   
   A program that makes a computer run
   however,
   k is the wave number of said wave propagating;
   k' _x1 , k' _y1 , k' _z1 are the spherical waves of said wave 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 ,
   k' _x2 , k' _y2 , k' _z2 are the spherical surfaces of the waves propagating between the reflecting point (x, y, z) and the receiving point p ₂ (x' ₂ , y' ₂ , z' ₂ ) the components of the wavenumber vector of the wave,
   k _x = k' _x1 + k' _x2 , u = k' _x1 - k' _x2 , k _y = k' _y1 + k' _y2 , v = k' _y1 - k' _y2
   is.
6. The measured value s _a (x' ₁ , x' ₂ , y' ₁ , y' ₂ , k) is a first univalent function of (x' ₁ , y' ₁ ) in a plane parallel to the yz plane Waves radiated to the object from a plurality of transmitting points _{p 1 (} x _{' 1} , y' ₁ , z' ₁ ) arranged on a curve of z' ₁ =g 1 (x' 1 , y' ₁ ) is the scattered wave reflected at the reflection point (x, y, z) on the object with the reflectance f(x, y, z) in a plane parallel to the yz plane (x' ₂ , y' ₂ ) 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 ) with _respect to is the value received in
   6. A program according to claim 5.
7. The wavenumber and wavevector components of the wave satisfy equation (5),
   7. A program according to claim 5 or 6.
   

   
8. A data processing method for analyzing scattered waves of waves radiated to an object,
   A plurality of transmitting points arranged on the curve of the first univalent function z' ₁ =g ₁ (x' ₁ , y' ₁ ) with respect to (x' ₁ , y' ₁ ) in a plane parallel to the yz plane radiating said wave to said object from p ₁ (x' ₁ , y' ₁ , z' ₁ );
   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 _a (x', y' ₁ , y' ₂ , k),
   The measured value s _a (x', y' ₁ , y' ₂ , k) is subjected to a triple Fourier transform from equation (1) to obtain S _a (k' _x , k' _y1 , k' _y2 , k) ,
   

   

   
   Let the operators shown in equations (2) and (3) with eigenvalues (x', y' ₁ , y' ₂ ) for S _a ( _k ' x , k' _y1 , k' y2 , _k ) be define and
   

   

   
   Perform triple inverse Fourier transform from equation (4) to obtain the reflectance f (x, y, z),
   

   

   
   Data processing method.
   however,
   x' = x' ₁ = x' ₂
   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 ). the components of the wave vector of the spherical wave,
   k _y = k' _y1 + k' _y2 , v = k' _y1 - k' _y2
   is.
9. The wavenumber and wavevector components of the wave satisfy equation (5),
   The data processing method according to claim 8.
   

   
10. A measurement system for analyzing scattered waves of waves radiated to an object,
    a transmitting/receiving unit,
    A plurality of transmitting points arranged on the curve of the first univalent function z' ₁ =g ₁ (x' ₁ , y' ₁ ) with respect to (x' ₁ , y' ₁ ) in a plane parallel to the yz plane a transmitter that radiates the wave to the object from p ₁ (x' ₁ , y' ₁ , z' ₁ );
    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 ) a receiver for receiving as s _a (x', y' ₁ , y' ₂ , k);
    a transceiver having
    A processing device,
    The measured value s _a (x', y' ₁ , y' ₂ , k) is subjected to a triple Fourier transform from equation (1) to obtain S _a (k' _x , k' _y1 , k' _y2 , k) a procedure;
    

    

    
    Let the operators shown in equations (2) and (3) with eigenvalues (x', y _{' 1 ,} y' ₂ ) for S _a ( _k ' x , k' _y1 , k' y2 , k) be a procedure to define
    

    

    
    A procedure for obtaining the reflectance f (x, y, z) by performing a triple inverse Fourier transform from Equation (4);
    

    

    
    a processor for performing
    A measurement system.
    however,
    x' = x' ₁ = x' ₂
    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 ). the components of the wave vector of the spherical wave,
    k _y = k' _y1 + k' _y2 , v = k' _y1 - k' _y2
    is.
11. The wavenumber and wavevector components of the wave satisfy equation (5),
    The measurement system according to claim 10.
    

    
12. A program for analyzing scattered waves of waves radiated to an object,
    A procedure for obtaining _{S a} (k' x , k' _y1 , k' _y2 , k) by performing a triple Fourier transform on the measured value s a ( _x ', y' ₁ , y' ₂ , k) from the formula (1) and,
    

    

    
    Let the operators shown in equations (2) and (3) with eigenvalues (x', y' ₁ , y' ₂ ) for S _a ( _k ' x , k' _y1 , k' y2 , _k ) be a procedure to define
    

    

    
    A procedure for obtaining the reflectance f (x, y, z) by performing a triple inverse Fourier transform from Equation (4);
    

    

    
    A program that makes a computer run
    however,
    x' = x' ₁ = x' ₂
    k is the wave number of said wave propagating;
    k' _x1 , k' _y1 , k' _z1 are the spherical waves of said wave 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 ,
    k' _x2 , k' _y2 , k' _z2 are the spherical surfaces of the waves propagating from the reflecting point (x, y, z) to the receiving point p ₂ (x' ₂ , y' ₂ , z' ₂ ) the components of the wavenumber vector of the wave,
    k _y = k' _y1 + k' _y2 , v = k' _y1 - k' _y2
    is.
13. _The measured value s _a (x', y' ₁ , y' ₂ , k) is a first univalent function _z ' ₁ =g Waves radiated to the object from a plurality of transmission points p ₁ (x _{' 1 ,} y' ₁ , z' ₁ ) arranged on a _curve of 1 (x' 1 , y' 1 ₎ are The scattered wave reflected with the reflectance f(x, y, z) at the reflection point (x, y, z) of (x' ₂ , y' ₂ ) in a plane parallel to the yz plane Values received at multiple receiving points p ₂ (x' ₂ , y' ₂ , z' ₂ ) arranged on the curve of a single-valued function of 2 z' 2 = _{g 2 (} x' ₂ , y' ₂ ) is
    13. A program according to claim 12.
14. The wavenumber and wavevector components of the wave satisfy equation (5),
    14. A program according to claim 12 or 13.
    

    

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