CN107765230B - Application method of chain relation in near-field-to-far-field conversion of near-field measurement system - Google Patents

Abstract

The invention discloses an application method of a chain relation in near field to far field conversion of a near field measurement system, which changes the chain relation of NFFFT into a new expression form and provides F₀、F_NAnd through the target in rotationHeart and field distribution Ei in a plane perpendicular to the line of the radar illumination and the line of reflection. The original relation and the new relation are completely equivalent, and the original relation and the new relation belong to different expression modes of chain relations. But the new relational expression solves the original problem of inverse convolution. It makes the chain relation easier to enter engineering applications. Another aspect of the present invention is to provide a method for performing near-field RCS measurement, including background cancellation, F_NScaling, NFFFT scaling, etc. Compared with the NFFFT method based on the imaging concept and the plane wave synthesis, the near-field RCS measuring technology and method are strict in theory, have simple mathematical expressions, clear in physical concept and convenient to use in engineering.

Description

Application method of chain relation in near-field-to-far-field conversion of near-field measurement system

Technical Field

The invention belongs to the technical field of low observability and radar, and particularly relates to an application method of a chain relational expression in near-field-to-far-field conversion of a near-field measurement system.

Background

Traditionally, the static measurement of RCS has been performed by external and compact fields. The external field measurement occupies a large area, the cost is high, the number of environmental interference sources is large, the external field measurement is influenced by climate, and the measurement efficiency is low. The compact range quiet zone is small in size and is mainly used for RCS testing of scale models and parts.

In 2008, the U.S. los-march company introduced an RCS test system based on an indoor point source near field for factory performance detection of stealth aircraft.

Passing the near-field scattering coefficient F without satisfying the far-field condition_NMeasuring and calculating far-field scattering coefficient F₀Then, the RCS under far field conditions is obtained. The key of the near-field measurement system is near-field far-field transformation (NFFFT for short).

There are several methods of NFFFT, including: a method based on imaging; a method based on plane wave loading; and thirdly, a method based on a convolution formula.

The convolution formula of NFFFT is called the chain relation (see "calculation and measurement of electromagnetic scattering" authored by ho yog et al, 2006, beijing aerospace university press).

F_N(θ,φ|θ′,φ′)＝C₁F₀(θ,φ|θ′,φ′)*[S_T(θ,φ)*S_R(θ′,φ′)] (1)

The symbol "+" in formula (1) represents convolution,

representing a deconvolution. The meanings of other symbols are shown in figure 1.

In fig. 1, the distance from the phase center of the transmitting antenna to the target rotation center O is R1, and the distance from the phase center of the receiving antenna to the target rotation center O is R2. The plane wave angle spectra (PWS) of the transmitting and receiving antennas are S_T(theta, phi) and S_R(theta ', phi'). Far field scattering coefficient of target is F₀(θ, φ | θ ', φ'). If R1 and R2 tend to be infinite, the output signal of the receiver is F₀(θ, φ | θ ', φ'), otherwise F_N(θ, φ | θ ', φ'). In the figure, (theta, phi) is the irradiation angle of the two-station radar, and (theta ', phi') is the scattering angle of the two-station radar.

The physical significance of formula (1) is the near field scattering coefficient F_NIs equal to the far field scattering coefficient F₀And system impulse response function a ═ S_T*S_R]Is performed.

The physical significance of the formula (2) is that the far-field scattering coefficient F₀Equal to the near field scattering coefficient F_NAnd system impulse response function a ═ S_T*S_R]Is deconvolved. Thus, from F_NAnd the impulse response function A ═ S_T*S_R]Can calculate F₀。

From the known far field scattering coefficient F₀(true value) calculation PresenceNear field scattering coefficient F of measurement error_NThe calculation process is a normal convolution calculation. Under backscatter conditions, the computational block diagram is shown in fig. 2.

Near field scattering coefficient F obtained by measurement_NCalculating far field scattering coefficient F₀Deconvolution (or deconvolution) calculations are required. Deconvolution is generally more complex. For this reason, the near-field RCS measurement needs to be modified from equation (2).

Disclosure of Invention

The technical problem to be solved by the invention is as follows: the invention provides an application method of a chain relational expression in near field to far field conversion of a near field measurement system and an implementation method of near field RCS measurement, comprising background cancellation and F_NScaling, NFFFT scaling.

The technical scheme adopted by the invention is as follows: an application method of a chain relation in near-field to far-field transformation of a near-field measurement system is based on a chain relation of near-field to far-field transformation (NFFFT), and the chain relation is expressed as:

F_N(θ,φ|θ′,φ′)＝C₁F₀(θ,φ|θ′,φ′)*[S_T(θ,φ)*S_R(θ′,φ′)]

in the formula F_NAnd F₀For near-field and far-field scattering coefficients, C₁Is a constant term, S_T(θ,φ)，S_R(θ ', φ') are the transmitting antenna plane spectrum and the receiving antenna plane spectrum, θ and φ are the pitch angle and azimuth angle, respectively, in the transmitting antenna coordinate system, θ 'and φ' are the pitch angle and azimuth angle, respectively, in the receiving antenna coordinate system, and the scattering coefficient is defined as:

wherein the scattering coefficient F is a complex number, wherein E^sTo scatter the electric field, EⁱFor an incident electric field, k is a wave number, and R is a distance, the radar cross section can be used for a far field (R satisfies a far field condition) and a near field (R does not satisfy the far field condition), and the radar cross section formula is as follows:

in the formula, λ is wavelength, and as can be seen from the above formula, for a radar transmission signal, a signal received by a radar is proportional to a scattering coefficient, and a system impulse function is:

the transmitting antenna and receiving antenna patterns may be different, and their distances to the target rotation center may also be unequal;

in the backward RCS, the plane wave angular spectrums (PWS) of the transmitting antenna and the receiving antenna are the same, and have S_T(θ,φ)＝S_R(θ, Φ) ═ S (θ, Φ), when the near-field RCS measurement system impulse response function is equal to the self-convolution of S (θ, Φ), i.e.:

A＝S(θ,φ)*S(θ,φ)＝IFFT[Eⁱ(x,y)×Eⁱ(x,y)]

the calculation process is simplified, and under the condition of backscattering, the FFT of the impulse response function of the system is Eⁱ(x,y)×Eⁱ(x, y), IFFT and FFT cancel each other out, a new relation graph is obtained after FFT and IFFT cancel each other out, namely F_NSum of plane wave angle spectrum with transmitting and receiving antenna₀Is converted into F_NAnd electric field distribution EⁱAnd F₀F, and performing inverse operation to obtain point source and line source NFFFT respectively_NCalculating F₀The method of (1).

The specific implementation method comprises the following steps of under the two conditions of point source and line source:

first, the complex reflection signals F of the background and the stent are measured^B；

Then, a calibration ball is placed on the support, and a plurality of reflected signals F are measured^C；

Next, the measured target is erected to a measurement height through two support rods and a lifting rope, the rotating platform rotates to drive the target to rotate at an azimuth angle phi, the lifting rope is located at the rotating center of the rotating platform, and the telescopic action of the lifting rope changes the pitch angle theta of the target;

then, given the pitch angle of the target, when the azimuth angle of the rotary table is 0 degree, the radar transmits a signal with one frequency to irradiate the target, and the receiver receives a complex reflected signal F of the target^T(θ,φ₁) Including amplitude and phase;

then, the pitch angle is unchanged, the azimuth angle of the rotary table is increased by a fixed increment delta phi to rotate to a new position, the radar transmits the same frequency to irradiate the target, and the receiver receives a complex reflected signal F of the target^T(θ,φ₂) Including amplitude and phase;

then, repeating the cycle to obtain F^T(θ,φ_n1)；

Next, the pitch angle is changed to obtain F^T(θ_n2,φ_n1)；

Next, the near-field echo signals are scaled:

in the formula F_CRadar cross section sigma given to calibration sphere_CThe corresponding reflected signals, namely:

σ_C＝20×log(F_C)

then, for F_NPerforming difference operation, and performing 2DFFT to obtain E_NThe appropriate difference will be such that E_NThe equal spacing distribution in the x and y planes;

then, by the formula Eⁱ(x,y)＝A(x,y)exp[-jφ(x,y)]Calculation of EⁱFrom the measured near field scattering coefficient F_NObtaining corresponding field distribution E on an x and y plane through interpolation and 2DFFT conversion_NOf the type using

And (3) calculating:

the method for determining the scaling coefficient C of NFFFT in the formula:

measuring near-field scattering coefficient F of calibration sphere under near-field condition_N(φ)；

② to F_N(phi) calculating far field coefficient F of calibration sphere by inverse operation₀(φ)；

③ changing the coefficient C when F₀(φ)＝F_N(φ) time, C converges;

next, from E⁰2DIFFT and interpolation are carried out to obtain a far field scattering coefficient F₀(θ, φ), it is distributed in the angular domain (θ, φ) equally spaced;

finally, the RCS is calculated

σ(θ,φ)＝20log|F₀(θ,φ)|。

The principle of the invention is as follows: the chain relation is a convolution-form near-field-to-far-field transform (NFFFT) formula that describes the far-field scattering coefficient F₀Near field scattering coefficient F_NAnd the transmit and receive antenna plane angular spectrum S.

The invention changes the chain relation of NFFFT into a new expression form, in which F is given₀、F_NAnd a field distribution E in a plane passing through the center of rotation of the target and perpendicular to the line of partial angles of the radar radiation and the reflection radiationⁱThe relationship between them. The original relation and the new relation are completely equivalent, and the original relation and the new relation belong to different expression modes of chain relations.

But the new relational expression solves the original problem of inverse convolution. It makes the chain relation easier to enter engineering applications.

Another aspect of the invention is to provide a method for performing near-field RCS measurement, comprising background cancellation, F_NScaling, NFFFT scaling, etc.

Compared with the prior art, the near-field RCS measuring technology and the method have the advantages that:

(1) the invention is strict in theory, has simple mathematical expression, clear physical concept and convenient engineering use.

(2) All aspects of the invention are applicable to point-source NFFFT and line-source NFFFT.

(3) The invention introduces a new relational expression, avoids the calculation of inverse convolution, and ensures that the NFFFT method is more convenient and simpler and is easier to enter engineering application.

(4) The method is a more convenient and effective near-field measurement method for the target with large size and low radar scattering cross section (RCS) scattering characteristics.

(5) The method has the advantages of large information amount, convenient indoor operation, high measurement precision, strong confidentiality, small interference by environmental climate and capability of working all day long.

Drawings

FIG. 1 is a schematic diagram of two-station scattering;

FIG. 2 shows the results of the measurement of the back-scattering effect of F₀(true value) calculation of F_NA block diagram of;

FIG. 3 is a block diagram of a system impulse response self-convolution;

FIG. 4 is a block diagram of the merged images of FIGS. 2 and 3;

FIG. 5 is a new block diagram after FFT and IFFT cancellation;

FIG. 6 is a diagram of a point source case, represented by F_NCalculating F₀A block diagram of;

FIG. 7 is a block diagram of a more regular calculation of FIG. 6;

FIG. 8 shows a line source case, represented by F_NCalculating F₀A block diagram of;

FIG. 9 is a schematic view of a point or line source illuminating a target;

FIG. 10 is a schematic of a point source near-field RCS measurement.

Detailed Description

The invention is further described with reference to the following figures and detailed description.

Current near-field RCS measurements are mainly backward (single station) RCS measurements. For backward RCS measurement, the transmitting antenna and the receiving antenna are at the same spatial point, if the transmitting antenna and the receiving antenna have the same direction and directional diagram, the plane wave angle spectrums of the two antennas are equal, namely S_T(θ,φ)＝S_R(θ, Φ) ═ S (θ, Φ). The system impulse response is a self convolution S (θ, Φ) × S (θ, Φ), and the block diagram of the self convolution is shown in fig. 3. E in FIG. 3ⁱ(x, y) is the complex amplitude in the plane perpendicular to the antenna through the target center of rotation O.

Fig. 2 and fig. 3 are combined to obtain fig. 4. The FFT and IFFT in fig. 4 cancel each other, and fig. 4 is simplified to fig. 5. Fig. 5 corresponds to fig. 2, but is not already an expression for convolution.

As can be seen from the view of figure 5,

E_N(x,y)＝E₀×Eⁱ(x,y)×Eⁱ(x,y) (3)

the inverse operation of fig. 5 is performed to obtain fig. 6. The slash in the circle in fig. 6 represents a division operation, i.e.:

the constant C in equation (4) is a scaling coefficient of NFFFT.

Fig. 6 is equivalent to fig. 7, which is more regular. Within the circle is a function of the coordinates on the target reference surface, which is a function of the airspace. Outside the circle, after Fourier transformation, it becomes a function of the angular domain (azimuth and elevation). Fig. 6 and 7 are derived from the deconvolution of equation (2), but they are not already an expression for deconvolution.

In the measurement, one usually samples equally in the angular domain, not in the spatial domain. Therefore, an interpolation operation is required.

For cylindrical fields, the convolution transform is simplified to a one-dimensional case, see FIG. 8.

A schematic diagram of a point source and a line source illuminating a target is shown in fig. 9.

The point source antenna is positioned at the point O ', the center of the target to be measured is positioned at the origin O of the coordinate system x and y, the width of the test area is D, and the distance between the O' O is R. A spherical surface is drawn by taking O' as a circle center and R as a radius, and represents wavefronts with equal phases. The distance from the point O' to any point on the xy plane is S,

d(x,y)＝S(x,y)-R

the phase of each point on the xy plane, except for one constant, is:

the amplitude is inversely proportional to the distance S over which the electromagnetic wave travels,

in this way,

Eⁱ(x,y)＝A(x,y)exp[-jφ(x,y)] (5)

referring to FIG. 7, the measured near-field scattering coefficient F_NObtaining corresponding field distribution E on an x and y plane through interpolation and 2DFFT conversion_N(x, y), and a spherical field E obtained by adding the formula (5)ⁱ(x, y) far-field scattering coefficient F can be calculated₀。

A schematic representation of the cylindrical field geometry is shown in fig. 9. As can be seen from the figure, the drawing,

d(x)＝S(x)-R

the relationship between the amplitude and the distance S over which the electromagnetic wave travels is,

in this way,

Eⁱ(x)＝A(x)exp[-jφ(x)] (6)

referring to FIG. 8, the near field scattering coefficient F is measured_NObtaining corresponding field distribution E on an x-axis through interpolation and FFT conversion_N(x) Adding the cylindrical field E obtained by the formula (6)ⁱ(x) The far field scattering coefficient F can be calculated₀。

In image processing, inverse convolution becomes a well-known problem. For example, a "photograph" has only amplitude and no phase, and deconvolution can be difficult. Sometimes it is not known what camera is used for the photograph, and a "blind convolution" is performed, which involves a complex estimation problem.

For near-field RCS measurements, both the amplitude and phase of the near-field scattering coefficient are completely known. At this time, the convolution and deconvolution operations are as simple as FFT and IFFT.

Calculating the near field from the far field is multiplication, and Fourier transformation is added;

calculating the far field from the near field is division, and Fourier transformation is added;

all these operations do not present a "morbidity" problem.

The above-described modifications to equations (1) and (2) are a key step in bringing chain relationships into engineering applications.

The method comprises the following specific steps:

step 1, measuring a plurality of reflection signals F of a background and a support^B；

Step 2, placing the calibration ball on the bracket, and measuring a plurality of reflection signals F^C；

And 3, erecting the measured target to a measuring height through two support rods and a lifting rope, and referring to fig. 10. The turntable rotates to drive the target to rotate at an azimuth angle phi, the lifting rope is positioned at the rotating center of the turntable, and the telescopic action of the lifting rope changes the pitch angle theta of the target;

step 4, the pitch angle of the target is given, when the azimuth angle of the rotary table is 0 degree, the radar transmits a signal with one frequency to irradiate the target, and the receiver receives a plurality of reflected signals F of the target^T(θ,φ₁) Including amplitude and phase;

step 5, the pitch angle is unchanged, the azimuth angle of the rotary table is increased by a fixed increment delta phi and is rotated to a new position, the radar transmits the same frequency to irradiate the target, and then the target is connectedReceiver receiving complex reflected signal F of target^T(θ,φ₂) Including amplitude and phase;

step 6, repeating the steps to obtain F^T(θ,φ_n1)；

Step 7, changing the pitch angle to obtain F^T(θ_n2,φ_n1)；

Step 8, calibrating the near-field echo signals:

in the formula F_CRadar cross section sigma given to calibration sphere_CThe corresponding reflected signals, namely:

σ_C＝20×log(F_C)

step 9, for F_NPerforming difference operation, and performing 2DFFT to obtain E_NThe appropriate difference will be such that E_NThe equal spacing distribution in the x and y planes;

step 10, from E of formula (5)ⁱAnd E_NCalculating using equation (4):

the method for determining the scaling coefficient C of NFFFT in the formula:

measuring near-field scattering coefficient F of calibration sphere under near-field condition_N(φ)；

Second, the block diagram of FIG. 7 is used to calculate the far field coefficient F of the calibration sphere₀(φ)；

③ changing the coefficient C when F₀(φ)＝F_NWhen (phi), C converges.

Step 11, from E⁰2DIFFT and interpolation are carried out to obtain a far field scattering coefficient F₀(theta, phi) which are equally spaced in the angular domain (theta, phi).

Step 12, calculating RCS

σ(θ,φ)＝20log|F₀(θ,φ)|。

Claims (2)

1. A method of applying a chain relation to a near-field to far-field transformation in a near-field measurement system, comprising: the method is based on a chain relation of near-field far-field transformation, wherein the near-field far-field transformation is called NFFFT for short, and the relation is expressed as follows:

F_N(θ,φ|θ′,φ′)＝C₁F₀(θ,φ|θ′,φ′)*[S_T(θ,φ)*S_R(θ′,φ′)]

in the formula F_NAnd F₀For near-field and far-field scattering coefficients, C₁Is a constant term, S_T(θ,φ)，S_R(θ ', φ') are the transmitting antenna plane spectrum and the receiving antenna plane spectrum, θ and φ are the pitch angle and azimuth angle, respectively, in the transmitting antenna coordinate system, θ 'and φ' are the pitch angle and azimuth angle, respectively, in the receiving antenna coordinate system, and the scattering coefficient is defined as:

wherein the scattering coefficient F is a complex number, wherein E^sTo scatter the electric field, EⁱFor an incident electric field, k is a wave number, R is a distance, namely R is used for a far field when meeting a far field condition, and R is used for a near field when not meeting the far field condition, and the radar scattering cross section formula is as follows:

in the formula, λ is wavelength, and as can be seen from the above formula, for a radar transmission signal, a signal received by a radar is proportional to a scattering coefficient, and a system impulse function is:

the transmitting antenna and the receiving antenna have the same or different directional patterns, and the distances from the transmitting antenna and the receiving antenna to the target rotation center are equal or unequal;

in the backward RCS, the plane wave angular spectrums (PWS) of the transmitting antenna and the receiving antenna are the same, and have S_T(θ,φ)＝S_R(θ, Φ) ═ S (θ, Φ), when the near-field RCS measurement system impulse response function is equal to the self-convolution of S (θ, Φ), i.e.:

A＝S(θ,φ)*S(θ,φ)＝IFFT[Eⁱ(x,y)×Eⁱ(x,y)]

the calculation process is simplified, and under the condition of backscattering, the FFT of the impulse response function of the system is Eⁱ(x,y)×Eⁱ(x, y), IFFT and FFT cancel each other out, a new relation graph is obtained after FFT and IFFT cancel each other out, namely F_NSum of plane wave angle spectrum with transmitting and receiving antenna₀Is converted into F_NAnd electric field distribution EⁱAnd F₀F, and performing inverse operation to obtain point source and line source NFFFT respectively_NCalculating F₀The method of (1).

2. The method of applying a chain relation in a near-field to far-field transformation of a near-field measurement system of claim 1, wherein: in both cases of point source and line source, the specific implementation method comprises the following steps:

first, the complex reflection signals F of the background and the stent are measured^B；

Then, a calibration ball is placed on the support, and a plurality of reflected signals F are measured^C；

Next, the measured target is erected to a measurement height through two support rods and a lifting rope, the rotating platform rotates to drive the target to rotate at an azimuth angle phi, the lifting rope is located at the rotating center of the rotating platform, and the telescopic action of the lifting rope changes the pitch angle theta of the target;

then, given the pitch angle of the target, when the azimuth angle of the rotary table is 0 degree, the radar transmits a signal with one frequency to irradiate the target, and the receiver receives a complex reflected signal F of the target^T(θ,φ₁) Including amplitude and phase;

then, the pitch angle is unchanged, the azimuth angle of the rotary table is increased by a fixed increment delta phi to rotate to a new position, and the radar transmits the same frequency illuminationTarget, receiver receiving complex reflected signal F of target^T(θ,φ₂) Including amplitude and phase;

then, repeating the cycle to obtain F^T(θ,φ_n1)；

Next, the pitch angle is changed to obtain F^T(θ_n2,φ_n1)；

Next, the near-field echo signals are scaled:

in the formula F_CRadar cross section sigma given to calibration sphere_CThe corresponding reflected signals, namely:

σ_C＝20×log(F_C)

then, for F_NPerforming difference operation, and performing 2DFFT to obtain E_NThe appropriate difference will be such that E_NThe equal spacing distribution in the x and y planes;

then, by the formula Eⁱ(x,y)＝A(x,y)exp[-jφ(x,y)]Calculation of EⁱFrom the measured near field scattering coefficient F_NObtaining corresponding field distribution E on an x and y plane through interpolation and 2DFFT conversion_NOf the type using

And (3) calculating:

the method for determining the scaling coefficient C of NFFFT in the formula:

measuring near-field scattering coefficient F of calibration sphere under near-field condition_N(φ)；

② carrying out inverse operation to calculate far field coefficient F of calibration sphere₀(φ)；

③ changing the coefficient C when F₀(φ)＝F_N(φ) time, C converges;

next, from E⁰2DIFFT and interpolation are carried out to obtain a far field scattering coefficient F₀(θ, φ), it is distributed in the angular domain (θ, φ) equally spaced;

finally, the RCS is calculated

σ(θ，φ)＝20log|F₀(θ，φ)|。

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