CN115561725A - Near-field extrapolation far-field RCS measurement method - Google Patents

Near-field extrapolation far-field RCS measurement method Download PDF

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CN115561725A
CN115561725A CN202211317609.2A CN202211317609A CN115561725A CN 115561725 A CN115561725 A CN 115561725A CN 202211317609 A CN202211317609 A CN 202211317609A CN 115561725 A CN115561725 A CN 115561725A
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far
rcs
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antenna
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CN115561725B (en
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黄金海
周建江
邓峣
彭翌玲
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Guilin Institute Of Information Technology
Nanjing University of Aeronautics and Astronautics
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Nanjing University of Aeronautics and Astronautics
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
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Abstract

The invention discloses a measuring method of near-field extrapolation far-field RCS, which comprises the steps of presetting a near-field antenna equivalent current density excitation scanning model according to preset antenna parameters; constructing a diagonal translation operator according to electromagnetic wave emission parameters, establishing an antenna emission excitation function model, designing a forward correction equation to solve a near-field electric field, and deducing a far-field RCS by combining a correction operator; and constructing a far-field electromagnetic scattering model according to the complex exponential model, establishing an inverse source correction equation, carrying out inverse source correction on the forward-derived near-field RCS, designing a near-field far-field RCS constraint term, and obtaining an optimal inverse source correction equation. By the inverse source correction method, the problem of large error of the predicted far-field RCS in the prior art is solved, the problem of response error in the output process of an integral electric field is solved, and the problem of forward correction function correction in the process of inverting a near field from a far field is solved.

Description

Near-field extrapolation far-field RCS measurement method
Technical Field
The invention relates to the technical field of far-field RCS measurement, in particular to a method for measuring far-field RCS by near-field extrapolation.
Background
Extrapolation of far-field Radar Cross Section (RCS) from near-field measurement data under test conditions without expensive RCS is a common method for engineering researchers. Under the near-field condition, the target is generally measured in the anechoic chamber, and for any near-field antenna scanning method, amplitude and phase data are acquired by scanning and measuring according to a preset mode. In consideration of the prediction of the far-field RCS of the test antenna, the near-field extrapolation far field needs to be effectively transformed according to parameters such as the attribute of the reference antenna, the target geometric structure and the like to achieve the aim.
Currently, the most common antenna scanning methods are: planar field scanning (PNF), cylindrical field scanning (CNF), and spherical field Scanning (SNF), each of which requires translation and rotation to complete the scan of the target surface. However, the existing near-field to far-field transformation model is obtained by forward deriving the attribute characteristics of the known system, probe, gain and multi-level scattering diffraction to complete test data, and the effectiveness of the transformation model is not subjected to inverse source correction. In addition, due to complex electromagnetic calculations, the forward derived transformation model still cannot predict sufficient accuracy in practical engineering applications.
Disclosure of Invention
This section is for the purpose of summarizing some aspects of embodiments of the invention and to briefly introduce some preferred embodiments. In this section, as well as in the abstract and title of the application, simplifications or omissions may be made to avoid obscuring the purpose of the section, the abstract and the title, and such simplifications or omissions are not intended to limit the scope of the invention.
The present invention has been made in view of the above-mentioned conventional problems.
Therefore, the invention provides a measuring method of far-field RCS by near-field extrapolation, which can solve the problem of large error of RCS prediction.
In order to solve the technical problem, the invention provides the following technical scheme that the method for measuring the far-field RCS by using the near-field extrapolation comprises the following steps:
presetting a near-field antenna equivalent current density excitation scanning model according to the antenna parameter to be solved;
constructing a diagonal translation operator according to electromagnetic wave emission parameters, establishing an antenna emission excitation function model, designing a forward correction equation to solve a near-field electric field, and deducing a far-field RCS by combining a correction operator;
and constructing a far-field electromagnetic scattering model according to the complex exponential model, establishing an inverse source correction equation, carrying out inverse source correction on the forward-derived near-field RCS, designing a near-field far-field RCS constraint term, and obtaining an optimal inverse source correction equation.
As a preferred embodiment of the measuring method of near-field extrapolation far-field RCS according to the present invention, wherein: the near-field far-field RCS constraint terms include,
max||σ′ FF -σ FF || 2 ≤ε 1
|A H E FF -A H AE FF |≤ε 2
wherein, σ' FF For far field radar scattering area, sigma, after inverse source correction FF Far field radar scattering area, epsilon, deduced for the forward direction 1 And epsilon 2 To define the threshold, E FF Is far field electric field, | | | | luminance 2 Is a 2 norm symbol, A H Is the complex conjugate transpose of A, and A is the inverse source corrector.
As a preferred embodiment of the measuring method of near-field extrapolation far-field RCS according to the present invention, wherein: the near-field far-field RCS constraint term further includes,
if the inverse source correction error is larger than the threshold value, returning to perform iteration;
and if the inverse source correction error is smaller than the threshold value, updating the inverse source correction function.
As a preferable scheme of the measuring method of the near-field extrapolation far-field RCS of the present invention, wherein: the far-field electromagnetic scattering model includes,
Figure BDA0003909147770000021
Figure BDA0003909147770000022
σ′ FF ＝IFFT(ψ′(k,r))
wherein E is FF (k, r) is the far field electric field scattering function, k is the free space wavenumber vector, r is the free space source point distance vector, M is the number of scattering models, A i Is the amplitude, α i For the dispersion factor, i is the ith of the number of scattering models, ω (k) is additive white Gaussian noise, ψ' (k, r) is the far field scattering distribution function, gn (r, r) i ) Is a dyadic Green function, r i Is the distance vector of the free space field with respect to the field source.
As a preferred embodiment of the measuring method of near-field extrapolation far-field RCS according to the present invention, wherein: the inverse source-correction equation includes,
the correction coefficient C (k, r) is expressed as,
Figure BDA0003909147770000031
Figure BDA0003909147770000032
A·E(k,r)-E FF (k,r)＝0
wherein E (k, r) is a discretized near-field electromagnetic scattering model, mu is a free space medium constant, i AUT is the number of rays of the electromagnetic wave emitted by the antenna, and t (k, r) is the excitation function of the emission of the antenna.
As a preferred embodiment of the measuring method of near-field extrapolation far-field RCS according to the present invention, wherein: the antenna transmit excitation function includes a function of,
t(k,r)＝U(k,r)exp(-jk·||r-r i ||)
where k · t (r) =0 is a constraint term indicating that the electromagnetic wave polarization direction is orthogonal to the transmission direction, U (k, r) is the updated excitation voltage, | | r-r i | is distanceAnd (4) an off-vector modulus value.
As a preferred embodiment of the measuring method of near-field extrapolation far-field RCS according to the present invention, wherein: the forward correction equation includes a forward correction of,
E(k,r)＝C·E i (r)+λP(k,r)
P(k,r)＝A m exp(-jk·r)
wherein P (k, r) is a forward corrector, A m And C is an amplitude value, C is a correction coefficient, and lambda is a Lagrange optimization objective function coefficient.
As a preferred embodiment of the measuring method of near-field extrapolation far-field RCS according to the present invention, wherein: the near-field RCS includes a near-field RCS,
Figure BDA0003909147770000033
wherein σ NF Is near field RCS, E i (r) is the incident electric field of the PNF probe.
As a preferred embodiment of the measuring method of near-field extrapolation far-field RCS according to the present invention, wherein: the near field antenna equivalent current density excitation scanning model comprises,
J s (r)＝U i (r)w T (r)
w T (r)＝ω(r)·Z T
wherein, J s Represents the equivalent current density, U i (r) is the input excitation voltage, w T (r) is a normalized field source distribution function, ω (r) is a weight coefficient, r is a free space source point distance vector, Z T Is the antenna transmit impedance.
As a preferable scheme of the measuring method of the near-field extrapolation far-field RCS of the present invention, wherein: the actuation voltage may be selected from the group consisting of,
the updated excitation voltage is represented as,
Figure BDA0003909147770000041
wherein, T L (k, r) is a diagonal translation operator,
Figure BDA0003909147770000042
is a unit dyadic, kk is the multiplication of the wave number points,
Figure BDA0003909147770000043
equivalent current densities in the pitch and azimuth directions, theta being the azimuth angle,
Figure BDA0003909147770000044
is the pitch angle, k x Wave number component in x-axis, k y The wave number component in the y-axis direction is x, which is a coordinate axis x, and y is a coordinate axis y.
The invention has the beneficial effects that: the invention provides a measuring method of near-field extrapolation far-field RCS, which solves the problem of large error of prediction of far-field RCS in the prior art, solves the problem of response error in the output process of an integral electric field and solves the problem of forward correction function correction in the process of inverting a near field in a far field by an inverse source correction method.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without inventive exercise. Wherein:
FIG. 1 is a flowchart illustrating a design of a method for measuring far-field RCS by near-field extrapolation according to an embodiment of the present invention;
FIG. 2 is a flowchart of a method for measuring far-field RCS using near-field extrapolation, according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a PNF scanning geometry of a near-field extrapolated far-field RCS measurement method according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of an improved method for near-field extrapolated far-field RCS measurement compared to a prior art method for extrapolating far-field RCS according to an embodiment of the present invention;
Detailed Description
In order to make the aforementioned objects, features and advantages of the present invention more comprehensible, embodiments accompanying figures of the present invention are described in detail below, and it is apparent that the described embodiments are a part, not all or all of the embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without making creative efforts based on the embodiments of the present invention, shall fall within the protection scope of the present invention.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, but the present invention may be practiced in other ways than those specifically described and will be readily apparent to those of ordinary skill in the art without departing from the spirit of the present invention, and therefore the present invention is not limited to the specific embodiments disclosed below.
Furthermore, reference herein to "one embodiment" or "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one implementation of the invention. The appearances of the phrase "in one embodiment" in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments.
The present invention will be described in detail with reference to the drawings, wherein the cross-sectional views illustrating the structure of the device are not enlarged partially in general scale for convenience of illustration, and the drawings are only exemplary and should not be construed as limiting the scope of the present invention. In addition, the three-dimensional dimensions of length, width and depth should be included in the actual fabrication.
Also in the description of the present invention, it should be noted that the terms "upper, lower, inner and outer" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, which are only for convenience of description and simplification of description, but do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus, should not be construed as limiting the present invention. Furthermore, the terms first, second, or third are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
The terms "mounted, connected and connected" in the present invention are to be understood broadly, unless otherwise explicitly specified or limited, for example: can be fixedly connected, detachably connected or integrally connected; they may be mechanically, electrically, or directly connected, or indirectly connected through intervening media, or may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
Example 1
Referring to fig. 1-4, a first embodiment of the present invention provides a method for measuring near-field extrapolated far-field RCS, comprising:
step 102, presetting a near-field antenna equivalent current density excitation scanning model according to antenna parameters to be solved; wherein the near-field antenna equivalent current density excitation scanning model comprises,
J s (r)＝U i (r)w T (r)
w T (r)＝ω(r)·Z T
wherein, J s Represents the equivalent current density, U i (r) is the input excitation voltage, w T (r) is a normalized field source distribution function, ω (r) is a weight coefficient, r is a free space source point distance vector, Z T Is the antenna transmit impedance.
104, constructing a diagonal translation operator according to electromagnetic wave emission parameters, establishing an antenna emission excitation function model, designing a forward correction equation to solve a near-field electric field, and deducing a far-field RCS (radar cross section) by combining a correction operator;
the method is mainly used for solving the problem of the number of unknown transformation operators in the free space coordinate system.
Specifically, a dyadic Green function Gn (r, r) is utilized i ) With excitation of equivalent current density J s (r) performing space distance vector integration to obtain the incident electric field E of the PNF probe i (r)，
Figure BDA0003909147770000061
Figure BDA0003909147770000062
Further, reference is made to the known diagonal translation operator T L (k, r) and testing the output response of the probe at different frequencies, and integrating the wave number.
Meanwhile, take forward syndrome P (k, r) = a m exp (-jk r) is used as a constraint term of the objective optimization function to correct response errors. Thereby improving the probe output voltage U (k, r) equation:
Figure BDA0003909147770000063
Figure BDA0003909147770000064
wherein the content of the first and second substances,
Figure BDA0003909147770000065
as a second type of Hankel function, P l (k, r) is a Legendre polynomial,
Figure BDA0003909147770000066
for equivalent current density, T, of the probe with respect to plane field pitch and azimuth L (k, r) is a diagonal translation operator,
Figure BDA0003909147770000067
is a unit vector of parallel, kk is the multiplication of wave number points,
Figure BDA0003909147770000071
equivalent current densities in the pitch and azimuth directions, theta being the azimuth angle,
Figure BDA0003909147770000072
to be bent overElevation angle, k x Wave number component in x-axis, k y The wave number component in the y-axis direction, x is the coordinate axis x, and y is the coordinate axis y.
Furthermore, a Lagrange optimization objective function of the probe output voltage is constructed, and a coefficient lambda is obtained:
Figure BDA0003909147770000073
Figure BDA0003909147770000074
further, the probe output voltage is updated as:
Figure BDA0003909147770000075
further, an antenna transmission excitation function t (k, r) is obtained:
t(k,r)＝U(k,r)exp(-jk·||r-r i ||)
where k · t (r) =0 is a constraint term indicating that the electromagnetic wave polarization direction is orthogonal to the transmission direction, U (k, r) is the updated excitation voltage, | | r-r i And | is a distance vector modulus value.
Furthermore, a near-field electromagnetic scattering model is derived according to the antenna transmission excitation function:
Figure BDA0003909147770000076
further, discretizing the near-field electromagnetic scattering model:
Figure BDA0003909147770000077
further, using the forward corrector P (k, r), the forward correction equation is designed:
E(k,r)＝C·E i (r)+λP(k,r)
wherein P (k, r) is a forward corrector, A m And C is an amplitude value, C is a correction coefficient, and lambda is a Lagrange optimization objective function coefficient.
Further, near-field RCS:
Figure BDA0003909147770000078
wherein σ NF Is near field RCS, E i (r) is the incident electric field of the PNF probe.
It should be noted that depending on the far-field distance condition, irradiation with a plane wave requires an electric field in the far field
Figure BDA0003909147770000081
Under known conditions, a corrector F (k, r) is added to calculate a scattering distribution function ψ (k, r), and an inverse Fourier transform (IFFT) is performed on ψ (k, r) to obtain a far-field RCS.
It should be noted that, in order to derive the far-field RCS process, the distance vector of the near-field model needs to be corrected to the far-field distance vector to obtain the far-field electric field equation
Figure BDA0003909147770000082
Far field scattering distribution function psi (k, r), far field RCS sigma FF ：
Figure BDA0003909147770000083
Figure BDA0003909147770000084
σ FF ＝IFFT(ψ(k,r))
Wherein the content of the first and second substances,
Figure BDA0003909147770000085
as far field electric field equation, E i (r) incident electric field of PNF probeK is the free space wavenumber vector, r is the free space source point distance vector, i is the ith of the scattering model number, ψ (k, r) is the far field scattering distribution function, gn (r, r) i ) And r is a distance vector of the free space field relative to the field source.
And 106, constructing a far-field electromagnetic scattering model according to the complex exponential model, establishing an inverse source correction equation, carrying out inverse source correction on the forward-derived near-field RCS, designing a near-field far-field RCS constraint term, and obtaining an optimal inverse source correction equation.
Wherein a far field electric field scattering function E is constructed by using a complex exponential model FF (k,r)。
Specifically, the scattering distribution function ψ ' (k, r) and the far-field RCS σ ' are calculated according to the far-field condition ' FF 。
Figure BDA0003909147770000086
Figure BDA0003909147770000087
σ′ FF ＝IFFT(ψ′(k,r))
Wherein E is FF (k, r) is far field electric field scattering function, k is free space wave number vector, r is free space source point distance vector, M is scattering model number, A i Is the amplitude, α i For the dispersion factor, i is the ith of the number of scattering models, ω (k) is additive white Gaussian noise, ψ' (k, r) is the far field scattering distribution function, gn (r, r) i ) Is a dyadic Green function, r i Is the distance vector of the free space field with respect to the field source.
Further, a correction coefficient C (k, r) is added to the near-field electric field model:
Figure BDA0003909147770000091
Figure BDA0003909147770000092
establishing an inverse source correction equation of the far field and the near field:
A·E(k,r)-E FF (k,r)＝0
wherein E (k, r) is a discretized near-field electromagnetic scattering model, mu is a free space medium constant, i AUT is the number of rays of the electromagnetic wave emitted by the antenna, and t (k, r) is the excitation function of the emission of the antenna.
It should be noted that the threshold value ε is set sufficiently small 1 ,ε 2 ，ε 1 Is self-defined according to the error condition, such as-50 dBsm to-80 dBsm. Epsilon 2 Is self-defined according to error conditions, e.g. -50 to-80 dB, where the unit is equal to epsilon 1 Not the same.
Further, the RCS constraint term is designed for the inverse source correction equation:
max||σ′ FF -σ FF || 2 ≤ε 1
|A H E FF -A H AE FF |≤ε 2
wherein, σ' FF For far field radar scattering area, sigma, after inverse source correction FF Far field radar scattering area, epsilon, deduced for the forward direction 1 And e 2 To define the threshold, E FF Is far field electric field, | | | calving 2 Is a 2 norm symbol, A H Is the complex conjugate transpose of A, and A is the inverse source corrector.
Deriving an approximate solution for the inverse source corrector A by least squares and calculating the iterative residual e = A H E FF -A H AE FF Thereby obtaining an optimal inverse source correction equation.
It should be noted that, among others:
A·E(k,r)-E FF (k,r)＝0
Figure BDA0003909147770000093
Figure BDA0003909147770000101
Figure BDA0003909147770000102
further, | A H ·E FF (k,r)-E FF (k,r)|＝|A H ·E FF (k,r)-A H A·E FF (k,r)|≤ε 2 The above formula is abbreviated: | A H E FF -A H AE FF |≤ε 2 。
It should be noted that the correction coefficient derived in the forward direction
Figure BDA0003909147770000103
And correction coefficient obtained by using inverse source correction equation
Figure BDA0003909147770000104
A significant improvement is obtained with near-field extrapolation to far-field RCS error σ' FF -σ FF The | is significantly reduced.
Example 2
Referring to fig. 1 to 4, a method for measuring near-field extrapolation far-field RCS is provided as an embodiment of the present invention, and scientific demonstration is performed through comparative experiments in order to verify the beneficial effects of the present invention.
TABLE 1 distinguishing features of the conventional technical means from the present application
Figure BDA0003909147770000105
FIG. 4 is an improvement of the present invention over existing extrapolation methods, particularly RCS extrapolation prediction for stealth targets, which is more realistic by correcting for the extrapolation prediction for the far field. Under the condition of the same parameters of free space wave number and distance vector, the RCS range predicted by the method can better meet the detection requirement of the system. The RCS error precision shown in the graph (a) reaches-80 dBsm, and the predicted range capacity shown in the graph (b) reaches-90 dBsm, which is obviously superior to that of the existing method.
It should be noted that the above-mentioned embodiments are only for illustrating the technical solutions of the present invention and not for limiting, and although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions may be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, which should be covered by the claims of the present invention.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and so forth) having computer-usable program code embodied therein. The scheme in the embodiment of the application can be implemented by adopting various computer languages, such as object-oriented programming language Java and transliterated scripting language JavaScript.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
While the preferred embodiments of the present application have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. Therefore, it is intended that the appended claims be interpreted as including the preferred embodiment and all changes and modifications that fall within the scope of the present application.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present application without departing from the spirit and scope of the application. Thus, if such modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application is intended to include such modifications and variations as well.

Claims (10)

1. A measuring method of near-field extrapolation far-field RCS is characterized by comprising the following steps: comprises the steps of (a) preparing a substrate,
presetting a near-field antenna equivalent current density excitation scanning model according to the antenna parameter to be solved;
constructing a diagonal translation operator according to electromagnetic wave emission parameters, establishing an antenna emission excitation function model, designing a forward correction equation to solve a near-field electric field, and deducing a far-field RCS by combining a correction operator;
and constructing a far-field electromagnetic scattering model according to the complex exponential model, establishing an inverse source correction equation, carrying out inverse source correction on the forward-derived near-field RCS, designing a near-field far-field RCS constraint term, and obtaining an optimal inverse source correction equation.
2. The method of near-field extrapolated far-field RCS measurement of claim 1, wherein: the near-field far-field RCS constraint terms include,
max||σ′ FF -σ FF || 2 ≤ε 1
Figure FDA0003909147760000011
wherein, σ' FF For far field radar scattering area, sigma, after inverse source correction FF Far field radar scattering area, epsilon, deduced for the forward direction 1 And epsilon 2 To define the threshold, E FF Is far field electric field, | | | | luminance 2 Is a 2 norm symbol, A H Is the complex conjugate transpose of A, and A is the inverse source corrector.
3. The method of near-field extrapolated far-field RCS measurement of claim 2, wherein: the near-field far-field RCS constraint term further includes,
if the inverse source correction error is larger than the threshold value, returning to perform iteration;
and if the inverse source correction error is smaller than the threshold value, updating the inverse source correction function.
4. The method of near-field extrapolated far-field RCS measurement of claim 3, wherein: the far-field electromagnetic scattering model includes,
Figure FDA0003909147760000012
Figure FDA0003909147760000013
σ′ FF ＝IFFT(ψ′(k,r))
wherein E is FF (k, r) is the far field electric field scattering function, k is the free space wavenumber vector, r is the free space sourcePoint distance vector, M is the number of scattering models, A i Is the amplitude, α i For the dispersion factor, i is the ith of the number of scattering models, ω (k) is additive white Gaussian noise, ψ' (k, r) is the far field scattering distribution function, gn (r, r) i ) Is a dyadic Green function, r i Is the distance vector of the free space field with respect to the field source.
5. The method of near-field extrapolated far-field RCS measurement of claim 4, wherein: the inverse source-correction equation includes,
the correction coefficient C (k, r) is expressed as,
Figure FDA0003909147760000021
Figure FDA0003909147760000022
A·E(k,r)-E FF (k,r)＝0
wherein E (k, r) is a discretized near-field electromagnetic scattering model, mu is a free space medium constant, i AUT is the number of rays of the electromagnetic wave emitted by the antenna, and t (k, r) is the excitation function of the emission of the antenna.
6. The method of near-field extrapolated far-field RCS measurement of claim 5, wherein: the antenna transmit excitation function includes a function of,
t(k,r)＝U(k,r)exp(-jk·||r-r i ||)
where k · t (r) =0 is a constraint term indicating that the electromagnetic wave polarization direction is orthogonal to the transmission direction, U (k, r) is the updated excitation voltage, | | r-r i And | is a distance vector modulus value.
7. The method of near-field extrapolated far-field RCS measurement of claim 6, wherein: the forward correction equation includes a forward correction of,
E(k,r)＝C·E i (r)+λP(k,r)
P(k,r)＝A m exp(-jk·r)
wherein P (k, r) is a forward corrector, A m And C is an amplitude value, C is a correction coefficient, and lambda is a Lagrange optimization objective function coefficient.
8. The method of measuring near-field extrapolated far-field RCS of claim 7, wherein: the near-field RCS includes a near-field RCS,
Figure FDA0003909147760000023
wherein σ NF Is near field RCS, E i (r) is the incident electric field of the PNF probe.
9. The near-field extrapolated far-field RCS measurement system of claim 8, wherein: the near field antenna equivalent current density excitation scanning model comprises,
J s (r)＝U i (r)w T (r)
w T (r)＝ω(r)Z T
wherein, J s Represents the equivalent current density, U i (r) is the input excitation voltage, w T (r) is a normalized field source distribution function, ω (r) is a weight coefficient, r is a free space source point distance vector, Z T Is the antenna transmit impedance.
10. The method of near-field extrapolated far-field RCS measurement of claim 9, wherein: the excitation voltage is a voltage that includes,
the updated actuation voltage is represented as,
Figure FDA0003909147760000031
wherein, T L (k, r) is a diagonal translation operator,
Figure FDA0003909147760000032
is a unit vector of parallel, kk is the multiplication of wave number points,
Figure FDA0003909147760000033
equivalent current densities in the pitch and azimuth directions, theta being the azimuth angle,
Figure FDA0003909147760000034
is the pitch angle, k x Wave number component in x-axis, k y The wave number component in the y-axis direction is x, which is a coordinate axis x, and y is a coordinate axis y.
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