CN106772298B - Point source forcing lower conductor plate and non-parallel medium side strong scattering point predictor method - Google Patents

Point source forcing lower conductor plate and non-parallel medium side strong scattering point predictor method Download PDF

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CN106772298B
CN106772298B CN201611031149.1A CN201611031149A CN106772298B CN 106772298 B CN106772298 B CN 106772298B CN 201611031149 A CN201611031149 A CN 201611031149A CN 106772298 B CN106772298 B CN 106772298B
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吴语茂
高鹏程
杨杨
张楠
童广德
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Fudan University
Shanghai Radio Equipment Research Institute
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Abstract

The present invention relates to a kind of source forcing lower conductor plates and non-parallel medium side strong scattering point predictor method, include: S1, the Green's function that infinitely great conductor plate is obtained using single image method；S2, the Green's function that Half space medium face is obtained using discrete complex image method；S3, edge diffraction amendment is carried out to the limited conductor plate of size, obtains the Green's function of finite size conductor plate；The Green's function of S4, the Green's function based on Half space medium face and finite size conductor plate carry out two-dimensional imaging, obtain the location information of strong scattering point between point source forcing lower conductor plate and non-parallel medium side.The Green's function for having modified finite size conductor plate in the present invention by edge diffraction effectively improves the precision that strong scattering point position is estimated；And calculation amount is small, meets the needs of engineer application.

Description

Point source forcing lower conductor plate and non-parallel medium side strong scattering point predictor method
Technical field
The present invention relates to the strong scattering point predictor methods of conductor plate and non-parallel medium side under a kind of source forcing, belong to In electromagnetic scattering simulation calculation field.
Background technique
In the non-dark room conditions near field measurement of large-scale low Scattering Targets, target, which exists to couple with ground immediately below it, to be dissipated It penetrates, and is difficult to inhibit to couple clutter with elimination in such a way that interference path blocks.In order to improve the precision of near field measurement, it is necessary to Accurate Prediction target and the strong scattering dot position information formed between ground immediately below it.Delay in view of target bottom often meets The problem reduction can be the strong scattering between the conductor plate and non-parallel medium side under point source forcing by the characteristic of slow deformation The pre-estimation problem of point position.
Currently, in scattering problems, at this moment the general effect for using complex image method equivalence replacement boundary face needs to solve more Layer Green's function.The fast algorithm for calculating the integral of the Sommerfeld in Green's function is given in the prior art, but not Provide the method for solving multilayer Green's function in complex image method.And patent CN104778286 " sea skimming device Electromagnetic Scattering Characteristics Rapid simulation method " in then give the quick calculation method of a kind of target and medium side combination scattering, but with target electricity ruler Very little increase, great calculating time and memory requirements needed for two-dimensional imaging often exceed the ability to bear of computer.
Based on above-mentioned, need to propose that conductor plate under a kind of source forcing and non-parallel medium side strong scattering point are pre- at present Method is estimated, effectively to solve above-mentioned problems of the prior art.
Summary of the invention
The purpose of the present invention is to provide a kind of source forcing lower conductor plates and non-parallel medium side strong scattering point to estimate Method, the Green's function based on conductor plate and Half space medium face carry out two-dimensional imaging, obtain the position of strong scattering point, have The advantages of precision is high, and calculation amount is small, meets engineering application requirement.
In order to achieve the above object, the present invention provides a kind of source forcing lower conductor plate and non-parallel medium side strong scattering Point predictor method comprising the steps of:
S1, the Green's function for obtaining infinitely great conductor plate；
S2, the Green's function for obtaining Half space medium face；
S3, edge diffraction amendment is carried out to the limited conductor plate of size, obtains Green's letter of finite size conductor plate Number；
S4, it is based on S2 and S3, the position for carrying out strong scattering point is estimated.
In the S1, the Green's function of infinitely great conductor plate is obtained using single image method.
In the S2, the Green's function in Half space medium face is obtained using discrete complex image method.
In the S2, discrete complex image method is that spectral Green's function is divided into quasi-static, surface wave, multiple three portions of mirror image Divide and is calculated, comprising the following steps:
S21, quasi-static item are sought:
Spectral Green's function are as follows:
Wherein, kzsThe wave number in the direction z of layer where indicating source point；F(kρ) expression Green's function component be kρFourier Component；
Quasi-static contribution are as follows:
Wherein, work as kρWhen → ∞, F0(kρ) value be intended to constant K0, it is quasi-static contribution；
Using Sommerfeld integrals identity, the quasi-static contribution of spatial domain is obtained are as follows:
Wherein, ρ is the ρ component of site cylindrical coordinates；ksFor the wave number of source point；
S22, surface wave item are sought:
Spectral Green's function after extracting quasi-static contribution are as follows:
The residual of surface wave pole in above formula is extracted, and the contribution of surface wave is obtained according to the residual of each pole are as follows:
Wherein, kpiIndicate kρPole location in plane；The residual of Resi expression pole；
Using Sommerfeld integrals identity, the surface wave contribution of spatial domain is obtained are as follows:
Wherein,For zeroth order Hankel function of the second kind；
S23, again mirror image item are sought:
Green's function after extracting quasi-static contribution and surface wave contribution are as follows:
Wherein, F3(kρ) it be Green's function component after extracting quasi-static item and surface wave is kρFourier components；
Using Sommerfeld integrals identity, the multiple mirror image contribution of spatial domain is obtained are as follows:
Wherein, aiFor residual, biFor pole.
In the S22, the method for extracting the residual of surface wave pole, comprising the following steps:
S221, the positioning of surface wave pole: in kρA rectangular area is confined in plane, and numerical value is made to the rectangle four edges line Integral；If loop wire integral is zero, show in the rectangular area without pole；It is on the contrary then show in rectangular area there are pole, And the rectangular area is divided into four sub- rectangles again, respectively to four sub- recursive progress loop wire integrals of rectangle, until finding institute There is pole；
S222, a loop wire is taken near each pole, numerical integration is made to every loop wire, obtains staying for each pole Number.
In the S3, the Green's function of finite size conductor plate is corrected by edge diffraction, specifically includes following step It is rapid:
S31, according to wedge diffraction model, edge diffraction field is in the case where spherical wave is incident are as follows:
Wherein, Ei(QD) it is Diffraction Point QDThe in-field at place, β are the real part of wave number, and L is the equivalent length for meeting boundary condition Degree, (s ', β0', φ ') it is incidence point coordinate, (s, β0, φ) be site coordinate, n be wedge two face exterior angles；DyadUsing Ray basis coordinates indicate the component of field using one group of unit vector being fixed on incident ray and emergent ray, constitute side The ray basis coordinates of edge diffraction ray are as follows:
DyadDiffraction coefficient are as follows:
Wherein,β0', the unit vector that φ ' is incident ray coordinator, whereinFor incident ray unit vector；β0, φ be site ray coordinator unit vector, whereinFor the unit vector of Diffraction Point to site；
S32, conductor plate right in the face be half-plane when diffraction coefficient are as follows:
Ds(L；φ,φ'；n；β0')=Di(L,φ-φ',n,β0')+Dr(L,φ+φ',n,β0')；
Dh(L；φ,φ'；n；β0')=Di(L,φ-φ',n,β0')+Dr(L,φ+φ',n,β0')；
S33, n=2 is taken, shows that the right in the face of conductor plate is half-plane, obtains edge diffraction field, and diffraction field is added to In resultant field, to carry out diffraction amendment to conductor plate edge, the Green's function of finite size conductor plate is obtained.
In the S4, limited ruler obtained in Green's function and S3 based on Half space medium face obtained in S2 The Green's function of very little conductor plate carries out two-dimensional imaging, obtains strong between point source forcing lower conductor plate and non-parallel medium side The location information of scattering point.
In conclusion provided by the invention source forcing lower conductor plate and the non-parallel medium side strong scattering point side of estimating Method, the Green's function based on acquired conductor plate and Half space medium face carry out two-dimensional imaging, to obtain strong scattering point Position.Due to having modified the Green's function of finite size conductor plate in this method by edge diffraction, strong dissipate is effectively improved The precision that exit point position is estimated；And calculation amount is small, meets the needs of engineer application.
Detailed description of the invention
Fig. 1 is the process of point the source forcing lower conductor plate and non-parallel medium side strong scattering point predictor method in the present invention Figure；
Fig. 2 is the mirror image equivalent schematic of the Half space Green's function of the conductor boundary in the present invention；
Fig. 3 is the multiple mirror image equivalent schematic of the Half space Green's function of the medium side in the present invention.
Specific embodiment
Below in conjunction with FIG. 1 to FIG. 3, the preferred embodiment that the present invention will be described in detail.
As shown in Figure 1, of the present invention source forcing lower conductor plate and the non-parallel medium side strong scattering point side of estimating Method comprising the steps of:
S1, the Green's function for obtaining infinitely great conductor plate；
S2, the Green's function for obtaining Half space medium face；
S3, edge diffraction amendment is carried out to the limited conductor plate of size, obtains Green's letter of finite size conductor plate Number；
S4, it is based on S2 and S3, the position for carrying out strong scattering point is estimated.
In the S1, the Half space Green's function of conductor boundary can the equivalent free space Green as point source mirror image Function.As shown in Fig. 2, obtaining the Green's function of infinitely great conductor plate using single image method in the present embodiment.
In the S2, the Half space Green's function of medium side can equivalent Green's letter as several discrete multiple mirror images The summation of number contribution.As shown in figure 3, obtaining the lattice in Half space medium face using discrete complex image method (DCIM) in the present embodiment Woods function.
In the S2, the process of discrete complex image method is that spectral Green's function is divided into quasi-static, surface wave, multiple mirror image Three parts are calculated, comprising the following steps:
S21, quasi-static item are sought:
Spectral Green's function are as follows:
Wherein, kzsThe wave number in the direction z of layer where indicating source point；F(kρ) expression Green's function component be kρFourier Component；
Quasi-static contribution can be expressed as:
Wherein, above formula is one group of base function expansion, K0、K1、K2... it is expansion coefficient,For basic function；
Work as kρWhen → ∞, the item in above formula containing exponential factor is all intended to zero, at this time F0(kρ) value be intended to constant K0, it is believed that K0It is exactly quasi-static contribution, value is exactly to work as kρF when → ∞0(kρ) value；
Using Sommerfeld integrals identity, the quasi-static contribution of spatial domain is obtained are as follows:
Wherein, ρ is the ρ component of site cylindrical coordinates；ksFor the wave number of source point；
S22, surface wave item are sought:
Spectral Green's function after extracting quasi-static contribution are as follows:
Due to the presence of surface wave pole, so that above formula decaying is slow, it is therefore necessary to first extract surface wave pole in above formula Residual, and the contribution of surface wave is obtained according to the residual of each pole；
Since spectral Green's function is about kρEven function, occur in pairs so its pole is inevitable, therefore surface wave Contribution are as follows:
Wherein, kpiIndicate kρPole location in plane；The residual of Resi expression pole；
Using Sommerfeld integrals identity, the surface wave contribution of spatial domain is obtained are as follows:
Wherein,For zeroth order Hankel function of the second kind；
S23, again mirror image item are sought:
Green's function after extracting quasi-static contribution and surface wave contribution are as follows:
Wherein, F3(kρ) it be Green's function component after extracting quasi-static item and surface wave is kρFourier components；
Using Sommerfeld integrals identity, the multiple mirror image contribution of spatial domain is obtained are as follows:
Wherein, aiFor residual, biFor pole.
In the S22, the method for extracting the residual of surface wave pole, comprising the following steps:
S221, the positioning of surface wave pole: in kρConfined in plane a rectangular area (rectangular area wants relatively large, So that the functional value on the four edges of the rectangle all close to 0, can carry out four points to rectangular area thus to find The contribution of pole), numerical integration then is made to the rectangle four edges line；If loop wire integral is zero, from residue theorem Without pole in the rectangular area；It is on the contrary then show that there are poles in rectangular area, and the rectangular area is divided into four sub- squares again Shape, respectively to four sub- recursive progress loop wire integrals of rectangle, until finding all poles；
S222, a loop wire is taken near each pole, numerical integration is made to every loop wire, obtains staying for each pole Number.
In the S3, since the size of conductor plate in reality is all limited, it is therefore desirable to be repaired by edge diffraction The Green's function of positive finite size conductor plate, comprising the following steps:
S31, according to wedge diffraction model, edge diffraction field is in the case where spherical wave is incident are as follows:
Wherein, Ei(QD) it is Diffraction Point QDThe in-field at place, β are the real part of wave number, and L is the equivalent length for meeting boundary condition Degree, (s ', β0', φ ') it is incidence point coordinate, (s, β0, φ) be site coordinate, n be wedge two face exterior angles；
If using rectangular coordinate system, dyadThere should be 9 components, therefore introduce ray basis coordinates, using being fixed on One group of unit vector on incident ray and emergent ray indicates the component of field, constitutes the ray basis coordinates of edge diffraction ray Are as follows:
Using ray basis coordinates, dyad can be obtainedDiffraction coefficient are as follows:
Wherein,β0', the unit vector that φ ' is incident ray coordinator, whereinFor incident ray unit vector；β0, φ be site ray coordinator unit vector, whereinFor the unit vector of Diffraction Point to site；
S32, for when the right in the face of conductor plate is half-plane, diffraction coefficient at this time are as follows:
Ds(L；φ,φ'；n；β0')=Di(L,φ-φ',n,β0')+Dr(L,φ+φ',n,β0')；
Dh(L；φ,φ'；n；β0')=Di(L,φ-φ',n,β0')+Dr(L,φ+φ',n,β0')；
S33, as n=1, indicate that conductor plate does not have an edge, boundary face is exactly infinitely great ideal conducting plane, this When diffraction coefficient be zero；As n=2, the right in the face of conductor plate is half-plane, therefore only needs n taking 2, and edge can be obtained Diffraction field, and diffraction field is added in resultant field, to carry out diffraction amendment to conductor plate edge, it is flat to obtain finite size conductor The Green's function of plate.
In the S4, limited ruler obtained in Green's function and S3 based on Half space medium face obtained in S2 The Green's function of very little conductor plate carries out two-dimensional imaging, obtains strong between point source forcing lower conductor plate and non-parallel medium side The location information of scattering point.
In conclusion provided by the present invention source forcing lower conductor plate and the non-parallel medium side strong scattering point side of estimating Method obtains the Green's function of finite size conductor plate by single image method and edge diffraction amendment, passes through discrete multiple mirror image Method obtains the Green's function in Half space medium face, and carries out two-dimensional imaging, thus estimate a source forcing lower conductor plate with it is non-flat The location information of strong scattering point between row medium side.
Provided by the present invention source forcing lower conductor plate and non-parallel medium side strong scattering point predictor method, have with Lower advantage: 1, having modified the Green's function of finite size conductor plate by edge diffraction, and it is pre- to effectively improve strong scattering point position The precision estimated；2, calculation amount is small, meets the needs of engineer application.
It is discussed in detail although the contents of the present invention have passed through above preferred embodiment, but it should be appreciated that above-mentioned Description is not considered as limitation of the present invention.After those skilled in the art have read above content, for of the invention A variety of modifications and substitutions all will be apparent.Therefore, protection scope of the present invention should be limited to the appended claims.

Claims (5)

1. a kind of source forcing lower conductor plate and non-parallel medium side strong scattering point predictor method, which is characterized in that comprising with Lower step:
S1, the Green's function for obtaining infinitely great conductor plate；
S2, the Green's function that Half space medium face is obtained using discrete complex image method；
S3, edge diffraction amendment is carried out to the limited conductor plate of size, obtains the Green's function of finite size conductor plate；
S4, it is based on S2 and S3, the position for carrying out strong scattering point is estimated；
In the S2, discrete complex image method be spectral Green's function is divided into quasi-static, surface wave, multiple three parts of mirror image into Row calculates, comprising the following steps:
S21, quasi-static item are sought:
Spectral Green's function are as follows:
Wherein, kzsThe wave number in the direction z of layer where indicating source point；F(kρ) expression Green's function component be kρFourier components；
Quasi-static contribution are as follows:
Wherein, work as kρWhen → ∞, F0(kρ) value be intended to constant K0, it is quasi-static contribution；
Using Sommerfeld integrals identity, the quasi-static contribution of spatial domain is obtained are as follows:
Wherein, ρ is the ρ component of site cylindrical coordinates；ksFor the wave number of source point；
S22, surface wave item are sought:
Spectral Green's function after extracting quasi-static contribution are as follows:
The residual of surface wave pole in above formula is extracted, and the contribution of surface wave is obtained according to the residual of each pole are as follows:
Wherein, kpiIndicate kρPole location in plane；The residual of Resi expression pole；
Using Sommerfeld integrals identity, the surface wave contribution of spatial domain is obtained are as follows:
Wherein,For zeroth order Hankel function of the second kind；
S23, again mirror image item are sought:
Green's function after extracting quasi-static contribution and surface wave contribution are as follows:
Wherein, F3(kρ) it be Green's function component after extracting quasi-static item and surface wave is kρFourier components；
Using Sommerfeld integrals identity, the multiple mirror image contribution of spatial domain is obtained are as follows:
Wherein, aiFor residual, biFor pole.
2. point source forcing lower conductor plate and non-parallel medium side strong scattering point predictor method as described in claim 1, special Sign is, in the S1, the Green's function of infinitely great conductor plate is obtained using single image method.
3. point source forcing lower conductor plate and non-parallel medium side strong scattering point predictor method as claimed in claim 2, special Sign is, in the S22, the method for extracting the residual of surface wave pole, comprising the following steps:
S221, the positioning of surface wave pole: in kρA rectangular area is confined in plane, and numerical integration is made to the rectangle four edges line； If loop wire integral is zero, show in the rectangular area without pole；It is on the contrary then show that there are poles in rectangular area, and again should Rectangular area is divided into four sub- rectangles, respectively to four sub- recursive progress loop wire integrals of rectangle, until finding all poles；
S222, a loop wire is taken near each pole, numerical integration is made to every loop wire, obtains the residual of each pole.
4. point source forcing lower conductor plate and non-parallel medium side strong scattering point predictor method as claimed in claim 3, special Sign is, in the S3, the Green's function of finite size conductor plate is corrected by edge diffraction, specifically includes following step It is rapid:
S31, according to wedge diffraction model, edge diffraction field is in the case where spherical wave is incident are as follows:
Wherein, Ei(QD) it is Diffraction Point QDThe in-field at place, β are the real part of wave number, and L is the equivalent length for meeting boundary condition, (s′,β0', φ ') it is incidence point coordinate, (s, β0, φ) be site coordinate, n be wedge two face exterior angles；DyadUsing penetrating Line basis coordinates indicate the component of field using one group of unit vector being fixed on incident ray and emergent ray, constitute edge The ray basis coordinates of diffraction ray are as follows:
DyadDiffraction coefficient are as follows:
Wherein,For the unit vector of incident ray coordinator, whereinFor incident ray unit vector；For the unit vector of the ray coordinator of site, whereinFor the unit vector of Diffraction Point to site；
S32, conductor plate right in the face be half-plane when diffraction coefficient are as follows:
Ds(L；φ,φ'；n；β0')=Di(L,φ-φ',n,β0')+Dr(L,φ+φ',n,β0')；
Dh(L；φ,φ'；n；β0')=Di(L,φ-φ',n,β0')+Dr(L,φ+φ',n,β0')；
S33, n=2 is taken, shows that the right in the face of conductor plate is half-plane, obtains edge diffraction field, and diffraction field is added to resultant field In, to carry out diffraction amendment to conductor plate edge, obtain the Green's function of finite size conductor plate.
5. point source forcing lower conductor plate and non-parallel medium side strong scattering point predictor method as claimed in claim 4, special Sign is, in the S4, finite size obtained in Green's function and S3 based on Half space medium face obtained in S2 The Green's function of conductor plate carries out two-dimensional imaging, obtains and dissipates by force between point source forcing lower conductor plate and non-parallel medium side The location information of exit point.
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