CN113808266A - Novel bright temperature imaging method for exponential type rough surface - Google Patents

Novel bright temperature imaging method for exponential type rough surface Download PDF

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CN113808266A
CN113808266A CN202110936583.9A CN202110936583A CN113808266A CN 113808266 A CN113808266 A CN 113808266A CN 202110936583 A CN202110936583 A CN 202110936583A CN 113808266 A CN113808266 A CN 113808266A
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rough surface
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尹川
徐鹏鹏
张鹏泉
耿友林
韦杜鹃
张忠海
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Hangzhou Dianzi University
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Abstract

The invention discloses a novel bright temperature imaging method for an exponential type rough surface. Traditional rough surface radiation model is comparatively simple, only treats rough surface as the rough surface of gaussian when considering rough surface and handles, has neglected the scene that index type rough surface exists, even replace index type rough surface model with rough surface model of gaussian, the drawback of handling like this lies in can't accurately simulate out the bright temperature that has index type rough surface scene to greatly restrict passive millimeter wave radiation simulation's range of application. The invention is as follows: firstly, an exponential rough surface radiation characteristic model is provided. Secondly, the difference between the Gaussian-type rough surface and the exponential-type rough surface is researched. And thirdly, calculating the brightness temperature of the exponential type rough surface with different roughness. And fourthly, comparing the bright temperature difference of the Gaussian rough surface and the exponential rough surface under different roughness. The method improves the rough surface imaging scene and improves the imaging accuracy in the rough surface scene.

Description

Novel bright temperature imaging method for exponential type rough surface
Technical Field
The invention belongs to the technical field of computer aided analysis and design and software design, and particularly relates to a novel bright temperature imaging method for an exponential type rough surface.
Background
The passive millimeter wave imaging simulation is an important link in the field of passive millimeter wave imaging, and can help to know the radiation characteristic of a target, explain the radiation phenomenon, search the radiation rule and judge the quality of an actual measurement result. The above advantages have led to increased importance in recent years for millimeter wave imaging simulations. So far, most of the work for imaging rough surfaces focuses on that the surface to be measured is a gaussian rough surface, and the scene that the object to be measured is an exponential rough surface is mentioned. For example, in actual life, scenes such as rough soil and mountain peaks are closer to an exponential rough surface, but in the conventional imaging process, the scenes are regarded as gaussian rough surfaces, which may cause a certain error in the simulated brightness temperature distribution compared with the actual brightness temperature distribution. Therefore, a calculation model and a calculation method for the exponential type rough surface are needed to improve the imaging accuracy.
Disclosure of Invention
The invention aims to provide a novel bright temperature imaging method for an exponential type rough surface.
The method comprises the following specific steps:
the method comprises the following steps of firstly, carrying out physical modeling on a detected scene to obtain a three-dimensional virtual model of the detected scene.
And step two, subdividing the three-dimensional virtual model obtained in the step one.
And step three, regarding the measured surfaces belonging to the forest land, the mountain peak and the sand land in the three-dimensional virtual model as exponential type rough surfaces, regarding the other measured surfaces as Gaussian type rough surfaces, and performing ray tracing.
And fourthly, after the ray tracing part is finished, inverting the bright temperature to the emission source point from the terminal of each ray to obtain the bright temperatures of different positions in the detected scene to form a bright temperature graph.
Preferably, the physical modeling is performed in step one using gmsh software, and the subdivision is performed in step two.
Preferably, in the second step, the subdivided cells are tetrahedrons.
Preferably, the ray tracing in the third step is to emit rays outwards from the emission end of the radiometer; for any ray, the first layer ray is traced in the reflection direction, and the intersection point of the ray and the incident surface is scattered to the periphery as a scattering point.
Preferably, in the ray tracing of the measured surface regarded as the exponential type rough surface, the mathematical expression of the scattered field at any point in the passive region with the closed surface as the boundary is as shown in the formula (1-1).
Figure BDA0003213434610000021
In the formula (1-1),
Figure BDA0003213434610000022
a scattered field which is a passive field of any point;
Figure BDA0003213434610000023
solving the position of the field point for the replacement; j is an imaginary unit; k is a radical ofsThe wave number of electromagnetic wave propagating in the medium is defined by the wave number k in the first medium1Replacement;
Figure BDA0003213434610000024
unit vector which is the scattering direction;
Figure BDA0003213434610000025
a unit vector that is a normal vector of the boundary surface; etasFor the impedance of the medium, the value of which uses the impedance of medium one1Replacement; r0Is the distance between the field point and the observation point;
Figure BDA0003213434610000026
the expression of the total tangential electromagnetic field is shown in formulas (1-2) and (1-3).
Figure BDA0003213434610000027
Figure BDA0003213434610000028
In the formulae (1-2) and (1-3),
Figure BDA0003213434610000029
is a unit polarization vector;
Figure BDA00032134346100000210
a unit vector that is the incident direction;
Figure BDA00032134346100000211
R⊥is the horizontally polarized fresnel reflection coefficient; r//Is the vertically polarized fresnel reflection coefficient; e0Is the field strength of the incident electromagnetic wave.
Establishing a scattering field in a medium I as shown in a formula (1-4) by combining the formulas (1-1), (1-2) and (1-3):
Figure BDA00032134346100000212
approximate solution of the formula (1-4) is shown in the formula (2):
Figure BDA00032134346100000213
in the formula (2), Q is a phase factor, k1Is the wave number in the first medium,
Figure BDA00032134346100000214
is the unit vector of the scattering direction,
Figure BDA00032134346100000215
unit vector of incident direction，
Figure BDA00032134346100000216
As source point location, qx、qy、qzThe phase components in the x, y, z-axis directions, respectively.
Figure BDA00032134346100000217
qx、qy、qzIs represented by the formula (3).
Figure BDA0003213434610000031
In the formula (3), θsPitch angle, theta, being the direction of scatteringiWhich is the pitch angle of the incident direction,
Figure BDA0003213434610000032
is the azimuth angle of the scattering direction,
Figure BDA0003213434610000033
is the azimuth angle of the incident direction.
Figure BDA0003213434610000034
The direction vectors of the x axis, the y axis and the z axis are respectively.
Substituting the formula (2) and the formula (3) into the formula (1-4), and scattering the electric field
Figure BDA0003213434610000035
The expression is expressed as:
Figure BDA0003213434610000036
in the formula (4), the reaction mixture is,
Figure BDA0003213434610000037
is the unit vector of the scattering direction,
Figure BDA0003213434610000038
is the unit vector of the direction of incidence,
Figure BDA0003213434610000039
unit vector, k, being the normal vector of the boundary surfacesThe wave number, R, of electromagnetic wave propagating in a medium0Is the distance, η, between the field point and the observation point1Is the impedance of the medium.
The fringe fields that establish the perpendicular polarization, parallel polarization and cross polarization are shown in equation (5).
Figure BDA00032134346100000310
In the formula (5), the reaction mixture is,
Figure BDA00032134346100000311
q is a phase factor and q is a phase factor,
Figure BDA00032134346100000312
Figure BDA00032134346100000313
in order to polarize the scattered field in parallel,
Figure BDA00032134346100000314
in order to polarize the scattered field vertically,
Figure BDA00032134346100000315
and
Figure BDA00032134346100000316
for cross-polarized scattered fields, R⊥Is the horizontally polarized Fresnel reflection coefficient, R//Is the fresnel reflection coefficient for the vertical polarization,
Figure BDA00032134346100000317
is the unit polarization component of the scattered horizontal wave,
Figure BDA00032134346100000318
is a scattering sagThe unit polarization component of the direct wave,
Figure BDA00032134346100000319
is the unit polarization component of the incident horizontal wave,
Figure BDA00032134346100000320
is the unit polarization component of the incident vertical wave,
Figure BDA00032134346100000321
is the unit vector of the scattering direction,
Figure BDA00032134346100000322
is the unit vector of the direction of incidence. U shapehh、Uvh、Uhv、UvvIs represented by formula (6):
Figure BDA0003213434610000041
in the formula (6), R⊥Is the horizontally polarized Fresnel reflection coefficient, R//Is the vertically polarized fresnel reflection coefficient.
The bistatic scattering coefficient in medium one is expressed by equation (7):
Figure BDA0003213434610000042
in formula (7), UpqFor substituting the aforementioned Uhh、Uvh、Uhv、Uvv；k1Wave number in Medium one, σ is root mean square height of rough surface, qx、qy、qzIs represented by formula (8):
Figure BDA0003213434610000043
the expression of the height fluctuation correlation coefficient G (R) of the exponential type rough surface is shown as a formula (9);
G(R)＝σ2exp (- | R |/l) formula (9)
In the formula (9), R is the distance between two points of the exponential type rough surface; l is the relative length of the rough surface;
the expression of a second-order derivative rho' (0) of the rough surface height fluctuation correlation coefficient at 0 is shown as a formula (10);
Figure BDA0003213434610000044
establishing
Figure BDA0003213434610000045
Is represented by formula (11):
Figure BDA0003213434610000051
the bistatic scattering coefficient of the measured surface regarded as an exponential-type rough surface is obtained by equations (6), (7), (8), (10), and (11).
The invention has the beneficial effects that:
1. in passive millimeter wave imaging, forest lands, mountain peaks and sand lands are all regarded as index rough surfaces, and a scattering coefficient calculation method based on the index rough surfaces is provided, so that parameters in operation are closer to real environmental conditions, and the accuracy of bright temperature maps obtained by passive millimeter wave imaging is remarkably improved.
2. The invention enables the passive millimeter wave to be imaged in a simulation mode, and can detect the difference between high roughness and low roughness when facing an exponential rough surface scene with different roughness degrees, thereby greatly improving the resolution capability of passive millimeter wave imaging.
3. The invention scatters the intersection point of the ray and the surface as a scattering point to the periphery except that the ray of the first layer continuously traces along the reflection direction. The scattering coefficient of the radiation varies depending on the incident surface roughness.
Drawings
FIG. 1 is a diagram of a physical model of an exemplary scene under test;
FIG. 2 is a schematic diagram of a measured scene after being split;
FIG. 3 is a schematic view of a local coordinate system;
FIG. 4 is a schematic diagram of a single ray tracing of a new model of an air-to-ground scene;
FIG. 5 is a schematic diagram of a single ray inversion of a new model of an air-to-ground scenario;
FIG. 6 is a graph showing the distribution of brightness and temperature of different roughness under a Gaussian-shaped rough surface;
FIG. 7 is a graph of brightness and temperature distribution for different roughness levels under an exponential-type matte surface;
FIG. 8 is a comparison graph of brightness and temperature of a Gaussian rough surface and an exponential rough surface at different roughness;
FIG. 9(a) is a graph showing a comparison between a Gaussian-type rough surface and an exponential-type rough surface;
FIGS. 9(b) and (c) are simulation diagrams of a Gaussian-shaped rough surface and an exponential-shaped rough surface, respectively;
FIG. 10(a) is a plot of variance comparison of one-dimensional Gaussian-shaped roughness and exponential-shaped roughness;
FIG. 10(b) is a comparison of the variance of a two-dimensional Gaussian-shaped rough surface and an exponential-shaped rough surface;
FIG. 11 is a graph comparing the bright temperature difference between a Gaussian-shaped rough surface and an exponential-shaped rough surface at different RMS heights;
FIG. 12 is a graph comparing the light temperature difference between a Gaussian-shaped rough surface and an exponential-shaped rough surface at different correlation lengths.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
A novel bright temperature imaging method for an exponential type rough surface comprises the following specific steps:
step one, utilizing existing subdivision software to subdivide a detected scene, and selecting a tetrahedron by a subdivision unit. In the embodiment, a three-dimensional virtual modeling scene is used as a detected scene; as shown in fig. 1, four runways are arranged side by side in the three-dimensional virtual modeling scene, and the numbers of the four runways are 1, 2, 3 and 4 respectively; the surfaces of the four runways are four measured surfaces with the same dielectric constant, the same rough surface type and different roughness degrees. The subdivided model map of the measured scene is shown in fig. 2. The mediums of the four runways are forest lands, mountain peaks or sand lands, and are all close to the exponential type rough surface.
Step three, a ray tracing part is carried out, wherein one ray is selected for ray tracing, and when the ray meets a smooth surface, the ray is emitted towards the reflection direction; when the ray is incident on the rough surface, the ray is emitted in the reflection direction by the first layer, and then the intersection point of the ray and the rough surface is the emission point of the second layer, and the ray is emitted (scattered) to the periphery. Reflection coefficients and scattering coefficients of rays are different when the rays are incident on different rough surfaces, a kirchhoff dwell phase approximation method is used for calculation, and the dwell phase approximation method is also needed for calculation of the scattering coefficients of the exponential rough surfaces. For convenience of calculation, a map system diagram using a local coordinate system is shown in fig. 3, and it can be known from the second law of green vectors that the mathematical expression of the scattered field of any point in the passive region with the closed surface as the boundary is:
Figure BDA0003213434610000061
in the formula (1-1),
Figure BDA0003213434610000062
a scattered field which is a passive field of any point;
Figure BDA0003213434610000063
solving the position of the field point for the replacement; j is an imaginary unit; k is a radical ofsThe wave number of electromagnetic wave propagating in the medium is defined by the wave number k in the first medium1Replacement;
Figure BDA0003213434610000064
unit vector which is the scattering direction;
Figure BDA0003213434610000065
a unit vector that is a normal vector of the boundary surface; etasFor impedance of the medium, using the mediumImpedance of one eta1Replacement; r0Is the distance between the field point and the observation point;
Figure BDA0003213434610000066
the expression of the total tangential electromagnetic field is shown in formulas (1-2) and (1-3).
Figure BDA0003213434610000067
Figure BDA0003213434610000068
In the formulae (1-2) and (1-3),
Figure BDA0003213434610000069
is a unit polarization vector;
Figure BDA00032134346100000610
a unit vector that is the incident direction;
Figure BDA00032134346100000611
R⊥is the horizontally polarized fresnel reflection coefficient; r//Is the vertically polarized fresnel reflection coefficient; e0Is the field strength of the incident electromagnetic wave.
Establishing a scattering field in a medium I as shown in a formula (1-4) by combining the formulas (1-1), (1-2) and (1-3):
Figure BDA0003213434610000071
approximate solution of the formula (1-4) is shown in the formula (2):
Figure BDA0003213434610000072
in the formula (2), Q is a phase factor, k1Is the wave number in the first medium,
Figure BDA0003213434610000073
is the unit vector of the scattering direction,
Figure BDA0003213434610000074
is the unit vector of the direction of incidence,
Figure BDA0003213434610000075
as source point location, qx、qy、qzThe phase components in the x, y, z-axis directions, respectively. Wherein the expression of some variables is shown in formula (3).
Figure BDA0003213434610000076
In the formula (3), the reaction mixture is,
Figure BDA0003213434610000077
is the unit vector of the scattering direction,
Figure BDA0003213434610000078
is the unit vector of the incident direction, θsPitch angle, theta, being the direction of scatteringiWhich is the pitch angle of the incident direction,
Figure BDA0003213434610000079
is the azimuth angle of the scattering direction,
Figure BDA00032134346100000710
azimuth angle of incidence, qx、qy、qzAre the phase components in the x, y, z directions, respectively, k1Is the wave number in medium one.
Figure BDA00032134346100000711
The direction vectors of the x axis, the y axis and the z axis are respectively.
Substituting the formula (2) and the formula (3) into the formula (1-4), and scattering the electric field
Figure BDA00032134346100000712
The expression is expressed as:
Figure BDA00032134346100000713
in the formula (4), the reaction mixture is,
Figure BDA00032134346100000714
is the unit vector of the scattering direction,
Figure BDA00032134346100000715
is the unit vector of the direction of incidence,
Figure BDA00032134346100000716
unit vector, k, being the normal vector of the boundary surfacesThe wave number, R, of electromagnetic wave propagating in a medium0Is the distance, η, between the field point and the observation point1Is the impedance of the medium.
Further obtaining the vertical polarization, parallel polarization and cross polarization scattered fields:
Figure BDA0003213434610000081
in the formula (5), the reaction mixture is,
Figure BDA0003213434610000082
q is a phase factor and q is a phase factor,
Figure BDA0003213434610000083
Figure BDA0003213434610000084
in order to polarize the scattered field in parallel,
Figure BDA0003213434610000085
in order to polarize the scattered field vertically,
Figure BDA0003213434610000086
and
Figure BDA0003213434610000087
for cross-polarized scattered fields, R⊥Is the horizontally polarized Fresnel reflection coefficient, R//Is the fresnel reflection coefficient for the vertical polarization,
Figure BDA0003213434610000088
is the unit polarization component of the scattered horizontal wave,
Figure BDA0003213434610000089
is the unit polarization component of the scattered vertical wave,
Figure BDA00032134346100000810
is the unit polarization component of the incident horizontal wave,
Figure BDA00032134346100000811
is the unit polarization component of the incident vertical wave,
Figure BDA00032134346100000812
is the unit vector of the scattering direction,
Figure BDA00032134346100000813
is the unit vector of the direction of incidence. Wherein the expression of some variables is shown in formula (6).
Figure BDA00032134346100000814
In the formula (6), q is a phase component and q iszIs a phase component in the z direction, R⊥Is the horizontally polarized Fresnel reflection coefficient, R//Is the fresnel reflection coefficient for the vertical polarization,
Figure BDA00032134346100000815
is the unit polarization component of the scattered horizontal wave,
Figure BDA00032134346100000816
is the unit polarization component of the scattered vertical wave,
Figure BDA00032134346100000817
is the unit polarization component of the incident horizontal wave,
Figure BDA00032134346100000818
is the unit polarization component of the incident vertical wave,
Figure BDA00032134346100000819
is the unit vector of the scattering direction,
Figure BDA00032134346100000820
unit vector of incident direction, k1The wave number in medium one.
The bistatic scattering coefficient in medium one is expressed by equation (7):
Figure BDA0003213434610000091
in formula (7), UpqFor substituting the aforementioned Uhh、Uvh、Uhv、Uvv；k1Wave number in Medium one, σ is root mean square height of rough surface, qx qy qzAre the phase components in the x, y, z directions, respectively, and qx，qy，qzExpressed as:
Figure BDA0003213434610000092
wherein, rho' (0) is a second-order derivative of the rough surface height fluctuation correlation coefficient at 0, and the index rough surface height fluctuation correlation coefficient G (R) is as follows:
G(R)＝σ2exp (- | R |/l) formula (9)
In the formula (9), σ represents the root-mean-square height of the rough surface; r is the distance between two points of the exponential type rough surface; l is the relative length of the rough surface;
the second order derivative calculation process of equation (9) is as follows:
Figure BDA0003213434610000093
when x >0 when x <0
Figure BDA0003213434610000094
Figure BDA0003213434610000095
Figure BDA0003213434610000096
Therefore, it is not only easy to use
Figure BDA0003213434610000097
L in the formula (10) is the correlation length of the matte surface. In the above formula
Figure BDA0003213434610000101
Wherein,
Figure BDA0003213434610000102
is the unit polarization component of the scattered horizontal wave,
Figure BDA0003213434610000103
is the unit polarization component of the scattered vertical wave,
Figure BDA0003213434610000104
is the unit polarization component of the incident horizontal wave,
Figure BDA0003213434610000105
is the unit polarization component of the incident vertical wave,
Figure BDA0003213434610000106
is the unit vector of the scattering direction,
Figure BDA0003213434610000107
is the unit vector of the incident direction, θsPitch angle, theta, being the direction of scatteringiWhich is the pitch angle of the incident direction,
Figure BDA0003213434610000108
is the azimuth angle of the scattering direction,
Figure BDA0003213434610000109
is the azimuth angle of the incident direction.
The exponential bistatic scattering coefficient of the rough surface can be obtained through the formulas (6), (7), (8), (10) and (11). FIG. 4 is a model of single ray tracing.
And fourthly, a bright temperature inversion part, and FIG. 5 is a single ray inversion model of a multilayer bright temperature tracking method. And calculating the brightness temperature represented by all the rays through inversion to obtain the brightness temperature distribution condition of the virtual model.
And step five, changing the roughness statistical parameters corresponding to the four runways in the measured scene, wherein the roughness statistical parameters are respectively (sigma-1.8 lambda, and l-10 lambda), (sigma-2.4 lambda, and l-10 lambda), (sigma-3.0 lambda, and l-10 lambda), (sigma-3.6 lambda, and l-10 lambda). The brightness temperature distribution of the gaussian rough surface and the exponential rough surface at different roughness levels is obtained by bright temperature imaging, and is shown in fig. 6 and 7. And respectively taking out the single bright temperature lines from the four runways to compare, and obtaining a bright temperature comparison graph of the Gaussian rough surface and the exponential rough surface under different roughness, as shown in fig. 8. The difference between the physical models of the gaussian rough surface and the exponential rough surface and the height variance of the rough surface is different, and the brightness and temperature of the two are different as shown in fig. 9 and 10. The contrast shows that the brightness temperature distribution conditions of the Gaussian rough surface and the exponential rough surface are different under the conditions of different roughness, and the brightness temperature difference also exists between the Gaussian rough surface and the exponential rough surface under the same roughness. The bright temperature difference as a function of the rough surface is shown in fig. 11 and 12. By observing fig. 11 and 12, it is found that the exponential type rough surface bright temperature simulation diagram has a certain bright temperature difference with the conventional rough surface bright temperature simulation diagram, and the bright temperature difference changes with the change of the root mean square height and the related length. When the detected scene is a forest land, a mountain peak and a sand land which are shown as an exponential type rough surface scene, a traditional Gaussian type rough surface bright temperature imaging method has bright temperature errors, and the exponential type rough surface bright temperature imaging method has smaller errors and more accurate results.

Claims (5)

1. A novel bright temperature imaging method for an exponential type rough surface is characterized in that: firstly, carrying out physical modeling on a detected scene to obtain a three-dimensional virtual model of the detected scene;
step two, subdividing the three-dimensional virtual model obtained in the step one;
step three, regarding the measured surfaces belonging to the forest land, the mountain peak and the sand land in the three-dimensional virtual model as index rough surfaces, regarding the other measured surfaces as Gaussian rough surfaces, and performing ray tracing;
and fourthly, after the ray tracing part is finished, inverting the bright temperature to the emission source point from the terminal of each ray to obtain the bright temperatures of different positions in the detected scene to form a bright temperature graph.
2. The novel bright temperature imaging method for the exponential type rough surface as claimed in claim 1, wherein: and carrying out physical modeling in the step one by using the gmsh software, and carrying out subdivision in the step two.
3. The novel bright temperature imaging method for the exponential type rough surface as claimed in claim 1, wherein: in the second step, the subdivided cells are tetrahedrons.
4. The novel bright temperature imaging method for the exponential type rough surface as claimed in claim 1, wherein: step three, ray tracing is to emit rays outwards from the emission end of the radiometer; for any ray, the first layer ray is traced in the reflection direction, and the intersection point of the ray and the incident surface is scattered to the periphery as a scattering point.
5. The novel bright temperature imaging method for the exponential type rough surface as claimed in claim 1, wherein: in the ray tracing of the measured surface which is regarded as an exponential type rough surface, the mathematical expression of the scattered field of any point in the passive region which takes the closed surface as the boundary is shown as the formula (1-1);
Figure FDA0003213434600000011
in the formula (1-1),
Figure FDA0003213434600000012
a scattered field which is a passive field of any point;
Figure FDA0003213434600000013
solving the position of the field point for the replacement; j is an imaginary unit; k is a radical ofsThe wave number of electromagnetic wave propagating in the medium is defined by the wave number k in the first medium1Replacement;
Figure FDA0003213434600000014
unit vector which is the scattering direction;
Figure FDA0003213434600000015
a unit vector that is a normal vector of the boundary surface; etasFor the impedance of the medium, the value of which uses the impedance of medium one1Replacement; r0Is the distance between the field point and the observation point;
Figure FDA0003213434600000016
the expression of the total tangential electromagnetic field is shown as formulas (1-2) and (1-3);
Figure FDA0003213434600000017
Figure FDA0003213434600000021
in the formulae (1-2) and (1-3),
Figure FDA0003213434600000022
is a unit polarization vector;
Figure FDA0003213434600000023
a unit vector that is the incident direction;
Figure FDA0003213434600000024
Figure FDA0003213434600000025
is the horizontally polarized fresnel reflection coefficient; r//Is the vertically polarized fresnel reflection coefficient; e0Is the field strength of the incident electromagnetic wave;
establishing a scattering field in a medium I as shown in a formula (1-4) by combining the formulas (1-1), (1-2) and (1-3):
Figure FDA0003213434600000026
approximate solution of the formula (1-4) is shown in the formula (2):
Figure FDA0003213434600000027
in the formula (2), Q is a phase factor, k1Is the wave number in the first medium,
Figure FDA0003213434600000028
is the unit vector of the scattering direction,
Figure FDA0003213434600000029
is the unit vector of the direction of incidence,
Figure FDA00032134346000000210
as source point location, qx、qy、qzPhase components in the x, y, z axis directions, respectively;
Figure FDA00032134346000000211
qx、qy、qzthe expression of (b) is shown in formula (3);
Figure FDA00032134346000000212
in the formula (3), θsPitch angle, theta, being the direction of scatteringiWhich is the pitch angle of the incident direction,
Figure FDA00032134346000000213
is the azimuth angle of the scattering direction,
Figure FDA00032134346000000214
azimuth angle of the incident direction;
Figure FDA00032134346000000215
direction vectors of an x axis, a y axis and a z axis are respectively;
substituting the formula (2) and the formula (3) into the formula (1-4), and scattering the electric field
Figure FDA00032134346000000216
The expression is expressed as:
Figure FDA00032134346000000217
in the formula (4), the reaction mixture is,
Figure FDA00032134346000000218
Figure FDA00032134346000000219
is the unit vector of the scattering direction,
Figure FDA00032134346000000220
is the unit vector of the direction of incidence,
Figure FDA00032134346000000221
unit vector, k, being the normal vector of the boundary surfacesThe wave number, R, of electromagnetic wave propagating in a medium0Is the distance, η, between the field point and the observation point1Is the impedance of the medium;
the scattered fields of vertical polarization, parallel polarization and cross polarization are established as shown in a formula (5);
Figure FDA0003213434600000031
in the formula (5), the reaction mixture is,
Figure FDA0003213434600000032
q is a phase factor and q is a phase factor,
Figure FDA0003213434600000033
Figure FDA0003213434600000034
in order to polarize the scattered field in parallel,
Figure FDA0003213434600000035
in order to polarize the scattered field vertically,
Figure FDA0003213434600000036
and
Figure FDA0003213434600000037
in order to cross-polarize the scattered field,
Figure FDA0003213434600000038
is the horizontally polarized Fresnel reflection coefficient, R//Is the fresnel reflection coefficient for the vertical polarization,
Figure FDA0003213434600000039
is the unit polarization component of the scattered horizontal wave,
Figure FDA00032134346000000310
is the unit polarization component of the scattered vertical wave,
Figure FDA00032134346000000311
is the unit polarization component of the incident horizontal wave,
Figure FDA00032134346000000312
is the unit polarization component of the incident vertical wave,
Figure FDA00032134346000000313
is the unit vector of the scattering direction,
Figure FDA00032134346000000314
a unit vector that is the incident direction; u shapehh、Uvh、Uhv、UvvIs represented by formula (6):
Figure FDA00032134346000000315
in the formula (6), the reaction mixture is,
Figure FDA00032134346000000316
is horizontally polarizedFresnel reflection coefficient, R//Is the vertically polarized fresnel reflection coefficient;
the bistatic scattering coefficient in medium one is expressed by equation (7):
Figure FDA00032134346000000317
in formula (7), UpqFor substituting the aforementioned Uhh、Uvh、Uhv、Uvv；k1Wave number in Medium one, σ is root mean square height of rough surface, qx、qy、qzIs represented by formula (8):
Figure FDA0003213434600000041
the expression of the height fluctuation correlation coefficient G (R) of the exponential type rough surface is shown as a formula (9);
G(R)＝σ2exp (- | R |/l) formula (9)
In the formula (9), R is the distance between two points of the exponential type rough surface; l is the relative length of the rough surface;
the expression of a second-order derivative rho' (0) of the rough surface height fluctuation correlation coefficient at 0 is shown as a formula (10);
Figure FDA0003213434600000042
establishing
Figure FDA0003213434600000043
Is represented by formula (11):
Figure FDA0003213434600000044
the bistatic scattering coefficient of the measured surface regarded as an exponential-type rough surface is obtained by equations (6), (7), (8), (10), and (11).
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Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109884619A (en) * 2018-12-13 2019-06-14 杭州电子科技大学 A kind of passive millimeter wave radiomimesis method that can distinguish different rough surfaces

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109884619A (en) * 2018-12-13 2019-06-14 杭州电子科技大学 A kind of passive millimeter wave radiomimesis method that can distinguish different rough surfaces

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* Cited by examiner, † Cited by third party
Title
尹川: "毫米波被动辐射成像模拟方法的研究", 信息科技辑, pages 2 - 4 *

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