Rough Surface Emissivity Analysis Method and System

Abstract

The present invention discloses a method and system for analyzing the emissivity of a rough surface. The method is as follows: First, a geometric model of the rough surface is generated and decomposed into several groups through octree grouping; Second, the Stratton-Chu formula is used to calculate the scattered electric field after phase compensation for each group; Then, the scattered electric fields of each group are interpolated in three angular domains of the scattering elevation angle, the scattering azimuth angle, and the incident elevation angle, and the scattered electric field of the entire rough surface is obtained through phase recovery and aggregation; Finally, the calculated scattered electric field is converted into the bistatic scattering coefficient and integrated in the hemispherical space to obtain the reflectivity, and the emissivity at each incident angle is calculated according to the law of conservation of energy. Compared with the approximate analytical method, this method breaks through the limitation of the roughness of the rough surface and is applicable to analyzing the emissivity of rough surfaces with any roughness; Compared with numerical methods such as the method of moments, finite difference, and finite element, it has a faster calculation speed.

Description

Technical Field

[0001] The present invention relates to the technical field of numerical calculation of passive electromagnetic radiation characteristics, and particularly to a method and system for analyzing the emissivity of a rough surface. Background Art

[0002] In millimeter-wave passive imaging, the electromagnetic waves radiated by a target include the thermal radiation of the target itself and the radiation reflected by the target from other radiation sources. Among them, the thermal radiation of the target itself is closely related to the emissivity, and the accuracy of the emissivity directly affects the difference in the brightness temperature in the millimeter-wave image at the K level. The emissivity refers to the ratio of the heat radiated per unit area of an object to the heat radiated by a black body at the same temperature, which characterizes the degree of approximation of the thermal radiation ability of the object to the thermal radiation of the black body. Most objects in nature, such as the human body in body security inspection, no longer meet the criterion of a smooth plane in the millimeter-wave band. If the emissivity of a smooth plane is still used, a large error will be introduced. Therefore, more and more research has been carried out on the analysis method of the emissivity of a rough surface.

[0003] Currently, there are mainly three methods for analyzing the emissivity of a rough surface reported in the literature: the Kirchhoff approximation method (F.T. Ulaby, R.K. Moore, and A.K. Fung, Microwave Remote Sensing, Active and Passive. Norwood, MA: Artech House, 1982, vol. 2), the perturbation method (L. Tsang, J.A. Kong, and R.T. Shin, Theory of Microwave Remote Sensing, New York: Wiley, 1985), and the integral equation method (K.S. Chen, T.D. Wu, L. Tsang, Q. Li, J.C. Shi, and A.K. Fung, Emission of Rough Surfaces Calculated by the Integral Equation Method With Comparison to Three-Dimensional Moment Method Simulations, IEEE Transactions on Geoscience and Remote Sensing, vol. 41, no. 1, pp. 90 - 101, Jan. 2003). These three methods all belong to approximate analytical methods and have a relatively fast calculation speed, and are widely used in calculating the emissivity of a rough surface. However, they all have strict applicable conditions for the roughness of the rough surface, and no method can be found that is applicable to the analysis of the emissivity of a rough surface with any roughness. Summary of the Invention

[0004] The object of the present invention is to provide a rough surface emissivity analysis method and system for the deficiencies of the existing technology. Starting directly from the PO integral, when using the surface element method and the Gordon integral method to solve the PO integral, by grouping the rough surface, calculating the bistatic scattering coefficient of each group, interpolation and aggregation to speed up this process, and finally using these bistatic scattering coefficients for emissivity calculation.

[0005] The technical solution for achieving the object of the present invention is: a rough surface emissivity analysis method, including the following steps:

[0006] Step 1, generate a rough surface geometric model, set the grouping size according to the physical size of the entire rough surface, and determine which groups are non-empty groups;

[0007] Step 2, utilize the compressibility of the scattered electric field data, place discrete points in three angular domains of the scattered elevation angle, scattered azimuth angle, and incident elevation angle, calculate the scattered electric field at the discrete points using the Stratton-Chu formula, perform phase compensation at the non-discrete points, and obtain the scattered electric field of the entire rough surface and convert it into the bistatic scattering coefficient through three-dimensional interpolation, phase recovery, and aggregation;

[0008] Step 3, calculate the emissivity of each incident angle according to the integral of the bistatic scattering coefficient in the hemispherical space.

[0009] A rough surface emissivity analysis system, including:

[0010] The first module is used to generate a rough surface geometric model, set the grouping size according to the physical size of the entire rough surface, and determine which groups are non-empty groups;

[0011] The second module utilizes the compressibility of the scattered electric field data, places discrete points in three angular domains of the scattered elevation angle, scattered azimuth angle, and incident elevation angle, calculates the scattered electric field at the discrete points using the Stratton-Chu formula, performs phase compensation at the non-discrete points, and obtains the scattered electric field of the entire rough surface and converts it into the bistatic scattering coefficient through three-dimensional interpolation, phase recovery, and aggregation;

[0012] The third module calculates the emissivity of each incident angle according to the integral of the bistatic scattering coefficient in the hemispherical space.

[0013] An electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor, where the processor implements the above-mentioned rough surface emissivity analysis method when executing the program.

[0014] A computer-readable storage medium, on which a computer program is stored, and when the program is executed by a processor, it implements the above-mentioned rough surface emissivity analysis method.

[0015] Compared with the prior art, the significant advantages of the present invention are as follows: (1) Modeling the rough surface sample breaks through the limitation on the roughness of the rough surface compared with the Kirchhoff approximation method, the perturbation method, and the integral equation method. (2) Calculating the scattered electric field only at some sampling points, and obtaining the scattered electric fields at the remaining scattering angles and incident angles through interpolation method, which has higher calculation efficiency compared with the physical optics method. (3) There is no very complex formula derivation compared with the integral equation method, and it is simple and practical. Brief Description of the Drawings

[0016] Figure 1 is the rough surface model.

[0017] Figure 2 is the schematic diagram of rough surface grouping. Detailed Description of the Preferred Embodiment

[0018] The present invention will be further described in detail below with reference to the accompanying drawings.

[0019] Combined with the accompanying drawings, the present invention is a method for analyzing the emissivity of a rough surface, and the steps are as follows:

[0020] Step 1: Generate a rough surface geometric model, set the grouping size according to the physical size of the entire rough surface, and determine which groups are non-empty groups, so that the number of non-empty groups is controlled to be several hundred. Specifically as follows:

[0021] The rough surface geometric model is as Figure 1 shown, and the upper hemispherical space is the integration region of the bistatic scattering coefficient. The schematic diagram of rough surface grouping is as Figure 2 shown, is the grouping size, which is calculated by where R q is the radius of the smallest circumscribed circle of each group. The grouping size is preferably set to 1 / 10 to 1 / 30 of the physical size of the entire rough surface in the X or Y direction.

[0022] Step 2: Utilize the compressibility of the scattered electric field data, place discrete points in the three angular domains of the scattering elevation angle, the scattering azimuth angle, and the incident elevation angle, calculate the scattered electric field at the discrete points using the Stratton-Chu formula, perform phase compensation at the non-discrete points, and obtain the scattered electric field of the entire rough surface through three-dimensional interpolation, phase recovery, and aggregation, and convert it into the bistatic scattering coefficient;

[0023] According to the physical optics method, the scattered electric field in the far field region can be expressed by the following formula:

[0024]

[0025] where, θ i and are the incident elevation angle and the incident azimuth angle respectively, θ s and They are the scattering elevation angle and the scattering azimuth angle respectively. j is the imaginary unit. k and η are the wave number and the wave impedance in free space respectively. and are the unit vectors in the incident direction and the scattering direction respectively. r represents the distance between the source point and the observation point. represents the position vector on the integration region. represents the outer normal vector of the rough surface. represents the incident magnetic field. ds′ is the area element.

[0026] The dependence of the above PO integral on the scattering azimuth angle can be considered as the superposition of the exponential terms where and are the azimuth angles of the field point and the source point respectively. The parameter β = 4πfr′sinθ′ / c, where f is the frequency, r′ is an arbitrary point on the rough surface, θ′ is the elevation angle of the source point, and c is the speed of light. The exponential terms are expanded into Fourier series as

[0027]

[0028] In the formula, J 0 (·) and J n (·) are the Bessel functions of the first kind of order 0 and order n respectively. The advantage of the expansion is that the attenuation of the Bessel function at high orders is faster than that of the exponential function. For the rough surface surrounded by the circumcircle, the increment |β| ≤ 4πf max R / c is bounded, where f max is the maximum value of the frequency within the frequency band, and R is the radius of the smallest circumcircle surrounding the rough surface. Therefore, truncation can be performed when calculating the scattering amplitude, and the high-order part can be ignored. So, for the number of sampling points of the scattering azimuth angle within 2π is

[0029]

[0030] In the formula is the oversampling rate of the scattering azimuth angle, satisfying usually taken as 1.5.

[0031] The number of sampling points of the scattering elevation angle and the incident elevation angle can also be obtained through the above process. The difference is that the angular ranges of both are π / 2. Thus, the number of sampling points of the scattering elevation angle and the incident elevation angle is

[0032]

[0033]

[0034] In the formula and are the oversampling rates of the scattering elevation angle and the incident elevation angle respectively.

[0035] According to (3)-(5), it can be seen that the number of sampling points is determined by the value of R. Through grouping, R is reduced to the radius of the minimum circumscribed circle enclosing each group, denoted by Thus, the number of sampling points for the scattering azimuth angle, scattering elevation angle, and incident elevation angle of each group is

[0036]

[0037]

[0038]

[0039] The scattered electric field values of the remaining scattering angles and incident angles can be calculated by interpolation. Since the PO integral exponential term changes too fast and is prone to oscillation, phase compensation needs to be performed on the calculated scattered electric field before the interpolation operation. The phase compensation field of the nth group is

[0040]

[0041] where represents the number of triangular patches in the nth group, represents the coordinates of the center of the nth group, and ds i ′ is the area element of the nth group.

[0042] Using these phase compensation fields, three-dimensional interpolation is performed in the three angular domains of the scattering elevation angle, scattering azimuth angle, and incident elevation angle to obtain the scattered electric field at all the angle points to be solved for each group. Before superimposing the scattering contributions of each group, the following phase recovery needs to be performed on the scattered electric field.

[0043]

[0044] In summary, the scattered electric field of the entire rough surface in the upper half space can be obtained, and further, the bistatic scattering coefficient in the upper half space can be solved. The bistatic scattering coefficient refers to the bistatic radar cross section per unit area, and the expression is

[0045]

[0046] where and are the incident electric field and the scattered electric field respectively, R represents the distance between the radar and the target, A represents the area irradiated on the target. For Figure 1 , A is the length in the X direction of the rough surface multiplied by the length in the Y direction.

[0047] Step 3: Calculate the emissivity for each incident angle according to the integral of the bistatic scattering coefficient in the hemispherical space.

[0048] For the upper half-space of the rough surface, there is no transmission. The reflectivity of the rough surface is obtained by integrating the bistatic scattering coefficient of the upper half-space, and the emissivity is further obtained based on the conservation of energy.

[0049]

[0050] The above integral can adopt the two-dimensional composite trapezoidal integral formula, specifically

[0051]

[0052] where the x-dimensional integral interval is [a, b], which is divided into m equal parts, h is the length of the sub-interval, the y-dimensional integral interval is [c, d], which is divided into n equal parts, and k is the length of its sub-interval.

[0053] Furthermore, the present invention also provides a rough surface emissivity analysis system, including:

[0054] The first module is used to generate a rough surface geometric model, set the grouping size according to the physical size of the entire rough surface, and determine which groups are non-empty groups;

[0055] The second module utilizes the compressibility of the scattered electric field data, places discrete points in three angular domains of the scattering elevation angle, scattering azimuth angle, and incident elevation angle, calculates the scattered electric field at the discrete points using the Stratton-Chu formula, performs phase compensation at the non-discrete points, and obtains the scattered electric field of the entire rough surface through three-dimensional interpolation, phase recovery, and aggregation and converts it into the bistatic scattering coefficient;

[0056] The third module calculates the emissivity of each incident angle according to the integral of the bistatic scattering coefficient in the hemispherical space.

[0057] The specific implementation methods of the above first to third modules are the same as the specific implementations of steps 1 to 3 of the foregoing rough surface emissivity analysis method, and will not be elaborated here.

[0058] The present invention improves the calculation speed of the emissivity by two orders of magnitude while maintaining the accuracy; compared with the approximate analytical method, the method of the present invention breaks through the limitation of the roughness of the rough surface and is applicable to analyzing the emissivity of rough surfaces with any roughness; compared with numerical methods such as the method of moments, finite difference, and finite element, it has a faster calculation speed.

[0059] The beneficial effects of the present method are verified by simulation below.

[0060] Embodiment

[0061] The simulation target is a Gaussian rough surface, and the emissivity of this rough surface is calculated. The frequency of the incident wave is 90 GHz, the size of the rough surface is 21λ × 21λ, the root mean square height is 1 / 3λ, and the correlation length is 3λ. Table 1 shows the emissivity time and error calculated by the method of the present invention and PO at different oversampling rates.

[0062] Table 1 Emissivity time and error calculated by the method of the present invention and PO

[0063]

[0064]

[0065] As can be seen from Table 1, the error of the method of the present invention compared with PO is 0.03% and a significant speedup is achieved.

[0066] The above description of the embodiments is the preferred implementation manner of the present invention, but the implementation manner of the present invention is not limited by the above embodiments. Based on the principle and technical solution of the present invention, various modifications or deformations that can be made by those skilled in the art without creative labor are still within the protection scope of the present invention.

Claims

1. A method for analyzing the emissivity of a rough surface, characterized in that, it includes the following steps: Step 1: Generate a geometric model of the rough surface, set the grouping size according to the physical size of the entire rough surface, and determine which groups are non-empty groups; Step 2: Utilize the compressibility of the scattered electric field data, place discrete points in three angular domains of the scattering elevation angle, scattering azimuth angle, and incident elevation angle, calculate the scattered electric field at the discrete points using the Stratton-Chu formula, perform phase compensation at non-discrete points, and obtain the scattered electric field of the entire rough surface through three-dimensional interpolation, phase recovery, and aggregation and convert it into the bistatic scattering coefficient; specifically as follows: According to the physical optics method, the scattered electric field in the far field region is expressed by the following formula: where θ i and are the incident elevation angle and the incident azimuth angle respectively, θ s and are the scattered elevation angle and the scattered azimuth angle respectively, j is the imaginary unit, k and η are the wave number and the wave impedance in free space respectively, and are the unit vectors in the incident direction and the scattered direction respectively, r represents the distance between the source point and the observation point, represents the position vector on the integration region, represents the outer normal vector of the rough surface, represents the incident magnetic field, ds′ is the area element; discretized by N t triangular surface elements, we can obtain: The emissivity at each incident angle is obtained by integrating the bistatic scattering coefficient over the hemispherical space. The bistatic scattering coefficient is equal to the scattered electric field divided by the illuminated area. Therefore, enough incident angles need to be calculated before the emissivity integration as the scattering angle is the scattered electric field at this time; the number of sampling points for each group is reduced by grouping, and the scattered electric field values for the remaining scattering angles and incident angles are calculated by interpolation and then aggregated to obtain the scattered electric field of the entire rough surface; Before the interpolation operation, perform phase compensation on the calculated scattered electric field. The phase compensation field of the nth group is wherein, represents the number of triangular surface elements in the nth group, represents the coordinates of the center of the nth group, and ds i ' is the area element of the nth group; Utilize these phase compensation fields to perform three-dimensional interpolation in three angular domains of the scattering elevation angle, scattering azimuth angle, and incident elevation angle to obtain the scattered electric field at all the angle points to be calculated for each group; before superimposing the scattering contributions of each group, perform the following phase recovery on the scattered electric field: In summary, the scattered electric field of the entire rough surface in the upper half space can be obtained, and it is converted into the bistatic scattering coefficient for facilitating the calculation of the emissivity of the rough surface in Step 3; Step 3: Calculate the emissivity of each incident angle according to the integral of the bistatic scattering coefficient in the hemispherical space.

2. The method for analyzing the emissivity of a rough surface according to claim 1, characterized in that, Bistatic scattering coefficient Refers to the bistatic radar cross section per unit area, and the expression is: In the formula, and are the incident electric field and the scattered electric field respectively, R represents the distance between the radar and the target, and A represents the area irradiated on the target.

3. The method for analyzing the emissivity of a rough surface according to claim 2, characterized in that, The calculation of the emissivity of each incident angle according to the integral of the bistatic scattering coefficient in the hemispherical space in Step 3 has: For the upper half space of the rough surface, there is no transmission. Integrate the bistatic scattering coefficient of the upper half space to obtain the reflectivity of the rough surface, and the emissivity is further obtained according to the law of conservation of energy; The above integral adopts the two-dimensional composite trapezoidal integral formula, specifically where the x-dimensional integral interval is [a, b], which is divided into m equal parts, h is the length of the sub-interval, the y-dimensional integral interval is [c, d], which is divided into n equal parts, and k is the length of its sub-interval.

4. A system for analyzing the emissivity of a rough surface, characterized in that, it includes: The first module is used to generate a geometric model of the rough surface, set the grouping size according to the physical size of the entire rough surface, and determine which groups are non-empty groups; The second module utilizes the compressibility of the scattered electric field data, places discrete points in three angular domains of the scattering elevation angle, scattering azimuth angle, and incident elevation angle, calculates the scattered electric field at the discrete points using the Stratton-Chu formula, performs phase compensation at non-discrete points, and obtains the scattered electric field of the entire rough surface through three-dimensional interpolation, phase recovery, and aggregation and converts it into the bistatic scattering coefficient; the specific implementation is as follows: According to the physical optics method, the scattered electric field in the far field region is expressed by the following formula: where θ i and are the incident elevation angle and the incident azimuth angle respectively, θ s and are the scattered elevation angle and the scattered azimuth angle respectively, j is the imaginary unit, k and η are the wave number and the wave impedance in free space respectively, and are the unit vectors in the incident direction and the scattered direction respectively, r represents the distance between the source point and the observation point, represents the position vector on the integration region, represents the outer normal vector of the rough surface, represents the incident magnetic field, ds′ is the area element; discretized by N t triangular surface elements, we can get: The emissivity at each incident angle is obtained by integrating the bistatic scattering coefficient over the hemispherical space. Since the bistatic scattering coefficient is equal to the scattered electric field divided by the illuminated area, it is necessary to calculate the scattered electric fields at enough incident angles before the emissivity integration, where the incident angles are and the scattering angles are ; the number of sampling points for each group is reduced by grouping, and the scattered electric field values at the remaining scattering angles and incident angles are calculated by interpolation and then aggregated to obtain the scattered electric field of the entire rough surface; Before the interpolation operation, perform phase compensation on the calculated scattered electric field. The phase compensation field of the nth group is In the formula, represents the number of triangular surface elements in the nth group, represents the coordinates of the center of the nth group, and ds i ' is the area element of the nth group; Using these phase compensation fields, three-dimensional interpolation is performed in three angular domains of the scattering elevation angle, the scattering azimuth angle, and the incident elevation angle to obtain the scattered electric fields at all the to-be-solved angular points of each group; before superimposing the scattering contributions of each group, the following phase recovery is performed on the scattered electric fields: In summary, the scattered electric field of the entire rough surface in the upper half space can be obtained and converted into the bistatic scattering coefficient for facilitating the calculation of the emissivity of the rough surface; The third module calculates the emissivity at each incident angle according to the integral of the bistatic scattering coefficient in the hemispherical space.

5. The rough surface emissivity analysis system according to claim 4, characterized in that Bistatic Scattering Coefficient Refers to the bistatic radar cross section per unit area, and the expression is Wherein, and are the incident electric field and the scattered electric field respectively, R represents the distance between the radar and the target, and A represents the area irradiated on the target.

6. The rough surface emissivity analysis system according to claim 5, characterized in that The third module is specifically implemented as follows: For the upper half space of the rough surface, there is no transmission. The reflectivity of the rough surface is obtained by integrating the bistatic scattering coefficient of the upper half space, and the emissivity is further obtained according to the conservation of energy; The above integral uses the two-dimensional composite trapezoidal integral formula, specifically where the x-dimensional integral interval is [a, b], which is divided into m equal parts, h is the length of the sub-interval, the y-dimensional integral interval is [c, d], which is divided into n equal parts, and k is the length of its sub-interval.

7. An electronic device, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that when the processor executes the program, it implements the rough surface emissivity analysis method as described in any one of claims 1-3.

8. A computer-readable storage medium, on which a computer program is stored, characterized in that when the program is executed by the processor, it implements the rough surface emissivity analysis method as described in any one of claims 1-3.

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