A Modeling Method and System for the Radar Cross Section of a Dihedral Angle Reflector Quantum Radar

Abstract

The present invention discloses a modeling method and device for the quantum radar cross section (QRCS) of a dihedral reflector. The method includes: Step 1: Construct a physical model for the dihedral structure detected by the quantum radar, and calculate the total projected area of the two facets of the dihedral perpendicular to the incident direction of the incident wave; Step 2: Set the distance R between the radar and the dihedral reflector to approach infinity, decompose the incident wave vector and the echo vector according to the vector calculation rule, and calculate the incident wave direction vector and the echo direction vector according to the geometric relationship; Calculate the Fourier transform of the atomic distribution on the surface of the dihedral reflector from the incident wave vector, the echo vector, the incident wave direction vector and the echo direction vector; Step 3: Convert the QRCS numerical calculation formula into an integral form, substitute the results of Step 1 and Step 2, and simplify to obtain the Fourier expression form of the QRCS. The present invention can quickly model and calculate the QRCS value of the dihedral reflector through the Fourier representation form of the QRCS.

Description

Technical Field

[0001] The present invention belongs to the technical field of quantum radar, and in particular relates to a modeling method and system for the quantum radar cross section of a dihedral reflector. Background Art

[0002] With the application of single-photon detection devices and the development of microwave single-photon detectors, quantum radar is expected to become a powerful means for detecting stealth targets. In recent years, extensive research has been carried out in aspects such as quantum signal sources, quantum atmospheric transmission characteristics, quantum scattering, quantum remote sensing schemes, and quantum signal detection and estimation. Among them, quantum scattering is the result of the interaction between a quantum and a target, and its characteristics play an important guiding role in the detection of targets by quantum radar and the design of stealth targets. The quantum radar cross section (QRCS) is an important parameter in quantum scattering and an important manifestation of the scattering characteristics of a target. At present, many researchers have conducted extensive research in this area. Some methods have given the analytical definition formula of QRCS and the closed expressions for simple planar objects, and simulated and calculated the QRCS of rectangular plates, circular plates, and triangular plates, and discussed in detail the influence of parameters such as the distance between the radar and the target, the atomic spacing on the target surface, the size of the planar target, the aspect ratio of the planar length to width, the number of incident photons, and polarization on QRCS (M. Lanzagorta, "Quantum radar cross sections," Proc. of SPIE., vol. 7727, p. 77270K, 2010.) (K. Liu, H. Xiao, and H. Fan, "Analysis and simulation of quantum radar cross section," Chinese Physics Letters., vol. 31, no. 3, 2014.). There are also some methods that have corrected the proposed definition formula, simulated and calculated the QRCS of rectangular planes, cylindrical surfaces, and straight dihedral angles, and discussed the influence of parameters such as the atomic spacing on the target surface, the size of the planar target, the aspect ratio of the planar length to width, and the wavelength of the incident wave on QRCS. Existing research almost all targets planar or convex surface targets, such as planar targets, cone-column targets, and three-dimensional convex surface targets. This type of target only involves the problem of single scattering and lacks a quantum scattering model for three-dimensional targets with dihedral reflectors that involve double scattering.

[0003] In addition, due to the complexity of calculating the target scattering characteristics of dihedral angles, the existing numerical calculation methods need to set the sampling interval of the atomic distribution on the target surface. The higher the sampling interval, the higher the calculation accuracy, and the closer the QRCS characteristic curve is to the theoretical value. The computational cost of the numerical calculation of dihedral QRCS is proportional to the fourth power of the number of samples and the third power of the surface element size. The reduction of the sampling interval will lead to a sharp increase in the computational cost of the QRCS numerical calculation. Therefore, the numerical calculation method is difficult to calculate and analyze the quantum scattering characteristics of targets with electrically large sizes. At the same time, the physical meaning of the numerical calculation results is not clear, and the analysis is difficult, which is not conducive to the signal design of quantum radars and the design of stealth targets. Summary of the Invention

[0004] Aiming at the problems of large computational cost and unclear physical meaning in the numerical calculation of the QRCS of a dihedral reflector, the present invention proposes a modeling method and system for the quantum radar cross section of a dihedral reflector, which can quickly model and calculate the QRCS value of the dihedral reflector through the Fourier representation form of the QRCS.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] On the one hand, the present invention proposes a modeling method for the quantum radar cross section of a dihedral reflector, including:

[0007] Step 1: Construct a physical model for a quantum radar to detect a dihedral structure, and calculate the total projected area of the two surface elements of the dihedral perpendicular to the incident direction of the incident wave;

[0008] Step 2: Set the distance R between the radar and the dihedral reflector to approach infinity. Decompose the incident wave vector and the echo vector according to the vector calculation rule, and calculate the incident wave direction vector and the echo direction vector according to the geometric relationship; calculate the Fourier transform of the atomic distribution on the surface of the dihedral reflector from the incident wave vector, the echo vector, the incident wave direction vector and the echo direction vector;

[0009] Step 3: Convert the QRCS numerical calculation formula into an integral form, substitute the results of Step 1 and Step 2, and simplify to obtain the Fourier expression form of the QRCS.

[0010] Further, the Step 1 includes:

[0011] Establish a right-handed space coordinate system x-y-z at the position of the dihedral reflector, where the rectangular flat plate with length a and width b on the x0z plane is the surface element 1 of the dihedral reflector, and the rectangular flat plate with length a and width c on the y0z plane is the surface element 2 of the dihedral reflector, to obtain the pitch angle azimuth angle θ of the radar relative to the dihedral reflector; calculate the total projected area of the two surface elements of the dihedral perpendicular to the incident direction of the incident wave according to the following formula:

[0012]

[0013] Wherein, is the total projected area perpendicular to the incident wave direction of the two surface elements of the dihedral angle when the pitch angle of the radar relative to the dihedral angle reflector is the azimuth angle is θ, the length of surface element 1 is a and the width is b, and the length of surface element 2 is a and the width is c.

[0014] Further, step 2 includes:

[0015] Decompose the incident wave vector and the echo vector into where is the position vector of the atoms on the surface of surface element 1, is the position vector of the atoms on the surface of surface element 2, is the distance vector from the radar to the origin;

[0016] Calculate the incident wave direction vector according to the following formula the echo direction vector

[0017]

[0018]

[0019] Substitute the expressions of the incident wave vector, the echo vector, the incident wave direction vector and the echo direction vector into the following formula:

[0020]

[0021] Wherein, is the Fourier transform of the atomic distribution on the surface of the dihedral angle reflector, is the vector from the atoms on the surface of surface element 1 to the atoms on the surface of surface element 2, S 1 represents surface element 1, S 2 represents surface element 2;

[0022] The Fourier transform of the atomic distribution on the surface of the dihedral angle reflector changes to:

[0023]

[0024] Wherein, k represents the wave number, g a (x) represents the gate function with a gate width of a, g c (x) represents the gate function with a gate width of c, x represents the atomic position variable of surface element 1, and y represents the atomic position variable of surface element 2.

[0025] Further, step 3 includes:

[0026] The result of integrating the scattered echo intensity in the direction is where k 0 is a constant, χ(a, c) is a term related to the ratio of the side lengths of the two plane elements of the dihedral angle, and λ is the wavelength of the incident wave;

[0027] Determine the gate width and gate function in the Fourier transform of the atomic distribution on the surface of the plane element according to the shape and size of the plane element, and determine the integration limits of the integral of the scattered echo intensity in the direction according to the scattered echo direction;

[0028] Determine whether χ(a, c) is a constant 1 according to the symmetry of the plane element size;

[0029] Calculate the QRCS value of the dihedral angle reflector using FFT;

[0030] Obtain the Fourier expression form of QRCS through the above simplification process:

[0031]

[0032] On the other hand, the present invention proposes a modeling system for the quantum radar cross section of a dihedral angle reflector, including:

[0033] The first calculation module is used to construct a physical model for the quantum radar to detect the dihedral angle structure and calculate the total projected area of the two plane elements of the dihedral angle perpendicular to the incident direction of the incident wave;

[0034] The second calculation module is used to set the distance R between the radar and the dihedral angle reflector to →∞, decompose the incident wave vector and the echo vector according to the vector calculation rule, and calculate the incident wave direction vector and the echo direction vector according to the geometric relationship; calculate the Fourier transform of the atomic distribution on the surface of the dihedral angle reflector from the incident wave vector, the echo vector, the incident wave direction vector and the echo direction vector;

[0035] The conversion module is used to convert the QRCS numerical calculation formula into an integral form, substitute the results of the first calculation module and the second calculation module, and simplify to obtain the Fourier expression form of QRCS.

[0036] Furthermore, the first calculation module is specifically used for:

[0037] Establish a right-angle space coordinate system x-y-z at the position of the dihedral angle reflector, where the rectangular flat plate with length a and width b on the x0z plane is the plane element 1 of the dihedral angle reflector, and the rectangular flat plate with length a and width c on the y0z plane is the plane element 2 of the dihedral angle reflector, and obtain the pitch angle azimuth angle θ of the radar relative to the dihedral angle reflector; calculate the total projected area of the two plane elements of the dihedral angle perpendicular to the incident direction of the incident wave according to the following formula:

[0038]

[0039] Among them, when the pitch angle of the radar relative to the dihedral reflector is and the azimuth angle is θ, the length of element 1 is a and the width is b, and the length of element 2 is a and the width is c, the total projected area of the two elements of the dihedral perpendicular to the incident direction of the incident wave.

[0040] Furthermore, the second calculation module is specifically configured to:

[0041] Decompose the incident wave vector and the echo vector into where is the surface atomic position vector of element 1, is the surface atomic position vector of element 2, is the distance vector from the radar to the origin;

[0042] Calculate the incident wave direction vector and the echo direction vector

[0043]

[0044]

[0045] Substitute the expressions of the incident wave vector, the echo vector, the incident wave direction vector and the echo direction vector into the following formula:

[0046]

[0047] where is the Fourier transform of the surface atomic distribution of the dihedral reflector, is the vector from the surface atoms of element 1 to the surface atoms of element 2, S 1 represents element 1, S 2 represents element 2;

[0048] The Fourier transform of the surface atomic distribution of the dihedral reflector changes to:

[0049]

[0050] where k represents the wave number, g a (x) represents a gate function with a gate width of a, g c (x) represents a gate function with a gate width of c, x represents the atomic position variable of element 1, and y represents the atomic position variable of element 2.

[0051] Furthermore, the conversion module is specifically configured to:

[0052] The result of integrating the scattered echo intensity in the direction is Among them, k 0 is a constant, χ(a, c) is a term related to the length ratio of the side lengths of the two surface elements of the dihedral angle, and λ is the wavelength of the incident wave;

[0053] Determine the gate width and gate function in the Fourier transform of the atomic distribution on the surface element according to the shape and size of the surface element, and determine the integration limits of the integral of the scattered echo intensity in the direction according to the direction of the scattered echo;

[0054] Determine whether χ(a, c) is a constant 1 according to the symmetry of the surface element size;

[0055] Use FFT to calculate the QRCS value of the dihedral angle reflector;

[0056] Obtain the Fourier expression form of QRCS through the above simplification process:

[0057]

[0058] Compared with the prior art, the beneficial effects of the present invention are:

[0059] The present invention solves the problems of large computational amount and unclear physical meaning in the numerical calculation of the QRCS of the dihedral angle reflector. The present invention first establishes a physical model for quantum radar to detect the dihedral angle reflector, calculates the total projected area of the two surface elements of the dihedral angle perpendicular to the incident direction of the incident wave, and then uses vector decomposition to calculate the Fourier transform of the atomic distribution on the surface of the dihedral angle reflector, and finally obtains the Fourier expression form of QRCS. The present invention can realize the rapid calculation of the QRCS of the dihedral angle reflector by using the two-dimensional Fourier transform of the atomic distribution of the two surface elements of the dihedral angle, and is not affected by the sampling interval of the atomic distribution of the surface element, providing a reliable and practical method for the rapid modeling of the QRCS of the dihedral angle reflector. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 is a flowchart of a modeling method for the quantum radar scattering cross section of a dihedral angle reflector according to an embodiment of the present invention;

[0061] Figure 2 is a schematic diagram of a physical model of a quantum radar detecting a dihedral angle structure constructed by a modeling method for the quantum radar scattering cross section of a dihedral angle reflector according to an embodiment of the present invention;

[0062] Figure 3 is a schematic diagram of the geometric decomposition of the quantum scattering of a dihedral angle structure constructed by a modeling method for the quantum radar scattering cross section of a dihedral angle reflector according to an embodiment of the present invention;

[0063] Figure 4 is a curve graph of the change of the integration result constructed by a modeling method for the quantum radar scattering cross section of a dihedral angle reflector according to an embodiment of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0064] The present invention will be further explained below with reference to the accompanying drawings and specific embodiments:

[0065] As Figure 1 shown, a modeling method for the quantum radar cross section of a dihedral reflector includes:

[0066] Step 1: Construct a physical model of the dihedral structure detected by the quantum radar, and calculate the total projected area of the two facets of the dihedral perpendicular to the incident direction of the incident wave;

[0067] Step 2: Set the distance R between the radar and the dihedral reflector to R→∞, decompose the incident wave vector and the echo vector according to the vector calculation rule, and calculate the incident wave direction vector and the echo direction vector according to the geometric relationship; calculate the Fourier transform of the atomic distribution on the surface of the dihedral reflector from the incident wave vector, the echo vector, the incident wave direction vector, and the echo direction vector;

[0068] Step 3: Convert the QRCS numerical calculation formula into an integral form, substitute the results of Step 1 and Step 2, and simplify to obtain the Fourier expression form of QRCS.

[0069] In Step 1, as Figure 2 shown, the parameters that need to be set for the physical model of the dihedral structure detected by the quantum radar are: the pitch angle azimuth angle θ of the radar relative to the dihedral reflector, the length am (meters) and width bm of facet 1, the length am and width cm of facet 2, the wavelength λ of the incident wave, and the distance R between the quantum radar and the dihedral target. Then the incident angle in the azimuth of the incident wave is θ, so the total projected area of the two facets of the dihedral perpendicular to the incident direction of the incident wave is expressed as

[0070]

[0071] In Step 2, as Figure 3 shown, in order to convert the QRCS numerical calculation formula into an integral formula of the atomic distribution on the facet surface, the incident wave vector and the echo vector are decomposed into the superposition of the facet surface vector and the distance vector between the quantum radar and the dihedral reflector, which is expressed as

[0072]

[0073] Both facets of the dihedral reflector are rectangular flat plates, and the Fourier transform term of the secondary scattering is

[0074]

[0075] where is the atomic position vector on the surface of facet 1, is the surface atomic position vector of the surface element 2, is the vector from the surface atom of the surface element 1 to the surface atom of the surface element 2, and the distance vector from the radar to the origin is incident wave direction vector is the direction vector between the surface atoms of the two surface elements, the echo direction vector k is the wave number, S 1 represents the surface element 1, S 2 represents the surface element 2. When R→∞, is a constant, and the numerator and denominator cancel each other out in the calculation formula of the QRCS. Substitute formula (2) into formula (3), and each exponential term in formula (3) is respectively

[0076]

[0077]

[0078]

[0079] In case, there is

[0080]

[0081] According to the definition of the Fourier transform, we can further obtain that the Fourier transform of the surface atomic distribution of the dihedral reflector is

[0082]

[0083] where g a (x) represents the gate function with a gate width of a, and g c (x) represents the gate function with a gate width of c, x represents the atomic position variable of the surface element 1, and y represents the atomic position variable of the surface element 2.

[0084] In step 3, for the straight dihedral angle with two rectangular surface elements, according to the energy conservation of the incident wave signal and the echo signal, the energy of the incident wave is equal to the result of integrating the scattered echo intensity in the direction. The result of integrating the scattered echo intensity in the direction is

[0085]

[0086] where k 0 is a constant, λ is the wavelength of the incident wave, the term χ(a, c) is related to the ratio of the side lengths of the two faces of the dihedral angle, and when the side lengths of the two faces are approximately equal, the value of χ(a, c) tends to 1, as Figure 4 shown. In the case of a≈c, the Fourier expression form of the QRCS is simplified to

[0087]

[0088] The process of simplifying the expression of QRCS includes the following three steps:

[0089] 1) Determine the gate function and gate width in the Fourier transform of the atomic distribution on the surface of the surface element according to the shape and size of the surface element, and determine the integration limits of the integration of the scattered echo intensity in the direction according to the direction of the scattered echo, so as to obtain the integral representation forms of formula (7) and formula (9);

[0090] 2) Check whether χ(a, c) is a constant 1 according to the symmetry of the surface element size. If the sizes of the two surface elements of the dihedral angle are symmetric, χ(a, c) = 1; if the sizes of the two surface elements of the dihedral angle are asymmetric, the integral formula in formula (9) needs to be integrated separately;

[0091] 3) Use FFT to calculate the two-dimensional Fourier transform of formula (8), and the value of QRCS is the value at (k cos(θ), k sin(θ)) in the frequency domain of this two-dimensional Fourier transform.

[0092] The above decision method utilizes two characteristics of the present invention: one is to utilize the characteristic that the physical meaning of the method of the present invention is clear, and directly determine the integration limits by using the size of the dihedral angle reflector and the surface element boundary conditions; the other is the characteristic that the method of the present invention can use FFT for fast calculation, and directly obtain the QRCS value by taking the value at the coordinates (k cos(θ), k sin(θ)) in the two-dimensional Fourier transform domain.

[0093] On the basis of the above embodiments, the present invention also proposes a modeling system for the quantum radar cross section of a dihedral angle reflector, including:

[0094] A first calculation module, configured to construct a physical model for the quantum radar to detect the dihedral angle structure, and calculate the total projected area of the two surface elements of the dihedral angle perpendicular to the incident direction of the incident wave;

[0095] A second calculation module, configured to set the distance R between the radar and the dihedral angle reflector to ∞, decompose the incident wave vector and the echo vector according to the vector calculation rule, and calculate the incident wave direction vector and the echo direction vector according to the geometric relationship; calculate the Fourier transform of the atomic distribution on the surface of the dihedral angle reflector from the incident wave vector, the echo vector, the incident wave direction vector and the echo direction vector;

[0096] A conversion module, configured to convert the QRCS numerical calculation formula into an integral form, substitute the results of the first calculation module and the second calculation module, and simplify to obtain the Fourier expression form of QRCS.

[0097] Further, the first calculation module is specifically configured to:

[0098] A right - angled space coordinate system x - y - z is established with the position of the dihedral reflector. Among them, the rectangular flat plate with length a and width b on the xOz plane is the surface element 1 of the dihedral reflector, and the rectangular flat plate with length a and width c on the yOz plane is the surface element 2 of the dihedral reflector, and the elevation angle of the radar relative to the dihedral reflector is obtained Azimuth angle θ; calculate the total projected area of the two surface elements of the dihedral perpendicular to the incident direction of the incident wave according to the following formula:

[0099]

[0100] Among them, is the total projected area of the two surface elements of the dihedral perpendicular to the incident direction of the incident wave when the elevation angle of the radar relative to the dihedral reflector is the azimuth angle is θ, the length of the surface element 1 is a and the width is b, and the length of the surface element 2 is a and the width is c.

[0101] Furthermore, the second calculation module is specifically used for:

[0102] Decompose the incident wave vector and the echo vector into Among them is the position vector of the atoms on the surface of the surface element 1, is the position vector of the atoms on the surface of the surface element 2, is the distance vector from the radar to the origin;

[0103] Calculate the incident wave direction vector according to the following formula Echo direction vector

[0104]

[0105]

[0106] Substitute the expressions of the incident wave vector, echo vector, incident wave direction vector and echo direction vector into the following formula:

[0107]

[0108] Among them, is the Fourier transform of the atomic distribution on the surface of the dihedral reflector, is the vector from the atoms on the surface of the surface element 1 to the atoms on the surface of the surface element 2, S 1 represents the surface element 1, S 2 represents the surface element 2;

[0109] The Fourier transform of the atomic distribution on the surface of the dihedral reflector changes to:

[0110]

[0111] where k represents the wave number, and g a (x) represents a gate function with a gate width of a, and g c (x) represents a gate function with a gate width of c. x represents the atomic position variable of the first surface element, and y represents the atomic position variable of the second surface element.

[0112] Furthermore, the conversion module is specifically configured to:

[0113] The result of integrating the scattered echo intensity in the direction is where k 0 is a constant, χ(a, c) is a term related to the ratio of the side lengths of the two surface elements of the dihedral angle, and λ is the wavelength of the incident wave;

[0114] Determine the gate width and gate function in the Fourier transform of the atomic distribution on the surface of the surface element according to the shape and size of the surface element, and determine the integration limits of the integration of the scattered echo intensity in the direction according to the scattered echo direction;

[0115] Determine whether χ(a, c) is a constant 1 according to the symmetry of the surface element size;

[0116] Calculate the QRCS value of the dihedral angle reflector using FFT;

[0117] Obtain the Fourier expression form of QRCS through the above simplification process:

[0118]

[0119] In summary, the present invention solves the problems of large computational amount and unclear physical meaning in the numerical calculation of the QRCS of the dihedral angle reflector. The present invention first establishes a physical model for quantum radar to detect the dihedral angle reflector, calculates the total projected area of the two surface elements of the dihedral angle perpendicular to the incident direction of the incident wave, and then uses vector decomposition to calculate the Fourier transform of the atomic distribution on the surface of the dihedral angle reflector, and finally obtains the Fourier expression form of QRCS. The present invention can realize the rapid calculation of the QRCS of the dihedral angle reflector by using the two-dimensional Fourier transform of the atomic distribution of the two surface elements of the dihedral angle, and is not affected by the sampling interval of the atomic distribution of the surface element, providing a reliable and practical method for the rapid modeling of the QRCS of the dihedral angle reflector.

[0120] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. A modeling method for the quantum radar cross section of a dihedral reflector, characterized in that, it includes: Step 1: Construct a physical model for the quantum radar to detect the dihedral structure, and calculate the total projected area of the two surface elements of the dihedral perpendicular to the incident direction of the incident wave; The said Step 1 includes: A right - angled space coordinate system x - y - z is established with the position of the dihedral - angle reflector. Among them, the rectangular flat plate with length a and width b on the xOz plane is the surface element 1 of the dihedral - angle reflector, and the rectangular flat plate with length a and width c on the yOz plane is the surface element 2 of the dihedral - angle reflector, and the elevation angle of the radar relative to the dihedral - angle reflector is obtained azimuth angle θ; The total projected area of the two surface elements of the dihedral angle perpendicular to the incident direction of the incident wave is calculated according to the following formula: Among them, when the pitch angle of the radar relative to the dihedral reflector is the azimuth angle is θ, the length of element 1 is a and the width is b, and the length of element 2 is a and the width is c, the total projected area of the two elements of the dihedral perpendicular to the incident direction of the incident wave; Step 2: Set the distance R between the radar and the dihedral reflector to →∞, decompose the incident wave vector and the echo vector according to the vector calculation rule, and calculate the incident wave direction vector and the echo direction vector according to the geometric relationship; calculate the Fourier transform of the atomic distribution on the surface of the dihedral reflector from the incident wave vector, the echo vector, the incident wave direction vector and the echo direction vector; The said Step 2 includes: Decompose the incident wave vector and the echo vector into where is the position vector of the surface atoms of element 1, is the position vector of the surface atoms of element 2, is the distance vector from the radar to the origin; Calculate the incident wave direction vector according to the following formula Echo direction vector Substitute the expressions of the incident wave vector, the echo vector, the incident wave direction vector and the echo direction vector into the following formula: Among them, is the Fourier transform of the atomic distribution on the surface of the dihedral reflector, is the vector from the surface atoms of surface element 1 to the surface atoms of surface element 2, S 1 represents surface element 1, S 2 represents surface element 2, is the direction vector between the surface atoms of the two surface elements; The Fourier transform of the atomic distribution on the surface of the dihedral reflector changes to: where k represents the wave number, and g a (x) represents a gate function with a gate width of a, and g c (x) represents a gate function with a gate width of c, x represents the atomic position variable of the first bin, and y represents the atomic position variable of the second bin; Step 3: Convert the QRCS numerical calculation formula into an integral form, substitute the results of Step 1 and Step 2, and simplify to obtain the Fourier expression form of QRCS; The said Step 3 includes: The result of integrating the scattered echo intensity in the direction is where k 0 is a constant, χ(a, c) is a term related to the ratio of the side lengths of the two facets of the dihedral angle, and λ is the wavelength of the incident wave; Determine the gate width and the gate function in the Fourier transform of the atomic distribution on the surface of the surface element according to the shape and size of the surface element, and determine the integration limits of the scattered echo intensity integrated by direction according to the scattered echo direction; Determine whether χ(a,c) is a constant 1 according to the symmetry of the surface element size; Use FFT to calculate the QRCS value of the dihedral reflector; Obtain the Fourier expression form of QRCS through the simplification process:

2. A modeling system for the quantum radar cross section of a dihedral reflector, characterized in that, it includes: The first calculation module is used to construct a physical model for the quantum radar to detect the dihedral structure, and calculate the total projected area of the two surface elements of the dihedral perpendicular to the incident direction of the incident wave; The said first calculation module is specifically used for: A right - angled space coordinate system x - y - z is established with the position of the dihedral - angle reflector. Among them, the rectangular flat plate with length a and width b on the xOz plane is the surface element 1 of the dihedral - angle reflector, and the rectangular flat plate with length a and width c on the yOz plane is the surface element 2 of the dihedral - angle reflector, and the elevation angle of the radar relative to the dihedral - angle reflector is obtained azimuth angle θ; Calculate the total projected area of the two surface elements of the dihedral angle perpendicular to the incident direction of the incident wave according to the following formula: Among them, when the pitch angle of the radar relative to the dihedral reflector is the azimuth angle is θ, the length of element 1 is a and the width is b, and the length of element 2 is a and the width is c, the total projected area of the two elements of the dihedral perpendicular to the incident direction of the incident wave; The second calculation module is used to set the distance R between the radar and the dihedral reflector to →∞, decompose the incident wave vector and the echo vector according to the vector calculation rule, and calculate the incident wave direction vector and the echo direction vector according to the geometric relationship; calculate the Fourier transform of the atomic distribution on the surface of the dihedral reflector from the incident wave vector, the echo vector, the incident wave direction vector and the echo direction vector; The said second calculation module is specifically used for: Decompose the incident wave vector and the echo vector into where is the position vector of the surface atoms of element 1, is the position vector of the surface atoms of element 2, is the distance vector from the radar to the origin; Calculate the incident wave direction vector according to the following formula Echo direction vector Substitute the expressions of the incident wave vector, the echo vector, the incident wave direction vector and the echo direction vector into the following formula: Among them, is the Fourier transform of the atomic distribution on the surface of the dihedral reflector, is the vector from the atoms on the surface of element 1 to the atoms on the surface of element 2, S 1 represents element 1, S 2 represents element 2, is the direction vector between the atoms on the surfaces of the two elements; The Fourier transform of the atomic distribution on the surface of the dihedral reflector changes to: where k represents the wave number, and g a (x) represents a rectangular function with a gate width of a, and g c (x) represents a rectangular function with a gate width of c, x represents the atomic position variable of bin 1, and y represents the atomic position variable of bin 2; The conversion module is used to convert the QRCS numerical calculation formula into an integral form, substitute the results of the first calculation module and the second calculation module, and simplify to obtain the Fourier expression form of QRCS; The said conversion module is specifically used for: The result of integrating the scattered echo intensity in the direction is where k 0 is a constant, χ(a, c) is a term related to the ratio of the side lengths of the two surface elements of the dihedral angle, and λ is the wavelength of the incident wave; Determine the gate width and the gate function in the Fourier transform of the atomic distribution on the surface of the surface element according to the shape and size of the surface element, and determine the integration limits of the scattered echo intensity integrated by direction according to the scattered echo direction; Determine whether χ(a,c) is a constant 1 according to the symmetry of the surface element size; Use FFT to calculate the QRCS value of the dihedral reflector; Obtain the Fourier expression form of QRCS through the simplification process:

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