A method for reconstructing small-angle multi-region scattering sources based on fast Fourier transform

Abstract

The present invention provides a small-angle multi-region scattering source reconstruction method based on fast Fourier transform, which belongs to the field of microwave imaging and RCS testing. First, a microwave signal with a certain bandwidth is used in a small angle range in a rotation mode to obtain the scattered echo data of multiple finished parts at one time; the received echo signal is mixed with the corresponding reference signal to obtain a coherent echo signal, and the coherent echo signal contains the spatial spectrum information at the center of the target; a two-dimensional imaging of multiple finished parts is obtained by a two-dimensional fast Fourier transform, and the imaging area where each component is located is selected to perform a two-dimensional fast inverse Fourier transform separately to obtain a two-dimensional scattered echo signal with angle-frequency distribution corresponding to a single component, and finally the radar scattering cross section of the corresponding component can be obtained by calibration processing. The present invention can be applied to the scattering measurement of multiple targets, which improves the test efficiency; no interpolation processing is required, which improves the reconstruction accuracy of the scattering source; the algorithm is fast and reduces the calculation time.

Description

Technical Field

[0001] The invention belongs to the field of microwave imaging and RCS testing, and in particular relates to a small-angle multi-region scattering source reconstruction method based on fast Fourier transform. Background Art

[0002] In order to test the scattering characteristics of stealth equipment, RCS (Radar Cross Section) test is required after the equipment is manufactured. Stealth equipment contains multiple finished parts. In order to obtain the RCS information of the parts, a single test can only be performed on a single part in the traditional mode, which greatly increases the time and manpower required for the test. In order to improve the efficiency of RCS testing, multiple finished parts need to be measured at the same time.

[0003] However, what is tested in this way is the scattered echo of the combined components, and the received signal needs to be properly processed to obtain the scattering characteristics of each single component.

[0004] During the test, the signal usually has a certain frequency bandwidth, which allows the signal to contain the radial distance information of the target. When the radial distances between the finished components are different, it can be transformed into the time domain for filtering and separation to obtain the time domain signal of a single component, and then further transformed back to the frequency domain and calibrated to obtain the RCS of the corresponding component. Publication number CN115808667, publication date March 17, 2023, the invention patent named "A non-uniform stepped frequency RCS measurement method" separates the target by filtering in the time domain. However, this method has great limitations. When multiple components are at the same radial distance, it is impossible to separate the echo information of each component through this method.

[0005] During the test, multiple components are mounted at different positions on a low-scatter carrier and the components are separated in space. Therefore, separating the components in two-dimensional imaging is a feasible method.

[0006] Publication number CN109932719, publication date June 25, 2019, the invention patent named "High-precision RCS measurement method based on SAR imaging" discloses a high-precision RCS measurement method based on SAR imaging. This method uses the BP algorithm for two-dimensional imaging, separates the target from the two-dimensional image, and obtains the RCS of the target through further transformation and calibration. However, the BP algorithm used in the invention has a large number of interpolation operations, which increases the computational cost of imaging and subsequent scattering source reconstruction based on imaging. Summary of the invention

[0007] In order to solve the above technical problems, the present invention provides a small-angle multi-region scattering source reconstruction method based on fast Fourier transform, which can obtain the scattering characteristics of each single component in a multi-component test by Fourier transform and other related operations after a sweep frequency test at a small angle, thereby solving the problem of reduced efficiency of the current imaging-based multi-region scattering source reconstruction method due to the large number of steps and large amount of calculation.

[0008] The technical solution adopted by the present invention is as follows:

[0009] A small-angle multi-region scattering source reconstruction method based on fast Fourier transform, firstly, the scattered echo data of multiple finished parts are obtained at one time within a small angle range in a rotating mode, wherein the transmitting signal used for the test has a certain bandwidth; secondly, the scattered received echo signal is mixed with the time reference signal according to the test frequency and distance to obtain a coherent echo signal, and the coherent echo signal contains the spatial spectrum information at the center of the measured target; then, two-dimensional imaging of multiple measured targets is obtained by two-dimensional fast Fourier transform (2D-FFT, Two-Dimensional Fast Fourier Transformation), and it is known that the measured targets are located in different areas, so each measured target can be distinguished in the image, and the imaging area where each measured target is located is selected to perform two-dimensional fast inverse Fourier transform (2D-IFFT) separately to obtain the two-dimensional scattered echo signal corresponding to the single measured target with angle-frequency distribution, and finally the radar scattering cross section of the corresponding measured target can be obtained by calibration processing. The specific implementation steps of the reconstruction method are as follows:

[0010] Step 1: Obtain scattered echo data of multiple targets

[0011] A Cartesian coordinate system is established with the centers of multiple measured targets as the origin. At the test distance R0, that is, the transceiver source is located at (0, -R0), the transmitting signal s(t) is used to simultaneously perform a small angle θ on multiple measured targets. m The range of the angle sweep test, get the receiving scattered echo signal E at a distance R from the transmitting and receiving source r (t-2R / c,f,θ):

[0012] s(t)=e j2πft (1)

[0013] E r (t-2R / c,f,θ)=∫ x ∫ y σ(x,y)e -j2πf(t-2R / c) dxdy (2)

[0014] R=R0+y cosθ-x sinθ (3)

[0015] Where t is time, c is the speed of light, f is the frequency of the transmitted signal, θ is the azimuth angle, and σ(x, y) is the two-dimensional scattering center distribution of the target being measured, which is not only a function of the target coordinates (x, y), but also a function of the frequency f and the azimuth angle θ.

[0016] The angle interval of the angle sweep test is Δθ, and the transmission signal has a certain bandwidth B, and its starting frequency is f min , the termination frequency is f max , the step frequency is Δf.

[0017] Furthermore, the transmission signal frequency f is in the range of 1-18 GHz, and a signal with a bandwidth of B is selected, wherein the starting frequency is f min , the termination frequency is f max , the small angle θ m The range is ±20°.

[0018] Step 2: Mix with the time reference signal to obtain a coherent received signal

[0019] The received scattered echo signal E r (t-2R / c,f,θ) is mixed with the time reference signal Ref(t) to obtain the coherent received signal E c (f,θ):

[0020]

[0021] Wherein, the time reference signal Ref(t) is related to the test distance R0, specifically:

[0022]

[0023] Where s is the transmitted signal s(t), and the coherent received signal E after mixing is c (f,θ) contains the spatial spectrum information at the center of the target being measured.

[0024] Step 3: 2D Fast Fourier Transform Imaging Processing

[0025] The spatial spectrum contained in the coherent received signal obtained by mixing during the angle sweep test is fan-shaped in Cartesian coordinates. When the rotation angle is small, its spatial spectrum distribution can be approximated as a rectangular spectrum window, that is, the received scattered echo data of the imaging is two-dimensionally decoupled in the range and azimuth directions. In addition, the received scattered echo data obtained during the test are sampled at equal intervals in frequency f and angle θ. Therefore, the coherent received signal obtained in step 2 can be directly subjected to a two-dimensional fast Fourier transform to obtain a two-dimensional image of the target. Since θ m is small, so that cosθ≈1, sinθ≈θ, so the imaging formula derived based on equation (4) can be simplified as:

[0026]

[0027] For the coherent received signal E c After processing (f,θ) It contains the two-dimensional scattering center distributions of P measured targets, and the scattering center distributions between the measured targets are separated.

[0028] Furthermore, the smaller rotation angle refers to a rotation angle within ±20°.

[0029] Step 4: Reconstruction of scattering sources in different regions

[0030] By using the two-dimensional image of the target obtained in step 3 Perform filtering to sort out the scattering center distribution of each measured target Then, the scattering field distribution of the pth target varying with angle-frequency is reconstructed through two-dimensional fast inverse Fourier transform. Finally, the radar cross section of the corresponding component can be obtained through calibration processing.

[0031] Beneficial effects of the present invention:

[0032] 1) The small-angle multi-region scattering source reconstruction method based on fast Fourier transform proposed in the present invention can be applied to the scattering measurement of multiple targets, thereby improving the test efficiency;

[0033] 2) The conventional imaging algorithm undergoes interpolation processing, which reduces the accuracy of subsequent reconstruction of scattering sources based on imaging. The present invention does not require interpolation processing, thereby improving the accuracy of scattering source reconstruction;

[0034] 3) The present invention is based on fast Fourier transform, and the algorithm is fast, which reduces the calculation time required for imaging processing. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is a flowchart of the implementation process of the present invention;

[0036] Figure 2 It is a schematic diagram of receiving scattered echo data in a rotation mode according to the present invention;

[0037] Figure 3 To obtain spatial spectrum information of received scattered echo data in the rotation mode of the present invention;

[0038] Figure 4 This is a layout diagram of the targets to be measured according to an embodiment of the present invention, which includes three targets;

[0039] Figure 5It is a two-dimensional imaging based on fast Fourier transform according to an embodiment of the present invention; wherein a is a two-dimensional imaging of multiple targets; b is a two-dimensional imaging of the first target extracted by filtering; c is a two-dimensional imaging of the second target extracted by filtering; d is a two-dimensional imaging of the third target extracted by filtering;

[0040] Figure 6 : is the scattering field distribution of the target according to the embodiment of the present invention as the frequency changes; wherein a is the scattering field frequency curve of multiple targets; b is a comparison diagram of the theoretical scattering field distribution and the reconstructed scattering field distribution of the first target; c is a comparison diagram of the theoretical scattering field distribution and the reconstructed scattering field distribution of the second target; d is a comparison diagram of the theoretical scattering field distribution and the reconstructed scattering field distribution of the third target;

[0041] Figure 7 1 is the scattering field distribution of the target according to the embodiment of the present invention as the azimuth angle changes; wherein a is the azimuth angle distribution of the scattering fields of multiple targets; b is a comparison diagram of the theoretical scattering field distribution and the reconstructed scattering field distribution of the first target; c is a comparison diagram of the theoretical scattering field distribution and the reconstructed scattering field distribution of the second target; d is a comparison diagram of the theoretical scattering field distribution and the reconstructed scattering field distribution of the third target. DETAILED DESCRIPTION

[0042] The present invention is further described below with reference to the accompanying drawings and specific embodiments.

[0043] The present invention provides a small-angle multi-region scattering source reconstruction method based on fast Fourier transform. In order to further verify the effectiveness of the present invention, a simulation experiment was carried out. The simulation includes three objectives, such as Figure 4 As shown. The first target contains two points, and the coordinate positions are (0.5, -0.5) and (0.5, -1); the second target contains three points, and the coordinate positions are (-0.5, 0), (-1, -0.5), and (-1, 0.5); the third target contains four points, and the coordinate positions are (0, 1), (0.5, 1.5), (1, 0.5), and (1, 1). The specific steps of the reconstruction method are as follows Figure 1 As shown, it is mainly divided into 4 steps:

[0044] Step 1: Acquisition of scattered echo data of multiple targets

[0045] At the test distance R0, the starting frequency is f min , the termination frequency is f max , a microwave signal with a step frequency of Δf and a certain bandwidth B simultaneously transmits a small angle θ to multiple targets m The test angle interval is Δθ.

[0046] When performing the angle sweep test at a small angle, the radial resolution obtained by the signal bandwidth is

[0047] δ y =c / 2B (7)

[0048] Where c is the speed of light, and the lateral resolution obtained by rotating the test signal Doppler is

[0049] δ x =λ c / 2θ m (8)

[0050] In the formula, λ c is the wavelength corresponding to the center frequency. The maximum radial unambiguous distance is determined by the step frequency and is

[0051] W y =c / Δf (9)

[0052] The maximum lateral unambiguous distance is related to the test angle interval and the signal center frequency, which is

[0053] W x =λ c / 2Δθ (10)

[0054] According to the resolution requirements in the x and y directions, the required parameters bandwidth B and rotation angle θ are determined by equations (7) and (8): m ; Determine the radial maximum unambiguous distance W according to the target imaging area y and the maximum horizontal unambiguous distance W x , and then determine the required parameter step frequency Δf and angle interval Δθ through equations (9) and (10), where the target imaging area is greater than or equal to the target size. In this embodiment, the simulation parameters are shown in Table 1:

[0055] Table 1 Simulation parameters

[0056] Start frequency 16GHz Stop frequency 18GHz Frequency step 10MHz bandwidth 2GHz Angle range 10° Angle interval 0.1° Angle points 101 points Sweep frequency points 201 points Radial resolution 0.075 Horizontal resolution 0.05

[0057] The schematic diagram of obtaining echo signals in rotation mode is as follows: Figure 2 As shown in formula (1), the transmitted signal is established at the center of the test target. The transceiver source is located at (0, -R0), which can be expressed as shown in formula (3). The received signal at a distance R from the transceiver source is E r (t-2R / c,f,θ), expressed as equation (2), where σ(x,y) is the two-dimensional scattering center distribution of the target, which is not only a function of the target coordinates (x, y), but also a function of the frequency f and the azimuth θ. Step 2: Mix with the time reference signal to obtain a coherent received signal

[0058] The received scattered echo signal E r(t-2R / c,f,θ) is mixed with the time reference signal Ref(t), where Ref(t) is related to the test distance R0, as shown in formula (5). After mixing, a coherent received echo can be obtained, as shown in formula (4). The coherent signal E after mixing c (f,θ) contains the spatial spectrum information at the center of the target.

[0059] Step 3: 2D Fast Fourier Transform Imaging Processing

[0060] The spatial spectrum contained in the signal during the corner sweep test is fan-shaped in Cartesian coordinates, such as Figure 3 As shown in Figure 1, when the rotation angle is within ±20°, its spatial spectrum distribution can be approximated as a rectangular spectrum window, that is, the imaging echo data is two-dimensionally decoupled in the range and azimuth directions. In addition, due to θ m is small, so that cosθ≈1, sinθ≈θ, so the imaging formula derived based on equation (4) can be simplified as equation (6). If the acquired echo data are sampled at equal intervals at frequency f and angle θ, the coherent received signal can be directly subjected to a two-dimensional fast Fourier transform to obtain a two-dimensional image of the target scattering. In this embodiment, the two-dimensional imaging of the three targets is as follows: Figure 5 shown.

[0061] Step 4: Reconstruction of scattering sources in different regions

[0062] For the coherent scatter echo E r After processing (f,θ) The two-dimensional scattering center distribution of P measured targets is included in . The scattering center distributions between the measured targets are separated, so the scattering center distribution of each measured target can be sorted out by filtering. Then, a two-dimensional fast inverse Fourier transform can be performed to reconstruct the scattering field distribution of the pth target as it changes with angle-frequency.

[0063] Consider a simpler case. For any target to be measured, there exists a rectangular window such that the scattering center distribution of the target is p (x,y) is isolated from the scattering center distribution of other targets. Then the filtering function is:

[0064]

[0065] Sort out the scattering center distribution of each target under test:

[0066]

[0067] In the formula, x pmin Represents the minimum x-axis coordinate value of the pth target selection area, x pmaxRepresents the maximum x-axis coordinate value of the pth target selection area, y pmin Represents the minimum y-axis coordinate value of the pth target selection area, y pmax Represents the maximum y-axis coordinate value of the p-th target selection area.

[0068] According to the extracted The scattered field distribution of the pth target is reconstructed by the following formula:

[0069]

[0070] Finally, the radar cross section of the corresponding component can be obtained through calibration processing.

[0071] In this embodiment, the parameters of the sorting target filter are shown in Table 2.

[0072] Table 2 Sorting target filter parameters (unit: m)

[0073]

[0074] according to Figure 6 Figure 7 It can be seen that the reconstructed scattering field distributions of the three targets are highly consistent with the theoretical scattering field distributions, whether in the angular domain or the frequency domain, which illustrates the effectiveness of this method.

[0075] The present embodiment is merely illustrative and not a complete embodiment. All other embodiments improved or adjusted by a person skilled in the art are within the protection scope of the present invention.

Claims

1. A small-angle multi-region scattering source reconstruction method based on fast Fourier transform, characterized in that: First, the scattered echo data of multiple finished parts are obtained at one time within a small angle range in the rotation mode, where the transmission signal used for the test has a certain bandwidth; secondly, the received echo signal is mixed with the time reference signal to obtain a coherent echo signal, which contains the spatial spectrum information at the center of the target to be measured; then, two-dimensional imaging of multiple targets to be measured is obtained through two-dimensional fast Fourier transform; the imaging area where each target to be measured is selected to perform two-dimensional fast inverse Fourier transform separately, and the two-dimensional scattered echo signal corresponding to the single target to be measured with the angle-frequency distribution is obtained, and finally the radar scattering cross section of the corresponding target to be measured is obtained through calibration processing; The specific implementation steps of the reconstruction method are as follows: Step 1: Obtain scattered echo data of multiple targets A Cartesian coordinate system is established with the centers of multiple measured targets as the origin. At the test distance R0, that is, the transceiver source is located at (0, -R0), the transmitting signal s(t) is used to simultaneously perform a small angle θ on multiple measured targets. m The range of the corner sweep test is to obtain the received scattered echo signal E at a distance R from the transmitting and receiving source. r (t-2R / c,f,θ): E r (t-2R / c,f,θ)=∫ x ∫ y σ(x,y)e -j2πf(t-2R / c) dxdy(2) R=R0+ycosθ-xsinθ(3) Where t is time, c is the speed of light, f is the frequency of the transmitted signal, θ is the azimuth, σ(x, y) is the two-dimensional scattering center distribution of the target, and (x, y) is the target coordinate; The angle interval of the angle sweep test is Δθ, and the transmission signal has a certain bandwidth B, and its starting frequency is f min , the termination frequency is f max , the step frequency is Δf; Step 2: Mix with the time reference signal to obtain a coherent received signal The received scattered echo signal E r (t-2R / c,f,θ) is mixed with the time reference signal Ref(t) to obtain the coherent received signal E c (f,θ): Where s is the transmitted signal s(t), and the coherent received signal E after mixing is c (f,θ) contains the spatial spectrum information at the center of the measured target; Step 3: 2D Fast Fourier Transform Imaging Processing Perform a two-dimensional fast Fourier transform on the coherent received signal obtained in step 2 to obtain a two-dimensional image of the target being measured. Since θ m is small enough so that cosθ≈1, sinθ≈θ, so the imaging formula derived based on equation (4) is simplified as follows: For the coherent received signal E c After processing (f,θ) It contains the two-dimensional scattering center distribution of P measured targets, and the scattering center distributions between the measured targets are separated; Step 4: Reconstruction of scattering sources in different regions By using the two-dimensional image of the target obtained in step 3 Perform filtering to sort out the scattering center distribution of each measured target Then, the scattering field distribution of the pth target varying with angle-frequency is reconstructed through two-dimensional fast inverse Fourier transform. Finally, the radar cross section of the corresponding component is obtained through calibration processing.

2. The method for reconstructing small-angle multi-region scattering sources based on fast Fourier transform according to claim 1, characterized in that: In step 1, the transmission signal frequency f is in the range of 1-18 GHz, and a signal with a bandwidth of B is selected, where the starting frequency is f min , the termination frequency is f max , the small angle θ m The range is ±20°.

3. The method for reconstructing small-angle multi-region scattering sources based on fast Fourier transform according to claim 1, characterized in that: When performing angular sweep test at small angles, the radial resolution obtained by the signal bandwidth is: δ y =c / 2B(7) Where c is the speed of light, and the lateral resolution obtained by rotating the test signal Doppler is: d x =λ c / 2θ m (8) In the formula, λ c is the wavelength corresponding to the center frequency; the maximum radial unambiguous distance is determined by the step frequency and is: W y =c / Δf(9) The maximum lateral unambiguous distance is related to the test angle interval and the signal center frequency, which is: W x =λ c / 2Δθ(10) According to the resolution requirements in the x and y directions, the required bandwidth B and the rotation angle θ are determined by equations (7) and (8): m ; Determine the radial maximum unambiguous distance W according to the target imaging area y and the maximum horizontal unambiguous distance W x , and then determine the required step frequency Δf and angle interval Δθ through equations (9) and (10), where the target imaging area is greater than or equal to the target size.

4. The method for reconstructing small-angle multi-region scattering sources based on fast Fourier transform according to claim 1, characterized in that: In step 1, the transmitted signal s(t) is expressed as: s(t)=e j2 π ft (1)。 5. The method for reconstructing small-angle multi-region scattering sources based on fast Fourier transform according to claim 1, characterized in that: In step 2, the time reference signal Ref(t) is related to the test distance R0, specifically:

6. The method for reconstructing small-angle multi-region scattering sources based on fast Fourier transform according to claim 1, characterized in that: In step 4, taking a simple case into consideration, for any target to be measured, there exists a rectangular window such that the scattering center distribution σ of the target is p (x, y) is isolated from the scattering center distribution of other targets; then the filtering function is: Sort out the scattering center distribution of each target under test: In the formula, x pmin Represents the minimum x-axis coordinate value of the pth target selection area, x pmax Represents the maximum x-axis coordinate value of the pth target selection area, y pmin Represents the minimum y-axis coordinate value of the pth target selection area, y pmax Represents the maximum y-axis coordinate value of the p-th target selection area; According to the extracted The scattered field distribution of the pth target is reconstructed by the following formula:

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