Rapid generation method of Rayleigh speckle field based on coding metasurface

Abstract

The invention discloses a Rayleigh speckle field rapid generation method based on a coding metasurface, and the method comprises the steps: randomly generating phase codes [D1, D2,..., DX] of X groups of metasurface units, and enabling each code to correspond to an electric field of a target plane; mATLAB software is utilized, electric fields of target planes corresponding to all X codes are calculated according to the superposition principle, X groups of electric fields are included: [E1, E2,..., EX], and the amplitude of each electric field obeys Rayleigh distribution and is a Rayleigh speckle field; for each code, the phase of one metasurface unit is overturned in sequence each time, so that a new electric field is generated, the contrast ratio of the new electric field is compared with the original contrast ratio, if the contrast ratio is reduced, the change is reserved, and if the contrast ratio is not reduced, the phase of the metasurface unit is recovered to the original state; the operation is repeated until the last metasurface unit ends; and repeating until an expected contrast value is obtained or the maximum number of iterations I is reached, and outputting X phase codes [D '1, D' 2,..., D 'X], X Rayleigh speckle fields [E' 1, E '2,..., E' X] and corresponding contrast values [C1, C2,..., CX] after iteration. According to the iterative algorithm provided by the invention, the contrast ratio of the electric field is effectively reduced, so that the Rayleigh speckle field is quickly generated, and the resolution ratio of microwave phase-free imaging is improved.

Description

Technical Field

[0001] The present invention relates to the field of microwave computational imaging, and in particular to a method for quickly generating a sub-Rayleigh speckle field based on a coding metasurface. Background Art

[0002] In order to reconstruct the target, traditional microwave computational imaging usually needs to measure the amplitude and phase of the scattered echo at the same time. However, the frequency of the microwave band is relatively high, and it is difficult for coherent receivers to accurately obtain phase information, which increases the difficulty of imaging. Phaseless microwave imaging only needs to measure the amplitude information of the echo, avoiding the phase recovery problem, greatly simplifying the system, and is of great significance in some scenarios where it is difficult to measure phase information.

[0003] However, the resolution of phase-free computational imaging systems is limited by Rayleigh diffraction. Traditional microwave imaging mainly improves resolution by reducing the size of imaging units and subdividing the target scattering distribution. However, as the size of imaging units decreases, the discreteness between the radiation fields on the surfaces of adjacent units decreases, resulting in a decrease in the effective rank of the measurement matrix and deterioration of correlation, which is particularly serious in phase-free imaging that lacks phase information.

[0004] Optics can generate a Sub-Rayleigh speckle field by performing a nonlinear transformation on the electric field of the target plane, thereby improving the system resolution. However, the generation method is too complicated and requires repeated Fourier transformation between the aperture plane and the target plane, which greatly increases the system cost. Therefore, it is necessary to find a fast method for generating a Sub-Rayleigh speckle field. Summary of the invention

[0005] The object of the present invention is to provide a method for quickly generating a Sub-Rayleigh speckle field based on a coded metasurface, so as to quickly generate a Sub-Rayleigh speckle field and improve the resolution of a microwave phaseless computational imaging system.

[0006] The technical solution to achieve the purpose of the present invention is: a method for quickly generating a sub-Rayleigh speckle field based on a coded metasurface, comprising the following steps:

[0007] Step 1: Set the input parameters and randomly generate phase encodings of X groups of metasurface units [D1, D2, …, D X ], each code corresponds to the electric field of a target plane;

[0008] Step 2: Using MATLAB software, calculate the electric field of all X codes corresponding to the target plane according to the superposition principle. There are X groups of electric fields: [E1, E2, …, E X ], each electric field amplitude obeys Rayleigh distribution, which is Rayleigh speckle field;

[0009] Step 3: For each code, flip the phase of one metasurface unit in sequence each time to generate a new electric field. Compare the contrast of the new electric field with the original contrast. If the contrast is reduced, keep the change. If it is not reduced, restore the phase of the metasurface unit to its original state. Repeat this operation until the last metasurface unit ends;

[0010] Step 4: Repeat step 3 until the desired contrast value is obtained or the maximum number of iterations I is reached, and output the X phase codes after iteration [D'1, D'2, ..., D' X ], X sub-Rayleigh speckle fields [E'1,E'2,…,E' X ] and the corresponding contrast values ​​[C1,C2,…,C X ].

[0011] Furthermore, in step 1, the input parameters are set to randomly generate X sets of metasurface phase encodings [D1, D2, …, D X ], each code corresponds to the electric field of a target plane, where:

[0012] The input parameters include the number of measurements X, the distance between the hypersurface units d1, the number of hypersurface units M×N, M units per row, N units per column, the distance R from the target plane to the hypersurface, the distance d2 between the pixels on the target plane, the number of pixels on the target plane P×Q, P pixels per row, Q pixels per column, and the number of iterations I;

[0013] The phase code D of the metasurface unit is composed of a set of 0 or 1 codes with a length of M×N number of units, where 0 represents that the transmission phase of the metasurface unit is 0°, and 1 represents that the transmission phase of the metasurface unit is 180°.

[0014] Further, in step 2, using MATLAB software, we calculate X codes [D1, D2, …, D X ] corresponding to the X target plane electric fields [E1, E2, …, E X ],in:

[0015] Each element in the electric field E corresponding to the phase encoding D of the metasurface unit is calculated by the following formula:

[0016]

[0017] Among them, E pq is the electric field of the (p,q)th pixel on the target plane, E0 is the initial electric field formed by the electromagnetic wave radiated by the feed source to the metasurface, k0 is the wave vector, R1(m,n,p,q) is the distance from the metasurface unit (m,n) to the pixel (p,q), A(m,n) is the transmission coefficient of the unit (m,n), r ph(m,n) is the transmission phase of unit (m,n), that is, the phase difference determined by the phase encoding 0 or 1. pq They are pieced together into a column vector to form a radiated electric field E.

[0018] Further, in step three, for each code, the phase of a metasurface unit is flipped in sequence each time, thereby generating a new electric field, and the contrast of the new electric field is compared with the original contrast. If the contrast is reduced, the change is retained, and if it is not reduced, the phase of the metasurface unit is restored to the original state. This operation is repeated until the last metasurface unit is finished. The specific method is:

[0019] For X codes [D1,D2,…,D X ] Perform the following operation for each encoding in the metasurface unit. For each metasurface unit, if the phase encoding is 0, change it to 1; if the phase encoding is 1, change it to 0. Calculate the newly obtained electric field, compare the contrast C of the new and old electric fields, and if the contrast decreases, keep the changed result; if the contrast does not decrease, restore the changed encoding. Repeat this operation until the end of the last metasurface unit, where:

[0020] The calculation formula of contrast ratio C is:

[0021]

[0022] where I=|E| 2 is the intensity of the electric field, and <…> represents the ensemble average.

[0023] A system for rapidly generating a sub-Rayleigh speckle field based on a coded metasurface implements the method for rapidly generating a sub-Rayleigh speckle field based on a coded metasurface to achieve optimization of the metasurface radiation field for microwave computational imaging.

[0024] A computer device comprises a memory, a processor and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the method for rapidly generating a Sub-Rayleigh speckle field based on a coded metasurface is implemented to achieve rapid generation of a Sub-Rayleigh speckle field.

[0025] A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the method for rapidly generating a Sub-Rayleigh speckle field based on a coded metasurface is implemented to achieve rapid generation of a Sub-Rayleigh speckle field.

[0026] Compared with the prior art, the present invention has the significant advantage that the target plane electric field is directly optimized by using an iterative algorithm, the contrast of the target plane electric field is reduced, and a sub-Rayleigh speckle field is quickly generated, thereby improving the resolution compared with the Rayleigh speckle field generated by random coding. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 It is a flow chart of a method for rapidly generating a sub-Rayleigh speckle field based on a coded metasurface according to the present invention;

[0028] Figure 2 It is a Rayleigh speckle field randomly generated in the simulation experiment of the embodiment of the present invention and a sub-Rayleigh speckle field generated by an iterative algorithm;

[0029] Figure 3 is a functional relationship diagram of radiation electric field contrast-iteration number in a simulation experiment provided by an embodiment of the present invention;

[0030] Figure 4 These are the original scene of the simulation experiment, the reconstructed image of the Rayleigh speckle field, the reconstructed image of the sub-Rayleigh speckle field, and the lateral PSFs of the two reconstructed images of the speckle fields provided by the embodiments of the present invention, where the blue one is the Rayleigh speckle field and the red one is the sub-Rayleigh speckle field. DETAILED DESCRIPTION

[0031] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0032] A fast method for generating sub-Rayleigh speckle field based on coded metasurface, such as Figure 1 As shown, the following steps are included:

[0033] Step 1: Input parameters and randomly generate phase encodings of X groups of metasurface units [D1, D2, …, D X ], each code corresponds to the electric field of a target plane;

[0034] The input parameters include the number of measurements X, the distance between the hypersurface units d1, the number of hypersurface units M×N, M units per row, N units per column, the distance R from the target plane to the hypersurface, the distance between the target plane pixels d2, the number of target plane pixels P×Q, P pixels per row, Q pixels per column, and the number of iterations I.

[0035] The phase code D of the metasurface unit is composed of a set of 0 or 1 codes with a length of M×N number of units, where 0 represents that the transmission phase of the metasurface unit is 0°, and 1 represents that the transmission phase of the metasurface unit is 180°.

[0036] Step 2: Using MATLAB software, calculate the phase encoding [D1, D2, …, D X ] corresponding to the X electric fields [E1, E2, …, E X ],in:

[0037] Each element in the radiated electric field E corresponding to the phase encoding D of the metasurface unit is calculated by the following formula:

[0038]

[0039] Among them, E pq is the electric field of the (p,q)th pixel on the target plane, E0 is the initial electric field formed by the electromagnetic wave radiated by the feed source to the metasurface, k0 is the wave vector, R1(m,n,p,q) is the distance from the metasurface unit (m,n) to the pixel (p,q), A(m,n) is the transmission coefficient of the unit (m,n), r ph (m,n) is the transmission phase of unit (m,n), that is, the phase difference determined by the phase encoding 0 or 1. pq They are pieced together into a column vector to form a radiated electric field E.

[0040] Step 3: For each code, flip the phase of one metasurface unit in sequence each time to generate a new electric field. Compare the contrast of the new electric field with the original contrast. If the contrast is reduced, keep the change. If it is not reduced, restore the unit phase to its original state. Repeat this operation until the last metasurface unit ends, where:

[0041] The calculation formula of contrast ratio C is:

[0042]

[0043] where I=|E| 2 is the intensity of the electric field, and <…> represents the ensemble average.

[0044] Step 4: Repeat step 3 until the desired contrast value is obtained or the maximum number of iterations I is reached, and output the X phase codes after iteration [D'1, D'2, ..., D' X ], X sub-Rayleigh speckle fields [E'1,E'2,…,E' X ] and the corresponding contrast values ​​[C1,C2,…,C X ].

[0045] The present invention also provides a system for rapidly generating a sub-Rayleigh speckle field based on a coded metasurface, and implements the method for rapidly generating a sub-Rayleigh speckle field based on a coded metasurface to achieve rapid generation of a sub-Rayleigh speckle field.

[0046] A computer device comprises a memory, a processor and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the method for rapidly generating a Sub-Rayleigh speckle field based on a coded metasurface is implemented to achieve rapid generation of a Sub-Rayleigh speckle field.

[0047] A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the method for rapidly generating a Sub-Rayleigh speckle field based on a coded metasurface is implemented to achieve rapid generation of a Sub-Rayleigh speckle field.

[0048] In summary, the present invention directly optimizes the target plane electric field by using an iterative algorithm, thereby reducing the contrast of the target plane electric field and quickly generating a sub-Rayleigh speckle field, thereby improving the resolution compared with the Rayleigh speckle field generated by random coding.

[0049] Embodiment 1

[0050] In order to verify the effectiveness of the solution of the present invention, this embodiment provides a set of simulation experiments, where the imaging targets are two point targets each occupying one pixel, the interval between the two points is one pixel, and their reflectivities are both "1".

[0051] Step 1: Set the input parameters, 100 measurements, 18 GHz feed center frequency, 7.7 mm metasurface unit spacing, 20×20 metasurface antenna units, R=0.3 m from the scene center to the metasurface center, 15 mm pixel spacing, 30×30 target plane pixels, 900 pixels in total, and 120 iterations. Randomly generate 200 sets of metasurface phase codes [D1, D2, …, D 100 ], each code corresponds to the electric field of a target plane.

[0052] Step 2: Using MATLAB software, calculate the phase encoding [D1, D2, …, D 100 ] corresponding to the 100 radiated electric fields [E1, E2, …, E 100 ],in:

[0053] Each element of each radiated electric field E is calculated by the following formula:

[0054]

[0055] Among them, E pq is the electric field of the (p,q)th pixel on the target plane, E0 is the initial electric field formed by the electromagnetic wave radiated by the feed source to the metasurface, k0 is the wave vector, R1(m,n,p,q) is the distance from the metasurface unit (m,n) to the pixel (p,q), A(m,n) is the transmission coefficient of the unit (m,n), r ph (m,n) is the transmission phase of unit (m,n), that is, the phase difference determined by the phase encoding 0 or 1. pq They are pieced together into a column vector to form a radiated electric field E.

[0056] Step 3: For each code, flip the phase of one metasurface unit in sequence each time to generate a new electric field. Compare the contrast of the new electric field with the original contrast. If the contrast is reduced, keep the change. If it is not reduced, restore the unit phase to its original state. Repeat this operation until the last metasurface unit ends, where:

[0057] The calculation formula of contrast ratio C is:

[0058]

[0059] where I=|E| 2 is the intensity of the electric field, and <…> represents the ensemble average.

[0060] Step 4: Repeat step 3 until the desired contrast value is obtained or the maximum number of iterations is 120, and output the 100 phase codes [D'1, D'2, ..., D' 100 ], 100 sub-Rayleigh speckle fields [E'1,E'2,…,E' 100 ] and the corresponding contrast values ​​[C1,C2,…,C 100 ]. A Rayleigh speckle field generated by random coding is shown in Figure 2 In (a), a sub-Rayleigh speckle field generated by the iterative algorithm is shown in Figure 2 (b). The relationship between the electric field contrast and the number of iterations in the iterative process is shown in Figure 3 middle.

[0061] from Figure 3 It can be seen that the initial Rayleigh speckle field contrast C is 1.01. As the number of iterations increases, the contrast value gradually decreases. When the number of iterations reaches 120, C decreases to 0.36. Figure 3 It can also be seen that as the iteration proceeds, the contrast decreases slower and slower, so the setting of the number of iterations is also very important. Too many iterations will not bring good results, but will lead to a waste of computing resources.

[0062] The target is imaged using 100 sets of randomly encoded Rayleigh speckle fields and 100 sets of sub-Rayleigh speckle fields generated by iterative algorithms. The reconstruction algorithm uses the SPARTA phase-free algorithm. The original scene is displayed in Figure 4 (a), and the normalized imaging reconstruction results under different electric field illumination are shown in Figure 4 (b) with Figure 4 In (c), the lateral PSF of the two speckle field reconstructed images are shown in Figure 4 (d). From Figure 4It can be seen that the reflectivity of the pixel point between two points in the Rayleigh speckle field reconstructed image is 0.81, so it is considered that the two point targets cannot be distinguished, while the reflectivity of the pixel point between two points in the sub-Rayleigh speckle field reconstructed image is 0.28, so it is considered that the two point targets can be distinguished.

[0063] Numerically speaking, the resolution of the Rayleigh speckle field generated by random coding is limited by the Rayleigh diffraction limit, which is calculated as:

[0064]

[0065] Where λ is the wavelength, R is the distance from the metasurface to the target plane, and D is the size of the metasurface.

[0066] In this embodiment, σ is calculated to be 23 mm, while the target plane pixel pitch is 15 mm, so the Rayleigh speckle field cannot distinguish two point targets separated by one pixel. However, the sub-Rayleigh speckle field clearly distinguishes two point targets, indicating that the sub-Rayleigh speckle field breaks through the diffraction limit and improves the system resolution by more than 30%. Compared with the Rayleigh speckle field generated by random coding, the sub-Rayleigh speckle field generated by the iterative algorithm shows great advantages in super-resolution.

[0067] The above-described embodiment only expresses one implementation method of the present application, and its description is relatively specific and detailed, but it cannot be understood as limiting the scope of the invention patent. It should be pointed out that for ordinary technicians in this field, several modifications and improvements can be made without departing from the concept of the present application, which all belong to the protection scope of the present application. Therefore, the protection scope of the patent of this application shall be based on the attached claims.

Claims

1. A method for rapidly generating a sub-Rayleigh speckle field based on a coded metasurface, characterized in that: The following steps are involved: Step 1: Randomly generate X groups of metasurface units with phase encoding [D1, D2, …, D X ], each code corresponds to the electric field of a target plane; Step 2: Using MATLAB software, calculate the electric field of all X codes corresponding to the target plane according to the superposition principle. There are X groups of electric fields: [E1, E2, …, E X ], each electric field amplitude obeys Rayleigh distribution, which is Rayleigh speckle field; Step 3: For each code, flip the phase of one metasurface unit in sequence each time to generate a new electric field, and compare the contrast of the new electric field with the original contrast. If the contrast is reduced, keep the change; if it is not reduced, restore the phase of the metasurface unit to its original state, and repeat this operation until the last metasurface unit ends; Step 4: Repeat step 3 until the desired contrast value is obtained or the maximum number of iterations I is reached, and output the X phase codes after iteration [D'1, D'2, ..., D' X ], X sub-Rayleigh speckle fields [E'1,E'2,…,E' X ] and the corresponding contrast values ​​[C1,C2,…,C X ].

2. The method for rapidly generating a sub-Rayleigh speckle field based on a coded metasurface according to claim 1, characterized in that: Step 1: randomly generate phase codes [D1, D2, …, D X ], each code corresponds to the electric field of a target plane, where: The input parameters include the number of measurements X, the distance between the hypersurface units d1, the number of hypersurface units M×N, M units per row, N units per column, the distance R from the target plane to the hypersurface, the distance d2 between the pixels on the target plane, the number of pixels on the target plane P×Q, P pixels per row, Q pixels per column, and the number of iterations I; The phase code D of the metasurface unit is composed of a set of 0 or 1 codes of length M×N, where 0 represents that the transmission phase of the metasurface unit is 0°, and 1 represents that the transmission phase of the metasurface unit is 180°.

3. The method for rapidly generating a sub-Rayleigh speckle field based on a coded metasurface according to claim 2, characterized in that: Step 2: Using MATLAB software, calculate the electric field of all X codes corresponding to the target plane according to the superposition principle. There are X groups of electric fields: [E1, E2, …, E X ],in: Each element in the electric field E corresponding to the phase encoding D of the metasurface unit is calculated by the following formula: Among them, E pq is the electric field of the (p,q)th pixel on the target plane, E0 is the initial electric field formed by the electromagnetic wave radiated by the feed source to the metasurface, k0 is the wave vector, R1(m,n,p,q) is the distance from the metasurface unit (m,n) to the pixel (p,q), A(m,n) is the transmission coefficient of the unit (m,n), r ph (m,n) is the transmission phase of unit (m,n), that is, the phase difference determined by the phase encoding 0 or 1, and the E pq They are pieced together into a column vector to form a radiated electric field E.

4. The method for rapidly generating a sub-Rayleigh speckle field based on a coded metasurface according to claim 1, characterized in that: Step 3: For each code, flip the phase of one metasurface unit in sequence each time to generate a new electric field. Compare the contrast of the new electric field with the original contrast. If the contrast is reduced, keep the change. If it is not reduced, restore the phase of the metasurface unit to its original state. Repeat this operation until the last metasurface unit ends. The specific method is: For X codes [D1,D2,…,D X ] perform the following operation for each code in it: for each metasurface unit, if the phase code is 0, change it to 1; if the phase code is 1, change it to 0; calculate the newly obtained electric field; compare the contrast C of the new and old electric fields; if the contrast is reduced, retain the changed result; if the contrast is not reduced, restore the changed code; repeat this operation until the end of the last metasurface unit.

5. The method for rapidly generating a sub-Rayleigh speckle field based on a coded metasurface according to claim 4, characterized in that: The calculation formula of contrast ratio C is: where I=|E| 2 is the intensity of the electric field, and <…> represents the ensemble average.

6. A system for rapid generation of sub-Rayleigh speckle field based on coded metasurface, characterized in that: The method for rapidly generating a Sub-Rayleigh speckle field based on a coded metasurface as described in any one of claims 1 to 5 is implemented to achieve rapid generation of a Sub-Rayleigh speckle field.

7. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the method for rapidly generating a Sub-Rayleigh speckle field based on a coded metasurface according to any one of claims 1 to 5 is implemented to realize rapid generation of a Sub-Rayleigh speckle field.

8. A computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the method for rapidly generating a Sub-Rayleigh speckle field based on a coded metasurface according to any one of claims 1 to 5 is implemented to achieve rapid generation of a Sub-Rayleigh speckle field.

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