Fast generation method of sub-airy speckle field based on coded metasurface

Abstract

The application discloses a kind of sub-Rayleigh speckle field fast generation method based on coding metasurface, the phase coding [D1, D2, …, D of X groups of metasurface units is randomly generated X ];Each coding corresponds to the electric field of a target plane;Using MATLAB software, the electric field of the target plane corresponding to all X coding is calculated according to the superposition principle, and there are X groups of electric fields: [E1, E2, …, E X ];Each electric field amplitude obeys Rayleigh distribution, and is a Rayleigh speckle field;For each coding, the phase of a metasurface unit is flipped in order 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 the contrast is not reduced, the phase of the metasurface unit is restored to the original state, and the operation is repeated until the last metasurface unit is completed;Repeat until the desired contrast value is obtained or the maximum number of iterations I is reached, output the X phase coding [D'1, D'2, …, D' X ] after iteration, X sub-Rayleigh speckle field [E'1, E'2, …, E' X ] and the corresponding contrast value [C1, C2, …, C X ];The iterative algorithm provided by the application effectively reduces the contrast of the electric field, thereby realizing the fast generation of sub-Rayleigh speckle field and improving the resolution of microwave non-phase imaging.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of microwave computational imaging, and particularly relates to a fast generation method of sub-Rayleigh speckle field based on coded metasurface. BACKGROUND

[0002] Traditional microwave computational imaging usually needs to measure the amplitude and phase of the scattered echo at the same time in order to reconstruct the target. However, the frequency of the microwave band is high, and it is difficult for the coherent receiver to accurately obtain the phase information, which increases the difficulty of imaging. The phaseless microwave imaging only needs to measure the amplitude information of the echo, avoids the phase recovery problem, greatly simplifies the system, and has important significance in some scenes where it is difficult to measure the phase information.

[0003] However, the resolution of the phaseless computational imaging system is limited by Rayleigh diffraction. Traditional microwave imaging mainly improves the resolution by reducing the size of the imaging unit and subdividing the target scattering distribution. However, with the reduction of the size of the imaging unit, the discreteness between the radiation fields of adjacent unit surfaces decreases, resulting in a decrease in the effective rank number of the measurement matrix and a deterioration of the correlation, which is particularly serious in the phaseless imaging without phase information.

[0004] Optics can generate sub-Rayleigh speckle field by performing nonlinear transformation on the target plane electric field, and improve the system resolution. However, the generation method is too complex, and needs to repeatedly perform Fourier transform between the aperture plane and the target plane, which greatly increases the system cost. Therefore, it is necessary to find a fast generation method of sub-Rayleigh speckle field. SUMMARY

[0005] The purpose of the present application is to provide a fast generation method of sub-Rayleigh speckle field based on coded metasurface, so as to quickly generate sub-Rayleigh speckle field and improve the resolution of the microwave phaseless computational imaging system.

[0006] The technical solution for achieving the purpose of the present application is as follows: a fast generation method of sub-Rayleigh speckle field based on coded metasurface, comprising the following steps:

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

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

[0009] Step 3: For each encoding, sequentially flip the phase of one metasurface unit at a time to generate a new electric field. Compare the contrast of the new electric field with the original contrast. If the contrast decreases, retain the change; otherwise, restore the phase of the metasurface unit to its original state. Repeat this operation until the last metasurface unit is used.

[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 [D'1, D'2, ..., D'] after iteration. X X Rayleigh speckle fields [E'1, E'2, ..., E'] X ] and the corresponding contrast values ​​[C1, C2, ..., C X ].

[0011] Further, in step one, set the input parameters and randomly generate X sets of phase codes for the metasurfaces [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 spacing between metasurface units d1, the number of metasurface units M×N, M units per row, N units per column, the distance from the target plane to the metasurface R, the pixel spacing between the target plane d2, 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 consists of a set of 0 or 1 codes of length M×N, where 0 represents the transmission phase of the metasurface unit is 0° and 1 represents the transmission phase of the metasurface unit is 180°.

[0014] Furthermore, in step two, using MATLAB software, X codes [D1, D2, ..., D] are calculated based on the superposition principle. X The corresponding 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 Let R1(m,n,p,q) be the electric field at the (p,q)-th pixel on the target plane, E0 be the initial electric field formed by the electromagnetic wave radiated from the feed source onto the metasurface, k0 be the wave vector, R1(m,n,p,q) be the distance from the metasurface element (m,n) to the pixel (p,q), A(m,n) be the transmission coefficient of the element (m,n), and r ... R0 be the initial electric field formed by the electromagnetic wave radiated from ph(m,n) is the transmission phase of unit (m,n), that is, the phase difference determined by phase coding 0 or 1. E pq is composed of a column vector to form a radiation electric field E.

[0018] Further, step three, 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 the contrast is not reduced, restore the phase of the metasurface unit to the original state. Repeat the operation until the last metasurface unit ends, and the specific method is:

[0019] For each code in X codes [D1, D2, …, D X ], the following operation is performed, 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 new electric field, compare the contrast C of the new and old electric fields, if the contrast is reduced, keep the change result, if the contrast is not reduced, restore the changed code. Repeat the operation until the last metasurface unit ends, wherein:

[0020] The contrast C is calculated according to the formula

[0021]

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

[0023] A coded metasurface-based sub-Rayleigh speckle field fast generation system implements the coded metasurface-based sub-Rayleigh speckle field fast generation method, and realizes optimization of a metasurface radiation field for microwave computational imaging.

[0024] A computer device includes a memory, a processor, and a computer program stored on the memory and executable on the processor, and when the processor executes the computer program, the coded metasurface-based sub-Rayleigh speckle field fast generation method is implemented, and fast generation of a sub-Rayleigh speckle field is realized.

[0025] A computer readable storage medium has a computer program stored thereon, and when the computer program is executed by a processor, the coded metasurface-based sub-Rayleigh speckle field fast generation method is implemented, and fast generation of a sub-Rayleigh speckle field is realized.

[0026] Compared with the prior art, the present application has the following advantages: by using an iterative algorithm to directly optimize the target plane electric field, 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 a Rayleigh speckle field generated by random coding. BRIEF DESCRIPTION OF DRAWINGS

[0027] Figure 1 is a flow chart of the method for fast generation of sub-Rayleigh speckle field based on coded metasurface according to the present application;

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

[0029] Figure 3 is a graph of the function relationship between the contrast of the electric field and the number of iterations in the simulation experiment provided by an embodiment of the present application;

[0030] Figure 4 is a reconstructed image of the original scene, a reconstructed image of the Rayleigh speckle field, a reconstructed image of the sub-Rayleigh speckle field and the lateral PSF of the reconstructed images of the two speckle fields provided by an embodiment of the present application, wherein the blue color is the Rayleigh speckle field and the red color is the sub-Rayleigh speckle field. DETAILED DESCRIPTION

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

[0032] A method for fast generation of sub-Rayleigh speckle field based on coded metasurface, as shown in Figure 1 , comprises the following steps:

[0033] Step one: input parameters, randomly generate X sets of phase encoding [D1, D2, …, D X ] of metasurface units, each encoding corresponds to an electric field of a target plane;

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

[0035] The phase encoding D of the metasurface unit is composed of a group of 0 or 1 encodings with a length of M×N unit number, wherein 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 two, using MATLAB software, calculating X electric fields [E1, E2, …, E X ] corresponding to X sets of phase encoding [D1, D2, …, D X ] of metasurface units according to the superposition principle, wherein:

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

[0038]

[0039] wherein E pq is the electric field of the (p, q)th pixel point on the target plane, E0 is the initial electric field formed by the feed source radiation electromagnetic wave 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 point (p, q), A(m, n) is the transmission coefficient of the unit (m, n), r ph (m, n) is the transmission phase of the unit (m, n), that is, the phase difference determined by the phase coding 0 or 1. The E pq of all pixel points is combined into a column vector to form a radiation electric field E.

[0040] Step three: for each coding, 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 not, restore the phase of the unit to the original state. Repeat the operation until the last metasurface unit, wherein:

[0041] The contrast C is calculated by the formula

[0042]

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

[0044] Step four: repeat step three until the desired contrast value is obtained or the maximum iteration number I is reached, output the X phase codings [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 application also provides a sub-Rayleigh speckle field fast generation system based on coded metasurface, which implements the sub-Rayleigh speckle field fast generation method based on coded metasurface to realize the fast generation of sub-Rayleigh speckle field.

[0046] A computer device includes a memory, a processor and a computer program stored on the memory and executable on the processor, when the processor executes the computer program, the sub-Rayleigh speckle field fast generation method based on coded metasurface is implemented to realize the fast generation of sub-Rayleigh speckle field.

[0047] A computer readable storage medium, having stored thereon a computer program, which, when executed by a processor, implements the method for fast generation of sub-Rayleigh speckle field based on coded metasurface.

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

[0049] Embodiment one

[0050] In order to verify the effectiveness of the scheme of the present application, a set of simulation experiments are provided in this embodiment, and the imaging target is two point targets each occupying one pixel point, and the interval between the two points is one pixel point, and the reflectivity of each point target is "1".

[0051] Step one: set the input parameters, the number of measurements is 100 times, the center frequency of the feed source is 18GHz, the metasurface unit spacing is 7.7mm, the metasurface antenna is designed as 20*20 units, the distance from the scene center to the metasurface center is R=0.3m, the pixel point spacing is 15mm, the target plane pixel point is 30*30, a total of 900 pixel points, and the iteration number is 120 times. 200 groups of phase codes [D1, D2, …, D 100 ] of the metasurface are randomly generated, and each code corresponds to an electric field of a target plane.

[0052] Step two, using MATLAB software, according to the superposition principle, the 100 radiation electric fields [E1, E2, …, E 100 ] corresponding to the 100 phase codes [D1, D2, …, D 100 ] of the metasurface units are calculated, wherein:

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

[0054]

[0055] Wherein, E pq is the electric field of the (p, q)th pixel point on the target plane, E0 is the initial electric field formed by the radiation electromagnetic wave of 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 point (p, q), A(m, n) is the transmission coefficient of the unit (m, n), and r ph (m, n) is the transmission phase of the unit (m, n), that is, the phase difference determined by the phase code 0 or 1. All pixel points E pq are spliced into a column vector to form a radiation electric field E.

[0056] Step three: flip the phase of one metasurface unit at a time in order for each encoding, so that a new electric field is generated. Compare the contrast of the new electric field with the original one, if the contrast is reduced, keep the change, if not, restore the phase of the unit to the original state. Repeat the operation until the last metasurface unit is finished, wherein:

[0057] The contrast C is calculated as

[0058]

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

[0060] Step four: repeat step three until the desired contrast value is obtained or the maximum number of iterations 120 is reached, output the 100 phase encodings [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 ] after iteration. A Rayleigh speckle field generated by random encoding is shown in Figure 2 (a), a sub-Rayleigh speckle field generated by the iterative algorithm is shown in Figure 2 (b). The relationship between the contrast of the electric field and the number of iterations in the iterative process is shown in Figure 3 .

[0061] As can be seen from Figure 3 , the initial Rayleigh speckle field contrast C is 1.01, and as the number of iterations increases, the contrast value gradually decreases, and when the number of iterations reaches 120, C decreases to 0.36. As can also be seen from Figure 3 , as the iteration proceeds, the contrast decreases more and more slowly, so the number of iterations is also very important, too many iterations cannot bring good results, but will lead to waste of computing resources.

[0062] Imaging of the target is performed using 100 groups of Rayleigh speckle fields generated by random encoding and 100 groups of sub-Rayleigh speckle fields generated by the iterative algorithm, respectively, and the SPARTA phaseless algorithm is used for reconstruction. The original scene is shown in Figure 4 (a), and the normalized imaging reconstruction results under different electric field irradiation are shown in Figure 4 (b) and Figure 4 (c), respectively. The lateral PSF of the reconstructed images of the two speckle fields is shown in Figure 4 (d). From Figure 4It can be seen that the reflectivity of the pixel points between the two points in the Rayleigh speckle field reconstruction image is 0.81, so it is considered that the two point targets cannot be distinguished, and the reflectivity of the pixel points between the two points in the sub-Rayleigh speckle field reconstruction image is 0.28, so it is considered that the two point targets can be distinguished.

[0063] Numerically, the resolution of the Rayleigh speckle field generated by random coding is limited by the Rayleigh diffraction limit, and the calculation formula is:

[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, and the pixel point spacing of the target plane is 15 mm, so the Rayleigh speckle field cannot distinguish two point targets separated by one pixel point. The sub-Rayleigh speckle field clearly distinguishes the 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 has great advantages in super-resolution.

[0067] The above-described embodiments only express one embodiment of the present application, and the description is more specific and detailed, but it cannot be understood as limiting the scope of the patent. It should be noted that for ordinary skilled persons in the art, without departing from the concept of the present application, a number of modifications and improvements can be made, which are all within the scope of the present application. Therefore, the scope of protection of the patent of the present application should be subject to the appended claims.

Claims

1. A method for rapid generation of Rayleigh speckle fields based on coded metasurfaces, characterized in that, Includes the following steps: Step 1: Randomly generate the phase codes [D1, D2, ..., D] of X groups of metasurface units. X Each code corresponds to the electric field of a target plane; Step 2: Using MATLAB software, calculate the electric field of the target plane corresponding to all X codes based on the superposition principle. There are X sets of electric fields: [E1, E2, ..., E X Each electric field amplitude follows a Rayleigh distribution, which is a 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. Compare the contrast of the new electric field with the original contrast. If the contrast decreases, retain the change. If it does not decrease, restore the phase of the metasurface unit to its original state. 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 [D'1, D'2, ..., D'] after iteration. X X Rayleigh speckle fields [E'1, E'2, ..., E'] X ] and the corresponding contrast values ​​[C1, C2, ..., C X ]; in, Step 1: Randomly generate the phase codes [D1, D2, ..., D] of X groups of metasurface units. X Each code corresponds to the electric field of a target plane, where: The input parameters include the number of measurements X, the spacing between metasurface units d1, the number of metasurface units M×N, M units per row, N units per column, the distance from the target plane to the metasurface R, the pixel spacing between the target plane d2, 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 consists of a set of 0 or 1 codes of length M×N, where 0 represents the transmission phase of the metasurface unit is 0° and 1 represents the transmission phase of the metasurface unit is 180°. Step two: Using MATLAB software, calculate the electric field of all X codes corresponding to the target plane based on the superposition principle. There are X sets 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 Let R1(m,n,p,q) be the electric field at the (p,q)-th pixel on the target plane, E0 be the initial electric field formed by the electromagnetic wave radiated from the feed source onto the metasurface, k0 be the wave vector, R1(m,n,p,q) be the distance from the metasurface element (m,n) to the pixel (p,q), A(m,n) be the transmission coefficient of the element (m,n), and r ... R0 be the initial electric field formed by the electromagnetic wave radiated from ph (m,n) represents the transmission phase of unit (m,n), i.e., the phase difference determined by phase encoding 0 or 1, which applies to the E values ​​at all pixels. pq These vectors are combined to form a column vector, which constitutes a radiated electric field E.

2. The method for rapid generation of Rayleigh speckle fields based on coded metasurfaces according to claim 1, characterized in that, Step 3: For each encoding, sequentially flip the phase of one metasurface unit at a time to generate a new electric field. Compare the contrast of the new electric field with the original contrast. If the contrast decreases, retain the change; otherwise, restore the phase of the metasurface unit to its original state. Repeat this operation until the last metasurface unit is used. The specific method is as follows: For X codes [D1, D2, ..., D X For each code in the [], perform the following operation: 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 and compare the contrast C between the old and new electric fields. If the contrast decreases, retain the changed result; if the contrast does not decrease, restore the changed code. Repeat this operation until the last metasurface unit ends.

3. The method for rapid generation of Rayleigh speckle fields based on coded metasurfaces according to claim 2, characterized in that, The formula for calculating contrast ratio C is: where I=|E| 2 It represents the electric field strength value, and <...> indicates the ensemble average.

4. A rapid generation system for Rayleigh speckle fields based on coded metasurfaces, characterized in that, Implement the rapid generation method of Rayleigh speckle field based on coded metasurface as described in any one of claims 1-3 to achieve rapid generation of Rayleigh speckle field.

5. 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, it implements the rapid generation method for Rayleigh speckle fields based on coded metasurfaces as described in any one of claims 1-3, thereby achieving rapid generation of Rayleigh speckle fields.

6. A computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, it implements the rapid generation method for Rayleigh speckle fields based on coded metasurfaces as described in any one of claims 1-3, thereby realizing the rapid generation of Rayleigh speckle fields.

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