High-contrast target super-resolution imaging method based on orbital angular momentum

Abstract

The invention belongs to the technical field of two-dimensional electromagnetic inverse scattering imaging, and discloses a high-contrast target super-resolution imaging method based on orbital angular momentum, and compared with traditional electromagnetic wave inverse scattering imaging, OAM electromagnetic waves carry orbital angular momentum in the propagation process, orthogonality exists between the OAM electromagnetic waves in different modes, and the OAM electromagnetic waves carry orbital angular momentum in the propagation process. According to the method, more known information can be provided for the electromagnetic inverse scattering problem, so that the imaging accuracy and resolution are improved. In a two-dimensional inverse scattering model, an OAM electromagnetic wave generated by using a uniform circular ring array is used as an incident field in an imaging model. And a contrast initial value is obtained through Born approximation and is used as an initial contrast value of the CIE-I inversion model. The initial contrast value contains evanescent wave information of a related target, and super-resolution imaging can be realized through three rounds of optimization iteration. According to the method, super-resolution imaging of a high-contrast target can be realized.

Description

Technical Field

[0001] The invention belongs to the technical field of two-dimensional electromagnetic inverse scattering imaging, and in particular relates to a high-contrast target super-resolution imaging method based on orbital angular momentum. Background Art

[0002] Electromagnetic inverse scattering (ISPs) imaging is widely used in remote sensing, oil exploration, partition imaging, and medical imaging. The electromagnetic inverse scattering problem aims to reconstruct the position, geometry, and constitutive parameters of the scatterer target in the region of interest using the known incident field and the scattered field information received by the receiver. Since the number of receiving antennas is much smaller than the number of discretized unknowns, the electromagnetic inverse scattering problem presents an inherent pathological nature; at the same time, the multiple inverse scattering effects of electromagnetic waves inside the object lead to serious nonlinearity, which poses great challenges to the solution of the problem. To address these challenges, the solutions to the nonlinear inverse scattering problem can generally be divided into two categories: linear inversion methods and nonlinear iterative methods. The linear inversion method is usually based on the Born approximation and is suitable for dealing with weak scatterers. By ignoring the multiple scattering effects in the region of interest, the total scattered field in the region of interest is approximated as the incident field for inversion. However, with the increase of the dielectric constant, the influence of the multiple scattering effects in the region of interest becomes significant, making such linear methods only applicable to weak scatterers. Nonlinear iterative methods transform the inverse problem into an optimization problem, by updating parameters to minimize the objective function, such as contrast source inversion (CSI) and subspace optimization method (SOM). These LSIE model-based methods are suitable for medium scatterers, but may fall into local solutions when dealing with strong scatterers with high contrast or large size. Summary of the invention

[0003] The present invention aims to provide a high-contrast target super-resolution imaging method based on orbital angular momentum to solve the above-mentioned technical problems.

[0004] In order to solve the above technical problems, the specific technical solution of a high-contrast target super-resolution imaging method based on orbital angular momentum of the present invention is as follows:

[0005] A high-contrast target super-resolution imaging method based on orbital angular momentum comprises the following steps:

[0006] Step 1: In a two-dimensional electromagnetic inverse scattering model, a uniform circular ring array with a radius of 3*λ is used to generate OAM electromagnetic waves of different modes. The OAM electromagnetic waves of different modes illuminate the target in the region of interest, and the receiver detects the scattered field data, where λ is the wavelength;

[0007] Step 2, using the orbital angular momentum diffraction tomography (OAM-DT) method, after obtaining the scattered field data, the initial value information of the contrast is obtained by the Born approximation;

[0008] Step 3: After obtaining the initial information of the contrast, the target area is inverted and imaged by the electromagnetic inverse scattering nonlinear imaging FBE-CIE-I method to obtain the target information and realize super-resolution imaging.

[0009] Furthermore, the step 1 includes the following specific steps:

[0010] The incident field of OAM electromagnetic wave generated by the uniform circular ring array is:

[0011]

[0012] The phase difference between adjacent emission sources l represents the topological charge, also known as the OAM electromagnetic wave mode number.

[0013] Furthermore, the step 2 includes the following specific steps:

[0014] The scattered field after Born approximation under the incidence of OAM electromagnetic wave is:

[0015]

[0016] The Tikhonov regularization method is used to solve the contrast χ to obtain the initial value of the contrast:

[0017] χ=(A * ·A+αI * I) -1 ·A * ·E s (3)

[0018] Furthermore, the step 3 includes the following specific steps:

[0019] In FBE-CIE-I, the contrast source function is expressed by a discrete Fourier basis, i.e.

[0020]

[0021] Where IDFT(·) represents the two-dimensional inverse discrete Fourier transform, vec{·} represents the vectorization operation, Represents a two-dimensional Fourier coefficient tensor, whose size is M1XM2, The four corners of the tensor contain four non-zero blocks of size MF. The non-zero elements correspond to the Fourier low-frequency components, while the zero elements correspond to the Fourier high-frequency components. The two-dimensional discrete Fourier inverse transform is recorded as The contrast source is expressed as:

[0022]

[0023] The objective equation of the inversion is defined as:

[0024]

[0025] in, They are the data equation and state equation of the CIE-I model,

[0026]

[0027] Furthermore, the detailed inversion process in step 3 includes the following steps:

[0028] Step 3.1, n = 0: Initialize parameters, calculate the corrected contrast R, initial Fourier coefficients 0

[0029] As well as the initial gradient gp,0 is set to 0, a larger value is set for β, and a suitable MF value is selected.

[0030] Step 3.2: Update coefficients using the conjugate gradient method

[0031]

[0032] Where dp,n is the step size of the nth iteration, and vp,n is the conjugate gradient direction of the nth iteration;

[0033] Step 3.3, Update the comparison source and total field

[0034] Step 3.4, update the corrected contrast by the least squares method;

[0035] Step 3.5: Update the contrast function according to the modified contrast function:

[0036] Step 3.6: Set the termination condition. If the termination condition is met, stop the iteration. Otherwise, set n=n+1.

[0037] Return to step 3.2.

[0038] The high-contrast target super-resolution imaging method based on orbital angular momentum of the present invention has the following advantages:

[0039] The high-contrast target super-resolution imaging method based on orbital angular momentum of the present invention designs an orbital angular momentum incident wave in the case of a high-contrast target, uses the Born approximation OAM-DT method to obtain the initial contrast, and the target evanescent wave information contained in the initial contrast can be fully utilized through three rounds of iterative optimization using the CIE-I inversion method. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1It is a two-dimensional electromagnetic inverse scattering model diagram;

[0041] Figure 2 Schematic diagram of amplitude distribution and phase distribution of OAM electromagnetic waves when different modes l = 1, 2, 3;

[0042] Figure 3 This is the inversion result diagram obtained using this method. DETAILED DESCRIPTION

[0043] In order to better understand the purpose, structure and function of the present invention, the present invention is described below in conjunction with the accompanying drawings.

[0044] The high-contrast target super-resolution imaging method based on orbital angular momentum is described in further detail.

[0045] In order to solve the highly nonlinear problem, a new integral equation (NIE) based on the LSIE model is proposed.

[0046] A new inverse scattering method, followed by the Fourier basis expansion integral contraction equation inversion method (FBE-CIE-

[0047] I) effectively suppresses the nonlinearity caused by the multiple scattering effect and provides a method for dealing with strong scatterers.

[0048] New solutions.

[0049] Electromagnetic waves carrying orbital angular momentum (OAM) can be used to generate

[0050] Electromagnetic inverse scattering problems provide more known information, thereby improving the accuracy and resolution of imaging.

[0051] The resolution is a key indicator for evaluating the performance of electromagnetic inverse scattering imaging algorithms. According to the Rayleigh criterion, the resolution is usually

[0052] Limited by half wavelength (0.5λ). This is due to the diffraction effect, which makes it difficult to

[0053] It is difficult to distinguish two independent scatterers within a certain distance. If the resolution can exceed the Rayleigh limit, it is called

[0054] Super-resolution imaging. To solve the problem of super-resolution imaging of high-contrast targets, we proposed a new super-resolution imaging method that combines OAM super-resolution imaging technology with the CIE-I model.

[0055] The high-contrast target super-resolution imaging method based on orbital angular momentum of the present invention comprises the following steps:

[0056] Step 1: In a two-dimensional electromagnetic inverse scattering model, a uniform circular ring array with a radius of 3*λ is used to generate OAM electromagnetic waves of different modes. The OAM electromagnetic waves of different modes illuminate the target in the area of ​​interest, and the receiver detects the scattered field data, where λ is the wavelength.

[0057] The incident field of OAM electromagnetic wave generated by the uniform circular ring array is:

[0058]

[0059] The phase difference between adjacent emission sources l represents the topological charge, also known as the OAM electromagnetic wave mode number.

[0060] Step 2: After obtaining the scattered field data, the initial value information of the contrast is obtained by using the orbital angular momentum diffraction tomography (OAM-DT) method through the Born approximation.

[0061] The scattered field after Born approximation under the incidence of OAM electromagnetic wave is:

[0062]

[0063] The Tikhonov regularization method is used to solve the contrast χ to obtain the initial value of the contrast:

[0064] X=(A * ·A+αI * I) -1 ·A * ·E s (3)

[0065] Step 3: After obtaining the initial information of the contrast, the target area is inverted and imaged by the electromagnetic inverse scattering nonlinear imaging FBE-CIE-I method to obtain the target information and realize super-resolution imaging.

[0066] In FBE-CIE-I, the contrast source function is expressed by a discrete Fourier basis, i.e.

[0067]

[0068] Where IDFT(·) represents the two-dimensional inverse discrete Fourier transform, vec{·} represents the vectorization operation, Represents a two-dimensional Fourier coefficient tensor, whose size is M1XM2, The four corners of the tensor contain four non-zero blocks of size MF. The non-zero elements correspond to the low-frequency components of Fourier transform, while the zero elements correspond to the high-frequency components of Fourier transform. For convenience, the two-dimensional discrete Fourier transform is denoted as The contrast source can be expressed as:

[0069]

[0070] The objective equation of the inversion is defined as;

[0071]

[0072] in, They are the data equation and state equation of the CIE-I model respectively

[0073]

[0074] A detailed inversion process is summarized as follows:

[0075] Step 3.1, n = 0: Initialize parameters, calculate the corrected contrast R, initial Fourier coefficients 0 and the initial gradient gp,0 are set to 0, a larger value is set for β, and a suitable MF value is selected.

[0076] Step 3.2: Update coefficients using the conjugate gradient method

[0077]

[0078] Where dp,n is the step size of the nth iteration and vp,n is the conjugate gradient direction of the nth iteration.

[0079] Step 3.3, Update the comparison source and total field

[0080] Step 3.4: Update the corrected contrast using the least squares method.

[0081] Step 3.5: Update the contrast function according to the modified contrast function:

[0082] Step 3.6: Set the termination condition. If the termination condition is met, stop the iteration; otherwise, set n=n+1 and return to step 3.2.

[0083] like Figure 1 The DOI shown is selected as a rectangular area of ​​2*λx2*λ, and the grid division accuracy is λ / 30. 30 transmitting sources are evenly placed on a circle with a radius of 3*λ centered at the origin, and the scattered field is measured at the same position. The OAM electromagnetic wave irradiation mode L=0,±1,±2,±3,…±L, and the frequency is selected as 110GZ.

[0084] like Figure 2The figure shows the amplitude distribution and phase distribution of OAM electromagnetic waves when l = 1, 2, and 3. It can be seen that a significant feature of OAM electromagnetic waves is that their amplitude distribution presents a "donut" shape; as the OAM electromagnetic wave mode number L increases, the energy hole in the "donut" structure becomes more obvious. The phase of OAM electromagnetic waves changes periodically, and the mode number L is the number of phase change cycles.

[0085] The side length of the four uniform rectangular targets is λ / 2, the distance between the boundaries of two adjacent targets is λ / 4, and the relative dielectric constant of the target is 6, such as Figure 3 The real shape of the target and the reconstruction result obtained by the imaging algorithm are shown. It can be seen that the high-contrast target super-resolution imaging method based on orbital angular momentum can well distinguish the shapes and node constants of the four rectangular targets. Figure 3 It can be seen that when the OAM electromagnetic wave mode is selected as L=17, the approximate shape of the target is restored in the second round of three rounds of optimization, and the target shape and dielectric constant can be well reconstructed after three rounds of optimization.

[0086] It is to be understood that the present invention is described by some embodiments, and it is known to those skilled in the art that various changes or equivalent substitutions may be made to these features and embodiments without departing from the spirit and scope of the present invention. In addition, under the teachings of the present invention, these features and embodiments may be modified to adapt to specific circumstances and materials without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the scope of protection of the present invention.

Claims

1. A high-contrast target super-resolution imaging method based on orbital angular momentum, characterized in that: The following steps are involved: Step 1: In a two-dimensional electromagnetic inverse scattering model, a uniform circular ring array with a radius of 3*λ is used to generate OAM electromagnetic waves of different modes. The OAM electromagnetic waves of different modes illuminate the target in the region of interest, and the receiver detects the scattered field data, where λ is the wavelength; Step 2, using the orbital angular momentum diffraction tomography (OAM-DT) method, after obtaining the scattered field data, the initial value information of the contrast is obtained by the Born approximation; Step 3: After obtaining the initial information of the contrast, the target area is inverted and imaged by the electromagnetic inverse scattering nonlinear imaging FBE-CIE-I method to obtain the target information and realize super-resolution imaging.

2. The high-contrast target super-resolution imaging method based on orbital angular momentum according to claim 1, characterized in that: The step 1 comprises the following specific steps: The incident field of OAM electromagnetic wave generated by the uniform circular ring array is: The phase difference between adjacent emission sources l represents the topological charge, also known as the OAM electromagnetic wave mode number.

3. The high-contrast target super-resolution imaging method based on orbital angular momentum according to claim 1, characterized in that: The step 2 comprises the following specific steps: The scattered field after Born approximation under the incidence of OAM electromagnetic wave is: The Tikhonov regularization method is used to solve the contrast χ to obtain the initial value of the contrast: χ=(A * ·A+αI * ·I) -1 ·A*·E s 。 (3) 4. The high-contrast target super-resolution imaging method based on orbital angular momentum according to claim 1, characterized in that: The step 3 comprises the following specific steps: In FBE-CIE-I, the contrast source function is expressed by a discrete Fourier basis, i.e. Where IDFT(·) represents the two-dimensional inverse discrete Fourier transform, vec{·} represents the vectorization operation, Represents a two-dimensional Fourier coefficient tensor, whose size is M1XM2, The four corners of the tensor contain four non-zero blocks of size MF. The non-zero elements correspond to the Fourier low-frequency components, while the zero elements correspond to the Fourier high-frequency components. The two-dimensional discrete Fourier inverse transform is recorded as The contrast source is expressed as: The objective equation of the inversion is defined as: in, They are the data equation and state equation of the CIE-I model, .

5. The high-contrast target super-resolution imaging method based on orbital angular momentum according to claim 1, characterized in that: The detailed inversion process in step 3 includes the following steps: Step 3.1, n = 0: Initialize parameters, calculate the corrected contrast R, initial Fourier coefficients 0 As well as the initial gradient gp,0 is set to 0, a larger value is set for β, and a suitable MF value is selected. Step 3.2: Update coefficients using the conjugate gradient method Where dp,n is the step size of the nth iteration, and vp,n is the conjugate gradient direction of the nth iteration; Step 3.3, Update the comparison source and total field Step 3.4, update the corrected contrast by the least squares method; Step 3.5: Update the contrast function according to the modified contrast function: Step 3.6: Set the termination condition. If the termination condition is met, stop the iteration; otherwise, set n=n+1 and return to step 3.2.

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