Space time symmetric imaging model based on RUN optimization algorithm

Abstract

The invention provides a space time symmetry imaging model based on an RUN (Runge-Kutta optimizer), the space time symmetry imaging model comprises a point light source, two groups of multilayer films and an air layer, and the two groups of multilayer films meet the PT symmetry characteristic. Light emitted by the point light source is negatively refracted between the two groups of multilayer films, so that an image is generated at the emergent end. The optimization module analyzes the image signal and adjusts the dielectric constant and thickness of the multilayer film by using an RUN optimizer. According to the invention, aberration can be effectively reduced, and ideal aberration-free imaging is realized; compared with an existing model, fewer materials are adopted, the process is simpler, and other data do not need to be set; compared with other meta-heuristic optimization algorithms, the method has the advantages that higher efficiency is shown in the PT symmetric imaging model design aspect, the convergence speed is high, the probability of falling into a local extreme value is low, the adaptability to different dielectric parameters is high, and the imaging capacity of a PT symmetric imaging system can be brought into full play.

Description

Technical Field

[0001] The present invention belongs to the field of optical imaging technology, and specifically relates to a parity-time symmetric imaging model based on a RUN optimization algorithm. The present invention is a parity-time symmetry (PT symmetry) multilayer film structure designed based on the RUN optimization algorithm, and is used to realize ideal spatial imaging of a plane lens. Background Art

[0002] Imaging is the process of accurately transforming a point source in a three-dimensional (3D) space into another three-dimensional image space. However, due to the limitations of traditional imaging systems, this process can usually only be performed on two two-dimensional (2D) planes, resulting in images that are often not completely true. Although the PT symmetry theory has provided new perspectives and progress in optical imaging, its effective application in optical imaging still faces many challenges.

[0003] Optical imaging systems often exhibit various monochromatic aberrations, such as spherical aberration, coma, and astigmatism, which make it difficult to obtain a perfect image, even for a simple object plane. Therefore, a relevant question is whether there is a theoretically completely aberration-free two-dimensional or three-dimensional optical imaging system, and whether such an ideal imaging still obeys the laws of reflection and refraction. For more than a century, it was generally believed that the only real example of a flat optical instrument is a plane mirror. However, this understanding has its limitations, because the image points produced by a plane mirror are virtual, that is, they cannot be directly projected onto a screen unless additional lenses are used (which may introduce aberrations).

[0004] The PT-symmetric system based on RUN (RUNge Kutta optimizer) exploits the symmetry of space and time and aims to achieve specific physical properties. In recent years, several optimization algorithms are commonly used for the design of PT-symmetric imaging systems, such as genetic algorithms, particle swarm optimization algorithms, and differential evolution algorithms. These methods often suffer from slow convergence or insufficient global search efficiency, which makes them challenging to use in practical applications. Summary of the invention

[0005] In view of the deficiencies in the prior art, the present invention provides a parity-time symmetric imaging model based on the RUN optimization algorithm, designs an appropriate PT symmetric system to reduce aberrations, and realizes ideal aberration-free imaging.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] The present invention provides a parity-time symmetric imaging model based on a RUN optimization algorithm, which is characterized by comprising: a point light source, two groups of multilayer films, an air layer and an optimization module; the two groups of multilayer films satisfy the PT symmetry property, and there is an air layer between the two groups of multilayer films; the light emitted by the point light source irradiates the two groups of multilayer films composed of multiple layers of lossy materials, and negative refraction occurs between the two groups of multilayer films, thereby generating an image at the output end; the optimization module analyzes the image signal and uses the RUN optimization algorithm to adjust the dielectric constant and thickness of the multilayer film.

[0008] Optionally, the optimization module uses the RUN optimization algorithm to adjust the dielectric constant and thickness of the multilayer film, specifically including the following steps:

[0009] Step 1: The sum of the reflectivity and transmittance at different angles through the multilayer film is used as the objective function of the optimization algorithm;

[0010] Step 2: Set the initial population x and the population size np, x n ,n=1,2,…,np, used to solve the dim dimension optimization problem, the size of dim depends on the number of layers of the multilayer film;

[0011] Step 3: Apply the initialized population x as input parameters to the multilayer film as its initial dielectric constant and thickness, calculate the objective function through transfer matrix and scattering matrix operations, and analyze the current global optimal solution x-best;

[0012] Step 4: Update the position of each particle in the population and adjust the optimal value x-best at the same time, apply x-best as the current optimal design parameter to the multilayer film for aberration correction, and complete the current iteration;

[0013] Step 5: Repeat steps 3 and 4. When the global optimal design parameters meet the correction requirements, the optimization design is completed.

[0014] Optionally, in step 2, the population is initialized using the following formula:

[0015] x = rand·(UB-LB)+LB;

[0016] Where x is a one-dimensional vector consisting of the dielectric constant and thickness of each film layer, LB and UB are the lower and upper boundaries of the search space, respectively, and rand is a random number in the range of [0, 1].

[0017] Optionally, step 4 specifically includes the following steps:

[0018] Step 4.1: Calculate the exploration mechanism SM using the RUN method, and then randomly generate a value rand between [0, 1]. If rand < 0.5, the particle enters the exploration phase, conducts a global search in the search space, and performs a local search near the current position. Update the position x-new according to the search results.

[0019] Step 4.2: If rand ≥ 0.5, the particle enters the exploitation phase, conducts a local search around the new position generated by the current global optimal solution and the optimal solution of each iteration, and updates the position x-new according to the search results.

[0020] Optionally, in step 4.1, the quality of the solution is enhanced through the ESQ phase.

[0021] Optionally, enhancing the quality of the solution through the ESQ phase is specifically as follows:

[0022] Generate the perturbation factor w:

[0023] w = rand(a, b)·exp(-c(rand));

[0024] In the formula, a, b, and c are constants, and rand is a random number less than 0.5. If w < 1, the particle enters the exploitation phase and obtains the new position x-new2 according to the exploitation results. If w ≥ 1, the particle enters the exploration phase and obtains the new position x-new2 according to the exploration results. If the fitness of the new solution x-new2 is not better than the current solution and satisfies the condition rand < w, a local search is performed near x-new to obtain the new position x-new.

[0025] Complete the position update by comparing the fitness of the solution of ESQ and the current optimal solution.

[0026] The beneficial effects of the present invention are as follows: (1) The parity-time symmetric imaging model based on the RUN optimization algorithm proposed by the present invention can effectively reduce aberrations and achieve ideal aberration-free imaging. (2) Compared with other existing models, the model proposed by the present invention uses less materials, has a simpler process, and does not require setting other data. (3) Compared with other existing meta-heuristic optimization methods, the present invention shows higher efficiency in the design of the PT symmetric imaging model and has a faster convergence speed. (4) The present invention has a low probability of falling into local extrema, strong adaptability to different dielectric parameters, and can fully exert the imaging ability of the PT symmetric imaging system. Description of the Drawings

[0027] Figure 1 It is a schematic structural diagram of the parity-time symmetric imaging model based on the RUN optimization algorithm of the present invention.

[0028] Figure 2It is a schematic diagram of the RUN optimization algorithm flow of the present invention.

[0029] Figure 3 This is the light field distribution diagram before optimization of the present invention.

[0030] Figure 4 This is the light field distribution diagram after optimization of the present invention. DETAILED DESCRIPTION

[0031] The technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application.

[0032] The PT symmetric system based on RUN (RUNge Kutta optimizer) uses the symmetry of space and time to achieve specific physical properties. In order to achieve this symmetry, the present invention takes a structure containing ten layers of lossy materials as an example, and sets the value of the specific parameter reflectivity R to -0.5 and the transmittance T to 0.5.

[0033] To optimize the transmission and reflection characteristics, the objective function is designed:

[0034] REFLECTION=∑(|k1-0.5|)+∑(|k2|)+∑(|k3+0.5|)+∑(|k4|) (1)

[0035] In the formula, the four coefficient factors k1, k2, k3, and k4 are the real part of transmission, the imaginary part of transmission, the real part of reflection, and the imaginary part of reflection, respectively. |k1-0.5| ensures that the real part of the transmitted wave is close to 0.5, representing the expected transmission characteristics of the system under specific conditions. |k2| ensures that the imaginary part of the transmitted wave is as small as possible. |k3+0.5| focuses on the real part of the reflected wave and makes it as close to -0.5 as possible. |k4| ensures that the imaginary part of the reflected wave is as small as possible to reduce the negative impact on the transmission characteristics of the system.

[0036] This function aims to minimize the real part of the transmittance close to 0.5 and the imaginary part as small as possible, and the real part of the reflectance close to -0.5 and the imaginary part as small as possible, so as to achieve the ideal imaging effect and ensure the superior imaging capability of the system under specific conditions.

[0037] like Figure 1As shown, the present invention proposes a parity-time symmetric imaging model based on the RUN optimization algorithm, and the overall structure is bilaterally symmetrical. The model includes: a point light source, a multilayer film, an air layer and an optimization module. The two groups of multilayer films satisfy the PT symmetry (Parity Time Symmetry) characteristic. The light emitted by the point light source is irradiated onto a film composed of ten layers of lossy materials to generate an image. The optimization module analyzes the image signal and calculates the objective function value using the RUN optimization algorithm. According to the objective function value, the dielectric constant and thickness of the multilayer film are adjusted to complete the optimization design.

[0038] like Figure 2 As shown, the optimization module uses the RUN optimization algorithm to adjust the dielectric constant and thickness of the multilayer film, including the following steps:

[0039] Step 1: The sum of the reflectivity and transmittance at different angles through the multilayer film is used as the objective function of the optimization algorithm. As the RUN algorithm continuously optimizes the design parameters, the objective function gradually becomes smaller.

[0040] Step 2: Initialize all parameters of the RUN optimizer and set the population size np. According to the dielectric parameters, set the population particle dimension and the number of optimization parameters dim; specifically, the following steps are included:

[0041] Step 2.1: Generate the initial position of the population through the initialization formula to generate the initialization population x:

[0042] x=rand(np,dim)·(UB-LB)+LB (2)

[0043] Where x is a one-dimensional vector consisting of the dielectric constant and thickness of each film layer, LB and UB are the lower and upper boundaries of the search space, respectively, and rand is a random number in the range of [0, 1].

[0044] Step 3: Apply the initialized population as input parameters to the multilayer film as its initial dielectric constant, calculate the objective function through transfer matrix and scattering matrix operations, and analyze the current global optimal solution x-best; specifically, the following steps are included:

[0045] Step 3.1: Calculate the wave number in the z direction in the material at this time based on the dielectric constant of the multilayer film and the wave number of free space and ensure that it is a positive number;

[0046] Step 3.2: Determine the electromagnetic wave mode at this time, and calculate the characteristic impedance in different modes according to the different electromagnetic wave modes. TE is the transverse electric mode, and TM is the transverse magnetic mode. The calculation methods of the characteristic impedance zc in TE and TM modes are different:

[0047] For TE mode:

[0048]

[0049] For TM mode:

[0050]

[0051] Step 3.3: Calculate layer by layer:

[0052] For each layer, the code extracts the relative permittivity ε and thickness d from the x vector. The wave number in the z direction (kzi) is calculated by the formula:

[0053]

[0054] in is the wave number in vacuum; μ is the magnetic permeability of vacuum, and θ is the angle of the light.

[0055] The phase difference (delta) of each layer is calculated as:

[0056] δ=kzi·d (6)

[0057] The matrix Mt of each layer is:

[0058]

[0059] The overall transfer matrix M is updated by multiplying it with Mt.

[0060] Final reflection and transmission coefficient calculation: After processing all layers, the code calculates the characteristic impedance of the medium beyond the last layer. The calculation is divided into two modes:

[0061] For TE mode:

[0062]

[0063] For TM mode:

[0064]

[0065] Where ηO is the wave impedance constant in vacuum. After the calculation is completed, the final reflection coefficient R and transmission coefficient T are calculated from the elements A, B, C and D of the transfer matrix:

[0066]

[0067] The objective function is further calculated according to formula (1).

[0068] Step 4: Update the position of each particle in the population and adjust the optimal value x-best, and apply x-best as the current optimal design parameter to the multilayer film to complete the current iteration. Specifically, it includes the following steps:

[0069] Step 4.1: Use the Runge-Kutta method to calculate the exploration mechanism SM. Then randomly generate a value rand between [0, 1]. If rand < 0.5, the particle will enter the exploration stage, perform a global search in the search space, and perform a local search near the current position, and update the position x-new according to the search results.

[0070] Step 4.2: If rand ≥ 0.5, the particle will enter the exploitation stage. In this stage, the particle performs a local search around the new position generated by the current global optimal solution and the optimal solution of each iteration, and updates the position x-new according to the search results.

[0071] In some embodiments, in Step 4.1, the quality of the solution is enhanced through the ESQ (ESQ-Enhanced Solution Quality) stage.

[0072] When rand < 0.5, the specific method for enhancing the quality of the solution through the ESQ stage is: generate a perturbation factor w:

[0073] w = rand(1, dim)·exp(-5·rand) (12)

[0074] In the formula, dim is the number of optimization parameters, and rand is a random number less than 0.5; if w < 1, the particle will enter the exploitation stage and obtain a new position x-new2 according to the exploitation results; if w ≥ 1, the particle will enter the exploration stage and obtain a new position x-new2 according to the exploration results; if the fitness of the new solution x-new2 is not better than the current solution and satisfies the condition rand < w, a local search will be performed near x-new to explore potential regions, thereby obtaining a new position x-new. Finally, compare the fitness of the solution of ESQ and the current optimal solution to complete the position update.

[0075] Step 5: When the global optimal design parameter meets the design requirements, complete the optimization design. If not, increase the number of iterations and return to Step 4 to continue the process.

[0076] As Figure 3 、 4 shown, where Figure 3 is the light field distribution diagram before optimization, Figure 4 is Figure 3The corresponding light field distribution diagram based on RUN optimization parameters. It can be seen that the present invention uses the sum of the reflectivity and transmittance at different angles through the multilayer film as the optimization algorithm objective function, uses the RUN algorithm to optimize the PT symmetric imaging system parameters, and obtains the optimal dielectric constant and thickness value of the multilayer film through multiple iterations of the algorithm, thereby obtaining near-ideal imaging.

[0077] The above are only preferred embodiments of the present invention, and the protection scope of the present invention is not limited to the above embodiments. All technical solutions under the concept of the present invention belong to the protection scope of the present invention. It should be pointed out that for ordinary technicians in this technical field, some improvements and modifications without departing from the principle of the present invention should be regarded as the protection scope of the present invention.

Claims

1. A parity-time symmetric imaging model based on the RUN optimization algorithm, characterized in that: Including: A point light source, two groups of multilayer films, an air layer, and an optimization module; the two groups of multilayer films satisfy PT symmetry characteristics, and there is an air layer between the two groups of multilayer films; the light emitted by the point light source irradiates the two groups of multilayer films composed of multilayer lossy materials, and negative refraction occurs between the two groups of multilayer films, so as to generate an image at the output end; the optimization module analyzes the image signal and uses the RUN optimization algorithm to adjust the dielectric constant and thickness of the multilayer film.

2. A parity-time symmetric imaging model based on the RUN optimization algorithm as claimed in claim 1, characterized in that: The optimization module uses the RUN optimization algorithm to adjust the dielectric constant and thickness of the multilayer film, specifically including the following steps: Step 1: Use the sum of the reflectivity and transmittance at different angles of the multilayer film as the objective function of the optimization algorithm; Step 2: Set the initial population x and the population size np, x n ,n=1,2,…,np, used to solve the dim dimension optimization problem, the size of dim depends on the number of layers of the multilayer film; Step 3: Apply the initialized population x as an input parameter to the multilayer film as its initial dielectric constant and thickness, calculate the objective function through transfer matrix and scattering matrix operations, and analyze the current global optimal solution x-best; Step 4: Update the position of each particle in the population and adjust the optimal value x-best at the same time. Apply x-best as the current optimal design parameter to the multilayer film to complete the current iteration; Step 5: Repeat Step 3 and Step 4. When the global optimal design parameter meets the design requirements, the optimization design is completed.

3. A parity-time symmetric imaging model based on the RUN optimization algorithm as claimed in claim 2, characterized in that: In Step 2, the population is initialized using the following formula: x = rand·(UB - LB) + LB; In the formula, x is a one-dimensional vector composed of the dielectric constant and thickness of each layer of film, LB and UB are the lower and upper boundaries of the search space respectively, and rand is a random number in the range of [0, 1].

4. A parity-time symmetric imaging model based on the RUN optimization algorithm as claimed in claim 2, characterized in that: Step 4 specifically includes the following steps: Step 4.1: Use the RUN method to calculate the exploration mechanism SM, and then randomly generate a value rand between [0, 1]. If rand < 0.5, the particle enters the exploration stage, performs a global search in the search space, and performs a local search near the current position, and updates the position x-new according to the search results; Step 4.2: If rand ≥ 0.5, the particle enters the exploitation stage, performs a local search around the current global optimal solution and the new position generated by the optimal solution of each iteration, and updates the position x-new according to the search results.

5. A parity-time symmetric imaging model based on the RUN optimization algorithm as claimed in claim 4, characterized in that: In Step 4.1, the quality of the solution is enhanced through the ESQ stage.

6. A parity-time symmetric imaging model based on the RUN optimization algorithm as claimed in claim 5, characterized in that: The enhancement of the solution quality through the ESQ stage is specifically as follows: Generate a perturbation factor w: w = rand(a, b)·exp(-c(rand)); In the formula, a, b, and c are constants, and rand is a random number less than 0.5; if w < 1, the particle enters the exploitation stage and obtains a new position x-new2 according to the exploitation result; if w ≥ 1, the particle enters the exploration stage and obtains a new position x-new2 according to the exploration result; if the fitness of the new solution x-new2 is not better than the current solution and satisfies the condition rand < w, a local search is performed near x-new to obtain a new position x-new; The position update is completed by comparing the fitness of the solution of ESQ and the current optimal solution.

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