A deep learning-based planar super-oscillatory lens optimization design method

Abstract

The application provides a kind of plane super-oscillating lens optimization design method based on deep learning, it is related to super-oscillating lens technical field, this method includes steps S1: initial eigenvalue definition is focused on the focusing plane of plane super-oscillating lens, when the value of focusing spot half-width on the focusing plane is greater than the diffraction limit, initial eigenvalue is defined as 0;When the half-width of focusing spot on the focusing plane is less than the diffraction limit, the initial eigenvalue is defined as the ratio of side lobe and main lobe;S2: obtain the corresponding eigenvalue of super-oscillating, construct the training set and test set of deep learning modeling, and divide the data set into small batches;S3: construct the super-oscillation eigenvalue prediction model based on convolutional neural network.The method can reduce the computing power cost required for designing plane super-oscillating lens, shorten the optimization cycle, so as to realize the rapid design of plane super-oscillating lens.

Description

Technical Field

[0001] This invention relates to the field of super-oscillating lens technology, and more specifically, to a deep learning-based method for optimizing the design of planar super-oscillating lenses. Background Technology

[0002] Optical superoscillation refers to the phenomenon where the band-limited function of an optical field oscillates at a frequency faster than its fastest Fourier component (Nano Lett., 2009, 9(3): 1249). A planar superoscillation lens is a lens that utilizes micro / nano structures to precisely control the optical field behind the lens, achieving specific interference at specific locations and thus generating a superoscillation phenomenon (Sci.Appl., 2019, 8: 56). Therefore, planar superoscillation lenses can achieve focusing beyond the diffraction limit in the far field and ultra-far field, and do not rely on subwavelength unit structures. They have significant advantages in mass production and low-cost promotion, and are currently the main means of achieving focusing beyond the diffraction limit. They have already demonstrated superior performance in achromatic, multifocal, optical needle, and optical sheet optical field customization.

[0003] The optimal design of planar superoscillating lenses mainly relies on a genetic algorithm-based optimization method, which consists of genetic algorithm optimization and numerical simulation of the superoscillating optical field. The numerical simulation of the superoscillating optical field calculates and predicts the light intensity distribution of the planar superoscillating lens's optical field based on traditional diffraction theory. The predicted results are processed by a fitness function and transformed into fitness values ​​for genetic algorithm optimization. However, the numerical simulation of the superoscillating optical field requires tedious integral iterations and repeated loop calculations, as well as a high sampling frequency to ensure prediction accuracy. Therefore, the design cycle of planar superoscillating lenses is very long, and the entire optimization cycle consumes a large amount of computational resources, hindering the application and widespread adoption of planar superoscillating lenses. Summary of the Invention

[0004] The problem addressed by this invention is how to reduce the computational cost required for the design of planar super-oscillating lenses and shorten the optimization cycle, thereby enabling the rapid design of planar super-oscillating lenses.

[0005] To address the above problems, this invention provides a deep learning-based method for optimizing the design of planar super-oscillating lenses, comprising the following steps:

[0006] S1: The initial eigenvalue is defined on the focusing plane of the planar super-oscillating lens. When the half-width at half-maximum (WHM) of the focused spot on the focusing plane is greater than the diffraction limit, the initial eigenvalue is 0. When the WHM of the focused spot on the focusing plane is less than the diffraction limit, the initial eigenvalue is the ratio of the side lobe to the main lobe.

[0007] S2: Obtain the corresponding feature values ​​of the super-oscillating lens, construct the training set and test set for deep learning modeling, and divide the dataset into mini-batches;

[0008] S3: Construct a super-oscillatory eigenvalue prediction model based on convolutional neural network. For a binary planar super-oscillatory lens, the structure of the planar super-oscillatory lens is represented by a binary vector, which serves as the input to the super-oscillatory eigenvalue prediction model based on convolutional neural network.

[0009] S4: Arrange the input of the super-oscillatory eigenvalue prediction model based on convolutional neural network into a two-dimensional matrix with a given number of rows and columns to obtain the planar super-oscillatory lens matrix feature map;

[0010] S5: Input the planar superoscillatory lens matrix feature map into a convolutional block, where each convolutional block contains a two-dimensional convolutional layer, an activation function layer, and a max pooling downsampling layer; input the output of the convolutional block into a linear block, where each linear block contains a fully connected layer and an activation function layer, and the output of the linear block is the superoscillatory feature value;

[0011] S6: Define the loss function as the average of the sum of squares of the differences between the predicted and actual values;

[0012] S7: By optimizing the algorithm and adjusting the learning rate, the predicted feature values ​​and target feature values ​​output by the super oscillating feature value prediction model based on the convolutional neural network are input into the loss function to calculate the error, and the parameters of the convolutional neural network are updated by backpropagation based on the error.

[0013] S8: Combine neural networks with genetic algorithms to output the optimal solution.

[0014] In the above method, given a planar superoscillating lens structure, the input to the superoscillating eigenvalue prediction model based on a convolutional neural network can obtain eigenvalues ​​in a very short time, thus replacing the numerical simulation process of the light field using angular spectral diffraction theory, saving a significant amount of time and computational resources. Combining the superoscillating eigenvalue prediction model based on a convolutional neural network with a genetic optimization algorithm can greatly improve optimization efficiency and shorten the design cycle by eliminating the need for numerical simulation of the light field of the planar superoscillating lens using diffraction theory.

[0015] Further, step S8 includes:

[0016] S81: Constructing a super-oscillatory eigenvalue prediction model based on convolutional neural networks. A planar super-oscillatory lens optimization design method based on deep learning is proposed. An initial population is constructed in a random manner through an initial population generator. Each individual in the initial population consists of several binary bits, representing the structure of a super-oscillatory lens.

[0017] S82: Input the binary vectors representing individuals in the initial population into the superoscillatory eigenvalue prediction model based on a convolutional neural network, and the output value is the superoscillatory eigenvalue;

[0018] S83: Input the overoscillatory eigenvalue into the fitness calculator to obtain the fitness value of the individual in the population, and input it into the termination condition judge to determine whether the optimization condition is met. If it is met, output the best individual and end; otherwise, proceed to the next step.

[0019] S84: Perform a survival-of-the-fittest operation on the population, sort the individuals according to their fitness values, select individuals with high fitness values, and eliminate individuals with low fitness values ​​according to a given ratio based on the sorting results;

[0020] S85: After step S83 is completed, perform genetic operations on individuals in the population according to probability; then, perform mutation operations on the binary population chromosomes with a small probability.

[0021] S86: After the survival of the fittest and mutation operations, the offspring population is obtained. The fitness value of each individual in the offspring population is recalculated and input into the termination condition judge to determine whether the termination condition is met. If it is met, the best individual is output and the process ends; otherwise, step S83 is executed.

[0022] Furthermore, the loss function in step S6 is expressed as:

[0023]

[0024] Among them, y i This represents the predicted value, y' i Represents the actual value.

[0025] Furthermore, the optimization algorithm in step S7 uses Adam, and the learning rate adjustment algorithm uses adaptive learning rate adjustment.

[0026] The Adam optimization algorithm updates the first and second moments of the gradient calculated in each iteration and calculates the moving average to update the current parameter information.

[0027] Adaptive learning rate adjustment involves adaptively scaling the learning rate while keeping a given metric constant.

[0028] Furthermore, if the hyperoscillatory eigenvalue prediction model of the convolutional neural network in step S7 does not converge, the hyperparameters of the convolutional kernel size, the number of convolutional blocks, the number of linear layer nodes, and the number of linear blocks are adjusted until the hyperoscillatory eigenvalue prediction model of the convolutional neural network converges.

[0029] The present invention employing the above technical solution has the following beneficial effects:

[0030] This invention quantifies the focusing behavior of a super-oscillating light field focusing plane by defining eigenvalues, and constructs a super-oscillating eigenvalue prediction model based on a convolutional neural network to achieve a fast response from the super-oscillating lens structure to its eigenvalues. The fast response capability of the super-oscillating eigenvalue prediction model based on the convolutional neural network avoids the cumbersome and time-consuming numerical simulation process of super-oscillating light fields based on diffraction theory, and realizes a planar super-oscillating lens optimization design method based on deep learning. Attached Figure Description

[0031] Figure 1 The flowchart of the deep learning-based planar super-oscillating lens optimization design method provided in the embodiments of the present invention Figure 1 ;

[0032] Figure 2 The flowchart of the deep learning-based planar super-oscillating lens optimization design method provided in the embodiments of the present invention Figure 2 ;

[0033] Figure 3 The flowchart of the deep learning-based planar super-oscillating lens optimization design method provided in the embodiments of the present invention Figure 3 ;

[0034] Figure 4 This is a schematic diagram illustrating the calculation of eigenvalues ​​in the deep learning-based planar super-oscillating lens optimization design method provided in an embodiment of the present invention.

[0035] Figure 5 This diagram illustrates the construction of a super-oscillatory eigenvalue prediction model based on a convolutional neural network in the deep learning-based planar super-oscillatory lens optimization design method provided in this embodiment of the invention. Detailed Implementation

[0036] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0037] The following are specific embodiments of the present invention, which are described in conjunction with the accompanying drawings. However, the present invention is not limited to these embodiments.

[0038] Example

[0039] This embodiment provides a deep learning-based method for optimizing the design of planar super-oscillating lenses, such as... Figure 1 As shown, this method includes the following steps:

[0040] S1: The initial eigenvalue is defined on the focusing plane of the planar super-oscillating lens. When the half-width at half-maximum (WHM) of the focused spot on the focusing plane is greater than the diffraction limit, the initial eigenvalue is 0. When the WHM of the focused spot on the focusing plane is less than the diffraction limit, the initial eigenvalue is the ratio of the side lobe to the main lobe.

[0041] S2: Obtain the corresponding feature values ​​of the super-oscillating lens, construct the training set and test set for deep learning modeling, and divide the dataset into mini-batches;

[0042] S3: Construct a super-oscillatory eigenvalue prediction model based on convolutional neural network. For a binary planar super-oscillatory lens, the structure of the planar super-oscillatory lens is represented by a binary vector, which serves as the input to the super-oscillatory eigenvalue prediction model based on convolutional neural network.

[0043] S4: Arrange the input of the super-oscillatory eigenvalue prediction model based on convolutional neural network into a two-dimensional matrix with a given number of rows and columns to obtain the planar super-oscillatory lens matrix feature map;

[0044] S5: Input the planar superoscillatory lens matrix feature map into a convolutional block, where each convolutional block contains a two-dimensional convolutional layer, an activation function layer, and a max pooling downsampling layer; input the output of the convolutional block into a linear block, where each linear block contains a fully connected layer and an activation function layer, and the output of the linear block is the superoscillatory feature value;

[0045] S6: Define the loss function as the average of the sum of squares of the differences between the predicted and actual values;

[0046] S7: By optimizing the algorithm and adjusting the learning rate, the predicted feature values ​​and target feature values ​​output by the super oscillating feature value prediction model based on the convolutional neural network are input into the loss function to calculate the error, and the parameters of the convolutional neural network are updated by backpropagation based on the error.

[0047] S8: Combine neural networks with genetic algorithms to output the optimal solution.

[0048] Specifically, such as Figure 3 and Figure 4 As shown, the system includes an initial population generator (1), a super-oscillatory eigenvalue prediction model based on a convolutional neural network (2), a fitness calculator (3), a termination condition checker (4), a survival-of-the-fittest operation (5), and genetic and mutation operations (6). The focusing behavior of the super-oscillatory light field at the focal plane is quantified by defining eigenvalues. Then, a super-oscillatory eigenvalue prediction model based on a convolutional neural network (2) is constructed to achieve a fast response from the super-oscillatory lens structure to its eigenvalues. Finally, the fast response capability of the super-oscillatory eigenvalue prediction model based on a convolutional neural network (2) avoids the cumbersome and time-consuming numerical simulation process of the super-oscillatory light field based on diffraction theory, ultimately realizing a deep learning-based planar super-oscillatory lens optimization design method. The specific steps of this method are as follows:

[0049] Step S1: Calculate the eigenvalue. The eigenvalue is defined as follows: on the focusing plane 8 of the planar super-oscillating lens 7, if the full width at half maximum (FWHM) of the focused spot on the focusing plane 8 is greater than the diffraction limit, the eigenvalue is assigned a value of 0; if the FWHM of the focused spot on the focusing plane 8 is less than the diffraction limit, the eigenvalue is defined as the ratio of the side lobe 10 to the main lobe 11.

[0050] Step S2: Collect the superoscillating lens structure and its corresponding feature values ​​to construct training and test sets for deep learning modeling. The training set size is 80,000, and the test set size is 20,000. Divide the dataset into batches, with each mini-batch size being 64.

[0051] Step S3: Construct a superoscillatory eigenvalue prediction model based on a convolutional neural network. (See also...) Figure 5 For a binary planar superoscillating lens, the planar superoscillating lens structure is represented by a binary vector with a length of 200, which serves as the input 12 to the superoscillating eigenvalue prediction model 2 based on a convolutional neural network.

[0052] Step S4: Arrange the input 12 of the super oscillatory eigenvalue prediction model 2 based on convolutional neural network into a two-dimensional matrix of 50 rows and 4 columns to obtain the planar super oscillatory lens matrix feature map 13.

[0053] Step S5: The planar hyperoscillating lens matrix feature map 13 is input into convolutional blocks 14, where each convolutional block contains a two-dimensional convolutional layer, an activation function layer, and a max-pooling downsampling layer. There are three convolutional blocks 14, where the height and width of the convolutional kernels are both 2, and the number of output channels for the convolutional layers are 4, 8, and 12, respectively. The pooling layers use max-pooling downsampling, and the height and width of the pooling kernels are both 2. The output of convolutional blocks 14 is then input into linear blocks 15, where each linear block contains a fully connected layer and an activation function layer. There are seven linear blocks 15, with the number of nodes in the linear layers being 512, 1024, 128, 32, 8, 2, and 1, respectively. All activation functions are ReLU. The output of linear blocks 15 is the hyperoscillating feature value 16.

[0054] Step S6: Define the loss function. The loss function is defined as MSE (mean squared error), which is the average of the squares of the differences between the predicted and actual values. The specific formula is as follows:

[0055]

[0056] Step S7: Select the optimization algorithm and learning rate adjustment algorithm. Use the Adam optimization algorithm and adaptive learning rate adjustment. The Adam (adaptive moment estimation) algorithm is a stochastic gradient descent optimization method based on the momentum concept. It updates the first and second moments of the gradient calculated in each iteration and calculates the moving average to update the current parameters. The adaptive learning rate adjustment method scales the learning rate to 10% of its original value when the given metric remains unchanged.

[0057] The predicted and target feature values ​​output by the hyperoscillatory feature value prediction model 2 based on a convolutional neural network are input into the loss function to calculate the error; the parameters of the convolutional neural network are updated through backpropagation based on the error. If convergence is not achieved, hyperparameters such as kernel size, number of convolutional blocks, number of linear layer nodes, and number of linear blocks can be adjusted until the loss function converges.

[0058] See Figure 2 and Figure 3 As shown, step S81: Constructing a deep learning-based planar superoscillating lens optimization design method based on the superoscillating eigenvalue prediction model 2 based on convolutional neural networks. First, an initial population is constructed randomly using the initial population generator 1, containing 30,000 individuals. Each individual consists of 200 binary bits, representing the structure of a superoscillating lens.

[0059] In step S82, the binary vector representing an individual in the population is input into the super oscillatory eigenvalue prediction model 2 based on a convolutional neural network, and the output value is the super oscillatory eigenvalue 16.

[0060] In step S83, the hyperoscillatory eigenvalue 16 is input into the fitness calculator 3 to obtain the fitness value of individuals in the population. This value is then input into the termination condition judge 4 to determine if the optimization condition is met. If it is met, the optimal individual is output and the process ends; otherwise, step 12 is executed.

[0061] Step S84: Perform a survival-of-the-fittest operation on the population. Individuals with higher fitness values ​​have a greater probability of being selected, and 20% of the weaker individuals are eliminated based on the ranking results.

[0062] In step S85: After the survival of the fittest operation 5 is completed, genetic operations 6 are performed on individuals in the population with a 70% probability. Then, mutation operations 6 are performed on the binary population chromosomes with a 1% probability.

[0063] In step S86: After completing the above operations, the offspring population is obtained. The fitness value of each individual in the offspring population is recalculated and input into the termination condition judge 4 to determine whether the termination condition is met. If it is met, the optimal individual is output and the process ends; otherwise, step S83 is executed.

[0064] By using the above method, genetic operations are continuously performed until the optimization conditions are met, at which point the optimization process ends and the optimal solution is output.

[0065] Given a planar superoscillating lens structure, inputting it into a superoscillating eigenvalue prediction model based on a convolutional neural network can yield eigenvalues ​​in a very short time, thus replacing the numerical simulation of the light field using angular spectral diffraction theory and saving significant time and computational resources. Combining the superoscillating eigenvalue prediction model based on a convolutional neural network with a genetic optimization algorithm can greatly improve optimization efficiency and shorten the design cycle by eliminating the need for numerical simulation of the light field of the planar superoscillating lens using diffraction theory.

[0066] This method quantifies the focusing behavior of the focusing plane of the super-oscillating optical field by defining eigenvalues, and constructs a super-oscillating eigenvalue prediction model based on convolutional neural network to achieve a fast response from the super-oscillating lens structure to its eigenvalues. The fast response capability of the super-oscillating eigenvalue prediction model based on convolutional neural network avoids the cumbersome and time-consuming numerical simulation process of super-oscillating optical field based on diffraction theory.

[0067] While the disclosure is as stated above, its scope of protection is not limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of this disclosure, and all such changes and modifications will fall within the protection scope of this invention.

Claims

1. A planar super-oscillating lens optimization design method based on deep learning, characterized in that, Including the following steps: S1: The initial eigenvalue is defined on the focusing plane of the planar super-oscillating lens. When the half-width at half-maximum (WHM) of the focused spot on the focusing plane is greater than the diffraction limit, the initial eigenvalue is 0. When the WHM of the focused spot on the focusing plane is less than the diffraction limit, the initial eigenvalue is the ratio of the side lobe to the main lobe. S2: Obtain the corresponding feature values ​​of the super-oscillating lens, construct the training set and test set for deep learning modeling, and divide the dataset into mini-batches; S3: Construct a super-oscillatory eigenvalue prediction model based on convolutional neural network. For a binary planar super-oscillatory lens, the structure of the planar super-oscillatory lens is represented by a binary vector, which serves as the input to the super-oscillatory eigenvalue prediction model based on convolutional neural network. S4: Arrange the input of the super-oscillatory eigenvalue prediction model based on convolutional neural network into a two-dimensional matrix with a given number of rows and columns to obtain the planar super-oscillatory lens matrix feature map; S5: Input the planar superoscillatory lens matrix feature map into a convolutional block, where each convolutional block contains a two-dimensional convolutional layer, an activation function layer, and a max pooling downsampling layer; input the output of the convolutional block into a linear block, where each linear block contains a fully connected layer and an activation function layer, and the output of the linear block is the superoscillatory feature value; S6: Define the loss function as the average of the sum of squares of the differences between the predicted and actual values; S7: By optimizing the algorithm and adjusting the learning rate, the predicted feature values ​​and target feature values ​​output by the super oscillating feature value prediction model based on the convolutional neural network are input into the loss function to calculate the error, and the parameters of the convolutional neural network are updated by backpropagation based on the error. S8: Combine neural networks with genetic algorithms to output the optimal solution; Step S8 includes: S81: Constructing a super-oscillatory eigenvalue prediction model based on convolutional neural networks. A planar super-oscillatory lens optimization design method based on deep learning is constructed by using an initial population generator to randomly construct an initial population. Each individual in the initial population consists of several binary bits, representing the structure of a super-oscillatory lens. S82: Input the binary vectors representing individuals in the initial population into the superoscillatory eigenvalue prediction model based on a convolutional neural network, and the output value is the superoscillatory eigenvalue; S83: Input the overoscillatory eigenvalue into the fitness calculator to obtain the fitness value of the individual in the population, and input it into the termination condition judge to determine whether the optimization condition is met. If it is met, output the best individual and end; otherwise, proceed to the next step. S84: Perform a survival-of-the-fittest operation on the population, sort the individuals according to their fitness values, select individuals with high fitness values, and eliminate individuals with low fitness values ​​according to a given ratio based on the sorting results; S85: After step S83 is completed, perform genetic operations on individuals in the population according to probability; then, perform mutation operations on the binary population chromosomes with a small probability. S86: After the survival of the fittest and mutation operations, the offspring population is obtained. The fitness value of each individual in the offspring population is recalculated and input into the termination condition judge to determine whether the termination condition is met. If it is met, the best individual is output and the process ends; otherwise, step S83 is executed.

2. The deep learning-based planar super-oscillating lens optimization design method according to claim 1, characterized in that, The loss function in step S6 is expressed as follows: ； in, Indicates the predicted value. Represents the actual value.

3. The deep learning-based planar super-oscillating lens optimization design method according to claim 1, characterized in that, The optimization algorithm in step S7 uses Adam, and the learning rate adjustment algorithm uses adaptive learning rate adjustment. The Adam optimization algorithm updates the first and second moments of the gradient calculated in each iteration and calculates the moving average to update the current parameter information. Adaptive learning rate adjustment involves adaptively scaling the learning rate while keeping a given metric constant.

4. The deep learning-based planar super-oscillating lens optimization design method according to claim 3, characterized in that, If the hyperoscillatory eigenvalue prediction model of the convolutional neural network in step S7 does not converge, the hyperparameters of the convolutional kernel size, the number of convolutional blocks, the number of linear layer nodes, and the number of linear blocks are adjusted until the hyperoscillatory eigenvalue prediction model of the convolutional neural network converges.

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