An automatic optimization design method for polarization optical systems based on deep learning

Abstract

A method for automatic optimization design of polarization optical system based on deep learning belongs to the field of optical design. In order to solve the problem that the influence of polarization aberration has not been considered in optical design based on deep learning, a normalized optical system sample data set is generated; deep neural network model training; network output result standardization, the established deep neural network output result is standardized, and the output after processing is the curvature, thickness variable, optical glass refractive index and Abbe number of the optical system, wherein the curvature, glass refractive index and Abbe number remain unchanged, and only the original thickness variable is standardized. Ray tracing is performed to calculate the unsupervised loss and the standardized result and the label data are used to calculate the supervised loss; the supervised loss and the supervised loss are combined; the back propagation is more like the network parameters; it is judged whether the iteration is completed, if the iteration is not completed, the previous steps are repeated until the iteration is completed, if the iteration is completed, the indicators are input into the deep neural network, and the polarization optical system is automatically optimized and designed.

Description

Technical Field

[0001] The present invention belongs to the field of optical design, and in particular relates to an automatic optimization design method for a polarization optical system based on deep learning. Background Art

[0002] The development of integrated circuits has an important impact on my country's economy, military and science and technology. Improving the integration of integrated circuits is the key to the further development of integrated circuits. The manufacturing of chips in integrated circuits relies on lithography machines. The rapid development of large-scale integrated circuits has led to the continuous development of lithography technology, and the precision requirements for lithography machines are getting higher and higher. Improving the numerical aperture of the projection objective and using a polarized light source are effective ways to improve the resolution of the system. In the lithography objective, in order to improve the resolution, the numerical aperture will be increased. When the numerical aperture is not high, the influence of polarization aberration on the imaging of the objective can be ignored, but when the numerical aperture is higher than 0.6, the polarization aberration of the system must be considered. Polarization aberration has an important influence on the imaging quality of the optical system, especially the lithography system. How to reduce the influence of polarization aberration has become a hot topic of concern and a difficult problem to be solved.

[0003] With the continuous development of deep learning, deep learning is gradually used in optical imaging optimization or optical design to realize the automatic design of optical systems, which reduces the difficulty of optical design, provides a better initial structure, shortens the time of optical design, and improves the design efficiency. It can solve the problems of traditional optical system design algorithm optimization being greatly affected by the damping factor and difficult to ensure convergence. However, in the process of studying the automatic design of optical systems using deep learning, no scholar has introduced the influence of polarization aberration into automatic optical design. Therefore, there is an urgent need for a method to automatically optimize the design of polarization optical systems using deep learning. Summary of the invention

[0004] In order to solve the problem that the influence of polarization aberration has not been considered in optical design based on deep learning, the present invention proposes an automatic optimization design method for a polarization optical system based on deep learning. The method realizes the automatic optimization design of a polarization optical system. The designed system has a small polarization degree and good imaging performance. The automatic design process reduces the participation of designers and improves efficiency.

[0005] The specific contents of the present invention are as follows:

[0006] The automatic optimization design method of polarization optical system based on deep learning comprises the following steps:

[0007] Step 1: Generate a normalized optical system sample dataset. Select a reference lens from the public lens library, normalize the reference lens, and generate corresponding feature data based on the features of the reference lens as an optical system sample dataset, which contains supervised training data and unsupervised training data.

[0008] Step 2: Deep neural network model training. According to the feature data and label data in the normalized optical system sample data set, the corresponding network model input layer and output layer are established, and the corresponding network hidden layer is constructed. The normalized optical system sample data set is input into the deep neural network model for calculation.

[0009] Step 3: Standardize the network output results. Standardize the output results of the established deep neural network. After processing, the output is the curvature, thickness variable, optical glass refractive index and Abbe number of the optical system. The curvature, glass refractive index and Abbe number remain unchanged, and only the original thickness variable is standardized.

[0010] Step 4: Perform ray tracing to calculate unsupervised loss and normalize the result with the labeled data to calculate supervised loss. Perform ray tracing on the output of the network after normalization to calculate unsupervised loss. At the same time, normalize the output result with the labeled data to calculate supervised loss, where the labeled data has been generated in step 1.

[0011] Step 5: Combine supervised loss and unsupervised loss. Perform a weighted addition of supervised loss and unsupervised loss, and finally use the result of the sum of the two as the loss of this training.

[0012] Step 6: Back propagation is more like network parameters. The network parameters are derived according to the calculated loss, and then the deep neural network parameters established earlier are calculated and updated.

[0013] Step 7: Determine whether the iteration is completed. Before training, the designer sets the corresponding number of iterations. This method sets the number of iterations to 20,000. If the iteration is not completed, repeat steps 2, 3, 4, 5, 6, and 7 until the iteration is completed. If the iteration is completed, jump directly to step 8.

[0014] Step 8: Input indicators into the deep neural network to automatically optimize the design of the polarization optical system. Input the corresponding aperture, field of view, thickness and thickness range parameters into the trained deep neural network, and the network will automatically output the corresponding polarization optical system parameters.

[0015] Beneficial effects of the present invention:

[0016] 1. The present invention performs ray tracing and polarization ray tracing based on deep learning. After the training is completed, the polarization optical system designed has a small degree of polarization and good imaging performance.

[0017] 2. The present invention uses deep learning training to achieve automatic optimization design of optical systems, which can help designers automatically design polarization optical systems and reduce labor costs.

[0018] 3. The present invention is based on deep learning for training and learning. The deep neural network after training and learning can output more polarization optical system structures at the same time, thereby improving design efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 This is a flow chart of a method for automatic optimization design of a polarization optical system based on deep learning of the present invention.

[0020] Figure 2 The network structure diagram of the deep neural network used for training and the deep neural network used for learning.

[0021] Figure 3 This is the loss curve of training during the iteration process DETAILED DESCRIPTION

[0022] The present invention is further described below with reference to the accompanying drawings and specific embodiments:

[0023] like Figure 1 As shown, the automatic optimization design method of polarization optical system based on deep learning includes the following steps:

[0024] Step 1: Generate a normalized optical system sample dataset. Select a reference lens from the public lens library, normalize the reference lens, and generate corresponding feature data as the optical system sample dataset based on the characteristics of the reference lens. The characteristics of the reference lens include the aperture, field of view, curvature, thickness, glass refraction and Abbe number of the optical system. The generated optical system sample dataset contains supervised training data and unsupervised training data. The supervised training data has corresponding label data. The label data is the reference result of the supervised training data. The label data includes the radius of curvature, thickness, and the refractive index and Abbe number of the glass. The unsupervised training data has no corresponding label.

[0025] Step 2: Deep neural network model training. According to the feature data and label data in the normalized optical system sample data set, the corresponding network model input layer and output layer are established, and a nonlinear network hidden layer containing neurons and activation functions is constructed. Then, the normalized optical system sample data set is input into the deep neural network model for calculation.

[0026] Step 3: Standardization of network output results. The output results of the established deep neural network are standardized. The processed output is the curvature, thickness variable, optical glass refractive index and Abbe number of the optical system. The curvature, glass refractive index and Abbe number remain unchanged, and only the original thickness variable is standardized. The minimum thickness between optical surfaces and the thickness range between optical surfaces in the input data are also involved in the calculation. The specific calculation formula (1) is as follows:

[0027] tout =t min +ln(1+exp(t raw -t min ))-ln(1+exp(t raw -(t range +t min ))(1)

[0028] Among them, t out is the result after thickness standardization, t raw is the original thickness variable, t min is the minimum thickness between optical surfaces, t range is the thickness range between optical surfaces.

[0029] Step 4: Perform ray tracing to calculate the unsupervised loss and normalize the results with the labeled data to calculate the supervised loss.

[0030] The output of the network after normalization is used for ray tracing to calculate the unsupervised loss. At the same time, the normalized output is combined with the label data to calculate the supervised loss, where the label data has been generated in step 1.

[0031] The output of the network after normalization is used for ray tracing to calculate the degree of polarization and spot radius, and then input into the unsupervised loss function to calculate the unsupervised loss. The specific unsupervised loss function is:

[0032]

[0033] Among them, L polarization is the size of the unsupervised loss, the subscript H represents the field of view, the subscript λ represents the wavelength, the subscript p represents the entrance pupil, and N H is the number of fields of view, N λ is the number of wavelengths, N p is the number of apertures, y Hλp is the image height at a certain wavelength and aperture in a certain field of view, Image height in a certain field of view, M H,p,λ is the degree of polarization.

[0034] While calculating the unsupervised loss, the standardized output results and the label data are input into the supervised loss function to calculate the supervised loss, where the label data has been generated in step 1. The supervised loss function is:

[0035]

[0036] Where: r i ,t out,i ,(g n,k , g v,k ) is the radius of curvature, thickness, refractive index and Abbe number of the network normalized result, ri '、t' out,i ,(g' n,k , g' v,k ) are the curvature radius, thickness variables of the reference lens and the refractive index and Abbe number label data of the glass.

[0037] Step 5: Combine supervised loss and unsupervised loss. Perform a weighted addition calculation on the supervised loss and unsupervised loss calculation values, and finally use the result of the two calculations as the final loss of this training. The specific calculation process is:

[0038] L final =L s +ω'×L polarization (4)

[0039] Among them, L final is the final loss; ω' is the weighting factor of the unsupervised loss function.

[0040] Step 6: Back propagation is more like network parameters. According to the calculated final loss, the network parameters are derived, and the network parameters are set as θ. Then the derivative of the final loss to the network parameters is Then calculate and update the parameters of the deep neural network established previously. The calculation process is: Where α is the learning rate of training.

[0041] Step 7: Determine whether the iteration is completed. Before training, the designer sets the corresponding number of iterations. If the iteration is not completed, repeat steps 2, 3, 4, 5, 6, and 7 until the iteration is completed. If the iteration is completed, jump directly to step 8.

[0042] Step 8: Input indicators into the deep neural network to automatically optimize the design of the polarization optical system. Through the repeated execution of steps 2, 3, 4, 5, 6, and 7, the training of the deep neural network model is completed. The corresponding aperture, field of view, thickness, and thickness range parameters are input into the trained deep neural network model. The network will automatically output the corresponding polarization optical system parameters, including curvature, thickness variable, refractive index of glass, and Abbe number.

[0043] Example:

[0044] The automatic optimization design method of polarization optical system based on deep learning comprises the following steps:

[0045] Step 1: Generate a normalized optical system sample data set. Select 8 groups of lenses consisting of two pieces of glass from the public lens library, and determine the minimum and maximum ranges of the generated entrance pupil diameter, field of view, minimum thickness, and thickness range based on the 8 groups of lenses. The specific data is shown in Table 1:

[0046] Table 1 The supervised data range and unsupervised data range generated by 8 sets of shots

[0047]

[0048] The first G1~G8 is the data generation range of supervised training data. Just generate 1000 sets of data according to the range. u is the data generation range of the unsupervised data, which is determined by the maximum and minimum values ​​of a feature in G1 to G8. For example, for the aperture feature, the maximum value in G1 to G8 is 0.355 and the minimum value is 0.071, then G u The range of the aperture determined in is 0.071 to 0.355. The label data is composed of corresponding data according to the curvature, thickness, glass refractive index and Abbe number of the 8 groups of lenses. The label data table is shown in Table 2:

[0049] Table 2 Label data corresponding to 8 sets of lenses

[0050]

[0051]

[0052] Step 2: Deep neural network model training. According to the feature data and label data in the normalized optical system sample data set, the corresponding network model input layer and output layer are established, and a nonlinear network hidden layer containing neurons and activation functions is constructed. Then, the normalized optical system sample data set is input into the deep neural network model for calculation.

[0053] The specific structure of the constructed deep neural network model is as follows Figure 2 The deep neural network structure consists of an input layer, an output layer, and a nonlinear hidden layer. A group of neurons and an activation function constitute a nonlinear hidden layer. In the deep neural network structure, x is the parameter of the input layer, which corresponds to the optical system aperture (EPD), field of view (FOV), and the minimum thickness between optical surfaces (t min，1 , ..., t min,j ), the thickness range between the optical surfaces (t range，1 , ..., t range，j ), y is the parameter of the output layer, corresponding to the optical surface curvature radius (r1,...,r j-1 ), original thickness variable (t raw，1 , ..., t raw，j ), normalized glass variables (g n,1 ,g v,1 ,…,g n,k ,g v,k), j is the number of optical surfaces, k is the number of glass materials, ω is the neurons in the hidden layer, and σ is the activation function. The activation function used is the SELU (scaled exponential linear units) activation function. The SELU activation function can keep the data standardized, avoid large fluctuations in the gradient, and is conducive to the convergence of the loss function.

[0054] Then, the aperture, field of view, minimum thickness between optical surfaces, and thickness range between optical surfaces generated in step 1 are input into the network for calculation.

[0055] Step 3: Standardization of network output results. Standardization of network output results. The output results of the established deep neural network are standardized. The curvature, glass refractive index and Abbe number in the output results remain unchanged. After processing, the output is the curvature, thickness variable, optical glass refractive index and Abbe number of the optical system. Only the original thickness variable is standardized, and the minimum thickness between optical surfaces and the thickness range between optical surfaces in the input data are also involved in the calculation. The specific calculation formula (1) is as follows:

[0056] t out =t min +ln(1+exp(t raw -t min ))-ln(1+exp(t raw -(t range +t min )) (1)

[0057] Among them, t out is the result after thickness standardization, t raw is the original thickness variable, t min is the minimum thickness between optical surfaces, t range is the thickness range between optical surfaces.

[0058] Step 4: Perform ray tracing to calculate the unsupervised loss and normalize the result with the label data to calculate the supervised loss. The output of the network normalization is used to perform ray tracing to calculate the polarization degree and spot radius, and then input into the unsupervised loss function to calculate the unsupervised loss. The specific unsupervised loss function is:

[0059]

[0060] Among them, L polarization is the size of the unsupervised loss, the subscript H represents the field of view, the subscript λ represents the wavelength, the subscript p represents the entrance pupil, and N H is the number of fields of view, N λ is the number of wavelengths, N p is the number of apertures, y Hλpis the image height at a certain wavelength and aperture in a certain field of view, Image height in a certain field of view, M H,p,λ In this example, the number of fields of view is 3, and the field angles are 0, 7 / 10 of the normalized field of view, and the normalized field of view; the number of wavelengths is 3, and the wavelengths are 486nm, 588nm, and 656nm.

[0061] While calculating the unsupervised loss, the standardized output results and the label data are input into the supervised loss function to calculate the supervised loss, where the label data has been generated in step 1. The supervised loss function is:

[0062]

[0063] Where: r i ,t out,i ,(g n,k , g v,k ) is the radius of curvature, thickness, refractive index and Abbe number of the network normalized result, r i '、t' out,i ,(g' n,k , g' v,k ) are the reference lens’ radius of curvature, thickness, and glass’s refractive index and Abbe number label data.

[0064] Step 5: Combine supervised loss and unsupervised loss. Perform a weighted addition calculation on the supervised loss and unsupervised loss calculation values, and finally use the result of the two calculations as the final loss of this training. The specific calculation process is:

[0065] L final =L s +ω'×L polarization (4)

[0066] Among them, L final is the final loss; ω' is the weighting factor of the unsupervised loss function. In this example, the weighting factor is set to 10.

[0067] Step 6: Back propagation is more like network parameters. Derivative the network parameters based on the calculated final loss. Here, we define the network parameters as θ, then the derivative of the final loss to the network parameters is Then calculate and update the parameters of the deep neural network established previously. The calculation process is: Where α is the learning rate of training, and the learning rate in this example is 0.0001.

[0068] Step 7: Determine whether the iteration is completed. Before training, the designer sets the corresponding number of iterations. This method sets the number of iterations to 20,000. If the iteration is not completed, repeat steps 2, 3, 4, 5, 6, and 7 until the iteration is completed. If the iteration is completed, jump directly to step 8. The loss curve of the training during the iteration process is as follows: Figure 3 As shown in the figure, the loss function converges normally. The convergence of the loss indicates that there is no overfitting in the training, and the deep neural network can correctly design a reasonable optical system structure.

[0069] Step 8: Input indicators into the deep neural network to automatically optimize the design of the polarization optical system. Through the repeated execution of steps 2, 3, 4, 5, 6, and 7, the training of the deep neural network model is completed. The corresponding aperture, field of view, thickness, and thickness range parameters are input into the trained deep neural network model. The network will automatically output the corresponding polarization optical system parameters, including curvature, thickness variable, refractive index of glass, and Abbe number. The unit of thickness is millimeter.

[0070] Table 3 Optical system structure of the trained network output

[0071]

Claims

1. A method for automatic optimization design of polarization optical systems based on deep learning, characterized in that: The method comprises the following steps: Step 1: Generate a normalized optical system sample dataset; select a reference lens from the public lens library, normalize the reference lens, and generate corresponding feature data as the optical system sample dataset based on the features of the reference lens. The dataset contains supervised training data and unsupervised training data. Step 2: Deep neural network model training: According to the feature data and label data in the normalized optical system sample data set, the corresponding network model input layer and output layer are established, and the corresponding network hidden layer is constructed, and the normalized optical system sample data set is input into the deep neural network model for calculation; Step 3: Standardize the network output results. Standardize the output results of the established deep neural network. After processing, the output is the curvature, thickness variable, optical glass refractive index and Abbe number of the optical system. The curvature, glass refractive index and Abbe number remain unchanged, and only the original thickness variable is standardized. Step 4: Perform ray tracing to calculate the unsupervised loss and the standardized result and label data to calculate the supervised loss. Perform ray tracing on the output of the network after standardization to calculate the unsupervised loss. At the same time, the standardized output result and label data are used to calculate the supervised loss, where the label data has been generated in step 1. Step 5: Combine the supervised loss and the unsupervised loss, perform a weighted addition of the supervised loss and the unsupervised loss, and finally use the result of the addition of the two as the loss of this training; Step 6: Back propagate to update the network parameters, derive the network parameters according to the calculated loss, and then calculate and update the parameters of the deep neural network established previously; Step 7: Determine whether the iteration is completed. Before training, the designer sets the corresponding number of iterations. The number of iterations set in this method is 20,000. If the iteration is not completed, repeat steps 2, 3, 4, 5, 6, and 7 until the iteration is completed. If the iteration is completed, jump directly to step 8. Step 8: Input indicators into the deep neural network to automatically optimize the design of the polarization optical system. Input the corresponding aperture, field of view, thickness and thickness range parameters into the trained deep neural network, and the network will automatically output the corresponding polarization optical system parameters.

2. The method for automatic optimization design of polarization optical system based on deep learning according to claim 1, characterized in that: The characteristics of the reference lens in step 1 include the aperture, field of view, curvature, thickness, glass refraction and Abbe number of the optical system; the label data includes the radius of curvature, thickness, and the refractive index and Abbe number of the glass.

3. The method for automatic optimization design of polarization optical system based on deep learning according to claim 1, characterized in that: The specific method of step 4 is to perform ray tracing on the output results after network standardization to calculate the degree of polarization and spot radius, and input them into the unsupervised loss function to calculate the unsupervised loss. The specific unsupervised loss function is: Among them, L polarization is the size of the unsupervised loss, the subscript H represents the field of view, the subscript λ represents the wavelength, the subscript p represents the entrance pupil, and N H is the number of fields of view, N λ is the number of wavelengths, N p is the number of apertures, y Hλp is the image height at a certain wavelength and aperture in a certain field of view, Image height in a certain field of view, M H,p,λ is the degree of polarization; While calculating the unsupervised loss, the standardized output results and the label data are input into the supervised loss function to calculate the supervised loss, where the label data has been generated in step 1. The supervised loss function is: Where: r i ,t out,i ,(g n,k , g v,k ) is the radius of curvature, thickness, refractive index and Abbe number of the network normalized result, r i '、t' out,i ,(g' n,k , g' v,k ) are the curvature radius, thickness variables of the reference lens and the refractive index and Abbe number label data of the glass.

Images