Method for generating off-axis three-mirror system easy to install and adjust based on small sample machine learning

Abstract

The invention provides a small sample machine learning-based off-axis three-reflector system generation method easy to install and adjust, relates to the technical field of optical system design, and provides a small sample machine learning-based off-axis three-reflector system generation scheme for solving the off-axis three-reflector system design problem under the requirement of rapid design and easy installation and adjustment. In order to reduce the installation and adjustment difficulty of an off-axis three-reflector system and reduce the training and data collection difficulty of machine learning, the method for training an SVR model by using a small sample data set and then automatically generating an off-axis multi-reflector system easy to install and adjust is constructed. When a data set is constructed, a small sample data collection method is designed, and the number of features in samples is reduced, so that the difficulty of construction of a training set and development of a machine learning model is reduced; then, constructing an SVR model, and training the SVR model based on the data set; and finally, generating a parameter combination of the off-axis three-mirror spherical system by using the trained SVR model, and generating the off-axis three-mirror free-form surface system based on the parameter combination.

Description

Technical Field

[0001] The present invention relates to the technical field of optical system design, and in particular to a method for generating an easy-to-install and off-axis three-mirror system based on small sample machine learning. Background Art

[0002] The off-axis three-mirror system has unique advantages such as no chromatic aberration, foldability and no center occlusion, and is widely used in various optical observation fields. Since the reflectors in the off-axis three-mirror system are generally free-form surfaces, the asymmetry of their surface shape and system structure greatly increases the difficulty of installation and adjustment. To this end, it is necessary to use an integrated processing method, that is, to fix the three reflectors on a cylindrical reference surface and then grind them as a whole. The off-axis three-mirror system manufactured using this processing method does not require secondary adjustment, thus greatly reducing the difficulty of adjustment. Therefore, it is necessary to introduce adjustment constraints in the design stage of the off-axis three-mirror system. However, although some researchers have proposed design methods that take adjustment constraints into account, these methods mainly provide targeted solutions for single design tasks. When encountering new design requirements, the entire set of design steps need to be re-implemented, which increases the cost of time investment.

[0003] Since machine learning can extract valuable patterns and relationships from a large amount of data, it can reduce the design time and cost. Therefore, some researchers have combined machine learning with the design of off-axis three-mirror systems. However, these methods have not yet considered the difficulty of adjustment in parallel during the design process. Therefore, the designed off-axis three-mirror system can theoretically meet high imaging quality, but does not have the characteristics of easy adjustment. At the same time, most of the samples used in the design methods using machine learning often contain a large number of features. When applying machine learning to the design of an easy-to-install off-axis three-mirror system, since the system needs to meet both imaging quality and adjustment constraints, there are more stringent restrictions on key features such as the position and tilt angle of the reflector. In order to enable the model to learn and capture these key features more accurately, if existing machine learning methods are used, it is usually necessary to design a larger data set to provide sufficient training samples, which increases the cost of data collection. At the same time, although the increase in the data set can ensure the diversity of data, it will increase the difficulty of tuning and the number of iterations during the training process, thereby increasing the complexity of developing machine learning models. Summary of the invention

[0004] In view of the shortcomings of the prior art, the present invention provides a method for generating an off-axis three-mirror system that is easy to install and adjust based on small sample machine learning; the method aims to automatically generate an off-axis three-mirror system that is easy to install and adjust, and reduce the difficulty of data collection and tuning.

[0005] A method for generating an easy-to-install and off-axis three-mirror system based on small sample machine learning comprises the following steps:

[0006] Step 1: Build a dataset;

[0007] The data set includes an input set and an output set; the input set includes multiple sets of design requirement parameters, i.e., multiple sets of combinations of F numbers, entrance pupil diameters, and field angles; the output set includes multiple sets of combinations of parameters of an easily mounted and adjustable off-axis three-mirror spherical imaging system, i.e., multiple sets of {r1, r2, r3, d1, d2, d3, α1, α2, α3}, wherein r1, r2, and r3 are the curvature radii of the primary mirror, the secondary mirror, and the third mirror, respectively; d1, d2, and d3 are the distances between the primary and secondary mirrors, the secondary and third mirrors, and the third mirror and the image plane, respectively; and α1, α2, and α3 are the tilt angles of the primary mirror, the secondary mirror, and the third mirror, respectively. The specific number of sets T is determined by the number of samples, T=T F ×T ED ×T FOV , T F 、T ED and T FOV are the number of samples for entrance pupil, F number and field of view respectively.

[0008] Design the comprehensive objective function of the off-axis three-mirror system, expressed as:

[0009]

[0010] Among them, r n is the curvature radius of the nth reflector; α n is the inclination angle of the nth reflector; d n represents the distance between adjacent reflectors; K is the total number of reflectors; g1 to g4 are sub-functions required to construct an off-axis three-mirror spherical imaging system that is easy to install and adjust, t1 to t4 are the weights of each sub-function, and the sub-function expressions are:

[0011]

[0012] Among them, g1 is the image quality evaluation function; g2 is the adjustment constraint function; g3 is the off-axis degree function; g4 is the margin constraint function; N is the total number of sampling rays; i is the sequence number of the sampling rays; (x i ,y i ) is the imaging point of the i-th sampling light; (HI x ,HI y ) is the coordinate of the ideal image point; S is the total number of sampling points; (x j ,y j ) is the coordinate of the sampling point; RM is the reference radius of the adjustment constraint; (x M ,y M ) is the coordinate of the reference point of the adjustment constraint; B i is a Boolean number. When the reflector does not block the light, B i =0, otherwise B i=1; l n A is the shortest distance from the reflector to the edge of the blocked beam; n is the margin value, and the reserved margin value is Q. When the current margin value is greater than Q, A n =0, otherwise A n =|QA n |.

[0013] Input the design requirement parameters, and use the search method to search for the minimum value of formula (1) to calculate the parameter combination of the off-axis three-mirror spherical imaging system that meets the adjustment constraints and converges the light rays of each field of view on the image plane; therefore, when the input set is determined, the corresponding output set is obtained;

[0014] The adjustment constraint is that all reflectors are infinitely fitted with the same cylindrical reference surface;

[0015] Step 2: Build the SVR model;

[0016] The SVR model is a support vector regression model, which is based on the regression analysis method of a support vector machine and realizes model prediction by constructing a tolerance interval;

[0017] The training loss function of the SVR model is:

[0018]

[0019] Where ω is the normal vector of the hyperplane; b is the displacement of the hyperplane; M is the number of independent variables; f(x m ) represents the SVR model for the mth input sample x m The predicted value, y m is the corresponding true value; C is the regularization parameter, l ε It is an insensitive loss function, and its expression is:

[0020]

[0021] Using RBF kernel as the kernel function, its expression is:

[0022] K(x m ,y m ) = exp(-γ||x m -y m || 2 ) (8)

[0023] Among them, γ and ε are hyperparameters in the SVR model.

[0024] Step 3: Train the SVR model;

[0025] A random search method is used to find the optimal hyperparameter combination, and the data set is divided into a training set and a test set using a cross-validation method to train the SVR model, using the maximum number of iterations as the termination condition.

[0026] Step 4: Use the trained SVR model to predict the new design requirement parameters to obtain a combination of parameters of the off-axis three-mirror spherical imaging system, and then combine it with the improved WW method to obtain an easy-to-install free-form surface off-axis three-mirror system.

[0027] The improved WW method is a free-form surface design method.

[0028] The beneficial effects of adopting the above technical solution are:

[0029] The present invention provides a method for generating an easy-to-install and off-axis three-mirror system based on small sample machine learning, which has the following beneficial effects:

[0030] 1. By combining the design of an easy-to-install and off-axis three-mirror system with machine learning, a machine learning-based design method for an easy-to-install and off-axis three-mirror system is designed. When faced with new design requirements, compared with the current method for designing an easy-to-install and off-axis three-mirror system, there is no need to re-implement the entire set of design steps, and the time investment cost is lower;

[0031] 2. By reducing the number of features contained in each sample in the data set, a small sample data set is constructed. Compared with the existing method of using machine learning to build an off-axis three-mirror system, the data collection cost is lower, the key features are more obvious, and it can help the model capture key features faster;

[0032] 3. By using a support vector regression (SVR) model adapted to a small sample data set to design an easy-to-install off-axis three-mirror system, the prediction accuracy of the system is automatically improved and the dependence on large amounts of data is reduced. Compared with traditional machine learning methods that rely on large-scale data sets, the applied SVR model shows lower model complexity in the design of off-axis three-mirror systems, so the training cost is lower and the design efficiency is higher. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is a flow chart of a method for generating an easy-to-install and off-axis three-mirror system based on small sample machine learning of the present invention;

[0034] Figure 2 It is a structural schematic diagram of an off-axis three-reaction system that is easy to install and adjust in a specific implementation manner of the present invention. DETAILED DESCRIPTION

[0035] The specific implementation of the present invention is further described in detail below in conjunction with the accompanying drawings and examples. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0036] A method for generating an easy-to-install off-axis three-mirror system based on small sample machine learning, such as Figure 1 As shown, the following steps are included:

[0037] Step 1: Build a dataset;

[0038] The data set includes an input set and an output set; the input set includes multiple sets of design requirement parameters, i.e., multiple sets of combinations of F numbers, entrance pupil diameters, and field angles; the output set includes multiple sets of combinations of parameters of an easily mounted and adjustable off-axis three-mirror spherical imaging system, i.e., multiple sets of {r1, r2, r3, d1, d2, d3, α1, α2, α3}, wherein r1, r2, and r3 are the curvature radii of the primary mirror, the secondary mirror, and the third mirror, respectively; d1, d2, and d3 are the distances between the primary and secondary mirrors, the secondary and third mirrors, and the third mirror and the image plane, respectively; and α1, α2, and α3 are the tilt angles of the primary mirror, the secondary mirror, and the third mirror, respectively. The specific number of sets T is determined by the number of samples, T=T F ×T ED ×T FOV , T F 、T ED and T FOV are the number of samples for entrance pupil, F number and field of view respectively.

[0039] In order to construct the data set, the comprehensive objective function of the off-axis three-mirror system is designed, and the expression is:

[0040]

[0041] Among them, r n is the curvature radius of the nth reflector; α n is the inclination angle of the nth reflector; d n represents the distance between adjacent reflectors; K is the total number of reflectors; g1 to g4 are sub-functions required to construct an off-axis three-mirror spherical imaging system that is easy to install and adjust, t1 to t4 are the weights of each sub-function, and the sub-function expressions are:

[0042]

[0043] Among them, g1 is the image quality evaluation function; g2 is the adjustment constraint function; g3 is the off-axis degree function; g4 is the margin constraint function; N is the total number of sampling rays; i is the sequence number of the sampling rays; (x i ,y i ) is the imaging point of the i-th sampling light; (HI x ,HI y ) is the coordinate of the ideal image point; S is the total number of sampling points; (x j ,y j ) is the coordinate of the sampling point; RM is the reference radius of the adjustment constraint; (x M,y M ) is the coordinate of the reference point of the adjustment constraint; B i is a Boolean number. When the reflector does not block the light, B i =0, otherwise B i =1; l n A is the shortest distance from the reflector to the edge of the blocked beam; n is the margin value, and the reserved margin value is Q. When the current margin value is greater than Q, A n =0, otherwise A n =|QA n |.

[0044] Input the design requirement parameters, and use the search method to search for the minimum value of formula (1) to calculate the parameter combination of the off-axis three-mirror spherical imaging system that meets the adjustment constraints and converges the light rays of each field of view on the image plane; therefore, when the input set is determined, the corresponding output set is obtained;

[0045] The adjustment constraint is that all reflectors are infinitely fitted with the same cylindrical reference surface;

[0046] Step 2: Build the SVR model;

[0047] The SVR model is a support vector regression model, which is based on the regression analysis method of a support vector machine and realizes model prediction by constructing a tolerance interval;

[0048] The training loss function of the SVR model is:

[0049]

[0050] Where ω is the normal vector of the hyperplane; b is the displacement of the hyperplane; M is the number of independent variables; f(x m ) represents the SVR model for the mth input sample x m The predicted value, y m is the corresponding true value; C is the regularization parameter, which controls the complexity of the model and avoids overfitting; l ε It is an insensitive loss function, which is used to deal with the error between the predicted value and the true value. Its expression is:

[0051]

[0052] Using RBF kernel as the kernel function, its expression is:

[0053] K(x m ,y m ) = exp(-γ||x m -y m || 2 ) (8)

[0054] Among them, γ is the parameter of the kernel function and one of the hyperparameters of the SVR model. Hyperparameters refer to parameters that need to be set before model training. These parameters cannot be learned through the training process. γ and ε are both hyperparameters in the SVR model.

[0055] Step 3: Train the SVR model;

[0056] There is a clear mapping relationship between a specific set of hyperparameters and the final trained model. Therefore, after selecting a set of hyperparameters, it is necessary to train the SVR model under the guidance of this set of hyperparameters. A random search method is used to find the optimal hyperparameter combination, and a cross-validation method is used to divide the data set into a training set and a test set to train the SVR model. To prevent the training process from being carried out indefinitely, the maximum number of iterations is used as the termination condition.

[0057] Step 4: Use the trained SVR model to predict the new design requirement parameters to obtain a combination of parameters of the off-axis three-mirror spherical imaging system, and then combine it with the improved WW method to obtain an easy-to-install free-form surface off-axis three-mirror system.

[0058] The improved WW method is an existing algorithm and one of the free-form surface design methods. This method has the advantage of low time complexity and is convenient for quickly generating free-form surfaces.

[0059] In this implementation, the input pupil diameter, F number and field of view angle of the data set are 80mm-100mm, 3-3.5 and 2°×2°-4°×4° respectively. The radius of the cylindrical reference surface is 150mm. The pupil diameter, F number, field of view angle and total number of samples are T ED =17, T F =3, T FOV =3, T = 153. When training the SVR model, the maximum number of iterations was set to 2000, and the five-fold cross validation method was used to divide the training set and the test set. After using the trained SVR model to generate a set of off-axis three-mirror spherical imaging system parameter combinations, the improved WW method was used to generate the free-form surface. The obtained easy-to-adjust free-form surface off-axis three-mirror system is shown in Figure 2As shown. The results show that each reflector of the generated off-axis three-mirror system is in contact with the cylindrical reference surface, and each field of view light converges at the ideal image plane. This shows that the system meets the requirements of easy installation and imaging quality. It can be concluded that the method for generating an off-axis three-mirror system based on small sample machine learning that is easy to install and adjust proposed in the present invention can generate an off-axis multi-mirror free-form surface system that meets the requirements of integrated grinding and has good imaging quality. Among them, the method of combining the design of an off-axis three-mirror system that is easy to install and adjust with machine learning can improve the design efficiency, the construction of a small sample data set can reduce the cost of data collection and enable the model to capture key features more easily, and the use of an SVR model adapted to a small sample can reduce the difficulty and cost of training.

[0060] The above description is only a preferred embodiment of the present disclosure and an explanation of the technical principles used. Those skilled in the art should understand that the scope of the invention involved in the embodiments of the present disclosure is not limited to the technical solutions formed by a specific combination of the above-mentioned technical features, but should also cover other technical solutions formed by any combination of the above-mentioned technical features or their equivalent features without departing from the above-mentioned inventive concept. For example, the above-mentioned features are replaced with the technical features with similar functions disclosed in the embodiments of the present disclosure (but not limited to) to form a technical solution.

Claims

1. A method for generating an easy-to-install and off-axis three-mirror system based on small sample machine learning, characterized in that: The following steps are involved: Step 1: Build a dataset; Step 2: Build the SVR model; Step 3: Train the SVR model; Step 4: Use the trained SVR model to predict the new design requirement parameters to obtain a combination of parameters of the off-axis three-mirror spherical imaging system, and then combine it with the improved WW method to obtain an easy-to-install free-form surface off-axis three-mirror system.

2. The method for generating an easy-to-install and off-axis three-mirror system based on small sample machine learning according to claim 1, characterized in that: The data set includes an input set and an output set; the input set includes multiple sets of design requirement parameters, i.e., multiple sets of combinations of F numbers, entrance pupil diameters and field angles; the output set includes multiple sets of combinations of parameters of an easily mounted and adjustable off-axis three-mirror spherical imaging system, i.e., multiple sets of {r1, r2, r3, d1, d2, d3, α1, α2, α3}, wherein r1, r2 and r3 are respectively the curvature radii of the primary mirror, the secondary mirror and the third mirror, d1, d2 and d3 are respectively the distances between the primary and secondary mirrors, the secondary and third mirrors and the third mirror to the image plane, and α1, α2 and α3 are respectively the tilt angles of the primary mirror, the secondary mirror and the third mirror; the specific number of groups T is determined by the number of samples, T=T F ×T ED ×T FOV , T F , T ED and T FOV are the number of samples for entrance pupil, F number and field of view respectively.

3. The method for generating an easy-to-install and off-axis three-mirror system based on small sample machine learning according to claim 2, characterized in that: The step 1 also includes: designing a comprehensive objective function of the off-axis three-mirror system, which is expressed as: Among them, r n is the curvature radius of the nth reflector; α n is the inclination angle of the nth reflector; d n represents the distance between adjacent reflectors; K is the total number of reflectors; g1 to g4 are sub-functions required to construct an off-axis three-mirror spherical imaging system that is easy to install and adjust, t1 to t4 are the weights of each sub-function, and the sub-function expressions are: Among them, g1 is the image quality evaluation function; g2 is the adjustment constraint function; g3 is the off-axis degree function; g4 is the margin constraint function; N is the total number of sampling rays; i is the sequence number of the sampling rays; (x i ,y i ) is the imaging point of the i-th sampling light; (HI x ,HI y ) is the coordinate of the ideal image point; S is the total number of sampling points; (x j ,y j ) is the coordinate of the sampling point; RM is the reference radius of the adjustment constraint; (x M ,y M ) is the coordinate of the reference point of the adjustment constraint; B i is a Boolean number. When the reflector does not block the light, B i =0, otherwise B i =1; l n A is the shortest distance from the reflector to the edge of the blocked beam; n is the margin value, and the reserved margin value is Q. When the current margin value is greater than Q, A n =0, otherwise A n =|QA n |.

4. The method for generating an easy-to-install and off-axis three-mirror system based on small sample machine learning according to claim 3, characterized in that: For the comprehensive objective function of the off-axis three-mirror system, the design requirement parameters are input, and the minimum value of formula (1) is searched by the search method to calculate the parameter combination of the off-axis three-mirror spherical imaging system that meets the adjustment constraint and converges all field light on the image plane; therefore, when the input set is determined, the corresponding output set is obtained; The adjustment constraint is that all reflectors are infinitely fitted with the same cylindrical reference surface.

5. The method for generating an easy-to-install and off-axis three-mirror system based on small sample machine learning according to claim 1, characterized in that: The SVR model described in step 2 is a support vector regression model. The support vector regression model is based on the regression analysis method of the support vector machine and realizes model prediction by constructing a tolerance interval. The training loss function of the SVR model is: Where ω is the normal vector of the hyperplane; b is the displacement of the hyperplane; M is the number of independent variables; f(x m ) represents the SVR model for the mth input sample x m The predicted value, y m is the corresponding true value; C is the regularization parameter, l ε It is an insensitive loss function, and its expression is: Using RBF kernel as the kernel function, its expression is: K(x m ,y m )=exp(-γ||x m -y m || 2 ) (8) Among them, γ and ε are hyperparameters in the SVR model.

6. The method for generating an easy-to-install and off-axis three-mirror system based on small sample machine learning according to claim 1, characterized in that: Step 3 is as follows: Use the random search method to find the optimal hyperparameter combination, and use the cross-validation method to divide the data set into a training set and a test set to train the SVR model, using the maximum number of iterations as the termination condition.

7. The method for generating an easy-to-install and off-axis three-mirror system based on small sample machine learning according to claim 1, characterized in that: The improved WW method described in step 4 is a free-form surface design method.

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