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

Abstract

The application provides a small sample machine learning-based easy alignment off-axis three-mirror system generation method, relates to the technical field of optical system design, and aims to solve the problem of off-axis three-mirror system design under the requirement of easy alignment and rapid design, and provides a small sample machine learning-based easy alignment off-axis three-mirror system generation scheme, specifically a method for automatically generating an easy alignment off-axis multi-mirror system by using a small sample data set to train an SVR model, so as to reduce the alignment difficulty of the off-axis three-mirror system and the training and data collection difficulty of the machine learning. In the construction of the data set, a small sample data collection method is designed, the number of features in the sample is reduced, so as to reduce the construction of the training set and the development difficulty of the machine learning model. Then, an SVR model is constructed, and the SVR model is trained based on the data set. Finally, the trained SVR model is used to generate the parameter combination of the off-axis three-mirror spherical surface system, and the off-axis three-mirror free-form surface system is generated based on the parameter combination.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of optical system design, and particularly relates to a small-sample machine learning-based easy-to-assemble off-axis three-mirror system generation method. BACKGROUND

[0002] Off-axis three-mirror systems have unique advantages such as no chromatic aberration, foldability, and no central obstruction, and are widely used in various optical observation fields. Since the mirrors in the off-axis three-mirror system are generally free-form surfaces, the surface shape and the asymmetry of the system structure greatly increase the difficulty of assembly and adjustment. Therefore, an integrated machining method is needed, that is, the three mirrors are fixed on a cylindrical reference surface and then integrally ground. The off-axis three-mirror system manufactured using this machining method does not need to be adjusted twice, thus greatly reducing the difficulty of assembly and adjustment. Therefore, it is necessary to introduce the assembly and adjustment constraints in the design stage of the off-axis three-mirror system. However, although some researchers have proposed design methods considering assembly and adjustment constraints, these methods mainly provide targeted solutions for single design tasks, and when new design requirements are encountered, a complete set of design steps need to be implemented again, 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 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 considered the assembly and adjustment difficulty in parallel during the design process. Therefore, the designed off-axis three-mirror system can theoretically meet higher imaging quality, but does not have the easy-to-assemble feature. At the same time, most of the design methods using machine learning use samples containing a large number of features. When applying machine learning to the design of easy-to-assemble off-axis three-mirror systems, since the system needs to meet both imaging quality and assembly and adjustment constraints, there are more stringent restrictions on key features such as the position and tilt angle of the mirrors. In order to enable the model to more accurately learn and capture these key features, if the existing machine learning method is used, a larger data set usually needs to be designed to provide enough training samples, increasing the cost of data collection. At the same time, although the increase in the data set can ensure the diversity of the data, it will lead to an increase in the difficulty of tuning and the number of iterations during the training process, thereby increasing the complexity of developing the machine learning model. SUMMARY

[0004] In view of the deficiencies of the prior art, the present application provides a small-sample machine learning-based easy-to-assemble off-axis three-mirror system generation method; and aims to automatically generate an easy-to-assemble off-axis three-mirror system for easy assembly, reduced data collection difficulty, and tuning difficulty.

[0005] A small-sample machine learning-based easy-to-assemble off-axis three-mirror system generation method, comprising the following steps:

[0006] Step 1: Constructing the dataset;

[0007] The dataset includes an input set and an output set; the input set contains multiple sets of design requirement parameters, i.e., multiple combinations of F-number, entrance pupil diameter, and field of view; the output set contains multiple combinations of parameters of the easy-to-assemble and adjust off-axis three-mirror spherical imaging system, i.e., multiple sets of {r1, r2, r3, d1, d2, d3, a1, a2, a3}, where r1, r2, and r3 are the radii of curvature of the primary mirror, the secondary mirror, and the tertiary mirror, respectively, d1, d2, and d3 are the distances between the primary-secondary mirror, the secondary-tertiary mirror, and the tertiary mirror to the image plane, respectively, and a1, a2, and a3 are the tilt angles of the primary mirror, the secondary mirror, and the tertiary mirror, respectively. 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 sampling numbers of the entrance pupil, F-number, and field of view, respectively.

[0008] The comprehensive objective function for designing the off-axis three-mirror system is expressed as:

[0009]

[0010] where r n is the radius of curvature of the nth mirror; a n is the tilt angle of the nth mirror; d n represents the distance between adjacent mirrors; K is the total number of mirrors; g1 to g4 are sub-functions needed when constructing the easy-to-assemble and adjust off-axis three-mirror spherical imaging system, and t1 to t4 are the weights of each sub-function. The expressions of the sub-functions are as follows:

[0011]

[0012] where g1 is the image quality evaluation function; g2 is the assembly and adjustment constraint function; g3 is the off-axis degree function; g4 is the residual constraint function; N is the total number of sampling rays; i is the serial number of the sampling ray; (x i , y i ) is the imaging point of the ith sampling ray; (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 assembly and adjustment constraint reference radius; (x M , y M ) is the coordinate of the assembly and adjustment constraint reference point; B i is a Boolean number, B i = 0 when the mirror does not block the light ray, otherwise B i= 1; l n is the shortest distance from the mirror to the edge of the blocked beam; A n is the remaining value, and let the reserved remaining value be Q, then when the current remaining value is greater than Q, A n = 0, otherwise A n = |Q-A n |.

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

[0014] The alignment constraint is that all mirrors are infinitely attached to the same cylindrical reference surface;

[0015] Step 2: Construct an 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 predicted value of the mth input sample x m of the SVR model, y m is the corresponding true value; C is a regularization parameter, l ε is an insensitive loss function, and its expression is:

[0020]

[0021] An RBF kernel is used as the kernel function, and its expression is:

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

[0023] Where γ and ε are hyperparameters in the SVR model.

[0024] Step 3: Train the SVR model;

[0025] The random search method is used to find the optimal super parameter combination, the data set is divided into a training set and a test set by using the cross-validation method, and the SVR model is trained, and the maximum iteration number is used as a termination condition.

[0026] Step 4: The trained SVR model is used to predict new design requirement parameters, a combination of parameters of an off-axis three-mirror aspheric imaging system is obtained, and then an improved W-W method is combined to obtain an easy-to-adjust freeform off-axis three-mirror system.

[0027] The improved W-W method is a freeform surface design method.

[0028] The above technical solution has the following beneficial effects:

[0029] The present application provides an easy-to-adjust off-axis three-mirror system generation method based on small sample machine learning, which has the following beneficial effects:

[0030] 1. By combining the design of the easy-to-adjust off-axis three-mirror system with machine learning, an easy-to-adjust off-axis three-mirror system design method based on machine learning is designed. Compared with the current method of designing an easy-to-adjust off-axis three-mirror system, the method does not need to implement a complete set of design steps again, 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 construct an off-axis three-mirror system, the data collection cost is lower, the key features are more obvious, and the model can help to capture the key features faster;

[0032] 3. By using a support vector regression (SVR) model suitable for small sample data sets to design an easy-to-adjust off-axis three-mirror system, the prediction accuracy of the system is automatically improved and the dependence on a large amount of data is reduced. Compared with the traditional machine learning method which depends on a large-scale data set, the SVR model applied in the off-axis three-mirror system design exhibits lower model complexity, so the training cost is lower and the design efficiency is higher. BRIEF DESCRIPTION OF DRAWINGS

[0033] Figure 1 The flowchart of the easy-to-adjust off-axis three-mirror system generation method based on small sample machine learning of the present application is shown.

[0034] Figure 2 The structure diagram of the easy-to-adjust off-axis three-mirror system in the specific embodiment of the present application is shown. DETAILED DESCRIPTION

[0035] The specific embodiments of the present application will be further described in detail below in combination with the drawings and examples. The following examples are used to illustrate the present application, but are not used to limit the scope of the present application.

[0036] A small sample machine learning-based easy-to-assemble off-axis three-mirror system generation method, as shown in Figure 1 includes the following steps:

[0037] Step 1: Construct a data set;

[0038] The data set includes an input set and an output set; the input set contains multiple sets of design requirement parameters, i.e., multiple combinations of F number, entrance pupil diameter and field of view; the output set contains multiple combinations of parameters of the easy-to-assemble 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 radii of curvature of the primary mirror, the secondary mirror and the tertiary mirror, respectively, d1, d2 and d3 are the distances between the primary-secondary mirror, the secondary-tertiary mirror and the tertiary mirror to the image plane, respectively, and α1, α2 and α3 are the tilt angles of the primary mirror, the secondary mirror and the tertiary mirror, respectively. The specific number T is determined by the number of samples, T = T F ×T ED ×T FOV , T F , T ED and T FOV are the sampling numbers of the entrance pupil, the F number and the field of view, respectively.

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

[0040]

[0041] wherein r n is the radius of curvature of the nth mirror; α n is the tilt angle of the nth mirror; d n represents the distance between adjacent mirrors; K is the total number of mirrors; g1 to g4 are sub-functions needed when constructing the easy-to-assemble off-axis three-mirror spherical imaging system, and t1 to t4 are the weights of each sub-function, and the expression of the sub-function is:

[0042]

[0043] wherein g1 is an image quality evaluation function; g2 is an assembly constraint function; g3 is an off-axis degree function; g4 is a margin constraint function; N is the total number of sampling rays; i is the serial number of the sampling ray; (x i ,y i ) is the imaging point of the ith sampling ray; (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 assembly constraint reference radius; (x M,y M B represents the coordinates of the assembly constraint reference point; i Let B be a Boolean number, when the mirror does not block light. i =0, otherwise B i =1;l n A is the shortest distance from the reflector to the edge of the blocked beam. n Let Q be the margin value. Then, when the current margin value is greater than Q, A n =0, otherwise A n =|QA n |

[0044] Input the design requirements parameters, and use the search method to search for the minimum value of equation (1) to calculate the parameter combination of the off-axis three-reflector spherical imaging system that satisfies the assembly and adjustment constraints and whose light rays from each field of view converge on the image plane; therefore, once the input set is determined, the corresponding output set is obtained.

[0045] The assembly constraint is that all mirrors are infinitely fitted to the same cylindrical reference surface;

[0046] Step 2: Construct the SVR model;

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

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

[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 m-th input sample x. m The predicted value, y m This corresponds to the true value; C is the regularization parameter, which controls model complexity and avoids overfitting; l ε It is an insensitive loss function used to handle the error between the predicted and the true values. Its expression is:

[0051]

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

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

[0054] Here, γ is a parameter of the kernel function, and is 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 these hyperparameters. A random search method is used to find the optimal combination of hyperparameters, and cross-validation is used to divide the dataset into training and test sets for training the SVR model. To prevent the training process from going on indefinitely, a maximum number of iterations is used as the termination condition.

[0057] Step 4: Use the trained SVR model to predict the new design requirements parameters to obtain a set of parameters for the off-axis three-mirror spherical imaging system. Then, combine the improved WW method to obtain an easy-to-assemble and adjust free-form surface off-axis three-mirror system.

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

[0059] In this implementation scheme, the input dataset has entrance pupil diameter, F-number, and field of view ranges of 80mm-100mm, 3-3.5, and 2°×2°-4°×4°, respectively. The radius of the cylindrical reference surface is 150mm. The entrance pupil diameter, F-number, field of view, 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 training and test sets were divided using five-fold cross-validation. After generating a set of parameter combinations for an off-axis three-mirror spherical imaging system using the trained SVR model, a freeform surface was generated using the improved WW method. The resulting easily adjustable freeform surface off-axis three-mirror system is shown below. Figure 2As shown in the figure. The results show that all mirrors of the generated off-axis three-mirror system are in contact with the cylindrical reference surface, and all light rays from each field of view converge at the ideal image plane. This indicates that the system meets the requirements for easy assembly and adjustable imaging quality. In conclusion, the method for generating an easy-to-assemble, adjustable off-axis three-mirror system based on few-sample machine learning proposed in this invention can generate an off-axis multi-mirror freeform surface system that meets the requirements of integrated grinding and has good imaging quality. Specifically, combining the design of the easy-to-assemble, adjustable off-axis three-mirror system with machine learning can improve design efficiency; constructing a few-sample dataset can reduce data collection costs and make it easier for the model to capture key features; and using an SVR model adapted to few samples can reduce training difficulty and cost.

[0060] The above description is merely a preferred embodiment of this disclosure and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of the invention involved in the embodiments of this disclosure is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the above-described inventive concept. For example, technical solutions formed by substituting the above-described features with (but not limited to) technical features with similar functions disclosed in the embodiments of this disclosure.

Claims

1. A method for generating an easily assembled, adjustable-axis three-reflector system based on few-sample machine learning, characterized in that, Includes the following steps: Step 1: Build the dataset; The dataset includes an input set and an output set. The input set contains multiple sets of design requirement parameters, namely, multiple combinations of F-numbers, entrance pupil diameters, and field of view angles. The output set contains multiple combinations of parameters for an easily mounted, off-axis, three-mirror spherical imaging system, namely, multiple sets {r1,r2,r3,d1,d2,d3,α1,α2,α3}, where r1,r2, andr3 are the radii of curvature of the primary, secondary, and tertiary mirrors, respectively; d1,d2, and d3 are the distances between the primary, secondary, and tertiary mirrors and the image plane, respectively; and α1,α2, and α3 are the tilt angles of the primary, secondary, and tertiary mirrors, respectively. The specific number of sets T is determined by the number of samples, T = T0. F ×T ED ×T FOV T F T ED and T FOV These represent the number of samples for the entrance pupil, F-number, and field of view, respectively. Step 1 further includes: designing the comprehensive objective function of the off-axis three-reflector system, expressed as: (1)； Where, r n Let α be the radius of curvature of the nth reflecting mirror; n Let d be the tilt angle of the nth reflecting mirror; n This represents the distance between adjacent mirrors; K is the total number of mirrors; g1 to g4 are sub-functions needed to construct an easily adjustable off-axis three-mirror spherical imaging system; t1 to t4 are the weights of each sub-function, and their expressions are as follows: (2)； (3)； (4)； (5)； Where g1 is the image quality evaluation function; g2 is the assembly 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 ray; (x i , y i (HI) represents the imaging point of the i-th sampling ray; x HI y (x) represents the coordinates of the ideal image point; S represents the total number of sampling points; (x) represents the coordinates of the image point. j , y j (x) represents the coordinates of the sampling point; RM represents the assembly constraint reference radius; (x) M , y M B represents the coordinates of the assembly constraint reference point; n Let B be a Boolean number, when the mirror does not block light. n =0, otherwise B n =1;l n A is the shortest distance from the reflector to the edge of the blocked beam. n Let Q be the margin value. Then, when the current margin value is greater than Q, A n =0, otherwise A n =|QA n |; Step 2: Construct the SVR model; The SVR model is the support vector regression model, which is based on the regression analysis method of support vector machines and achieves model prediction by constructing a tolerance interval. The training loss function of the SVR model is as follows: (6)； 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 m-th input sample x. m The predicted value, y m It corresponds to the true value; C is the regularization parameter, l ε It is an insensitive loss function, and its expression is: (7)； Using the RBF kernel as the kernel function, its expression is: (8)； Among them, γ and ε are both hyperparameters in the SVR model; Step 3: Train the SVR model; Step 4: Use the trained SVR model to predict the new design requirements parameters to obtain a set of parameters for the off-axis three-mirror spherical imaging system. Then, combine the improved WW method to obtain an easy-to-assemble and adjust free-form surface off-axis three-mirror system.

2. The method for generating an easily assembled, adjustable-axis three-reflector system based on few-sample machine learning according to claim 1, 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 equation (1) is searched by the search method to calculate the parameter combination of the off-axis three-mirror spherical imaging system that satisfies the assembly and adjustment constraints and whose light rays from each field of view converge on the image plane; therefore, once the input set is determined, the corresponding output set is obtained. The assembly constraint is that all mirrors are infinitely fitted to the same cylindrical reference surface.

3. The method for generating an easily assembled, adjustable-axis three-reflector system based on few-sample machine learning according to claim 1, characterized in that, Step 3 specifically involves: using a random search method to find the optimal combination of hyperparameters, and using cross-validation to divide the dataset into training and test sets to train the SVR model, with the maximum number of iterations used as the termination condition.

4. The method for generating an easily assembled, adjustable-axis three-reflector system based on few-sample machine learning according to claim 1, characterized in that, The improved WW method described in step 4 is a freeform surface design method.

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