Multi-mirror off-axis reflective imaging system automatic generation method based on machine learning

Abstract

The invention provides a multi-mirror off-axis reflective imaging system automatic generation method based on machine learning, and relates to the technical field of optical systems. The method comprises the following steps: firstly, constructing a multi-mirror off-axis reflective imaging system data set, and unifying sample dimensions in the data set; performing partition coding on each parameter in the sample to obtain a sample data set; a random forest model is constructed, and a sample data set is adopted for training; for a new design requirement, generating a predicted value through a random forest model, and obtaining a coded physical parameter corresponding to the design requirement; by defining a decoding rule, restoring a final prediction value output by the random forest model into a physical parameter with clear physical significance; and obtaining the free-form surface off-axis reflective imaging system by taking the physical parameter combination obtained by decoding as input and combining with an improved W-W method. According to the method, multiple independent models do not need to be switched or retrained when the requirements of different reflector numbers and design indexes are met.

Description

Technical Field

[0001] This invention relates to the field of optical system design technology, and in particular to an automatic generation method for multi-mirror off-axis reflective imaging systems based on machine learning. Background Technology

[0002] Off-axis reflective imaging systems offer advantages such as chromatic aberration-free operation, foldability, and no central obstruction, making them widely applicable in various optical imaging fields. In recent years, the design methods for off-axis reflective imaging systems have gradually shifted from experience-based patent matching to automated methods such as vector aberration theory and freeform surface design. The emergence of these methods has significantly improved the speed and efficiency of designing high-performance off-axis reflective imaging systems. However, these methods often provide specific solutions for individual design tasks and struggle to generate systems in real-time according to design requirements. Since machine learning allows computers to learn patterns and rules from data, enabling real-time prediction or decision-making, researchers have combined machine learning with the design of off-axis reflective imaging systems. However, existing machine learning models for predicting off-axis reflective imaging system parameters are mostly limited to generating parameters for systems with a specific number of mirrors. Therefore, designers need to switch between different dedicated models for design tasks with different numbers of mirrors, leading to redundant investment of computational resources. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide an automatic generation method for multi-mirror off-axis reflective imaging systems based on machine learning, which addresses the shortcomings of the prior art and aims to reduce the investment of computing resources by automatically generating multi-mirror off-axis reflective imaging systems.

[0004] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: an automatic generation method for multi-mirror off-axis reflective imaging systems based on machine learning, comprising:

[0005] The design requirements and physical parameters of multiple off-axis reflective imaging systems were obtained, a dataset of multi-mirror off-axis reflective imaging systems was constructed, and the sample dimensions in the dataset were unified.

[0006] Each parameter in the sample is partitioned and encoded to obtain the sample dataset;

[0007] Construct a random forest model and train it using a partitioned, encoded sample dataset;

[0008] To address the design requirements of a new off-axis reflective imaging system, a random forest model is used to generate predicted values, thereby obtaining the coded physical parameters of the off-axis reflective imaging system that correspond to the design requirements.

[0009] By defining decoding rules, the final predicted values ​​output by the random forest model are restored to physical parameters with clear physical meaning;

[0010] Using the combination of physical parameters obtained from decoding as input, and combining it with the improved WW method, a free-form surface off-axis reflection imaging system is obtained.

[0011] Furthermore, the multi-mirror off-axis reflective imaging system dataset refers to a dataset that includes various off-axis reflective imaging systems with different numbers of mirrors; the samples in the dataset include the design requirements and physical parameters of each off-axis reflective imaging system; the design requirements include the number of mirrors, F-number, entrance pupil diameter, maximum field of view in the x-direction, and maximum field of view in the y-direction; the physical parameters include the radius of curvature, conic coefficient, tilt angle, and mirror spacing of each mirror.

[0012] Furthermore, the method for unifying the sample dimensions in the dataset is as follows:

[0013] Based on the maximum number of mirrors in the multi-mirror off-axis reflective imaging system dataset, a uniform fixed-length dimension is constructed for each sample; for physical parameters that do not exist in the sample, a specific padding identifier "x" is filled in at the corresponding parameter position.

[0014] Furthermore, the specific method for partitioning and encoding each parameter in the sample is as follows:

[0015] The encoding of each parameter in the sample is divided into an identifier area and a value area. The identifier area consists of the two highest bits of the encoding, i.e., the first two bits of the encoding. These two bits are not used to store the parameter, but to convey information about the parameter. The first bit of the identifier area is the padding bit. When this bit is "1", it indicates that the parameter corresponding to the encoding is in a padded state, i.e., the position of the identifier "x". When it is "0", it indicates that the parameter corresponding to the encoding is a valid physical parameter. The second bit of the identifier area is the sign bit. When the parameter corresponding to the encoding is negative, this bit is "1", otherwise it is "0". When the first bit of the identifier area is "1", the second bit is also "0". The value area includes an integer field and a decimal field. When the parameter corresponding to the encoding is a valid physical parameter, the integer and decimal parts of the physical parameter are written into the corresponding positions respectively. When the parameter corresponding to the encoding is the identifier "x", both the integer field and the decimal field are 0.

[0016] Furthermore, the specific method for constructing the random forest model and training it using the partitioned encoded sample dataset is as follows:

[0017] The partitioned and encoded sample dataset is divided into a training set and a test set. First, the training set is randomly sampled multiple times to generate multiple differentiated sub-training sets, allowing each tree to learn from different data samples. Then, when constructing each decision tree, a candidate feature set is randomly selected from all sample features to further increase the diversity between trees. Subsequently, for each sub-training set and its corresponding candidate feature set, node splitting and feature selection are recursively performed until a preset stopping condition is met, completing the construction of a single decision tree. This process is repeated to generate multiple decision trees, which are then integrated into a random forest model. The sample features include the number of mirrors, F-number, entrance pupil diameter, maximum field of view in the x and y directions, radius of curvature, conic coefficient, tilt angle, and mirror spacing of each mirror.

[0018] Furthermore, the specific method for obtaining the coded physical parameters of the off-axis reflective imaging system corresponding to the design requirements by generating predicted values ​​through a random forest model to meet the new off-axis reflective imaging system design requirements is as follows:

[0019] The design requirements for a new off-axis reflective imaging system are as follows: p The random forest model generates predictions by aggregating the outputs of all decision trees;

[0020] Let h t (x p ) represents the decision tree t for the new design requirement x. p The predicted output; the final predicted value of the random forest is the arithmetic mean of the predicted values ​​of all T decision trees, expressed as:

[0021] (1);

[0022] Among them, y p is the final prediction value of the random forest, that is, the physical parameters of the coded off-axis reflective imaging system corresponding to the design requirements, and T is the total number of decision trees in the random forest model.

[0023] Furthermore, the specific method for restoring the final predicted value output by the random forest model to physical parameters with explicit physical meaning by defining decoding rules is as follows:

[0024] First, the identifier region of the final predicted value output by the random forest model is read: if the padding bit is "1", the parameter is decoded as the padding identifier "x"; if the padding bit is "0", the sign of the parameter is determined according to the sign bit, and the numerical region is parsed into the corresponding physical parameter value; then, by filtering out all parameters marked as "x", the variable-length combination of actual physical parameters corresponding to the actual optical system is recovered.

[0025] Secondly, this application proposes an electronic device, including: one or more processors, and a memory for storing instructions, which, when executed by the one or more processors, cause the one or more processors to execute the machine learning-based multi-mirror off-axis reflective imaging system automatic generation method.

[0026] Thirdly, this application proposes a computer-readable storage medium storing executable instructions that, when executed, cause a processor to perform the machine learning-based multi-mirror off-axis reflective imaging system automatic generation method.

[0027] Fourthly, this application proposes a computer program product, including a computer program or instructions that, when executed by a processor, implement the aforementioned automatic generation method for a multi-mirror off-axis reflective imaging system based on machine learning.

[0028] The beneficial effects of the above technical solutions are as follows: The present invention provides an automatic generation method for multi-mirror off-axis reflective imaging systems based on machine learning, (1) by combining the design of multi-mirror off-axis reflective imaging systems with machine learning and data encoding and decoding methods, when faced with different requirements for the number of reflectors and design indicators, compared with the current method that requires the development of a special model for a specific number of reflectors, it does not require switching or retraining multiple independent models, significantly reducing the investment of computing resources and the time investment cost; (2) by using a partitioned encoding method, the problem of inconsistent sample dimensions caused by different numbers of reflectors is solved. Compared with the current method of directly using physical parameters for training, the present invention improves training efficiency by constructing a unified data structure, eliminates the model's dependence on the mask matrix, and reduces model complexity; (3) by using a random forest model adapted to the encoded data to design multi-mirror off-axis reflective imaging systems, the prediction accuracy of the system is automatically improved. Compared with machine learning methods that use other models (such as neural networks and support vector machines), the random forest model exhibits lower model complexity in the design of multi-mirror off-axis reflective imaging systems, thus resulting in lower training costs and higher design efficiency. Attached Figure Description

[0029] Figure 1 A flowchart of an automatic generation method for a multi-mirror off-axis reflective imaging system based on machine learning provided in an embodiment of the present invention;

[0030] Figure 2 A schematic diagram of the partitioning encoding method provided in an embodiment of the present invention;

[0031] Figure 3 This is a schematic diagram of the structure of the free-form surface off-axis two-reflection imaging system provided in an embodiment of the present invention;

[0032] Figure 4 This is a schematic diagram of the structure of the free-form surface off-axis three-mirror imaging system provided in this embodiment of the invention. Detailed Implementation

[0033] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0034] This invention addresses the design problem of multi-mirror off-axis reflective imaging systems by proposing a machine learning-based generation scheme. Specifically, it involves constructing an automatic generation method combining encoding / decoding methods and a random forest model to improve the versatility of machine learning models for off-axis reflective imaging systems with different numbers of mirrors and reduce the training difficulty of machine learning models. In the data preparation stage, a partitioned encoding method is designed to uniformly map physical parameters with different dimensions due to varying numbers of mirrors into fixed-dimensional codes, thereby constructing a dataset that can be directly processed by the model. Subsequently, a random forest model is built and trained based on this encoded dataset to learn the high-dimensional mapping between encoded design requirements and encoded system parameters. Finally, the trained random forest model is used to predict encoded parameters based on new requirements, and the system parameters with clear physical meaning are recovered through a decoding step. This, combined with an improved WW method, automatically generates the corresponding freeform surface off-axis multi-mirror imaging system.

[0035] In this embodiment, a machine learning-based automatic generation method for multi-mirror off-axis reflective imaging systems is used, such as... Figure 1 As shown, the specific steps include:

[0036] Step 1: Obtain the design requirements and physical parameters of multiple off-axis reflective imaging systems, construct a dataset of multi-mirror off-axis reflective imaging systems, and unify the sample dimensions in the dataset;

[0037] The multi-mirror off-axis reflective imaging system dataset refers to a dataset that includes various off-axis reflective imaging systems with different numbers of mirrors, such as an off-axis two-mirror imaging system and an off-axis three-mirror imaging system.

[0038] The dataset includes the design requirements (number of mirrors, F-number, entrance pupil diameter, maximum field of view in the x-direction and maximum field of view in the y-direction) and physical parameters (radius of curvature, conic coefficient, tilt angle, and mirror spacing of each mirror) for each off-axis reflective imaging system.

[0039] In the dataset of a multi-mirror off-axis reflective imaging system, the design requirements form the input set, and the physical parameters form the output set.

[0040] In this embodiment, a uniform fixed-length dimension is constructed for each sample based on the maximum number of mirrors contained in the multi-mirror off-axis reflective imaging system dataset. For physical parameters that are not present in a specific sample, a specific padding identifier "x" is filled in at the corresponding parameter position. For example, when the dataset contains both off-axis two-mirror imaging systems and off-axis three-mirror imaging systems, the off-axis two-mirror imaging system will fill in the identifier "x" at all parameter positions such as the radius of curvature, conic coefficient, and tilt angle of the third mirror, thereby achieving dimensional alignment of all samples.

[0041] Step 2: Partition and encode each parameter in the sample to obtain the sample dataset;

[0042] The encoding of each parameter in the sample is divided into an identifier area and a numerical area, such as... Figure 2 As shown. The identifier area consists of the two highest bits of the code, i.e., the first two bits. These two bits are not used to store parameters, but rather to convey "information about the parameters". The first bit of the identifier area is the padding bit. When this bit is "1", it indicates that the parameter corresponding to the code is in a padded state, i.e., the position of the identifier "x"; when it is "0", it indicates that the parameter corresponding to the code is a valid physical parameter. The second bit of the identifier area is the sign bit. When the parameter corresponding to the code is negative, this bit is "1", otherwise it is "0". When the first bit of the identifier area is "1", the second bit is also "0". The numeric area includes an integer field and a decimal field. When the parameter corresponding to the code is a valid physical parameter, the integer and decimal parts of the physical parameter are written into the corresponding positions respectively; when the parameter corresponding to the code is "x", both the integer and decimal fields are 0.

[0043] Step 3: Construct a random forest model and train it using the partitioned and encoded sample dataset;

[0044] The partitioned and encoded sample dataset is divided into training and test sets. First, the training set is randomly sampled multiple times to generate several slightly different sub-training sets, allowing each tree to learn from different data samples. Next, when constructing each decision tree, a candidate feature set is randomly selected from all sample features to further increase the diversity between trees. Then, for each sub-training set and its corresponding candidate feature set, node splitting and feature selection are recursively performed until a preset stopping condition is met, completing the construction of a single decision tree. The above steps are repeated to generate multiple decision trees, which are then integrated into a random forest model. The sample features include the number of mirrors, F-number, entrance pupil diameter, maximum field of view in the x and y directions, radius of curvature, conic coefficient, tilt angle, and mirror spacing for each mirror.

[0045] Step 4: To meet the design requirements of the new off-axis reflective imaging system, predictive values ​​are generated using a random forest model to obtain the physical parameters of the coded off-axis reflective imaging system corresponding to the design requirements.

[0046] The design requirements for a new off-axis reflective imaging system are as follows: p The random forest model generates predictions by aggregating the outputs of all decision trees;

[0047] Let h t (x p ) represents the decision tree t for the new design requirement x. p The predicted output; the final predicted value of the random forest is the arithmetic mean of the predicted values ​​of all T decision trees, expressed as:

[0048] (1);

[0049] Among them, y p is the final prediction value of the random forest, that is, the physical parameters of the coded off-axis reflective imaging system corresponding to the design requirements, and T is the total number of decision trees in the random forest model.

[0050] Step 5: By defining decoding rules, the final predicted values ​​output by the random forest model are restored to physical parameters with clear physical meaning;

[0051] First, the identifier region of the final predicted value output by the random forest model is read: if the padding bit is "1", the parameter is decoded as the padding identifier "x"; if the padding bit is "0", the sign of the parameter is determined by the sign bit, and the numerical region is parsed into the corresponding physical parameter value. Then, by filtering out all parameters marked as "x", the variable-length combination of actual physical parameters corresponding to the actual optical system is recovered, completing the conversion from machine-processable data to engineering-understandable physical parameters.

[0052] Step 6: Using the combination of physical parameters obtained from decoding as input, and combining it with the improved WW method, a free-form surface off-axis reflection imaging system is obtained;

[0053] The improved WW method is a type of freeform surface design method. This method has the advantage of low time complexity and is convenient for quickly generating freeform surfaces.

[0054] Using the physical parameters obtained from decoding as input, the improved WW method is used to obtain the discrete point coordinates describing the reflective mirror shape. Then, by fitting these discrete point coordinates, a freeform off-axis reflective imaging system can be automatically generated.

[0055] In this embodiment, the multi-mirror off-axis reflective imaging system dataset includes parameters for 90 off-axis two-mirror imaging systems and 153 off-axis three-mirror imaging systems. The entrance pupil diameter, F-number, and field of view ranges for the off-axis two-mirror imaging systems in the input set are 20mm-30mm, 3.6-4mm, and 15mm, respectively. ° ×15 ° -20 ° ×20 ° The entrance pupil diameter, F-number, and field of view range of the off-axis three-mirror imaging system are 80mm-100mm, 3-3.5mm, and 2mm, respectively. ° ×2 ° -4 ° ×4 ° The output set for the off-axis two-mirror imaging system includes eight physical parameters: the radius of curvature (r1, r2), tilt angle (α1, α2), conic coefficient (k1, k2), and mirror spacing (d1, d2) for each mirror. The output set for the off-axis three-mirror imaging system includes nine parameters: the radius of curvature (r1, r2, r3), tilt angle (α1, α2, α3), and mirror spacing (d1, d2, d3) for each mirror. Considering the parameter types in the output set, a filler symbol "x" is inserted at positions r3, d3, k3, and α3 in the off-axis two-mirror imaging system, and at positions k1, k2, and k3 in the off-axis three-mirror imaging system.

[0056] This embodiment addresses the data characteristics of physical parameters (the absolute values ​​of all physical parameters are less than 500). The integer and fractional fields of the physical parameter encoding value area are both fixed at 4 bits, with 2 bits reserved for identifiers. Thus, the parameters of each off-axis two-mirror imaging system and off-axis three-mirror imaging system are losslessly converted into a 10-bit fixed-length code. When training the random forest model, the sample dataset is randomly divided into training and test sets in an 8:2 ratio. The number of decision trees is 200, the maximum depth of a single decision tree is 15, and the minimum number of samples required for further splitting of internal nodes is 3. After obtaining the predicted codes generated by the random forest, the actual physical parameter combinations corresponding to the actual optical system are recovered according to the decoding rules. Discrete point coordinates are generated using the improved WW method and fitted to a freeform surface. The resulting freeform surface off-axis two-mirror imaging system and freeform surface off-axis three-mirror imaging system are as follows: Figure 3 and Figure 4 As shown in the figure. The results show that the light rays from each field of view of the generated off-axis two-mirror imaging system and the off-axis three-mirror imaging system converge at the ideal image plane, indicating that both off-axis reflective imaging systems meet the imaging quality requirements.

[0057] It can be seen that the automatic generation method for multi-mirror off-axis reflective imaging systems based on machine learning proposed in this invention can generate freeform off-axis reflective imaging systems with excellent imaging quality. The method of combining the design of multi-mirror off-axis reflective imaging systems with machine learning and data encoding methods can reduce the investment of computing resources. The designed partition encoding method solves the problem of inconsistent sample dimensions caused by different numbers of reflectors. The use of a random forest model adapted to the encoded data improves the design efficiency.

[0058] Example 2:

[0059] This embodiment proposes an electronic device, including: one or more processors, and a memory, wherein the memory is used to store instructions, and when the instructions are executed by the one or more processors, the one or more processors execute the automatic generation method of the multi-mirror off-axis reflective imaging system based on machine learning.

[0060] The electronic device may be a mobile phone, computer, or tablet computer, etc., and includes a memory and a processor. The memory stores a computer program, which, when executed by the processor, implements the automatic generation method for a multi-mirror off-axis reflective imaging system based on machine learning as described in the embodiments. It is understood that the electronic device may also include an input / output (I / O) interface and communication components.

[0061] The processor is used to execute all or part of the steps in the machine learning-based automatic generation method for multi-mirror off-axis reflective imaging systems as described in the above embodiments. The memory is used to store various types of data, which may include, for example, instructions for any application or method in the electronic device, as well as application-related data.

[0062] The processor can be implemented as an Application Specific Integrated Circuit (ASIC), Digital Signal Processor (DSP), Programmable Logic Device (PLD), Field Programmable Gate Array (FPGA), controller, microcontroller, microprocessor, or other electronic components, and is used to execute the automatic generation method for multi-mirror off-axis reflective imaging system based on machine learning described in the above embodiments.

[0063] Example 3:

[0064] This embodiment proposes a computer-readable storage medium that stores executable instructions. When these instructions are executed, if they are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium.

[0065] The computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the automatic generation method for a multi-mirror off-axis reflective imaging system based on machine learning as described in the various embodiments of this application.

[0066] The aforementioned storage media include: flash memory, hard disks, multimedia cards, card-type memory (e.g., SD (Secure Digital Memory Card) or DX (Memory Data Register, MDR) memory), random access memory (RAM), static random-access memory (SRAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), programmable read-only memory (PROM), magnetic storage, disks, optical discs, servers, APP (Application) app stores, and other media capable of storing program verification codes. These media store computer programs, which, when executed by a processor, can implement the various steps of the aforementioned automatic generation method for a multi-mirror off-axis reflective imaging system based on machine learning.

[0067] Example 4:

[0068] This embodiment proposes a computer program product, including a computer program or instructions, which, when executed by a processor, implements the aforementioned automatic generation method for a multi-mirror off-axis reflective imaging system based on machine learning.

[0069] Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or part of the technical solution, can be embodied in the form of a computer program product.

[0070] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the present invention.

Claims

1. A method for automatically generating multi-mirror off-axis reflective imaging systems based on machine learning, characterized in that, include: The design requirements and physical parameters of multiple off-axis reflective imaging systems were obtained, a dataset of multi-mirror off-axis reflective imaging systems was constructed, and the sample dimensions in the dataset were unified. Each parameter in the sample is partitioned and encoded to obtain the sample dataset; Construct a random forest model and train it using a partitioned, encoded sample dataset; To address the design requirements of a new off-axis reflective imaging system, a random forest model is used to generate predicted values, thereby obtaining the coded physical parameters of the off-axis reflective imaging system that correspond to the design requirements. By defining decoding rules, the final predicted values ​​output by the random forest model are restored to physical parameters with clear physical meaning; Using the combination of physical parameters obtained from decoding as input, and combining it with the improved WW method, a free-form surface off-axis reflection imaging system is obtained.

2. The automatic generation method for a multi-mirror off-axis reflective imaging system based on machine learning according to claim 1, characterized in that, The multi-mirror off-axis reflective imaging system dataset refers to a dataset that includes various off-axis reflective imaging systems with different numbers of mirrors. The samples in the dataset include the design requirements and physical parameters of each off-axis reflective imaging system. The design requirements include the number of mirrors, F-number, entrance pupil diameter, maximum field of view in the x-direction, and maximum field of view in the y-direction. The physical parameters include the radius of curvature, conic coefficient, tilt angle, and mirror spacing of each mirror.

3. The automatic generation method for a multi-mirror off-axis reflective imaging system based on machine learning according to claim 2, characterized in that, The method for unifying the sample dimensions in the dataset is as follows: Based on the maximum number of mirrors in the multi-mirror off-axis reflective imaging system dataset, a uniform fixed-length dimension is constructed for each sample; for physical parameters that do not exist in the sample, a specific padding identifier "x" is filled in at the corresponding parameter position.

4. The automatic generation method for a multi-mirror off-axis reflective imaging system based on machine learning according to claim 3, characterized in that, The specific method for partitioning and encoding each parameter in the sample is as follows: The encoding of each parameter in the sample is divided into an identifier area and a value area. The identifier area consists of the two highest bits of the encoding, i.e., the first two bits of the encoding. These two bits are not used to store the parameter, but to convey information about the parameter. The first bit of the identifier area is the padding bit. When this bit is "1", it indicates that the parameter corresponding to the encoding is in a padded state, i.e., the position of the identifier "x". When it is "0", it indicates that the parameter corresponding to the encoding is a valid physical parameter. The second bit of the identifier area is the sign bit. When the parameter corresponding to the encoding is negative, this bit is "1", otherwise it is "0". When the first bit of the identifier area is "1", the second bit is also "0". The value area includes an integer field and a decimal field. When the parameter corresponding to the encoding is a valid physical parameter, the integer and decimal parts of the physical parameter are written into the corresponding positions respectively. When the parameter corresponding to the encoding is the identifier "x", both the integer field and the decimal field are 0.

5. The automatic generation method for a multi-mirror off-axis reflective imaging system based on machine learning according to claim 4, characterized in that, The specific method for constructing a random forest model and training it using a partitioned, encoded sample dataset is as follows: The partitioned and encoded sample dataset is divided into a training set and a test set. First, the training set is randomly sampled multiple times to generate multiple differentiated sub-training sets, allowing each tree to learn from different data samples. Then, when constructing each decision tree, a candidate feature set is randomly selected from all sample features to further increase the diversity between trees. Subsequently, for each sub-training set and its corresponding candidate feature set, node splitting and feature selection are recursively performed until a preset stopping condition is met, completing the construction of a single decision tree. This process is repeated to generate multiple decision trees, which are then integrated into a random forest model. The sample features include the number of mirrors, F-number, entrance pupil diameter, maximum field of view in the x and y directions, radius of curvature, conic coefficient, tilt angle, and mirror spacing of each mirror.

6. The automatic generation method for a multi-mirror off-axis reflective imaging system based on machine learning according to claim 5, characterized in that, The specific method for obtaining the coded physical parameters of the off-axis reflective imaging system corresponding to the design requirements by generating predicted values ​​through a random forest model to meet the new design requirements is as follows: The design requirements for a new off-axis reflective imaging system are as follows: p The random forest model generates predictions by aggregating the outputs of all decision trees; Let h t (x p ) represents the decision tree t for the new design requirement x. p The predicted output; the final predicted value of the random forest is the arithmetic mean of the predicted values ​​of all T decision trees, expressed as: (1)； Among them, y p is the final prediction value of the random forest, that is, the physical parameters of the coded off-axis reflective imaging system corresponding to the design requirements, and T is the total number of decision trees in the random forest model.

7. The automatic generation method for a multi-mirror off-axis reflective imaging system based on machine learning according to claim 6, characterized in that, The specific method for restoring the final predicted value output by the random forest model into physical parameters with clear physical meaning by defining decoding rules is as follows: First, the identifier region of the final predicted value output by the random forest model is read: if the padding bit is "1", the parameter is decoded as the padding identifier "x"; if the padding bit is "0", the sign of the parameter is determined according to the sign bit, and the numerical region is parsed into the corresponding physical parameter value; then, by filtering out all parameters marked as "x", the variable-length combination of actual physical parameters corresponding to the actual optical system is recovered.

8. An electronic device for executing the automatic generation method for a multi-mirror off-axis reflective imaging system based on machine learning as described in any one of claims 1-7, characterized in that, include: One or more processors, and a memory for storing instructions that, when executed by the one or more processors, cause the one or more processors to perform the machine learning-based automatic generation method for a multi-mirror off-axis reflective imaging system.

9. A computer-readable storage medium storing executable instructions for performing the automatic generation method for a multi-mirror off-axis reflective imaging system based on machine learning as described in any one of claims 1-7, characterized in that... When the instruction is executed, it causes the processor to perform the automatic generation method for the multi-mirror off-axis reflective imaging system based on machine learning.

10. A computer program product for executing the automatic generation method for a multi-mirror off-axis reflective imaging system based on machine learning as described in any one of claims 1-7, characterized in that, Includes a computer program or instructions that, when executed by a processor, implement the described automatic generation method for a machine learning-based multi-mirror off-axis reflective imaging system.

Images