Optical system imaging quality prediction method based on assembly error

Abstract

The present invention relates to the field of mechanical engineering, and specifically to a method for predicting the imaging quality of an optical system based on assembly errors. First, an accurate finite element model of the optical system is constructed, the bolt tightening process is simulated, the mirror deformation under the action of assembly stress is obtained, and the mirror surface shape is fitted using Zernike polynomials. Using this as an intermediate medium, Zemax is used to simulate the imaging of the optical system under the conditions of mirror deformation and assembly posture, and the influence of various assembly errors on the imaging quality of the optical system is explored. Then, an assembly data set is constructed through an integrated simulation method, an MLP-XGBoost combined neural network agent model is established, and model training is performed. Compared with single MLP, XGBoost models, and traditional regression models, the model has greater superiority and reliability in terms of prediction accuracy. Finally, the stochastic gradient descent method is used to optimize the preload force under different primary and secondary mirror assembly posture conditions. The energy concentration is increased by an average of 11.34% compared to before optimization, thereby improving the assembly efficiency and accuracy of the double-mirror optical system.

Description

Technical Field

[0001] The present invention relates to the technical field of mechanical engineering, and in particular to a method for predicting the imaging quality of an optical system based on assembly errors. Background Art

[0002] The coaxial twin-mirror optical system is mainly composed of a primary mirror, a secondary mirror, and a mirror frame. It has the advantages of no chromatic aberration, strong light-gathering ability, easy processing, and can reach the diffraction limit. It is widely used in astronomical observation, space remote sensing, precision guidance, chip lithography and other fields. With the improvement of product performance requirements and the complex and harsh service environment, the requirements for the imaging quality of coaxial twin-mirror optical systems are also getting higher and higher. The imaging quality of the twin-mirror optical system not only depends on the optical-mechanical structure design and processing accuracy, but also the assembly posture and connection fastening mechanical state during the assembly process, which significantly affect the final performance of the precision optical system. How to accurately evaluate the influence of various external loads on the deformation of the optical system mirror during the assembly process and realize the prediction of the imaging quality of the optical system have become key issues that need to be solved urgently. Summary of the Invention

[0003] In response to the above problems, an embodiment of the present invention provides an optical system imaging quality prediction method based on assembly error.

[0004] An embodiment of the present invention provides a method for predicting the imaging quality of an optical system based on assembly errors, comprising:

[0005] A finite element model of the double-mirror optical system was established, and the bolt tightening process was simulated to obtain the mirror deformation under different preload conditions;

[0006] The Zernike polynomials are used to fit the mirror surface shape in the double-mirror optical system to obtain the Zernike polynomial coefficients used to characterize the mirror surface shape error.

[0007] The mirror deformation is imported into the optical-mechanical-thermal coupling analysis module and the Zernike polynomial coefficients are used as the basis function to fit the mirror shape. A macro file including the mirror shape deviation and the primary and secondary mirror assembly posture deviation is obtained.

[0008] The obtained macro file is loaded into the optical simulation module to perform optical path imaging simulation to obtain the energy concentration used to characterize the imaging quality;

[0009] A dataset was constructed based on preload force, primary and secondary mirror assembly posture deviation, and energy concentration, and the constructed dataset was used to train the MLP model and XGBoost model.

[0010] Obtain the current preload force and primary and secondary mirror assembly posture deviations of the optical system to be predicted, and input the obtained preload force and primary and secondary mirror assembly posture deviations into the trained MLP model and XGBoost model respectively to obtain the first energy concentration and the second energy concentration;

[0011] The first weight matrix and the second weight matrix of the MLP model and the XGBoost model are obtained, and the first energy concentration and the second energy concentration are weightedly calculated using the determined first weight matrix and the second weight matrix to obtain the final energy concentration as a prediction result.

[0012] Optionally, also include:

[0013] The assembly posture deviations of the primary and secondary mirrors are taken as input values ​​and set as constants according to the actual assembly conditions. The preload force is taken as input value and set as an optimization variable. With the maximization of the predicted results as the optimization goal, the stochastic gradient descent algorithm is used to iteratively calculate the optimal preload force, and the actual assembly process is guided by the calculated optimal preload force.

[0014] Optionally, the process of establishing a finite element model of a double-reflective optical system includes:

[0015] Establish a three-dimensional geometric model of the double-mirror optical system, including the primary mirror, secondary mirror, and mirror frame. The primary mirror is fixed to the mirror frame with three sets of bolts and nuts, and the secondary mirror is assembled with the cylindrical hole on the mirror frame through a pressure ring.

[0016] The three-dimensional geometric model is meshed to establish a finite element model, wherein the bolts and nuts are meshed with hexahedrons, and the primary mirror, secondary mirror and mirror frame are meshed with tetrahedrons.

[0017] Optionally, the process of loading the obtained macro file into the optical simulation module to perform light path imaging simulation includes:

[0018] Establish the corresponding reflective surfaces of the primary mirror and the secondary mirror, where the primary mirror is a rotating parabola and the secondary mirror is an even-order hyperboloid. At the same time, set the size of the opening at the center of the primary mirror and the distance between the primary and secondary mirrors.

[0019] The mirror surface deviation is adjusted by inserting the mirror coordinate discontinuity surface to achieve the setting of the primary mirror and secondary mirror eccentricity and tilt;

[0020] The assembly posture deviations of the primary and secondary mirrors are superimposed on the reflecting surface to generate a composite surface, thereby fitting the mirror deformation to the mirror surface.

[0021] Optionally, the process of constructing a data set based on preload force, primary and secondary mirror assembly posture deviation, and energy concentration includes:

[0022] The preload force and the primary and secondary mirror assembly posture deviation are used as feature variables, and the energy concentration is used as the target variable to construct a data set. The primary and secondary mirror assembly posture deviation includes the eccentricity error of the primary and secondary mirrors along the X and Y axes, as well as the deflection error around the X and Y axes.

[0023] The feature variables and target variables in the constructed dataset are randomly sorted and normalized, and finally the dataset is divided into training set and test set according to the set ratio.

[0024] Optionally, the process of training the MLP model and XGBoost model using the constructed dataset includes:

[0025] Use the training set to train the MLP model and XGBoost model separately;

[0026] The MLP model and XGBoost model were tested using the test set to obtain the energy concentration prediction values ​​of the MLP model and the XGBoost model under the test set;

[0027] Calculate a first weight matrix and a second weight matrix according to the obtained energy concentration prediction value under the test set and the true value of the energy concentration under the test set;

[0028] The energy concentration prediction values ​​of the MLP model and the XGBoost model under the test set are weightedly calculated using the first weight matrix and the second weight matrix to obtain the prediction value of the MLP-XGBoost combination model;

[0029] The mean absolute error, mean square error, and mean error percentage are calculated based on the number of samples in the test set, the predicted value of the combined model, and the true value of the energy concentration;

[0030] When the mean absolute error, mean square error, and average error percentage meet expectations, the MLP-XGBoost combined model is used as the final model for predicting the imaging quality of the optical system. If they do not meet expectations, the training set and test set are repartitioned and the training set is used again to train the MLP model and XGBoost model separately.

[0031] Optionally, the first weight matrix and the second weight matrix are determined using the following expressions:

[0032]

[0033] Among them, W * The weight matrix for combining a single model, matrix I1 = [1,1,…,1] T , S is the prediction error information matrix of a single model, S = e T e, e is the prediction error matrix, e=[E1,E2,…,Ei ] T , where E i is the prediction error vector of the i-th model:

[0034] E i =Z i -Y i =[e i1 ,e i2 ,…,e iN ] T

[0035] Among them, Z i =[z1,z2,…,z j ,…,z N ] T is the true value of energy concentration, Y i =[y i1 ,y i2 ,…,y ij ,…,y iN ] T is the predicted value of energy concentration.

[0036] Optionally, the prediction result is expressed as:

[0037] Compared with the prior art, the present invention has the following beneficial effects:

[0038] 1) Using an optical-mechanical integration simulation method for an optical system, we analyzed the impact of different assembly errors on the imaging quality of the optical system. We found that when the primary and secondary mirrors have posture deviations, different bolt preloads have different effects. It is necessary to adjust the appropriate preload to correct the degradation in imaging quality caused by posture deviations. Segregation and skew errors of the primary and secondary mirrors along the X and Y axes significantly affect imaging quality, while segregation and skew errors along the Z axis (optical axis) have almost no effect.

[0039] 2) Considering the mirror deformation and optical element pose deviation caused by preload during assembly, a combined MLP-XGBoost-based prediction model for the energy concentration of a dual-mirror optical system was constructed. The average error of the training set was only 4.70%, significantly outperforming the single MLP and XGBoost models, as well as traditional regression models (BP and SVR).

[0040] 3) A preload force optimization method based on the MLP-XGBoost model and the stochastic gradient descent algorithm was proposed. Under different assembly posture conditions, the energy concentration of the optical system was improved by an average of 11.34% compared with the pre-optimization method, which can be used to guide the actual optical system assembly process. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] The drawings described herein are used to provide a further understanding of the present invention, constitute a part of the present invention, and do not constitute a limitation of the present invention. In the drawings:

[0042] Figure 1 It is a three-dimensional geometric model of the double-reflective optical system;

[0043] Figure 2 It is the finite element model of the double-reflective optical system;

[0044] Figure 3 This is the mirror deformation result diagram;

[0045] Figure 4 Torsion-tension relationship diagram obtained for simulation and theoretical model;

[0046] Figure 5 It is the residual graph of the fitting between the sag plane and the mirror deformation;

[0047] Figure 6 This is the optical path diagram of the double-reflective optical system;

[0048] Figure 7 To circle the energy distribution diagram;

[0049] Figure 8 This is the influence diagram of bolt preload on energy concentration;

[0050] Figure 9 This is a diagram showing the influence of posture deviation on energy concentration;

[0051] Figure 10 It is the dot diagram under the influence of assembly error;

[0052] Figure 11 This is the schematic diagram of the MLP neural network;

[0053] Figure 12 This is a comparison chart of energy concentration before and after optimization;

[0054] Figure 13 A block diagram for predicting imaging quality and guiding the actual assembly process. DETAILED DESCRIPTION

[0055] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments and the accompanying drawings. Here, the exemplary embodiments of the present invention and their descriptions are used to explain the present invention, but are not intended to limit the present invention.

[0056] An embodiment of the present invention provides a method for predicting the imaging quality of an optical system based on assembly errors, comprising:

[0057] Step 1: Establish a finite element model of the double-mirror optical system and simulate the tightening process of the bolts to obtain the mirror deformation under different preload conditions.

[0058] During implementation, a three-dimensional geometric model of the double-reflective optical system is established, such as Figure 1 As shown, the optical system comprises a primary mirror, a secondary mirror, and a mirror frame. The primary mirror is secured to the frame via three sets of bolts and nuts, while the secondary mirror is assembled into a cylindrical hole in the frame via a pressure ring. In practice, light is incident parallel to the axis and reflected twice by the primary and secondary mirrors before converging into an image. Mirror surface deformation caused by the preload of the bolts and nuts during assembly, as well as deviations in the assembly posture of the primary and secondary mirrors, can significantly affect the optical path and imaging quality of the assembled optical system.

[0059] The commercial pre-processing software Hypermesh 12.0 can be used to mesh the three-dimensional geometric model and establish a finite element model. In order to realize the simulation of the tightening process of bolts and nuts, the existing thread mesh precise modeling method can be used to perform hexahedral meshing of the bolts and nuts; the automatic meshing method is used to perform tetrahedral meshing on the primary mirror, secondary mirror and mirror frame. Figure 2 The partitioned finite element model of the double-reflective optical system is shown, which includes 152,937 tetrahedral meshes and 251,136 hexahedral meshes.

[0060] Then, the parameters of the finite element model were set. All meshes used Solid185 elements. This type of mesh is mainly used for three-dimensional solid structures and is sensitive to deformation and stress. In terms of material properties, the bolts and the mirror frame are made of 1045 steel, and the primary and secondary mirrors are made of aluminum alloy. The specific parameters are shown in Table 1.

[0061] Table 1 Material parameters of double-reflective optical system

[0062]

[0063] The finite element model of the twin-mirror optical system includes 11 pairs of contact interfaces: the threaded interface, the nut-primary mirror interface, the primary mirror-frame interface, and the frame-secondary mirror interface. During simulation, these interfaces are divided into contact and target surfaces, meshed using CONTA173 and TARGE170 elements, respectively. The friction coefficient for each contact interface is set to 0.15. Boundary conditions include fixing the bolts to the bottom of the frame and constraining the translation of the primary mirror base to simulate a realistic assembly. Loading is performed by sequentially applying the same rotation angle to the nodes on the nut surface to simulate the bolt tightening process. The bolt size is M3. The actual preload generated in the project is approximately 1 kN, resulting in a nut rotation angle of approximately 3°.

[0064] ANASYS Workbench 19.0 was used to simulate the assembly process of the double-mirror optical system. The mirror deformation obtained by simulation is as follows: Figure 3 Figure 1 shows the deformation of the primary mirror, with a maximum deformation of 6.1935e-4mm, and Figure 1 shows the deformation of the secondary mirror, with a maximum deformation of 1.975e-8mm. It can be seen that the deformation of the primary mirror during assembly is much greater than that of the secondary mirror. Judging from the magnitude of the deformation, the deformation of the secondary mirror can be ignored.

[0065] In order to ensure the reliability and accuracy of the simulation results, the relationship curve between torque and preload obtained by simulation is compared with the theoretical results. Specifically, the theoretical formula for the torsion-tension relationship of bolt connections is:

[0066]

[0067] Among them, μ b is the end surface friction coefficient, r b is the effective radius of the end face, P is the pitch, μ t is the thread friction coefficient, r t is the effective thread radius, and α is the tooth angle. It can be seen that the tightening torque T and the preload force F are linearly related. For an M3 bolt connection, given the above parameters, a quantitative relationship curve between the tightening torque and preload force can be obtained.

[0068] Extract the tightening force and pre-tightening force from the finite element simulation results and obtain discrete data points at different tightening moments. Figure 4 The figure shows the discrete data points of the torsion-tension relationship obtained by finite element simulation and the torsion-tension curve obtained from the theoretical formula for the torsion-tension relationship of bolted connections. As can be seen from the figure, the discrete data points obtained by simulation essentially fall on the torsion-tension curve obtained by the theoretical formula, and the two are in close agreement. Further linear fitting of the discrete data points yielded a slope of 0.881, while the slope of the torsion-tension relationship obtained by the theoretical formula was 0.874. The error between the two is less than 1%, confirming that the finite element model constructed by this invention is accurate and reliable.

[0069] Step 2: Use Zernike polynomials to fit the mirror surface shape in the double-reflecting optical system to obtain Zernike polynomial coefficients for characterizing the mirror surface shape error.

[0070] In practice, Zernike polynomials can accurately fit the optical mirror surface shape, which can be described using mathematical polar coordinates as follows:

[0071]

[0072] Among them, P nm , Q mmis the Zernike coefficient, the angle is the angle measured counterclockwise from the local +x axis, ρ is the normalized radial coordinate, ρ∈[0,1].

[0073] The Zernike polynomial radial function is as follows:

[0074]

[0075] Where m and n are integer values, representing the circumferential and radial wave numbers respectively, nm must be an even number, and n ≥ m, s is The free variable of the interval.

[0076] The Zernike polynomial can accurately fit the mirror surface shape. Each of its terms has a clear material meaning and is easy to correspond to the Seidel aberration terms in optical design. The coefficients of the first nine terms of the Zernike polynomial and their corresponding Seidel aberrations are shown in Table 2.

[0077] Table 2 Zernike polynomial coefficients and their corresponding Seidel aberrations

[0078]

[0079] Step 3: Import the mirror deformation into the optical-mechanical-thermal coupling analysis module and use the Zernike polynomial coefficients as the basis function to fit the mirror surface shape, and obtain a macro file including the mirror surface shape deviation and the primary and secondary mirror assembly posture deviation.

[0080] In the implementation, the optical-mechanical-thermal coupling analysis module uses Sigfit software, which can convert the mirror deformation into a form readable by the optical simulation software, and realize the accurate fitting of the mirror deformation; and through polynomial fitting, an optical macro file with Zernike coefficients can be generated. The macro file can be used to directly load the sagittal height surface obtained by fitting into the optical simulation software. The fitting residual between the sagittal height surface obtained by polynomial fitting and the input mirror deformation is as follows: Figure 5 As shown in the figure, the unit waves = 1e-9m, the fitting residual distribution is relatively uniform, and most of the residuals are less than 1e-6mm, the maximum residual is 4.488e-6mm, and the maximum deformation obtained by finite element simulation is 6.1935e-4mm, which is much larger than the fitting residual, proving that the fitting error is very small and the fitting effect is good.

[0081] Step 4: Load the obtained macro file into the optical simulation module to perform light path imaging simulation to obtain energy concentration used to characterize imaging quality.

[0082] During implementation, Zemax simulation software was used for the optical simulation module. During the optical simulation process, the double-mirror optical system needs to be modeled. Specifically, according to Table 3, the reflecting surfaces corresponding to the primary mirror and the secondary mirror are established. The primary mirror is a rotating parabola, and the secondary mirror is an even-order hyperboloid. At the same time, the size of the opening at the center of the primary mirror is set, with the center opening being 16.2 mm, and the distance between the primary and secondary mirrors is set to 38 mm.

[0083] Table 3 Optical system structural parameters

[0084]

[0085]

[0086] Then load the macro file into the Zemax simulation software to realize the setting of the eccentricity and tilt of the primary and secondary mirrors by inserting the mirror coordinate discontinuity surface; superimpose the primary and secondary mirror assembly posture deviations with the reflective surface to generate a composite surface, so as to fit the mirror deformation to the mirror surface. As for the light source, a parallel light with an entrance pupil diameter of 84mm is set. The light is incident parallel to the axis direction and is reflected twice by the primary mirror and the secondary mirror before converging into an image. The ideal optical path is as follows Figure 6 As shown, the focal length of this system is 120mm and the wavelength of the incident light is 3.7-5.3μm.

[0087] In terms of imaging quality evaluation, since this optical system is mainly used for point target imaging detection, that is, energy detection, the imaging quality of the optical system is evaluated mainly from the perspective of energy. The optical system is an energy collection system. The energy concentration can directly reflect the energy collection ability of the optical system and can also comprehensively describe the imaging quality of the system. Therefore, energy concentration is selected as a quantitative evaluation indicator of the imaging quality of the optical system. In engineering, the diameter of the circle containing 83% of the energy is generally used to judge the energy concentration. Therefore, the energy concentration of the optical system is evaluated by the percentage of the enclosed energy in an Airy disk to the total energy. Optical simulation with Zemax software can obtain the Airy disk radius of the optical system and the fractional curve of the enclosed energy, such as Figure 7 As shown in Figure 1, the enclosed energy fraction curve shows the distribution of spot energy with the spot diameter. In the obtained enclosed energy fraction curve, the enclosed energy fraction corresponding to the Airy disk radius is the energy concentration of the analyzed optical system.

[0088] Step 5: Construct a data set based on the preload force, primary and secondary mirror assembly posture deviation, and energy concentration, and use the constructed data set to train the MLP model and XGBoost model.

[0089] In practice, there are many factors that affect the imaging quality of the twin-mirror optical system. Usually, the mirror deformation error caused by bolt preload is 3-4 orders of magnitude higher than the processing error of the mirror itself. Therefore, two aspects of assembly errors are mainly considered during the research process: the mirror deformation error caused by bolt preload and the position deviation of the primary and secondary mirrors.

[0090] Influence of bolt pre-tightening force: A set of primary and secondary mirror position deviations are randomly generated. The double-mirror optical system will have a certain initial deflection and eccentricity error. On this basis, the influence of different pre-tightening forces on the imaging quality of the optical system is studied. For different bolt pre-tightening forces, the nut angle can be adjusted to characterize the effect. Figure 8 The preload forces corresponding to bolt connections No. 1, 2, and 3 are F1, F2, and F3 respectively. Using the single factor control variable concept, when analyzing the preload force of one bolt, the preload forces of the other bolts are all set to 1000N. The law of energy concentration changing with preload force is shown in the figure below. Figure 8 As shown in the figure, as the preload of bolt No. 1 increases, the energy concentration gradually increases and the imaging quality gradually improves. For bolt No. 2, the energy concentration gradually decreases as the preload increases. For bolt No. 3, the energy concentration decreases as F3 increases. When the preload exceeds 1000N, the energy concentration fluctuates and tends to be stable. In summary, considering the influence of the position deviation of the primary and secondary mirrors, the influence of different bolt preloads on energy concentration varies. Precise control of the preload is required to ensure the optimal imaging quality of the optical system.

[0091] The influence of the posture deviation of the primary and secondary mirrors: The posture deviation of the primary and secondary mirrors can be characterized by adjusting the eccentricity and tilt of the mirror in the Zemax software. In the Cartesian coordinate system, the six degrees of freedom of the primary and secondary mirrors are the eccentricity errors along the X, Y and Z axes (D x , D y and D z ), and the skew errors around these three axes (T x , T y and T z ). Applying a set of random bolt pre-tightening forces will cause the mirror surface to deform to a certain extent, and explore the influence of posture deviation on the imaging quality of the optical system. Considering the posture deviation of the primary and secondary mirrors with 12 degrees of freedom: the primary mirror eccentricity error D x1 , D y1 and D z1 ; Primary mirror tilt error T x1 , T y1 and T z1 Secondary mirror eccentricity error D x2 , D y2 and D z2 ; Secondary mirror tilt error T x2 , T y2 and Tz2 Using the single factor control variable idea, when analyzing the posture deviation of one degree of freedom, the other posture deviations are set to 0. The variation law of energy concentration with posture deviation is as follows: Figure 9 As shown in the figure, the decentration and skew errors around the Z axis have little effect on the energy concentration of the optical system, but the other eight posture deviation parameters have a significant impact on energy concentration. When the decentration and skew are within ±0.01mm, the energy concentration changes little, but when the decentration and skew are greater than 0.01mm, the energy concentration drops rapidly, especially for the primary mirror. When the decentration and skew are ±0.03, the energy concentration of the primary mirror drops by nearly 60% and 50%, respectively.

[0092] To intuitively demonstrate the impact of overall assembly errors on the energy concentration of an optical system, the concept of a spot diagram is introduced. In a real optical system, light rays are not perfectly straight lines; instead, the image is a diffuse spot. This resulting spot image is called a spot diagram. The distribution of points in a spot diagram approximately represents the energy distribution of the image point. Based on the definition of energy concentration, if all points in the spot diagram fall within the Airy disk, the energy concentration has reached its maximum. Figure 10 The following are optical system point diagrams under different conditions. The black circles in the diagrams represent the Airy disk of the optical system. Diagram a corresponds to the imaging result under an ideal optical path, Diagrams b and c correspond to the imaging results under the influence of mirror deformation and posture deviation, respectively, and Diagram d shows the imaging result under the combined effects of mirror deformation and posture deviation. The energy concentration in Diagrams a and b is 83.8%, in Diagram c is 52.4%, and in Diagram d is 47.5%. As can be seen from the diagrams, energy concentration can be affected by the combined effects of mirror deformation caused by preload and posture deviation. Posture deviation, in particular, can easily cause the light spot to extend beyond the Airy disk, significantly reducing image quality.

[0093] from Figure 10 It can be seen that within the allowable error range, the influence of the eccentricity and skew errors of the primary and secondary mirrors in the Z-axis direction on the imaging quality can be ignored. Therefore, the mirror posture deviation only considers the eccentricity errors of the primary and secondary mirrors along the X-axis and Y-axis, as well as the skew errors around the X-axis and Y-axis. The sample format of the dataset is shown in Table 4.

[0094] Table 4 Datasets of assembly error and imaging quality

[0095]

[0096] After that, the feature variables and target variables in the constructed dataset are randomly sorted and normalized, and finally the dataset is divided into training set and test set according to the set ratio.

[0097] In practice, a single model is often limited to a specific data distribution or pattern and may perform poorly when faced with new data. Therefore, the present invention introduces the idea of ​​a combined model, combining multiple different models, fully leveraging the advantages of a single model algorithm, obtaining information about the prediction target from multiple angles, and improving the generalization ability and prediction accuracy of the overall model. In one implementation, an MLP-XGBoost model can be constructed, which is a combined prediction model that combines a multi-layer perceptron (MLP) with a gradient boosting tree (XGBoost).

[0098] (1) MLP model

[0099] The MLP multilayer perceptron neural network is a multilayer feedforward neural network that can achieve nonlinear mapping between input and output and is widely used in machine learning, pattern recognition and other fields. Figure 11 As shown, the entire neural network consists of an input layer, a hidden layer, and an output layer, where x = [x1, x2, x3, ..., x i ] is the input variable, k=[k1,k2,k3,…,k j ] is the hidden layer output variable, y is the final output variable, and the relationship between y and k is as follows:

[0100]

[0101] Where w j is the weight of the connection between the jth neuron and y, θ y is the bias of y, k j is the output of the jth hidden neuron, and the relationship between k and x is as follows:

[0102]

[0103] Where, v ij is the weight of the connection between the i-th input variable x and the j-th neuron, x i is the i-th input variable, is the bias of the jth neuron in the kth hidden layer.

[0104] (2) XGBoost model

[0105] XGBoost is a gradient boosting ensemble machine learning model that helps avoid overfitting. It mainly uses an iterative regression tree algorithm to construct multiple regression trees in a serial manner. The goal of the newly generated regression tree is to fit the residual of the previous tree. In each round of iteration, the new model will contribute to reducing the total loss of all previous models. In general, the goal of XGBoost is to learn a prediction function To minimize a given loss function, the loss function can be expressed as:

[0106]

[0107] Where x i is the feature vector of the i-th sample, y i is the corresponding output, l is a differentiable convex loss function used to measure the prediction and the true value y i The gap between k is the kth weak learner, Ω represents the complexity of the model, which is usually in the form of Where T is the number of leaf nodes in the tree, w is the vector of leaf node weights, and γ and λ are regularization parameters.

[0108] In each iteration t, XGBoost adds a new weak learner f t , used to predict the residual or error The prediction function is updated as: In order to find the best f t , will define a t The second-order approximate loss function of

[0109]

[0110] where g i It is about The first derivative of h i is the second-order derivative. In each round of training, XGBoost uses a greedy algorithm to traverse all possible split points and selects the split point with the smallest loss function to split the tree node. This method can effectively handle discrete data and missing value problems.

[0111] In practice, the main advantage of MLP is that the model structure is flexible, with sufficient hidden layers and neurons, and it can approximate any complex function. However, it relies on a large number of parameter adjustments and requires sufficient data to reduce the risk of overfitting, and its computational efficiency is low; XGBoost performs well in capturing the structured features of the data set, but may not be comparable to neural networks when processing complex nonlinear relationships in input data. Therefore, the present invention combines the MLP and XGBoost models to give full play to the advantages of both and make up for each other's shortcomings. MLP can extract highly abstract features through its deep structure, while XGBoost can effectively integrate these features and has better coordination with outliers and unbalanced data. The combination of these two models to predict the imaging quality of the double-reflective optical system can achieve more accurate and stable prediction results.

[0112] During the specific training process, the MLP model and XGBoost model are trained separately using the training set.

[0113] Then, the MLP model and XGBoost model were tested using the test set to obtain the energy concentration prediction values ​​of the MLP model and XGBoost model under the test set;

[0114] Calculate a first weight matrix and a second weight matrix according to the obtained energy concentration prediction value under the test set and the true value of the energy concentration under the test set;

[0115] The energy concentration prediction values ​​of the MLP model and the XGBoost model under the test set are weightedly calculated using the first weight matrix and the second weight matrix to obtain the prediction value of the MLP-XGBoost combination model;

[0116] The mean absolute error, mean square error, and mean error percentage are calculated based on the number of samples in the test set, the predicted value of the combined model, and the true value of the energy concentration;

[0117] When the mean absolute error, mean square error, and average error percentage meet expectations, the MLP-XGBoost combined model is used as the final model for predicting the imaging quality of the optical system. If they do not meet expectations, the training set and test set are repartitioned and the training set is used again to train the MLP model and XGBoost model separately.

[0118] To evaluate the prediction accuracy of the MLP-XGBoost combination model, the MLP and XGBoost models, along with two common prediction models: the BP neural network and the SVR regression model, were selected as control groups. The dataset construction and partitioning methods, model training, and error evaluation methods were all kept consistent. Table 5 shows the error evaluation results of the above models in the test set. As can be seen from the table, the average prediction errors of the single models, MLP and XGBoost, were 4.83% and 7.85%, respectively, both higher than the proposed MLP-XGBoost prediction model (4.70%). The MAE and MSE indicators were also lower than those of the proposed MLP-XGBoost model. This indicates that the prediction accuracy of the combination model is superior to the two single models, and the proposed MLP and XGBoost combination model is reliable. Furthermore, compared with the other two regression prediction models, the average prediction errors of the BP neural network and SVR regression models reached 6.07% and 24.96%, respectively, far exceeding the prediction errors of MLP-XGBoost. MLP-XGBoost also achieved the lowest MAE and MSE indicators. Therefore, the proposed MLP-XGBoost combination model exhibited the best optical imaging quality prediction accuracy.

[0119] Table 5 Comparison of prediction model error evaluation indicators

[0120] Prediction Model MAE / mm MSE / mm MPE MLP-XGBoost 0.0320 0.0416 4.70％ MLP 0.0335 0.0430 4.83％ XGBoost 0.0551 0.0707 7.85％ BP 0.0379 0.0615 6.07％ SVR 0.1204 0.1729 24.96％

[0121] Step 6: Obtain the current preload force and primary and secondary mirror assembly posture deviations of the optical system to be predicted, and input the obtained preload force and primary and secondary mirror assembly posture deviations into the trained MLP model and XGBoost model respectively to obtain the first energy concentration and the second energy concentration.

[0122] Step 7: Obtain the first weight matrix and the second weight matrix of the MLP model and the XGBoost model, and use the determined first weight matrix and the second weight matrix to perform weighted calculation on the first energy concentration and the second energy concentration to obtain the final energy concentration as the prediction result.

[0123] In implementation, the first weight matrix and the second weight matrix can be determined using the following expressions:

[0124]

[0125] Among them, W * The weight matrix for combining a single model, matrix I1 = [1,1,…,1] T , S is the prediction error information matrix of a single model, S = e T e, e is the prediction error matrix, e=[E1,E2,…,E i ] T , where E i is the prediction error vector of the i-th model:

[0126] E i =Z i -Y i =[e i1 ,e i2 ,…,e iN ] T

[0127] Among them, Z i =[z1,z2,…,z j ,…,z N ] T is the true value of energy concentration, Y i =[y i1 ,y i2 ,…,y ij ,…,y iN ] T is the predicted value of energy concentration.

[0128] Correspondingly, the predicted value of the MLP-XGBoost combination model is expressed as:

[0129]

[0130] In a specific implementation, during the actual assembly and adjustment of a twin-mirror optical system, positional deviations between the primary and secondary mirrors are inevitable and difficult to completely eliminate. They can only be controlled within a certain range. This often requires adjusting the bolt preload to improve the imaging quality of the twin-mirror optical system. For primary and secondary mirror assemblies with a certain positional deviation, the preload can be optimized using a stochastic gradient descent algorithm to maximize the optical system's imaging quality and guide the actual bolt connection assembly process.

[0131] The core idea of ​​the stochastic gradient descent algorithm is to randomly select a sample in each iteration and iteratively update the parameters using the gradient of that sample to minimize the loss function. This method improves optimization efficiency while avoiding falling into local minima, making the training results more accurate. Specifically, for the loss function L(θ), where θ is the parameter vector, the update rule of stochastic gradient descent is as follows:

[0132]

[0133] Where θ t is the parameter value after the tth iteration, η is the learning rate, is the loss function at the current parameter value θ t About the sample (x i ,y i ) gradient.

[0134] Based on this, after obtaining the energy concentration predicted by the MLP-XGBoost combined model, the assembly posture deviation of the primary and secondary mirrors can be used as input values ​​and set as constants according to the actual assembly situation; the preload force can be used as input value and set as an optimization variable; with the maximization of the predicted energy concentration result as the optimization goal, the stochastic gradient descent algorithm is used to iteratively calculate the optimal preload force, and the actual assembly process is guided by the calculated optimal preload force.

[0135] Effect verification: 10 sets of primary and secondary mirror posture errors and initial bolt preloads were randomly generated. The energy concentration was calculated by combining the models. Then, the initial preload was optimized using the stochastic gradient descent algorithm to obtain the optimized energy concentration. Figure 12 As shown in the figure, the energy concentration of the 10 groups of experiments increased by an average of 11.34% compared to before optimization, proving that the optimization algorithm used is effective. Preload optimization using this method can significantly improve the energy concentration of the optical system and can be used to guide the actual assembly process.

[0136] See also Figure 13The overall design concept of the present invention includes: constructing an accurate finite element model of a double-reflective optical system, simulating the bolt tightening process, obtaining the mirror deformation under the action of assembly stress, using Zernike polynomials to fit the mirror surface shape, and using this as an intermediate medium. Zemax is used to simulate the imaging of the optical system under the conditions of mirror deformation and assembly posture, and explore the influence of various relevant assembly parameters on the imaging quality of the optical system, and then construct a data set; the data set is used to train the established MLP-XGBoost combination model, and then the trained MLP-XGBoost combination model can be used to predict the imaging quality according to the relevant assembly parameters, so as to evaluate the assembly quality; in addition, it is also possible to use the maximization of the predicted energy concentration result as the optimization goal, use the stochastic gradient descent algorithm to iteratively calculate the optimal preload, and guide the actual assembly process according to the calculated optimal preload.

[0137] The imaging quality of the optical system was accurately and quickly predicted under different assembly error conditions, with a prediction accuracy of up to 95%. Finally, considering the different primary and secondary mirror posture deviations, the stochastic gradient descent method was used to optimize the bolt preload, and the following conclusions were obtained:

[0138] 1) Through the optical-mechanical integration simulation method of the optical system, the influence of different assembly errors on the imaging quality of the optical system was analyzed. It was found that when there was a posture deviation between the primary and secondary mirrors, different bolt preloads had different effects. It was necessary to adjust the appropriate preload size to correct the degradation of imaging quality caused by the posture deviation. The eccentricity and skew errors of the primary and secondary mirrors along the X and Y axes had a significant impact on the imaging quality, while the segregation and skew errors in the Z axis (optical axis) had almost no effect.

[0139] 2) Considering the mirror deformation and optical element posture deviation caused by the preload during the assembly process, a combined energy concentration prediction model for the double-mirror optical system based on MLP-XGBoost was constructed. The average error of the training set was only 4.70%, which is significantly better than the single MLP and XGBoost models, as well as the traditional regression models (BP and SVR).

[0140] 3) A preload force optimization method based on the MLP-XGBoost model and the stochastic gradient descent algorithm was proposed. Under different assembly posture conditions, the energy concentration of the optical system was improved by an average of 11.34% compared with the pre-optimization method, which can be used to guide the actual optical system assembly process.

[0141] The above description is only a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention are included in the scope of protection of the present invention.

Claims

1. A method for predicting the imaging quality of an optical system based on assembly error, characterized in that: include: A finite element model of the double-mirror optical system was established, and the bolt tightening process was simulated to obtain the mirror deformation under different preload conditions; The Zernike polynomials are used to fit the mirror surface shape in the double-mirror optical system to obtain the Zernike polynomial coefficients used to characterize the mirror surface shape error. The mirror deformation is imported into the optical-mechanical-thermal coupling analysis module and the Zernike polynomial coefficients are used as the basis function to fit the mirror shape. A macro file including the mirror shape deviation and the primary and secondary mirror assembly posture deviation is obtained. The obtained macro file is loaded into the optical simulation module to perform optical path imaging simulation to obtain the energy concentration used to characterize the imaging quality; A dataset was constructed based on preload force, primary and secondary mirror assembly posture deviation, and energy concentration, and the constructed dataset was used to train the MLP model and XGBoost model. Obtain the current preload force and primary and secondary mirror assembly posture deviations of the optical system to be predicted, and input the obtained preload force and primary and secondary mirror assembly posture deviations into the trained MLP model and XGBoost model respectively to obtain the first energy concentration and the second energy concentration; The first weight matrix and the second weight matrix of the MLP model and the XGBoost model are obtained, and the first energy concentration and the second energy concentration are weightedly calculated using the determined first weight matrix and the second weight matrix to obtain the final energy concentration as a prediction result.

2. The optical system imaging quality prediction method based on assembly error according to claim 1, characterized in that: Also includes: The assembly posture deviation of the primary and secondary mirrors is used as an input value and set as a constant according to the actual assembly situation; the preload force is used as an input value and set as an optimization variable; Taking the maximization of the prediction results as the optimization goal, the stochastic gradient descent algorithm is used to iteratively calculate the optimal preload force, and the actual assembly process is guided by the calculated optimal preload force.

3. The method for predicting optical system imaging quality based on assembly error according to claim 1, wherein: The process of establishing a finite element model of a double-reflective optical system includes: Establish a three-dimensional geometric model of the double-mirror optical system, including the primary mirror, secondary mirror, and mirror frame. The primary mirror is fixed to the mirror frame with three sets of bolts and nuts, and the secondary mirror is assembled with the cylindrical hole on the mirror frame through a pressure ring. The three-dimensional geometric model is meshed to establish a finite element model, wherein the bolts and nuts are meshed with hexahedrons, and the primary mirror, secondary mirror and mirror frame are meshed with tetrahedrons.

4. The method for predicting optical system imaging quality based on assembly error according to claim 1, wherein: The process of loading the obtained macro file into the optical simulation module for light path imaging simulation includes: Establish the corresponding reflective surfaces of the primary mirror and the secondary mirror, where the primary mirror is a rotating parabola and the secondary mirror is an even-order hyperboloid. At the same time, set the size of the opening at the center of the primary mirror and the distance between the primary and secondary mirrors. The mirror surface deviation is adjusted by inserting the mirror coordinate discontinuity surface to achieve the setting of the primary mirror and secondary mirror eccentricity and tilt; The assembly posture deviations of the primary and secondary mirrors are superimposed on the reflecting surface to generate a composite surface, thereby fitting the mirror deformation to the mirror surface.

5. The optical system imaging quality prediction method based on assembly error according to claim 1, wherein: The process of constructing a data set based on preload, primary and secondary mirror assembly posture deviation, and energy concentration includes: The preload force and the primary and secondary mirror assembly posture deviation are used as feature variables, and the energy concentration is used as the target variable to construct a data set. The primary and secondary mirror assembly posture deviation includes the eccentricity error of the primary and secondary mirrors along the X and Y axes, as well as the deflection error around the X and Y axes. The feature variables and target variables in the constructed dataset are randomly sorted and normalized, and finally the dataset is divided into training set and test set according to the set ratio.

6. The method for predicting optical system imaging quality based on assembly error according to claim 5, wherein: The process of training the MLP model and XGBoost model using the constructed dataset includes: Use the training set to train the MLP model and XGBoost model separately; The MLP model and XGBoost model were tested using the test set to obtain the energy concentration prediction values ​​of the MLP model and the XGBoost model under the test set; Calculate a first weight matrix and a second weight matrix according to the obtained energy concentration prediction value under the test set and the true value of the energy concentration under the test set; The energy concentration prediction values ​​of the MLP model and the XGBoost model under the test set are weightedly calculated using the first weight matrix and the second weight matrix to obtain the prediction value of the MLP-XGBoost combination model; The mean absolute error, mean square error, and mean error percentage are calculated based on the number of samples in the test set, the predicted value of the combined model, and the true value of the energy concentration; When the mean absolute error, mean square error, and average error percentage meet expectations, the MLP-XGBoost combined model is used as the final model for predicting the imaging quality of the optical system. If they do not meet expectations, the training set and test set are repartitioned and the training set is used again to train the MLP model and XGBoost model separately.

7. The method for predicting optical system imaging quality based on assembly error according to claim 6, wherein: The first weight matrix and the second weight matrix are determined using the following expressions: Among them, W * The weight matrix for combining a single model, matrix I1 = [1,1,…,1] T , S is the prediction error information matrix of a single model, S = e T e, e is the prediction error matrix, e=[E1,E2,…,E i ] T , where E i is the prediction error vector of the i-th model: E i =Z i -Y i =[e i1 ,e i2 ,…,e iN ] T Among them, Z i =[z1,z2,…,z j ,…,z N ] T is the true value of energy concentration, Y i =[y i1 ,y i2 ,…,y ij ,…,y iN ] T is the predicted value of energy concentration.

8. The method for predicting optical system imaging quality based on assembly error according to claim 7, wherein: The prediction results are expressed as:

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