Optical system imaging quality prediction model construction method considering both surface shape error and pose error

Abstract

The invention relates to the field of optical system imaging, in particular to an optical system imaging quality prediction model construction method giving consideration to surface shape errors and pose errors, which adopts a Zernike polynomial to perform accurate fitting on mirror surface shape errors caused by bolt pre-tightening force, and adopts a finite element mode to perform simulation on an optical system bolt tightening process. According to the method, Zernike polynomial fitting is taken as a basic parameter, various mirror surface shape errors and assembly pose deviations are fully considered when Zemax is adopted to carry out optical path imaging simulation, and the energy concentration degree is taken as an imaging quality quantitative evaluation index, so that the optical path imaging simulation of the two-mirror optical system is realized. According to the method, an SVR proxy model containing local and global mixed kernel functions is established, sensitivity analysis is performed on mirror surface shape and assembly pose parameters, an assembly data set is obtained through assembly and imaging joint simulation, and the model is trained to obtain an imaging quality prediction model so as to realize rapid and accurate prediction of imaging quality.

Description

Technical Field

[0001] The present invention relates to the technical field of optical systems, and in particular to a method for constructing an optical system imaging quality prediction model taking both surface shape error and position error into consideration. Background Art

[0002] The seeker is a device equipped with detection parts, signal processing equipment and servo control system. It is one of the important components of weapons and equipment. Its main function is to realize target detection, identification and tracking. Its performance directly affects the hit accuracy of weapons and equipment. The seeker generally adopts a coaxial two-reflective optical system, that is, the primary mirror and the secondary mirror are located on the same axis, so as to effectively reduce optical distortion and improve imaging resolution.

[0003] In practice, most optical systems include a primary mirror, a secondary mirror, and a bracket, and are assembled by bolting. Bolts, nuts, and other fasteners are used to fix the primary mirror and the secondary mirror to the bracket. However, the assembly stress during the assembly process will inevitably cause the mirror surface to deform structurally, causing surface errors in the optical components, affecting the imaging quality of the optical system. Therefore, quantitative evaluation of the imaging quality of the optical system is an important part of measuring the service performance of the optical system. Traditional imaging quality evaluation methods include the star point method, the knife edge method, the slit method, and the Ronchi method. However, the test requires that each optical component be placed one by one in a specified order and distance, which is inefficient and requires a lot of time and labor costs. Therefore, it is necessary to establish a fast and accurate prediction method for imaging quality. Summary of the invention

[0004] In view of the above problems, an embodiment of the present invention provides a method for constructing an optical system imaging quality prediction model that takes into account both surface error and posture error.

[0005] An embodiment of the present invention provides a method for constructing an optical system imaging quality prediction model taking into account both surface error and posture error, comprising:

[0006] S1. Using Zernike polynomials to fit the mirror surface shape in the optical system to obtain Zernike polynomial coefficients for characterizing the mirror surface shape error;

[0007] S2. Establish a finite element model of the optical system, simulate the tightening process of the bolt connection in the finite element model, and obtain the deformation of the mirror surface;

[0008] S3, importing the mirror deformation into the optical-mechanical-thermal coupling analysis module and inserting the Zernike polynomial coefficients to obtain the mirror surface error parameters and the mirror assembly posture deviation;

[0009] S4, importing the mirror surface error parameters and the mirror assembly posture deviation into the optical simulation module to perform light path imaging simulation, and obtain the energy concentration used to characterize the imaging quality;

[0010] S5. Construct a data set based on mirror surface error parameters, mirror assembly posture deviation, and energy concentration, and establish an SVR proxy model containing local and global hybrid kernel functions;

[0011] S6. Use the data set to train the SVR proxy model to obtain the optical system imaging quality prediction model.

[0012] Optionally, S1 uses Zernike polynomials to fit the mirror surface shape in the optical system to obtain Zernike polynomial coefficients for characterizing the mirror surface shape error, specifically including:

[0013] Set the translation of the mirror surface relative to the ideal position of the X, Y and Z axes to u after deformation x 、u y and u z , the rotation amounts around the X, Y and Z axes are θx, θy and θz respectively, and cosθx=cosθy=cosθz=1, sinθx=θx, sinθy=θy, sinθz=θz; according to the homogeneous coordinate transformation method, the coordinate transformation before and after the mirror deformation is shown in formula (1):

[0014]

[0015] Among them, X i ,Y i ,Z i )(i=1,2…n) are the node coordinates before mirror deformation, (X i ',Y i ',Z i ')(i=1,2…n) are the node coordinates after mirror deformation, T is the rigid body displacement of mirror deformation obtained based on the least squares method;

[0016] Multiply the left side of the node coordinates after mirror deformation by the transposed matrix T -1 , the node coordinates of the surface error after removing the displacement of the mirror cylinder are obtained, as shown in formula (2):

[0017]

[0018] Using Zernike polynomials as basis functions to fit the surface error of optical components, solving the coefficients of Zernike polynomials is to solve the surface error function W. N The linear combination coefficients of the Zernike polynomials of (x, y) are shown in formula (3):

[0019]

[0020] Among them, Z i (x, y) is the Zernike polynomial in the i-th Cartesian coordinate system, C i is the coefficient of the i-th Zernike polynomial, and n is the number of Zernike polynomial terms;

[0021] The actual measured discrete point displacement is substituted into formula (3), and the least square method is used to solve the Zernike polynomial coefficient matrix. The fitting accuracy of the coefficient matrix is ​​evaluated by the root mean square error. The coefficient matrix obtained after the fitting accuracy is the polynomial coefficient that characterizes the mirror surface error.

[0022] Optionally, it is characterized in that the process of establishing the finite element model of the optical system in S2 includes:

[0023] Establish a finite element model of the optical system including the threaded connection structure, and establish the free tetrahedral mesh of the primary mirror, secondary mirror and bracket;

[0024] The mathematical expressions for the cross-sectional profiles of internal and external threads are established as follows:

[0025] According to the thread parameters, the thread profile is divided into three different parts: the thread root part, the thread side part and the thread crest part; the three divided parts are extended to the plane to obtain the thread profile along the transverse section. The thread root is selected as the starting point, and θ represents the rotation angle of the point on the thread cross-sectional profile relative to the starting point. The expression of the cross-sectional profile of the thread is established, as shown in formula (4):

[0026]

[0027] in, d represents the nominal diameter, d1 represents the thread pitch, r represents the distance from the thread profile to the center axis of the bolt, and ρ represents the radius of the arc at the root of the thread.

[0028] Based on the mathematical expressions of the cross-sectional profiles of internal and external threads and the rotational invariance of the cross-sectional profiles of threads, the mesh models of internal and external threads are established using the thread meshing method.

[0029] Optionally, it is characterized in that S4, the process of importing the mirror surface error parameter and the mirror assembly posture deviation into the optical simulation module to perform light path imaging simulation includes:

[0030] Establish the reflecting surfaces corresponding to the primary mirror and the secondary mirror, where the primary mirror is a rotating parabola and the secondary mirror is an even-order hyperboloid, and set the size of the opening at the center of the primary mirror, the distance between the primary and secondary mirrors, the thickness tolerance of the primary and secondary mirrors, the surface shape error, and the concentricity;

[0031] The mirror assembly posture deviation is superimposed with the reflection surface to generate a composite surface, thereby fitting the mirror deformation to the mirror surface;

[0032] The mirror surface error is adjusted by inserting the mirror coordinate discontinuity surface to achieve the setting of the eccentricity and tilt of the primary mirror and the secondary mirror.

[0033] Optionally, the process of constructing a data set based on the mirror surface error parameter, the mirror assembly posture deviation, and the energy concentration in S5 includes:

[0034] The mirror surface error parameters are selected from the defocus, first-order astigmatism-Y axis and first-order trefoil aberration-Y axis in the Zernike polynomial coefficients. The mirror assembly posture deviation is selected from the eccentricity error of the primary mirror and the secondary mirror along the X and Y directions and the tilt error around the X and Y directions. A total of 11 sensitive parameters are selected as characteristic variables, and the energy concentration is selected as the target variable.

[0035] The feature variables and target variables are normalized, and the normalized feature variables and target variables are divided into training sets and test sets according to the set ratio.

[0036] Optionally, the process of establishing an SVR proxy model including local and global hybrid kernel functions in S5 includes:

[0037] The Gaussian kernel function is selected as the local kernel function, the polynomial kernel function is selected as the global kernel function, and the hybrid kernel function form is constructed as shown in formula (5):

[0038] K mix =λK local +(1-λ)K global (5)

[0039] Among them, K local Refers to the local kernel function, K global Refers to the global kernel function, λ is the scaling factor, which is used to adjust the ratio between the local kernel function and the global kernel function;

[0040] Set the parameters of the SVR agent model, including the regularization parameter C, the tolerance parameter ε, the polynomial kernel order, the scaling factor, and the Gaussian kernel width.

[0041] Optionally, the process of using the data set to train the SVR proxy model in S6 to obtain the optical system imaging quality prediction model includes:

[0042] S61. Use the training set data to train the SVR proxy model, use the test set data to test the trained SVR proxy model and calculate the determination coefficient R 2 , root mean square error RMSE and mean relative error MRE, as shown in equations (6), (7) and (8) respectively:

[0043]

[0044]

[0045]

[0046] Among them, n is the number of test set samples, y i is the true value of energy concentration, y is the average value of the true value of energy concentration, f(x i ) is the predicted value of energy concentration, and m is the number of model training cycles;

[0047] S62, based on the calculated determination coefficient, root mean square error and mean relative error, determine whether the prediction accuracy and generalization ability of the SVR proxy model meet expectations, and if they meet expectations, terminate the training; if they do not meet expectations, adjust the parameters of the model and execute S63;

[0048] S63: Re-divide the data into a training set and a test set according to the set ratio and return to execute S61.

[0049] Compared with the prior art, the beneficial effects of the present invention are: using Zernike polynomials to accurately fit the mirror surface error caused by the bolt preload, and using finite element modeling to accurately simulate the mirror deformation during the bolt tightening process; thus, a joint simulation method for assembly and imaging of two-mirror optical systems is proposed, using Zernike polynomial fitting as the basic parameter, using Zemax software to fully consider various mirror surface errors and assembly posture deviations when performing optical path imaging simulation, and using energy concentration as a quantitative evaluation index for imaging quality. Then, an SVR proxy model containing local and global hybrid kernel functions is established, sensitivity analysis of mirror surface shape and assembly posture parameters is performed, an assembly data set is obtained through joint simulation of assembly and imaging, and the model is trained. Finally, the established proxy model is compared with the SVR model of a single kernel function / no kernel function, and the traditional regression model. The results show that the established hybrid kernel function SVR model has the smallest imaging quality prediction error, and shows excellent imaging quality prediction capabilities under different assembly error conditions, laying a foundation for real-time adjustment of optical systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] 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:

[0051] Figure 1 It is a schematic diagram of the principle framework of the present invention;

[0052] Figure 2 is the Zernike standard polynomial pyramid diagram;

[0053] Figure 3 The two-dimensional wave surface shape represented by the first 16 standard Zernike polynomials;

[0054] Figure 4 The three-dimensional wave surface shape represented by the first 16 standard Zernike polynomials;

[0055] Figure 5 is the surface error cloud diagram of the primary mirror;

[0056] Figure 6 is the fitting residual between the fitted sag surface and the mirror deformation;

[0057] Figure 7 It is the structural diagram of the two-mirror optical system;

[0058] Figure 8 is the external thread profile of one pitch along the axial section;

[0059] Fig. 9 is the external thread profile along the transverse section;

[0060] Fig.10 This is a schematic diagram of the modeling process of internal and external thread meshes, where Figure a is an external thread mesh and Figure b is an internal thread mesh;

[0061] Fig.11 It is the finite element mesh model of the bolted connection structure;

[0062] Fig.12 It is the finite element mesh model of the two-mirror optical system;

[0063] Fig.13 The torsion-tension relationship curves under different mesh sizes and shapes;

[0064] Fig.14 The deformation cloud diagrams of the primary mirror and the secondary mirror, where Figure a is the primary mirror and Figure b is the secondary mirror;

[0065] Fig.15 It is the ideal optical path entity model;

[0066] Fig.16 is the ideal optical path MTF curve;

[0067] Fig.17 is the energy concentration curve of the ideal optical path;

[0068] Fig.18 The imaging results of the optical system at different rotation angles of the Z axis, where Figure a is a rotation of 0°, Figure b is a rotation of 90°, and Figure c is a rotation of 180°;

[0069] Fig.19are the Zernike polynomial coefficients of the primary mirror shape fitting under different bolt preloads;

[0070] Fig. 20 The point diagrams of the optical system under different conditions, where Figure a corresponds to the imaging result of the ideal optical path, Figure b and Figure c correspond to the imaging results under the influence of the mirror surface shape and assembly posture error respectively, and Figure d is the imaging result under the combined effect of the two.

[0071] Fig.21 is the ε pipeline model for linear regression;

[0072] Fig. 22 It is a scatter plot of the predicted value and the true value of the SVR proxy model;

[0073] Fig.23 is the average relative error of the test set under repeated experiments;

[0074] Fig.24 Comparison chart of prediction errors of different kernel functions;

[0075] Fig.25 The mean relative error of different regression models. DETAILED DESCRIPTION

[0076] In order to make the purpose, technical solution 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 illustrative embodiments of the present invention and their descriptions are used to explain the present invention, but are not intended to limit the present invention.

[0077] The embodiment of the present invention provides a method for constructing an optical system imaging quality prediction model that takes into account both surface error and posture error. The principle framework is as follows: Figure 1 As shown, the specific process includes:

[0078] S1. Use Zernike polynomials to fit the mirror surface shape in the optical system to obtain Zernike polynomial coefficients for characterizing the mirror surface shape error.

[0079] In practice, Zernike polynomials are a set of equations expressed in polar coordinates, usually described as:

[0080]

[0081] Where n = 0, 1, 2... is the order of the polynomial, l is a parameter related to the angle, the radial coordinate ρ is the normalized radial distance, and θ is the polar coordinate angle; n and l are both odd and even and n ≥ |l|, so (nl) is always an even number; and l = n-2m, m = 1, 2, 3...n, the following expression can be obtained:

[0082]

[0083]

[0084] Any k-order wave surface F(ρ,θ) can be fitted using Zernike polynomials, as shown in the following formula:

[0085]

[0086]

[0087] In the formula, a k is the coefficient of the k-order Zernike polynomial. The essence of fitting the optical system mirror with the Zernike polynomial is to solve the coefficients of each order of Zernike polynomial.

[0088] There are two different normalization methods and arrangement orders for standard Zernike polynomials. The present invention adopts the amplitude normalization method, setting the maximum amplitude of each unit term to 1. The sorting strategy is as follows: Figure 2 As shown. The standard Zernike polynomial has countless terms. Considering that too many Zernike polynomial terms will cause overfitting, ill-conditioned equations, and low calculation efficiency, but if the number of terms is too small, it may cause low mirror surface fitting accuracy. Therefore, 45 standard Zernike polynomials are used to fit the mirror surface. Table 1 shows the specific meanings of the first 16 standard Zernike polynomials. Figure 3 and Figure 4 The two-dimensional wavefront shape and three-dimensional wavefront shape represented by the Zernike polynomials are shown respectively. It can be seen that each term of the Zernike polynomials has a specific physical meaning, its key coefficients have a one-to-one correspondence with the Seidel aberration, and the sub-terms are linearly independent and orthogonal within the unit circle, which can accurately reflect the system wave aberration or the surface shape change of the optical element.

[0089] Table 1 The first 16 terms of the standard Zernike polynomial and their meanings

[0090]

[0091]

[0092] The optical mirror deformation obtained by finite element simulation or actual measurement includes rigid body displacement and surface error (surface distortion). Rigid body displacement includes translation, off-axis, and tilt. Rigid body displacement can be eliminated by adjusting the relative position between optical elements, but surface error cannot be eliminated. Therefore, when using Zernike polynomials to fit the surface error, the rigid body displacement of the mirror needs to be removed first.

[0093] Based on the above analysis, the translation of the mirror surface relative to the ideal position after deformation on the X, Y and Z axes can be set as u x 、u y and u z , the rotation amounts around the X, Y and Z axes are θx, θy and θz respectively, and cosθx=cosθy=cosθz=1, sinθx=θx, sinθy=θy, sinθz=θz; according to the homogeneous coordinate transformation method, the coordinate transformation before and after the mirror deformation is shown in formula (1):

[0094]

[0095] Among them, X i ,Y i ,Z i )(i=1,2…n) are the node coordinates before mirror deformation, (X i ',Y i ',Z i ')(i=1,2…n) are the node coordinates after mirror deformation, T is the rigid body displacement of mirror deformation obtained based on the least squares method;

[0096] Multiply the left side of the node coordinates after mirror deformation by the transposed matrix T -1 , the node coordinates of the surface error after removing the displacement of the mirror cylinder are obtained, as shown in formula (2):

[0097]

[0098] Using Zernike polynomials as basis functions to fit the surface error of optical components, solving the coefficients of Zernike polynomials is to solve the surface error function W. N The linear combination coefficients of the Zernike polynomials of (x, y) are shown in formula (3):

[0099]

[0100] Among them, Z i (x, y) is the Zernike polynomial in the i-th Cartesian coordinate system, C i is the coefficient of the i-th Zernike polynomial, and n is the number of Zernike polynomial terms;

[0101] The actual measured discrete point displacement is substituted into formula (3), and the least square method is used to solve the Zernike polynomial coefficient matrix. The fitting accuracy of the coefficient matrix is ​​evaluated by the root mean square error. The coefficient matrix obtained after the fitting accuracy is the polynomial coefficient that characterizes the mirror surface error.

[0102] Taking the double-mirror optical system as the specific research object, its mechanical deformation result can be obtained after tightening with the standard preload. The deformation result at this time includes both rigid body displacement and surface error. Based on expressions (1) and (2), matrix operations are performed on the coordinates of the mirror after deformation to obtain the surface error node coordinates after removing the rigid body displacement, and the surface error cloud diagram of the primary mirror is obtained, as shown in Figure 5 As shown. Use expression (3) to solve the Zernike polynomial coefficient matrix to achieve surface error fitting. The fitting residual between the sag surface and the mirror deformation is as follows: Figure 6 As shown in the figure, the unit waves = 1e-9m. It can be seen that the fitting residual distribution is relatively uniform, and most of the residuals are less than 1e-6mm. The maximum residual is 4.488e-6mm. The maximum deformation obtained by conventional finite element simulation is 6.1935e-4mm, which is much larger than the fitting residual. This proves that the fitting error is very small and the surface fitting effect is good.

[0103] S2. Establish a finite element model of the optical system, simulate the tightening process of the bolt connection in the finite element model, and obtain the deformation of the mirror surface.

[0104] In the implementation, two-mirror optical system is taken as the research object, such as Figure 7 The structure shown mainly consists of a primary mirror, a secondary mirror, a bracket and three bolt-connected structures, wherein the primary mirror is fixed to the bracket by bolt connection, and the secondary mirror is installed in the cylindrical hole of the bracket through a pressure ring.

[0105] In the specific implementation, the finite element pre-processing software Hypermesh12.0 can be used to establish a finite element model of the optical system including the threaded connection structure, and in order to realize the assembly process simulation of the bolt, the internal and external threads need to be finely meshed. The meshing requires the establishment of a mathematical expression of the cross-sectional profile of the internal and external threads, and the process is as follows:

[0106] According to the thread parameters (nominal diameter, thread diameter, pitch, etc.), the thread profile is divided into three different parts: the thread root part, the thread side part and the thread top part. Taking the external thread as an example Figure 8 The external thread profile of one pitch along the axial section is shown; the thread profile along the transverse section is obtained by expanding the three divided parts to the plane. Fig. 9 As shown, the root of the thread is selected as the starting point, θ represents the rotation angle of the point on the thread cross-sectional profile relative to the starting point, and the expression of the cross-sectional profile of the thread is established, as shown in formula (4):

[0107]

[0108] in, d represents the nominal diameter, d1 represents the thread pitch, r represents the distance from the thread profile to the center axis of the bolt, and ρ represents the radius of the arc at the root of the thread.

[0109] Then, based on the mathematical expressions of the cross-sectional profiles of the internal and external threads and the rotational invariance of the cross-sectional profiles of the threads, a thread meshing method is used to establish mesh models of the internal and external threads. Specifically, the thread meshing method proposed by Fukuoka and Nomura can be used.

[0110] like Fig.10 As shown, the nominal diameter of the bolt is M3, the pitch is 0.5mm, Fig.11 The completed finite element mesh model of the bolt and nut connection is shown. All meshes use a hexahedral structure with a reasonable sparse transition. The primary mirror, secondary mirror and bracket all use free tetrahedral meshes. The final result is as follows Fig.12 As shown in the figure, the meshing and solving efficiency are significantly improved.

[0111] Then define the model and material parameters:

[0112] 1) Contact setting: The finite element model sets 11 contact pairs, and the contact areas include the contact between the bracket and the secondary mirror, the contact between the bracket and the primary mirror, the contact between the nut and the primary mirror, the contact between the nut and the bracket, and the contact between the internal and external threads. Among them, except for the binding contact between the bracket and the secondary mirror, the other contacts are defined as friction contacts. Each contact pair consists of a contact surface (CONTA173) and a target surface (TARGE170), and the friction coefficient of all contact areas is set to 0.15.

[0113] 2) Material setting: The bracket is made of aluminum alloy (LY12), the primary mirror and secondary mirror are made of different aluminum alloys (6061-t6), and the bolts and nuts are made of 5.6 grade structural steel.

[0114] 3) Constraints and loads: The contact area between the primary mirror and the nut is set as constraints in the X and Y directions, and the bracket and the bottom surface of the bolt head are set as full constraints. When the bolt is tightened, an angular load is applied to the nut, and all directions except the Z direction are constrained.

[0115] Finally, in order to verify whether the mesh size and shape have an impact on the calculation results, a sensitivity analysis is conducted on the mesh of the bolt external thread of a bolt connection structure. Six different mesh division methods are used to divide the bolt finite element model. The mesh type, number of nodes and number of meshes are detailed in Table 2. The three-dimensional mesh unit type used is Solid185, and the mesh type and number of other components remain unchanged. During the simulation, only this bolt connection structure is tightened, and the torque-preload relationship under each finite element model is extracted to obtain the torsion-tension relationship curve under different mesh sizes and shapes, such as Fig.13As shown, the preload result under ideal conditions is calculated based on the torsion-tension relationship theoretical formula. It can be clearly seen that the smaller the mesh size, the closer the result is to the ideal value, and compared with the tetrahedral mesh, the solution accuracy of the hexahedral mesh is significantly higher.

[0116] Table 2 Six different bolt head meshing methods

[0117]

[0118] According to the theoretical formula of torsion-tension relationship, a tightening angle of 3° was applied to the outer surfaces of the three nuts to simulate the assembly process. The preload force at this time met the preload force requirement when tightening 5.6-grade structural steel bolts, and the static analysis module in Ansysworkbench 19.2 was used to solve the problem. Fig.14 The deformation cloud maps of the primary mirror and the secondary mirror are displayed. It can be seen that the deformation of the primary mirror is much greater than that of the secondary mirror. In comparison, the deformation of the secondary mirror can be ignored.

[0119] S3. Import the mirror deformation into the optical-mechanical-thermal coupling analysis module and insert the Zernike polynomial coefficients to obtain the mirror surface error parameters and the mirror assembly posture deviation.

[0120] During implementation, finite element simulation can obtain the mirror deformation results, import the deformation result data into the optomechanical thermal coupling analysis tool Sigfit software, and fit the optical surface deformation through Zernike polynomials to obtain the Zernike polynomial coefficient file and zpl vector height file containing the mirror surface error parameters and mirror assembly posture deviation respectively.

[0121] S4. Import the mirror surface error parameters and the mirror assembly posture deviation into the optical simulation module to perform light path imaging simulation to obtain the energy concentration used to characterize the imaging quality.

[0122] In the implementation, Zemax software was selected for optical imaging simulation. When Zemax software was used for optical imaging simulation, it was necessary to first establish the reflective surfaces corresponding to the primary and secondary mirrors. The primary mirror was a rotating parabola with a 16.2 mm hole at the center. The secondary mirror was an even-order hyperboloid. The primary and secondary mirrors were spaced 38 mm apart. The thickness tolerance of the primary and secondary mirrors was less than 0.01 mm. The surface error PV value was less than 0.3 μm, the RMS value was less than 0.05 μm, and the concentricity was controlled at about 10 μm. The specific design parameters are shown in Table 3. Fig.15The ideal optical path shown in the figure has a focal length of 120mm, a field of view of ±12.2°, and an F number of 1.4. The incident light wavelength is set to 3.7-5.3μm, the light source entrance pupil diameter is set to 84mm, and then the imaging quality is evaluated by MTF (Modulation Transfer Function) and energy concentration. The MTF curve is shown in Fig.16 As shown, the full-field MTF is greater than 0.9 at 9.6lp / mm and still greater than 0.8 at 19.2lp / mm, close to the diffraction limit. The energy concentration curve is as follows Fig.17 As shown, more than 80% of the energy of the incident light beam is concentrated in the Airy disk with a radius of 8.021 μm. Combining the above two evaluation indicators, it can be determined that the designed optical system has excellent imaging quality without considering mirror deformation and posture deviation, as well as the ideal optical path.

[0123] Next, the fitted zpl vector height file is loaded through the Zemax macro file, and the mirror assembly posture deviation is superimposed on the reflection surface to generate a composite surface, so that the mirror deformation is fitted to the mirror surface; the mirror surface error is realized by inserting the mirror coordinate discontinuity surface to realize the setting and adjustment of the eccentricity and tilt of the primary and secondary mirrors.

[0124] Table 3 Design parameters of primary and secondary mirrors

[0125]

[0126] The optical system designed by the present invention is mainly used for point target imaging detection in engineering practice. The energy concentration determines the level of energy collected by a single pixel to the point target, which directly affects the image signal-to-noise ratio of the point target detection system. Compared with the modulation transfer function (MTF), the energy concentration index has more advantages in evaluating the beam quality and energy distribution. Based on this, from the perspective of energy, energy concentration is selected as a quantitative evaluation index of the imaging quality of the optical system. It should be noted that the energy concentration is related to the detector pixel size. The optical system designed by the present invention has a detection pixel size that is exactly equal to the Airy disk diameter, that is, the detection pixel size is 16μm×16μm. At this time, the energy concentration of the ideal optical path is 83.8%.

[0127] S5. Construct a data set based on the mirror surface error parameters, mirror assembly posture deviation and energy concentration, and establish an SVR proxy model containing local and global hybrid kernel functions.

[0128] In practice, the assembly posture errors of the primary and secondary mirrors include eccentricity errors along the X, Y and Z directions, as well as tilt errors around these three coordinate axes in the Cartesian coordinate system. The Z-axis direction is the incident direction of the parallel light path. In the actual assembly process, the relative distance between the primary and secondary mirrors in the Z-axis direction is easy to adjust to achieve the optimal imaging quality of the optical system. The primary and secondary mirrors are circularly symmetrical structures, and the rotation error in the Z-axis direction has very little effect on the imaging quality. Fig.18 The energy concentration of the primary mirror changes at different rotation angles under the condition of mirror surface error. The deviation between the energy concentration of the optical system is less than 1% when the Z axis rotates 0°, 90°, and 180°. Therefore, the posture error of the primary and secondary mirrors mainly considers the eccentricity error along the X and Y directions and the tilt error around the X and Y directions.

[0129] For the mirror surface error, different tightening angles (2° to 6°) were applied to the bolts during the simulation process to generate different preload forces. Then, the mirror surface error was fitted using the Zernike polynomial, and the first 45 Zernike polynomial coefficients were obtained, such as Fig.19 It can be seen that as the bolt preload increases, the changes in the 5th (defocus), 6th (first-order astigmatism-Y axis) and 10th (first-order trefoil aberration-Y axis) of the Zernike polynomial coefficients are much greater than those of the other terms, indicating that these three Zernike polynomial coefficients have a significant impact on the primary mirror shape error. Therefore, the 5th, 6th and 10th Zernike polynomial coefficients are selected as sensitive parameters of the mirror surface shape.

[0130] On the basis of analyzing the mirror surface error parameters and assembly posture error parameters respectively, the most obvious factors affecting the imaging quality in the assembly process are analyzed and discussed. For this purpose, the concept of spot diagram is introduced: for the actual optical system, the light is not an ideal straight line, and the imaging is a diffuse light spot. The formed light spot image is called a spot diagram. The distribution of points in the spot diagram approximately represents the energy distribution of the image point. From the definition of energy concentration, it can be seen that if all the points in the spot diagram fall within the Airy disk, the energy concentration reaches the maximum value. Fig. 20 The point diagrams of the optical system under different conditions are shown, among which, Figure a corresponds to the imaging result of the ideal optical path, Figure b and Figure c correspond to the imaging results under the influence of mirror surface shape and assembly posture errors respectively, and Figure d is the imaging result under the combined effect of the two, and the energy concentration results are 83.8%, 83.8%, 52.4% and 47.5% respectively. It can be clearly seen that compared with the mirror surface error, the assembly posture error has a more obvious impact on the change of the imaging quality of the optical system.

[0131] Based on the above analysis, the mirror surface error parameters are selected as defocus, first-order astigmatism-Y axis and first-order trefoil aberration-Y axis in the Zernike polynomial coefficients. The mirror assembly posture deviation is selected as the eccentricity error of the primary mirror and the secondary mirror along the X and Y directions and the tilt error around the X and Y directions. A total of 11 sensitive parameters are selected as characteristic variables, and energy concentration is selected as the target variable.

[0132] In order to eliminate the impact of different dimensions, the feature variables and target variables are normalized so that their values ​​fall within the interval [0, 1]. The normalized feature variables and target variables are divided into training set and test set according to the set ratio, which can be 8:2.

[0133] In the specific implementation, the bolt fasteners can be assembled by the torque method, the preload deviation is about ±30%, the friction coefficient is set to be consistent, and the bolts are tightened at 9 different angles to generate 9 sets of bolt preloads to simulate the actual assembly error of the bolts. The eccentricity error of the primary and secondary mirrors along the X and Y axes is ±0.01mm, and the tilt error around the X and Y axes is ±0.0167mm. For each set of bolt preloads, 128 sets of eccentricity errors and tilt errors are randomly generated within the error range, and a total of 1152 sets of data are generated. For each set of assembly error conditions, the energy concentration index of the optical system is calculated based on the finite element assembly simulation, the Zernike polynomial surface fitting method and the optical system imaging simulation, thereby constructing a data set.

[0134] Support Vector Machine (SVM) is a supervised learning method based on statistical learning VC dimension (Vapnik-Chervonenkis Dimension) and structural risk minimization theory, mainly used for classification. For linearly separable problems, SVM is usually abstracted as a line or a plane, which is used as a dividing line to distinguish different categories; for linearly inseparable problems, kernel functions can be used to map low-dimensional data to high-dimensional space, transforming linearly inseparable problems in low-dimensional space into linearly separable problems in high-dimensional space, and then mapping them to low-dimensional space after solving them.

[0135] Support Vector Regression (SVR) is an extension of SVM. It is mainly used for regression problems. SVM is used to fit the curve to achieve regression analysis of data. The regression principle can be used Fig.21 The ε pipeline model shown in the figure is used to illustrate: Assume that the function y(x) is described with accuracy ε, and another function f(x) is used to predict y(x), so that y(x) is in the range of f(x) ± ε, which is in the range of Fig.21In the ε-elastic pipe shown in Figure 1, the support vectors at its edge prevent the pipe from expanding further, while the existence of the relaxation vector allows some training points to be outside the pipe, but the penalty coefficient is needed to measure the impact of these points on the regression results.

[0136] Taking the linear regression problem as an example, the function sought by the regression problem is limited to a linear function. First, an objective function is set. The equation is expressed as:

[0137] f(x)=ω·x+b

[0138] In the formula, ω is the normal vector, b is the bias term, and x is the input sample. Assuming that all training data can be fitted with a linear function under the accuracy ε, the problem of finding the minimum ω can be expressed as a convex optimization problem, that is, minimizing Secondly, considering that there may be regression errors exceeding the accuracy ε in practice, two slack variables ξ are introduced i ,ξ i * ≥0, according to the structural risk minimization criterion of statistical learning theory, the regression estimation problem is transformed into:

[0139]

[0140] In the formula, C is the penalty coefficient. Use the duality theory to solve the constrained optimization problem, transform it into a quadratic programming problem, and construct the Lagrangian function L.

[0141]

[0142] In the formula, the Lagrange multiplier a i 、a i * , η i , η i * should all be greater than or equal to 0, and the parameters w, b, ξ i , i * The partial derivatives of are all zero, and the following dual optimization form can be obtained:

[0143]

[0144]

[0145] For nonlinear problems, it is necessary to introduce kernel functions to map them to high-dimensional space, transform the linearly separable dividing line f(x) into a hyperplane, and determine the position by solving the optimal solution under the dual optimization problem. Commonly used kernel functions include linear kernel functions, polynomial kernel functions, Gaussian kernel functions, and Sigmoid kernel functions. Kernel functions are divided into global kernel functions and local kernel functions. The former can well extract the global features of samples, has strong generalization ability, and weak learning ability, such as the polynomial kernel function; the latter can well reflect the local information of samples, has strong learning ability, but weak generalization ability, such as the Gaussian kernel function.

[0146] In the specific implementation, a Gaussian kernel function is selected as the local kernel function and a polynomial kernel function is selected as the global kernel function to construct a hybrid kernel function. By adjusting the weights of the global kernel function and the local kernel function, the hybrid kernel function has the advantages of both the global kernel function and the local kernel function, as shown in formula (5).

[0147] K mix =λK local +(1-λ)K global (5)

[0148] Among them, K local Refers to the local kernel function, K global Refers to the global kernel function, and λ is a scaling factor used to adjust the weight between the local kernel function and the global kernel function.

[0149] S6. Use the data set to train the SVR proxy model to obtain the optical system imaging quality prediction model.

[0150] In the implementation, the training set data is used to train the SVR proxy model, and the test set data is used to test the trained SVR proxy model and calculate the determination coefficient R 2 , root mean square error RMSE and mean relative error MRE, as shown in equations (6), (7) and (8) respectively:

[0151]

[0152]

[0153]

[0154] Among them, n is the number of test set samples, y i is the true value of energy concentration, y is the average value of the true value of energy concentration, f(x i ) is the predicted value of energy concentration, and m is the number of model training cycles;

[0155] S62, based on the calculated determination coefficient, root mean square error and mean relative error, determine whether the prediction accuracy and generalization ability of the SVR proxy model meet expectations, and if they meet expectations, terminate the training; if they do not meet expectations, adjust the parameters of the model and execute S63;

[0156] S63. Re-divide the data into training set and test set according to the set ratio and return to execute S61. Combine the single-cycle prediction accuracy and multi-cycle prediction fluctuation to judge the prediction accuracy and generalization ability of the model, and tune the regularization parameter C, fault tolerance parameter ε, polynomial kernel order, scaling factor and Gaussian kernel width multiple times to obtain an optical system imaging quality prediction model that meets expectations.

[0157] In the implementation, for the 230 test set data constructed above, in order to intuitively demonstrate the prediction ability of the constructed proxy model, Fig. 22 The scatter plot of the predicted values ​​of the surrogate model and the true values ​​is shown. It can be seen from the figure that the predicted values ​​of most data coincide with the true values, or are very close, and only a few data points have a certain deviation. The coefficient of determination and root mean square error of the predicted values ​​in the test set are calculated according to the formula, where R 2 The value is 0.95, and the corresponding RMSE value is 0.05, which shows that the model has high reliability and accuracy in predicting imaging quality. The average relative error of the predicted value is calculated again, and its value is 6.51%, that is, the average prediction accuracy of the constructed proxy model reaches 93.49%.

[0158] In order to test the robustness and reliability of the proxy model and reduce the accidental errors caused by random factors, the data set was randomly divided again in a ratio of 8:2 (repeated 10 times), and the corresponding relative error data was calculated, as shown in Fig.23 As shown, it can be seen that the maximum relative error is 7.33%, the minimum relative error is 5.85%, and the average is 6.51%, which shows that under the conditions of multiple repeated tests, the prediction accuracy of the SVR proxy model proposed in the present invention exceeds 93%. Therefore, the proxy model shows high accuracy and consistency in predicting the imaging quality of the optical system.

[0159] Comparison of prediction accuracy after selecting different kernel functions

[0160] Three commonly used single kernel functions are compared: linear kernel function, polynomial kernel function and Gaussian kernel function, as well as the case of no kernel function. Similarly, in order to reduce the test error and reduce the influence of accidental factors, the data set is randomly divided into training set and test set in a ratio of 8:2, and the experiment is repeated 10 times. The average prediction error of the test set in 10 experiments is calculated, as shown in Fig.24As shown in the figure, it can be seen that the average errors of the kernel-free function and the linear kernel function are both greater than 30%, with an average of about 40%, showing poor optical imaging quality prediction performance. Using the Gaussian kernel function, the prediction errors of the three groups of experiments were all greater than 15%, and the average prediction error was 10%; using the polynomial kernel function, the prediction error of one group of experiments exceeded 13%, and the average error was 8%. In contrast, using the hybrid kernel function proposed in the present invention, the test errors of 10 groups of experiments were all less than 8%, and the average error was only 6.51%. Therefore, compared with the single kernel function and the kernel-free function, the proposed hybrid kernel function shows the best optical imaging quality prediction performance.

[0161] Comparison of prediction accuracy after selecting other proxy models

[0162] Using the SVR regression model and the hybrid kernel function, a prediction model for the two-mirror optical system was constructed, which showed excellent prediction accuracy. Several other common proxy models were selected for comparison, including random forest regression (RFR), multi-layer perceptron (MLP), decision tree regression (DTR) and generalized additive model (GAM). The training set and test set were divided in the same way, and the experiment was repeated 10 times. In order to achieve the best prediction accuracy for these four models, fine-tuning parameters were performed respectively. The prediction errors of different proxy models are shown in Figure 2. Fig.25 As shown in the figure, it can be seen that the decision tree regression model shows the worst prediction accuracy, with an average prediction error of 13.15%, followed by the multilayer perceptron model, with an average prediction error of 11.38%. The prediction accuracy of the random forest regression model and the generalized additive model are comparable, with average prediction errors of 10.38% and 10.37%, respectively, but both are smaller than the proposed SVR model containing a hybrid kernel function (6.51%). Therefore, compared with other proxy models, the SVR regression model and hybrid kernel function proposed in the present invention show the best optical imaging quality prediction performance.

[0163] The present invention uses Zernike polynomials to accurately fit the mirror surface shape caused by assembly stress, and based on this, establishes an optical-mechanical integration simulation method for a two-transverse optical system that takes assembly error into consideration; proposes an SVR proxy model based on local and global hybrid kernel functions, extracts sensitive mirror surface shape errors and assembly posture error parameters, constructs assembly error and imaging quality data sets, and achieves high-precision prediction of imaging quality under different assembly error conditions through model training. The following conclusions are obtained:

[0164] 1) Through the combined finite element simulation of the assembly process, Zernike polynomial mirror surface fitting and Zemax optical path simulation, an effective approach is provided for the imaging simulation and quality evaluation of optical systems considering different assembly errors, an energy concentration index is established, and the quantitative evaluation of the imaging quality of the optical system is achieved.

[0165] 2) Through sensitive factor analysis, it was found that the key assembly parameters affecting the imaging quality of the optical system include the 5th, 6th and 10th items of the mirror surface Zernike polynomial fitting coefficients, as well as the eccentricity and tilt error parameters of the primary and secondary mirrors along the X and Y axes (the Z axis is the incident direction of the parallel light path).

[0166] 3) A SVR proxy model based on local and global hybrid kernel functions is proposed, which can achieve high-precision prediction of energy concentration under different assembly error conditions. Compared with the SVR model with a single kernel function / no kernel function and other regression models, the average prediction error is only 6.51%, showing excellent imaging quality prediction performance.

[0167] The above description is only a preferred embodiment of the present invention and is not intended to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention are included in the protection scope of the present invention.

Claims

1. A method for constructing an optical system imaging quality prediction model taking into account both surface error and posture error, characterized in that: include: S1. Using Zernike polynomials to fit the mirror surface shape in the optical system to obtain Zernike polynomial coefficients for characterizing the mirror surface shape error; S2. Establish a finite element model of the optical system, simulate the tightening process of the bolt connection in the finite element model, and obtain the deformation of the mirror surface; S3, importing the mirror deformation into the optical-mechanical-thermal coupling analysis module and inserting the Zernike polynomial coefficients to obtain the mirror surface error parameters and the mirror assembly posture deviation; S4, importing the mirror surface error parameters and the mirror assembly posture deviation into the optical simulation module to perform light path imaging simulation, and obtain the energy concentration used to characterize the imaging quality; S5. Construct a data set based on mirror surface error parameters, mirror assembly posture deviation, and energy concentration, and establish an SVR proxy model containing local and global hybrid kernel functions; S6. Use the data set to train the SVR proxy model to obtain the optical system imaging quality prediction model.

2. The method for constructing an optical system imaging quality prediction model taking into account both surface error and posture error as claimed in claim 1, characterized in that: S1 uses Zernike polynomials to fit the mirror surface shape in the optical system to obtain the Zernike polynomial coefficients used to characterize the mirror surface shape error, which specifically include: Set the translation of the mirror surface relative to the ideal position of the X, Y and Z axes to u after deformation x 、u y and u z , the rotation amounts around the X, Y and Z axes are θx, θy and θz respectively, and cosθx=cosθy=cosθz=1, sinθx=θx, sinθy=θy, sinθz=θz; according to the homogeneous coordinate transformation method, the coordinate transformation before and after the mirror deformation is shown in formula (1): Among them, X i ,Y i ,Z i )(i=1,2…n) are the node coordinates before mirror deformation, (X i ',Y i ',Z i ')(i=1,2…n) are the node coordinates after mirror deformation, T is the rigid body displacement of mirror deformation obtained based on the least squares method; Multiply the left side of the node coordinates after mirror deformation by the transposed matrix T -1 , the node coordinates of the surface error after removing the displacement of the mirror cylinder are obtained, as shown in formula (2): Using Zernike polynomials as basis functions to fit the surface error of optical components, solving the coefficients of Zernike polynomials is to solve the surface error function W. N The linear combination coefficients of the Zernike polynomials of (x, y) are shown in formula (3): Among them, Z i (x, y) is the Zernike polynomial in the i-th Cartesian coordinate system, C i is the coefficient of the i-th Zernike polynomial, and n is the number of Zernike polynomial terms; The actual measured discrete point displacement is substituted into formula (3), and the least square method is used to solve the Zernike polynomial coefficient matrix. The fitting accuracy of the coefficient matrix is ​​evaluated by the root mean square error. The coefficient matrix obtained after the fitting accuracy is the polynomial coefficient that characterizes the mirror surface error.

3. The method for constructing an optical system imaging quality prediction model taking into account both surface error and posture error as claimed in claim 1, characterized in that: The process of establishing the finite element model of the optical system in S2 includes: Establish a finite element model of the optical system including the threaded connection structure, and establish the free tetrahedral mesh of the primary mirror, secondary mirror and bracket; The mathematical expressions for the cross-sectional profiles of internal and external threads are established as follows: According to the thread parameters, the thread profile is divided into three different parts: the thread root part, the thread side part and the thread crest part; the three divided parts are extended to the plane to obtain the thread profile along the transverse section. The thread root is selected as the starting point, and θ represents the rotation angle of the point on the thread cross-sectional profile relative to the starting point. The expression of the cross-sectional profile of the thread is established, as shown in formula (4): in, d represents the nominal diameter, d1 represents the thread pitch, r represents the distance from the thread profile to the center axis of the bolt, and ρ represents the radius of the arc at the root of the thread. Based on the mathematical expressions of the cross-sectional profiles of internal and external threads and the rotational invariance of the cross-sectional profiles of threads, the mesh models of internal and external threads are established using the thread meshing method.

4. The method for constructing an optical system imaging quality prediction model taking into account both surface error and posture error as claimed in claim 1, characterized in that: S4, the process of importing the mirror surface error parameters and the mirror assembly posture deviation into the optical simulation module to perform light path imaging simulation includes: Establish the reflecting surfaces corresponding to the primary mirror and the secondary mirror, where the primary mirror is a rotating parabola and the secondary mirror is an even-order hyperboloid, and set the size of the opening at the center of the primary mirror, the distance between the primary and secondary mirrors, the thickness tolerance of the primary and secondary mirrors, the surface shape error, and the concentricity; The mirror assembly posture deviation is superimposed with the reflection surface to generate a composite surface, thereby fitting the mirror deformation to the mirror surface; The mirror surface error is adjusted by inserting the mirror coordinate discontinuity surface to achieve the setting of the eccentricity and tilt of the primary mirror and the secondary mirror.

5. The method for constructing an optical system imaging quality prediction model taking into account both surface error and posture error as claimed in claim 1, wherein the process of constructing a data set based on mirror surface error parameters, mirror assembly posture deviation and energy concentration in S5 comprises: The mirror surface error parameters are selected from the defocus, first-order astigmatism-Y axis and first-order trefoil aberration-Y axis in the Zernike polynomial coefficients. The mirror assembly posture deviation is selected from the eccentricity error of the primary mirror and the secondary mirror along the X and Y directions and the tilt error around the X and Y directions. A total of 11 sensitive parameters are selected as characteristic variables, and the energy concentration is selected as the target variable. The feature variables and target variables are normalized, and the normalized feature variables and target variables are divided into training sets and test sets according to the set ratio.

6. In the method for constructing an optical system imaging quality prediction model taking into account both surface error and posture error as claimed in claim 5, the process of establishing an SVR proxy model including local and global hybrid kernel functions in S5 comprises: The Gaussian kernel function is selected as the local kernel function, the polynomial kernel function is selected as the global kernel function, and the hybrid kernel function form is constructed as shown in formula (5): K mix =λK local +(1-λ)K global (5) Among them, K local Refers to the local kernel function, K global Refers to the global kernel function, λ is the scaling factor, which is used to adjust the ratio between the local kernel function and the global kernel function; Set the parameters of the SVR agent model, including the regularization parameter C, the tolerance parameter ε, the polynomial kernel order, the scaling factor, and the Gaussian kernel width.

7. The method for constructing an optical system imaging quality prediction model taking into account both surface error and posture error as claimed in claim 6, wherein the process of using the data set to train the SVR proxy model to obtain the optical system imaging quality prediction model in S6 comprises: S61. Use the training set data to train the SVR proxy model, use the test set data to test the trained SVR proxy model and calculate the determination coefficient R 2 , root mean square error RMSE and mean relative error MRE, as shown in equations (6), (7) and (8) respectively: Among them, n is the number of test set samples, y i is the true value of energy concentration, is the average value of the true value of energy concentration, f(x i ) is the predicted value of energy concentration, and m is the number of model training cycles; S62, based on the calculated determination coefficient, root mean square error and mean relative error, determine whether the prediction accuracy and generalization ability of the SVR proxy model meet expectations, and if they meet expectations, terminate the training; if they do not meet expectations, adjust the parameters of the model and execute S63; S63: Re-divide the data into a training set and a test set according to the set ratio and return to execute S61.

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