A cassette optical system structure optimization design method

Abstract

This application discloses a structural optimization design method for a cassette optical system to address the technical problem of image quality degradation caused by structural deformation under high-impact and high-overload conditions. The method includes: establishing a parametric finite element model comprising a primary mirror, a secondary mirror, and a supporting structure; obtaining the displacement vector through equivalent static analysis; calculating the structural stiffness characterization function and three image quality characterization functions (change in primary-secondary mirror spacing, primary mirror deformation, and secondary mirror deformation); establishing a multi-objective weighted optimization model; solving for the optimized structural element density distribution; and reconstructing the structural model. This method can effectively suppress structural deformation under high-impact and high-overload conditions, improving the stability and reliability of the system's image quality.

Description

Technical Field

[0001] This invention relates to the field of optical system structure optimization design technology, specifically to a structural optimization design method for card-type optical systems under high impact and high overload conditions. Background Technology

[0002] Cassegrain optical systems (Cassegrain systems for short) are widely used in imaging due to their compact structure and ability to achieve long focal length and large aperture imaging. A typical Cassegrain optical system mainly consists of a primary mirror, a secondary mirror, and their corresponding support structures. The imaging quality of the system directly depends on the surface accuracy of the optical elements and the stability of the relative positions between the elements. In high-dynamic applications such as aerospace, optical systems often need to operate under extreme mechanical environments, such as withstanding severe loads like large impacts and high overloads.

[0003] Chinese patent CN106990517A discloses a large relative aperture, long focal length, uncooled infrared athermalized optical system. This system employs a cassette system to extend the optical path through multiple reflections of light, achieving a long focal length. The patent utilizes the negative dispersion and negative thermal expansion coefficient of diffractive elements, and through the rational allocation of optical power by a hybrid refractive / diffractive element, reduces the defocusing amount caused by temperature changes in the infrared optical system, achieving image plane defocus compensation within a temperature range of -40℃ to +60℃. However, this technical solution primarily focuses on the defocusing problem caused by temperature changes and does not address the impact of structural deformation on image quality under high-impact, high-overload conditions. Under extreme mechanical conditions, huge inertial loads are transmitted to the supporting structure of the optical system, causing elastic deformation of the lenses and their supports. This leads to distortion of the lens surface and deviations in the relative positions of optical elements such as primary and secondary mirrors from the preset optical path, thereby reducing the system's imaging quality and stability.

[0004] Chinese patent CN121634486A discloses a design method for an off-axis three-mirror freeform surface imaging system. This method establishes an initial structure of the optical system, consisting of a primary mirror, a secondary mirror, and a third mirror, based on the design values ​​of the optical system's performance and structural parameters. The radius, eccentricity, and tilt of the primary, secondary, and third mirrors are updated sequentially. The optimization objective is to minimize the wavefront difference of the optical system, and the initial structure is optimized using the damped least squares method. While this method involves the optimization design of the optical system, it primarily focuses on optimizing optical parameters (such as radius, eccentricity, and tilt). It does not establish an explicit mapping relationship between optical performance and structural mechanical properties, making it impossible to directly optimize the system with optical performance as the objective during the structural design stage. Furthermore, it struggles to effectively assess the impact of structural deformation on imaging quality under high-impact and high-overload conditions.

[0005] Currently, structural design methods for cassette optical systems still primarily rely on experience-based design and static stiffness and strength verification. Designers typically use engineering experience to employ structural forms such as stiffeners and openings, and achieve lightweighting through material selection and local reinforcement. This traditional approach has several prominent problems: the design process is highly dependent on the experience accumulated by individuals or teams, lacking systematic and quantitative design criteria, resulting in poor consistency and repeatability of design results; it often requires multiple cycles of trial and error in "design-analysis-modification," which is time-consuming, costly, and makes it difficult to guarantee that the final solution is close to the theoretical optimum; in multi-physics coupled environments such as impact and vibration, static verification and local reinforcement alone are insufficient to comprehensively evaluate the optical performance stability of the system under dynamic loads, easily leading to under-design or over-design; existing methods usually separate structural design from optical performance evaluation, failing to establish an explicit mapping relationship between optical image quality and structural mechanical properties, thus making it impossible to directly optimize the system with optical performance as the target during the structural design stage.

[0006] Therefore, a design method that integrates optical performance indicators and structural mechanical behavior with systematic optimization capabilities is needed. This method can reduce reliance on engineering experience and simplify the design process while ensuring that card-type optical systems still have excellent imaging quality and stability under high-impact and high-overload conditions, thereby improving the reliability and overall performance of such optical systems in extreme environments. Summary of the Invention

[0007] Technical problems to be solved

[0008] The purpose of this invention is to provide a method for optimizing the structure of a card-type optical system, so as to solve the following technical problems existing in the prior art:

[0009] (1) Existing card-type optical system structural design methods rely heavily on engineering experience and lack systematic and quantitative design criteria, resulting in poor consistency and repeatability of design results. They often require multiple cycles of trial and error in "design-analysis-modification", resulting in long design cycles and high costs.

[0010] (2) Existing technologies separate structural design from optical performance evaluation, and do not establish an explicit mapping relationship between optical image quality and structural mechanical performance, making it impossible to directly optimize the system with optical performance as the target during the structural design stage;

[0011] (3) Under high impact and high overload conditions, static verification and local reinforcement alone are insufficient to fully evaluate the optical performance stability of the system under dynamic load. The huge inertial load is transmitted to the support structure of the optical system, causing lens surface distortion and the relative positional relationship between optical components such as primary and secondary mirrors deviating from the preset optical path, which seriously reduces the imaging quality and stability of the system.

[0012] Technical solution

[0013] To achieve the above objectives, the present invention adopts the following technical solution:

[0014] A method for optimizing the structure of a card-type optical system, comprising establishing a finite element model of the optical system and solving it using an optimization algorithm, characterized in that the method further includes the following steps:

[0015] Step 1: Establish a parametric finite element model including the primary mirror, secondary mirror and supporting structure, with the structural element density value as the design variable;

[0016] Step 2: Simulate the impact overload condition through equivalent static analysis to obtain the displacement vectors of the main reflector, the secondary reflector, the structure, the center point displacement vector of the main reflector, and the center point displacement vector of the secondary reflector.

[0017] Step 3: Calculate the structural stiffness characterization function, the first imaging quality characterization function reflecting the change in the relative distance between the primary and secondary mirrors, the second imaging quality characterization function reflecting the overall deformation of the primary mirror, and the third imaging quality characterization function reflecting the overall deformation of the secondary mirror based on the displacement vector.

[0018] Step 4: Establish a multi-objective weighted optimization model. The objective function of the optimization model comprehensively considers the structural stiffness characterization function and the three imaging quality characterization functions. The constraint condition is the total weight of the structure.

[0019] Step 5: Solve the optimization model using an optimization algorithm to obtain the optimized structural unit density value distribution;

[0020] Step 6: Reconstruct the structural model based on the optimized structural unit density distribution, thereby rationally distributing materials and simplifying features while ensuring the main force transmission path.

[0021] By establishing a parametric finite element model and using structural element density as the design variable, this invention employs a variable density topology optimization framework, providing design space for optimizing material distribution and breaking through the traditional experience-dependent design mode. Through equivalent static analysis simulating impact overload conditions, computational complexity is reduced and it adapts to optimization iteration requirements. The obtained displacement vector data provides a data foundation for subsequently constructing an optical quality characterization function. This invention constructs a multi-dimensional imaging quality characterization function for impact conditions, transforming optical stability into a quantifiable optimization objective. It establishes failure modes of the optical system under impact from two dimensions: "spacing stability" and "mirror morphology preservation," solving the problem that traditional methods struggle to directly optimize optical performance. By establishing a multi-objective weighted optimization model, optical performance indicators are directly incorporated into the optimization objective layer rather than in the post-processing verification stage, ensuring the optical stability of the optimization results from a mechanistic perspective and achieving synergistic optimization of structural-optical multidisciplinary performance.

[0022] Furthermore, in step 1, the parameterized finite element model includes a primary reflector, a secondary reflector, and a support structure, thereby clarifying the complete scope of the optimization object and ensuring the accuracy of the model.

[0023] Furthermore, in step 1, the design variable is the density value corresponding to the structural element in the finite element model.

[0024]

[0025] In the formula, n is the number of structural elements in the finite element model. Let be the density of the i-th structural unit; the mathematical expression clarifies the definition of design variables, providing clear design freedom for the optimization algorithm.

[0026] Furthermore, in step 2, the impact overload analysis is an equivalent static analysis; by using equivalent static analysis instead of dynamic analysis, the computational complexity can be significantly reduced while ensuring the accuracy of the analysis, making the optimization iteration process more efficient.

[0027] Furthermore, in step 2, the deformation result of the optical system includes the displacement vector of the primary mirror. Secondary mirror displacement vector Structural displacement vector Displacement vector of the center point of the primary mirror Displacement vector of the center point of the secondary mirror By separating and extracting displacement data, a complete data foundation is provided for the subsequent construction of an optical quality characterization function that distinguishes between rigid body displacement and surface deformation.

[0028] Furthermore, in step 3, the structural stiffness characterization function is compliance C; compliance is the inverse index of structural stiffness. The smaller the compliance, the better the structural stiffness. This index is used to macroscopically control the overall impact resistance of the structure.

[0029] The formula for calculating the compliance C is as follows:

[0030]

[0031] In the formula, T is the matrix transpose identifier, and K is the structural stiffness matrix;

[0032] The first imaging quality characterization function The calculation formula is:

[0033]

[0034] In the formula, These are the initial design values. Represents the Euclidean norm. This represents the absolute value function; this characterization function reflects the change in the relative distance between the primary and secondary mirrors, and is directly related to the defocus sensitivity of the optical system, which is a key indicator to ensure the imaging quality of the optical system.

[0035] The second imaging quality characterization function The calculation formula is:

[0036]

[0037] In the formula, and These represent functions for the maximum and minimum values, respectively.

[0038] The third imaging quality characterization function The calculation formula is:

[0039]

[0040] These two characterization functions reflect the overall deformation of the primary and secondary mirrors, respectively. By extracting the extreme range of mirror displacement, the rigid body tilt and local deformation of the mirror can be controlled, thereby constraining the ability to maintain the mirror shape.

[0041] Further, in step 4, the optimization model is:

[0042]

[0043] In the formula, This is the upper limit of the weight constraint;

[0044] The formula for calculating the objective function Obj is as follows:

[0045]

[0046] In the formula, , , , These are the compliance function C and the first imaging quality characterization function, respectively. Second imaging quality characterization function Third imaging quality characterization function The corresponding weighting coefficients; by adjusting the combination of weighting coefficients, the different design requirements of different optical systems for stiffness, defocus, and mirror deformation sensitivity can be flexibly adapted, realizing the synergistic optimization of the performance of the structural-optical multidisciplinary system.

[0047] The constraint function is the total weight of the structure, mass, and the calculation formula is:

[0048]

[0049] In the formula, Let be the volume of the i-th structural element in the finite element model; this constraint function achieves precise control over the total weight of the structure by accumulating the mass of all structural elements, thus ensuring the achievement of the lightweight design goal;

[0050] Furthermore, in step 5, the optimization algorithm for solving the optimization design model is either the moving asymptotic algorithm or the intelligent optimization algorithm. The moving asymptotic algorithm is an efficient optimization algorithm based on gradient information and is suitable for large-scale optimization problems. Intelligent optimization algorithms (such as ant colony algorithm, genetic algorithm, etc.) have the characteristic of strong global search capability. Both types of algorithms can effectively solve the optimization model of this invention, and designers can choose the appropriate algorithm according to actual needs.

[0051] Beneficial effects

[0052] The beneficial effects of this invention are as follows:

[0053] (1) This invention breaks through the traditional experience-dependent design pattern, and significantly reduces the design threshold, improves design efficiency and consistency through automatic algorithm optimization, and avoids the inefficient process of multiple cycles of trial and error in "design-analysis-modification";

[0054] (2) This invention is the first to directly incorporate optical performance indicators into the structural optimization target layer, and establishes an imaging quality characterization function system with two dimensions: "spacing stability" and "mirror morphology preservation". This ensures the optical stability of the optimization results from a mechanism perspective and solves the problem of separating structural design from optical performance evaluation in traditional methods.

[0055] (3) The present invention can effectively suppress structural deformation under high impact and high overload conditions, guide the systematic structural deformation to the "rigid body displacement" mode that has the least impact on imaging quality, and significantly improve the imaging quality stability and reliability of the optical system under extreme mechanical environment.

[0056] (4) This invention achieves synergistic optimization of structural-optical multidisciplinary performance. By adjusting the weighting coefficients, it can flexibly adapt to the differentiated design requirements of different optical systems. It has strong reference and promotion value and can be extended to the optimization design of other optical system structural components.

[0057] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0058] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0059] Figure 1 This is a schematic diagram of the components of a card-type optical system;

[0060] Figure 2 This is a schematic diagram of the structural optimization design method for the card-type optical system of the present invention. Detailed Implementation

[0061] The embodiments of the present invention are described in detail below. These embodiments are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0062] This embodiment provides a structural optimization design method for a card-type optical system. It addresses the technical problem in the prior art that the structural design and optical performance evaluation are separated, and that it is impossible to directly optimize the structure with optical performance as the target under high impact and high overload conditions. By constructing a multi-dimensional imaging quality characterization function system and establishing a multi-objective weighted optimization model, it achieves an integrated design of structural lightweighting and optical stability under a given impact load.

[0063] Reference Figure 1 As shown, the cassette optical system consists of a primary mirror, a secondary mirror, and a support structure. The primary mirror, located at the rear of the optical system, receives incident light and reflects it to the secondary mirror. The secondary mirror, located at the front of the optical system, receives the light reflected from the primary mirror and reflects it again to the focal plane. The support structure connects the primary and secondary mirrors, maintaining their relative position. Under high-impact, high-overload conditions, the support structure bears enormous inertial loads and is prone to deformation, leading to relative positional shifts in the primary and secondary mirrors and distortion of the mirror surface, thereby reducing the system's imaging quality.

[0064] Reference Figure 2 As shown, the structural optimization design method described in this embodiment includes the following steps:

[0065] Step 1: Establish a parametric finite element model that includes the primary mirror, secondary mirror, and supporting structure.

[0066] A three-dimensional digital model of the cassette optical system was established using finite element analysis software. The model includes the primary mirror, the secondary mirror, and the supporting structure connecting the two.

[0067] The model is divided into several structural elements, each corresponding to a density value ranging from 0 to 1, where 0 represents voids and 1 represents solid material. The density values ​​of all structural elements are used as design variables. This constitutes the set of design variables, where n is the number of structural elements in the finite element model. The parametric finite element model adopts a variable density method topology optimization framework. By adjusting the density values ​​of each structural element, the optimal distribution of material in the design space is achieved, providing design freedom for subsequent searching of the optimal structural configuration.

[0068] Step 2: Simulate the impact overload condition through equivalent static analysis.

[0069] An equivalent static load is applied to the parametric finite element model established in step 1. This load is used to simulate the impact overload experienced by the cassette optical system in actual operation. The equivalent static analysis transforms the dynamic impact load into an equivalent static load, significantly reducing computational complexity while ensuring analytical accuracy, thus making the optimization iteration process more efficient.

[0070] The deformation data of the optical system under equivalent static load, including the displacement vector of the primary mirror, were obtained by calculating using a finite element method. Secondary mirror displacement vector Displacement vector of supporting structure Displacement vector of the center point of the primary mirror and the displacement vector of the center point of the secondary mirror These displacement vector data record the spatial position changes of each component under impact load, providing a data foundation for the subsequent construction of imaging quality characterization functions.

[0071] Step 3: Calculate the structural stiffness characterization function and the imaging quality characterization function based on the displacement vector.

[0072] Structural stiffness is characterized by compliance, which is obtained through operations on the displacement vector of the supporting structure, the structural stiffness matrix, and the matrix transpose.

[0073]

[0074] Where T is the matrix transpose identifier and K is the structural stiffness matrix. The smaller the compliance value, the better the structural stiffness. This index is used to macroscopically assess the overall impact resistance of the structure.

[0075] The imaging quality characterization function includes three dimensions:

[0076] First imaging quality characterization function The value used to reflect the change in the relative distance between the primary and secondary reflectors is obtained by calculating the Euclidean norm difference between the displacement vectors of the primary and secondary reflector centers and comparing it with the initial design value.

[0077]

[0078] in, These are the initial design values. Represents the Euclidean norm. It represents an absolute value function; this index is directly related to the defocus sensitivity of the optical system.

[0079] Second imaging quality characterization function The value used to reflect the overall deformation of the primary reflector is obtained by extracting the difference between the maximum and minimum values ​​of the Euclidean norm of the primary reflector's displacement vector.

[0080]

[0081] in, and These represent the maximum and minimum value functions, respectively; this index is used to control the rigid body tilt and local deformation of the primary reflector.

[0082] Third imaging quality characterization function The value used to reflect the overall deformation of the secondary mirror is obtained by extracting the difference between the maximum and minimum values ​​of the Euclidean norm of the secondary mirror's displacement vector.

[0083]

[0084] This index is used to constrain the surface stability of the secondary mirror.

[0085] The three imaging quality characterization functions mentioned above transform optical stability into a quantifiable optimization objective from two dimensions: "stability of the distance between primary and secondary mirrors" and "preservation of the mirror's own shape," thus solving the technical problem that traditional methods cannot directly optimize optical performance.

[0086] Step 4: Establish a multi-objective weighted optimization model:

[0087]

[0088] The optimization model aims to maintain the image quality stability of the optical system under a given impact condition. The objective function is constructed by weighted summation of the structural stiffness characterization function and three imaging quality characterization functions:

[0089]

[0090] in, , , , These are the compliance function C and the first imaging quality characterization function, respectively. Second imaging quality characterization function Third imaging quality characterization function The corresponding weighting coefficients, and the weighting coefficients corresponding to each characterization function, can be adjusted according to the performance priority of specific application scenarios. By adjusting the combination of weighting coefficients, the different design requirements of different optical systems for stiffness, defocus, and mirror deformation sensitivity can be flexibly adapted, realizing the synergistic optimization of the performance of structural-optical multidisciplinary systems.

[0091] The constraint condition is that the total weight of the structure (mass) does not exceed the set upper limit of the weight constraint. The total weight of the structure is obtained by multiplying the density values ​​of all structural elements by the corresponding element volumes:

[0092]

[0093] in, Let be the volume of the i-th structural element in the finite element model.

[0094] This optimization model directly incorporates optical performance indicators into the optimization objective layer, rather than the post-processing verification stage in traditional methods. This ensures, from a mechanistic perspective, that the optimization results simultaneously meet the requirements of structural stiffness and optical stability, thus achieving synergistic optimization of structural and optical multidisciplinary performance.

[0095] Step 5: Solve the optimization model using an optimization algorithm.

[0096] The optimization model is solved iteratively using the moving asymptote algorithm or intelligent optimization algorithm based on gradient information. The moving asymptote algorithm constructs an approximate model of the objective function and constraint functions, and gradually approaches the optimal solution by moving the position of the asymptote in each iteration. This algorithm has high computational efficiency and is suitable for large-scale optimization problems.

[0097] Intelligent optimization algorithms, such as ant colony optimization and genetic algorithms, perform global searches by simulating the collective intelligence behavior of swarms in nature, exhibiting strong global optimization capabilities. During the iterative solution process, the optimization algorithm continuously adjusts the density values ​​of each structural unit, gradually reducing the objective function value until the convergence criterion is met, ultimately obtaining the optimized distribution of structural unit density values.

[0098] Step 6: Reconstruct the structural model based on the optimized density distribution of structural elements. The density distribution obtained from the optimization solution presents a continuous numerical field, which needs to be transformed into a manufacturable engineering structure. The reconstruction process follows these principles: retain elements with higher density values ​​as the main force transmission paths, delete elements with density values ​​close to zero, and smooth the transition regions with density values ​​in the middle range. The reconstructed structural model maintains the optimization effect while having clear structural boundaries and simplified geometric features, facilitating subsequent processing and manufacturing. The reconstruction principles ensure a reasonable distribution of materials within the design space, meeting the requirements of structural stiffness and optical stability while also considering manufacturing feasibility.

[0099] Through the implementation of the above six steps, the method of this invention can effectively suppress structural deformation under high impact and high overload conditions in the structural design of card-type optical systems, or guide systematic structural deformation to a rigid body displacement mode that minimizes the impact on imaging quality, thereby significantly improving the imaging quality stability and reliability of the system under extreme mechanical environments. Compared with traditional design methods that rely on engineering experience, the method of this invention overcomes the limitations of experience dependence through automatic algorithm optimization, lowers the design threshold, and improves design efficiency and consistency of results. Compared with existing methods that only focus on structural stiffness or single optimization of optical parameters, the method of this invention, for the first time, directly incorporates optical performance indicators into the structural optimization target layer, establishes an explicit mapping relationship between optical performance and structural mechanical performance, realizes the synergistic optimization of the two, and ensures the optical stability of the optimization results from a mechanistic perspective.

[0100] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A method for optimizing the design of a cassette optical system structure, comprising establishing a finite element model of the optical system and solving it using an optimization algorithm, characterized in that, The method also includes the following steps: Step 1: Establish a parametric finite element model of the optical system, using the structural element density as the design variable; Step 2: Simulate the impact overload condition through equivalent static analysis to obtain the displacement vectors of the main reflector, the secondary reflector, the structure, the center point displacement vector of the main reflector, and the center point displacement vector of the secondary reflector. Step 3: Calculate the structural stiffness characterization function, the first imaging quality characterization function reflecting the change in the relative distance between the primary and secondary mirrors, the second imaging quality characterization function reflecting the overall deformation of the primary mirror, and the third imaging quality characterization function reflecting the overall deformation of the secondary mirror based on the displacement vector. Step 4: Establish a multi-objective weighted optimization model. The objective function of the optimization model comprehensively considers the structural stiffness characterization function and the three imaging quality characterization functions. The constraint condition is the total weight of the structure. Step 5: Solve the optimization model using an optimization algorithm to obtain the optimized structural unit density value distribution; Step 6: Reconstruct the structural model based on the optimized structural unit density distribution.

2. The method of claim 1, wherein the optimization is performed by a genetic algorithm. In step 1, the parameterized finite element model includes a primary reflector, a secondary reflector, and a supporting structure.

3. The method of claim 1, wherein the method further comprises: In step 1, the design variable is the density value corresponding to the structural element in the finite element model: In the formula, n is the number of structural elements in the finite element model. Let be the density of the i-th structural unit.

4. The method for optimizing the structure of a card-type optical system according to claim 1, characterized in that, In step 2, the impact overload analysis is an equivalent static analysis.

5. The method for optimizing the structure of a card-type optical system according to claim 1, characterized in that, In step 2, the deformation result of the optical system includes the displacement vector of the primary mirror. Secondary mirror displacement vector Structural displacement vector Displacement vector of the center point of the primary mirror Displacement vector of the center point of the secondary mirror .

6. The method for optimizing the structure of a card-type optical system according to claim 1, characterized in that, In step 3, the structural stiffness characterization function is compliance C; the formula for calculating compliance C is: In the formula, T is the matrix transpose identifier, and K is the structural stiffness matrix; The first imaging quality characterization function The calculation formula is: In the formula, These are the initial design values. Represents the Euclidean norm. Represents the absolute value function; The second imaging quality characterization function The calculation formula is: In the formula, and These represent functions for the maximum and minimum values, respectively. The third imaging quality characterization function The calculation formula is: 。 7. The method for optimizing the structure of a card-type optical system according to claim 1, characterized in that, In step 4, the optimization model is: In the formula, This is the upper limit of the weight constraint; The formula for calculating the objective function Obj is as follows: In the formula, , , , These are the compliance function C and the first imaging quality characterization function, respectively. Second imaging quality characterization function Third imaging quality characterization function The corresponding weighting coefficients; The constraint function is the total weight of the structure, mass, and the calculation formula is: In the formula, Let be the volume of the i-th structural element in the finite element model.

8. The method for optimizing the structure of a card-type optical system according to claim 1, characterized in that, In step 5, the optimization algorithm for solving the optimal design model is either the moving asymptote algorithm or the intelligent optimization algorithm.

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