Initial structural design method of quasi-telecentric off-axis three-mirror optical system

Abstract

The present invention belongs to the technical field of optical system design, and in particular relates to a method for initial structural design of a quasi-telecentric off-axis three-mirror optical system. The method comprises: S1: setting optical design parameters of the quasi-telecentric off-axis three-mirror optical system; S2: establishing quasi-telecentric constraints and constructing an evaluation function in combination with the initial aberration expression of the quasi-telecentric off-axis three-mirror optical system; S3: setting a value range of the optical parameters to be optimized based on the design indicators and structural form of the quasi-telecentric off-axis three-mirror optical system; S4: within the corresponding value range, performing a joint optimization calculation on the evaluation function based on a global optimization algorithm and a local optimization algorithm to obtain the optimized structure of the quasi-telecentric off-axis three-mirror optical system. The present invention combines telecentric constraints and adopts a global-local optimization strategy to significantly improve the global search capability of variables. The optimized off-axis initial structure finally obtained has both high imaging quality and high telecentricity.

Description

Technical Field

[0001] The present invention belongs to the technical field of optical system design, and in particular relates to an initial structure design method of a quasi-telecentric off-axis three-mirror optical system. Background Art

[0002] Reflective optical systems are widely used in the field of space optics due to their advantages such as achromatic aberration and high stability. Coaxial reflective optical systems suffer from the problem of central obstruction, which can lead to a decrease in the frequency band of the MTF. Although off-axis reflective optical systems can avoid the central obstruction problem, they have the problem of difficulty in obtaining an optimization starting point. The more traditional optimization method is to calculate the mirror conic coefficient using the anastigmatism condition and the normalized aberration coefficient under the conditions of a given reflector obstruction ratio and magnification. However, the structural aberration coefficient used in this method is not sensitive to design indicators, and the off-axis aberration characteristics are poor. The final optimization result is significantly different from the initial structure. This places high demands on the experience of optical designers and greatly hinders the development of space optical precision instruments.

[0003] The initial structure acquisition problems for off-axis reflective systems mainly fall into the following three categories:

[0004] 1. Based on the system obscuration ratio, magnification, and normalized primary aberration expressions, combined with the astigmatism-free condition, the conic coefficients of each reflector are calculated to obtain the corresponding off-axis three-mirror initial structure. The initial structure obtained using this method has poor off-axis aberration characteristics, and the final optimization result often deviates significantly from the initial structure, making it easy to fall into a local optimal solution.

[0005] 2. Based on the global optimization algorithm, the evaluation function is constructed using the normalized primary aberration expression to find the optimal solution set within the given solution space. The primary aberration formula used in this method is often expressed in the form of the aperture stop at the position of the primary mirror. When the aperture stop position shifts, the off-axis aberration of the system will change. When the secondary mirror is selected as the aperture stop during the optimization process, the off-axis aberration characteristics of its initial structure will be different, which increases the difficulty of system optimization.

[0006] 3. Based on a global optimization algorithm, combined with vector aberration theory, the tilt and off-axis values ​​of the mirror are introduced to expand the degrees of freedom in optimization, achieving multi-parameter optimization and obtaining the initial structure of the component with off-axis tilt. However, while vector aberration introduces more degrees of freedom in optimization, it also significantly increases the difficulty of assembling and adjusting the off-axis optical system, making its application in practical engineering difficult.

[0007] In the image quality evaluation dimension, the evaluation functions used are mostly constructed only around the system surface curvature, mirror spacing, refractive index and cone coefficient, and do not include high-order aspheric terms, making it difficult to accurately characterize the impact of complex surface shapes on image quality; when using normalized structural aberration coefficients, due to low sensitivity to core design indicators such as optical system aperture and field of view, the initial system off-axis aberration suppression effect is poor, and the imaging quality is difficult to meet expectations; and relying only on a single optimization algorithm, it is easy to fall into local optimality during global search, and it is impossible to take into account both search breadth and accuracy, making it difficult to obtain refined and globally optimal design results. Summary of the Invention

[0008] In view of this, the present invention aims to provide an initial structure design method for a quasi-telecentric off-axis three-mirror optical system to solve the problem that the image quality evaluation functions in the prior art are mostly normalized aberration expressions, and there is often no clear constraint on the telecentricity, making it difficult to obtain refined and globally optimal design results. The present invention establishes a targeted evaluation function for the three-mirror configuration with the aperture stop at the secondary mirror, introduces a quartic term to increase the degree of freedom of optimization, combines the telecentricity constraint conditions, and adopts a global-local optimization strategy to greatly improve the global search capability of variables. The final optimized off-axis initial structure has both high imaging quality and high telecentricity.

[0009] To achieve the above object, the technical solution created by the present invention is implemented as follows:

[0010] An initial structural design method for a quasi-telecentric off-axis three-mirror optical system specifically comprises the following steps:

[0011] S1: Set the design parameters of the quasi-telecentric off-axis three-mirror optical system;

[0012] S2: Establish the quasi-telecentric constraint condition and construct the evaluation function F based on the initial aberration expression of the quasi-telecentric off-axis three-mirror optical system:

[0013] ;

[0014] Among them, S1 is the spherical aberration of the aspheric surface containing the fourth term, S2 is the coma structure coefficient of the aspheric surface containing the fourth term, S3 is the astigmatism structure coefficient of the aspheric surface containing the fourth term, S4 is the field curvature structure coefficient, S5 is the distortion aberration structure coefficient of the aspheric surface containing the fourth term, S6 is the quasi-telecentric constraint condition, and W1, W2, W3, W4, W5, and W6 are all weight coefficients;

[0015] S3: According to the structure and design indicators of the quasi-telecentric off-axis three-mirror optical system, the value range of the optical parameters to be optimized is set;

[0016] S4: Within the value range of the optical parameters to be optimized, the evaluation function is jointly optimized based on the global optimization algorithm and the local optimization algorithm to obtain the optimized structure of the quasi-telecentric off-axis three-mirror optical system.

[0017] Furthermore, in step S1, the design indicators of the quasi-telecentric off-axis three-mirror optical system include: the focal length of the quasi-telecentric off-axis three-mirror system, the field of view of the quasi-telecentric off-axis three-mirror system, and the aperture of the quasi-telecentric off-axis three-mirror system.

[0018] Furthermore, in step S2, the quasi-telecentric constraint S6 is:

[0019] ;

[0020] in, For half the field of view of the quasi-telecentric off-axis three-mirror optical system, is the obstruction ratio of the secondary mirror to the primary mirror, is the blocking ratio of the third mirror to the secondary mirror, is the magnification of the three mirrors.

[0021] Furthermore, the structure of the quasi-telecentric off-axis three-mirror optical system includes an intermediate image plane and an intermediate image plane.

[0022] Furthermore, in step S3, the optical parameters to be optimized include: the blocking ratio of the secondary mirror to the primary mirror is , the blocking ratio of the third mirror to the secondary mirror is , the magnification of the secondary mirror is , the magnification of the three mirrors is , the quartic aspheric coefficient , the primary mirror conic coefficient , secondary mirror cone coefficient , the three-mirror cone coefficient .

[0023] Furthermore, the primary mirror conic coefficient , secondary mirror cone coefficient and the three-mirror conic coefficient The value range of is [-50, 50]; when the focal length of the quasi-telecentric off-axis three-mirror optical system is f=2000mm, the fourth-order aspheric coefficient The value range is [-1E-10, 1E-10]. When the focal length of the quasi-telecentric off-axis three-mirror optical system is f=250mm, the fourth-order aspheric coefficient The value range is [-1E-9, 1E-9].

[0024] Furthermore, in step S2, the spherical aberration S1 of the aspheric surface containing the quartic term is:

[0025] ;

[0026] in, is the primary mirror conic coefficient, is the secondary mirror cone coefficient, is the three-mirror cone coefficient, is the semi-aperture of the quasi-telecentric off-axis three-mirror optical system, is the focal length of the quasi-telecentric off-axis three-mirror optical system;

[0027] The aspheric coma structure coefficient S2 containing the quartic term is:

[0028] ;

[0029] The aspheric astigmatism structural coefficient S3 containing the quartic term is:

[0030] ;

[0031] The field curvature structure coefficient S4 is:

[0032] ;

[0033] The aspheric distortion aberration structure coefficient S5 containing the fourth-order term is:

[0034] .

[0035] Furthermore, in step S4, the global optimization algorithm is a genetic algorithm, particle swarm optimization, simulated annealing or artificial bee colony algorithm; the local optimization algorithm is a sequential quadratic programming algorithm, L-BFGS, trust-region method or pattern search method.

[0036] Furthermore, the input of the global optimization algorithm is: the number of optical parameters to be optimized and the optimization range of the optical parameters to be optimized, and the output is 50 sets of optical parameters with the optimal evaluation function values; the input of the local optimization algorithm is: 50 sets of optical parameters with the optimal evaluation function values, and the output is 1 set of optical parameters with the minimum evaluation function value;

[0037] Both global optimization algorithms and local optimization algorithms are optimized based on evaluation functions.

[0038] Compared with the prior art, the present invention can achieve the following beneficial effects:

[0039] (1) The present invention creates an initial structural design method for the quasi-telecentric off-axis three-mirror optical system, which derives the primary aberration expression under specific structural conditions based on matrix optics to support accurate aberration evaluation during parameter optimization. An accurate mathematical model is established based on theoretical derivation, which can improve the controllability and reliability of the design, reduce the black box dependence on commercial optical software, and improve the transparency of system design. In addition, the mathematical model can support parameter sensitivity analysis, making it easier to discover the dominant aberration source during optimization.

[0040] (2) The present invention creates the initial structural design method of the quasi-telecentric off-axis three-mirror optical system, which introduces a fourth-order aspheric term on both the primary mirror and the third mirror. While improving the image quality of the system, it optimizes the spatial freedom of the system, so that the system can still maintain high image quality under off-axis large field of view conditions, and can effectively correct high-order aberrations (such as coma, field curvature, etc.), thereby improving the imaging consistency of the entire field of view.

[0041] (3) The present invention creates an initial structural design method for the quasi-telecentric off-axis three-mirror optical system, constructs an evaluation function with a "quasi-telecentric" constraint condition, and uses the square of the angle between the main ray and the optical axis as the constraint term, which is suitable for ground orthophoto imaging scenarios.

[0042] (4) The present invention creates the initial structural design method of the quasi-telecentric off-axis three-mirror optical system, which adopts a two-stage hybrid optimization process of global optimization and local optimization. First, a global search is performed to obtain a high-quality initial solution, and then local optimization is fine-tuned to avoid falling into the local optimum, thereby improving the global search coverage and significantly increasing the probability of successful design. In addition, local fine optimization can improve the boundary performance of image quality, taking into account both optimization efficiency and accuracy. In addition, the present invention can complete design convergence in one optimization, shorten the design cycle, improve project delivery efficiency, and improve overall design efficiency and stability.

[0043] (5) The present invention creates an initial structure design method for a quasi-telecentric off-axis three-mirror optical system. The method aims to obtain the initial structure of the off-axis three-mirror system and requires that the optimized initial structure has good aberration optimization potential, so as to accelerate the design of the space optical system. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] The accompanying drawings, which constitute part of the present invention, are intended to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are intended to explain the present invention and do not constitute an undue limitation of the present invention. In the accompanying drawings:

[0045] Figure 1 A schematic structural diagram of a quasi-telecentric off-axis three-mirror optical system according to an embodiment of the present invention;

[0046] Figure 2A schematic flow chart of the initial structural design method of the quasi-telecentric off-axis three-mirror optical system according to an embodiment of the present invention;

[0047] Figure 3 The GA-SQP optimization flow chart described in the embodiment of the present invention is created;

[0048] Figure 4 A grid distortion diagram of the initial system obtained after optimization according to the present invention as described in the embodiment of the present invention;

[0049] Figure 5 A point diagram of the initial system obtained after optimization according to the present invention as described in the embodiment of the present invention;

[0050] Figure 6 This is an MTF curve diagram of the initial system obtained after optimization by the present invention as described in the embodiment of the present invention.

[0051] Description of reference numerals:

[0052] 1. Primary mirror; 2. Secondary mirror; 3. Aperture stop; 4. Tertiary mirror. DETAILED DESCRIPTION

[0053] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and do not constitute a limitation of the present invention.

[0054] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other.

[0055] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention. In addition, the terms "first", "second" and the like are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Thus, features defined as "first", "second" and the like may explicitly or implicitly include one or more of the features. In the description of the present invention, unless otherwise specified, "multiple" means two or more.

[0056] In the description of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "installed," "connected," and "connected" should be understood in a broad sense. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to mechanical connections or electrical connections; they can refer to direct connections or indirect connections through an intermediate medium; and they can refer to internal connections between two components. Those skilled in the art can understand the specific meanings of the above terms in the present invention based on specific circumstances.

[0057] The present invention will be described in detail below with reference to the accompanying drawings and in combination with embodiments.

[0058] like Figure 1 As shown, the quasi-telecentric off-axis three-mirror optical system includes: a primary mirror 1, a secondary mirror 2 and a tertiary mirror 4 arranged in sequence along the light transmission direction, the distance between the primary mirror 1 and the secondary mirror 2 is the same as the distance between the secondary mirror 2 and the tertiary mirror 4, the aperture stop 3 is set at the secondary mirror 2, and a quaternary aspheric structure is added to the primary mirror 1 and the tertiary mirror 4. A quasi-telecentric constraint condition is set, and a GA-SQP algorithm is used for hybrid optimization to obtain an excellent initial structure.

[0059] It should be noted that the quasi-telecentric off-axis three-mirror optical system includes a primary mirror 1, a secondary mirror 2, a third mirror 4, and an aperture stop 3 arranged at the secondary mirror 2. The three mirrors are arranged at equal distances along the optical axis of the system to maintain the symmetry of the system structure and the convenience of adjustment. The present invention combines matrix optics and aberration theory to derive the primary aberration expression of the off-axis three-mirror optical system in which the primary mirror 1, the secondary mirror 2, and the third mirror 4 are arranged at equal distances along the axial direction and the aperture stop 3 is located at the secondary mirror 2, and structural optimization is achieved based on the derivation result. The initial structure optimized by the present invention is unobstructed, has good off-axis aberration characteristics, has quasi-telecentric characteristics, and the main three mirrors are at the same distance along the axis, which is conducive to actual adjustment. In addition, the present invention can be extended to the initial structural design of coaxial three-mirror structures and curved field imaging systems.

[0060] In some embodiments, the semi-aperture h of the quasi-telecentric off-axis three-mirror optical system is 12.5 mm, the focal length is 250 mm, and the field of view angle is 13.2°.

[0061] To improve the imaging performance of a quasi-telecentric off-axis three-mirror optical system and ensure that its structure remains unobstructed under off-axis wide-angle conditions, this invention introduces quartic aspheric terms for primary mirror 1 and tertiary mirror 4, while maintaining a spherical surface for secondary mirror 2. Based on a matrix optical model, the primary structural aberration coefficients of the quasi-telecentric off-axis three-mirror optical system under these structural conditions, including high-order aspheric terms, are derived and used as the core calculation basis in the optimization evaluation function.

[0062] like Figure 2As shown, an initial structural design method for a quasi-telecentric off-axis three-mirror optical system specifically includes the following steps:

[0063] S1: Set the design parameters of the quasi-telecentric off-axis three-mirror optical system;

[0064] S2: Establish the quasi-telecentric constraint condition and construct the evaluation function F based on the initial aberration expression of the quasi-telecentric off-axis three-mirror optical system:

[0065] ;

[0066] Among them, S1 is the spherical aberration of the aspheric surface containing the fourth term, S2 is the coma structure coefficient of the aspheric surface containing the fourth term, S3 is the astigmatism structure coefficient of the aspheric surface containing the fourth term, S4 is the field curvature structure coefficient, S5 is the distortion aberration structure coefficient of the aspheric surface containing the fourth term, S6 is the quasi-telecentric constraint condition, and W1, W2, W3, W4, W5, and W6 are all weight coefficients;

[0067] S3: According to the structure and design indicators of the quasi-telecentric off-axis three-mirror optical system, the value range of the optical parameters to be optimized is set;

[0068] S4: Within the value range of the optical parameters to be optimized, the evaluation function is jointly optimized based on the global optimization algorithm and the local optimization algorithm to obtain the optimized structure of the quasi-telecentric off-axis three-mirror optical system.

[0069] In some embodiments, in step S1, the design indicators of the quasi-telecentric off-axis three-mirror optical system include: the focal length of the quasi-telecentric off-axis three-mirror system, the field of view of the quasi-telecentric off-axis three-mirror system, and the aperture of the quasi-telecentric off-axis three-mirror system.

[0070] In some embodiments, in step S2, the quasi-telecentricity constraint S6 is:

[0071] ;

[0072] in, For half the field of view of the quasi-telecentric off-axis three-mirror optical system, is the obstruction ratio of the secondary mirror 2 to the primary mirror 1, is the occlusion ratio of the third mirror 4 to the secondary mirror 2, The magnification of the three-mirror 4.

[0073] In some embodiments, the structure of the quasi-telecentric off-axis three-mirror optical system includes an intermediate image plane and an intermediate image plane.

[0074] In some embodiments, in step S3, the optical parameters to be optimized include: the blocking ratio of the secondary mirror 2 to the primary mirror 1 is , the blocking ratio of the third mirror 4 to the secondary mirror 2 is , the magnification of secondary mirror 2 is , the magnification of the three mirrors 4 is , the quartic aspheric coefficient , the cone coefficient of primary mirror 1 , the conic coefficient of secondary mirror 2 , the conic coefficient of the three mirrors 4 .

[0075] In some embodiments, the primary mirror 1 conic coefficient , cone coefficient of secondary mirror 2 and three mirrors and four cone coefficients The value range of is [-50, 50]; when the focal length of the quasi-telecentric off-axis three-mirror optical system is f=2000mm, the fourth-order aspheric coefficient The value range is [-1E-10, 1E-10]. When the focal length of the quasi-telecentric off-axis three-mirror optical system is f=250mm, the fourth-order aspheric coefficient The value range is [-1E-9, 1E-9].

[0076] In some embodiments, in step S2, the spherical aberration S1 of the aspheric surface containing the quartic term is:

[0077] ;

[0078] in, is the cone coefficient of the primary mirror 1, is the cone coefficient of secondary mirror 2, is the coefficient of the three-mirror 4 cone, is the semi-aperture of the quasi-telecentric off-axis three-mirror optical system, is the focal length of the quasi-telecentric off-axis three-mirror optical system;

[0079] The aspheric coma structure coefficient S2 containing the quartic term is:

[0080] ;

[0081] The aspheric astigmatism structural coefficient S3 containing the quartic term is:

[0082] ;

[0083] The field curvature structure coefficient S4 is:

[0084] ;

[0085] The aspheric distortion aberration structure coefficient S5 containing the fourth-order term is:

[0086] .

[0087] In some embodiments, the structure of the three-mirror optical system is mainly divided into two categories: including one with an intermediate image plane and one without an intermediate image plane. Different structural forms require 、 There are different value ranges. There are four structural forms without intermediate image. Table 1 shows the variable value ranges corresponding to the three-mirror structure without intermediate image:

[0088] Table 1

[0089]

[0090] The corresponding value ranges of the four structural forms with intermediate image planes are as follows:

[0091] Table 2

[0092]

[0093] According to design requirements, select the appropriate Value range.

[0094] Cone coefficient in actual machining process Too large will increase the surface slope, thereby increasing the difficulty of surface processing inspection. Therefore, the cone coefficient The general value is between [-50,50], and the specific value is selected according to the actual processing conditions.

[0095] Quartic aspheric coefficients The value range is generally small. For a telephoto system such as f=2000mm, the coefficient value is controlled between [-1E-10, 1E-10]. For a short focal length such as f=250mm, the value range is controlled between [-1E-9, 1E-9].

[0096] Combined with the design indicators of the optical system, after selecting the corresponding optical structure, the optical parameters are given: Value range.

[0097] like Figure 3 As shown, first, the characteristics of the quasi-telecentric off-axis three-mirror optical system model are deeply analyzed, covering the laws of light propagation, causes of aberrations, etc.; combined with actual needs (such as imaging resolution, field of view, etc.), optical structure characteristics are selected, and the reasonable value range of structural parameters and aspheric high-order coefficients is limited. An objective function with image quality evaluation (MTF, wave aberration) and structural constraints (quasi-telecentricity) as the core is constructed to clarify the optimization direction.

[0098] Start the Genetic Global Optimization Algorithm (GA), set the initial population size, maximum number of iterations, and the iteration stopping threshold. Within the solution space, the GA generates initial candidate solutions after parameter initialization. The GA then iterates through fitness calculation (i.e., evaluation function calculation) and crossover and mutation. After each iteration, determine whether the threshold conditions are met. If so, select the top 50 solutions with the best evaluation function values ​​as the starting point for subsequent local optimization to avoid being trapped in local optima.

[0099] Based on the high-quality starting point output by the GA, a sequential quadratic programming (SQP) local optimization is initiated. At the current iteration point, the nonlinear optimization problem is approximated as an SQP subproblem with a quadratic objective and linear constraints. Gradient calculations are performed using a standard QP algorithm to determine the direction of gradient descent, allowing for rapid iterative refinement of parameters. Threshold conditions are continuously evaluated, and a local optimal solution is output when they are met.

[0100] The optimization results output by SQP are numerical solutions that need to be converted into parameters recognizable by the optical system (such as reflector curvature, aspheric coefficients, and relative positions). Ultimately, the initial structure of the quasi-telecentric off-axis three-mirror optical system is formed, providing a foundation for subsequent engineering (assembly, adjustment, and tolerance analysis). The conversion relationship is shown below:

[0101] ;

[0102] ;

[0103] in is the obstruction ratio of the secondary mirror 2 to the primary mirror 1, is the occlusion ratio of the third mirror 4 to the secondary mirror 2, is the magnification of secondary mirror 2, is the magnification of the three-mirror 4, The radius of the primary mirror 1, is the surface radius of secondary mirror 2, is the radius of the three-mirror four-facet type; The distance from primary mirror 1 to secondary mirror 2 along the optical axis, is the distance from secondary mirror 2 to tertiary mirror 4 along the optical axis, is the distance from the third mirror 4 to the image plane along the optical axis.

[0104] The final output is the initial structure of an excellent quasi-telecentric off-axis three-mirror optical system.

[0105] In some embodiments, in step S4, the global optimization algorithm is a genetic algorithm, particle swarm optimization, simulated annealing or artificial bee colony algorithm; the local optimization algorithm is a sequential quadratic programming algorithm, L-BFGS, trust-region method or pattern search method.

[0106] In some embodiments, the input of the global optimization algorithm is: the number of optical parameters to be optimized and the optimization range of the optical parameters to be optimized, and the output is 50 sets of optical parameters with the optimal evaluation function values; the input of the local optimization algorithm is: 50 sets of optical parameters with the optimal evaluation function values, and the output is 1 set of optical parameters with the minimum evaluation function value;

[0107] Both global optimization algorithms and local optimization algorithms are optimized based on evaluation functions.

[0108] It should be noted that the global optimization algorithm also needs to set the maximum number of iterations, population size, crossover rate, selection function, and number of elites to be retained.

[0109] Taking the initial system design of a quasi-telecentric three-mirror system with a clear aperture h of 12.5mm, a focal length f of 250mm, and a field of view of 13.2° as an example, this design is an optical system without an intermediate image plane, so the value range of the optimization variable space is set as shown in the following table:

[0110] Table 3

[0111]

[0112] This optical system is a long focal length, large field of view optical system, and its on-axis aberrations, especially the aberration characteristics of coma and astigmatism are more prominent. Therefore, emphasis is placed on suppressing off-axis coma and astigmatism. At the same time, spherical aberration and field curvature are the mother aberrations of the optical system. When spherical aberration and field curvature are well corrected, other aberration characteristics are also satisfied. Therefore, a certain degree of suppression is required. Distortion has no effect on clarity, so a large weight is not required. The value of the telecentricity constraint item is relatively large. The telecentricity must be constrained while satisfying the imaging quality. Therefore, a smaller weight is required. Based on the above, the weights of each item are as follows: W1=40, W2=80, W3=60, W4=20, W5=1. When the quasi-telecentric off-axis three-mirror optical system has constraints on telecentricity, W6=0.3. A corresponding evaluation function was constructed. Based on the evaluation function, a genetic algorithm was used to realize the global optimization starting point search. The convergence threshold was set to 1E-7. The top 50 groups of optimal results were retained as the starting points of the sequential quadratic programming (SQP) optimization algorithm. Multi-starting point synchronous optimization processing was performed, and the solution set with the minimum evaluation function value was output as the final result.

[0113] The present invention is based on matrix optics and aberration theory, and derives the primary aberration expression of the aperture stop 3 at the position of the secondary mirror 2 under the condition that the distances between the primary mirror 1 and the secondary mirror 2 and between the secondary mirror 2 and the tertiary mirror 4 are consistent. By introducing the quartic aspheric term on the primary mirror 1 (M1) and the tertiary mirror 4 (M3), the image quality is improved by increasing the degree of freedom of the system; and a quasi-telecentric constraint condition is constructed to construct a corresponding evaluation function. The quasi-telecentric constraint condition adopts an approximate method to obtain the angle between the main ray of the maximum field of view and the normal of the image plane based on the paraxial ray tracing method, and uses it as the quasi-telecentric constraint condition. By adding a central constraint term to the objective function, an evaluation function with a quasi-telecentric constraint is constructed. A global optimization algorithm (such as a genetic algorithm) is then used to obtain a certain number of optimization starting points, i.e., multiple parameter combinations with good initial performance. A local optimization algorithm (SQP) is then employed for local optimization, improving the global detailed search capability. This results in a single pass for a quasi-telecentric, easily adjustable three-mirror initial configuration with an aperture stop 3 at the secondary mirror 2 and an unobstructed off-axis field of view (i.e., a quasi-telecentric, unobstructed, and easily adjustable off-axis three-mirror optical system). At small angles, the initial configuration's off-axis aberration characteristics approach the diffraction limit, and it exhibits unobstructed and high telecentricity, demonstrating the superiority of the optimization strategy.

[0114] Furthermore, it is assumed that the global optimization algorithm adopts the genetic algorithm, the local optimization algorithm adopts the sequential quadratic programming algorithm, the population size of the genetic algorithm (GA) is 500, the maximum number of iterations is 500, and the threshold is 10 -7 ; The convergence accuracy of the sequential quadratic programming algorithm (SQP) needs to be set to 10 -12 .

[0115] It should be noted that the hybrid approach can also use multi-layer nesting or adaptive switching strategies according to the form of the optimization function.

[0116] Based on a quasi-telecentric off-axis three-mirror optical system with a focal length of 250mm, a field of view of 13.2°, and a semi-aperture of 12.5mm, the initial structural parameters designed according to the present invention are as follows:

[0117] Table 4

[0118]

[0119] Figure 3 The hybrid optimization algorithm process adopted by the present invention is demonstrated, including processing nodes such as initial population generation, global search, introduction of quasi-telecentric constraints, and local SQP convergence steps. Figure 4 This is the grid distortion diagram of the initial system obtained after optimization by the present invention, showing the deviation between the actual image points of the system and the theoretical grid points within the full field of view, proving that the system has the characteristics of large field of view and small distortion. Figure 5This is the spot diagram of the initial system obtained after optimization by the present invention, showing the shape and size of the imaging spot in the typical field of view of the system, proving that the system has good light beam focusing ability. Figure 6 The MTF curve of the initial system obtained after optimization by the present invention shows the imaging contrast of the system within a typical field of view, proving that the system has high imaging quality. Finally, the initial system obtained after optimization by the present invention is unobstructed and has quasi-telecentric characteristics.

[0120] It should be understood that the various forms of the processes shown above can be used to reorder, add, or delete steps. For example, the steps described in the present disclosure can be performed in parallel, sequentially, or in a different order, as long as the desired results of the technical solutions disclosed in the present disclosure can be achieved. This is not limited herein.

[0121] The above specific embodiments do not limit the scope of protection of the present invention. Those skilled in the art will appreciate that various modifications, combinations, sub-combinations, and substitutions may be made based on design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention are intended to be included within the scope of protection of the present invention.

Claims

1. A method for initial structural design of a quasi-telecentric off-axis three-mirror optical system, characterized by: The quasi-telecentric off-axis three-mirror optical system includes: a primary mirror, a secondary mirror, and a tertiary mirror arranged in sequence along the light transmission direction, the distance between the primary mirror and the secondary mirror is the same as the distance between the secondary mirror and the tertiary mirror, the aperture stop is set at the secondary mirror, and the primary mirror and the tertiary mirror are both equipped with a 4-fold aspheric structure; The initial structural design method of the quasi-telecentric off-axis three-mirror optical system specifically includes the following steps: S1: Set the design parameters of the quasi-telecentric off-axis three-mirror optical system; S2: Establish the quasi-telecentric constraint condition and construct the evaluation function F based on the initial aberration expression of the quasi-telecentric off-axis three-mirror optical system: ； Among them, S1 is the spherical aberration of the aspheric surface containing the fourth term, S2 is the coma structure coefficient of the aspheric surface containing the fourth term, S3 is the astigmatism structure coefficient of the aspheric surface containing the fourth term, S4 is the field curvature structure coefficient, S5 is the distortion aberration structure coefficient of the aspheric surface containing the fourth term, S6 is the quasi-telecentric constraint condition, and W1, W2, W3, W4, W5, and W6 are all weight coefficients; S3: According to the structure and design indicators of the quasi-telecentric off-axis three-mirror optical system, the value range of the optical parameters to be optimized is set; S4: Within the value range of the optical parameters to be optimized, the evaluation function is jointly optimized based on the global optimization algorithm and the local optimization algorithm to obtain the optimized structure of the quasi-telecentric off-axis three-mirror optical system; In step S4, the global optimization algorithm is a genetic algorithm, a particle swarm optimization, a simulated annealing algorithm, or an artificial bee colony algorithm; the local optimization algorithm is a sequential quadratic programming algorithm, L-BFGS, a trust-region method, or a pattern search method; The input of the global optimization algorithm is: the number of optical parameters to be optimized and the optimization range of the optical parameters to be optimized, and the output is 50 sets of optical parameters with the optimal evaluation function values. The input of the local optimization algorithm is: 50 sets of optical parameters with the optimal evaluation function values, and the output is 1 set of optical parameters with the minimum evaluation function value. Both global optimization algorithms and local optimization algorithms are optimized based on evaluation functions.

2. The initial structural design method of a quasi-telecentric off-axis three-mirror optical system according to claim 1, characterized in that: In step S1 , the design indicators of the quasi-telecentric off-axis three-mirror optical system include: the focal length of the quasi-telecentric off-axis three-mirror system, the field of view of the quasi-telecentric off-axis three-mirror system, and the aperture of the quasi-telecentric off-axis three-mirror system.

3. The initial structural design method of a quasi-telecentric off-axis three-mirror optical system according to claim 1, characterized in that: In step S2, the quasi-telecentric constraint S6 is: ； in, For half the field of view of the quasi-telecentric off-axis three-mirror optical system, is the obstruction ratio of the secondary mirror to the primary mirror, is the blocking ratio of the third mirror to the secondary mirror, is the magnification of the three mirrors.

4. The initial structural design method of a quasi-telecentric off-axis three-mirror optical system according to claim 1, characterized in that: The structure of the quasi-telecentric off-axis three-mirror optical system includes an intermediate image plane and an intermediate image plane.

5. The initial structural design method of a quasi-telecentric off-axis three-mirror optical system according to claim 1, characterized in that: In step S3, the optical parameters to be optimized include: the blocking ratio of the secondary mirror to the primary mirror is , the blocking ratio of the third mirror to the secondary mirror is , the magnification of the secondary mirror is , the magnification of the three mirrors is , the quartic aspheric coefficient , the primary mirror conic coefficient , secondary mirror cone coefficient , the three-mirror cone coefficient .

6. The initial structural design method of a quasi-telecentric off-axis three-mirror optical system according to claim 5, characterized in that: Primary mirror conic coefficient , secondary mirror cone coefficient and the three-mirror conic coefficient The value range of is [-50, 50]; when the focal length of the quasi-telecentric off-axis three-mirror optical system is f=2000mm, the fourth-order aspheric coefficient The value range is [-1E-10, 1E-10]. When the focal length of the quasi-telecentric off-axis three-mirror optical system is f=250mm, the fourth-order aspheric coefficient The value range is [-1E-9, 1E-9].

7. The initial structural design method of a quasi-telecentric off-axis three-mirror optical system according to claim 5, characterized in that: In step S2, the spherical aberration S1 of the aspheric surface containing the quartic term is: ； in, is the primary mirror conic coefficient, is the secondary mirror cone coefficient, are the three-mirror cone coefficients, is the semi-aperture of the quasi-telecentric off-axis three-mirror optical system, is the focal length of the quasi-telecentric off-axis three-mirror optical system; The aspheric coma structure coefficient S2 containing the quartic term is: ； The aspheric astigmatism structural coefficient S3 containing the quartic term is: ； The field curvature structure coefficient S4 is: ； The aspheric distortion aberration structure coefficient S5 containing the fourth-order term is: 。

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