WO2024007370A1 - 一种折反射式不动型反摄远变焦系统设计方法 - Google Patents
一种折反射式不动型反摄远变焦系统设计方法 Download PDFInfo
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Definitions
- the invention relates to the field of photoelectric imaging technology, and in particular to a design method of a catadioptric fixed-type reverse telephoto zoom system.
- the zoom system has the optical property of adjusting the magnification of the imaging object while maintaining the stability of the image plane. It is widely used in reconnaissance and monitoring, aerospace, astronomical observation and other fields. The continuous zooming capability of the zoom system is reflected in maintaining high imaging quality while achieving range search with short focal lengths and large formats and high-resolution capture with long focal lengths and small fields of view.
- the traditional mechanical zoom system compensates for image plane position drift by moving optical elements, and achieves precise position calculation and control of moving components while meeting the object-image conjugation principle. It is a universal system that achieves large zoom ratios and high imaging quality at all focal lengths.
- zoom ratio 3-30 zoom ratio 3-30 system design plan; high requirements for optical surface accuracy and mechanical cam accuracy; from a macro structure perspective, with the increase in zoom magnification and performance requirements, the overall system structure is complex, bulky, and expensive.
- new zoom devices represented by transmissive liquid lenses and reflective deformable mirrors have promoted the development of new fixed zoom systems, which control the surface shape within the aperture range by calculating and inputting precise drive voltages to the device.
- Accurate and rapid deformation the system built has the advantages of high speed and integration.
- the zoom device used, in terms of reflective deformable mirrors is a multi-channel high-precision micro-optical electromechanical device. It is necessary to explore how to fully utilize the light of the device.
- the aperture method is to obtain an appropriate central deformation amount at the center of the device mirror to obtain support for rapid changes in focal length, obtain a complex and precise free-form surface shape in the full aperture range to achieve image quality correction, and achieve fast zoom and high precision.
- the resolution imaging system has currently achieved a zoom range with a zoom ratio of 3-6, a fast zoom imaging system.
- the problem of the designer's initial structure being difficult is solved, but there is still a need to further discuss the overall system image.
- the correlation between the difference characteristics and the system is convenient for subsequent guidance in the direction of system optimization; and the reflection system is limited by the small system working field of view, and the diameter of the deformable mirror restricts the system's need for a large entrance pupil aperture.
- the optical power of the three-piece reflective optical system in the reverse telephoto form presents a "negative, positive and positive" component structure.
- This component distribution can achieve a large, perfectly circular working field of view without introducing complex free-form surfaces into each mirror surface. detection.
- the reflection system due to the first convex reflector, it is usually necessary to introduce a pair of aspherical aberration conjugate points in the catadioptric optical path of the aspheric refractive lens to build a correction optical path to achieve surface shape detection, and the accuracy detection of the convex reflector is subject to other
- the limitation of the processing accuracy of detection optical components makes it difficult to accurately detect the surface shape of convex reflective surfaces with large curvatures; and in an assembly and adjustment system composed of a plane reflector and an interferometer, the main mirror is usually used as the assembly and adjustment reference surface, and the convex reflector
- the effect on beam divergence further increases the difficulty of optical axis installation and adjustment, further limiting the Gaussian structure power solution set distribution of
- the present invention proposes a design method of a catadioptric fixed-type reverse telephoto zoom system.
- the optimization potential is low, the reflection system is limited by the small system working field of view, the diameter of the deformable mirror restricts the system's need for a large entrance pupil diameter, and the optical axis is difficult to install and adjust.
- the invention discloses a design method of a catadioptric fixed-type reverse telephoto zoom system, which includes the following steps:
- the above S1 includes the following steps:
- A1 Determine the initial structural form of the catadioptric optical system, the position of the diaphragm, the number of mirror components, and the size of the system entrance pupil;
- A2 Determine the first-order parameters of the catadioptric optical system based on the system zoom ratio, focal length range, and field of view of the variable device;
- variable device deformation surface deformation range based on the reverse telephoto structural parameters of the large field of view zoom system
- the evaluation indicators are the focal length value and back intercept of a specific focal length
- 1 A m+1 represents the parameters of the fixed zoom equation
- step A5 the specific process of establishing the first-order evaluation function of the system based on multiple structures is:
- the evaluation indicators are the focal length value and back intercept of a specific focal length; its expression is as follows:
- F( xi ) is the first-order system evaluation function, is the power change range of the first deformable mirror, is the power change range of the second deformable mirror.
- the specific process of solving the first-order structure of the system using the global optimization algorithm is: solving using the global optimization algorithm to solve the problem of achieving a large working field of view under the constraints of the deformation amount and aperture of the double deformable mirror and the type of reverse telephoto.
- the above S2 includes the following steps:
- A8 Output the first-order Gaussian structure system under the optimal solution data, and calculate the wave aberration coefficient of the current system;
- A9. Determine the system incident angle and entrance pupil diameter, and use the Gaussian bracket method to characterize the thick lens system component parameter structure form and third-order aberration expression;
- the evaluation indicators are the focal length of the thin lens, principal point, third-order spherical aberration, coma, astigmatism, distortion, and chromatic aberration;
- A12. Determine the optimal form of thick lens components and the component composition of the catadioptric system.
- the first-order Gaussian structure system under the output optimal solution data includes: lens thickness, lens diameter, component spacing, and refractive index in the thick lens model; the calculated wave aberration coefficient of the current system Including: equivalent solution of the first-order focal length and third-order wave aberration (spherical aberration, astigmatism, coma, distortion) of the thin lens model, the effective focal length (EFL), the back intercept distance (BFL), the front focal length (FFL) Thick lens component allocation and aberration design form, and respectively discuss the third-order wave in the form of apochromatic lens under the thick lens structure (single lens, double separate lens, three components, double Gaussian, etc.) under the effective aperture and working field of view Mathematical expression of aberration distribution.
- W 040 , W 131 , W 222 , and W 311 respectively represent the wave aberration coefficient expressions of third-order spherical aberration, third-order coma, third-order astigmatism, and third-order distortion.
- Characterizes the equivalent wave aberration of each component surface Characterizes the third-order Seidel spherical aberration coefficient of the i-th optical element; Characterizes the third-order Seidel coma coefficient of the i-th optical element; Characterizes the third-order Seidel astigmatism coefficient of the i-th optical element; Characterizes the third-order Seidel distortion coefficient of the i-th optical element; Characterizes the Seidel primary lateral chromatic aberration coefficient of the i-th optical element; Characterizes the Seidel primary axial chromatic aberration coefficient of the i-th optical element; V i is the Abbe number of the i-th thick lens optical element; u j and u' j respectively represent the edge ray incident angle and exit angle of the j-th optical element , and represent the central ray incident angle and exit angle of the j-th optical element respectively; h i is the edge ray height of the i-th optical element; represents the central ray height of
- the third-order aberration evaluation function of the refractive element under the multi-structure is established as follows:
- c j represents the vertex curvature of the j-th optical element surface.
- the optimization termination conditions are as follows:
- Ti refers to the constraint range of the corresponding variable
- Vi is the Abbe number of the i-th thick lens optical element.
- the above S3 includes the following steps:
- A14 Determine the system tilt angle without obstruction of the mirror under the entrance pupil aperture, and find the quadratic surface coefficient of the mirror surface of the off-axis reflection system;
- the optical design software optimizes the aspheric coefficient of the refractive system and the high and low order surface shape coefficients of the mirror, and outputs the structure of the fixed catadioptric zoom system.
- the third-order wave aberration distribution of the off-axis reflection system aberration calculated based on the vector aberration theory includes: astigmatism, spherical aberration, coma, and distortion, where the wave aberration of the off-axis optical system
- the expression is:
- the third-order wave aberration distribution of the above-mentioned off-axis reflection system aberration includes: astigmatism, spherical aberration, coma, and distortion.
- the aberration expression is as follows:
- the aberration expression of the third-order spherical aberration of the off-axis reflection system expanded by the contributions of the spherical coefficient and the aspherical coefficient is:
- step A14 the specific operation of determining the unobstructed system tilt angle of the mirror under the entrance pupil aperture and finding the quadric coefficient of the mirror surface of the off-axis reflection system is: establishing the quadric coefficient of the off-axis mirror and Nonlinear global evaluation function for mirror tilt angle:
- T i refers to the constraint range of the corresponding variable
- k j represents the quadratic surface parameter of the j-th optical element surface.
- the optical design software optimizes the aspheric coefficient of the refractive system and the high and low order surface shape coefficients of the mirror, and outputs the structure of the fixed catadioptric zoom system.
- the specific operations are as follows: Solve the off-axis mirror under multiple structures The quadratic surface coefficient realizes the rapid convergence calculation of the non-rotationally symmetric off-axis aberration caused by the system's off-axis, and realizes the direct solution of the system structure under the high-order surface shape coefficient of the unobstructed off-axis mirror and the tilt angle of the mirror.
- the present invention uses a fixed catadioptric zoom system as a model, uses the Gaussian bracket method to discuss the Gaussian solution characteristics of the zoom equation of the new zoom system under the constraints of the double deformable mirror deformation variable, aperture, and reflex telephoto type, and establishes a multi-structure characterization group.
- the component design optimization method of the nonlinear evaluation function of element aberration characteristics and first-order parameters solves the structure of various typical apochromatic thick lens groups within the working aperture and field of view.
- the off-axis aberration under the structural distribution of the off-axis catadioptric zoom system under multiple structures can be realized with high-order surface shape balance optimization design, make full use of the MOEMS (micro-optical electromechanical system) flexible deformation device specifications and the device braking amount range within the effective aperture, and design a system structure with improved zoom sensitivity and aberration correction capabilities to solve the problem
- MOEMS micro-optical electromechanical system
- the subsequent calculation process is cumbersome and time-consuming, and the optimization potential is low.
- the reflection system is limited by the small system working field of view.
- the diameter of the deformable mirror restricts the system's need for a large entrance pupil diameter.
- the optical axis is difficult to install and adjust. This further improves the zoom efficiency of the system based on flexible mirrors and enables the design of a fixed zoom system with large zoom ratio, large field of view and large entrance pupil aperture characteristics.
- Figure 1 is an overall flow chart of the design of the catadioptric fixed-type reverse telephoto zoom system in an embodiment of the present invention
- Figure 2 is a detailed flow chart of the design of the catadioptric fixed-type reverse telephoto zoom system in the embodiment of the present invention
- Figure 3 is a solution diagram of equivalent components of thick lenses in the embodiment of the present invention.
- Figure 4 is a distribution diagram of thick lens components in an embodiment of the present invention.
- Figure 5 is a schematic diagram of the catadioptric off-axis optical system in an embodiment of the present invention.
- Figure 6a is a short-focus optical path diagram of a stationary catadioptric system designed and implemented through this method in an embodiment of the present invention
- Figure 6b is a mid-focus optical path diagram of a stationary catadioptric system designed and implemented through this method in an embodiment of the present invention
- Figure 6c is a telephoto optical path diagram of a stationary catadioptric system designed and implemented through this method in an embodiment of the present invention.
- orientation terms such as left, right, up, down, top, and bottom in this embodiment are only relative concepts to each other, or are based on the normal use state of the product, and should not be considered as having Restrictive.
- the embodiment of the present invention provides a design method for a catadioptric fixed-type reverse telephoto zoom system, which is based on the improvement of the three-piece reflective optical system in the reverse telephoto form. It mainly solves the problem that the reflection system is limited by the small working field of view of the system and the deformable mirror.
- the aperture restricts the system's requirement for a large entrance pupil diameter, and the difficulty of optical axis installation and adjustment.
- Introducing the design of a catadioptric system composed of four components, including a fixed lens group of the first component and an off-axis reflective structure of the second, third and fourth components.
- the second and fourth components are deformable.
- the mirror realizes system zoom and image plane compensation effects.
- the optical power is positive, which not only reduces the difficulty of mirror installation and adjustment, but also balances the primary astigmatism, high-order astigmatism, and coma introduced by the off-axis system. difference; the fourth component's optical power is positive, achieving large-aperture beam convergence and balancing on-axis defocus and spherical aberration generated during the zoom process.
- Step S1 Method for solving the component Gaussian structure of the fixed zoom system: Solve the solution of the four-component Gaussian structure of the retro-telephoto fixed zoom system based on dual variable elements. Specifically, it includes the following steps:
- A1 Determine the initial structural form of the catadioptric optical system, the position of the aperture, the number of mirror components, the system entrance pupil size, etc.;
- A2 Determine the first-order parameters of the catadioptric optical system based on the system zoom ratio, focal length range, and field of view of the variable device;
- variable device deformation surface deformation range based on the reverse telephoto structural parameters of the large field of view zoom system
- the evaluation indicators are the focal length value and back intercept of a specific focal length
- A1-A7 are further detailed as follows:
- A1. Determine the initial structural form of the catadioptric optical system as a refractive lens and a multi-component mirror.
- the aperture position is placed on the secondary mirror in the multi-component mirror.
- the system entrance pupil size determines the initial structural index parameters of the system;
- A2. Determine the first-order system parameters of the catadioptric optical system, and determine the structural design parameters such as system zoom ratio, focal length range, and field of view angle;
- 1 A m+1 represents the parameters of the fixed zoom equation
- GGC's Generalized Gaussian Constants
- variable device deformation surface deformation range based on the reverse telephoto structural parameters of the zoom system under large field of view
- F( xi ) is the first-order system evaluation function, is the power change range of the first deformable mirror, is the power change range of the second deformable mirror.
- Step S2 thick lens nonlinear evaluation function component design and optimization method: establish a nonlinear evaluation function component design and optimization method for multi-structure representation of component phase difference characteristics and first-order parameters, solve and select the optimal apochromatic lens Group structure. Specifically include:
- A8 Output the first-order Gaussian structure system under the optimal solution data, and calculate the wave aberration coefficient of the current system;
- A9. Determine the system incident angle and entrance pupil diameter, and use the Gaussian bracket method to characterize the thick lens system component parameter structure form and third-order aberration expression;
- the evaluation indicators are the focal length of the thin lens, principal point, third-order spherical aberration, coma, astigmatism, distortion, and chromatic aberration;
- A12. Determine the optimal form of thick lens components and the component composition of the catadioptric system.
- steps A1-A7 calculate the current system wave aberration coefficient by solving the first-order structure through the set entrance pupil parameters and incident angle;
- A9. Determine the incident angle and entrance pupil diameter of the system, set the lens curvature, lens thickness, lens diameter, component spacing, and refractive index as variables in the actual thick lens model, and equivalently solve for the effective focal length (EFL) of the thin lens model.
- W 040 , W 131 , W 222 , and W 311 respectively represent the wave aberration coefficient expressions of third-order spherical aberration, third-order coma, third-order astigmatism, and third-order distortion. Characterizes the equivalent wave aberration of each component surface, Characterizes the third-order Seidel spherical aberration coefficient of the i-th optical element; Characterizes the third-order Seidel coma coefficient of the i-th optical element; Characterizes the third-order Seidel astigmatism coefficient of the i-th optical element; Characterizes the third-order Seidel distortion coefficient of the i-th optical element; Characterizes the Seidel primary lateral chromatic aberration coefficient of the i-th optical element; Characterizes the Seidel primary axial chromatic aberration coefficient of the i-th optical element; V i is the Abbe number of the i-th thick lens optical element; u j and u' j respectively represent the edge ray
- the primary aberration, system equivalent focal length, equivalent back focal length, and equivalent front focal length of the thick lens system will be used as comprehensive evaluation indicators for thick lens solutions.
- the nonlinear global evaluation function is specifically expressed as follows:
- c j represents the vertex curvature of the j-th optical element surface.
- the system stops optimizing when the software optimizes to the optimal minimum value of the evaluation function, and outputs the thick lens system lens curvature, lens thickness, lens diameter, component spacing, and refractive index;
- the catadioptric off-axis optical system of the embodiment of the present invention is shown in Figure 5. The following steps are implemented based on the catadioptric off-axis optical system.
- Step S3 optimization design method of off-axis aberration and high-order surface balance under the system structure distribution: Based on the aberration characteristics of the off-axis catadioptric system, design the off-axis catadioptric zoom system structure distribution under the high-order surface balance optimization. Specifically include:
- A14 Determine the system tilt angle without obstruction of the mirror under the entrance pupil aperture, and find the quadratic surface coefficient of the mirror surface of the off-axis reflection system;
- the optical design software optimizes the aspheric coefficient of the refractive system and the high and low order surface shape coefficients of the mirror, and outputs the structure of the fixed catadioptric zoom system.
- A13-A15 are further detailed as follows:
- W 040 , W 131 , W 222 , W 220 W 311 respectively represent the wave aberration coefficient expressions of third-order spherical aberration, third-order coma, third-order astigmatism, third-order field curvature, and third-order distortion. Characterizes the equivalent wave aberration of each component surface, where the vector wave aberration is expanded, and the aberration expression of the third-order spherical aberration of the off-axis reflection system expanded through the contributions of the spherical coefficient and the aspherical coefficient is:
- sph and asph represent spherical and aspherical surfaces respectively;
- h j represents the edge ray height of the jth optical element, Represents the center ray height of the j-th optical element, u j and u' j respectively represent the edge ray incident angle and exit angle of the j-th optical element, and represent the central light incident angle and exit angle of the j-th optical element respectively;
- c j represents the vertex curvature of the j-th optical element surface, and k j represents the second square of the j-th optical element surface
- n j represents the refractive index behind the jth optical element.
- A14 Determine the system tilt angle without obstruction of the mirror under the entrance pupil aperture, and find the quadratic surface coefficient of the mirror surface of the off-axis reflection system.
- the full-field aberration can be optimized with multiple nodes, the aberration distribution and transfer characteristics of the off-axis reflection system after transmission through the coaxial fixed lens are clarified, and an off-axis mirror is established.
- Nonlinear global evaluation function of hyposurface coefficient and mirror tilt angle is established.
- ⁇ j is the tilt angle at the vertex of the j-th optical element surface
- n 1,2,3...j
- T i refers to the constraint range of the corresponding variable
- k j represents the quadratic surface parameter of the j-th optical element surface.
- A15 Use A14 to solve the surface shape coefficient of the quadratic surface of the mirror, and use the optical design software to set the surface shape coefficient of the refraction system as an optimization variable. Use the finite difference global optimization algorithm of ray tracing to further realize the aspherical coefficient of the refraction system.
- the non-rotationally symmetric off-axis aberration caused by the off-axis is quickly converged and calculated to realize the direct solution of the system structure under the high-order surface shape coefficient of the unobstructed off-axis mirror and the tilt angle of the mirror, and the structure of the fixed catadioptric zoom system is output.
- 6a, 6b, and 6c are respectively the short-focus optical path diagram, the medium-focus optical path diagram, and the long-focus optical path diagram of the large field of view and high zoom ratio fixed catadioptric reflection system designed and implemented by the method of the embodiment of the present invention.
- short focus achieves an observation field of view of 20° ⁇ 20°
- switching from long focus to short focus achieves ten times the optical effect.
- the Gaussian bracket method is used to characterize the zoom equation of the new fixed zoom system, and the important parameters related to the zoom capability of the new fixed zoom system and the change of the optical power of the adjustable optical power device are extracted.
- the four-component Gaussian solution set of the anti-telephoto type that satisfies the large zoom ratio system index and large field of view is established under the constraints of deformable mirror deformation, aperture, and system structure anti-telephoto type.
- an efficient design solution for system components is proposed, which is further described as follows: a nonlinear evaluation function component design optimization method based on multiple structures representing component aberration characteristics and first-order parameters is proposed.
- the nonlinear evaluation function of the primary wave aberration spherical aberration, coma, astigmatism, chromatic aberration
- first-order characteristics focal length, front focal length, back focal length
- the thin lens group optimization problem is transformed into a multi-component apochromatic lens group structure calculation problem targeting the focal length and aberration of the multi-component thick lens group, thereby achieving the optimal Gaussian initial structure of the new fixed catadioptric zoom system.
- the analytical expressions of system aberrations based on multiple apochromatic component structures are derived, and the extreme value distribution of the third-order aberration expressions of the system is calculated to determine the optimal apochromatic component form of the catadioptric system.
- the optimization calculation of the off-axis structure of the system is proposed, which is further explained as follows: Based on the aberration characteristics of the off-axis catadioptric system, an off-axis image under the structure distribution of the off-axis catadioptric zoom system under multiple structures is proposed. Differential and high-order surface shape balance optimization design methods. Analyze and extract the characteristics and transfer rules of the on-axis and off-axis primary aberrations of the catadioptric system under a fixed apochromatic lens group within the field of view, and optimize the calculation based on vector aberration theory and high-order surface aberration characteristics.
- the initial structure of the off-axis system distribution is designed to have the best optimized imaging quality and consider the actual installation and adjustment difficulty of the large-aperture, high-zoom-ratio catadioptric fixed-zoom off-axis system distribution structure in the mid-focal range.
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Abstract
一种折反射式不动型反摄远变焦系统设计方法，包括如下步骤：求解基于双可变元件的反摄远类型不动型变焦系统四组元高斯结构解（S1）；建立多重结构表征组元相差特性和一阶参数的非线性评价函数组元设计优化方法，求解并筛选最优复消色差透镜组结构（S2）；基于离轴折反射系统像差特征规律，设计离轴折反射变焦系统结构分布于高阶面形平衡优化（S3）。该方法解决了后续计算过程繁琐耗时、优化潜力低、光轴装调难度大的问题。
Description
本发明涉及光电成像技术领域，特别是涉及一种折反射式不动型反摄远变焦系统设计方法。
变焦系统具有在保持像面稳定下调节成像物体放大倍率的光学性质，广泛应用于侦察监控、航空航天、天文观测等领域。变焦系统的连续变焦能力体现在保持高成像质量下同时，实现短焦距大画幅的范围搜索和长焦距小视场高分辨率的捕捉。传统机械变焦系统通过移动光学元件补偿像面位置漂移，在满足物像共轭原则下实现移动组元的精准位置计算及控制，是一种通用的实现全焦段下大变焦比、高成像质量的(变倍比3-30)系统设计方案；对光学面形精度和机械凸轮精度要求高；从宏观结构来看随着变焦倍率和性能需求的提升，整体系统结构复杂笨重、造价昂贵。近些年来以透射式液体透镜、反射式可变形镜为代表的新型变焦器件，推动了新型不动型变焦系统的发展，其通过计算并输入器件精密驱动电压方式控制实现口径范围内的面形精确快速形变，所搭建的系统具备高速化、集成化的优势，但所应用的变焦器件，以反射式可变形镜来讲，作为多通道高精密微光机电器件，需要探讨充分利用器件通光口径的方法，即在器件镜面中心处获得合适的中心形变量以得到焦距快速改变的支撑，在全口径范围获得复杂和精确的自由曲面面形以实现像质校正，实现快速变焦和高精度高分辨的成像系统，目前已实现的变焦范围其变倍比在3-6快速变焦成像系统。综上所述，如何将传统固定透镜和可变形镜形变器件组合设计变焦光学系统，在焦距可变形变器件的有限形变范围内实现中小焦段下高变倍比的目标实现快速捕捉与成像，同时兼顾在大通光口径下连续光学变焦中全焦段下的成像质量，对新一代高机动高稳定的光电设备起到关键作用。
目前常用的光学变焦系统设计方法主要有三种：①建立移动组元下保持像面漂移量为零的微分方程组，计算系统各组元形式的薄透镜高斯初始解，通过第一辅助光线、第二辅助光线等形式计算原变焦系统基于像差最优的各个组元厚透镜的结构，如PW法、Lens module(镜头模组)求解法等；②检索成像参数相近的变焦光学系统专利，或查询光学设计手册查询变倍组元相近的厚组元结构，以缩放法等实现后续优化。③建立以高斯括号法表征新型变焦系统的变焦方程高斯解特性，自动检索新型不动变焦系统的最优高斯结构，以数值优化检索法为主。对于第一种传统计算方法，通过设定归一化数值下约束系统的结构和变倍曲线作为初始，需要一定经验的光学设计人员在不断调试优化系统结构，后续计算过程繁琐耗时。对于第二种设计方法，寻找到一种优化潜力高的类似光学性能的系统决定整个优化计算过程，决定了系统优化潜力和性能。对于第三种设计方法，通过将新型变焦系统的高斯结构设计问题转化为利用非线性全局评价函数检索最优解问题解决了设计者的初始结构难的问题，但依然需要进一步将讨论整体系统像差特性与系统的关联，方便于后续在系统优化方向进行指导；且反射系统受限于系统工作视场小，可变形镜的口径约束了系统大入瞳孔径的需求。
反摄远形式三片反射光学系统光焦度呈现“负正正”组元结构，该组元分配可以在各个镜面不引入自由曲面的复杂面形下实现大的正圆形的工作视场范围的探测。但在反射系统中由于第一面凸面反射镜，通常需在非球面折射透镜的折反射光路中引入一对消球差共轭点搭建校正光路实现面形检测，且凸面反射镜精度检测受到其他检测光学元件加工精度的限制，导致大曲率凸面反射面面形精确检测具有难度；且在以平面反射镜和 干涉仪组成的装调系统中，通常以主镜作为装调基准面，凸面反射镜对光束发散作用使得光轴装调进一步增大难度，进一步限制了三组元反射式系统组元的高斯结构光焦度解集分配。
需要说明的是，在上述背景技术部分公开的信息仅用于对本申请的背景的理解，因此可以包括不构成对本领域普通技术人员已知的现有技术的信息。
发明内容
为了弥补上述现有技术的不足，本发明提出一种折反射式不动型反摄远变焦系统设计方法。以解决后续计算过程繁琐耗时，优化潜力低，反射系统受限于系统工作视场小，可变形镜的口径约束了系统大入瞳孔径的需求，光轴装调难度大的问题。
为实现上述目的，本发明采用以下技术方案：
本发明公开了一种折反射式不动型反摄远变焦系统设计方法，包括如下步骤：
S1、求解基于双可变元件的反摄远类型不动型变焦系统四组元高斯结构解；
S2、建立多重结构表征组元相差特性和一阶参数的非线性评价函数组元设计优化方法，求解并筛选最优复消色差透镜组结构；
S3、基于离轴折反射系统像差特征规律，设计离轴折反射变焦系统结构分布于高阶面形平衡优化。
在一些实施例中，上述S1包括如下步骤：
A1、确定折反射光学系统初始结构形式，光阑位置、反射镜组元数量、系统入瞳尺寸；
A2、基于可变器件的系统变焦比、焦距范围、视场角，确定折反射光学系统一阶参数；
A3、建立高斯括号法不动型变焦方程，提取系统变倍能力与焦距可变器件、系统一阶数据的变化参数；
A4、基于大视场变焦系统下反摄远结构参数下分配可变器件形变量面形变化范围；
A5、建立基于多重结构下系统一阶评价函数：评价指标为特定焦段的焦距值、后截距；
A6、全局优化算法求解系统一阶结构；
A7、优化终止条件。
进一步地，上述步骤A3中，所述建立高斯括号法不动型变焦方程的具体方程为：
建立新型不动变焦方程Z为：
其中
1A
m+1表征不动型变焦方程参数，φ
1、φ
2、φ
m表征第(i＝1,2,3...m)组元光焦度。
进一步地，上述步骤A5中，所述建立基于多重结构下系统一阶评价函数的具体流程为：
通过高斯常量(Generalized Gaussian Constants,GGC’s)描述不动型变焦系统等效光焦度Φ为的表达式如下：
其中
固定透镜组φ
fix的高斯结构，φ
fix1到φ
fixm，φ
fixi(i＝1,2,3...m)表征由n个固定透镜φ
fix的等效组合形式，
为可变形反射镜的变倍组元高斯结构，
为可变形反射镜的补偿组元高斯结构，φ
ref中固定反射镜的高斯结构。d
i(i＝1,2,3...m)表征由m个固定透镜φ
fix的等效组合形式分别表征高斯结构基点间的距离，d
4(i＝4)为系统后截距。
更进一步地，建立基于多重结构下系统一阶评价函数：评价指标为特定焦段的焦距值、后截距；其表达式如下：
min F(x
i)
s.t.
φ
1＜0,
其中F(x
i)为一阶系统评价函数，
为第一个可变形镜的光焦度变化范围，
为第二个可变形镜的光焦度变化范围，变焦系统变倍能力评价参数高
2B
4＝[-d
2,φ
ref,-d
3]，T
i指对应变量的约束范围。
进一步地，上述步骤A6中，所述全局优化算法求解系统一阶结构的具体流程为：求解运用全局优化算法求解在双可变形镜形变量与口径以及反摄远类型约束下且实现大工作视场角度和大变倍比系统指标的一阶高斯结构的光焦度分配最优解集。
在一些实施例中，上述S2包括如下步骤：
A8、输出最优解数据下的一阶高斯结构系统，计算当前系统波像差系数；
A9、确定系统入射角和入瞳孔径，以高斯括号法表征厚透镜系统组元参数结构形式和三阶像差表达式；
A10、建立多重结构下折射元件三阶像差评价函数：评价指标为薄透镜焦距、主点、三阶球差、彗差、像散、畸变、色差；
A11、优化终止条件；
A12、确定厚透镜组元最优形式及折反射系统组元组成。
进一步地，上述步骤A8中，所述输出最优解数据下的一阶高斯结构系统包括：厚透镜模型中镜片厚度，镜片口径，组元间隔，折射率；所述计算当前系统波像差系数包括：等效求解薄透镜模型的有效焦距(EFL)、后截距(BFL)、前焦距(FFL)的一阶焦距及三阶波像差(球差、像散、彗差、畸变)下的厚透镜组元分配及像差设计形式，并分别讨论有效孔径和工作视场下厚透镜结构(单透镜、双分离透镜、三组元、双高斯等)复消色差透镜形式下三阶波像差分布的像差分布数学表达式。
进一步地，上述步骤A9中，所述以高斯括号法表征厚透镜系统组元参数结构形式和三阶像差表达式的具体表达式如下：
三阶球差：
三阶彗差：
三阶像散：
三阶畸变：
初阶横向色差：
初阶轴向色差：
其中W
040,W
131,W
222,W
311分别表示三阶球差、三阶彗差、三阶像散、三阶畸变的波像差系数表达式，
表征每个组元表面等效波像差，
表征第i个光学元件三阶赛德尔球差系数；
表征第i个光学元件三阶赛德尔彗差系数；
表征第i个光学元件三阶赛德尔像散系数；
表征第i个光学元件三阶赛德尔畸变系数；
表征第i个光学元件赛德尔初阶横向色差系数；
表征第i个光学元件赛德尔初阶轴向色差系数；V
i为第i个厚透镜光学元件阿贝数；u
j和u'
j分别表示第j个光学元件的边缘光线入射角和出射角，
和
分别表示第j个光学元件的中心光线入射角和出射角；h
i为第i个光学元件的边缘光线高度；
表示第j个光学元件的中心光线高度，k
j表示第j个光学元件面形的二次曲面参数，其中表征球面边缘光线追迹计算系数A
j＝(u'
j-u
j)/(1/n
j+1-1/n
j)，球面主光线追迹计算系数
拉赫不变量
n
j表示第j个光学元件后的折射率。
进一步地，上述步骤A10中，所述建立多重结构下折射元件三阶像差评价函数如下：
其中c
j表示第j个光学元件面形的顶点曲率。
进一步地，上述步骤A11中，所述优化终止条件如下：
min F(x
i)
s.t. e
1,...e
j,n
1,...n
j,c
1,...c
j,V
1...V
j/2∈T
i
其中T
i指对应变量的约束范围，V
i为第i个厚透镜光学元件阿贝数。
在一些实施例中，上述S3包括如下步骤：
A13、基于矢量像差理论计算离轴反射系统像差三阶波像差分布：像散、球差、彗差、畸变等；
A14、确定入瞳孔径下反射镜无遮拦的系统倾斜角度，求离轴反射系统反射镜面二次曲面系数；
A15、光学设计软件优化折射系统的非球面系数和反射镜高低阶面形系数，输出不动型折反射变焦系统结构。
进一步地，上述步骤A13中，所述基于矢量像差理论计算离轴反射系统像差三阶波像差分布包括：像散、球差、彗差、畸变，其中离轴光学系统的波像差表达式为：
其中
表示归一化的视场向量，
表示第j个光学元件的视场偏移矢量，
表示归一化的孔径向量，
展开到三阶波像差，可表示为：
进一步地，上述离轴反射系统像差三阶波像差分布包括：像散、球差、彗差、畸变的像差表达式如下：
离轴反射系统三阶球差通过球面系数和非球面系数贡献量展开的像差表达式为：
离轴反射系统三阶彗差通过球面系数和非球面系数贡献量展开的像差表达式为
离轴反射系统三阶像散通过球面系数和非球面系数贡献量展开的像差表达式为
离轴反射系统三阶畸变通过球面系数和非球面系数贡献量展开的像差表达式为
进一步地，上述步骤A14中，所述确定入瞳孔径下反射镜无遮拦的系统倾斜角度，求离轴反射系统反射镜面二次曲面系数的具体操作为：建立离轴反射镜二次曲面系数和反射镜倾斜角度的非线性全局评价函数：
其中α
j为第j个光学元件面形顶点处的倾斜角，n＝1,2,3...j，其中优化目标表达式如下：
min F(x
i)
s.t. k
1,...k
j,α
1...α
j∈T
i
其中T
i指对应变量的约束范围，k
j表示第j个光学元件面形的二次曲面参数。
进一步地，上述步骤A14中，所述光学设计软件优化折射系统的非球面系数和反射镜高低阶面形系数，输出不动型折反射变焦系统结构具体操作如下：求解多重结构下离轴反射镜二次曲面系数实现系统离轴引起的非旋转对称的轴外像差快速收敛计算，实现无遮拦离轴反射镜高阶面形系数和反射镜倾斜角度下系统结构直接求解。
本发明与现有技术对比的有益效果包括：
本发明采用不动折反射变焦系统为模型，运用高斯括号法讨论新型变焦系统在双可变形镜形变量、口径、反摄远类型约束下变焦方程高斯解特性，并建立了基于多重结构表征组元像差特性和一阶参数的非线性评价函数组元设计优化方法，求解工作口径和视场内多种典型复消色差厚透镜组结构。通过表征折反射系统轴上轴外初阶像差特征，筛选及分配最优初阶像差分布的固定透镜组元结构形式，实现多重结构下离轴折反射变焦系统结构分布下离轴像差与高阶面形平衡优化设计，充分利用MOEMS(微型光机电系统)柔性变形器件规格和有效作用口径内的器件制动量范围，设计具有提升变焦灵敏度和像差校正能力的系统结构，以解决后续计算过程繁琐耗时，优化潜力低，反射系统受限于系统工作视场小，可变形镜的口径约束了系统大入瞳孔径的需求，光轴装调难度大的问题。进而提升系统基于柔性镜面的变倍效率，实现大变倍比，大视场和大入瞳孔径特性的不动型变焦系统设计。
图1是本发明实施例中折反射式不动型反摄远变焦系统设计总体流程图；
图2是本发明实施例中折反射式不动型反摄远变焦系统设计细化流程图；
图3是本发明实施例中厚透镜等效组元求解图；
图4是本发明实施例中厚透镜组元分布形式图；
图5是本发明实施例中折反射离轴光学系统示意图；
图6a是本发明实施例中通过该方法设计实现不动型折反射系统短焦光路图；
图6b是本发明实施例中通过该方法设计实现不动型折反射系统中焦光路图；
图6c是本发明实施例中通过该方法设计实现不动型折反射系统长焦光路图。
下面对照附图并结合优选的实施方式对本发明作进一步说明。需要说明的是，在不冲突的情况下，本申请中的实施例及实施例中的特征可以相互组合。
需要说明的是，本实施例中的左、右、上、下、顶、底等方位用语，仅是互为相对概念，或是以产品的正常使用状态为参考的，而不应该认为是具有限制性的。
本发明实施例提供了一种折反射式不动型反摄远变焦系统设计方法，基于反摄远形式三片反射光学系统改进，主要解决反射系统受限于系统工作视场小，可变形镜的口径约束了系统大入瞳孔径的需求，光轴装调难度大的问题。引入设计由四组元组成的折反射系统，包含第一组元的固定透镜组和第二、三、四组元的离轴反射式结构，其中第二组元和第四组元引入可变形镜实现系统变倍和像面补偿效果。因此继续保留系统反摄远形式组元结构分布实现一阶高斯结构解集分配求解，将复消色差固定透镜作为负组元形式，实现压缩视场角度，平衡轴外由于大视场引入的初阶彗差；在第二组元、第三组元光焦度为正组元，在降低反射镜装调难度的同时，平衡由于离轴系统引入的初阶像散和高阶像散、彗差；第四组元光焦度为正，实现大口径光束汇聚及平衡变焦过程中产生的轴上离焦、球差。并引入固定透镜确定折反射系统中离轴像差传递规律，实现离轴像差 与高阶面形平衡优化设计，实现高速化、集成化的不动型变焦稳像一体化系统设计。
参考图1和图2，是本发明实施例折反射式不动型反摄远变焦系统设计方案的方案图和流程图，具体说明如下：
(1)步骤S1、不动型变焦系统组元高斯结构求解方法：求解基于双可变元件的反摄远类型不动型变焦系统四组元高斯结构解。具体包括如下步骤：
A1、确定折反射光学系统初始结构形式，光阑位置、反射镜组元数量、系统入瞳尺寸等；
A2、基于可变器件的系统变焦比、焦距范围、视场角，确定折反射光学系统一阶参数；
A3、建立高斯括号法不动型变焦方程，提取系统变倍能力与焦距可变器件、系统一阶数据的变化参数；
A4、基于大视场变焦系统下反摄远结构参数下分配可变器件形变量面形变化范围；
A5、建立基于多重结构下系统一阶评价函数：评价指标为特定焦段的焦距值、后截距；
A6、全局优化算法求解系统一阶结构；
A7、优化终止条件。
对A1-A7进一步详述如下：
A1、确定折反射光学系统初始结构形式为折射式透镜和多组元反射镜，光阑位置放置于多组元反射镜中的次镜，确定反射镜多组元数量确定变焦方程变量个数，系统入瞳尺寸确定系统初始结构指标参数；
A2、确定折反射光学系统一阶系统参数，确定系统变焦比、焦距范围、视场角等结构设计参数；
A3、以不动型变焦光学系统的一阶高斯结构通过高斯括号法进行模型表征，并建立新型不动变焦方程Z为：
其中
1A
m+1表征不动型变焦方程参数，φ
1、φ
2、φ
m表征第(i＝1,2,3...m)组元光焦度，通过高斯常量(Generalized Gaussian Constants,GGC's)描述不动型变焦系统等效光焦度Φ为：
A4、基于大视场下变焦系统反摄远结构参数下分配可变器件形变量面形变化范围
A5、其中
固定透镜组φ
fix的高斯结构，φ
fix1到φ
fixm，φ
fixi(i＝1,2,3...m)表征由n个固定透镜φ
fix的等效组合形式，
为可变形反射镜的变倍组元高斯结构，
为可变形反射镜的补偿组元高斯结构，φ
ref中固定反射镜的高斯 结构。d
i(i＝1,2,3...m)表征由m个固定透镜φ
fix的等效组合形式分别表征高斯结构基点间的距离，d
4(i＝4)为系统后截距。建立基于多重结构下系统一阶评价函数：评价指标为特定焦段的焦距值、后截距；
min F(x
i)
s.t.
φ
1＜0,
其中F(x
i)为一阶系统评价函数，
为第一个可变形镜的光焦度变化范围，
为第二个可变形镜的光焦度变化范围，变焦系统变倍能力评价参数高
2B
4＝[-d
2,φ
ref,-d
3]，T
i指对应变量的约束范围。
A6、求解运用全局优化算法求解在双可变形镜形变量、口径、反摄远类型约束下且实现大工作视场角度、大变倍比系统指标的一阶高斯结构的光焦度分配最优解集，求解(2)中
数值解。
A7、求解A6中变量满足T
i指对应变量的约束范围，并优化终止条件。
(2)步骤S2、厚透镜非线性评价函数组元设计优化方法：建立多重结构表征组元相差特性和一阶参数的非线性评价函数组元设计优化方法，求解并筛选最优复消色差透镜组结构。具体包括：
A8、输出最优解数据下的一阶高斯结构系统，计算当前系统波像差系数；
A9、确定系统入射角和入瞳孔径，以高斯括号法表征厚透镜系统组元参数结构形式和三阶像差表达式；
A10、建立多重结构下折射元件三阶像差评价函数：评价指标为薄透镜焦距、主点、三阶球差、彗差、像散、畸变、色差；
A11、优化终止条件；
A12、确定厚透镜组元最优形式及折反射系统组元组成。
对A8-A12进一步详述如下：
A8、通过A1-A7步骤，通过设定的入瞳参数、入射角度求解出的一阶结构，计算当前系统波像差系数；
A9、确定系统入射角和入瞳孔径，设定实际厚透镜模型中镜片曲率、镜片厚度、镜片口径、组元间隔、折射率为变量，等效求解薄透镜模型的有效焦距(EFL)、后截距(BFL)、前焦距(FFL)的一阶焦距及三阶波像差(球差、像散、彗差、畸变)下的厚透镜组元分配及像差设计形式，表征多种厚透镜结构(单透镜、双分离透镜、三组元、双高斯等)在有效孔径和工作视场下复消色差透镜形式下三阶波像差分布的像差分布数学表达式， 由于表征折反射系统的像差特性规律：
如图3所示，其中c
i(i＝1,2..,m)表征系统组元表面曲率，e
i(i＝1,2..,m)表征厚透镜组元厚度，n
i(i＝1,2..,m)表征厚透镜及其间隔的折射率，H,H'表征等效厚透镜组元物方主平面、像方主平面。其中分别根据如图4所示的单透镜、双胶合、三胶合、双高斯结构形式进行求解。
三阶球差：
三阶彗差：
三阶像散：
三阶畸变：
初阶横向色差：
初阶轴向色差：
W
040,W
131,W
222,W
311分别表示三阶球差、三阶彗差、三阶像散、三阶畸变的波像差系数表达式，
表征每个组元表面等效波像差，
表征第i个光学元件三阶赛德尔球差系数；
表征第i个光学元件三阶赛德尔彗差系数；
表征第i个光学元件三阶赛德尔像散系数；
表征第i个光学元件三阶赛德尔畸变系数；
表征第i个光学元件赛德尔初阶横向色差系数；
表征第i个光学元件赛德尔初阶轴向色差系数；V
i为第i个厚透镜光学元件阿贝数；u
j和u'
j分别表示第j个光学元件的边缘光线入射角和出射角，
和
分别表示第j个光学元件的中心光线入射角和出射角；h
i为第i个光学元件的边缘光线高度；
表示第j个光学元件的中心光线高度，k
j表示第j个光学元件 面形的二次曲面参数，其中表征球面边缘光线追迹计算系数A
j＝(u'
j-u
j)/(1/n
j+1-1/n
j)，球面主光线追迹计算系数
拉赫不变量
n
j表示第j个光学元件后的折射率。
A10、厚透镜系统的初阶像差、系统等效焦距、等效后焦距、等效前焦距将作为厚透镜求解的综合评价指标。该非线性全局评价函数具体表示如下：
优化目标：
min F(x
i) (10)
s.t. e
1,...e
j,n
1,...n
j,c
1,...c
j,V
1...V
j/2∈T
i
其中c
j表示第j个光学元件面形的顶点曲率。
A11、当建立全局优化评价函数时，软件优化到评价函数最优极小值时系统停止优化，输出厚透镜系统镜片曲率、镜片厚度、镜片口径、组元间隔、折射率；
A12、基于多种厚透镜结构下折反射系统反射镜三阶像散、彗差的像差分布及补偿形式，结合系统多重结构下的计算焦距与目标焦距差值、最小长焦下畸变像差系数，确定厚透镜组元最优形式及折反射系统组元组成。
本发明实施例的折反射离轴光学系统如图5所示，以下步骤根据折反射离轴光学系统实现。
(3)步骤S3、系统结构分布下离轴像差与高阶面形平衡优化设计方法：基于离轴折反射系统像差特征规律，设计离轴折反射变焦系统结构分布于高阶面形平衡优化。具体包括：
A13、基于矢量像差理论计算离轴反射系统像差三阶波像差分布：像散、球差、彗差、畸变等；
A14、确定入瞳孔径下反射镜无遮拦的系统倾斜角度，求离轴反射系统反射镜面二次曲面系数；
A15、光学设计软件优化折射系统的非球面系数和反射镜高低阶面形系数，输出不动型折反射变焦系统结构。
对A13-A15进一步详述如下：
A13、根据矢量像差理论，离轴光学系统的波像差表达式为
其中，
表示归一化的视场向量，
表示第j个光学元件的视场偏移矢量，第j个光学元件面形顶点处的倾斜角α
j。
其中，
表示第j个球面光学表面元件在y方向的视场偏移矢量；
表示第j个光学元件的边缘光线出射角；
表示第j个光学元件的中心光线高度；c
j表示第j个光学元件面形的顶点曲率。
将波像差表达式展开到三阶波像差，可表示为
W
040,W
131,W
222,W
220W
311分别表示三阶球差、三阶彗差、三阶像散、三阶场曲、三阶畸变的波像差系数表达式，
表征每个组元表面等效波像差，其中将矢量波像差展开，离轴反射系统三阶球差通过球面系数和非球面系数贡献量展开的像差表达式为
上标sph和asph分别表示球面和非球面；
h
j表示第j个光学元件的边缘光线高度，
表示第j个光学元 件的中心光线高度，u
j和u'
j分别表示第j个光学元件的边缘光线入射角和出射角，
和
分别表示第j个光学元件的中心光线入射角和出射角；其中在式(16)中，c
j表示第j个光学元件面形的顶点曲率，k
j表示第j个光学元件面形的二次曲面参数，n
j表示第j个光学元件后的折射率。
离轴反射系统三阶彗差通过球面系数和非球面系数贡献量展开的像差表达式为
离轴反射系统三阶像散通过球面系数和非球面系数贡献量展开的像差表达式为
离轴反射系统三阶畸变通过球面系数和非球面系数贡献量展开的像差表达式为
A14、确定入瞳孔径下反射镜无遮拦的系统倾斜角度，求离轴反射系统反射镜面二次曲面系数。
结合低阶赛德尔像差系数表达式和矢量像差理论全视场像差可优多节点理论，明确经过共轴固定透镜传递后离轴反射系统像差分布传递特性，建立离轴反射镜二次曲面系数和反射镜倾斜角度的非线性全局评价函数：
其中α
j为第j个光学元件面形顶点处的倾斜角，n＝1,2,3...j，其中优化目标：
T
i指对应变量的约束范围，k
j表示第j个光学元件面形的二次曲面参数。
A15、通过A14求解反射镜二次曲面面形系数，并通过光学设计软件将折射系统面形系数设为优化变量，利用光线追迹的有限差分全局优化算法，进一步折射系统的非球面系数实现系统离轴引起的非旋转对称的轴外像差快速收敛计算，实现无遮拦离轴反射镜高阶面形系数和反射镜倾斜角度下系统结构直接求解，并输出不动型折反射变焦系统结构。
求解多重结构下离轴反射镜二次曲面系数实现系统离轴引起的非旋转对称的轴外像差快速收敛计算，实现无遮拦离轴反射镜高阶面形系数和反射镜倾斜角度下系统结构直接求解。
如6a、6b、6c所示，分别为本发明实施例方法所设计实现的大视场高变倍比不动型折反射系统短焦光路图、中焦光路图、长焦光路图。其中短焦实现20°×20°的观测视场角，长焦到短焦切换实现十倍光学效果。
本发明一些实施例中：充分利用MOEMS有效工作口径内的器件制动量范围，提出一种具有大视场、高变倍比、无像面漂移特性的不动型变焦系统组元高斯结构求解方法，进一步地说明如下：运用高斯括号法表征了新型不动型变焦系统的变焦方程，提取新型不动型变焦系统变倍能力与可调光焦度器件光焦度变化的相关重要参数。建立在可变形镜形变量、口径、系统结构反摄远类型约束下，满足大变倍比系统指标和大视场的反摄远类型四组元高斯解集求解。
本发明一些实施例中，提出了系统组元高效设计求解，进一步地说明如下：提出一种基于多重结构表征组元像差特性和一阶参数的非线性评价函数组元设计优化方法。建立了全口径下工作视场下原薄透镜的初阶波像差(球差、彗差、像散、色差)和一阶特性(焦距、前焦距、后焦距)的非线性评价函数，将薄透镜镜组优化问题转变为以多组元厚透镜组焦距和像差为目标的多组元形式的复消色差透镜组结构计算问题，进而实现新型不动折反射变焦系统最优高斯初始结构和复消色差厚透镜组元形式的自动检索，提高了此类复杂光学系统的设计效率。并推导了基于多种复消色差的组元结构下系统像差解析表达式，计算系统三阶各项像差表达式的极值分布确定折反射系统最优复消色差组元形式。
本发明一些实施例中，提出了系统离轴结构优化计算，进一步地说明如下：基于离轴折反射系统像差特征规律，提出一种多重结构下离轴折反射变焦系统结构分布下离轴像差与高阶面形平衡优化设计方法。分析并提取表征视场范围内固定复消色差透镜组下的折反射系统轴上和轴外初阶像差特征规律特征及传递规律，基于矢量像差理论与高阶面形像差特性优化计算离轴系统分布初始结构，设计具有最佳优化成像质量、考虑实际装调难度下的大口径、中焦段下高变倍比折反射不动变焦离轴系统分布结构。
以上内容是结合具体的优选实施方式对本发明所作的进一步详细说明，不能认定本发明的具体实施只局限于这些说明。对于本发明所属技术领域的技术人员来说，在不脱离本发明构思的前提下，还可以做出若干等同替代或明显变型，而且性能或用途相同，都应当视为属于本发明的保护范围。
Claims (16)
- 一种折反射式不动型反摄远变焦系统设计方法，其特征在于，包括如下步骤：S1、求解基于双可变元件的反摄远类型不动型变焦系统四组元高斯结构解；S2、建立多重结构表征组元相差特性和一阶参数的非线性评价函数组元设计优化方法，求解并筛选最优复消色差透镜组结构；S3、基于离轴折反射系统像差特征规律，设计离轴折反射变焦系统结构分布于高阶面形平衡优化。
- 如权利要求1所述的折反射式不动型反摄远变焦系统设计方法，其特征在于，所述S1包括如下步骤：A1、确定折反射光学系统初始结构形式，光阑位置、反射镜组元数量、系统入瞳尺寸；A2、基于可变器件的系统变焦比、焦距范围、视场角，确定折反射光学系统一阶参数；A3、建立高斯括号法不动型变焦方程，提取系统变倍能力与焦距可变器件、系统一阶数据的变化参数；A4、基于大视场变焦系统下反摄远结构参数下分配可变器件形变量面形变化范围；A5、建立基于多重结构下系统一阶评价函数：评价指标为特定焦段的焦距值、后截距；A6、全局优化算法求解系统一阶结构；A7、优化终止条件。
- 如权利要求2所述的折反射式不动型反摄远变焦系统设计方法，其特征在于，步骤A3中，所述建立高斯括号法不动型变焦方程的具体方程如下表达式：
其中 1A m+1表征不动型变焦方程参数，φ 1、φ 2、φ m表征第(i＝1,2,3…m)组元光焦度。 - 如权利要求2所述的折反射式不动型反摄远变焦系统设计方法，其特征在于，步骤A5中，所述建立基于多重结构下系统一阶评价函数的具体流程如下：通过高斯常量(Generalized Gaussian Constants,GGC’s)描述不动型变焦系统等效光焦度Φ的表达式如下：
其中固定透镜组φ fix的高斯结构，φ fix1到φ fixm，φ fixi(i＝1,2,3…m)表征由n个固定透镜φ fix的等效组合形式，
为可变形反射镜的变倍组元高斯结构，
为可变形反射镜的补偿组元高斯结构，φ ref中固定反射镜的高斯结构。d i(i＝1,2,3…m)表征由m个固定透镜φ fix的等效组合形式分别表征高斯结构基点间的距离，d 4(i＝4)为系统后截距。
- 如权利要求4所述的折反射式不动型反摄远变焦系统设计方法，其特征在于，还包括建立基于多重结构下系统一阶评价函数：评价指标为特定焦段的焦距值、后截距；其表达式如下：
min F(x i)
φ 1＜0,其中F(x i)为一阶系统评价函数，为第一个可变形镜的光焦度变化范围，
为第二个可变形镜的光焦度变化范围，变焦系统变倍能力评价参数高 2B 4＝[-d 2,φ ref,-d 3]，T i指对应变量的约束范围。
- 如权利要求2所述的折反射式不动型反摄远变焦系统设计方法，其特征在于，步骤A6中，所述全局优化算法求解系统一阶结构的具体流程为：求解运用全局优化算法求解在双可变形镜形变量与口径以及反摄远类型约束下且实现大工作视场角度和大变倍比系统指标的一阶高斯结构的光焦度分配最优解集。
- 如权利要求1所述的折反射式不动型反摄远变焦系统设计方法，其特征在于，所述S2包括如下步骤：A8、输出最优解数据下的一阶高斯结构系统，计算当前系统波像差系数；A9、确定系统入射角和入瞳孔径，以高斯括号法表征厚透镜系统组元参数结构形式和三阶像差表达式；A10、建立多重结构下折射元件三阶像差评价函数：评价指标为薄透镜焦距、主点、三阶球差、彗差、像散、畸变、色差；A11、优化终止条件；A12、确定厚透镜组元最优形式及折反射系统组元组成。
- 如权利要求7所述的折反射式不动型反摄远变焦系统设计方法，其特征在于，步骤A8中，所述输出最优解数据下的一阶高斯结构系统包括：厚透镜模型中镜片厚度，镜片口径，组元间隔，折射率；所述计算当前系统波像差系数包括：等效求解薄透镜模型的有效焦距(EFL)、后截距(BFL)、前焦距(FFL)的一阶焦距及三阶波像差(球差、像散、彗差、畸变)下的厚透镜组元分配及像差设计形式，并分别讨论有效孔径和工作视场下厚透镜结构(单透镜、双分离透镜、三组元、双高斯等)复消色差透镜形式下三阶波像差分布的像差分布数学表达式。
- 如权利要求7所述的折反射式不动型反摄远变焦系统设计方法，其特征在于，步骤A9中，所述以高斯括号法表征厚透镜系统组元参数结构形式和三阶像差表达式的具体表达式如下：三阶球差：
三阶彗差：
三阶像散：
三阶畸变：
初阶横向色差：
初阶轴向色差：
其中W 040,W 131,W 222,W 311分别表示三阶球差、三阶彗差、三阶像散、三阶畸变的波像差系数表达式，表征每个组元表面等效波像差，
表征第i个光学元件三阶赛德尔球差系数；
表征第i个光学元件三阶赛德尔彗差系数；
表征第i个光学元件三阶赛德尔像散系数；
表 征第i个光学元件三阶赛德尔畸变系数；
表征第i个光学元件赛德尔初阶横向色差系数；
表征第i个光学元件赛德尔初阶轴向色差系数；V i为第i个厚透镜光学元件阿贝数；u j和u' j分别表示第j个光学元件的边缘光线入射角和出射角，
和
分别表示第j个光学元件的中心光线入射角和出射角；h i为第i个光学元件的边缘光线高度；
表示第j个光学元件的中心光线高度，k j表示第j个光学元件面形的二次曲面参数，其中表征球面边缘光线追迹计算系数A j＝(u' j-u j)/(1/n j+1-1/n j)，球面主光线追迹计算系数
拉赫不变量
n j表示第j个光学元件后的折射率。
- 如权利要求7所述的折反射式不动型反摄远变焦系统设计方法，其特征在于，步骤A10中，所述建立多重结构下折射元件三阶像差评价函数表达式如下：
其中c j表示第j个光学元件面形的顶点曲率。 - 如权利要求7所述的折反射式不动型反摄远变焦系统设计方法，其特征在于，步骤A11中，所述优化终止条件如下：min F(x i)s.t. e 1,...e j,n 1,...n j,c 1,...c j,V 1...V j/2∈T i其中T i指对应变量的约束范围，V i为第i个厚透镜光学元件阿贝数。
- 如权利要求1所述的折反射式不动型反摄远变焦系统设计方法，其特征在于，所述S3包括如下步骤：A13、基于矢量像差理论计算离轴反射系统像差三阶波像差分布：像散、球差、彗差、畸变等；A14、确定入瞳孔径下反射镜无遮拦的系统倾斜角度，求离轴反射系统反射镜面二次曲面系数；A15、光学设计软件优化折射系统的非球面系数和反射镜高低阶面形系数，输出不动型折反射变焦系统结构。
- 如权利要求12所述的折反射式不动型反摄远变焦系统设计方法，其特征在于，步骤A13中，所述基于矢量像差理论计算离轴反射系统像差三阶波像差分布包括：像散、球差、彗差、畸变，其中离轴光学系统的波像差表达式为：
其中表示归一化的视场向量，
表示第j个光学元件的视场偏移矢量，
表示归一化的孔径向量，展开到三阶波像差，可表示为：
- 如权利要求13所述的折反射式不动型反摄远变焦系统设计方法，其特征在于，所述离轴反射系统像差三阶波像差分布包括：像散、球差、彗差、畸变的像差表达式如下：离轴反射系统三阶球差通过球面系数和非球面系数贡献量展开的像差表达式为：
其中上标sph和asph分别表示球面和非球面；离轴反射系统三阶彗差通过球面系数和非球面系数贡献量展开的像差表达式为
离轴反射系统三阶像散通过球面系数和非球面系数贡献量展开的像差表达式为
离轴反射系统三阶畸变通过球面系数和非球面系数贡献量展开的像差表达式为
- 如权利要求13所述的折反射式不动型反摄远变焦系统设计方法，其特征在于，步骤A14中，所述确定入瞳孔径下反射镜无遮拦的系统倾斜角度，求离轴反射系统反射镜面二次曲面系数的具体操作为：建立离轴反射镜二次曲面系数和反射镜倾斜角度的非线性全局评价函数：
其中α j为第j个光学元件面形顶点处的倾斜角，n＝1,2,3…j，其中优化目标表达式如下：min F(x i)s.t. k 1,...k j,α 1...α j∈T i其中T i指对应变量的约束范围，k j表示第j个光学元件面形的二次曲面参数。 - 如权利要求13所述的折反射式不动型反摄远变焦系统设计方法，其特征在于，步骤A14中，所述光学设计软件优化折射系统的非球面系数和反射镜高低阶面形系数，输出不动型折反射变焦系统结构具体操作如下：求解多重结构下离轴反射镜二次曲面系数实现系统离轴引起的非旋转对称的轴外像差快速收敛计算，实现无遮拦离轴反射镜高阶面形系数和反射镜倾斜角度下系统结构直接求解。
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| CN112558296A (zh) * | 2020-12-11 | 2021-03-26 | 清华大学深圳国际研究生院 | 一种应用形变器件的高变倍比不动变焦成像方法 |
| CN113406792A (zh) * | 2021-05-28 | 2021-09-17 | 清华大学深圳国际研究生院 | 一种不动型双远心变焦扫描成像系统及主结构参数确定方法 |
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| GB9721991D0 (en) * | 1997-10-18 | 1997-12-17 | Secr Defence | Optical systems |
| CN107643592A (zh) * | 2017-10-27 | 2018-01-30 | 上海理工大学 | 一种长焦距可变焦折反射光学系统 |
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| CN113406792A (zh) * | 2021-05-28 | 2021-09-17 | 清华大学深圳国际研究生院 | 一种不动型双远心变焦扫描成像系统及主结构参数确定方法 |
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