离轴反射系统设计的关键环节是确定适用初始结构并进行优化，一般从同轴结构或者专利库中寻找相似的结构开始优化，这往往需要耗费大量的时间。以Seidel像差理论为依据，研究了一种获取离轴四反系统初始结构的设计方法。在设计之初引入视场偏置，通过追迹近轴光线给出五种单色像差的初级Seidel像差表示。以Seidel像差绝对值最小化作为目标函数，同时加入对光学和系统结构上的限制条件构建含有约束条件的单目标非线性优化模型，并通过粒子群优化算法进行求解。在此基础上，通过MATLAB调用CODE V API接口，判断此视场偏置情况下是否满足无遮拦的条件，并从中挑选出满足条件的初始结构。设计了一款焦距为 1 200 mm，视场 1。2°×20°，F数为 6的离轴四反光学系统，系统结构布局紧凑，成像质量良好，各项指标均满足设计要求。
Automatic Design Method for the Off-axis Four-mirror Initial Arrangement Using Seidel Aberration Theory
Reflective optical systems are normally divided into two types:coaxial reflective module and off-axis reflective module.Although the coaxial reflective module is capable of achieving a long focal length,it also has several obvious drawbacks such limited field of view and low utilization efficiency of propagating light due to obscuration.On the contrary,the off-axis reflective module has the particular capabilities of long focal length,wide field of view and high spatial resolution in diverse applications.Generally,an off-axis reflective systems are normally created from a coaxial reflective system based on the Seidel aberration theory.What is more,an unobscured off-axis system is obtained by using an offset aperture stop,a biased field,or combining both.However,the coaxial reflective systems are often far from the final off-axis reflective systems.Therefore,optimizing the coaxial reflective system without particularly constructing often costs much calculation time,and it is easy to fall into a local optimal solution during the optimization process.This paper proposes a new method for establishing the initial structure of an off-axis four-mirror optical system.At the beginning of the design,we chose a reasonably biased field to obtain off-axis reflective systems.Introduce the ray transmission matrix to simplify the paraxial ray tracing and calculate the Seidel aberration by tracing the chief and marginal ray.The Seidel aberration we obtained is a function including the radius of curvature and the mirror spacing.The traditional method of solving the initial structure is to make the Seidel aberration zero.When many constraints are defined,there may be no solution for all Seidel aberrations to be zero.This problem can be transformed into an optimization problem for solving the objective function.The objective function is to minimize the sum of the absolute values of the five primary aberration coefficients while adding some constraints,such as the back focal length and focal length requirement.Particle Swarm Optimization(PSO)suits high-dimensional nonlinear optimization problems.Therefore,the PSO algorithm is used in this paper to optimize the objective function.However,the PSO algorithm is affected by many factors,among which the initial particle value greatly influences the final result.Therefore,generating many random initial points is adopted to analyze and compare the results and select the solution results with a small objective function value.After that,we use a biased field to select the unobscured system through the data interaction of MATLAB and CODE V.The specific algorithm process is as follows:an initial biased field is given in advance,and the particle swarm optimization algorithm solves the objective function to find multiple sets of feasible solutions.The calculated radius of curvature and mirror spacing are imported into CODE V.Then,we call the CODEV API through MATLAB to obtain the data of the corresponding point.Judging whether the initial structure satisfies the unobscured condition by calculating the distance between points and lines.If a suitable unobscured structure is not found,change the biased field,re-find the optimal solution,and re-judge whether the corresponding point-line position relationship is satisfied.Since the diameter of the entrance pupil and the field of view is small when constructing the initial structure,it is necessary to gradually expand the diameter of the entrance pupil and the view in the optimization stage to meet the requirements of the design parameters.Generally speaking,if there is a large difference between the initial and final design parameters,increasing the entrance pupil diameter and view manually will take much time.However,if the entrance pupil diameter and view are too large for each iteration,it will lead to falling into a local optimal solution or being unable to realize ray tracing.To solve the time-consuming problem of manually increasing the entrance pupil diameter and field of view,this paper combines MATLAB and CODE V software to avoid repetitive optimization processes.By calling CODE V API through MATLAB to achieve data interaction between the two software,MATLAB can modify system parameters(entrance pupil diameter,the field of view,etc.).At the same time,the program for optimizing the off-axis four-mirror is saved in the form of a macro file,which is convenient for realizing the optimization of the off-axis four-mirror by calling the macro file in MATLAB.Through this method,the system's expansion from a small entrance pupil and a small field of view to a large entrance pupil and a large field can be realized more quickly and efficiently.At the same time,XY polynomials and high-order aspheric surfaces are introduced to correct high-order aberrations.The proposed automatic design method studied has certain theoretical and practical value in designing off-axis reflective systems.
万方数据
维普
