遗传算法在离轴四反光学系统设计中的应用

摘要

As existing optical design software depends on the selection of an initial structure,a solving method of initial structure for four-mirror optical systems based on genetic algorithm was proposed to obtain the initial structure with good image quality and special structural configuration.The aberration of a coaxial four-mirror optical system was analyzed according to primary aberration theory.The objective function composed of primary aberration coefficient with weight and constraint conditions of structural configuration was established.Then, optimization solution was implemented for the objective function by introducing genetic algorithm and the coaxial four-mirror initial structure with good image quality and special structural configuration was obtained.Finally,an off-axis four-mirror optical system with a long focus of 1 200 mm,a large visual field of 20°×4° and a large relative aperture of F/4 was designed based on the initial structure.Structural configuration of the system is compact.Modulation transfer functions of all fields are more than 0.52 in the position of 50 lp/mm.As compared with traditional methods,the design method based on genetic algorithm does not need given initial conditions.It provides the initial structure with good image quality and special structural configuration for four-mirror optical systems and has extensive application prospects in reflective optical system design.%现有的光学设计软件多依赖初始结构的选取,故提出了一种基于遗传算法的四反射光学系统初始结构求解方法,以获取像质良好和特定布局的初始结构.根据初级像差理论,对同轴四反光学系统进行像差分析,建立了由带权重的初级像差系数和结构布局约束条件所组成的目标函数;通过引入遗传算法对目标函数进行优化求解,获得了像质良好、特定布局的同轴四反初始结构.最后,基于该初始结构设计了一款长焦距(1 200 mm)、大视场(20°×4°)、大相对孔径(F/4)的离轴四反光学系统.该系统结构布局紧凑,各个视场的调制传递函数在50 lp/mm处均大于0.52.与传统设计方法相比,提出的设计方法不需要给定初始条件,可以为四反射光学系统提供像质良好和特定结构布局的初始结构,在反射式光学系统设计中具有广泛的应用前景.