将平面对称光学系统的像差理论应用于极紫外（XUV）光栅仪器的评价函数，可以得到评价函数关于光学参量的解析表达式。应用合作型协同进化遗传算法来解决多参量评价函数的优化问题，建立了优化程序。应用该程序对XUV摄谱仪系统进行优化设计，并运用光线追迹程序Shadow对该光学系统进行数值成像计算和比较，研究结果表明发展的评价函数在XUV多元件光栅光学系统优化设计中是十分有效的。

The aberration theory of planesymmetric optical systems recently developed is applied to the merit function of extreme ultraviolet (XUV) grating instrument defined; consequently the merit function can be expressed as a function of optical parameters. This merit function of multiple parameters is optimized with the cooperative coevolutionary genetic algorithms. The optimization program is set up, which is then used to optimize a XUV flatfield spectrograph system; the ray tracing calculations to the optical system are made with the program Shadow. The imaging calculations show that the merit function is a very useful means to optimize the XUV multielement grating instruments.