凹面全息光栅是光谱分析仪器的核心器件之一， 其成像质量直接决定了光谱分析仪器的分辨本领。 利用光程函数理论设计凹面全息光栅是一个繁琐的求解非线性方程组的过程， 该过程分两步进行， 每步需要求解四个非线性方程。 分两步求解不但过程麻烦， 还不可避免地引入了取舍误差， 降低了最优参数的精度。 为了解决该问题， 本文提出了一种设计单色仪凹面全息光栅的新方法——一步法， 该方法不但可以简化求解过程、 降低最优参数的误差， 还可以方便地控制整体像差的变化趋势。 采用有较强全局搜索能力的遗传算法求解该方法中非线性方程的极值问题， 并与传统的方法对比验证了该方法的可行性和正确性， 结果表明， 一步法不但在方法上比两步法简便， 其设计结果还优于两步法。

The present paper put forward a new method, named one step method, to design concave holographic grating for a monochromator. This new method is simple and direct and easy to understand. Additionally, in this new method, we can control the whole aberrations of concave grating very well. Genetic algorithm was applied to optimize the objective function of this new method for its strong ability to search the extremum of nonlinear functions and a comparison was made between this new method and the classical method. The result shows that, for coma correction or astigmatism correction, the imaging properties of the concave grating designed by the new method is much better than the grating designed by the classical method.