根据凹面光栅的几何像差理论, 提出了一种基于超环面均匀线距光栅的成像光谱仪优化设计方法, 该方法利用遗传算法和光学设计软件ZEMAX两次优化来获得最优的光学结构参数。 以设计一个远紫外成像光谱仪为实例, 工作波段110～180 nm, 狭缝尺寸50 μm×5 mm, 数值孔径0.1, 利用ZEMAX软件对设计结果进行了分析和评价, 结果表明, 不同波长的光学传递函数在奈奎斯特频率101 P/mm处均大于0.7, 点列图半径的均方根值小于14 μm, 在工作波段内获得了良好的成像质量, 满足空间分辨率0.5 mrad, 光谱分辨率0.6 nm的设计要求, 也证明了该优化设计方法是可行的, 可在其他波段推广应用, 对光栅色散型成像光谱仪的设计具有指导意义。

Based on the geometrical aberration theory, a optimum-design method for designing an imaging spectrometer based on toroidal uniform grating spectrometer is proposed. To obtain the best optical parameters, twice optimization is carried out using genetic algorithm(GA) and optical design software ZEMAX. A far-ultraviolet(FUV) imaging spectrometer is designed using this method. The working waveband is 110～180 nm, the slit size is 50 μm×5 mm, and the numerical aperture is 0.1. Using ZEMAX software, the design result is analyzed and evaluated. The results indicate that the MTF for different wavelengths is higher than 0.7 at Nyquist frequency 10 lp·mm-1, and the RMS spot radius is less than 14 μm. The good imaging quality is achieved over the whole working waveband, the design requirements of spatial resolution 0.5 mrad and spectral resolution 0.6 nm are satisfied. It is certificated that the optimum-design method proposed in this paper is feasible. This method can be applied in other waveband, and is an instruction method for designing grating-dispersion imaging spectrometers.