Offner成像光谱仪建模及像差分析

Modelling of Offner Imaging Spectrometers and Aberration Analysis

利用光线追迹方法得到系统的数值模型,然后运用级数展开方法,建立起系统的3阶解析模型,亦即3阶像差理论。该模型给出系统像差系数和计算系统点列图的解析表达式,可适应于包含变间距凸面光栅的系统,并具有良好的扩展性。通过追迹示例Offner系统中10000条不同波长、不同高度的光线,结果表明运用解析模型可以快速而准确地生成系统的点列图。利用解析的像差系数分析了系统中彗差、球差和像散等主要像差的几何特征,加深对系统成像特性的理解,为Offner系统优化设计提供理论指导。

The ray-tracing method is applied to get the numerical model of the system,and then a series expansion method is used to establish a three-order analytical model.The analytical model provides analytical expressions of aberration coefficients and spot diagrams,adapts to the system containing a varied line spacing convex grating,and has strong scalability.The complete imaging performance can be quickly evaluated by the analytical expressions of spot diagrams.By tracking 10000 rays with different wavelengths and heights in an Offner example system,the results show that analytical model can quickly reproduce the spot diagrams with a high degree of accuracy.With these formulas coma,spherical aberration,astigmatism and distortion are discussed in detail.The analytical model provides theoretical guidance for the optimal design of Offner imaging spectrometers.