分析了离面准李特洛（off-plane quasi-Littrow, OP-QL）色散光路中子午光束、 弧矢光束的对应关系, 揭示了离面角将引起弧矢光束旋转, 并使球面镜和光栅的弧矢光束不再相互对应的特性, 指出系统弧矢光程差（optical path difference, OPD）并非各元件自身弧矢光束光程差的简单叠加, 而是各元件上与光栅弧矢光束相对应光束的光程差之和。 基于以上结论, 提出了求解球面镜上沿任意方向的光线与主光线之间光程差的方向导数法, 并运用它求解出OP-QL光路的光程差。 最后, 基于小阶梯光栅和中阶梯光栅的实例共同验证了文中分析结论和计算方法的合理准确性。

The present paper analyzes the relative relation between the meridian and sagittal rays in off-plane quasi-Littrow (OP-QL) dispersion mountings. It’s concluded that the off-plane angle will cause the rotation of the beam and result in the mismatch between the sagittal beams on different optical elements. Therefore the total optical path difference (OPD) should be an accumulation of corresponding beams instead of the sagittal beam of each element itself. Then, a directional derivative based method is put forward to calculate the OPD for spherical mirrors in various directions. Based on the method, the numerical OPD for OP-QL mountings is solved. Finally, this methodology is validated with both echelette and echelle examples.