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摘要: 基于凹面光栅的几何理论，推导了子午、弧矢聚焦曲线的数学表达式和全息平像场凹面光栅制作参数的计算关系式. 提出了一种新的在整个使用波长范围内同时消除子午和弧矢像差的最佳优化设计方法. 这种方法不同于以光线追迹技术为基础的标准光学设计软件如CODE V或ZEMAX的优化设计方法，而是从数学表达式出发，采用光栅优化因子，对凹面光栅的子午聚焦曲线和弧矢聚焦曲线进行拟合，从理论上找到最佳的能够使子午和弧矢像差同时趋于零的像平面，然后再根据拟合参数设计制作光栅. 用Matlab软件解决了子午聚焦曲线超越方程无法解的困难；讨论了不同光栅常数和入射角度时对两聚焦曲线拟合程度的影响. 提出了在宽光谱使用条件下，可以通过减小入射角度和光栅刻线数来提高光谱像质.
Abstract: Based on the geometric theory of concave grating, we deduce the mathematical expressions of the meridional curve, Sagittal curve and the relational expression for the holographic flat-field image concave grating. We also propose a new optimal method in all used range for correcting the meridional and sagittal aberrations. Different from the design method using CODE V or ZEMAX, we use mathematical expression and adopt grating optimal factor instead. By fitting the meridional focusing curve and Sagittal focusing curve of concave grating, we find an image surface in theory to ensure that the meridional and also the Sagittal aberrations tend to zero, and then design and fabricate the grating based on the fitting parameters. We solve the problem that the meridional curve transcendental equation cannot solve by Matlab, and discuss the influence of two curves for different grating constants and different incidence angles. We find that the aberrations in a wide spectral range can be corrected by diminishing the incidence angle and increasing the grating scribed lines.
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