消像散的自由曲面棱镜光谱仪光学系统设计

Design of a freeform curved prism imaging spectrometer based on an anastigmatism

本文根据像差理论,开发了一种计算次镜外反射的Offner型自由曲面棱镜光谱仪初始结构的算法。通过光线追迹获得光线在次镜外反射Offner型光谱仪各光学表面传播的公式,该公式可以确定光学元件的结构参数。应用轴外细光束像散理论分析系统产生的像散,并设定合理阈值作为结构算法的判断依据。在Matlab中迭代优化出符合设计要求的初始结构,使用Zemax软件对获得的初始结构进行优化。为验证算法效果,本文设计了光谱范围为380~780 nm,数值孔径为0.15,光谱分辨率为6 nm的自由曲面棱镜光谱仪的初始结构。在Zemax中完成优化后系统可达到设计指标且谱线弯曲和色畸变均优于0.1 pixels。设计结果表明采用本文算法可以快速计算出符合要求的初始结构,大大简化了后续优化的复杂程度。

In this paper,an algorithm for calculating the initial structure of the Offner freeform curved prism imaging spectrometer with secondary mirror external reflection is designed.The ray tracing method is used to obtain the formula for the propagation of light on the optical surfaces of an Offner spectrometer with secondary mirror external reflection.The formula can determine the structural parameters of the optical component.The off-axis beam astigmatism theory commonly used in the analysis of off-axis systems is used to analyze image quality,and a reasonable threshold is set to judge the structure algorithm.The initial structure that meets the design requirements is obtained through iterative optimization in Matlab and the initial structure is optimized in Zemax.To verify the performance of the proposed algorithm,the initial structure of a free-form prism spectrometer with a spectral range of 380~780 nm,a numerical aperture of 0.15 and a spectral resolution of 6 nm is designed.After being optimized in Zemax,the system reached the design index and the spectral line bending and color distortion are both less than 0.1 pixels.The algorithm proposed in this paper can quickly calculate the initial structure such that the requirements are satisfied,and can simplify its complexity.