平面对称光学系统像差理论的扩展

Generalization of aberration theory of plane-symmetric optical systems

将平面对称光栅系统的波像差理论扩展于平面对称折射光学系统,指出在光学系统像差问题上,反射光学系统可以看成是折射光学系统在物像空间折射率相同情况下的特例。首先,把波像差表达式扩展于光线斜入射下平面对称折射光学系统;然后,根据折射光学系统的要求,对光栅像差的推导过程进行相应的修正,最终,导出了任意方位像平面上的像差。结果表明,导出的像差表达式同时适用于反射、衍射、折射3种光学系统的像差计算。与光线追迹解析法导出的像差系数进行了解析比较,并分别应用提出的像差表达式和光线追迹程序Zemax对一透镜光学系统在斜入射角为50°下的光束进行成像数值模拟,两种方法都验证了提出理论的正确性。

The aberration theory of plane-symmetric grating systems is extended to the plane-symmetric refractive optical systems in this paper. It is pointed out that, as far as the optical aberration is concerned, the reflective optical system can be regarded as a special case of refractive one when the refractive indexes of an object and an image spaces are identical. Firstly, the wave aberrations are generalized to the refractive plane-symmetric systems. Then according to the requirements of refractive system, the aberration is modified to derive the aberration formulae of an arbitrarily image plane. Analysis results show that the aberration formulae can be used to express a set of formulae for reflective, diffractive and refractive optical systems. The aberration coefficients are proved to be identical to those derived from the analytical formulae of the ray-tracing spot diagram. Moreover, the improved formulae and Zemax ray-tracing calculations are used to image numerically for a lens system with a light beam at an oblique angle of 50°, and both the results validate the proposed aberration theory.