光学ABCD定理的普适性、物理意义和它的应用

Generality of optical ABCD theorem, its physical meaning and applications

本文推广了几何光学近轴光线传输的ABCD定理,使之适用于远离光轴的空间光线的传输,无论光学系统是旋转对称的还是非旋转对称的。又注意到经典力学中的粒子运动也存在类似的ABCD定理.进一步研究发现在这宏观的定理背后的物理含义,即允许存在另一个更为普遍的规律“测不准关系”的可能性。此外应用推广的ABCD定理,可导出推广的含ABCD的衍射积分定理,用角程函的导数来表示。以此进行含初级(赛德耳)象差的衍射积分计算是方便的。文中给出含球差与含慧差的解析结果,及仅含球差时的数值计算.

We studied that the transfer matrix ABCD theorem for the passage of paraxial rays or the optical system possessing a rotational symmetry axis can be generalized for the skew rays propagated off-axis, whether the optical system possessing rotational symmetry axis or not. We noticed that the same ABCD relation exists in the classical mechanics also. This fact hints samething more need to be considered. As a consequence, the connection of ABCD theorem with the fundamental ' uncertainty principle ' in quantum mechanics had been established. Furthermore we applied the general ABCD theorem to evaluate the diffraction integral, matrix elements A ~ D expressed in terms of the angular eikonal function T, and the primary aberration included. Finally the numerical results in the case of only spherical aberrations are presented.