相干点源照明时消球差光学系统的像场结构

Structure of image fields in an aplanatic optical system with coherent point source illumination

利用矢量傅里叶变换和稳相法获得了相干点源位于光轴上任意位置时,消球差光学系统像场结构的积分表达式,详细研究了使用线偏振光照明时像平面上大物方孔径角对像场结构的影响.模拟计算表明,在像空间垂直于光轴的平面上,如果物方孔径角较大,磁场分布绕光轴旋转90°后不再与电场分布相同,电场能量密度、磁能量密度和玻印亭矢量分布的等高线始终近似为椭圆,并且物方孔径角是导致玻印亭矢量分布失去圆对称性的主要因素.同时当使用小像方孔径角时,电场能量密度分布形状的长轴方向垂直于物空间电场的振动方向;随着像方孔径角逐渐增大,电场能量密度分布形状的长轴方向将逐渐变为与物空间电场的振动方向相同.这些结论完全不同于以前理论所预测的结果.

Using the vector Fourier transform and stationary phase method, an integral representation of the structure of image field in an aplanatic system with polarized point source located at arbitrary position on the optical axis is obtained. Effects of wide aperture angle in object space on the structure of image field are examined numerically for the case of linearly polarized illumination. Simulation calcalations show that, in a plane perpendicalar to the optical axis, if the object space aperture angle is wide, the distribution of magnetic field will not be identical to that of electric field after they are rotated 90° around the optical axis with respect to each other, the contours of distribution of the electric and magnetic energy densities and the Poynting vector are approximately elliptical, and the object space aperture angle is the dominant factor that makes the distribution of Poynting vector lose circular symmetry. At the same time, the major axis of the contour of distribution of the electric energy density is perpendicalar to the direction of the electric vector in the object space when using small image aperture angle, and will turn graduately to the same direction as the electric vector in the object space with the increase of image aperture angle. These conclusions are completely different from the predications of the previous theory.