主要研究了平面系统成像引入像差的问题。由于平面系统的工作面为平面, 平行光束入射、出射光也是平行光束, 不会引起像差。一般认为, 对于平面系统成像不引入像差, 对于平面反射镜, 同心光束经平面反射镜后仍然是同心光束, 不存在像差, 但对于棱镜系统和平行平板, 只有在近轴条件下才能理想成像, 在离轴角较大时, 会引起像差, 即同心光束经棱镜系统和平行平板后不再是同心光束。

The limitation of paraxial condition of paraboloid refracting system in performing fractional Fourier transform acts like an aperture, which makes the system different from ideal systems. With aperture expanded as the sum of finite complex Gaussian terms, a more practical approximate analytical solution of fractional Fourier transform of Gaussian beam in an apertured paraboloid refracting system is obtained and also numerical investigation is presented. Complicated and practical fractional Fourier transform systems can be constructed by cascading several apertured paraboloid refracting systems which are the simplest and the most basic units for performing more precise transform.