The study of free form optical elements corrected aberrations of optical system

Based on the wavefront aberration theory and the coordinates transform, the free form optical induced aberration’s characteristic of optical system has been analyses in this paper. The optical wavefront error and the free form surface can be express as Fringe Zernike polynomial; the free form optical on the surface (Stop or Entrance pupil or Exit pupil) affects all the field angles equally. If the surface is not the pupil of optical system, the aberration observed is different from the free form itself because the footprint of the beam for an off-axis field point only covers part of the surface. For the Fringe Zernike surface figure on a surface not at pupil, it will transform into lower order Fringe Zernike aberration in the optical system, the relationship between different Fringe Zernike aberration and field is different, and the location zero for the lower aberration always reside at the center of the field of view.