Improvement of Scheimpflug systems with freeform surfaces

It is well known that freeform surfaces are used to improve the resolution in systems without rotational symmetry. For Scheimpflug systems, the tilted object plane leads to variant magnification in the system imaging. Thus, the system suffers from non-rotationally symmetric aberrations, non-uniform resolution, and non-uniform intensity distribution. In this paper, the paraxial imaging condition of Scheimpflug systems is discussed. From the classical viewpoint, the aberration theory is used to understand, balance, and improve the system performance for variant object distance. For large object distance shift, it is necessary to apply freeform surfaces. With the initial system design method based on Gaussian brackets, the starting configuration of a Scheimpflug system with large object distance shift is obtained. Based on the extension of the Nodal aberration theory concerning the aberrations of freeform surfaces, the rules of selecting the freeform surface position in the system are introduced. By adding two freeform surfaces far away from the pupil, the aberrations are effectively corrected in the Scheimpflug system. The aberrations along the field are decomposed and represented using Zernike fringe polynomials to show the improvement of uniformity and resolution. This work provides insight into Scheimpflug system design with freeform surfaces.