Starting configuration design method of freeform imaging and afocal systems with a real exit pupil

Optical system configurations with a real exit pupil have important applications. However, there are few effective design methods of these systems for choice, especially for the systems using freeform surfaces. In this paper, we propose a novel starting configuration design method of freeform optical systems with a real exit pupil before the image plane. This method works for both the cases of imaging systems with optical power and afocal systems. Each single freeform surface in the starting configuration is generated directly using the light rays of multiple fields and different pupil coordinates. With a proposed multi-step design strategy, not only the given system specifications and the desired object-image relationships (or magnification for the afocal system) are achieved, the generation of a real, small-distorted exit pupil with a given size and shape (which means the imaging relationships of the pupils) can be also considered. The system generated by this method can be taken as a good starting configuration for further optimization. The benefits and feasibility of this design method are demonstrated by two design examples. One example is a freeform off-axis three-mirror imaging system. The other example is a freeform off-axis three-mirror afocal telescope. Both of the systems have a modulation transfer function (MTF) that is closed to the diffraction limit.