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In this paper, we proposed a general direct design method for three-dimensional freeform surfaces and freeform imaging systems based on a construction-iteration process. In the preliminary surfaces-construction process, the coordinates as well as the surface normals of the data points on the multiple freeform surfaces can be calculated directly considering the rays of multiple fields and different pupil coordinates. Then, an iterative process is employed to significantly improve the image quality or achieve a better mapping relationship of the light rays. Three iteration types which are normal iteration, negative feedback and successive approximation are given. The proposed construction-iteration method is applied in the design of an easy aligned, low F-number off-axis three-mirror system. The primary and tertiary mirrors can be fabricated on a single substrate and form a single element in the final system. The secondary mirror is simply a plane mirror. With this configuration, the alignment difficulty of a freeform system can be greatly reduced. After the preliminary surfaces-construction stage, the freeform surfaces in the optical system can be generated directly from an initial planar system. Then, with the iterative process, the average RMS spot diameter decreased by 75.4% compared with the system before iterations, and the maximum absolute distortion decreased by 94.2%. After further optimization with optical design software, good image quality which is closed to diffraction-limited is achieved.
Yang et al. (Mon,) studied this question.