{'fraction_non_alphanumeric': 0.02042360060514372, 'fraction_numerical': 0.0, 'mean_word_length': 5.3, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Design of freeform unobscured reflective imaging systems using CI method

In this paper, we demonstrated the design method of freeform unobscured reflective imaging systems using the point-bypoint Construction-Iteration (CI) method. Compared with other point-by-point design methods, the light rays of multiple fields and different pupil coordinates are employed in the design. The whole design process starts from a simple initial system consisting of decentered and tilted planes. In the preliminary surfaces-construction stage, the coordinates as well as the surface normals of the feature data points on each freeform surface can be calculated point-by-point directly based on the given object-image relationships. Then, the freeform surfaces are generated through a novel surface fitting method considering both the coordinates and surface normals of the data points. Next, an iterative process is employed to significantly improve the image quality. In this way, an unobscured design with freeform surfaces can be obtained directly, and it can be taken as a good starting point for further optimization. The benefit and feasibility of this design method is demonstrated by two design examples of high-performance freeform unobscured imaging systems. Both two systems have good imaging performance after final design.