{'fraction_non_alphanumeric': 0.02150023889154324, 'fraction_numerical': 0.0023889154323936935, 'mean_word_length': 4.816666666666666, '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}}
Golay3 sparse aperture systems designed on a spherical surface

High resolution imaging from space telescope for surveillance and astrometry is currently limited by launch vehicles and systems cost. The weight of the telescope is one of major factors which limits the vehicles to be placed in orbit. Sparse aperture optical system uses a reduced aperture area to synthesize the optical performance of a filled aperture. It is more promising in virtue of its light weight, low cost and larger synthetic aperture. The sparse aperture optical system has two types, i.e. the multiple-mirror telescope (MMT) and the multiple-telescope telescope (MTT). A MMT of Golay3 sparse aperture optical system is investigated that three sub-mirrors are located on a spherical primary mirror. Three sub apertures of Golay3 are elliptic that in fact the circular sub-mirrors of spherical primary mirror are projected on the entrance pupil. The relationships between fill factor, radius of sub-mirrors and F number of the primary mirror are presented. The analytical formula is also completed, which shows that the maximum fill factor is limited by F number of the primary mirror. When the aperture radius is equal to curvature radius of the primary mirror approximately, the shape of sub-apertures exhibits to be elliptic obviously. The maximum fill factor reaches the largest one at that time. Modulation Transfer Function (MTF) of Golay3 system is studied. MTF is the correlation of three elliptic sub-apertures. The sub-MTFs are different from those of sub-mirrors located on a plane. The formula is verified by designing two Cassegrain telescopes which primary mirror is made up of three sub-mirrors of Golay3 configuration with Zemax optical program. Three sub-mirrors of primary mirror share a common asphercial secondary mirror. The errors caused by tilt and piston of three sub-apertures are also given out. Because of the loss of MTF for the sparse aperture optical system, the image quality is decreased. Wiener filter technique is utilized to improve the image quality for the sparse aperture system.