{'fraction_non_alphanumeric': 0.01762114537444934, 'fraction_numerical': 0.0, 'mean_word_length': 5.528735632183908, '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}}
An algorithm of lens surface error compensation based on Zernike polynomial

For high-precision optical systems, in addition to controlling the positional misalignment, the multi-lens system assembly needs to further compensate for the inherent errors of the lenses. This paper introduces a surface error rotation compensation algorithm based on Zernike polynomials. The algorithm uses the wavefront difference RMS as the evaluation standard. By deriving the aberration Zernike polynomials, the lens rotation optimization function is established. The optimization function has the same value as the wavefront difference RMS. Corresponding relationship, the quasi-Newton method is used to obtain the optimal rotation angle solution of the optimization function, and then the lens rotation compensation is used to minimize the wavefront difference. The feasibility of the algorithm is verified by a two-mirror system. Finally, in order to improve the efficiency of surface error compensation, an active error compensation method for lens selection is proposed, which is of great significance to the precision assembly of multiple lenses.