{'fraction_non_alphanumeric': 0.010699588477366255, 'fraction_numerical': 0.00411522633744856, 'mean_word_length': 4.846153846153846, '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}}
Extended Range Diffraction Based Merit Function For Lens Design Optimization

Approximate expressions for diffraction based image quality criteria like Strehl ratio or the relative Modulation Transfer Function in terms of the variance of the wave aberration function or the variance of the wave aberration difference function respectively have been used to obtain merit functions for lens design optimization. These merit functions are useful when the Strehl ratio or the relative M.T.F. of the optimized system is greater than 0.7. A few attempts have been made to develop techniques that extend the range of validity of the diffraction based criteria. This report presents a new approach to this problem. An expansion of the pupil function in terms of the orthogonal set of Block functions leads to an expression for the central intensity in terms of the average values of aberration over a finite number of subapertures. The range of validity of this expression depends on the number of subapertures used. It has been found that a rather small number is sufficient when the central intensity is greater than 0.25. A brief description of the use of this expression in least squares type optimization is presented.