{'fraction_non_alphanumeric': 0.017624521072796936, 'fraction_numerical': 0.0053639846743295016, 'mean_word_length': 5.160377358490566, '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}}
A freeform optics design with limited data for extended LED light sources

Abstract This paper proposes an optimization method for designing a freeform lens which can produce a good uniform circular illumination distribution and obtain high efficiency on the target plane. The initial surface profile of the freeform lens is calculated based on the laws of reflection and the energy conservation law, and then is fitted using the non-uniform rational basis spline (NURBS) method. The control points and weights are applied to parameterize the shape of freeform lens. The merit function for the optimization is defined as relative standard deviation (RSD) of the simulated illumination from the desired illumination and the efficiency of the lens. The simulation results indicate that the RSD is shown to be lower than 0.157, and maximum efficiency can be as high as 83.9%. In addition, it is demonstrated that this algorithm can obtain high uniform illumination distribution on the target plane with less variables. Compared with the conventional method, the simulation results show that the modified algorithm converges with less variables, good uniformity and high efficiency. Moreover, a freeform lens with different lighting patterns and non-rotational symmetry can be produced by the proposed method.