{'fraction_non_alphanumeric': 0.024147727272727272, 'fraction_numerical': 0.009943181818181818, 'mean_word_length': 5.152838427947598, 'pattern_counts': {'":': 0, '<': 1, '<?xml version=': 0, '>': 1, '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 and optimization of a collimating optical system for high divergence LED light sources

This paper presents the design of an efficient collimating optical system for an extended light source, namely a highbrightness high divergence light emitting diode (LED), sized 1x1mm, and viewing angle of 130°. The design lies in a catadioptric rotationally symmetrical system, which modeling and optimization has been done by specific optical design software, ZEMAX®, and its development was based on geometrical principles. The device consists of two optical systems, one for the rays emerging from the source with low numerical apertures (NA<0.26) and another one for those emerging with NA>0.26. The system for rays with low NA consists of an aspherical lens system which parameters are optimized by means of standard criterion for collimation. The system for high NA rays is a combination of a hyperbolic and a parabolic mirror, being the first one the only surface shared by both system (refractive near-axis, reflective offaxis). The result of this work is a system that reaches a collection efficiency of 80% of the LED emitted light. Moreover, the beam collimation quality has been analyzed obtaining a residual divergence of less than 2°. Thus, the results achieved by the proposed optical system improve those obtained with several commercially available devices and other previously proposed systems.