{'fraction_non_alphanumeric': 0.024229074889867842, 'fraction_numerical': 0.003964757709251102, 'mean_word_length': 5.488571428571428, '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}}
Synthesis of three-dimensional light fields and applications [Prolog]

This paper is concerned with the generation and application of three-dimensional (3-D) optical light-field distributions with emphasis on basic principles and design procedures. A light wave typically enters an optical system, is modulated, and then propagates in a homogeneous medium beyond the system where the desired 3-D optical field distribution is formed. The modulation takes place in optical systems that contain classical optical elements such as lenses, mirrors, prisms, polarizers, and apertures in addition to modulation elements. The primary design objective is to implement the proper spatial structure of the modulating element. A familiar example of a wavefront modulation element is the Fresnel lens, a structure that belongs to a wider class of modulation elements known as diffractive optical elements (DOEs). DOEs make use of masks, often fabricated by microlithographic techniques, that can modulate incoming light beams. Spatial light modulators, another class of modulation elements, are electronically or optically controlled transparencies such as liquid crystal displays, microelectromechanical systems, or magnetooptic or electrooptic modulators. Wavefront generation systems able to produce predesigned 3-D optical fields have applications in many areas, including the following. 1) Lithographic applications, where depth of focus, the extent to which the intensity structure of an optical wave can be kept close to constant, is as important as the resolution of the field. 2) Volume memories such as holographic memories in which light waves interact in a 3-D recording medium to store and retrieve data. Memory capacity can be determined by studying the 3-D fields in the memory space. Similar studies can be made for nonholographic optical memories. 3) Near-field optics, where efficient data gathering can be achieved by studying optical field changes with distance from the surface of an illuminated sample. 4) Invariant beams with light fields in which various beam parameters do not undergo dramatic changes during propagation. Invariant beams are important for design of interferometers, optical signal processors, optical interconnections, and laser resonators.