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It has been found possible to make a detailed mathematical and numerical study of the field structure at and near a line focus of a cylindrical electromagnetic wave train possessing any finite amount of cylindrical aberration of the first order. By a suitable choice of parameters all the possible wave-lengths and degrees of aberration can be expressed in terms of a single infinite integral of two independent parameters. Diagrams of the magnitude and phase of this integral are given, and only the final mathematical results are described.
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T. Pearcey (1946) studied this question.
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