Image sets

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Abstract
Crystallographers are familiar with vector sets and their properties because of their relation to the Patterson synthesis. There exists a generalization of vector sets, here called image sets, which bears a resemblance to the results of performing a convolution of two different functions. If two sets of points are given, vectors can be drawn from each point in the first set to each point in the second set. When these vectors are shifted to a common origin a sheaf of image vectors results. The set of points (properly weighted) at the ends of these vectors constitutes the image set. Such sets, which are treated in this paper, are of crystallographic interest.

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