Starting with the similarity of the radiation pattern from a pair of points to a harmonic function, it is shown that with a change in variable, the directional function can be put in a form which permits it to be analyzed into a Fourier series, each of whose terms represents a pair of sources. The same method is applied to other types of sources and arrays. The relationship is developed between source spacing and the range over which the function can be represented by the series. A number of examples are given to illustrate the application of this method.
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Irving Wolff (1937) studied this question.