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## Wave interference effects for circular arrays

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We now come to the question of how much can be deduced about the structure of a wave-field from an analysis of wave interference effects. The observations might consist of the fluctuations of the indicated bearing of a WADF as a function of time (this Chapter) or a sequence of phase difference measurements on various pairs of elements in an interferometer (Chapter 9). Not surprisingly, the amount of information that can be derived with an orthodox DF, wbich provides only one indicated bearing at any one moment, proves to be very limited. In the numerical simulations for this type of problem, therefore, attention will be confined to two-ray wave fields and the basic question is whether the ray azimuths can be found. In order to distinguish between the zero-aperture bearing defined in Chapter 4 and the indicated bearing from a DF of finite aperture, we shall refer to the former as the tangent bearing; it is the direction normal to the tangent to a curve of constant phase at a specified point in the horizontal plane and is a property of the wave-field. A phase-measuring DF of finite aperture, centred on the same point, would produce an approximation to the same bearing but would average in some way (to be investigated below) over a finite segment of the curve. Thus, the 'segment bearing' for a finite aperture approaches the tangent bearing as the aperture approaches zero.

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