Array shading for a broadband constant directivity transducer

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Abstract
The theory of a broadband constant directivity transducer is developed. The transducer is an array of isophase, omnidirectional elements on an acoustically transparent spherical surface. It is shown that, with appropriate amplitude shading of the array elements, the beam pattern has no side lobes and the directivity is constant at all frequencies above a cutoff frequency (determined by the beam width and the radius of the sphere.) A shading function is derived, which consists of a simple linear combination of powers of cos ϑ, and several beam patterns are calculated.

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