Amplitude shading of sonar transducer arrays.

Amplitude shading is an important technique for controlling the beamwidth and sidelobe level of transmitting and receiving arrays in sonar and radar. The traditional method of Dolph-Tchebyscheff synthesis for the determination of array amplitude shading or weighting coefficients is, however, highly restrictive despite the extension and generalizations by many workers following Dolph. This paper outlines an entirely new method of finding these shading coefficients by minimizing the power received by the array in an isotropic noise field exclusive of a three-dimensional spatial slice around the mainbeam direction. The method is completely general in the sense that it is applicable to any discrete array of transducers arbitrarily distributed in a three-dimensional space. As an illustrative example, nonuniformly spaced linear arrays (which are necessary for reasons of economy and operation over a band of frequencies) are shown to have been successfully shaded to acceptable pattern shape and sidelobe levels. In the special case of equally spaced linear transducer arrays, the new method of shading yields an essentially identical mainbeam shape as Dolph-Tchebyscheff's for the same sidelobe level, while the total power received (or transmitted) via the sidelobes is actually slightly less than one half of that by the latter synthesis. Necessary detailed mathematical formulas for applying the method to circular or arc arrays are also suggested. Subject Classification: 30.82; 20.15; 60.30. [ABSTRACT FROM AUTHOR]