ASA 125th Meeting Ottawa 1993 May

3aEA13. A universal shading method---successive approximation method.

J. Lan

M. J. Simoneau

R. K. Jeffers

S. G. Boucher

Airmar Technol. Corp., 69 Meadowbrook Dr., Milford, NH 03055

A completely new shading method, called the successive approximation method, is developed. The foundation of the method is the energy extreme theorem with a constraint condition: Construct a function L, which is the integration of the square of the expression of sound pressure multiplied by a control function, letting L reach minimum will give a set of unknown numbers, therefore a sound pressure can be obtained for the specified control function, which is based on the expected function and the sound pressure obtained during the last iteration. After several iterations, the sound pressure will approach expected function. This method can be applied to any arrays, both in the far field and near field. A variety of patterns can be obtained by either amplitude shading, phase shading, or using unequally spaced arrays. Changing the constraint condition can alter the fitting way between the pattern to be shaded and the expected one. Several computed and experimental examples will be given, which includes: unequally spaced arrays; superdirectivity arrays; using unsymmetric amplitude shading to obtain fan-shaped patterns with any low sidelobe level; using amplitude shading only to steer mainbeam.