### ASA 125th Meeting Ottawa 1993 May

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

**J. Lan
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M. J. Simoneau
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R. K. Jeffers
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S. G. Boucher
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*Airmar Technol. Corp., 69 Meadowbrook Dr., Milford, NH 03055
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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.