THE USE OF SPHEROIDAL WAVE FUNCTIONS IN THE EMPIRICAL DESCRIPTION OF SCALAR EAVE FIELDS

摘要

The empirical description of scalar wave fields by spherical wave functions with experimentally determined expansion coefficients is critically reviewed and its restric¬tions to spherical surfaces of measurement noted. To avoid these restrictions a modified theory is developed which abandons spherical wave functions in favor of spherical wave functions thereby permitting measurement over ellip¬soidal surfaces. Formulas are developed for determining the analytical and empirical expansion coefficients of sca¬lar wave fields in spheroidal wave functions. Traveling waves and standing waves in echoic chambers are analyti¬cally separated, and formulas for the far-field directivity patterns are obtained.