Obtaining far-field spherical directivities from arbitrarily shaped arrays using the Helmholtz equation least-squares method

Commonly, directivities of sound sources are measured using surrounding spherical arrays. However, in some cases, such as when measurement hardware is limited, or when an array shape would ideally conform to the radiating object's geometry, obtaining spherical far-field directivities using an arbitrarily shaped array could be useful. This work illustrates how the Helmholtz equation least-squares method applies to accomplish this task. Both numerical models and the measured directivities of various guitar amplifiers validate the technique.