Source centering of directivity patterns using acoustical holography and magnitude far-field pattern equivalence

Two essential points of consideration for spherical directivity measurements are the measurement radius and the sound source's location relative to the evaluation surface. When spatial constraints, such as anechoic chamber size, limit the measurement radius, both points may lead to measured near-field directivity patterns deviating from the desired far-field radiation characteristics. To clarify the impact of source placement on near-field and far-field radiation patterns, this work develops far-field magnitude and phase relations between untranslated and translated sources. The resulting theory shows that far-field propagation via acoustical holography is sufficient to correct for source-positioning uncertainties, provided that the measurements incorporate sufficient sampling positions to avoid spatial aliasing. The magnitude equivalence of translated and untranslated far-field directivity patterns also enables an acoustic centering procedure that overcomes previous low-frequency limitations.