Near-field acoustical holography: Understanding sound generation from musical instruments to military aircraft

Near-field acoustical holography (NAH), like its optical cousin, is a method by which measurements made along a two-dimensional surface are used to create a three-dimensional reconstruction. Its basic principles provide the physics student with a rich understanding of wave superposition and propagation, the Helmholtz equation, separable geometries, wavenumber spectra, and near-fields, i.e., evanescence. Implementing NAH requires an understanding of temporal and spatial Fourier transforms, signal-to-noise ratio, windows, filters, and other signal processing concepts. This paper introduces key concepts of NAH and explains its application to understanding sound radiation from the hammered dulcimer, the caj\'{o}n drum, and a military jet aircraft.