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Because its underlying principles are so fundamental, holography has been studied and applied in many areas of science. Recently, a technique has been developed which takes the maximum advantage of the fundamental principles and extracts much more information from a hologram than is customarily associated with such a measurement. In this paper the fundamental principles of holography are reviewed, and a sound radiation measurement system, called nearfield acoustic holography (NAH), which fully exploits the fundamental principles, is described.

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The reconstruction of the pressure and normal surface velocity provided by near-field acoustical holography (NAH) from pressure measurements made near a vibrating structure is a linear, ill-posed inverse problem due to the existence of strongly decaying, evanescentlike waves. Regularization provides a technique of overcoming the ill-posedness and generates a solution to the linear problem in an automated way. We present four robust methods for regularization; the standard Tikhonov procedure along with a novel improved version, Landweber iteration, and the conjugate gradient approach. Each of these approaches can be applied to all forms of interior or exterior NAH problems; planar, cylindrical, spherical, and conformal. We also study two parameter selection procedures, the Morozov discrepancy principle and the generalized cross validation, which are crucial to any regularization theory. In particular, we concentrate here on planar and cylindrical holography. These forms of NAH which rely on the discrete Fourier transform are important due to their popularity and to their tremendous computational speed. In order to use regularization theory for the separable geometry problems we reformulate the equations of planar, cylindrical, and spherical NAH into an eigenvalue problem. The resulting eigenvalues and eigenvectors couple easily to regularization theory, which can be incorporated into the NAH software with little sacrifice in computational speed. The resulting complete automation of the NAH algorithm for both separable and nonseparable geometries overcomes the last significant hurdle for NAH.

A square microphone array with 256 elements has been constructed along with interfacing electronics to study low-frequency (1–5 kHz) sound sources in air using the principles of acoustical holography. The array is used in the nearfield of a radiating object and the sound source structure of that object is reconstructed with an on-line minicomputer. Reconstruction of the source structure of a point source and an unbaffled, free rectangular plate point excited below its coincidence frequency are presented. The latter shows clear evidence of ’’corner’’ and ’’edge’’ modes in which the respective areas of the plate are the dominant radiating sources. A new imaging process which is not limited in resolution by the wavelength of the radiated sound is introduced.