Series Expansion Prediction of the Farfield from the Nearfield

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A series expansion method for determining the farfield from nearfield measurements of coherent and partially coherent sound fields is presented. Current investigations have generally been based on a Helmholtz integral or Green's-function approach, although one of the earliest methods for sinusoidal oscillation [J. Pachner, J. Acoust. Soc. Am. 28, 86–89 (1956)] was actually based on a series expansion of the nearfield solution in spherical wave-functions. By confining the measurements to a spherical surface, Pachner was able to evaluate the expansion coefficients through the orthogonality of the Legendre polynomials. However, in the method presented here, the expansion is truncated to include only the number of terms equal to the number of nearfield measuring points. In this way, the coefficients may be evaluated through a matrix inversion for nearfield measuring points at any location. A comparison of exact and predicted farfields is presented for some simple source distributions. The method has been extended for crosspower nearfield spectral measurements. [Work supported by the Office of Naval Research.]