The determination of the far field of an acoustic radiator from sparse measurement samples in the near field

Abstract

The near-field to far-field projection procedure here introduced has the following novel features. (1) The measured near-field samples do not need to belong to a separable coordinate surface. (2) The number of samples is, in principle, as small as the theoretical number of degrees of freedom of the far field, related to the dimensions of the source in wavelengths. (3) The samples do not need to belong to a regular grid. (4) If the projection is sought only within a limited angular sector, a further reduction of the number of measurement samples is possible. The technique is based on the identification from the measured data of an equivalent monopolar distribution of acoustic sources on a surface completely surrounding the radiator. The far field of these sources, straightforwardly computed, constitutes the estimate of the far field of the radiator. The identification is based on the pseudo inversion of the matrix representing the mapping of the equivalent sources into near-field samples, which is obtained by resorting to the singular value decomposition of the matrix. Representative results of the extensive numerical simulations are here included.