Measuring the relative strengths of a set of partially coherent acoustic sources

The measurement of the relative contributions to the acoustic field made by a set of sources, which by necessity must operate simultaneously, is of importance in many areas of noise control technology. A partial solution to this problem, proposed in the 1970s, was the Polar Correlation Technique. This recognized, initially, the Fourier transform relationship between cross-spectra, measured in the acoustic far field, and the distribution of source strength of a line array of sources, typical of an aero-engine, for example. In a second development (1981) a parametric method was developed. Essentially, the position of the contributing sources was assumed to be known and a least squares error procedure was employed to establish an optimum fit between the source strength distribution and the cross-spectral data. A major restriction, however, was the necessary assumption of mutually incoherent sources. In the present work it is demonstrated that this restriction is unnecessary, albeit at the expense of some extra data processing. Specifically, we show that by employing several reference microphones, as opposed to one for incoherent sources, both the amplitude of and coherence between an array of sources may be determined. The potential capability of the method is established both analytically and through extensive numerical simulation