Experimental validation of Helmholtz equation least squares when the Nyquist spatial sampling requirement is violated.

Abstract

Previous numerical studies [Dziklinsky and Wu, J. Acoust. Soc. Am. (2009)] have shown that Helmholtz equation least squares (HELSs) enable one to violate the spatial Nyquist sampling frequency and stand‐off distance requirements inherent in Fourier acoustics. A direct benefit of this severe under sampling using HELS is a significant saving in measurement and computational effort in locating acoustic point sources in practice without loss of the required spatial resolution. The presented paper aims at validating the previous numerical studies by conducting experiments on locating two incoherent point sources separated by a small distance of 6.25 mm via HELS. The acoustic pressures are measured by a 5 × 5 microphone array over a 50 × 50 mm square plane at varying stand‐off distances with fixed microphone spacing of 12.5 mm. The considered source frequencies are well above the spatial Nyquist sampling frequency. Results show that HELS is capable of locating point sources when stand‐off distance is 10 mm or less and SNR is 10 dB or higher. Similar results obtained by using planar Fourier acoustics are also presented for comparison purposes.