Reconstruction of ultrasonic fields by deconvolving the hydrophone aperture effects II. Experiment

Abstract

The correction of the averaging effect of finite-size hydrophones is at present realized by various methods which are based on idealized models for the sound field and thus are valid only to a limited extent. In the present article three methods for inverting the aperture effects of the hydrophone viz. the Wiener method, the power spectral equalization (PSE) method and the maximum a posteriori (MAP) method, are experimentally tested and their efficiency is compared. It is shown that both for a rectangular and for a circular hydrophone aperture all three methods are suitable to reconstruct complex sound field structures from spatially averaged data. The results of this paper confirm the finding of Part I [Ultrasonics 39 (2002) 603], i.e. the quality of reconstruction depends on the spatial frequency bandwidth of the sound field investigated. Good quality reconstructions are obtained when the effective dimensions of the hydrophone's sensing area are directly derived from the spatial frequency spectrum of the measurement signal. The Wiener method and the MAP method are superior to the PSE method, since the PSE filter does not take phase information into account. For the Wiener and the MAP method normalized correlation coefficients, r p ̂ p , between the reconstructed sound pressure field and that of a reference measurement of typically 0.97 are obtained provided that the axial distance is not too small. Although the working frequency used for the experiments is rather low, it can be expected that the results obtained are applicable at higher frequencies provided that the complex spatial transfer function is determined with the necessary high precision.