Wave-number domain separation of the incident and scattered sound field in Cartesian and cylindrical coordinates

Abstract

Two-surface Cartesian coordinate system and cylindrical coordinate system measurement techniques are applied to obtain the scattered sound fields of a general shape. This decomposition method is based on the principle that any waveform can be decomposed using a two-dimensional spatial Fourier transform into wave components that propagate in a known manner. The Cartesian method was developed by Tamara [J. Acoust. Soc. Am. 88, 2259–2264 (1990)] to measure the reflection coefficients of waves incident at oblique angles onto planar surfaces, so our paper focuses on the optimization of this method when applied to scattering investigations. A two-surface technique to separate the incident and scattered field is also developed in cylindrical coordinates. The separation process is carried out in the wave-number domain in a manner similar to what has been developed for Cartesian coordinates. However, because the incident and scattered fields are not directly separable in cylindrical coordinates, knowing general properties of the incident field make the separation process feasible. The formulation of the separation techniques and the spatial windowing and wave-number filtering needed to obtain accurate results is discussed. Numerical simulations were performed and experimental studies were conducted inside an anechoic chamber with a baffled loud speaker as the source that illuminates spheres, and a cylinder. The experiments demonstrate the feasibility of the field separation technique.