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.

An equivalent source technique for recovering the free sound field in a noisy environment

“…By performing the separation before the holographic reconstruction, the influence of the disturbing source or the reflection can be removed. The spatial Fourier transform method-based SFST (Refs,(4)(5)(6)(7)(8)(9)(10), which has generally been used for measuring reflection coefficients [4][5][6][7][8] and separating incident and scattered fields, 9,10 was developed by Hallman and Bolton 11,12 to perform NAH in reflective environments, and by Williams 13 and Yu et al 14 to remove the effect of a disturbing source in NAH applications. Statistically optimized near-field acoustical holography (SONAH) has also been implemented by using a two-layer handheld array, 15,16 an array of pressure-velocity probes, [17][18][19] and a double-layer velocity transducer array.…”

Separation theory of the incident and scattered sound fields in spherical coordinate

“…[11], it is also restricted because of the BEM. Cheng [10] realized the separation of the incident and scattered fields based on two measurement surfaces (Cartesian and cylindrical coordinates), but because the planar and cylindrical surfaces are not enclosed, the leakage of the acoustic field information will influence the separation precision, especially when the direction of the incident field is parallel with the holographic plane and the axis of the cylindrical surface.…”

“…The first approach has high calculation speed, but only can be applied in separable coordinates. The other can be used for any coordinate, but it is more complicated, and has low calculation speed.The research on the scattered field is very important in underwater acoustics [9][10][11] . Because the sound field is composed of the scattered and incident fields, the scattered field cannot be meas-…”

“…The research on the scattered field is very important in underwater acoustics [9][10][11] . Because the sound field is composed of the scattered and incident fields, the scattered field cannot be measured directly.…”

A sound field separation technique based on measurements with pressure-velocity probes

“…Such sound field separation techniques based on double layer pressure measurements have been investigated for years. [3][4][5][6] An alternative single layer technique for separating the primary source from the disturbing source was recently proposed by Jacobsen and Jaud. 7 This method is based on the statistically optimized version of NAH ͑SONAH͒ developed by Hald et al, 8,9 and requires measurement of both the sound pressure and the normal component of the particle velocity in the measurement plane.…”