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

Abstract

By the spherical wave spectrum transform, the sound pressures on the two spherical surfaces surrounding the scattering objects with arbitrarily-shaped surfaces are decomposed into spherical wave components that propagate in a known manner, the relationships between the spherical wave components of the same order on the two spherical surfaces are established by the wave field extrapolation theorem, and the formula of the separation theory in the spherical coordinate is established in the wave-number domain. After separating the scattered pressure, the total scattered field can be obtained by holographic reconstruction and prediction. In order to overcome the instability of acoustic inverse problem, a new wave-number domain filter technique is proposed. It is proved that, as long as the two holographic spherical surfaces are taken to be close enough, the singularity of the separation formula can be avoided. The results of numerical simulation demonstrate the feasibility and validity of the separation theory.spherical coordinate, sound field separation, spherical wave spectrum transform, wave-number domain filter As a method for source identification and visualization in vibro-acoustic problems, nearfield acoustic holography (NAH) is widely used in many areas nowadays. In this technique, by the measured acoustic pressure on the holographic surface which is located in the near field of the sources, such acoustic quantities as acoustic pressure, particle velocity, acoustic intensity, far-field directivity and total radiated power in three-dimension acoustic field can be calculated successfully [1][2][3][4][5][6][7][8] . So far, the algorithms to realize the NAH mainly include FFT [1][2][3][4][5] and boundary element method (BEM) [6][7][8] . 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-

Evaluation of the Accuracy of the Sound Field Separation Method under Variations in the Location of the Sampling Points

“…The behavior of the denominator will constrain the stability of the estimation of the radiated field, as there might be values for kr where both Eqs. ( 14) and (15) might become singular [8].…”

“…by combining Eqs. ( 7), (8), and ( 9). The coefficients for the outgoing waves of the total acoustic field are A T mn = A O mn + A I mn .…”

“…By comparing the data obtained from the experimental characterization with each method, the SFS method proved to be the most accurate at estimating the radiated field. Other application areas of the SFS method include the estimation of the scattered sound field from a rigid sphere under the incident propagation of a spherical sound field [8]. In recent years, several methods have been proposed to estimate characteristics of an acoustic signal using a decomposition on spherical harmonics, such as the estimation of the power spectral density [9] and spatial perception of a source [10].…”

Influences of prolate spheroidal baffle of sound diffraction on spatial directivity of acoustic vector sensor

“…In the prolate spheroidal coordinates, the length of the major axis is b, the length of the minor axis is a, so the focal length of the spheroid The scattered pressure field is [14,15,18] ( …”

Method of Separation of Incidental Acoustic Field on Cylindrical Shell by Vector Processing

“…For the incident and scattered sound fields, wave-field extrapolation theory in the wavenumber domain and the scalar superposition principle of sound pressure was used to establish a dual-holographic surface sound field separation method and a single-layer nearfield, based on the principle of vector velocity superposition [11,12]. For the holographic sound-field separation method, Li et al established the separation formula of incident and scattered sound fields in spherical coordinates in the wavenumber domain through the sound pressure decomposition of two concentric spheres [13].…”