Near field acoustic holography based on the equivalent source method and pressure-velocity transducers

Abstract

The advantage of using the normal component of the particle velocity rather than the sound pressure in the hologram plane as the input of conventional spatial Fourier transform based near field acoustic holography ͑NAH͒ and also as the input of the statistically optimized variant of NAH has recently been demonstrated. This paper examines whether there might be a similar advantage in using the particle velocity as the input of NAH based on the equivalent source method ͑ESM͒. Error sensitivity considerations indicate that ESM-based NAH is less sensitive to measurement errors when it is based on particle velocity input data than when it is based on measurements of sound pressure data, and this is confirmed by a simulation study and by experimental results. A method that combines pressure-and particle velocity-based reconstructions in order to distinguish between contributions to the sound field generated by sources on the two sides of the hologram plane is also examined.

Dictionary-based Equivalent Source Method for Near-Field Acoustic Holography

“…NAH can be approached in a simple and efficient way by discretizing (2) [9]. More specifically, we consider a finite set of N equivalent sources located at al, .…”

“…This makes the standard ESM method very sensitive to the measurement noise present in the acoustic hologram p and highly dependent on the choice of the set of equivalent sources (i.e., number of sources and their positioning) [9]. As a consequence, although (2) is a valid and equivalent formulation of the KH integral (1), its discretization and the measurement noise may severely impact on the NAH solution.…”

“…Then, the vibration mode at w is given by the surface normal velocity at B discrete points on the object surface, estimated as [9] v(w) = G v(w)q(w) , (5) where SI , . .. , SB are the surface points coordinates, b = 1, ... , B ; nb denotes the unit vector normal to the surface at Sb.…”

“…An interesting approximation of IBEM is the Equivalent Source Method (ESM) for NAH [9], originally introduced as the wave superposition method [10]. ESM models the radiated soundfield as being generated by a set of equivalent (virtual) sources located within (or in proximity of) the vibrating objects.…”

Single layer planar near-field acoustic holography for compact sources and a parallel reflector

“…From a data-acquisition point of view, it is a common practice to measure pressure or particle velocity in two closely spaced surfaces, or to measure Cauchy data in a single layer. Among these two categories, some studies formulate the problem with inverse boundary element and Helmholtz equation least-squares methods via the singular value decomposition [3,4,5,6,7,8], while others use the spherical wave superposition method [9,10,11], the equivalent source method [12,13,14,15,16,17] or the statistically optimized NAH method [18,19,20,21,22,23]. There is also a recent application of the equivalent source method in which the (double-layer) measurements completely cover the source region, allowing acoustic visualization of the field in small cavities [24].…”