Skip to main navigationSkip to main content
The University of Southampton
Southampton Marine and Maritime Institute

Forward and Inverse Methods using Spherical Measurement Arrays Seminar

16 April 2013
Building 13 room 3017

For more information regarding this seminar, please email Natasha Webb at .

Event details

ISVR Engineering Research Seminar

An array of microphones populating a spherical boundary provides an exciting new tool to study a broad range of acoustic problems from concert halls to the interiors of aircraft and automobiles. These studies have used open arrays (transparent to the incident field) and closed arrays (flush mounted on a rigid surface). In either case and when viewed from a mathematical prospective the open and the closed spheres are perhaps the only practical geometries in which the measured field can be expanded into orthogonal eigenfunctions (called spherical harmonics) and extrapolated without error off the surface (using spherical Hankel/Bessel functions) to predict the pressure in the space outside or inside the sphere. Outside the sphere these extrapolations can be reformulated as plane waves and can predict an equivalent three-dimensional distribution of plane waves that exist outside the array, extremely useful in studying the reflectivity of the bounding surfaces in auditoriums. Smaller confined spaces such as the interior of automobiles are better treated using inverse methods to extrapolate the field throughout the interior again using open or closed array measurements. These methods are a form of near-field acoustical holography (NAH) and are very powerful in their ability to image the acoustic intensity fields – the flow of energy in the interior - providing a powerful visual metric to identify structural sources of noise. Popular source imaging methods often promoted by instrument companies use delay-sum beamforming with open arrays and are attractive because of their mathematical simplicity.

This lecture provides a broad discussion of these approaches discussing the basic theories in a unified way and comparing results to illuminate capabilities. Although most of the literature deals with the frequency domain, we derive a new time-domain formulation using generalized function analysis that we hope will prove useful to the acoustics/ambisonics community.

Research supported by ONR.

Speaker information

Dr Williams, Senior Scientist for Structural Acoustics & Sound Field Reconstruction in the Acoustics Division at the Naval Research Laboratory (NRL) in Washington DC. where he has worked for 32 years. He is an internationally recognized scientist whose pioneering research in the field of near-field acoustical holography has impacted acoustics research and development throughout the world. His research was formally recognized by NRL as one of the 35 most innovative technologies there over the past 75 years where it has been a major contributor in changing and molding the thinking of navy and non-navy researchers towards the quieting of the U.S. submarines and surface ships. His recent work with spherical arrays has provided new and innovative methods to image and diagnose, in situ, noise sources inside aircraft and automobiles. In 2006 Dr. Williams turned to apply his techniques to the electromagnetic realm and has been very successful at developing methods to image the electromagnetic fields on ship hulls using navy silencing-range data. Dr. Williams’ depth of knowledge in the field of structural acoustics, including sound radiation, is demonstrated in his acclaimed book “Fourier Acoustics, Sound Radiation and Nearfield Acoustical Holography” published by Academic Press in 1999. As well as a reference book it is being used as a textbook in university graduate programs. In 2005 a Japanese translation was published by Springer, Tokyo. Over the past 32 years Dr. Williams has presented over 70 invited and keynote lectures throughout the world and has over 100 publications to his credit. In 2009 he was awarded the Per Bruel Gold Medal from the ASME “in recognition of eminent achievement and extraordinary merit in the field of noise control and acoustics”.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.