A method for reconstructing a pressure field at the surface of a radiating body or source is presented using recording data of a microphone array. The radiation is assumed to consist of many spherical radiators, as microphone positions are present in the array. These monopoles are weighted using a parameter α, which broadens or narrows the overall radiation directivity as an effective and highly intuitive parameter of the radiation characteristics. A radiation matrix is built out of these weighted monopole radiators, and for different assumed values of α, a linear equation solver reconstructs the pressure field at the body’s surface. It appears that from these many arbitrary reconstructions, the correct one minimizes the reconstruction energy. The method is tested, localizing the radiation points of a Balinese suling flute, reconstructing complex radiation from a duff frame drum, and determining the radiation directivity for the first seven modes of an Usbek tambourine. Stability in terms of measurement noise is demonstrated for the plain method, and additional highly effective algorithm is added for a noise level up to 0 dB. The stability of α in terms of minimal reconstruction energy is shown over the whole range of possible values for α. Additionally, the treatment of unwanted room reflections is discussed, still leading to satisfactory results in many cases.

1.
E. G.
Williams
,
J. D.
Maynard
, and
E.
Skurdzyk
, “
Sound source reconstructions using a microphone array
,”
J. Acoust. Soc. Am.
6
,
341
344
(
1980
).
2.
J. D.
Maynard
,
E. G.
Williams
, and
Y.
Lee
, “
Nearfield acoustic holography: I. Theory of generalized holography and the development of NAH
,”
J. Acoust. Soc. Am.
78
,
1395
1413
(
1985
).
3.
E. G.
Williams
,
B. H.
Houston
, and
P. C.
Herdic
, “
Fast Fourier transform and singular value decomposition formulations for patch nearfield acoustical holography
,”
J. Acoust. Soc. Am.
114
,
1322
1333
(
2003
).
4.
J.
Prager
, “
Approximate reconstruction of sound fields close to the source surface using spherical nearfield acoustical holography
,”
J. Acoust. Soc. Am.
122
,
2067
2073
(
2007
).
5.
Z.
Wang
and
S. F.
Wu
, “
Helmholtz equation-least-squares method for reconstructing the acoustic pressure field
,”
J. Acoust. Soc. Am.
102
,
2020
2032
(
1997
).
6.
N.
Rayess
and
S. F.
Wu
, “
Experimental validations of the HELS method for reconstructing acoustic radiation from a complex vibrating structure
,”
J. Acoust. Soc. Am.
107
,
2955
2964
(
2000
).
7.
S. F.
Wu
, “
On reconstruction of acoustic pressure fields using the Helmholtz equation least squares method
,”
J. Acoust. Soc. Am.
107
,
2511
2522
(
2000
).
8.
S. F.
Wu
,
H.
Lu
, and
M. S.
Bajwa
, “
Reconstruction of transient acoustic radiation from a sphere
,”
J. Acoust. Soc. Am.
117
,
2065
2077
(
2005
).
9.
M.
Ochmann
, “
The source simulation technique for acoustic radiation problems
,”
Acustica
81
,
512
527
(
1995
).
10.
M.
Ochmann
, “
The full-field equations for acoustic radiation and scattering
,”
J. Acoust. Soc. Am.
105
,
2574
2584
(
1999
).
11.
L.
Bouchet
and
Th.
Loyau
, “
Calculation of acoustic radiation using equivalent-sphere methods
,”
J. Acoust. Soc. Am.
107
,
2387
2397
(
2000
).
12.
M. B. S.
Magalhães
and
R. A.
Tenenbaum
, “
Sound source reconstruction techniques: A review of their evolution and new trends
,”
Acta. Acust. Acust.
90
,
199
220
(
2004
).
13.
G. B.
Arfken
and
H. J.
Weber
,
Mathematical Methods for Physicists
(
Elsevier
,
Amsterdam
,
2005
).
14.
W. A.
Veronesi
and
J. D.
Maynard
, “
Digital holographic reconstruction of sources with arbitrarily shaped surfaces
,”
J. Acoust. Soc. Am.
85
,
588
598
(
1989
).
15.
M. R.
Bai
, “
Application of BEM (boundary element method)-based acoustic holography to radiation analysis of sound sources with arbitrarily shaped geometries
,”
J. Acoust. Soc. Am.
92
,
533
549
(
1992
).
16.
R.
Scholte
,
N. B.
Roozen
, and
I.
Lopez Arteaga
, “
Regularization in PNAH by means of L-curve
,”
Proceedings of the Forum Acusticum Budapest
(
2005
), pp.
2579
2583
.
17.
L. M.
Wang
and
C. B.
Burroughs
, “
Acoustic radiation from bowed violins
,”
J. Acoust. Soc. Am.
110
,
543
555
(
2001
).
18.
G.
Bissinger
,
E. G.
Williams
, and
N.
Valdivia
, “
Violin f-hole contribution to far-field radiation via patch near-field acoustical holography
,”
J. Acoust. Soc. Am.
121
,
3899
3906
(
2007
).
You do not currently have access to this content.