Nearfield acoustical holography (NAH) is a useful tool for visualizing noise sources. However, to avoid spatial Fourier transform-related truncation effects, the measurement, or hologram, surface must extend beyond the source to a region where the sound pressure drops to a level significantly lower than the peak level within the measurement aperture. Statistically optimized nearfield acoustical holography (SONAH), first derived by Steiner and Hald in planar geometry, is based on a formulation similar to that of NAH. However, in SONAH, surface-to-surface projection of the sound field is performed by using a transfer matrix defined in such a way that all propagating waves and a weighted set of evanescent waves are projected with optimal average accuracy: i.e., no spatial Fourier transforms are performed. Thus the requirement that the measurement surface be extended is eliminated without compromising the accuracy of the procedure. In the present work, SONAH was re-formulated in cylindrical coordinates and was applied to the measurement of the sound field radiated by a refrigeration compressor. It was found that it is possible to visualize source regions accurately by using SONAH while using fewer measurement positions than would be required to achieve a similar level of accuracy when using conventional NAH procedures.

1.
R.
Steiner
and
J.
Hald
, “
Near-field acoustical holography without the errors and limitations caused by the use of spatial DFT
,”
Proceedings of ICSV6, 1999
, pp.
843
850
.
2.
J.
Hald
, “
Patch near-field acoustical holography using a new statistically optimal method
,”
Proc. INTER-NOISE 2003
,
2003
, pp.
2203
2210
.
3.
K.
Saijyou
and
S.
Yoshikawa
, “
Reduction methods of the reconstruction error for large-scale implementation of near-field acoustical holography
,”
J. Acoust. Soc. Am.
,
110
,
2007
2023
(
2001
).
4.
K.
Saijyou
and
H.
Uchida
, “
Data extrapolation method for boundary element method-based near-field acoustical holography
,”
J. Acoust. Soc. Am.
,
115
,
785
796
(
2004
).
5.
E. G.
Williams
, “
Continuation of acoustic near-fields
,”
J. Acoust. Soc. Am.
,
113
,
1273
1281
(
2003
).
6.
E. G.
Williams
and
B. H.
Houston
, “
Fast Fourier transform and singular value decomposition formulations for patch nearfield acoustical holography
,”
J. Acoust. Soc. Am.
,
114
,
1322
1333
(
2003
).
7.
Z.
Wang
, “
Helmholtz equation-least-squares (HELS) method for inverse acoustic radiation problem
,” Ph.D. dissertation,
Wayne State University
, Detroit (
1995
).
8.
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
).
9.
P. M.
Morse
and
K. U.
Ingard
,
Theoretical Acoustics
(
Princeton University Press
, Princeton, NJ,
1968
).
10.
G.
Weinreich
and
E. B.
Arnold
, “
Method for measuring acoustic radiation fields
,”
J. Acoust. Soc. Am.
,
68
,
404
411
(
1980
).
11.
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
).
12.
E. G.
Williams
,
H. D.
Dardy
, and
K. B.
Washburn
, “
Generalized nearfield acoustic holography for cylindrical geometry: Theory and experiment
,”
J. Acoust. Soc. Am.
,
81
(
2
),
389
407
(
1987
).
13.
E. G.
Williams
,
Fourier Acoustics: Sound Radiation and Nearfield Acoustical Holography
(
Academic Press
, London, UK,
1999
).
14.
H. S.
Kwon
,
Y. J.
Kim
, and
J. S.
Bolton
, “
Compensation for source non-stationarity in multi-reference, scan-based nearfield acoustical holography
,”
J. Acoust. Soc. Am.
,
113
,
360
368
(
2003
).
15.
S. H.
Yoon
and
P. A.
Nelson
, “
Estimation of acoustic source strength by inverse methods: Part II, experimental investigation of methods for choosing regularization parameters
,”
J. Sound Vib.
,
233
,
669
705
(
2000
).
16.
E. G.
Williams
, “
Regularization methods for near-field acoustical holography
,”
J. Acoust. Soc. Am.
,
110
,
1976
1988
(
2001
).
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