This paper investigates the sampling criterion needed to image objects within a circular ring array. The array consists of transducer elements deployed along a circular aperture at regular angular intervals. Each transducer excites waves which propagate towards the center of the array and detects outgoing fields traveling towards it. It is shown that while with conventional linear apertures the sampling criterion is dictated by the wavelength of the probing wave only, in the case of a circular aperture the sampling depends on the size of the object relative to the wavelength and its position with respect to the aperture.

Topics
Ultrasound, Electrodynamics, Wave propagation, Linear filters, Optical signal processing, Fourier analysis, Coordinate system, Generalized functions, Partial wave expansion, Tomography
1.
A. J.
 
Jerri
,
Proc. IEEE
 
65
,
1565
(
1977
).
Google Scholar
Crossref
Search ADS
 
2.
M. P.
 
Andre
,
H. S.
 
Janee
,
P.
 
Martin
,
G. P.
 
Otto
,
B. A.
 
Spivey
, and
D. A.
 
Palmer
,
Int. J. Imaging Syst. Technol.
https://doi.org/10.1002/(SICI)1098-1098(1997)8:1<137::AID-IMA15>3.3.CO;2-1
 
8
,
137
(
1997
).
Google Scholar
Crossref
Search ADS
 
3.
F.
 
Lin
,
A. I.
 
Nachman
, and
R. C.
 
Waag
,
J. Acoust. Soc. Am.
https://doi.org/10.1121/1.1285919
 
108
,
899
(
2000
).
Google Scholar
Crossref
Search ADS
PubMed
 
4.
F.
 
Simonetti
,
L.
 
Huang
, and
N.
 
Duric
 (unpublished).
5.
R. C.
 
Waag
 and
R. J.
 
Fedewa
,
IEEE Trans. Ultrason. Ferroelectr. Freq. Control
https://doi.org/10.1109/TUFFC.2006.104
 
53
,
1707
(
2006
).
Google Scholar
Crossref
Search ADS
PubMed
 
6.
J. W.
 
Goodman
,
Introduction to Fourier Optics
(
McGraw-Hill
,
New York
,
1996
).
Google Scholar
 
7.
G. B.
 
Arfken
 and
H. J.
 
Weber
,
Mathematical Methods for Physicists
(
Academic
,
London
,
2001
).
Google Scholar
 
© 2007 American Institute of Physics.
2007
American Institute of Physics
You do not currently have access to this content.