Abstract
The technique of wavefield backpropagation has been used quite extensively in the literature. We report on an analytical study of the resolution properties of this technique. Backpropagation as a form of holographic reconstruction suffers from poor axial resolution. We derive expressions for both the axial and the lateral resolutions. We also show that the axial resolution can be substantially improved by the use of multiple frequencies. We derive an expression relating the resolution and bandwidth.
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References
1.
Boyer
A. L.
Hirsch
P. M.
Jordan
J. A.
Jr.
Lesem
L. B.
Van Rooy
D. L.
, Reconstruction of Ultrasonic Images by Backward Propagation , in Acoustical Holography 3 ,
Metherell
A. F.
, ed., 333 –348 (Plenum Press , New York , 1971 ).
2.
Powers
J. P.
, Computer Simulation of Linear Acoustic Diffraction , in Acoustical Holography
7 ,
Kessler
L. W.
, ed., 193 –205 (Plenum Press , New York , 1976 ).
3.
Higgins
F. P.
Norton
S. J.
Linzer
M.
, Optical Interferometric Visualization and Computerized Reconstruction of Ultrasonic Fields
J. Acoust. Soc. Amer.
68 , 1169 –1176 (1980 ).
4.
Stepanishen
P. R.
Benjamin
K. C.
, Forward and Backward Projection of Acoustic Fields Using FFT Methods , J. Acoust. Soc. Amer.
71 , 803 –812 (1982 ).
5.
Devaney
A. J.
, A Filtered Backpropagation Algorithm for Diffraction Tomography , Ultrasonic Imaging
4 , 336 –350 (1982 ).
6.
Williams
E. G.
Maynard
J. D.
Skudrzyk
E.
, Sound Source Reconstructions Using a Microphone Array , J. Acoust. Soc. Amer.
68 , 340 –344 (1980 ).
7.
Goodman
J. W.
, Introduction to Fourier Optics, ch. 3 (McGraw-Hill , New York , 1968 ).
8.
Williams
E. G.
Maynard
J. D.
, Holographic Imaging Without the Wavelength Resolution Limit , Phys. Rev. Lett.
45 , 554 –557 (1980 ).
9.
Teo
T. J.
Reid
J. M.
, Spatial / Frequency Diversity in Inverse Scattering , in Proceedings of IEEE 1985 Ultrasonics Symposium 2 , pp. 800 –803 , IEEE , 1985 .
10.
Ermert
H.
Karg
R.
, Multifrequency Acoustical Holography , IEEE Tran. Sonics and Ultrason.
26 , 279 –286 (1979 ).
11.
Nagai
K.
, Multifrequency Acoustical Holography Using a Narrow Pulse , IEEE Tran. Sonics and Ultrason.
31 , 151 –156 (1984 ).
12.
Teo
T. J.
Reid
J. M.
, Angular Spectrum Decomposition: Improving the Resolution , in Acoustical Imaging 14 ,
Berkhout
A. J.
Ridder
J.
van der Wal
L. F.
, eds., 143 –154 (Plenum Press , New York , 1985 ).
13.
Banos
A.
Jr.
, Dipole Radiation in the Presence of a Conducting Half-Space, ch. 2 (Pergamon Press , Oxford , 1966 ).
14.
Berkhout
A. J.
, Seismic Migration vol. A, appendix F, third edition (Elsevier , Amsterdam , 1985 ).
15.
Shewell
J. R.
Wolf
E.
, Inverse Diffraction and a New Reciprocity Theorem , J. Opt. Soc. Amer.
58 , 1596 –1603 (1968 ).
16.
Wolf
E.
Shewell
J. R.
, The Inverse Wave Propagator , Phys. Lett.
25A , 417 –418 (1967 ).
17.
Gradshteyn
I. S.
Ryzhik
I. M.
, Table of Integrals, Series, and Products , 682 (Academic Press , New York , 1980 ).