Ultrasonic propagation can often be usefully described in terms of rays. As these rays are in general curved, transmission tomography is more complicated for ultrasound than for x-rays. It is shown here that in most media there are “forbidden” regions which are not intersected by any “minimum propagation time” rays. It is concluded that it is seldom feasible to obtain better images than those reconstructed on the assumption that the ultrasonic rays travel along straight lines.
GloverG. H., Characteristic of In Vivo Breast Tissue by Ultrasonic Time-of-Flight Tomography, in Ultrasonic Tissue Characterization II, LinzerM. ed., National Bureau of Standards Spec. Publ. 525, pp. 221–225 (U. S. Govt. Printing Office, Washington D. C., 1979).
6.
SchombergH., An improved approach to reconstructive ultrasound tomography, J. Phys. D: Appl, Phys. 11, L181–L185 (1978).
7.
JohnsonS. A.GreenleafJ. F.SamayoaW. A.DuckF. A.SjostrandJ., Reconstruction of Three Dimensional Velocity Fields and Other Parameters by Acoustic Ray Tracing, in 1975 Ultrasonics Symposium Proc., pp. 46–51 (IEEE Cat. #75 CHO 994-4SU).
8.
BatesR. H. T.DunlopG. R., Inverse Scattering and Tomography, in Ultrasonics International 1977 Conference Proc., pp. 104–110 (I. P. C. Science and Technology Press, Guildford, U. K.).
9.
BatesR. H. T.McKinnonG. C., Towards improving images in ultrasonic transmission tomography, Australasian Physical Sciences in Medicine 2-3, 134–140 (1979).
10.
FriedlanderF. G., Sound Pulses, (Cambridge University Press, 1958).
11.
LewittR. M.BatesR. H. T.PetersT. M., Image reconstruction from projections, Optik50, 19–33, 85–109, 189–204, 269–278 (1978).
12.
BullenK. E., Introduction to the Theory of Seismology, Chapt. 7 (Cambridge University Press, 1963).
13.
BornM.WolfE., Principles of Optics, Chapt. 3 (Pergamon Press, Oxford, 1970).