The theory of diffraction tomography for two-dimensional objects within the Born approximation is presented for cases where the scattered field is measured over arbitrarily shaped boundaries surrounding the object. Reconstruction algorithms are presented for both plane wave (parallel beam) and cylindrical wave (fan beam) insonification. Special attention is devoted to cases where the measurement and source boundaries are either lines or circles. The theory and algorithms presented are shown to be readily extended to the case of three-dimensional objects.
GreenleafJ. F., Computerized tomography with ultrasound, Proc. IEEE71, 330–337 (1983).
4.
DevaneyA. J., A filtered backpropagation algorithm for diffraction tomography, Ultrasonic Imaging4, 336–350 (1982).
5.
DevaneyA. J., A computer simulation study of diffraction tomography, IEEE Trans. Biomed. Eng.BME-30, 377–386 (1983).
6.
LipsonH.CochranW., The Determination of Crystal Structures (Cornell University Press, Ithaca, NY, 1966).
7.
VainshteinB. K., Diffraction of X-rays by Chain Molecules (John Wiley, NY, 1974).
8.
DevaneyA. J., Inverse source and scattering problems in ultrasonics, IEEE Trans. Sonics Ultrasonics, SU-30, 355–364 (1983).
9.
WolfE., Three-dimensional structure determination of semi-transparent objects from holographic data, Opt. Commun.1, 153–156 (1969).
10.
PorterR., Determination of structure of weak scatterers from holographic images, Opt. Commun.39, 362–364 (1981).
11.
MuellerR. K.KavehM.InversonR. D., A New Approach to Acoustic Tomography Using Diffraction Techniques, in Acoustical ImagingVol. 8, MetherellA. F., ed., pp. 615–628 (Plenum Press, New York, 1980).
12.
PanS. X.KakA. C., A computational study of reconstruction algorithms for diffraction tomography, IEEE Trans. Acoustics, Speech and Signal Processing (to appear).
13.
SlaneyMalcolmKakA. C., Diffraction tomography, in Inverse Optics, DevaneyA. J., ed., Proc. SPIEVol. 413, pp. 2–19 (1983).
14.
BeylkinG., The fundamental identify for iterated spherical means and the inversion formula for diffraction tomography and inverse scattering, J. Math. Phys.24, 1399–1400 (1983).
15.
MorseP. M.FeshbachH., Methods of Theoretical Physics, Vol. I (McGraw-Hill, New York, 1953).
16.
BeylkinG.DevaneyA. J., Theory of diffraction tomography within the Born and Rytov approximations, submitted to J. Math. Phys.
17.
KakA. C., Computerized tomography with x-ray emission and ultrasound sources, Proc. IEEE67, 1245–1272 (1979).
18.
DevaneyA. J., Inversion formula for inverse scattering within the Born approximation, Opt. Lett.7, 111–112 (1982).
