Inverse Scattering Theory Foundations Of Tomography With Diffracting Wavefields.

A. J. Devaney

doi:10.1117/12.940241

10 September 1987 Inverse Scattering Theory Foundations Of Tomography With Diffracting Wavefields.

A. J. Devaney

Proceedings Volume 0768, Pattern Recognition and Acoustical Imaging; (1987) https://doi.org/10.1117/12.940241
Event: International Symposium on Pattern Recognition and Acoustical Imaging, 1987, Newport Beach, CA, United States

Abstract

The underlying mathematical models employed in reflec-tion and transmission computed tomography using diffracting wavefields (called diffraction tomography) are reviewed and shown to have a rigourous basis in inverse scattering theory. In transmission diffraction tomography the underlying wave model is shown to be the Rytov approximation to the complex phase of the wavefield transmitted by the object being probed while in reflection diffraction tomography the under-lying wave model is shown to be the Born approximation to the backscattered wavefield from the object. In both cases the goal of the reconstruction process is the determination of the object's complex index of refraction as a function of position F and, possibly, the frequency w of the probing wavefield. By use of these approximations the reconstruction problem for both transmission and reflection diffraction tomography can be cast into the simple and elegant form of linearized in-verse scattering theory. Linearized inverse scattering theory is shown to lead directly to generalized projection-slice theo-rems for both reflection and transmission diffraction tomography that provide a simple mathematical relationship between the object's complex index of refraction (the unknown) and the data (the complex phase of the transmitted wave or the complex amplitude of the reflected wave). The conven-tional projection-slice theorem of X-ray CT is shown to result from the generalized projection-slice theorem for transmission diffraction tomography in the limit of vanishing wavelength (in the absence of wave effects). Fourier based and back-projection type reconstruction algorithms are shown to be directly derivable from the generalized projection-slice theorems.

Citation Download Citation

A. J. Devaney "Inverse Scattering Theory Foundations Of Tomography With Diffracting Wavefields.", Proc. SPIE 0768, Pattern Recognition and Acoustical Imaging, (10 September 1987); https://doi.org/10.1117/12.940241

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