6.8: Bibliographic Notes

6.8 Bibliographic Notes

The paper by Mueller et al. [Mue79] was responsible for focusing the interest of many researchers on the area of diffraction tomography, although from a purely scientific standpoint the technique can be traced back to the now classic paper by Wolf [Wol69] and a subsequent article by Iwata and Nagata [Iwa75].

The small perturbation approximations that are used for developing the diffraction tomography algorithms have been discussed by Ishimaru [Ish78] and Morse and Ingard [Mor68]. A discussion of the theory of the Born and the Rytov approximations was presented by Chernov in [Che60]. A comparison of Born and Rytov approximations is presented in [Kel69], [Sla84], [Sou83]. The effect of multiple scattering on first-order diffraction tomography is described in [Azi83], [Azi85]. Another review of diffraction tomography is presented in [Kav86].

Diffraction tomography falls under the general subject of inverse scattering. The issues relating to the uniqueness and stability of inverse scattering solutions are addressed in [Bal78], [Dev78], [Nas81], [Sar81]. The mathematics of solving integral equations for inverse scattering problems is described in [Col83].

The filtered backpropagation algorithm for diffraction tomography was first advanced by Devaney [Dev82]. More recently, Pan and Kak [Pan83] showed that by using frequency domain interpolation followed by direct Fourier inversion, reconstructions of quality comparable to that produced by the filtered backpropagation algorithm can be obtained. Interpolation-based algorithms were first studied by Carter [Car70] and Mueller et al. [Mue80], [Sou84b]. An interpolation technique based on the known support of the...