A Filtered Backpropagation Algorithm for Diffraction Tomography

A reconstruction algorithm is derived for parallel beam transmission computed tomography through two-dimensional structures in which diffraction of the insonifying beam must be taken into account. The algorithm is found to be completely analogous to the filtered backprojection algorithm of conventional transmission tomography with the exception that the backprojection operation has to be replaced by a backpropagation process whereby the complex phase of a field measured over a line outside the object is made to propagate back through the object space. The algorithm is applicable to diffraction tomography within either the first Born or Rytov approximations. Application of the algorithm to three-dimensional structures is also discussed.

[1]  W. Cochran,et al.  The determination of crystal structures , 1957 .

[2]  E. Wolf,et al.  Inverse Diffraction and a New Reciprocity Theorem , 1968 .

[3]  E. Wolf.  Three-dimensional structure determination of semi-transparent objects from holographic data , 1969 .

[4]  W. H. Carter.  Computational Reconstruction of Scattering Objects from Holograms , 1970 .

[5]  R. M. Mersereau,et al.  Digital reconstruction of multidimensional signals from their projections , 1974 .

[6]  A. J. Devaney,et al.  Spectral representations for free space propagation of complex phase perturbations of optical fields , 1975 .

[7]  Eytan Domany,et al.  The Born approximation in the theory of the scattering of elastic waves by flaws , 1977 .

[8]  H. Barrett,et al.  Computerized tomography: taking sectional x rays , 1977 .

[9]  H. Bartelt,et al.  Image formation by inversion of scattered field data: experiments and computational simulation. , 1979, Applied optics.

[10]  M. Kaveh,et al.  Reconstructive tomography and applications to ultrasonics , 1979, Proceedings of the IEEE.

[11]  Mostafa Kaveh,et al.  A New Approach to Acoustic Tomography Using Diffraction Techniques , 1980 .

[12]  A New Approach to Emission and Transmission CT , 1980 .

[13]  A. Devaney.  Inverse-scattering theory within the Rytov approximation. , 1981, Optics letters.

[14]  R. Hingorani,et al.  An Investigation of Computerized Tomography by Direct Fourier Inversion and Optimum Interpolation , 1981, IEEE Transactions on Biomedical Engineering.

[15]  Stephen J. Norton,et al.  Ultrasonic Reflectivity Imaging in Three Dimensions: Exact Inverse Scattering Solutions for Plane, Cylindrical, and Spherical Apertures , 1981, IEEE Transactions on Biomedical Engineering.

[16]  James F. Greenleaf,et al.  CLINICAL IMAGING WITH TRANSMISSIVE ULTRASONIC COMPUTERIZED TOMOGRAPHY , 1981 .

[17]  A. J. Devaney,et al.  A new perturbation expansion for inverse scattering from three-dimensional finite-range potentials , 1982 .