J.D. Sanchez, A.E. Morales-Porras, M. Testorf, and M.A. Fiddy, Dept. of Electrical & Computer Engin., Univ. of Massachusetts-Lowell, Lowell, MA.
For very weak scattering objects the first Born approximation can be applied, which assumes ψ ψi. Then Eq. 1 identifies ψs as the Fourier transform of the object V along a circle tangent to the origin in Fourier space. The superposition of data taken with different si yields the information about a low pass filtered image of V. To extend the range of objects that can be imaged, many attempts have been made to evaluate higher-order terms of the Born series approaching the solution of Eq. 1 by means of iterative numerical methods. However, without significant further sophistication, the convergence of the Born series, and hence the validity of reconstruction methods based on it, is still limited to objects with small k0Va, with "a" being a measure of the physical extent of V.
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