Higher order (nonlinear) diffraction tomography: inversion of the Rytov series

Nonlinear tomographic reconstruction algorithms are developed for inversion of data measured in scattering experiments in which the complex phase of the wavefields is modeled by an arbitrarily large (possibly infinite) number of terms in the Rytov series. The algorithms attain the form of a Volterra series of nonlinear operators, with the usual filtered backpropagation algorithm of diffraction tomography as the leading linear term. A computer simulation study is included to illustrate the performance of the algorithms for the case of scattering objects with cylindrical symmetry.