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In diffraction tomography, the generalized Radon theorem relates the Fourier transform (FT) of the diffracted field to the two-dimensional FT of the diffracting object. The relationship stands on algebraic contours, which are semicircles in the case of Born or Rytov first-order linear approximations. But the corresponding data are not sufficient to determine uniquely the solution. We propose a maximum entropy method to reconstruct the object from either the Fourier domain data or directly from the original diffracted field measurements. To do this, we give a new definition for the entropy of an object considered as a function of R2 to C. To take into account the presence of noise, a chi-squared statistic is added to the entropy measure. The objective function thus obtained is minimized using variational techniques and a conjugate-gradient iterative method. The computational cost and practical implementation of the algorithm are discussed. Some simulated results are given which compare this new method with the classical ones.
© 1987 Optical Society of America
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