We present an alternative numerical reconstruction algorithm for direct tomographic reconstruction of a sample's refractive indices from the measured intensities of its far-field coherent diffraction patterns. We formulate the well-known phase-retrieval problem in ptychography in a tomographic framework which allows for simultaneous reconstruction of the illumination function and the sample's refractive indices in three dimensions. Our iterative reconstruction algorithm is based on the Levenberg-Marquardt algorithm and we demonstrate the performance of our proposed method with simulated and real datasets.Ptychography or CDI phase retrieval algorithms replace the purpose of an image forming lens by recovering the unknown phase numerically, using iterative algorithms mostly based on some type of optimization scheme. A few exceptions to these methods exist with closed-form solutions [2], [3] but their high sampling requirements make their application practically infeasible.
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