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Conventional tomographic reconstruction algorithms assume that one hasobtained pure projection images, involving no within-specimen diffractioneffects nor multiple scattering. Advances in x-ray nanotomography are leadingtowards the violation of these assumptions, by combining the high penetrationpower of x-rays which enables thick specimens to be imaged, with improvedspatial resolution which decreases the depth of focus of the imaging system. Wedescribe a reconstruction method where multiple scattering and diffractioneffects in thick samples are modeled by multislice propagation, and the 3Dobject function is retrieved through iterative optimization. We show that thesame proposed method works for both full-field microscopy, and for coherentscanning techniques like ptychography. Our implementation utilizes theoptimization toolbox and the automatic differentiation capability of theopen-source deep learning package TensorFlow, which demonstrates a muchstraightforward way to solve optimization problems in computational imaging,and endows our program great flexibility and portability.

Three dimensions, two microscopes, one code: automatic differentiation for x-ray nanotomography beyond the depth of focus limit