Abstract: As the spatial resolution of X-ray imaging is pushed toward the diffraction limit, depth of focus emerges as a non-negligible problem for 3-D imaging. When the specimen becomes larger than the depth of focus, the pure-projection approximation fails. This issue has been addressed in part by the use of multislice methods to reconstruct several depth planes that are then combined to yield an approximation of a pure projection. However, these methods do not provide an isotropic resolution and suffer from interslice seeping when two slices are arranged too closely.

We describe here an optimization-based approach to recover extended 3-D with isotropic voxel size. In particular, the optimization of the object function in our algorithm is implemented by using the auto matic differentiation function of Tensorflow, a well-known deep learning software.This allows us to avoid the tough and tedious manual derivation of the update function and makes the interface of our program highly accessible and flexible. Moreover, since the proposed algorithm works with full-field transmission microscopy data, it is compatible with alternative high-resolution imaging techniques such as point-projection X-ray microscopy, where one may work with partially coherent sources where the propagation fringes from any single object feature do not extend beyond the coherence width.