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

## TL;DR

This paper introduces an automatic differentiation-based reconstruction method for x-ray nanotomography that models multiple scattering and diffraction effects, applicable to various microscopy techniques, using TensorFlow for flexible optimization.

## Contribution

It presents a novel iterative reconstruction approach that accounts for complex scattering phenomena in thick samples, leveraging deep learning tools for improved flexibility.

## Key findings

- Effective modeling of multiple scattering and diffraction in thick specimens.
- Versatile application to full-field and coherent microscopy techniques.
- Implementation demonstrates ease and adaptability using TensorFlow.

## Abstract

Conventional tomographic reconstruction algorithms assume that one has obtained pure projection images, involving no within-specimen diffraction effects nor multiple scattering. Advances in x-ray nanotomography are leading towards the violation of these assumptions, by combining the high penetration power of x-rays which enables thick specimens to be imaged, with improved spatial resolution which decreases the depth of focus of the imaging system. We describe a reconstruction method where multiple scattering and diffraction effects in thick samples are modeled by multislice propagation, and the 3D object function is retrieved through iterative optimization. We show that the same proposed method works for both full-field microscopy, and for coherent scanning techniques like ptychography. Our implementation utilizes the optimization toolbox and the automatic differentiation capability of the open-source deep learning package TensorFlow, which demonstrates a much straightforward way to solve optimization problems in computational imaging, and endows our program great flexibility and portability.