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

arXiv: https://arxiv.org/abs/1905.10433 · HTML: https://mlsanity.com/paper/1905.10433/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 May 2019.

## Built on by (most cited first, 5 of 5)

- [Compressive Ptychography using Deep Image and Generative Priors](https://mlsanity.com/paper/2205.02397/) (2022)
- [Differentiable Uncalibrated Imaging](https://mlsanity.com/paper/2211.10525/) (2022)
- [Learning neural representations for X-ray ptychography reconstruction with unknown probes](https://mlsanity.com/paper/2509.04402/) (2025)
- [Fidelity-preserving enhancement of ptychography with foundational text-to-image models](https://mlsanity.com/paper/2509.04513/) (2025)
- [A Deep Generative Approach to Oversampling in Ptychography](https://mlsanity.com/paper/2207.14392/) (2022)

## Abstract (arXiv)

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.