Abstract: The enhanced coherent flux of revolutionary fourth-generation synchrotron x-ray sources like the APS-U will enable a variety of experimental possibilities in materials science that have so far remained out of reach. It will become routine to characterize condensed matter systems in hitherto difficult-to-access length and time scales/intervals. These experimental capabilities will necessarily be accompanied by the need to develop new analysis and mathematical inversion methods to correctly handle and interpret the diffraction data.

In this talk I will describe some aspects of these development efforts in the context of multi-scale characterization of crystalline and poly-crystalline materials, using high-energy coherent x-rays. Specifically, I will cover signal processing and data manipulation methods that enable this highly anticipated capability at the APS-U, along with some experimental proofs of concept. I will demonstrate the faithfulness of these computational methods to even the phase discontinuities in highly defected crystalline materials (typically problematic for conventional inversion techniques like iterative phase retrieval), all while addressing the constraints imposed by new diffraction geometries and high-energy coherence. Looking forward, I will describe how these methods are crucial to the development of robust forward models that will inform future machine learning tools and deep neural networks.