SHARP: Math for Ptychography
Scientists at the Advanced Light Source (ALS), Uppsala University, and The Center for Advanced Mathematics for Energy Research Applications (CAMERA) have worked together to create new algorithms for the fast reconstruction of
ptychographic data. Ptychography works by combining from multiple overlapping reflections recorded on a two-dimensional CCD array in such a way as to recover the relative phase from neighboring measurements. Taken together, these images can reconstruct with high accuracy over a large field of view.
However, iterating through the information from all these interconnected images in order to perform a reconstruction is typically expensive. The goal is to try to understand the graph level communication involved in combining neighboring information with the intent of constructing a more efficient approach.
A highly efficient new approach "SHARP" has been developed by the ALS-Uppsala-CAMEA collaboration. SHARP (Scalable Heterogeneous Adaptive Real-time Ptychography), is now in use at the ALS. Rather than iterate locally on each neighboring frames, which can require many steps to converge, a central idea in the new mathematics behind SHARP is recast the problem in a higher dimensional space that leads to a very natural connectivity pattern, which can then be exploited to set the stage for a very efficient iterative technique. The result is a highly efficient approach which can perform reconstructions over large length scales.
Future challenges include dealing with polarization issues, noise and bias problems, and combined ptycho-tomography.
The effort includes work from S. Marchesini and D.A. Shapiro (ALS); H. Krishnan, T. Perciano, and J.A. Sethian (CAMERA); and B.J. Daurer and F.R.N.C. Maia (Uppsala). ,