Ptychographic imaging via set projection algorithms

Andrew Maiden
University of Sheffield

Ptychography is a diffractive imaging method where a coherent illumination source – from a laser, X-ray beam or electron gun – is scanned across a target sample, generating a series of scatter patterns that are recorded by a camera. These patterns are passed to an optimisation algorithm whose job is to find an image of the target sample that, when fed into an appropriate model of the experiment, results in a match to the measured data.

Set projection algorithms are one type of optimisation method particularly suited to this task. They solve optimization problems whose solution is subject to several constraints represented by sets within a search space, reaching this solution by combining and iterating between projections onto the sets. Ptychography fits very naturally into this framework, with each scatter pattern corresponding to a constraint set, and projections onto these sets implemented via the experimental model.

I will begin this talk using a simple geometric example to illustrate how set projection algorithms work. I will then use examples from visible light, X-ray and electron experiments to illustrate how they are applied to ptychographic imaging.

Back to Workshop II: Mathematical Advances for Multi-Dimensional Microscopy