UNDERWOOD1	Abel inversion of photoelectron and photoion imaging data
Type	Theoretical
#students	1
Orientation	Why is the scientific problem of interest at all? Velocity map imaging is a technique used in molecular physics to tomographically measure recoil velocity distributions of electrons and ions ejected during photofragmentation processes such as photoionization. The retrieval of the fragment distribution from the measured image is described mathematically by the inverse Abel transform. However, the naive implementation of this inversion is very noisy. As such, over the years various strategies to invert observed images have been proposed. Further reading: 1. "Imaging in Molecular Dynamics", Edited by B. J. Whitaker, Cambridge University Press 2003. http://dx.doi.org/10.1017/CBO9780511535437 2. "Photoelectron imaging spectroscopy: Principle and Inversion method", C. Bordas, F. Pauling, H. Helm and D. L. Huestis, Rev. Sci. Instrumen. 67, 2257 (1996).
How	How is the research going to shed light on the given problem?. The aim of this project is to compare different inversion methodsto determine the optimal approach to the problem. It is anticipated that a new approach to the inversion problem will result from this work.
What	What is the specific thing that the student will do, and how does it fit inside the overall project? This project will involve implementing a number of algorithms for doing the inversion process described above, allowing for a direct comparison of the properties of each approach in order to establish the best algorithm. Having established the optimum algorithm, a data pipeline will be constructed in order to process experimental images obtained recently. This work will build on an existing code base.
Special Knowledge	This computational project is suitable for a student with a keen interest in computing applied to physics experiments. This project requires a good working knowledge of Python.
Supervisor	Dr Jonathan G. Underwood j.underwood@ucl.ac.uk