Finite slice analysis (FINA)-A general reconstruction method for velocity mapped and time-sliced ion imaging.

Since the advent of ion imaging, one of the key issues in the field has been creating methods to reconstruct the initial 3D distribution of particles from its 2D projection. This has led to the development of a number of different numerical methods and fitting techniques to solve this fundamental issue in imaging. In recent years, slice-imaging methods have been developed that permit direct recording of the 3D distribution, i.e., a thin slice of the recoiling fragment distribution. However, in practice, most slice imaging experiments achieve a velocity slice width of around 10%-25% around the center of the distribution. This still carries significant out-of-plane elements that can blur the spectrum, lose fine resolution, and underestimate the contribution from slow recoiling products. To overcome these limitations, we developed a new numerical method to remove these out-of-plane elements from a sliced image. The finite sliced analysis method models the off-axis elements of the 3D particle distribution through the use of radial basis functions. Once applied, the method reconstructs the underlying central slice of the 3D particle distribution. The approach may be applied to arbitrarily sliced or unsliced data and has the further advantage that it neither requires nor enforces full cylindrical symmetry of the data. We demonstrate this reconstruction approach with a broad range of synthetic and experimental data that, at the same time, allows us to examine the impact of finite slicing on the recovered distributions in detail.