Arbitrary image reinflation: A deep learning technique for recovering 3D photoproduct distributions from a single 2D projection

Many charged particle imaging measurements rely on the inverse Abel transform (or related methods) to reconstruct three-dimensional (3D) photoproduct distributions from a single two-dimensional (2D) projection image. This technique allows for both energy- and angle-resolved information to be recorded in a relatively inexpensive experimental setup, and its use is now widespread within the field of photochemical dynamics. There are restrictions, however, as cylindrical symmetry constraints on the overall form of the distribution mean that it can only be used with a limited range of laser polarization geometries. The more general problem of reconstructing arbitrary 3D distributions from a single 2D projection remains open. Here, we demonstrate how artificial neural networks can be used as a replacement for the inverse Abel transform and-more importantly-how they can be used to directly "reinflate " 2D projections into their original 3D distributions, even in cases where no cylindrical symmetry is present. This is subject to the simulation of appropriate training data based on known analytical expressions describing the general functional form of the overall anisotropy. Using both simulated and real experimental data, we show how our arbitrary image reinflation (AIR) neural network can be utilized for a range of different examples, potentially offering a simple and flexible alternative to more expensive and complicated 3D imaging techniques.