Erratum: "DAVIS: A direct algorithm for velocity-map imaging system" [J. Chem. Phys. 148, 194101 (2018)]

Tomographic reconstruction techniques optimized for velocity-map imaging applications

Examples of extracting meaningful information from image projection data using tomographic reconstruction techniques can be found in many areas of science. Within the photochemical dynamics community, tomography allows for complete three-dimensional (3D) charged particle momentum distributions to be reconstructed following a photodissociation or photoionization event. This permits highly differential velocity- and angle-resolved measurements to be made simultaneously. However, the generalized tomographic reconstruction strategies typically adopted for use with photochemical imaging-based around the Fourier-slice theorem and filtered back-projection algorithms-are not optimized for these specific types of problems. Here, we discuss pre-existing alternative strategies-namely, the simultaneous iterative reconstruction technique and Hankel Transform Reconstruction (HTR)-and introduce them in the context of velocity-map imaging applications. We demonstrate the clear advantages they afford, and how they can perform considerably better than approaches commonly adopted at present. Most notably, with HTR we can set a bound on the minimum number of projections required to reliably reconstruct 3D photoproduct distributions. This bound is significantly lower than what is currently accepted and will help make tomographic imaging far more accessible and efficient for many experimentalists working in the field of photochemical dynamics.

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.