Deconvolving two-dimensional images of three-dimensional momentum trajectories

Abstract

A deconvolution technique to eliminate the azimuthal contribution from two-dimensional (2D) images of three-dimensional momentum trajectories is presented. The technique, which in some respects is superior to Abel and similar numerical inversion methods, exploits numerical simulation to generate a 2D polar representation of the dynamics where the radius from the center of the image is proportional to the magnitude of the momentum and the angle is the ejection angle relative to the polarization axis of the laser. A sample deconvolution for the three-body Coulomb explosion of NO2 is shown.

Toward real-time charged-particle image reconstruction using polar onion-peeling

“…Our method fundamentally differs from that of Zhao et al 17 in how g fit ͑r ; R , ␣͒ is generated. In order to retain the low computational expense of onion-peeling, we borrow ideas from the BASEX methods, 11,12 in which basis sets are used in order to fit the experimental 2D data.…”

“…At each r, g͑r ; R , ␣͒ is subtracted from G͑R , ␣͒, which effectively "peels away" the -contributions at each r. Hence, this method has been termed onion-peeling and it is particularly intuitive in polar coordinates. POP was first introduced by Zhao et al 17 who also present a thorough discussion of the benefits of onionpeeling in polar over Cartesian coordinates. The method presented here is in essence equivalent, however, the main restriction of their method has been its computational expense and general applicability.…”

“…However, in Cartesian coordinates it suffers from error accumulation because one must start at the outermost point on the detector, where the signal is smallest due to the Jacobian in going from 3D spherical coordinates ͑the laser-matter interaction system͒ to 2D Cartesian ͑the detection system͒. This problem can be alleviated by onion-peeling in polar coordinates, 17 in which the error at large radii is reduced and error accumulation is not a major concern. Additionally, it relaxes the need for a high kinetic energy at the detector with respect to the initial energy.…”

“…However, POP as currently developed is slow, thus loosing a lot of onion-peeling's appeal. 17 Additionally, POP has not been directly compared to other methods and onionpeeling in general is perceived to be inferior to BASEX and many other methods in terms of accuracy and its handling of noise.…”

“…Additionally, it relaxes the need for a high kinetic energy at the detector with respect to the initial energy. 17 Like pBASEX and the iterative methods, POP reduces the centerline noise to a spot at the center of the image. However, POP as currently developed is slow, thus loosing a lot of onion-peeling's appeal.…”