<i>μ</i> TRec: A muon trajectory reconstruction algorithm for enhanced scattering tomography

Abstract

Cosmic ray muons are highly penetrating subatomic particles, making muon tomography a powerful non-invasive technique for imaging dense and large-scale structures. As muons traverse matter, they undergo multiple Coulomb scattering (MCS), deviating from their original trajectory. The degree of scattering is dependent on the material’s atomic number (Z), enabling the identification and differentiation of materials. Muon tomography has found applications in diverse fields such as geology, archaeology, and nuclear security. Traditionally, reconstruction algorithms such as the Straight-Line Path (SLP) and Point of Closest Approach (PoCA) have been employed for muon imaging. However, these methods assume single scattering and fail to accurately represent the cumulative nature of MCS. This paper introduces a novel reconstruction method, the Muon Trajectory Reconstruction (μTRec) algorithm, which provides a more accurate approximation of the muon path by incorporating a statistical framework. Based on a Bayesian framework with Gaussian approximations, the proposed μTRec algorithm reconstructs the curved trajectories of muons as they traverse matter, incorporating both multiple Coulomb scattering and linear energy loss to accurately map scattering angles along the path. The proposed algorithm is applied to simulate imaging of dry casks used for spent nuclear fuel storage considering the horizontal orientation. Four cask loading conditions are evaluated: fully loaded, one row missing, one assembly missing, and half assembly missing. Simulations are performed using 105 and 106 muons to assess imaging performance. The results demonstrate improved accuracy and resolution in identifying missing assemblies compared to conventional methods. It is observed that the μTRec algorithm exhibits markedly superior performance over the classical PoCA method achieving respective improvements of 132% in signal-to-noise ratio, 43% in contrast-to-noise ratio, and 232% in detection power for the case of one missing fuel assembly with muon events of 106 and a voxel size of 5 cm. Furthermore, μTRec supports high-resolution reconstruction with voxel sizes as small as 1 cm, which enables the accurate localization of structural components such as the 2.5 cm thick steel canister. Notably, μTRec is also capable of reliably detecting a single missing fuel assembly at muon events as low as 105, a task that remains infeasible using PoCA under the same conditions.