Influence of experimental noise on densities reconstructed from line projections

TL;DR

This paper investigates how experimental noise affects the accuracy of density reconstructions from line projections, using simulations to analyze error propagation and anisotropy in reconstructed densities.

Contribution

It provides a detailed analysis of statistical noise impact on reconstructed densities and discusses the inherent errors of the reconstruction method, enhancing understanding of data reliability.

Findings

Error distribution peaks along symmetry directions

More density components reduce anisotropy in error distribution

Reconstruction errors are influenced by both noise and method limitations

Abstract

The influence of experimental noise on densities rho(p) reconstructed by the Cormack method from their line projections, e.g. 2D ACAR spectra, is investigated. Simulations of statistical noise are performed for various sets of 2D spectra for two model rho(p) having the cubic symmetry. For the reconstructed densities propagation of the statistical error in terms of standard deviations, sigma[rho(p)], is estimated. We observe that the distribution of sigma[rho(p)] has its extremes along the main symmetry directions and also a tendency to accumulate for small p. Moreover, the more density components, rho_n(p), have to be taken to description of rho(p) the less anisotropic is the distribution of sigma[rho(p)]. Additionally, the error generated by the reconstruction method itself is discussed.