  Extending our prior work, we propose a multi-energy X-ray measurement model
incorporating material variability with energy correlations to enable the
analysis and exploration of the performance of X-ray imaging and sensing
systems. Based on this measurement model, we provide analytical expressions for
bounds on the probability of error, $P_e$, to quantify the performance limits
of an X-ray measurement system for binary classification task. We analyze the
performance of a prototypical X-ray measurement system to demonstrate the
utility of our proposed material variability measurement model.
