MLEM Uncertainty Analysis For Neutron Spectroscopy Using SVD & KLT

Neutron spectroscopy is an important tool in the study of (p,n), (d,n), and (α,n) reactions. Due to their lack of charge, detecting neutrons, particularly their incident energy, is challenging. Typically, neutron spectroscopy is performed using the time-of-flight (ToF) method, however, an external timing signal is not always available. Therefore, spectrum unfolding, combined with deuterated liquid scintillators, allows for neutron energy detection without use of ToF. Spectrum unfolding using a Maximum Likelihood Expectation Maximization (MLEM) algorithm is a well-established approach for reconstructing incident neutron energy spectra. A key challenge in unfolding is the quantification of uncertainty in the reconstructed spectra. Without well-characterized uncertainties, the confidence in measured cross section uncertainties is limited. To address this, we incorporate methods for characterizing uncertainty propagation in the MLEM unfolding process such as Single Value Decomposition (SVD) and Karhunen-Loève Transform (KLT). These methods allow us to capture and identify how statistical noise and detector response influence the reconstructed spectra. This allows us to estimate the confidence intervals associated with each spectral bin and also improve signal to noise ratio.