Cascaded‐systems analyses and the detective quantum efficiency of single‐Z x‐ray detectors including photoelectric, coherent and incoherent interactions

Abstract

Theoretical models of the detective quantum efficiency (DQE) of x-ray detectors are an important step in new detector development by providing an understanding of performance limitations and benchmarks. Previous cascaded-systems analysis (CSA) models accounted for photoelectric interactions only. This paper describes an extension of the CSA approach to incorporate coherent and incoherent interactions, important for low-Z detectors such as silicon and selenium. A parallel-cascade approach is used to describe the three types of x-ray interactions. The description of incoherent scatter required developing expressions for signal and noise transfer through an "energy-labeled reabsorption" process where the parameters describing reabsorption are random functions of the scatter photon energy. The description of coherent scatter requires the use of scatter form factors that may not be accurate for some crystalline detector materials. The model includes the effects of scatter reabsorption and escape, charge collection, secondary quantum sinks, noise aliasing, and additive noise. Model results are validated by Monte Carlo calculations for Si and Se detectors assuming free-atom atomic form factors. The new signal and noise transfer expressions were validated by showing agreement with Monte Carlo results. Coherent and incoherent scatter can degrade the DQE of Si and sometimes Se detectors depending on detector thickness and incident-photon energy. Incoherent scatter can produce a substantial low-frequency drop in the modulation transfer function and DQE. A generally useful CSA model of the DQE is described that is believed valid for any single-Z material up to 10 cycles/mm at both mammographic and radiographic energies within the limitations of Fourier-based linear-systems models and the use of coherent-scatter form factors. The model describes a substantial low-frequency drop in the DQE of Si systems due to incoherent scatter above 20-40 keV.