Detector Response Matrices, Effective Areas, and Flash-Effective Areas for Radiation Detectors

TL;DR

This paper discusses the mathematical representation of radiation detectors' responses, including response matrices and effective areas, to improve understanding of how detectors interpret incident radiation.

Contribution

It introduces a formal framework for detector response matrices, effective areas, and flash-effective areas for simple radiation detectors, linking incident particle distributions to detector signals.

Findings

Defines the Detector Response Matrix (DRM) and its relation to detector response functions.

Derives effective areas and flash-effective areas from the counting DRM.

Provides a mathematical basis for interpreting detector measurements.

Abstract

A Detector Response Matrix (DRM) is a discrete representation of an instrument's Detector Response Function (DRF), which quantifies how many discrete energy depositions occur in a detector volume for a given distribution of particles incident on the detector. For simple radiation detectors that can count such energy depositions (such as scintillators, Proportional Counter Tubes (PCTs), etc), we consider the ideal counting DRF, $\mathbf{G}_\varphi (E_\mathrm{in}, E_\mathrm{dep})$, which relates the detector's counting histogram (number of energy depositions within a given channel) to an incident particles characterization, $\varphi$ (e.g. incident flux, fluence, intensity). From the counting DRF we can derive the counting DRM, the effective area, and the flash effective area (which measures the total energy deposited in the detector from a large, instantaneous fluence).