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

TL;DR

This work establishes a framework to quantify how incident particle environments produce detector energy depositions through discrete Detector Response Matrices (DRMs). By defining the counting DRF $\mathbf{G}_\varphi(E_\mathrm{in}, E_\mathrm{dep})$, discretizing it into a tally-based DRM, and introducing kernel concepts like the Counting Effective Area $\mathbf{A}_\varphi$ and the Flash Effective Area $\mathbf{F}_\varphi$, the paper enables efficient computation of instrument counts and energy deposition for specified incident spectra. It also provides practical normalization schemes for plane-wave and isotropic flux inputs, yielding explicit forms for the DRM under common geometries (e.g., $\mathbf{G}_\Phi^{(j,k)}$). The Total Average Effective Area and thresholded extensions offer a compact summary metric of detector response across energy ranges, facilitating rapid comparisons and integration into mission analyses for radiation detectors.

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).

Figures (3)

• Figure 1: Basic scintillation detector. An incident particle of ionizing radiation characterized by its incident energy, $E_{\mathrm{in}}$ (1), deposits an amount of energy $E_{\mathrm{dep}}$, in a volume of scintillator (cyan) and releases scintillation light (2). Some of this light travels through the scintillator and causes the emission of a photo-electron (3) at the cathode of an attached photomultiplier tube (PMT). This photo-electron cascades and multiplies through the high voltage dynode chain (4) and produces an analog current signal at the output (5), which can be input into a multichannel analyser (MCA). The size of this analog pulse is proportional to the energy deposition ($E_{dep}$) in the scintillator at (2).
• Figure 2: Geometry for describing intensity, $J$ of particles at a point in space. Adapted from "Radiative Processes in Astrophysics" by Rybicki and Lightman 1979rpa..book.....R.
• Figure 3: Tally Matrix, $n_\mathrm{j,k}$, of number of energy depositions occurring in detector volume within $E_\mathrm{dep}^{(j)} \le E_\mathrm{dep} < E_\mathrm{dep}^{(j+1)}$, for incident particles with energy within $E_\mathrm{in}^{(k)} \le E_\mathrm{in} < E_\mathrm{in}^{(k+1)}$. Red bins track number of incident particles that resulted in no energy deposition, $E^\mathrm{(j)}_\mathrm{dep}=0$ (which can also be thought of as 'underflow' bins).