TY - JOUR

T1 - The index of dispersion as a metric of quanta - unravelling the Fano factor

AU - Fullagar, Wilfred K.

AU - Paziresh, Mahsa

AU - Latham, Shane J.

AU - Myers, Glenn R.

AU - Kingston, Andrew M.

PY - 2017/8

Y1 - 2017/8

N2 - In statistics, the index of dispersion (or variance-to-mean ratio) is unity (sigma(2)/< x > = 1) for a Poisson-distributed process with variance sigma(2) for a variable x that manifests as unit increments. Where x is a measure of some phenomenon, the index takes on a value proportional to the quanta that constitute the phenomenon. That outcome might thus be anticipated to apply for an enormously wide variety of applied measurements of quantum phenomena. However, in a photon-energy proportional radiation detector, a set of M witnessed Poisson-distributed measurements {W-1, W-2,... W-M} scaled so that the ideal expectation value of the quantum is unity, is generally observed to give sigma(2)/< W > < 1 because of detector losses as broadly indicated by Fano [Phys. Rev. (1947), 72, 26]. In other cases where there is spectral dispersion, sigma(2)/< W > > 1. Here these situations are examined analytically, in Monte Carlo simulations, and experimentally. The efforts reveal a powerful metric of quanta broadly associated with such measurements, where the extension has been made to polychromatic and lossy situations. In doing so, the index of dispersion's variously established yet curiously overlooked role as a metric of underlying quanta is indicated. The work's X-ray aspects have very diverse utility and have begun to find applications in radiography and tomography, where the ability to extract spectral information from conventional intensity detectors enables a superior level of material and source characterization.

AB - In statistics, the index of dispersion (or variance-to-mean ratio) is unity (sigma(2)/< x > = 1) for a Poisson-distributed process with variance sigma(2) for a variable x that manifests as unit increments. Where x is a measure of some phenomenon, the index takes on a value proportional to the quanta that constitute the phenomenon. That outcome might thus be anticipated to apply for an enormously wide variety of applied measurements of quantum phenomena. However, in a photon-energy proportional radiation detector, a set of M witnessed Poisson-distributed measurements {W-1, W-2,... W-M} scaled so that the ideal expectation value of the quantum is unity, is generally observed to give sigma(2)/< W > < 1 because of detector losses as broadly indicated by Fano [Phys. Rev. (1947), 72, 26]. In other cases where there is spectral dispersion, sigma(2)/< W > > 1. Here these situations are examined analytically, in Monte Carlo simulations, and experimentally. The efforts reveal a powerful metric of quanta broadly associated with such measurements, where the extension has been made to polychromatic and lossy situations. In doing so, the index of dispersion's variously established yet curiously overlooked role as a metric of underlying quanta is indicated. The work's X-ray aspects have very diverse utility and have begun to find applications in radiography and tomography, where the ability to extract spectral information from conventional intensity detectors enables a superior level of material and source characterization.

KW - Monte Carlo methods

KW - Detector development

KW - High-quality data refinement

KW - Polychromatic methods

KW - Quantum energy determination

KW - Spectrum modelling

UR - https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=anu_research_portal_plus2&SrcAuth=WosAPI&KeyUT=WOS:000406756100017&DestLinkType=FullRecord&DestApp=WOS_CPL

U2 - 10.1107/S2052520617009222

DO - 10.1107/S2052520617009222

M3 - Article

C2 - 28762978

VL - 73

SP - 675

EP - 695

JO - Acta Crystallographica Section B-structural Science Crystal Engineering and Materials

JF - Acta Crystallographica Section B-structural Science Crystal Engineering and Materials

ER -