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 -