3 years ago

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

The index of dispersion as a metric of quanta – unravelling the Fano factor
Glenn R. Myers, Mahsa Paziresh, Shane J. Latham, Andrew M. Kingston, Wilfred K. Fullagar
In statistics, the index of dispersion (or variance-to-mean ratio) is unity (σ2/⟨x⟩ = 1) for a Poisson-distributed process with variance σ2 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 {W1, W2,… WM} scaled so that the ideal expectation value of the quantum is unity, is generally observed to give σ2/⟨W⟩ < 1 because of detector losses as broadly indicated by Fano [Phys. Rev. (1947), 72, 26]. In other cases where there is spectral dispersion, σ2/⟨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.The need for high-quality assessments of data motivates appreciation of shot noise as a data resource. The index of dispersion is a critical but often overlooked metric in this regard. When properly understood and carefully used it reveals the energies of quanta, in both monochromatic and polychromatic situations. To accomplish this, and in due course its wider application, its conceptual origins and quantitative and physical bounds are identified. Situations are examined that involve large numbers of quanta, but in which individual quanta are below measurement noise threshold. Practical applications are extremely diverse, so relevant considerations and how to use the metric are shown in broad contexts.

Publisher URL: http://onlinelibrary.wiley.com/resolve/doi

DOI: 10.1107/S2052520617009222

You might also like
Discover & Discuss Important Research

Keeping up-to-date with research can feel impossible, with papers being published faster than you'll ever be able to read them. That's where Researcher comes in: we're simplifying discovery and making important discussions happen. With over 19,000 sources, including peer-reviewed journals, preprints, blogs, universities, podcasts and Live events across 10 research areas, you'll never miss what's important to you. It's like social media, but better. Oh, and we should mention - it's free.

  • Download from Google Play
  • Download from App Store
  • Download from AppInChina

Researcher displays publicly available abstracts and doesn’t host any full article content. If the content is open access, we will direct clicks from the abstracts to the publisher website and display the PDF copy on our platform. Clicks to view the full text will be directed to the publisher website, where only users with subscriptions or access through their institution are able to view the full article.