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Understanding the Probability Density Function of Light Detection from LED Beacons

This document explores the Probability Density Function (PDF), which quantifies the likelihood of detecting a photon emitted by an LED at a specific arrival time. By fitting the PDF to LED data, we can deduce critical properties of the medium through which the light travels. It covers essential topics, including light source characteristics, light propagation models, and specific absorption and scattering phenomena like Rayleigh and Mie scattering. This implementation enables the calculation of the PDF as a function of arrival time, distance, and detection orientation, offering valuable insights into photon behavior in various mediums.

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Understanding the Probability Density Function of Light Detection from LED Beacons

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  1. PDF for LED beacons M. de Jong

  2. Probability Density Function • What? • The PDFis a function that describes the relative likelihood of a photon from a LED to be detected at a given arrival time. • Why? • A fit of the PDFto LED dataallows for a direct determination of the properties of the medium.

  3. Topology z’ z y’ qr fr x’ PMT D 4D-bin q0 [D][cosq0][qr][fr] (0,0,0) LED

  4. Input • Light source characteristics • i.e: Valencia? • Light propagation model • absorption • scattering • Rayleigh • Mie • Implementation¶ • single light scattering approximation ¶ ANTARES-SOFT-2011-004

  5. Output • PDF as a function of arrival time for a given • distanceD • direction cosine cosq0 • orientation PMT qr, fr • Implementation • PDF = f(ls, labs, a, b, ...; t ) • where = f(a, b, ...)

  6. Measurements • absorption • labs(l) • scattering • Rayleigh • ls(l) ( is known from theory) • Mie • ls(l) and = f(a, b, ...)?

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