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Overview

Overview. Introduction & Motivation Likelihood Formulation wf-llh-reco project in IceTray Preliminary Results using Simulation V01-00-03 Connections to other projects & future directions Discussion. Introduction & Motivation. All reconstruction algorithms in IceRec are ported from AMANDA.

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Overview

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  1. Berkeley

  2. Overview • Introduction & Motivation • Likelihood Formulation • wf-llh-reco project in IceTray • Preliminary Results using Simulation V01-00-03 • Connections to other projects & future directions • Discussion Gary Hill & Sean Grullon

  3. Introduction & Motivation • All reconstruction algorithms in IceRec are ported from AMANDA. • Were originally developed for the Muon-DAQ… (TOTs, LEs, Peak Amp.) • Need new algorithm(s) to take advantage of the full waveform information Icecube provides. • A high priority since deployment has already begun. Gary Hill & Sean Grullon

  4. Likelihood Formulation • How can you formulate a likelihood function with the full waveform at your disposal? • Consider first the ideal case where the OM time response is a delta function • Ignore any possible amplitude fluctuations for the moment. • Given an expected distribution of photons μp(t), what is the probability of observing a waveform f(t)? • p(t) is normalized timing probability, μ is the total number of expected photons, given either numerically (Photonics) or analytically (e.g. Pandel) • f(t) is your observed waveform Gary Hill & Sean Grullon

  5. Probability of f(t) given p(t)? • Suppose you bin the photon distributions into k bins: Gary Hill & Sean Grullon

  6. Probability of {ni } | {μi} ? • The probability is given by Poisson statistics, as a product of Poisson probabilities over all the k bins: Gary Hill & Sean Grullon

  7. This product turns into something useful…. Gary Hill & Sean Grullon

  8. … Namely a multinomial distribution, the probability of arranging exactly N events into k bins, multiplied by the Poisson probability of these N events occurring. Gary Hill & Sean Grullon

  9. We have our Likelihood Function • Take the negative log of it Gary Hill & Sean Grullon

  10. Where is this applicable? • We assumed we knew the photon arrival times precisely, or have a waveform made from the superposition of many photons. • If we have a non-delta function time response, this form is still applicable as long as our PDF is slowly varying over the region described by the OM time response. • Should be the case for our optical modules, typical pulse widths are narrow relative to the scale of expected photon arrival time distribution. Gary Hill & Sean Grullon

  11. wf-llh-reco module • The icetray implementation of this likelihood reconstruction. • Currently looking at (non-directional) cascades. • Uses UPandel for the timing PDF and PHit-PNoHit to get the expected PEs. • Uses the MIGRAD minimizer in ROOT’s TMinuit class. • Module in the sandbox area of SVN, named wf-llh-reco. Gary Hill & Sean Grullon

  12. Preliminary Results using Simulation V01-00-03 • Newest version of Simulation meta-project just released over the weekend. • 500 100-GeV cascade events were simulated with the vertex at the origin. • Three reconstruction modules compared in icetray: CFirst, cscd-llh and wf-llh-reco. Gary Hill & Sean Grullon

  13. Preliminary Results Using Simulation V01-00-03: Vertex X Gary Hill & Sean Grullon

  14. Preliminary Results using Simulation V01-00-03: Vertex Y Gary Hill & Sean Grullon

  15. Preliminary Results using Simulation V01-00-03: Vertex Z Gary Hill & Sean Grullon

  16. Preliminary Results using Simulation V01-00-03: Vertex T Gary Hill & Sean Grullon

  17. Future Directions • First and foremost, continue development and check the algorithm. • Incorporate Photonics as the “PDF of choice” for waveform reconstruction. • Look at other event types (directional cascades, muon tracks, high energy tracks, etc) • Optimize the minimization, perhaps use another minimizer? Gary Hill & Sean Grullon

  18. Discussion • Thoughts and Comments • Possible connection with other waveform based algorithms? Gary Hill & Sean Grullon

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