Overview

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Overview

• Introduction Motivation
• Likelihood Formulation
• waveform-loglikelihood-reco project in IceCube
  software framework
• Preliminary Results using IceCube simulated Data
• Current Development and Future Directions

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Introduction Motivation

• All reconstruction algorithms in IceCube are
  ported from AMANDA.
• Originally developed for AMANDAs primary DAQ.
• records Time over Threshold (TOT), the leading
  edge time (LE), and the Peak Amplitude.
• The Full waveform is not captured
• Incorporates Leading Edge time peak amplitude
  information only.
• Uses the Pandel function which analytically
  parameterizes timing PDF in ice.
• Ice assumed to be homogeneous.
• Full detail regarding the AMANDA reconstruction
  algorithms can be found at Nuc. Ins. Meth. A 524
  169(2004)
• Focus of talk is on the development of a new
  reconstruction aglorithm using the full waveform

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IceCube waveforms

• IceCubes Analog Transient Waveform Digitizer
  (ATWD) captures and digitizes full waveform in
  situ with a 420 ns time window
• Should prove powerful for high energy
  non-contained events.
• FWHM of Waveform Depends linearly on the distance
  from the event to the optical module
• New algorithms need to be developed to take
  advantage of full waveform information
• A high priority since deployment has already
  begun.

Voltage (mV)
ATWD Sample
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Example Extracted waveform

• Event generated by Nitrogen laser located at a
  depth of 1850 m in AMANDA Array. Pulse Shapes
  recorded at 3 distances from laser. (45m, 115m,
  and 167m)

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Likelihood Formulation

• How can you formulate a likelihood function with
  the full waveform at your disposal?
• With the full waveform, we know
• arrival time distribution of the photons
• the probability of these arrival times.
• Given an expected distribution of photons µp(t),
  what is the probability of observing a waveform
  f(t)?
• p(t) is normalized timing PDF, µ is the total
  number of expected photons, given either
  numerically or analytically.
• f(t) is your observed waveform

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Probability of f(t) given p(t)?

• Suppose you bin the photon distributions into k
  time bins

• The probability is given by Poisson statistics,
  as a product of Poisson probabilities over all
  the k bins

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This product turns into something useful.
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We have our Likelihood Function

• Take the negative log of it

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Our likelihood function cont.

• Likelihood minimized for every optical module

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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.

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IceCube software framework

• The IceCube software framework is called IceTray.
• unified object oriented C framework for
  handling online filtering and offline-software
  for reconstruction, analysis, and simulation.
• IceTray modules operate on the IceCube data
  stream.
• Modules perform specialized tasks such as
  reconstructions, calibrations, etc.
• Uses boost C libraries for offline data. Data
  can be saved into a binary format or XML format.
  

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IceCube data stream
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Waveform loglikelihood reconstruction project

• This likelihood reconstruction algorithm is
  currently implemented in IceTray.
• Currently reconstructing electromagnetic
  cascades.
• User has the option of selecting an analytical
  PDF (Pandel function) or a numerical PDF.
• The numerical PDF in IceCube is Photonics, a
  numerical framework that simulates photon
  propagation in the ice.
• Uses the SIMPLEX minimizer.
• Uses calibrated ATWD waveform directly.

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Preliminary Results

• 2500 cascade events with an energy of 100 TeV
  generated
• Generated with a random vertex position and
  direction.
• Full IceCube simulation used.
• ¼ of the events are not contained in the array
  (Up to 50 m away)
• Free parameters of fit are the vertex, the
  energy, and the time.
• Results compared to the AMANDA style cascade
  reconstruction algorithm.

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Preliminary Results Using Full Simulation Vertex
X
RMS 38.15
RMS 49.62

• Accurate Vertex Reconstruction requires
  directional fit
• Results not a final performance indication

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Preliminary Results Using Full Simulation
Vertex Y
RMS 36.32
RMS 48.62
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Preliminary Results Using Full Simulation Vertex
Z
RMS 29.65
RMS 51.23
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Preliminary Results Using Full Simulation Energy
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Current Development and Future Directions

• Currently testing new Photon tables with 3-D
  photon tracking as the PDF for reconstruction
• Investigate reconstructing the cascade direction.
• Make the project part of the official IceTray
  release.
• Look at some sort of hit cleaning to improve
  results
• Improve algorithm performance for non-contained
  events.
• Look at other event types
• Optimize the performance