# Presentation: 925741

## New Vertex Location and Energy Reconstruction TechniquesUsing  the Arrival Information of All Measured Photons

- New Vertex Location and Energy Reconstruction TechniquesUsing  the Arrival Information of All Measured Photons

- Rodín Porrata

- UC Berkeley, Price Group

**Notes:**
If one looks at the number of articles published in the Journal of Applied Optics it would seem that there is really a lot of stuff to know. 

However the problem of photon propagation is still basically unsolved.

Having said that, I will at the end of this talk write down for you a generalized Green function scribing the 

## New Vertex and Energy Reconstruction Techniques for Cascades

- Requirements:
- Self-contained (no external minimizer) -> usable online
- Very accurate vertex and energy reco -> usable offline
- Some history:     Spiesberger -> Vanderbrouke -> Porrata
- Spiesberger: Passive acoustic location of marine fauna.
- -> 	Basic SVD localization algorithm (assumes no delays).
- Vanderbrouke: Use to locate EHE GZK acoustic signals?
- Porrata: Adapt for use in environments where signal is scattered, i.e., photons from cascades scattered by dust in ice.
- Energy reconstruction obvious:
- if allowed to use all photon info, e.g., DOMs, TWR,
- if have very good vertex location.

**Notes:**
If one looks at the number of articles published in the Journal of Applied Optics it would seem that there is really a lot of stuff to know. 

However the problem of photon propagation is still basically unsolved.

Having said that, I will at the end of this talk write down for you a generalized Green function scribing the 

## Spiesberger’s SVD Porpoise Location Algorithm

- For each of N hit OMs define the following N **spherical wave** equations:

- Nonlinear in parameters.

- Where:

- Subtract the first equation from the rest, get N-1 **paraboloid** equations:

- The i are time differences.
- The *t**i *are the measured times assuming no scattering.
- The T*i *are unscattered light propagation times.

- These equations are linear in the 4 unknowns.

**Notes:**
If one looks at the number of articles published in the Journal of Applied Optics it would seem that there is really a lot of stuff to know. 

However the problem of photon propagation is still basically unsolved.

Having said that, I will at the end of this talk write down for you a generalized Green function scribing the 

## Spiesberger’s SVD Porpoise Location Algorithm

- Have N-1 linear **paraboloid** equations and 4 unknowns.

- Define:

- Where:

- Perform the singular value decomposition of **A**:

- Then the solution is given by:

- As is, must use time of **first hit** only, as estimate of unscattered light propagation time.

**Notes:**
If one looks at the number of articles published in the Journal of Applied Optics it would seem that there is really a lot of stuff to know. 

However the problem of photon propagation is still basically unsolved.

Having said that, I will at the end of this talk write down for you a generalized Green function scribing the 

## Method of Energy Reconstruction

- *i   *= average number of photoelectrons expected.
- n*i *= measured number of photoelectrons.

- Product of Poisson probabilities for seeing exactly n photoelectrons.

- Take the derivative w.r.t. the energy. Set to zero. Solve.

- Do not need 4800 separate quantities to calculate. One scalar vs position only!

- The solution is trivial provided that (we can really count photoelectrons):
- DAQ response is linear.
- Feature extraction of waveforms is linear.
- Have a good model of photon propagation and through the ice.
- Have already obtained an accurate vertex location.

**Notes:**
If one looks at the number of articles published in the Journal of Applied Optics it would seem that there is really a lot of stuff to know. 

However the problem of photon propagation is still basically unsolved.

Having said that, I will at the end of this talk write down for you a generalized Green function scribing the 

## Simulation

- Loop over events:
- Obtain event position and energy
- Loop over OMs:
- Calculate number of photoelectrons, (d, ), according to diffusive approximation.
- Poisson distribute to obtain nhits at OM.
- Distribute in time taking into account:
- Un-scattered light propagation time, and
- Gamma distribution provides time delays due to scattering.
- Write out hits
- Write out Event
- End loop

- Vfid = 4.07 km3,
- Vtrig (M=1) = 1.83 km3,

- Simulated 1000 isotropic point source events at 100 TeV in **dusty**
-  ice with a 4800 OM Ice3 array.

- These studies indicative only!

**Notes:**
If one looks at the number of articles published in the Journal of Applied Optics it would seem that there is really a lot of stuff to know. 

However the problem of photon propagation is still basically unsolved.

Having said that, I will at the end of this talk write down for you a generalized Green function scribing the 

## Testing the Algorithm in Dust Free Ice

- Cuts:
- Ndir > 10
- Chi2 < 10

- Results (are ludicrous):
- Veff = 1.5 km3
-  E = 0.011 in log(E)
- Fom = 136.0

**Notes:**
If one looks at the number of articles published in the Journal of Applied Optics it would seem that there is really a lot of stuff to know. 

However the problem of photon propagation is still basically unsolved.

Having said that, I will at the end of this talk write down for you a generalized Green function scribing the 

## Testing the Algorithm Blind

**Dusty** ice.
-  Cut: fit < 1 km

- Results (so-so):
- Veff = 2.28 km3
-  E = 0.16 in log(E)
- Fom = 14.25

**Notes:**
If one looks at the number of articles published in the Journal of Applied Optics it would seem that there is really a lot of stuff to know. 

However the problem of photon propagation is still basically unsolved.

Having said that, I will at the end of this talk write down for you a generalized Green function scribing the 

## Taking into Account the Distribution of the Photon Arrival Times in Dusty Ice

- Weight rows of **A **with:
- Use variance of distribution and number of hits to estimate delay from direct time.
- Subtract off estimated delay from measured time of first hit.
- Require at least 4 photons to determine variance of the distribution.

**Notes:**
If one looks at the number of articles published in the Journal of Applied Optics it would seem that there is really a lot of stuff to know. 

However the problem of photon propagation is still basically unsolved.

Having said that, I will at the end of this talk write down for you a generalized Green function scribing the 

## Taking into Account the Distribution of the Photon Arrival Times in Dusty Ice

- Weighted **A**
- Cuts:
- Concentration > 25
-  fit < 600 m

- Results:
- Veff = 0.79 km3
-  E = 0.11 in log(E)
- Fom = 7.18

**Notes:**
If one looks at the number of articles published in the Journal of Applied Optics it would seem that there is really a lot of stuff to know. 

However the problem of photon propagation is still basically unsolved.

Having said that, I will at the end of this talk write down for you a generalized Green function scribing the 

## Taking into Account the Distribution of the Photon Arrival Times in Dusty Ice

- Weighted **A**
- Subtracted estimated delay time.
- N > 4
- Concentration > 20
-  fit < 600 m

- Results:
- Veff = 1.07 km3
-  E = 0.074 in log(E)
- Fom = 14.5

- R. Porrata, Berkeley, March 2005

- Energy Resolution = 0.074

**Notes:**
If one looks at the number of articles published in the Journal of Applied Optics it would seem that there is really a lot of stuff to know. 

However the problem of photon propagation is still basically unsolved.

Having said that, I will at the end of this talk write down for you a generalized Green function scribing the 

## Conclusions, Caveats and Outlook

- Will reach energy reconstruction specifications at “first guess”!
- Have not yet taken into account direction. Working on this.
- Method strongly depends on Ice3’s advertised ability to make sense of waveform information! Seckel’s method looks like it will produce the most physically meaningful photon times.
-  Plan to code into IceRec software.
- Expect improvements as photon propagation is better modeled (see my earlier talk on photon propagation).
- Expect improvements when method is iterated.

**Notes:**
If one looks at the number of articles published in the Journal of Applied Optics it would seem that there is really a lot of stuff to know. 

However the problem of photon propagation is still basically unsolved.

Having said that, I will at the end of this talk write down for you a generalized Green function scribing the