Development of a Liquid Scintillator and of Data ... - Borexino - Infn

4 Position Reconstruction of Scintillation Events
Figure 4.7: The probability density function for a single photoelectron Ø in the CTF, averaged
over all 100 PMTs for two different locations inside the scintillator: in the center (0,0,0) and at
(60cm,60cm,40cm).
4.3 The Reconstruction Program
The reconstruction is based on a maximum likelihood method. For a given measured event (=
a number of time and pulse height signals) the program scans the grid and calculates for each
grid point the probability that the event could have taken place at this grid point. The point
with the highest probability, with an interpolation to its nearest neighbours, is assumed to be
the place where the event occurred.
The Likelihood Function
The likelihood function can be written as
Ä Ü Ý Þ
ÆØ
Ô ØÒÜÝÞ
where Ô ØÒÜÝÞ is the normalized probability, that the i-th PMT registers Ò photoelectrons
after the time Ø, under the assumption that the photons were emitted at the point Ü Ý Þ .
In practice, one maximizes ÐÓ Ä, which is the sum of ÐÓ Ô ØÒÜÝÞ .
The Single Photoelectron Probability Density Function
The arrival time of each photoelectron follows a probability density function Ø which is a
convolution of the decay time of the scintillator, the time of flight of the photon through the
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