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

4.3 The Reconstruction Program
In fig. 4.8 the logarithm of the likelihood function is shown for one plane of the grid including
the maximum value. It can be seen from this picture that the shape of ÐÓ Ä around the
maximum is well approximated by a parabolic shape. The position of an event is calculated
by parabolic interpolation from the grid point with the maximal ÐÓ Ä to its nearest neighbours.
Applying an overall fit instead of a direct interpolation could help to further improve
the position resolution.
Error Estimation
As the likelihood function can be approximated with a Gaussian, ÐÓ Ä can be written as
Ý ÐÓÄ
Ü Ý
The inverse square root of the second derivative is taken as an estimate for the error of the
reconstructed position. A larger value of corresponds to a less pronounced maximum of the
likelihood function.
The Optimum Grid Size
The optimum grid size was chosen as a compromise between resolution and size of the grid file
(i.e. memory usage and computing time). Comparing the results obtained with a grid size of
50 cm, 20 cm, 10 cm and 5 cm in the CTF, it turned out that the resolution doesn’t improve for a
grid size finer than 20 cm. For the CTF a 20 cm grid was used for all the following calculations.
For BOREXINO a 50 cm grid was used for the simulations, due to limited computing power.
For the reconstruction of real BOREXINO events, one possibility would be to presort the events
according to their ‘center of light’-position into several subvolumes of the detector and use a
finer grid for the reconstruction in these smaller volumes. The ‘center of light’ usually lies
within 1 m distance from the real position, i.e. it is a good first guess for the real position of
the event.
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