[continues from 4.8]
The position of a photon is computed by the Electronics
Unit based on the output of the PMT.
This process introduces a geometrical distortion because of three effects :
The relevant distortion has been modelled using ground measurements with a
multipinhole mask, and it is given as a third-order polynomial relation
converting unlinearized x,y pixel positions into
linearized X,Y positions in mm:
- spatial disuniformity of the PMT gain
- different viewing angles of different scintillation positions
- curvature of the Be window
with associated distortion of the electric field (energy dependent), due
to the difference of pressure between the inside of the gas cell and the vacuum outside.
In practice the above formula corresponds to a stepwise procedure in which :
The ten coefficients A1 to A10 are kept in files
- the coordinates are referred to the detector centre
x' = x-A1
y' = y-A2
- the distortion is described by a third-order polynomial in x',y'
- the energy dependency is in the first-order terms only
- in the software a further step is added converting back from X,Y positions
in mm to pixels of user-selected (arbitrary) size X',Y'
- in addition the software randomizes the original x,y position within plus
or minus half a pixel, in order to prevent artifacts due to integer-to-real conversion