256
C. W. Fabjan and D. Fournier
was required. In all precision experiments, the gain of the front-end electronics is
monitored by injecting precision electrical pulses, allowing subsequent corrections
to be made with a precision of 10 −3 or better.
6.4 Auxiliary Measurements
The analysis of shower properties provides important additional information on
position, angular direction and arrival time of the particles which initiated them.
Shower shape analysis gives insight on the particle nature. The efforts lavished by
the LHC collaborations on electron and muon identification and spectroscopy are
eloquent testimony.
6.4.1 Position and Angular Measurements
Conceptually, two methods can be used to obtain spatial information: transverse and
longitudinal granularity of the instrument on a scale smaller than the characteristic
showers sizes gives position and direction by ‘design’. Alternatively, if the readout
volume is far larger than the shower dimensions, spatial information may be
obtained by ‘triangulation’ using signals from several sensors distributed over the
outer surface of the calorimeter volume.
The latter approach is used for calorimeters with large sensitive volume read
out by photomultipliers distributed over their surface (e.g. Superkamiokande).
The position is obtained by measuring the difference of light arrival times at the
photomultipliers. With a timing resolution between 1 and 3 ns (depending on the
pulse height) a position resolution of 70 cm is obtained for 10 MeV showers inside
the sensitive volume.
In calorimeters with a more classical tower structure, the position of the incident
particle is obtained by calculating the energy-weighted barycentre of energy deposition, using a cluster of cells around the local maximum energy deposition. Because
of the finite size of the cells as compared to the Molière radius, the barycentre
position is biased towards the centre of the cell with the largest energy deposition.
This systematic bias can be corrected by fitting empirical functions. After applying
this correction the position accuracy scales as 1/
√
E (decrease of shower fluctuations
with increasing energy) convoluted with a constant and a noise term.
In the homogeneous NA48 krypton calorimeter (2 × 2 cm cells) a position
resolution σ x,y = (4.2/
√
E(GeV) ⊕ 0.6) mm was measured, while the Babar CsI
crystal calorimeter (4x4 cm crystals) gave slightly better results (3.2 mm/
√
E(GeV).
This difference is explained by the smaller Molière radius of CsI (3.8 cm, against
5.5 cm for liquid krypton) and larger signal to noise ratio.
Segmented calorimeters, especially sampling calorimeters with ionization readout, allow lateral and longitudinal segmentation. With two or more samplings in
C. W. Fabjan and D. Fournier
was required. In all precision experiments, the gain of the front-end electronics is
monitored by injecting precision electrical pulses, allowing subsequent corrections
to be made with a precision of 10 −3 or better.
6.4 Auxiliary Measurements
The analysis of shower properties provides important additional information on
position, angular direction and arrival time of the particles which initiated them.
Shower shape analysis gives insight on the particle nature. The efforts lavished by
the LHC collaborations on electron and muon identification and spectroscopy are
eloquent testimony.
6.4.1 Position and Angular Measurements
Conceptually, two methods can be used to obtain spatial information: transverse and
longitudinal granularity of the instrument on a scale smaller than the characteristic
showers sizes gives position and direction by ‘design’. Alternatively, if the readout
volume is far larger than the shower dimensions, spatial information may be
obtained by ‘triangulation’ using signals from several sensors distributed over the
outer surface of the calorimeter volume.
The latter approach is used for calorimeters with large sensitive volume read
out by photomultipliers distributed over their surface (e.g. Superkamiokande).
The position is obtained by measuring the difference of light arrival times at the
photomultipliers. With a timing resolution between 1 and 3 ns (depending on the
pulse height) a position resolution of 70 cm is obtained for 10 MeV showers inside
the sensitive volume.
In calorimeters with a more classical tower structure, the position of the incident
particle is obtained by calculating the energy-weighted barycentre of energy deposition, using a cluster of cells around the local maximum energy deposition. Because
of the finite size of the cells as compared to the Molière radius, the barycentre
position is biased towards the centre of the cell with the largest energy deposition.
This systematic bias can be corrected by fitting empirical functions. After applying
this correction the position accuracy scales as 1/
√
E (decrease of shower fluctuations
with increasing energy) convoluted with a constant and a noise term.
In the homogeneous NA48 krypton calorimeter (2 × 2 cm cells) a position
resolution σ x,y = (4.2/
√
E(GeV) ⊕ 0.6) mm was measured, while the Babar CsI
crystal calorimeter (4x4 cm crystals) gave slightly better results (3.2 mm/
√
E(GeV).
This difference is explained by the smaller Molière radius of CsI (3.8 cm, against
5.5 cm for liquid krypton) and larger signal to noise ratio.
Segmented calorimeters, especially sampling calorimeters with ionization readout, allow lateral and longitudinal segmentation. With two or more samplings in