# The Laser calibration of the ATLAS Tile Calorimeter during the LHC run 1

ATLAS Tile Calorimeter system

###### Abstract

This article describes the Laser calibration system of the ATLAS hadronic Tile
Calorimeter that has been used during the run 1 of the LHC. First, the
stability of the system associated readout electronics is studied. It is found
to be stable with variations smaller than 0.6 %. Then, the method developed to
compute the calibration constants, to correct for the variations of the gain
of the calorimeter photomultipliers, is described. These constants were
determined with a statistical uncertainty of 0.3 % and a systematic
uncertainty of 0.2 % for the central part of the calorimeter and 0.5 % for the
end-caps. Finally, the detection and correction of timing mis-configuration of
the Tile Calorimeter using the Laser system are also presented.

The ATLAS Tile Calorimeter [1, 2] (TileCal) is the central hadronic
calorimeter of the ATLAS experiment at the Large Hadron Collider (LHC) at
CERN. The TileCal is a sampling calorimeter whose operation is based on the
detection of scintillation light using photomultiplier tubes (PMTs). On
average, around 30 % of the total energy of jets from quark and gluon
fragmentation is deposited in the TileCal. It therefore plays an important
role for the precise reconstruction of the kinematics of the physics event.
The control of its stability, within 1 %, and resolution is important for a
correct jet and missing transverse energy reconstruction in ATLAS111The
designed energy resolution of jets is
$\sigma/E=50\%/\sqrt{E\mathrm{(GeV)}}\oplus 3\%$ and the systematic
uncertainty on the jet energy scale in ATLAS must be at most 1 %. See details
in [2].. In order to obtain a precise and stable measurement of the energy
deposited in the calorimeter, it is mandatory to precisely monitor any
variation of the gain222What is really monitored is the product of the PMT
photocathode quantum efficiency by the PMT gain. In this article, it is
assumed that any quantum efficiency variation is negligible over the typical
time scale of a few months and therefore the term PMT gain is used instead of
the product. of the PMTs and, if needed, correct for these variations. Several
complementary hardware calibration systems have therefore been included in the
TileCal design (see figure 1), one of them being the Laser system described in
this article.

Figure 1: Flow diagram of the readout signal paths of the different TileCal
calibration systems.

The calorimeter is briefly described in section 1, and the Laser system as it
was operational during run 1 of the LHC is detailed in section 2. A major
upgrade of this system was performed in 2014, but falls outside the scope of
this article. The study of the stability of the Laser electronics is discussed
in section 3 before the description of the calibration procedure in section 4.
Timing mis-configuration detection and correction are detailed in section 5
while monitoring of pathological calorimeter channels is briefly described in
section 6. Finally, conclusions are drawn in section 7.

##  1 The ATLAS Tile Calorimeter

The ATLAS detector is made of a central part, called the barrel, and two
endcaps. In the barrel, the TileCal is the only hadronic calorimeter of ATLAS.
In the endcaps, TileCal constitutes the external part of the hadronic
calorimeter, the internal part using the liquid argon technology. The part of
TileCal that is in the ATLAS barrel is called the _long barrel_ (LB), while
the parts that are in the endcaps are called the _extended barrels_ (EB).

The Tile Calorimeter is the result of a long process of R&D and construction.
The Technical Design Report [3] has been completed in 1995 and the
construction of the mechanical part ended in 2006. After a period of operation
using cosmic muons, the TileCal was ready in 2009 to record the first LHC
proton–proton collisions.

###  1.1 Mechanical aspects

TileCal is a non-compensating sampling calorimeter made of steel plates that
act as absorber and provide mechanical structure into which the active
scintillating tiles are inserted. Charged particles going through the tiles
produce scintillation light that is collected by two wavelength-shifting (WLS)
fibres, on each side of a tile. These fibres are then grouped in bundles to
form cells, organised in three radial layers, as depicted in figure 3, thus
achieving a granularity of about 0.1 in $\eta$333ATLAS uses a right-handed
coordinate system with its origin at the nominal interaction point (IP) in the
centre of the detector and the $z$-axis coinciding with the axis of the beam
pipe. The $x$-axis points from the IP to the centre of the LHC ring, and the
$y$-axis points upward. Cylindrical coordinates ($r$,$\phi$) are used in the
transverse plane, $\phi$ being the azimuthal angle around the beam pipe. The
pseudorapidity is defined in terms of the polar angle $\theta$ as
$\eta=-\ln\tan({\theta/2})$. for the layers A and BC (the closest to the
collision point) and around 0.2 in the outermost layer. Azimuthally, the
detector is segmented in 64 wedge-shaped modules (see figure 3), thus
achieving a granularity of $\Delta\phi=0.1$. The E cells are non-standard
calorimeter cells made of single large scintillators. Their aim is to measure
the energy of particles lost in the inactive material located in front of the
TileCal. In total, there are 5182 cells.

In addition, 16 large scintillator plates are located between the barrel and
the endcaps, the Minimum Bias Trigger Scintillators (MBTS). They are mainly
used in the ATLAS low luminosity trigger. Although they are not TileCal cells,
their readout is performed by dedicated PMTs of the TileCal system, that were
originally planned to be connected to 8 pairs of E3 and E4 cells.

Figure 2: Schematic of the cell layout in a plane parallel to the beam axis,
showing only positive $\eta$ side (the detector being symmetric with respect
to $\eta=0$). The three radial layers (A, BC and D) are also visible. Special
scintillators, called gap (E1 and E2) and crack (E3 and E4) cells, are located
between the barrel and the endcap.

Figure 3: Sketch of a TileCal module, showing the light readout path between
the scintillating tiles and the photomultiplier tubes (PMTs).

###  1.2 Detector readout

Each fibre bundle, usually corresponding to one side of a cell, is read out by
a photomultiplier tube: each standard cell is thus read out by two PMTs, the E
cells being read out by a single PMT. Therefore, there are 9852 PMTs in total.
The electric pulses generated by the PMTs are shaped [4] and digitised [5] at
40 MHz with two different gains, with a ratio of 64, in order to achieve a
good precision in a wide energy range. These samples are then stored in a
pipeline memory until the level-1 trigger decision is taken (ATLAS has a
three-level trigger system, the first level giving a decision in 2.5 $\mu$s
during which the data are kept in the front-end electronics). If the decision
is positive, seven samples, in time with the signal and with appropriate gain
giving the best precision on the pulse amplitude, are sent to the off-detector
electronics (Read Out Drivers or RODs [6]). The amplitude of the signal is
reconstructed as the weighted linear combination of the digitised signal
samples, using an optimal filtering method [7, 8].

In parallel, the output of each PMT is also integrated over approximately 14
ms using an analog integration system, during Cesium calibrations (see below
and figure 1) and also to measure the PMT current induced by minimum bias
proton–proton collisions.

###  1.3 Hardware calibration systems

Three different and complementary hardware calibration systems have been
integrated in the TileCal design: the Cesium system [9], the Laser system and
the Charge Injection System (CIS) [4] (see figure 1).

About once or twice a month, a radioactive 137Cs source scans most444For
mechanical reasons, the special cells E3 and E4 cannot be calibrated by the
Cesium source, see Fig. 3 and Section 4.4 for more details. TileCal cells,
measuring the response of the tiles, including the WLS fibres and the PMTs, to
a known amount of deposited energy. For this Cesium calibration, the analog
integrator is used instead of the digital readout: it is therefore not
sensitive to potential variations of the gain of the readout electronics used
for physics.

The Laser calibration is performed about twice a week and allows monitoring
the stability of the PMT gain between two Cesium calibrations by illuminating
all PMTs with a Laser pulse of a known intensity. For this calibration, the
same readout electronics as for physics is used and is therefore also
monitored. This calibration is described in detail in the next sections.

During the CIS calibrations, performed about twice a week, a known electric
charge is injected into the readout electronics chain, simulating a PMT output
pulse. It is used to measure the conversion factor from ADC-counts to pico-
Coulomb (pC) and also to monitor the linearity of the ADCs.

Figure 4: Diagram of the contributions of the hardware calibration systems to
the energy reconstruction.

###  1.4 Energy reconstruction

In order to measure correctly the energy, several effects must be taken into
account, using the calibration systems described previously as well as results
from tests using special beams of particles (see figure 4). Hence, for each
PMT, the energy is reconstructed as

$E=A_{\rm opt}\times C_{\rm CIS}\times C_{e}\times f_{\rm Cs}\times f_{\rm
Las}$ (1)

where $A_{\rm opt}$ is the amplitude in ADC counts computed by the optimal
filtering method, $C_{\rm CIS}$ is the ADC$\rightarrow$pC conversion factor
measured by the CIS, $C_{e}$ is the pC$\rightarrow$GeV conversion factor
defining the energy scale as measured with electron beams in past beam tests
[10] and $f_{\rm Cs}$ and $f_{\rm Las}$ are correction factors extracted from
the Cesium and Laser calibrations. The Cesium calibration is able to correct
the residual non-uniformities after the gain equalisation of all channels and
thus to preserve the energy scale of the calorimeter that was determined
during the beam tests. The Laser calibration allows keeping stable this energy
scale between two Cesium scans and is therefore relative to the Laser
calibration immediately consecutive to the last Cesium calibration. The cell
energy is the sum of the energies from the two PMTs connected to this cell.

The computation of the Laser calibration constants $f_{\rm Las}$ will be
described in the next sections.

##  2 The Laser calibration system

The first prototype of the Laser system has been built in 1993 and the first
tests with a prototype module of the calorimeter were performed in October
1994 [11]. A second prototype was then built and tested in 1997 [12]. After
several improvements, a first version of the system has been used during the
qualification of the TileCal modules using particle beams [10]. Finally, the
system described in the following paragraphs was installed in its definitive
location in 2008, in time for the calibration of TileCal before the first LHC
collisions. After several years of running, the current Laser system has been
upgraded in October 2014 for the LHC run 2, starting in 2015. This new system
includes a new Laser source, new optical components and new electronic boards,
and is not described in this article.

The Laser system contains of course a Laser source but also other components.
Because the actual intensity of the pulses has variations of approximately 5
%, the system includes dedicated photodiodes to precisely measure the
intensity of each pulse. It also includes a tunable attenuation system to
cover the whole TileCal PMTs dynamic range (100 MeV to 1.5 TeV per PMT).

The Laser system consists of a Laser pump, the so-called Laser box, a light
distribution system and several electronic components in a VME crate to
control and monitor the system. The Laser box (see figure 5) contains the
Laser head, two photomultipliers, the so-called photodiodes box, a semi-
reflecting mirror, a filter wheel and a shutter. The photodiodes box contains
four PIN photodiodes from Hamamatsu [13] with their amplifiers and shapers.
These components are located in the USA15 cavern that hosts the back-end
electronics, and that is close to the main ATLAS cavern.

1234567810 cm Figure 5: Sketch of the Laser box, showing the Laser head (1),
the semi-reflecting mirror (2), the light mixer (3) that distributes the light
to the photodiodes box (4) and the two PMTs (5), the filter wheel (6), the
shutter (7) and the output liquid light guide (8).

The Laser system can be operated in four different modes, divided in two
categories: three internal calibration modes and one Laser mode.

#### Internal calibration modes:

the aim of these modes is to calibrate and monitor the Laser system
electronics, without any Laser light emission. There are three different
calibration modes:

  * •

two to measure the characteristics of the electronics: linearity (Linearity
mode), noise and pedestal level (Pedestals mode);

  * •

one to calibrate the photodiodes, with an embedded radioactive source (Alpha
mode).

#### Laser mode:

this mode represents the main operation mode, in order to calibrate the
TileCal PMTs using Laser light.

###  2.1 Choice of the light source

In order to synchronise all the TileCal channels, it is mandatory to be able
to send simultaneously a single light pulse to the 9852 PMTs, which requires a
powerful light source such as a Laser. Pulse shape requirements ($\sim$10 ns
pulse width) has driven our choice toward a commercial Q-switched DPSS (Diode-
Pumped Solid State) Laser manufactured by SPECTRA-PHYSICS. This is a
frequency-doubled infrared Laser emitting a 532 nm green light beam, this
wavelength being close to the one of the light coming out of the WLS fibres
(480 nm). It delivers 10 to 15 ns pulses of a few $\rm{\mu J}$ maximum energy,
which is sufficient to saturate all TileCal channels, and thus to test their
full dynamic range. Moreover, the pulse shape is sufficiently similar to the
shape of physiscs signals, so that the optimal filtering method does not have
to be adapted. The delay between triggering and actual light emission is of
the order of 1.2 $\mu$s, which depends on the pulse energy in a window of
about 60 ns; and a jitter of 25 ns due to the internal 40 MHz clock of the
Laser source electronics.

###  2.2 Laser light path

The light emitted by the Laser head passes first through a semi-reflecting
mirror (commercial metallic neutral density filter). About 10 % of the light
is redirected towards a specific calibration system in order to measure
precisely the amount of light that has been emitted, with a photodiode, and
also to precisely measure the time when the pulse was emitted with two PMTs.

Figure 6: Sketch of the light splitting scheme. The main light splitter
distributes the light to 400 optical fibres, 256 for the two extended barrels,
128 for the long barrel and 16 spares. In each module, the secondary light
splitter distributes the light to 17 (EB) or 48 (LB) fibres, connected to 16
(EB) or 45 (LB) photomultipliers.

5 cm

Figure 7: Sketch of the beam expander and light splitter. The light enters
from the right hand-side of the figure.

The light that passes through the semi-reflecting mirror then goes through a
rotating filter wheel, which is used to attenuate the outgoing light. This
wheel contains seven metallic neutral density filters, each one applying a
specific attenuation factor (from 3 to 1000). The filter wheel contains also
an empty slot in order to reach the maximum intensity.

Downstream of the filter wheel, a shutter allows controlling whether the light
is sent to TileCal or not. When this shutter is open, the light enters a 1 m
long light guide with a 5 mm diameter liquid core that acts as a first beam
expander (see figure 7). The liquid light guide has been chosen for its large
acceptance cone, high transmittance and very good resistance to powerfull
light pulses. At the output of the liquid light guide, the light enters in the
beam expander and light splitter [14] (see figure 7), where the Laser beam is
first enlarged by means of a divergent lens followed by a convergent one in
order to obtain a parallel light beam. In order to avoid any speckle effects,
the beam then goes into a coherence-killing light-mixer, made of a
parallelepipedic PMMA block. At the output of this block, the light is
transmitted to a bundle of 400 clear optical fibres (Mitsubishi ESKA GH4001).

In order to further improve the splitting uniformity, the amount of light
transmitted to the 400 secondary fibres can be varied with adjustable distance
optical connectors [15]. From these 400 outputs, 384 of them are connected to
80 m long clear fibres of similar model, that bring the light from the USA15
cavern to the TileCal modules. Inside a module, each clear fibre is connected
to 17 (EB) or 48 (LB) fibres of the same type but with lengths varying between
0.5 and 6 m; each of these fibres reaching one PMT. The light splitting is
performed by the mean of an empty anodized aluminium tube: the incoming beam
expands and reflects on the inner wall of the tube before reaching the bundle
of output fibres. These tubes are 26 mm (respectively 40 mm) long with an
internal diameter of 6 mm (10 mm) in the EB (LB). In total, each endcap module
is fed by two 80 m fibres (16 PMTs per fibre) and each barrel module is fed by
two fibres (45 PMTs per fibre). It should be noted that the light splitters
located in the modules can not be tuned.

Connected to the adjustable connectors, three additional fibres go back inside
the Laser box in order to measure the intensity of the light pulses downstream
of the filter wheel. Due to the large range of available attenuations (from 1
to 1000), the light sent to these three photodiodes has been tuned in order to
always have a measurable signal in at least one of them.

###  2.3 Radioactive source

The four photodiodes are located in a special box in which temperature and
humidity levels are monitored and controlled by Peltier elements and a dry air
flow. This box also contains a 16 mm diameter radioactive source of 241Am,
releasing mostly $\alpha$ particles of 5.6 MeV with an activity of 3.7 kBq.
This source provides an absolute calibration (independent from the Laser
source) of each photodiode. In order to calibrate all the diodes, the source
can be moved along them into the box.

###  2.4 Electronics

The VME 6U crate contains a VME processor, on which the software interface
between the system and the ATLAS data acquisition system (DAQ) is running, and
several custom-made electronic boards. The main boards that are needed for the
data acquisition are described in the following paragraphs and can be seen on
figure 8.

The LastQDC board is an eight channels charge Analog to Digital Converter, for
the digitisation of the signal coming from the four photodiodes and the two
photomultipliers. It has a resolution of 11 bits with a maximum range of 200
pC.

The LilasII board provides two distinct functions. The first function is a
charge injection system used in the Linearity mode, with a 16-bit Digital to
Analog Converter (DAC) producing a maximum output of 10 V that is injected in
a 1 pF capacitor. The second function is an interface between the TileCal
calibration requests system (Shaft555The Shaft board is also a VME board but
it is not located in the Laser VME crate, as it is not only used by the Laser
system but also by the CIS and the minimum bias current measurement system.
This is the board that defines when the various systems must be triggered.)
and Slama, containing mostly counters to know precisely how many requests were
sent by Shaft and by Slama.

The Slama board is the main component of the system, producing signals to
control other components like the LastQDC, LilasII or the Laser pump. It
contains three FPGAs (Altera ACEX EP1K300QC208): one is devoted to the VME
communication, the second one to the communication with LastROD via a
dedicated bus, and the last one to the management of the Laser pump and the
production of the various electronic signals that are described in the next
sections. This board contains also two 15-bit Time to Digital Converters (TDC)
with a resolution of 250 ps. The internal clock of Slama has a frequency of 80
MHz, either from an internal oscillator or provided by LastROD (see
hereafter).

The LastROD board is the dedicated Read Out Driver (ROD) of the Laser system,
included in the ATLAS trigger and data acquisition system. It receives timing
and trigger information from the standard ATLAS TTC systems, via an optical
fibre connected to a TTCrq mezzanine board [16]. This mezzanine includes a
QPLL that provides 40 MHz and 80 MHz clocks synchronised to the LHC clock.
LastROD also sends the data to the ATLAS data acquisition computers (ROS),
using another mezzanine board named HOLA [17], that contains a 2.5 Gbps
optical link. The various functions of LastROD are implemented in four FPGAs
(Altera Cyclone I EP1C12Q240C6N): the first one manages the communication with
the TTCrq mezzanine, the second one the communication with the HOLA board, the
third one is the VME decoder and the last one is devoted to the communication
with the Slama and LastQDC boards via the dedicated bus.

Two other custom VME boards are needed to control the movements of the filter
wheel and the radioactive source, and to monitor the low and high voltages,
temperatures and humidity levels.

Figure 8: Laser system electronic boards involved in the Laser mode. The
interactions between the various components are also shown. The board labelled
ADC is the LastQDC board.

###  2.5 Operating in internal calibration modes

Operating the Laser system in one of the three internal calibration modes
requires only a sub-set of the Laser system hardware.

#### Pedestals mode

The aim of this mode is to record a high number of events without any energy
in the photodiodes and the photomultipliers (neither from the Laser nor from
the radioactive source). Slama generates a random gate for the LastQDC.

#### Alpha mode

In this mode, the $\alpha$ radioactive source is moved in the photodiodes box,
in front of each photodiode. The signals coming out of the four photodiodes
are fed into Slama, where they generate an internal trigger if at least one of
them is above a given threshold. This internal trigger generates the gate
needed by the LastQDC to digitise the delayed photodiodes signals: for each
event, only one photodiode contains energy from the $\alpha$ radiation (see
figure 10). In very rare cases, two $\alpha$ particles hit the photodiode
within the same digitisation gate (as can be seen above ADC$\simeq$1000 in
figure 10) but the effect is negligible. The large dispersion of the $\alpha$
spectrum is due to the absence of collimation of the $\alpha$ particles,
resulting in a wide range of incidence angles666The source and the photodiode
have surfaces of approximately 200 mm2 and they are separated by about 1 mm.
Particles emitted perpendicular to the source travel a very short distance in
the air gap and loose a very small amount of energy, while particles emitted
almost parallel to the source travel much longer distances and therefore loose
much more energy. for the particles hitting the photodiode.

#### Linearity mode

This mode allows measuring the linearity of the photodiodes electronics
(amplifier, shaper and ADC): a tunable electric charge is injected in this
electronics (downstream of the photodiodes), the response of the photodiodes
electronics and the injected charge are recorded (see figure 10).

Figure 9: Example of distribution of the photodiode response in the Alpha
mode. Data around ADC=170 were taken while the radioactive source was in front
of the other photodiodes, data between 500 and 1000 correspond to the $\alpha$
spectrum.

Figure 10: Example of photodiode response as a function of the measured
injected charge in the Linearity mode. The saturation at high value of the
photodiode response is an effect due to the ADC, not to the photodiode itself.

###  2.6 Operating in Laser mode

The Laser system is operated in the Laser mode for two data-taking situations:

  * •

dedicated calibration runs, when TileCal is operated independently of the rest
of ATLAS and all events are Laser calibration events;

  * •

standard physics runs, when TileCal is synchronised with the other ATLAS sub-
detectors. In this configuration, the Laser pulses are emitted only during a
dedicated period of the LHC orbit, in which it is ensured there are no
collisions (see figure 12.2 of reference [18]), in order to separate physics
events from calibration events.

The main difficulty in this mode is the timing. First, the Laser system must
be synchronised with the other TileCal components, so that the events recorded
in TileCal correspond to the events when the Laser pulse is emitted. Second,
during standard physics runs, the Laser pulses must not be emitted during
proton–proton collisions. In order to achieve these two goals, the Laser
system is operated as a slave of the Shaft board. The frequency at which the
Laser pulses are emitted is about 1 kHz in the calibration runs and 1 Hz in
the physics runs.

Operating in Laser mode requires most of the components, in particular the
interfaces with ATLAS. The various boards located in the Laser VME crate that
are needed in this mode can be seen in figure 8, together with their
interactions.

The Shaft board is programmed to send a request to the Laser system at a fixed
time with respect to the beginning of the LHC orbit. Depending on the required
frequency, this signal is only sent during selected orbits. When Slama
receives this signal, it triggers a Laser pulse by the mean of a signal sent
to the Laser pump together with a DAC level to set the required Laser
intensity. However, a small delay occurs between the pump triggering and the
emission of the Laser pulse, and this delay is dependent on the pulse
intensity. In order to compensate for this variable delay, Slama sends the
trigger signal to the Laser pump only after a programmable time, by steps of
12.5 ns, as explained in figure 11.

Figure 11: Sequence of signals to trigger a Laser pulse. The time (tl) between
the reception of the trigger signal by the Laser pump and the pulse emission
depends on the pulse intensity. The programmable delay (d2) is chosen as a
function of the intensity in order to keep d2+tl constant.

The gates needed by the LastQDC to digitise the photodiodes response are then
produced by Slama from the response of one of the Laser box photomultipliers.
Using its TDC and the signal from these photomultipliers, Slama also measures
the time needed by the Laser pulse to be emitted. In order to get relevant
time values, the internal 80 MHz Slama clock is the one that is produced by
LastROD, which is synchronised with the LHC clock.

Once Slama has detected that the pulse is correctly emitted, it generates a
signal back to Shaft that then sends a Laser calibration request to the ATLAS
central trigger processor. This request is sent to Shaft when the pulse is
emitted in order to synchronise the pulse emission and the readout of TileCal.
Then, a level-1 trigger (L1A) signal associated to this Laser event is
distributed to the whole ATLAS detector, together with the TileCal Laser
calibration trigger type (TT).

Finally, when a L1A is received by LastROD, associated with the Laser TT, it
sends to the ATLAS DAQ the amplitude of the Laser light, measured by the
photodiodes, the time measured by the TDC, the average and RMS of the reponses
measured during the last Pedestals and Alpha runs, as well as the state of the
system (filter wheel position, shutter state, temperature and humidity in the
Laser box, status of the power supplies). All this information is then
available for offline analysis.

##  3 Stability of the electronics

Before any use of the Laser system to calibrate the TileCal, it is necessary
to monitor the behaviour of its readout electronics and in particular the
photodiodes. This is done in two steps: the first step is a measurement of the
electronics characteristics when no energy is deposited in the photodiodes (no
Laser light pulse nor $\alpha$ particle), the second step is a calibration of
the photodiodes response using the radioactive source. These two steps are
performed using the Pedestals and Alpha internal calibration modes, that are
taken regularly.

###  3.1 Characteristics of the electronics

Each readout channel can be characterised by two numbers: its noise and its
pedestal. The noise can be measured as the RMS of the distribution of the
responses when no energy is recorded in the channel. The pedestal is the
average response in the absence of deposited energy: its value is very
important because it must be subtracted from the response of each channel, in
order to obtain a response that is directly proportional to the intensity of
the Laser pulses.

Both the pedestal and noise can be measured in the Pedestals runs and in the
Alpha runs. Indeed, in the Alpha runs, for each event, only one photodiode is
hit by an $\alpha$ particle, thus the three other photodiodes contain no
energy; in this case, the pedestal and noise levels can be measured. It is
also very important for the photodiodes calibration to make sure that the
pedestal and noise are the same in the Pedestals and Alpha runs, in particular
that there is no cross-talk between the channels when some energy is deposited
in a photodiode.

The stability of the electronics has been studied during the LHC data taking
periods of 2011, 2012 and 2013, from February 2011 to February 2013. Figure 13
shows the evolution of the pedestal measured in the Pedestals runs (PPed) and
in the Alpha runs (Pα), together with the ratio
R${}^{\mathrm{Ped}}_{\alpha/\mathrm{Ped}}=$Pα/PPed, for photodiode 1 (similar
results are obtained for the three other photodiodes). The vertical dashed
lines separate the two years in four periods, named A to D, that correspond to
stable conditions separated by hardware interventions on the system. In
particular, in March 31st 2011 (between periods A and B), a new version of the
photodiodes amplifiers was installed, allowing to switch off photodiodes
collecting an amount of light sufficient to saturate the electronics and thus
generating cross-talk with the other channels. The second important
intervention, in July 6th 2011 (between periods B and C), was a change in the
photodiodes amplifiers grounding scheme in order to further reduce the cross-
talk between channels. As can be seen in figure 13, the pedestals measured in
Pedestals runs and in Alpha runs are similar (the ratio
R${}^{\mathrm{Ped}}_{\alpha/\mathrm{Ped}}$ is very close to 1 and is stable)
during periods C and D, thus showing that the cross-talk has been reduced to a
negligible value. This means that the pedestal measured in Pedestals runs can
be safely subtracted from the measured response of the photodiodes in Alpha
runs.

Figure 13 shows the evolution of the noise measured in the Pedestals runs
(RMSPed) and in the Alpha runs (RMSα), together with the ratio
R${}^{\mathrm{RMS}}_{\alpha/\mathrm{Ped}}=$RMSα/RMSPed. The change of
grounding scheme in July 2011 significantly improved the electronic noise.
Moreover, the noise is similar in the Pedestals and in the Alpha runs:
R${}^{\mathrm{RMS}}_{\alpha/\mathrm{Ped}}\sim 1$ with variations well within
$\pm 5$ %.

Figure 12: Evolution of the pedestal value measured in the Pedestals runs and
in the Alpha runs, and their ratio for the first photodiode from February 2011
to February 2013. The error bars represent the statistical uncertainties on
the averages and the ratios. The large variation early 2013 is due to the
stabilisation of the readout electronics after the end-of-year shutdown,
during which all systems were off.

Figure 13: Evolution of the noise value measured in the Pedestals runs and in
the Alpha runs, and their ratio for the first photodiode from February 2011 to
February 2013. The error bars represent the statistical uncertainties on the
averages and the ratios.

The linearity of the readout electronics can be measured by injecting a known
charge in the photodiodes amplifiers and varying this charge over the full
dynamic range (see figure 10). Using dedicated Linearity runs, the difference
between the electronics response and a straight line varies within $\pm 1$ %,
with an RMS of 0.2 %.

Finally, using standalone Laser runs during which the shutter was closed, it
was also possible to measure the pedestal and noise of the channels connected
to the three photodiodes that see the light after the light splitter, but in a
condition similar to a standard Laser run (Laser pump on and light pulses seen
by the photodiode 1). The pedestal variation with respect to standard
Pedestals runs is less than 1.5 % and the noise differs777It must be noted
that the noise is not systematically higher during Laser runs, but sometimes
higher sometimes lower, as in Alpha runs. by less than 5 %. This ensures that
no significant cross-talk between photodiodes is observed during Laser runs.

In conclusion, the readout electronics is found to be stable since April 2011.
Evolutions of the pedestal, probably due to environmental effects like
temperature and humidity, is not a problem since the value measured regularly
in the Pedestals runs can be used for the response renormalisation in the
Alpha and Laser runs. Moreover the electronic noise is perfectly stable and
similar in different types of runs.

For the rest of this article, the response of the photodiodes will always be
the value after pedestal subtraction.

###  3.2 Calibration of the photodiodes

In the Laser calibration of the TileCal, the photodiodes are necessary to
measure the intensity of each Laser pulse sent to the calorimeter PMTs, thus
requiring that the response of the photodiodes to a given energy does not vary
with time. The monitoring of this potential evolution is performed by
depositing a known amount of energy periodically in the photodiodes, i.e.
$\alpha$ particles of 5.6 MeV, using the Alpha runs.

Figure 14: Evolution of the scale factor and the normalised mean value of the
$\alpha$ spectra from February 2011 to February 2013. The error bars represent
the statistical uncertainties.

Two methods have been used to study the evolution of the response of the
photodiodes to $\alpha$ particles. In both methods, a high statistics Alpha
run is used as a reference and each Alpha run is compared to this reference.
Four reference runs have been defined, each one at the beginning of a period
as defined in the previous section. The reference run for period C contains
$3.8\times 10^{5}$ $\alpha$ events and the reference run for period D
$1.1\times 10^{6}$ events.

The first method is using the _normalised mean value_ that consists in
computing the ratio between the mean value of the $\alpha$ spectrum in the
Alpha run under study with the mean value of the $\alpha$ spectrum in the
reference run.

The second method has been developed specifically for this study. It is called
the _scale factor_ and it is based on the assumption that the variation in the
measured $\alpha$ spectra is due to a variation of the gain of the photodiodes
and/or their readout electronics, thus only implying a rescaling of the
spectra and not a distortion. Therefore, in this method, the spectrum under
study is compared to the reference spectrum. A test spectrum is first built by
rescaling the reference one, i.e. by multiplying the photodiode response for
each recorded event by a constant number, called the scale factor. Then, this
test scale factor is varied until the resulting distribution fits as well as
possible the $\alpha$ spectrum under study, using the Kolmogorov–Smirnov test
[19, 20]. The resulting scale factor is then a measurement of the gain
variation, being equal to one if no rescaling is needed to fit the reference
distribution to the studied one.

To compare the two methods and their sensitivity to pedestal and noise
variations, studies with simulated $\alpha$ spectra were performed. These
simulated $\alpha$ spectra were generated by randomly drawing photodiode
responses, according to a measured high statistics $\alpha$ distribution.
Then, these simulated $\alpha$ spectra were shifted (to simulate a pedestal
variation), rescaled (to simulate a gain variation) or smeared (to simulate an
increase of the noise), before being used as input to the photodiode
calibration procedure. These studies have shown that the scale factor method
has a smaller uncertainty (0.05 %) than the normalised mean value (0.1 %).
Moreover, they have also shown that the bias introduced by a wrong measurement
of the pedestal is the same for the two methods: if the true pedestal differs
from the subtracted one by $x$ %, the bias is $0.2\times x$ %. Finally, as has
been shown in the previous section, the noise in the Alpha runs may be up to 5
% larger or smaller than in the Pedestals runs. The simulation showed that an
error of 5 % on the noise would bias the scale factor by a negligible amount
(0.0003 %) and would have no measurable effect on the normalised mean value.
The noise measured in the reference runs (Ref${}_{\alpha}^{\mathrm{RMS}}$) can
be seen on figure 13 as the horizontal lines and shows a good agreement with
the noise measured in the studied Alpha runs. Therefore, the scale factor is
chosen as the main method to study the evolution of the response of the
photodiodes, with the normalised mean value as a cross-check.

Figure 14 shows the evolution of the normalised mean value and the scale
factor measured in the Alpha runs. It appears that the period D was more
stable than the previous ones. Concentrating on the scale factor, the largest
variation is 0.6 % in the periods C and D and usually even less, which is
small enough to safely use the response of the photodiodes to Laser pulses as
a reference.

##  4 Calibration of the calorimeter

As has been seen in equation 1, the reconstruction of the energy in TileCal
depends on several constants, some of them being updated regularly. The main
calibration of the TileCal energy scale is obtained using the Cesium system
[2]. However, since a Cesium scan needs a pause in the proton–proton
collisions of at least six hours, this calibration cannot be performed very
often. Therefore, regular relative calibrations are accomplished between two
Cesium scans using the Laser system. The method to compute the Laser constant
$f_{\rm Las}$ introduced in equation 1 is based on the analysis of specific
Laser calibration runs, taken about twice a week, for which both the Laser
system photodiodes and the TileCal PMTs are readout. By definition, if the
response of a channel to a given Laser intensity is stable (the gains of the
PMT and of the associated readout electronics are stable), the Laser constant
$f_{\rm Las}$ is 1.

In the next sections, the general method to determine these Laser calibration
constants $f_{\rm Las}$ is first described, the uncertainty on these constants
is then estimated, followed by the description of the actual procedure to
produce them.

###  4.1 Description of the method

A Laser calibration consists in two successive runs:

  * •

a Low Gain run (labelled LG) with $10^{4}$ pulses using the filter with an
attenuation factor of 3,

  * •

a High Gain run (labelled HG) with $10^{5}$ pulses using the filter with an
attenuation factor of 330.

For each type of run, $R_{i,p}$ is defined as the normalised response of
channel $i$:

$R_{i,p}=\frac{E^{\rm pmt}_{i,p}}{D1_{p}}$ (2)

where, for the pulse $p$, $D1_{p}$ is the signal measured in the photodiode
1888The photodiode 1 is the one that measures the light right after the semi-
reflecting mirror. The three other photodiodes have not been used in this
method because several hardware interventions occured during the two years,
affecting the optical fibres connected to these diodes. in the Laser box and
$E^{\rm pmt}_{i,p}$ is the signal measured by the TileCal photomultiplier
connected to the channel $i$. The analysis is performed with the mean value of
this ratio over all pulses for each channel, denoted $R_{i}=<R_{i,p}>$.

The Laser calibration is a relative calibration with respect to a Laser
reference run taken right after each Cesium scan. The raw relative gain
variation of a channel $i$ is defined as follows:

$\Delta_{i}=\frac{R_{i}-R^{\rm ref}_{i}}{R^{\rm ref}_{i}}$ (3)

where $R^{\rm ref}_{i}$ is the normalised response of the TileCal channel $i$
during the reference Laser run.

However, due to inhomogeneities in the light mixing of the light splitter or
radiation damage to the long clear optical fibres, the light intensity may
vary with time and from fibre to fibre (one fibre being linked to half of the
PMTs of the same TileCal module). Therefore, $\Delta_{i}$ is corrected by the
term $\Delta^{\rm fibre}_{f(i)}$ ($f(i)$ is the number of the fibre coming
from the Laser and connected to the given channel $i$) taking into account the
gain variation due to a light variation of this specific fibre, as explained
in the next paragraph.

To compute $\Delta^{\rm fibre}_{f(i)}$, an iterative method is used. First,
the distribution of $\Delta_{i}$ of channels fed by the same fibre is
considered (see figure 16). In this distribution, only PMTs connected to the D
cells for the long barrel modules and the B13, B14, B15, D5 and D6 cells for
the extended barrel modules are used, assuming that these selected channels
are stable between two Cesium scans999Since the D cells are the most distant
cells from the interaction point, they are less affected by the radiations
from the proton–proton collisions, unlike A cells that are more sensitive to
the high light dose. The level of radiations has been validated using the
minimum bias current measurements. The evolution of these cells between two
Cesium scans has been checked from the evolution of the Cesium calibration
constants and this evolution is well below 1 %.. The mean and the RMS of the
$\Delta_{i}$ distribution are then calculated from these selected channels. To
deal with single drifting channels that would bias the measurement of the
shift due to the fibre itself, an iterative procedure is applied: all the
channels that have a gain variation larger than twice the RMS are excluded
from the distribution for the next iteration. The mean gain variation after
five such iterations is the correction $\Delta^{\rm fibre}_{f(i)}$.

Figure 15: Example of distribution of $\Delta_{i}$ for all channels connected
to one fibre. The average of this distribution is $\Delta^{\rm fibre}_{f(i)}$
(see text).

Figure 16: Inhomogeneity due to light distribution instabilities as a function
of time.

The aim of this method is to correct the drifting channels of TileCal, not the
variations of the fibres or any global variation. Therefore, the correction
factor, $f^{i}_{\rm Las}$ for channel $i$, is defined as:

$f^{i}_{\rm Las}=\frac{1}{1+\Delta_{i}-\Delta^{\rm fibre}_{f(i)}}$ (4)

and is the Laser calibration constant that enters in equation 1.

###  4.2 Evolution of the fibre correction

Figure 16 gives a hint of the inhomogeneity of the light distribution during
year 2012, estimated as the RMS of the distribution of all the $\Delta^{\rm
fibre}_{f(i)}$ with respect to the latest Laser reference run. At the
beginning of each period, i.e. after each Cesium scan, the spread of the fibre
correction factor determination is 0 by definition and it increases up to 0.4
% in a one month period.

###  4.3 Uncertainty on the correction factor

The method assumes that the reference D and B cells are stable. Systematic
effects on the correction factor may arise, in particular from global
variations of the PMT gains of these cells, due to two effects. The first
effect, independent of the presence or absence of collisions, is a constant
increase of the gains, but it is negligible over a period of one month (less
than 0.1 $\%$) and has been first observed in 2009 by the Cesium system, prior
to collisions. The second effect, observed during collisions, is a decrease of
the gains. Its origin is not completely understood but the effect is less than
0.5 $\%$ between two Cesium scans.

Assuming that the scintillators ageing is negligible between two Cesium scans
(typically one month) and taking into account the fact that the precision of
Cesium calibration constants is at the per-mil-level, the Cesium system is a
good tool to determine the precision and the systematic uncertainty connected
with the Laser calibration constants. The two systems are expected to provide
compatible measurements. To compare the Laser and the Cesium calibration
constants, pairs of the closest Laser run/Cesium scan are selected.

For each pair of Laser run/Cesium scan, the ratio of Laser calibration
constants $f_{\rm Las}$ and Cesium calibration constants $f_{\rm Cs}$ is
considered. In this comparison, are considered only the channels for which the
quality of the two calibration constants is good. The distribution is fitted
to a Gaussian function. The mean obtained by the fit quantifies the
compatibility of the two calibration systems and its difference to one (called
$\delta$) is interpreted as the systematic uncertainty on the Laser
calibration constants. The $\sigma$ obtained by the fit can be interpreted as
the statistical precision of the Laser system assuming that the uncertainty on
the Cesium calibration constants is negligible with respect to the Laser one
(it is therefore a conservative estimate of the Laser system precision).

Figure 17: Example of distribution of the ratio $f_{\rm Las}$/$f_{\rm Cs}$ during one month for the long barrel (a) and the extended barrels (b). The runs were taken in July 9th and August 5th, 2012. Table 1: Difference between the mean and unity ($\delta$) and spread ($\sigma$) of a Gaussian fit to the distribution of the ratio $f_{\rm Las}$/$f_{\rm Cs}$ during 2012. The value of $\delta$ is always positive, due to the fact that the reference cells, that are assumed to be stable, have nonetheless a small decrease of the gain, yielding a systematic effect. | Long barrel | Extended barrel
---|---|---
Period |  $\delta$ in $\%$ |  $\sigma$ in $\%$ |  $\delta$ in $\%$ |  $\sigma$ in $\%$
Mar 18-Apr 27 | 0.20 $\pm$ 0.01 | 0.29 | 0.29 $\pm$ 0.01 | 0.29
Apr 28-Jun 18 | 0.21 $\pm$ 0.01 | 0.30 | 0.56 $\pm$ 0.01 | 0.36
Jun 18-Jul 9 | 0.20 $\pm$ 0.01 | 0.27 | 0.40 $\pm$ 0.01 | 0.27
Jul 10-Aug 4 | 0.10 $\pm$ 0.01 | 0.26 | 0.10 $\pm$ 0.01 | 0.24
Aug 5-Aug 16 | 0.10 $\pm$ 0.01 | 0.27 | 0.10 $\pm$ 0.01 | 0.25
Aug 17-Sep 11 | 0.0 $\pm$ 0.01 | 0.27 | 0.10 $\pm$ 0.01 | 0.25
Sep 11-Sep 20 | 0.10 $\pm$ 0.01 | 0.26 | 0.30 $\pm$ 0.01 | 0.22
Sep 22-Oct 9 | 0.02 $\pm$ 0.01 | 0.26 | 0.05 $\pm$ 0.01 | 0.24
Oct 10-Nov 3 | 0.03 $\pm$ 0.01 | 0.28 | 0.13 $\pm$ 0.01 | 0.29
Nov 6-Dec 4 | 0.20 $\pm$ 0.01 | 0.24 | 0.30 $\pm$ 0.01 | 0.25
Dec 7-Dec 10 | 0.0 $\pm$ 0.01 | 0.36 | 0.40 $\pm$ 0.01 | 0.46

Figure 17 shows a comparison between Laser and Cesium calibration constants,
the ratio $f_{\rm Las}$/$f_{\rm Cs}$, for long and extended barrels, for a one
month period in 2012\. Fitting the same distributions for 11 periods in 2012
(see results in table 1), the systematic uncertainty on $f_{las}$ is evaluated
to be at most 0.21 % for the long barrel and 0.56 % for the extended barrels,
and the statistical uncertainty of the Laser system varies between 0.22 % and
0.46 %. The second period corresponds to a period of high LHC luminosity. As
anticipated, this high luminosity has a more significative effect on the PMTs
of the extended barrels than on the ones of the long barrel, as can be seen
from table 1. The statistical and systematic uncertainties of the correction
factors obtained using the Laser system are then estimated:

  * •

statistical uncertainty: 0.3 %

  * •

systematic uncertainty for long barrel: about 0.2 %

  * •

systematic uncertainty for extended barrels: about 0.5 %

Combining together these results, the overall precision is estimated to be 0.4
% and 0.6 % for the long and the extended barrels respectively. However, the
precision on the Cesium calibration constants (of the order of 0.2 %) is not
completely negligible with respect to the Laser ones, thus the above values
must be considered as upper limits rather than exact values.

###  4.4 Determination of the calibration constants

In equation 1, $f_{\rm Las}$ represents the correction of the PMT gain
variation computed with the Laser system. However, only channels that have
undergone a significant deviation are corrected, i.e. the value of $f_{\rm
Las}$ is set to 1 if it is smaller than a predetermined threshold of about
three times the overall precision of the Laser system, thus a threshold of 1.5
% for the long barrel and 2 % for the extended barrels. The low gain (LG) and
the high gain (HG) Laser runs are used to determine the Laser calibration
constants. However, the LG data are more precise than the HG data because the
HG signal amplitude is much smaller than the LG one (a factor 100 between them
for the same channel). Therefore, the LG Laser calibration constants are used
for both gains, while the HG Laser calibration constants are used for cross-
checks. A readout electronics issue can be revealed by an incompatibility
between the LG and the HG Laser calibration constants.

Therefore, the production of the Laser calibration constants $f_{\rm Las}$
follows this procedure:

  * •

for each pair of the LG and the HG runs, a Laser calibration constant is
computed,

  * •

a channel is corrected if its LG gain variation is larger than 1.5 % (2 %) in
the LB (EB),

  * •

the compatibility of the Laser calibration constants for the LG and the HG is
required (both constants with same sign and above the thresholds), otherwise
the Laser calibration constants are set to 1 — this is to ensure the
calibration constant corrects only drifts due to the PMTs and not problems in
the readout electronics itself that are covered by the CIS,

  * •

a limit is applied to the constants values corresponding to a deviation
between -60 % and +60 %. A healthy channel is not supposed to drift up to
these values. However, a variation of up to -90 % is allowed for channels in a
module in reduced-HV mode101010During the so-called reduced-HV mode of a
module, the High Voltages (HV) regulation loop is turned off and then the HV
applied to each PMT is lower, preventing high trip rate. The PMT gain is
sensitive to variations of HV, so if the HV of the PMT decreases, the PMT gain
will also decrease and will be very low ($\sim$-60 %) with respect to PMTs
supplied with nominal HV.,

  * •

if a channel is known as bad, its Laser calibration constant is set to 1,
whatever is the nature of the problem. Indeed, this flag is very often due to
readout electronics, a gain variation or drift faster than Laser run
frequency, or corrupted data, and the Laser system is not presumed to correct
these cases.

Based on these criteria, only 60 channels among $\sim 10^{4}$ could not be
corrected by the Laser system during the LHC run 1.

A few additional conditions are needed for three different types of channels:
the ones linked to the E3 and E4 cells, the channels in reduced-HV modules and
some channels that have an erratic behaviour, likely due to readout
electronics problems. These latter channels are not calibrated.

The channels linked to E3 and E4 cells are not calibrated by the Cesium
system, while the Laser system monitors all the TileCal channels, including
those connected to these special cells. The fact that there is no Cesium
calibration implies that there are no references for these channels. The
chosen solution is to monitor these channels and provide constants with
respect to a reference date set to March $18^{\mathrm{th}}$ 2012 which is the
date of the first Laser reference run in 2012. Even though the precision of
the Laser system over a period of one year has been estimated to be less than
2 %, it is sufficient to calibrate these highly drifting cells.

Some reduced-HV modules can not be calibrated by the Cesium system. As for the
E3 and E4 cells, these channels are monitored and Laser constants are computed
starting from the Laser reference run taken just before the beginning of the
reduced-HV mode period.

Finally, the channels linked to E1, E2 cells111111The E1 and E2 cells are not
calibrated by the Laser because their measured variation, smaller than for the
E3 and E4 cells, is of the same order of magnitude as the Laser precision, due
to a lower precision non-standard Cesium calibration (the Cs source cannot
pass through these cells). and MBTS (see section 1.1) are not corrected by the
Laser system.

Over the large number of runs recorded and analysed in 2012, only 32 pairs of
Laser runs were needed to calibrate the data. Indeed, if several consecutive
runs lead to compatible constants, only the constants from the first pair are
implemented for the full period. The main periods during which a large number
of channels had to be calibrated (at most 432 in the long barrel and 148 in
the extended barrels) are at the end of April and the beginning of June 2012.
Indeed, during these periods high luminosity was delivered by LHC, producing
high current in the PMTs, thus modifying their gain. Other channels that
needed calibration in 2012 were the 224 channels reading the E3 and E4 cells
as well as the 167 channels of the reduced-HV mode modules.

###  4.5 Calibration with pulses during physics runs

Up to now, the Laser calibration constants have been computed using dedicated
Laser calibration runs, recorded on a regular basis between collision runs.
But, as explained in section 2.6, the Laser pulses are also emitted during
collision runs, and are used only so far to monitor the calorimeter timing
(see section 5). However, with the increase in instantaneous luminosity
expected from the LHC, resulting in possible fast variations of the gains of
the TileCal PMTs during collisions, being able to monitor these gains during
the physics runs will become important. Technically, the main difference with
standard Laser runs is that the number of Laser events is not fixed, since it
depends on the length of the physics run and therefore on the beam conditions.
An additional study was performed and showed that, applying the method
described in the previous paragraphs, Laser calibration constants can be
derived with a good precision using these runs: the statistical precision with
5000 pulses, corresponding to a rather short physics run (85 minutes), is
similar to a standard calibration run (0.3 %). Therefore, the physics runs
will probably be used in the future to derive Laser calibration constants.

##  5 Timing monitoring and correction

The TileCal does not only provide a measurement of the energy that is
deposited in the calorimeter, but also the time when this energy was
deposited. This information is in particular exploited in the removal of
signals that do not originate from proton–proton collisions as well as for
time-of-flight measurements of hypothetical heavy slow particles that would
enter in the calorimeter. Therefore, the time synchronisation of all
calorimeter channels represents one of the important issues in the calibration
chain.

###  5.1 Time reconstruction

As described in section 1.2, the signal coming from the PMTs is digitised
every 25 ns and seven samples are readout after a positive level-1 trigger
decision. The optimal filtering (OF) method that is applied on these samples
is able to determine the total amplitude of the signal but also the signal
phase, defined as the phase of the analog signal peak with respect to the TTC
clock signal corresponding to the fourth sample. The precision on this
measurement is better than 1 ns [10, 2]. The optimal filtering method is
applied online to all channels and later re-computed offline in channels that
have sufficiently large signals.

However, the parameters of the OF method depend on this signal phase, thus a
bad setting of the timing of a channel will produce a wrong measurement of the
signal amplitude. Studies have shown that a difference of 25 ns between the
actual and supposed phases degrades the reconstructed energy by 35 %. For
timing differences of a few nano-seconds, the effect on the measured energy is
small but the corresponding cells could be excluded from the reconstruction,
being falsely tagged as not coming from proton–proton collisions.

The PMT signal digitisation is performed by an electronic board called the
digitiser that is able to process the signal from six PMTs. Only the timing of
each digitiser can be adjusted independently of each other. Inside the
digitiser the six channels have the same relative timing.

The meaurement of the pulse timing is made in two steps. First, the phases of
the digitisers are set so that the physics signals from particles originated
in the interaction point and travelling with the speed of light peak close to
the fourth sample. Second, the residual offsets tphase are measured, using
dedicated runs, as the average of the reconstructed OF time tOF. The channel
time is then defined as
t${}_{\mathrm{channel}}^{\mathrm{phys}}=$t${}_{\mathrm{OF}}-$tphase. This
value should of course be close to zero for standard particles coming from the
interaction point at nearly the speed of light.

###  5.2 Timing jumps

During data taking, it was discovered that digitisers can suddenly change
their timing settings due to a mis-configuration, either at the beginning of a
run or after an automatic power cycling of the low voltage power supplies
(LVPS) feeding the TileCal front-end electronics. This mis-configuration of
the time settings is later referred to as timing jump. An example of such a
behaviour can be seen in figure 19 where the reconstructed time for a channel
is represented as a function of the luminosity block, that is the elementary
unit of time in a run (one or two minutes depending on data taking periods)
for which parameters like calibration constants can be modified if necessary.
Of course, this kind of feature has a negative impact on the calorimeter
performance since the reconstructed energy and time are mis-measured during
the period affected by the timing jump.

Figure 18: Example of measured channel time as a function of time during a
single ATLAS run, comparing timing from physics events and from Laser
calibration events, exhibiting a timing jump.

Figure 19: Example of reconstructed time from physics events after correcting
for the timing jump.

As stated previously, the Laser system emits light pulses also during physics
runs. Since all calorimeter channels are exposed to Laser light at the same
time, the statistics is sufficient to determine the reconstructed time to a
precision of about 1 ns. Because the Laser is not synchronised with the LHC
clock, the reconstructed time in each channel must be corrected for the Laser
phase using the Laser TDC information tTDC. In addition, the time of arrival
of the Laser pulses to the TileCal PMTs is different from the signal time for
particles from collisions, due to the path followed by the Laser light.
Therefore, in a channel perfectly timed-in for physics, the Laser pulse
arrives at a different time121212The reference Laser time
t${}^{\mathrm{laser}}_{\mathrm{ref}}$ represents the mean value of tOF
corrected for the Laser TDC on the per-event basis.
t${}^{\mathrm{laser}}_{\mathrm{ref}}$. The channel time for Laser events is
then defined as
t${}_{\mathrm{channel}}^{\mathrm{laser}}=$t${}_{\mathrm{OF}}-$t${}_{\mathrm{TDC}}-$t${}^{\mathrm{laser}}_{\mathrm{ref}}$.
If the time setting of the digitiser is correct,
t${}_{\mathrm{channel}}^{\mathrm{laser}}$ should be close to zero.

The Laser events are recorded in parallel to the physics data taking and this
stream gets reconstructed immediately once the run finishes. The reconstructed
Laser times t${}_{\mathrm{channel}}^{\mathrm{laser}}$ are histogrammed for
each channel as a function of the luminosity block. Since this time is
supposed to be close to zero, the monitoring program searches for differences
from this baseline. Identified cases — potential timing jumps — are
automatically reported to the data quality team for manual inspection. If the
timing jump is confirmed, the tphase value of the corresponding channel is
modified for the affected period, thus allowing to recover a correct
reconstructed time, as demonstrated on figure 19. These Laser results are
available still during the calibration loop and thus allow for time constants
correction before the full data processing starts.

Almost all timing jumps detected with Laser events can be corrected during the
subsequent data processing. However, few digitisers appeared to be very
unstable, exhibiting very large number of timing jumps. Such channels are
flagged as _bad timing_. This flag prevents the time from such channels to be
used in the further physics object reconstruction.

###  5.3 Impact of the timing jumps on the calorimeter time performance

The overall impact of the timing jump corrections on the reconstructed time
was studied with jet collision data using a sub-set of the 2012 data
representing $1.3~{}\mathrm{fb}^{-1}$ of collected physics data. To reduce the
impact of the time dependence on the reconstructed energy, the channel energy
was required $E_{\mathrm{channel}}>4$ GeV, but still read out with high
gain.131313This is important since the high gain response is delayed with
respect to that of low gain by about 2 ns. The high gain requirement imposes
an effective upper limit of about $E_{\mathrm{channel}}<12$ GeV.

The results are displayed in figure 20, where the reconstructed time is shown
for all calorimeter channels with and without the timing jump corrections.
While the Gaussian core, corresponding to channels (and events) not affected
by timing jumps, remains basically unchanged, the timing jump corrections
significantly reduce the number of events in the tails. The overall RMS is
improved by 9 % (from 0.90 ns to 0.82 ns after the corrections are applied).

Figure 20: The impact of the timing jump corrections on the reconstructed
channel time in jet collision data. Shown are all TileCal high gain channels
with $E_{\mathrm{channel}}>4$ GeV, being a part of reconstructed jets. Data
correspond to $1.3~{}\mathrm{fb}^{-1}$ of collected physics data in 2012.

##  6 Pathological channels monitoring

For a few channels, the monitoring shows that the PMT input high voltage is
unstable. This instability may be due to a true unstable input voltage or a
failure of the monitoring system. In order to disentangle the two
possibilities, the Laser system can be used to measure the real gain variation
(as described in the previous sections). Figure 21(a) presents an example of
such pathological channel behaviour. In this case, the Laser system does not
observe any variation of the PMT gain, meaning that the actual input high
voltage must be stable and the drift observed in the monitoring is not real.
In the case of figure 21(b), the Laser system confirms the instability of the
high voltage distribution system, the very large gain variations measured by
the Laser system being in agreement with the variations computed from the high
voltage monitoring.

(a) (b)

Figure 21: Example of pathological channels monitoring in 2012. These plots
present the comparison between the gain variation expected from the high
voltage monitoring (blue dots) and the one measured by the Laser (red squares)
and the Cesium (green dots) systems. The vertical structures are due to ON/OFF
switchings and are expected. However, between two switchings and for normal
channels, the gain should be constant.

##  7 Conclusions

The Laser system is one of the three calibration systems of the ATLAS Tile
Calorimeter. It is a key component for monitoring and calibrating the 9852
TileCal photomultipliers and their associated readout electronics. The Laser
calibration constant $f_{\rm Las}$ applied on each channel has been regularly
measured, with a statistical uncertainty at the level of 0.3 %, and is one
ingredient in the TileCal cell energy reconstruction. Comparing these
correction factors with the ones derived with the Cesium calibration system, a
good compatibility between them was found and the systematic uncertainty on
the Laser calibration constants is estimated to be 0.2 % for the long barrel
modules and 0.5 % for the extended barrel modules. The Laser system has also
been used to monitor the timing of the TileCal front-end electronics during
physics runs, allowing to correct for timing jumps provoked by mis-
configuration resulting from power supplies trips. It has also been used to
monitor the behaviour of pathological calorimeter channels.

In order to improve the stability and the reliability of the system for the
LHC run 2, a major upgrade was performed in October 2014, including a
completely new electronics, ten photodiodes to measure the light at various
stages in the Laser box, and a new light splitter.

## References

  * [1] ATLAS Collaboration, The ATLAS Experiment at the CERN Large Hadron Collider, JINST 3 (2008) S08003.
  * [2] ATLAS Collaboration, Readiness of the ATLAS Tile Calorimeter for LHC collisions, Eur.Phys.J. C70 (2010) 1193–1236, [arXiv:1007.5423].
  * [3] ATLAS Collaboration, ATLAS Tile Calorimeter: Technical Design Report, Tech. Rep. CERN/LHCC 96-42, 1996.
  * [4] K. Anderson et al., Design of the front-end analog electronics for the ATLAS tile calorimeter, Nucl.Instrum.Meth. A551 (2005) 469–476.
  * [5] S. Berglund et al., The ATLAS tile calorimeter digitizer, JINST 3 (2008) P01004.
  * [6] J. Poveda et al., ATLAS TileCal read-out driver system production and initial performance results, IEEE Trans.Nucl.Sci. 54 (2007) 2629–2636.
  * [7] W. E. Cleland and E. G. Stern, Signal processing considerations for liquid ionization calorimeters in a high rate environment, Nucl. Instrum. Meth. A338 (1994), no. 2-3 467–497.
  * [8] A. Valero on behalf of the ATLAS Tile Calorimeter system, The ATLAS TileCal Read-Out Drivers Signal Reconstruction, IEEE, Nuclear Science Symposium Conference Record (NSS/MIC) (2009) 593–596.
  * [9] E. Starchenko et al., Cesium monitoring system for ATLAS Tile Hadron Calorimeter, Nucl.Instrum.Meth. A494 (2002) 381–384.
  * [10] P. Adragna et al., Testbeam studies of production modules of the ATLAS Tile Calorimeter , Nucl.Instr.Meth. A606 (2009) 362–394.
  * [11] Z. J. Ajaltouni et al., The Tilecal laser monitoring, Tech. Rep. ATL-TILECAL-94-039. ATL-L-PN-39, CERN, Geneva, Dec, 1994.
  * [12] P. Grenier and L. Says, Analysis of the 1997 test beam laser data of the Tilecal extended barrel module 0, Tech. Rep. ATL-TILECAL-98-159, CERN, Geneva, May, 1998.
  * [13] “Photo-diode S3590-08 from Hamamatsu.” https://www.hamamatsu.com/resources/pdf/ssd/s3590-08_etc_kpin1052e.pdf.
  * [14] R. Alves, J. Carvalho, Y. Ivaniouchenkov, J. Mateu, F. Moita, and J. Pinhão, The distribution of laser light for the calibration and monitoring system of the ATLAS hadronic calorimeter, IEEE, Nuclear Science Symposium, Conference Record (1999).
  * [15] K. Aitamar, J. Carvalho, F. Moita, A. Onofre, N. Perpetua, J. Pinhão, and S. Uva, Optical fibre connectors for the laser calibration system, Tech. Rep. ATL-TILECAL-96-093. ATL-L-PN-93, CERN, Geneva, Oct, 1996.
  * [16] “TTCrq web site.” http://proj-qpll.web.cern.ch/proj-qpll/ttcrq.htm.
  * [17] “High-speed Optical Link for Atlas web site.” http://hsi.web.cern.ch/HSI/s-link/devices/hola/.
  * [18] L. Evans and P. Bryant, LHC Machine, JINST 3 (2008) S08001.
  * [19] A. Kolmogorov, Sulla determinazione empirica di una legge di distribuzione, G. Ist. Ital. Attuari 4 (1933) 83–91.
  * [20] N. Smirnov, Table for estimating the goodness of fit of empirical distributions, Ann. Math. Statist. 19 (1948) 279–281.

ATLAS Tile Calorimeter system

J. Abdallah20, C. Alexa29, Y. Amaral Coutinho37, S.P. Amor Dos Santos8,26,
K.J. Anderson14, G. Arabidze5, J.P. Araque26, A. Artamonov21, L. Asquith18, R.
Astalos17, J. Backus Mayes32, P. Bartos17, L. Batkova17, F. Bertolucci11, O.
Bessidskaia Bylund36, A. Blanco Castro26, T. Blazek17, C. Bohm36, D.
Boumediene27, A. Boveia14, H. Brown7, E. Busato27, R. Calkins6, D. Calvet27,
S. Calvet27, R. Camacho Toro27, R. Caminal Armadans20, T. Carli2, J.
Carvalho8,26, M. Cascella11, N.F. Castro26,4,3, V. Cavasinni11, A.S.
Cerqueira13, R. Chadelas27, D. Chakraborty6, S. Chekanov18, X. Chen34, L.
Chikovani12,†, G. Choudalakis14, D. Cinca27, M. Ciubancan29, C. Clement36, S.
Cole6, S. Constantinescu29, T. Costin14, M. Crouau27, C. Crozatier27, C.-M.
Cuciuc29, M.J. Da Cunha Sargedas De Sousa15,26, S. Darmora7, T. Davidek16, T.
Del Prete11, S. Dita29, T. Djobava19, J. Dolejsi16, A. Dotti11, E. Dubreuil27,
M. Dunford14, D. Eriksson36, S. Errede9, D. Errede9, J. Faltova16, A. Farbin7,
R. Febbraro27, P. Federic17, E.J. Feng18, A. Ferrer24, M. Fiascaris14, M.C.N.
Fiolhais8,26, L. Fiorini20, P. Francavilla20, E. Fullana Torregrosa2, B.
Galhardo8,26, K. Gellerstedt36, N. Ghodbane27, V. Giakoumopoulou31, V.
Giangiobbe20, N. Giokaris31, G.L. Glonti25, A. Gomes26,15, G. Gonzalez
Parra20, P. Grenier32, S. Grinstein20, Ph. Gris27, C. Guicheney27, H.
Hakobyan38,†, A.S. Hard10, S. Harkusha1, L. Heelan7, C. Helsens20, A.M.
Henriques Correia2, Y. Hernández Jiménez24, C.M. Hernandez7, E. Higón-
Rodriguez24, M. Hurwitz14, N. Huseynov25, J. Huston5, I. Jen-La Plante14, D.
Jennens33, K.E. Johansson36, K. Jon-And36, P.M. Jorge15,26, A. Juste Rozas20,
A. Kapliy14, S.N. Karpov25, A.N. Karyukhin35, H. Khandanyan36, E. Khramov25,
J. Khubua19, H. Kim36, P. Klimek36, I. Korolkov20, A. Kruse10, Y. Kulchitsky1,
Y.A. Kurochkin1, P. Lafarguette27, D. Lambert27, T. LeCompte18, R. Leitner16,
S. Leone11, H. Liao27, K. Lie9, M. Lokajicek23, O. Lundberg36, P.J. Magalhaes
Martins8,26, A. Maio26,15, M. Makouski35, J. Maneira15,26, L. Manhaes de
Andrade Filho37, A. Manousakis-Katsikakis31, B. Martin5, G. Mchedlidze19, S.
Meehan14, B.R. Mellado Garcia34, E. Meoni20, F.S. Merritt14, C. Meyer14, D.W.
Miller14, D.A. Milstead36, I.A. Minashvili25, L.M. Mir20, S. Molander36, J.
Montejo Berlingen20, M. Mosidze19, A.G. Myagkov35, S. Nemecek23, A.A.
Nepomuceno37, D.H. Nguyen18, V. Nikolaenko35, P. Nilsson7, L. Nodulman18, B.
Nordkvist36, C.C. Ohm2, A. Olariu29, L.F. Oleiro Seabra26, A. Onofre4,26, M.J.
Oreglia14, D. Pallin27, D. Pantea29, D. Paredes Hernandez27, M.I. Pedraza
Morales10, R. Pedro15,26, F.M. Pedro Martins26, H. Peng10, B. Penning14, J.E.
Pilcher14, J. Pina26, V. Pleskot16, E. Plotnikova25, F. Podlyski27, G.A.
Popeneciu28, J. Poveda10, R. Pravahan7, L. Pribyl2, L.E. Price18, J.
Proudfoot18, J.G. Rocha de Lima6, C. Roda11, D. Roda Dos Santos23, S.M. Romano
Saez27, V. Rossetti20, A. Ruiz-Martinez24, N.A. Rusakovich25, B.M. Salvachua
Ferrando18, C. Santoni27, H. Santos26, J.G. Saraiva26, L.P. Says27, A.
Schwartzman32, F. Scuri11, S. Shimizu2, J. Silva26, S.B. Silverstein36, C.A.
Solans24, A.A. Solodkov35, O.V. Solovyanov35, M. Spalla11, R.W. Stanek18, E.A.
Starchenko35, P. Starovoitov30, P. Stavina17, G. Stoicea29, A. Succurro20, C.
Suhr6, T. Sumida2, I. Sykora17, P. Tas16, A. Tavares Delgado15,26, S. Tokár17,
P.V. Tsiareshka1, V. Tsiskaridze19, V. Tudorache29, A. Tudorache29, J.M.
Tuggle14, M. Tylmad36, G. Usai7, A. Valero24, L. Valery27, E. Valladolid
Gallego24, J.A. Valls Ferrer24, F. Vazeille27, F. Veloso8,26, I. Vichou9,†,
V.B. Vinogradov25, S. Viret27, M. Volpi20, C. Wang22, Z. Weng22, A. White7,
H.G. Wilkens2, S. Yanush30, R. Yoshida18, L. Zhang22, Y. Zhu10, Z. Zinonos11,
V. Zutshi6, T. Ženiš17, M.C. van Woerden2.

† deceased
1 B.I. Stepanov Institute of Physics, National Academy of Sciences of Belarus,
Minsk, Republic of Belarus
2 CERN, Geneva, Switzerland
3 Departamento de Física e Astronomia, Faculdade de Ciências, Universidade do
Porto, Portugal
4 Departamento de Fisica, Universidade do Minho, Braga, Portugal
5 Department of Physics and Astronomy, Michigan State University, East Lansing
MI, United States of America
6 Department of Physics, Northern Illinois University, DeKalb IL, United
States of America
7 Department of Physics, The University of Texas at Arlington, Arlington TX,
United States of America
8 Department of Physics, University of Coimbra, Coimbra, Portugal
9 Department of Physics, University of Illinois, Urbana IL, United States of
America
10 Department of Physics, University of Wisconsin, Madison WI, United States
of America
11 Dipartimento di Fisica E. Fermi, Università di Pisa, Pisa, Italy
12 E. Andronikashvili Institute of Physics, Iv. Javakhishvili Tbilisi State
University, Tbilisi, Georgia
13 Electrical Circuits Department, Federal University of Juiz de Fora (UFJF),
Juiz de Fora, Brazil
14 Enrico Fermi Institute, University of Chicago, Chicago IL, United States of
America
15 Faculdade de Ciências, Universidade de Lisboa, Lisboa, Portugal
16 Faculty of Mathematics and Physics, Charles University in Prague, Praha,
Czech Republic
17 Faculty of Mathematics, Physics & Informatics, Comenius University,
Bratislava, Slovak Republic
18 High Energy Physics Division, Argonne National Laboratory, Argonne IL,
United States of America
19 High Energy Physics Institute, Tbilisi State University, Tbilisi, Georgia
20 Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of
Science and Technology, Barcelona, Spain
21 Institute for Theoretical and Experimental Physics (ITEP), Moscow, Russia
22 Institute of Physics, Academia Sinica, Taipei, Taiwan
23 Institute of Physics, Academy of Sciences of the Czech Republic, Praha,
Czech Republic
24 Instituto de Física Corpuscular (IFIC) and Departamento de Física Atómica,
Molecular y Nuclear and Departamento de Ingeniería Electrónica and Instituto
de Microelectrónica de Barcelona (IMB-CNM), University of Valencia and CSIC,
Valencia, Spain
25 Joint Institute for Nuclear Research, JINR Dubna, Dubna, Russia
26 Laboratório de Instrumentação e Física Experimental de Partículas - LIP,
Lisboa, Portugal
27 Laboratoire de Physique Corpusculaire, Clermont Université and Université
Blaise Pascal and CNRS/IN2P3, Clermont-Ferrand, France
28 National Institute for Research and Development of Isotopic and Molecular
Technologies, Physics Department, Cluj Napoca, Romania
29 National Institute of Physics and Nuclear Engineering, Bucharest, Romania
30 National Scientific and Educational Centre for Particle and High Energy
Physics, Minsk, Republic of Belarus
31 Physics Department, University of Athens, Athens, Greece
32 SLAC National Accelerator Laboratory, Stanford CA, United States of America
33 School of Physics, University of Melbourne, Victoria, Australia
34 School of Physics, University of the Witwatersrand, Johannesburg, South
Africa
35 State Research Center Institute for High Energy Physics (Protvino), NRC KI,
Russia
36 The Oskar Klein Centre, Stockholm, Sweden
37 Universidade Federal do Rio De Janeiro COPPE/EE/IF, Rio de Janeiro, Brazil
38 Yerevan Physics Institute, Yerevan, Armenia