figurec

LHCb VELO Timepix3 Telescope

Kazu Akibaa, Martin van Beuzekoma,1, Henk Boterenbrooda, Emma Buchananb, Jan
Buytaertc, Wiktor Byczynskic, Xabier Cid Vidald, Paula Collinsc, Elena
Dall’Occoa, Alvaro Dosil Suárezd, Raphael Dumpsc, Tim Evanse, Vinicius Franco
Limaf, Abraham Gallas Torreirad, Julián García Pardiñasd, Bas van der
Heijdena, Christoph Hombachg, Malcolm Johne, Szymon Kulisc, Xavi Llopart
Cudiec, Franciole Marinhoh, Eugenia Priceb, Sophie Richardsb, Pablo Rodriguez
Perezg, Daniel Saundersb, Åsmund Schiager Folkestadc, Heinrich Schindlerc,
Frans Schreudera, Hella Snoeka, Panagiotis Tsopelasa, Jaap Velthuisb, Maria
Vieites Diazd, Mark R. J. Williamsg

aNikhef
bBristol University
cCERN
dUniversity of Santiago de Compostela
eOxford University
fLiverpool University
gUniversity of Manchester
hUniversidade Federal de São Carlos
1 Corresponding author<EMAIL_ADDRESS>
The LHCb VELO Timepix3 telescope is a silicon pixel tracking system
constructed initially to evaluate the performance of LHCb VELO Upgrade
prototypes. The telesope consists of eight hybrid pixel silicon sensor planes
equipped with the Timepix3 ASIC. The planes provide excellent charge
measurement, timestamping and spatial resolution and the system can function
at high track rates. This paper describes the construction of the telescope
and its data acquisition system and offline reconstruction software. A timing
resolution of 350 ps was obtained for reconstructed tracks. A pointing
resolution of better than 2 $\,\upmu\rm m$ was determined for the 180 GeV/c
mixed hadron beam at the CERN SPS. The telescope has been shown to operate at
a rate of 5 million particles $\rm\,s^{-1}\cdot cm^{-2}$ without a loss in
efficiency.

###### Contents

  1. 1 Introduction
  2. 2 Hardware Description
  3. 3 Data Acquisition (DAQ)
  4. 4 Slow Control and Monitoring
  5. 5 Offline Reconstruction Software
    1. 5.1 Charge calibration
    2. 5.2 Time alignment
    3. 5.3 Clustering and tracking
    4. 5.4 Spatial alignment
  6. 6 Telescope Performance
    1. 6.1 Time resolution
    2. 6.2 Spatial residuals
    3. 6.3 Pointing resolution
    4. 6.4 Track purity
    5. 6.5 High rate performance
  7. 7 Summary
  8. 8 Acknowledgements

##  1 Introduction

Hybrid pixel detectors from the Medipix [1] ASIC family have been previously
employed for reconstruction of trajectories of high energy charged particles
[2, 3]. The combination of powerful integrated circuits and the high signal to
noise ratio of the sensor assemblies makes this technology ideal for precise
track reconstruction. The Timepix3 ASIC [4] offers very precise and
simultaneous measurements of the particle’s Time-of-Arrival (ToA) and Time-
over-Threshold (ToT), which is proportional to the deposited charge of the
corresponding signal. These two measurements provide an excellent input for
the pattern recognition algorithms, making the subsequent track reconstruction
fast and precise.

This paper describes a high performance particle telescope which has been
constructed based on the Timepix3 ASIC, in the view of the sensor
characterisation program for the upgrade of the LHCb Vertex Locator (VELO)
[5]. The telescope reconstructs timestamped tracks with a precise projected
position in the centre of the telescope. A Device-Under-Test (DUT) can be
mounted at this position and moved via remote-controlled rotation and
translation stages. The telescope has already integrated a variety of DUTs in
the telescope data acquisition system; either with an identical readout in the
case of Timepix3 assemblies, or via offline timestamp alignment. To
characterise DUT sensors in detail, charged particle beams at the PS and SPS
[6, 7] were used. These facilities provide protons with momenta of 24 GeV/c
(PS) and mixed hadrons (p, $\pi$, K) of about 120 GeV/c (SPS). Most of the
results presented are obtained with SPS hadrons that are provided in spills of
about 2 million particles during 4.5 seconds.

The telescope mechanical design is described in section 2, followed by the
readout chain and slow controls in sections 3 and 4, and the data analysis
software packages in section 5. Finally, the relevant telescope performance
figures required to assess the quality of DUTs are described in section 6.

##  2 Hardware Description

Figure 1: Mechanical design of the Timepix3 telescope, with the coordinate
system displayed at the top. The telescope stations are mounted on two
retractable arms around a central stage. The central stage is reserved for
studies on DUTs; it provides translations in $x$ and $y$ as well as rotations
about the $y$ axis.

The telescope consists of two arms of four detector planes each, as
illustrated in figure 1. A global right-handed coordinate frame is defined
with the $z$ axis in the direction of the beam and the $y$ axis pointing
upwards. This convention is adopted throughout this paper. The detector
modules are 300 $\,\upmu\rm m$ thick $p$-on-$n$ pixelised silicon sensors
bump-bonded to $\approx 700$ $\,\upmu\rm m$ thick Timepix3 ASICs. Hence, each
plane adds approximately 1 mm of silicon ($\approx 1\%~{}X_{0}$, where $X_{0}$
is the radiation length) to the material budget of the telescope. The printed
circuit boards that hold the sensor assemblies have a square cut-out beneath
the active area of the chip and thus do not contribute to the material budget,
except for an outer ring of about 0.5 mm. To improve the spatial resolution,
charge sharing between pixels is maximised by placing the planes under an
angle about the $x$ and $y$ with respect to the $z$ axis. For 300 $\,\upmu\rm
m$ thick sensors and 55 $\,\upmu\rm m$ pixel pitch the optimal angle
corresponds to approximately $9^{\circ}$. Given the pixel pitch and a matrix
size of 256$\times$256, the active area of the telescope is about
1.4$\times$1.4 cm2. The positions of the telescope planes along the $z$ axis
are adjustable; the telescope is operated typically with a distance of 31 mm
between the planes within one arm and about 200 mm between the two arms.
Cooling of the telescope planes is achieved with pre-cooled air circulating
inside the telescope protective enclosure, which is also light-tight.

A DUT can be installed on a remote-controlled motion stage between the two
telescope arms. The two telescope arms are mounted on rails such that the
distance between the arms can be adjusted depending on the size of the DUT.
The stage allows translations in $x$ and $y$ and rotations about the $y$ axis.
A second stage is available downstream of the telescope which is used by DUTs
larger than the available space or less demanding in terms of pointing
resolution. The telescope also includes two scintillators, one upstream and
one downstream of the telescope arms, which can be used to trigger the data
acquisition systems of external DUTs111External devices are detectors that are
not based on the Timepix3 ASIC..

Finally, the base of the telescope is mounted on a remote controlled motion
stage, which allows the entire telescope to be moved in $x$ and $y$. This
allows the alignment of the telescope with respect to the beam.

##  3 Data Acquisition (DAQ)

The telescope silicon sensor signals are processed by Timepix3 ASICs that can
be operated in different readout modes [4]. The acquisition mode used for the
telescope features simultaneous measurement of the Time-of-Arrival (ToA) and
Time-over-Threshold (ToT) per pixel. A pixel hit is timestamped with a Time-
to-Digital converter bin size of 1.56 ns, and a timestamp range of 409.6
$\,\upmu{\rm s}$. The ToT measurement provides information about the amount of
charge collected by the pixel. It has a range of 10 bits, with a configurable
resolution that can be set via the discharge current of the preamplifier. The
typical operational conditions for the telescope give a correspondence of each
ToT count to a charge of about 200 e-. The capacitance of the small pixels is
low and hence the noise contribution from the amplifier circuit is less than
100 e- RMS. The shot noise contribution from the sensor is negligible. Running
with a nominal threshold of 1000 e- for the telescope planes ensures that
there are virtually no noise hits, while allowing full detection efficiency
for multi pixel clusters.

For high rate tracking performance, the chip features a so-called data-driven
readout mode in which the 48 bit data packet of each pixel hit is sent off-
chip immediately after ToT conversion. The chip can send out up to 80 Mhits/s
over 8 serial links each running at 640 Mbit/s. To acquire the data from the
ASICs a readout system called Speedy PIxel Detector Readout (SPIDR) [8, 9] is
employed. The SPIDR system is specially tailored to the readout of the
Timepix3 and Medipix3 chips at their maximum rate, and can be operated with
both a 1 Gigabit and 10 Gigabit ethernet (GbE) interface. The 10 GbE interface
is $\approx 55\%$ occupied when reading out a single Timepix3 chip at its
maximum rate. The SPIDR version used in the telescope is based on the Xilinx
Virtex 7 VC707 evaluation board and can read out two telescope planes in
parallel. This is the default configuration of the readout, but to operate the
whole telescope at its maximum rate each telescope plane requires a single
dedicated SPIDR board.

Three data streams can be distinguished: slow control to and from the SPIDR
via TCP/IP, the (full) data stream from SPIDR to computer via the User
Datagram Protocol (UDP), and monitoring data from SPIDR to computer via UDP.

The two main tasks of the Virtex 7 FPGA board are the slow and fast (clock
synchronisation and timing) control of the Timepix3 chips, and the packing of
the data coming from the chips into UDP datagrams. Upon reception of the pixel
packets, the timestamp in the packet with a range of 409.6$\,\upmu{\rm s}$ is
extended by 16 bits, thereby increasing the range to 28.8 seconds to ease the
offline reconstruction. Synchronisation of the different telescope planes is
achieved via a central logic unit (TLU, Telescope Logic Unit) that provides
the clock to all SPIDR systems. The TLU hardware is based on a Xilinx SP601
evaluation board and the fan out of the signal is is done with boards
originally designed for a cosmic ray experiment [10]. The TLU also supplies a
signal to synchronise all time counters, and a shutter signal to synchronously
control the start and stop of the data flow. Each SPIDR supplies a _busy_
signal to the TLU which is used to signal buffer overflow either in the SPIDR
or its DAQ computer. If one of the systems overflows the shutter is closed by
the TLU and the entire data acquisition is paused until the buffers are
emptied. The SPIDR boards and the TLU receive commands from the run control
software via ethernet. The run control software provides a graphical user
interface for configuring the boards and ASICs and to start and stop runs.
Moreover, the run control graphically displays the volume of data acquired per
telescope plane. In this way problems in the data acquisition can be
monitored, which occasionally occur due to radiation induced Single Event
Upsets in the configuration registers of the Timepix3.

In order to simplify integration of other, non-Timepix3, detectors, the SPIDR
boards feature a TDC input with 260 ps bins. The trigger signal of such a
detector can then be timestamped in the clock domain of the telescope and
reconstructed tracks can be linked to these triggers in the offline software.
Since the telescope uses four SPIDR boards, up to four different detectors can
be run simultaneously with the telescope.

##  4 Slow Control and Monitoring

A dedicated slow control system has been developed to enable remote-control of
all motion stages and power supplies. The entire telescope can be moved in $x$
and $y$ to remotely align with the beam position, or be removed from the beam
path completely if required. The two DUT stages, one mounted at the centre
between the two telescope arms and the other mounted outside of the main
telescope enclosure, include precise remote-controlled translation and
rotation stages. The translation and rotation stages, supplied by PI [11], are
controlled by stepper motors and have a repeatability of 2 $\,\upmu\rm m$ for
translation and 50 $\,\upmu\rm rad$ for rotation. The vertical stages are
supplied by Festo [12]. Two Keithley 2410 Source Meters [13] are used to bias
independently the telescope planes and DUT. The telescope planes are usually
operated with a bias tension of 150 V, which is at least 100 V above the
sensor full depletion voltage. An additional power supply is also controlled
remotely for a Peltier based DUT cooling system. Humidity and temperature
sensors provide environmental monitoring of conditions within the telescope
enclosure. The positions of all motion stages as well as the bias voltages,
currents and environmental measurements are logged periodically to enable
recovery of all conditions for analysis. Figure 2 summarises all elements of
the slow control system.

Figure 2: Block diagram of the slow control system. The telescope and DUT bias
voltages and motion stages are operated remotely. The bias currents and
temperatures of the telescope environment are monitored and logged.

##  5 Offline Reconstruction Software

A software application, “Kepler 222in honour of the German astronomer Johannes
Kepler (1571-1630).”, based on the Gaudi event-processing framework [14] has
been developed to analyse the telescope data and provides track fitting,
alignment and charge calibration among other tasks. The application produces a
ROOT file with histograms and ntuples for further user analyses.

The Gaudi framework was developed to process data taken at colliders, where
there is a clear ‘event’ structure corresponding to the bunch crossing. No
such structure exists in the PS and SPS secondary beams, where there is a
continuous time profile during the flat top of a spill, which typically lasts
about 4.5 seconds for the CERN SPS. In contrast to frame-based telescopes [3],
the Timepix3 telescope data does not have an inherent event structure due to
the data-driven readout described in section 3. Because the typical dataset of
a run is hundreds of MBytes it is impractical to process the entire run in a
single pass. The data stream is therefore divided into time slices of
configurable length and each slice is processed individually. The length of
the time slice is chosen to be 400 $\,\upmu{\rm s}$ and with this setting the
number of tracks that are split up into different events is negligible.

For each event, a sequence of algorithms is executed, starting by decoding the
raw data files for each detector plane. The pixel packets are not received in
order with respect to their timestamps. In order to ensure all hits belonging
to the current event are found, it is necessary to read ahead in the file
until a packet with a timestamp newer than the next-to-next event, i.e. over
800 $\,\upmu{\rm s}$ after the start of the current event, is found.

The reconstruction of one spill ($\sim 10^{6}$ tracks) takes approximately 70
seconds on an Intel E3 2.6 GHz processor. The large-scale processing of runs
on a distributed analysis platform such as DIRAC is enabled in GANGA [15], a
process management interface.

In the following sections the general structure of the telescope
reconstruction software is described. The ToT to charge calibration method is
described in section 5.1, followed by the time alignment in section 5.2. The
clustering and tracking algorithms are detailed in section 5.3. Finally the
spatial alignment is described in section 5.4.

###  5.1 Charge calibration

The Timepix3 ToT measurement provides information about the charge deposited
in the sensor. In order to find the correspondence between ToT and charge, a
calibration procedure is performed using test pulses. The ToT values are
converted to charge with a surrogate function [16]. The parameters of this
function are obtained for each pixel by injecting known charges via a test-
pulse circuit and measuring the corresponding ToT values. The calibration has
been verified using monochromatic x-rays in the Brazilian Synchrotron Light
Laboratory. These two methods agree within 4% [17].

The charge collected in a typical telescope plane for clusters associated to a
track is shown in figure 3. After applying the charge calibration described
above, the distribution of charge deposited is well described by a Landau
function convoluted with a Gaussian distribution to account for the intrinsic
resolution of the charge measurement. The extracted Landau MPV (Most Probable
Value) is found to be $25.3\pm 0.7$ ke-, which is compatible with the expected
value of a MIP crossing a 300 $\,\upmu\rm m$ silicon layer.

Figure 3: Typical distribution of collected charge of associated clusters for
a telescope plane. The curve shows the Landau convoluted with a Gaussian fit.

###  5.2 Time alignment

There are small time offsets between the planes of the telescope due to the
time of flight of the particles and non equal delays in the cables and
electronics. Each plane is time aligned by minimising the variance of the
cluster times (as defined in section 5.3) with a set of offsets $\tau_{i}$.
This is equivalent to subtracting the mean of the biased track time residuals.
The offsets are measured for all runs, and found to be consistent with each
other to within a spread of about $15{\rm\,ps}$, showing stability over time.

###  5.3 Clustering and tracking

Neighbouring pixel hits within a time window of 100 ns are grouped into a
cluster. The cluster coordinates are calculated as the charge-weighted centre-
of-gravity of the pixel hits constituting the cluster. The difference in the
charge-weighted and ToT-weighted position resolution was studied and found to
be negligible. The timestamp of the earliest hit in the cluster is used as the
cluster timestamp, which mitigates the time spread due to the timewalk of hits
with low charge.

The pattern recognition is based on a simple track-following technique. Track
seeds are created from pairs of clusters on adjacent planes that are not yet
part of a track, and differ by less than 10 ns in their timestamps. The seed
tracks are extrapolated to the next plane following the beam propagation
direction (downstream) and the closest cluster in time is added to the track
if it is found within a temporal and spatial tolerance window. This is
repeated until all planes are searched. If the candidate track comprises 8
clusters, it is accepted and a straight-line fit is performed. The track time
is given by the arithmetic average of the timestamps of the clusters
constituting the track. A list of the standard selection requirements used in
the track reconstruction is shown in Table 1.

Table 1: List of the standard track reconstruction conditions. Requirement | Default value | Description
---|---|---
Cluster time window | < 100 $\rm\,ns$ | Maximum time difference of hits
|  | within the same cluster
Cluster width, in $x$ and $y$ |  $\leq$ 3 pixels | Rejects large clusters from
|  |  $\delta$-rays, nuclear interactions etc.
Track time window |  $<$ 10 $\rm\,ns$ | Clusters within 10 ns window are
|  | considered for the pattern recognition
Number of clusters | = 1 per plane | Rejects multi prong interaction vertices
in time window |  |
Number of clusters | = 8 | Maximizes track precision
per track |  |
Opening Angle |  $<$ 0.01 rad | Angle that defines the reconstruction
|  | window from plane to plane,
|  | assuming straight tracks
Fit $\chi^{2}$/ndof |  $<$ 10 | Cut on $\chi^{2}$ divided by the number of
|  | degrees of freedom for track quality

###  5.4 Spatial alignment

The planes of the telescope are aligned using the Millipede algorithm [18].
The principal advantage of this method is the simultaneous fit of both the
track states and the geometry. The algorithm is iterated several times with
progressively more restrictive selections on the tracks used. A sample
consisting of a fixed number of tracks, typically 8000, is reconstructed and
an alignment tool executed. This alignment is then used to update the geometry
constants, and the next sample of tracks can be reconstructed with reduced
spatial windows and more restrictive requirements on track fit qualities. This
is repeated until either all alignment tools have been executed, or the data
set has been exhausted. All runs are automatically aligned using the same
procedure. Alignment of DUTs that have a similar geometry as the telescope
planes is also provided by the Kepler software framework, and can be
integrated into the automated alignment sequence.

##  6 Telescope Performance

In this section the telescope performance results are presented. The most
relevant parameters assessed are the track time resolution (section 6.1), the
spatial resolution (section 6.2), together with its extrapolation to the track
pointing resolution (section 6.3). Finally, an assessment of the high rate
capabilities of the telescope is shown in section 6.5.

###  6.1 Time resolution

After the time alignment procedure described in section 5.2, the time
resolution of the telescope can be determined. The track timestamp is
calculated as the average of the associated cluster timestamps. The unbiased
time resolution for a single plane is given by the standard deviation of the
time residual of the clusters in one plane relative to the corresponding
track, where the track time is the average time of the other seven clusters on
the track. This resolution is given by the combination of the intrinsic time
resolution of a single plane and the track resolution:

$\sigma^{2}_{\rm unbiased}=\sigma^{2}_{\rm track}+\sigma^{2}_{\rm intrinsic}.$

If the intrinsic time resolution ($\sigma_{\rm intrinsic}$) is the same for
each plane and the errors on the time measurements are uncorrelated, the track
time resolution for a telescope with $N$ planes is given by $\sigma_{\rm
telescope}=\sigma_{\rm intrinsic}/\sqrt{N}$. Since the unbiased resolution is
measured on a seven plane telescope, $\sigma_{\rm
intrinsic}=\sqrt{\frac{7}{8}}\sigma_{\rm unbiased}$.

The unbiased distribution in a 2$\times$2 mm2 fiducial region shows a Gaussian
shape with a width of $1.04\pm 0.01$ ns and from this the intrinsic time
resolution is determined to be $\sigma_{\rm intrinsic}=0.99\pm 0.01$ ns per
plane for a bias voltage of 200 V. The difference between this result and the
naïvely expected value of $1.56{\rm\,ns}/\sqrt{12}$ is due to a mixture
effects such as timewalk in the chip, pixel-to-pixel variations, the spread in
charge collection times in the sensor, and possibly partial correlations of
the time measurements in the different planes. At 200 V bias the telescope
time resolution from the combination of the eight uncorrelated measurements
yields a value of 0.35 ns. Figure 4 shows the telescope time resolution as
function of the applied bias tension to all planes, where this improvement is
due to the lower charge collection time. Increasing the bias voltage beyond
200 V might still yield a better resolution but it was considered to pose a
risk of damaging the sensors.

Figure 4: Resolution of track timestamps as function of bias voltage, using
eight telescope planes.

This resolution was cross checked by measuring the time difference with
respect to two scintillators instrumented with constant fraction
discriminators. The scintillator signals are timestamped with the TDCs of the
SPIDR which have an average bin size of 260 ps and hence a resolution of about
75 ps. The time resolution of the scintillator system is determined to be
better than 0.3 ns and this measurement confirms the track time resolution of
$0.35$ ns.

###  6.2 Spatial residuals

The precision of the spatial alignment of a plane is measured in an unbiased
manner by excluding it from the pattern recognition and comparing the
extrapolated position of tracks with the corresponding cluster on that plane.
These unbiased residuals are displayed for a typical plane in figure 5,
integrated over the sensor and as a function of position. In this case the
residual is shown as a function of the orthogonal position, testing for
rotations around the z axis. Typically the variation across the beam spot
relative to all axes is less than 0.2 $\,\upmu\rm m$, and the residual width
is very stable. The unbiased residual resolution is a convolution of the
pointing resolution of the telescope with the intrinsic resolution of the
device.

Figure 5: Unbiased residuals in $x$ and $y$ on one telescope plane, both
integrated over the chip and as a function of position. The error bars show
the fitted gaussian width at each position.

The systematic error on the resolution of each plane is estimated from the
variation across the plane in both $x$ and $y$. A spread of 3-4% (0.15
$\,\upmu\rm m$) is obtained analysing the variations of the standard deviation
of the residuals distribution.

###  6.3 Pointing resolution

A quantity which is of great interest for any device being tested in the
telescope is the pointing resolution; the precision with which the position of
each track is known when extrapolated to the DUT position. For the Timepix3
telescope this resolution is a function of the measurement precision of each
plane, the spacing between the telescope planes, and the amount of material
traversed by the track. In the case of high energy ($>$ 10 GeV) hadronic beams
the dominant contribution in this case is the measurement error of each plane.

In order to determine the track-pointing resolution a simulation procedure is
used. The first step is to obtain an initial estimate of the cluster
resolution of each individual plane. Note that this varies plane by plane due
to the slightly different thresholds used and the variations in the angle
presented to the beam in both the $x$ and $y$ direction. The initial estimates
are found by taking the unbiased residuals and subtracting in quadrature a
reasonable first guess of the track-pointing resolution at the $z$ position of
that plane. The cluster resolution values so obtained are used as inputs to a
fast Monte Carlo simulation similar to the one described in Ref. [3]. The
simulation gives as output the expected biased residual distributions at each
plane, which are the track-cluster residuals measured at each plane for tracks
which use clusters from all 8 planes. The set of biased residuals obtained
from the simulation are then compared to the data, and the input errors are
scaled by a single number for all planes until the best overall agreement with
data is achieved. The cluster resolutions of the planes are found to be
between 3.7 and 4.2 $\,\upmu\rm m$ in $x$ and 2.8 and 3.4 $\,\upmu\rm m$ in
$y$. The output of the simulation is used to derive the $z$-dependent track-
pointing error. A conservative estimate of the error on this quantity is
derived by varying the intrinsic spatial resolution of each plane by $\pm 0.5$
$\,\upmu\rm m$.

The result of the study is illustrated in figure 6 for the $x$ and $y$
pointing resolution separately. There is a good agreement between the biased
residuals measured in data and the ones predicted by the simulation. The
predicted pointing resolution and uncertainty is shown by the blue band. The
best pointing resolution is achieved at the DUT position in the centre of the
telescope. Here the resolutions are $\sigma_{x}=1.69\pm 0.16$ $\,\upmu\rm m$
and $\sigma_{y}~{}=~{}1.55~{}\pm~{}0.16$ $\,\upmu\rm m$. Also at the DUT stage
downstream ($z\approx 800$ mm) of the telescope a reasonable pointing
precision (< 10 $\,\upmu\rm m$) is achieved.

Figure 6:  Predicted pointing resolution and uncertainty (solid blue curves)
in the $x$ coordinate (left plot) and $y$ coordinate (right plot). The green
dots show the Monte Carlo biased resolution and the applied uncertainty is
indicated by green bars. The red points show the biased resolution measured in
the data. The typical installation position for a DUT is illustrated by the
hatched grey region.

###  6.4 Track purity

The track purity is defined as the fraction of reconstructed tracks that are
due to a true charged particle traversing the telescope with respect to the
total number of reconstructed tracks. The precise time-stamping of each hit in
the telescope allows a very clean pattern recognition. Even at the highest
rates of about $6.25\times 10^{6}$ particles/second, the average time between
tracks is 16 times larger than the tracking time window, and 160 times larger
than the timestamp precision obtained in each of the planes. The use of timing
measurements and the requirement to have exactly one cluster in each of the
telescope planes reduce the rate of fake tracks to a negligible level. The
remaining contamination from fake tracks is estimated by performing a fit to
the spatial residuals of the telescope including a flat background component.
This component is taken as the upper bound of the number of fake tracks and
found to be below 2‰. Hence the purity of the tracks reconstructed by the
telescope is above 99.8%.

###  6.5 High rate performance

Figure 7: Fraction of clusters not associated to a reconstructed track in the
internal planes of the telescope. In the high-rate configuration the telescope
was constituted by 6 planes only. The plane-to-plane variation does not depend
on the rate and remains constant. This is attributed to slight differences
among the ASICs.

The beam intensity at the SPS experimental area can be modified by moving
collimators located upstream in the beam line. The maximum achievable
sustained intensity is $\approx 26$ million tracks per spill of length 4.5 s.
This limitation is imposed by the background radiation alarms that dump the
beam once they are triggered. In order to operate at high rates, the
configuration of the Timepix3 telescope was altered with respect to the one
described in section 3. The high-rate configuration consists of six planes
each read out by a dedicated SPIDR board to ensure enough throughput to run
the Timepix3 ASIC at its maximum rate. During the dedicated high-rate
performance runs, the beam average particle rate was gradually increased from
70k to 26M tracks per 4.5 s spill. Since the beam and the telescope are not
exactly parallel, some particles will not traverse all planes and hence not
result in a reconstructed track. To mitigate the impact of this effect, the
high rate performance is assessed in a fiducial region which contains the
highest concentration of reconstructable tracks.

The fraction of clusters in each plane which are not associated to a track is
studied in order to verify that the telescope maintains a good pattern
recognition efficiency at high track rates. The dominant source of
nonassociated clusters is particle interactions in the telescope material
which can generate $\delta$-rays, large angle scattering or vertices with
multiple secondary tracks. The background rate from noise hits in the
telescope is checked with runs without beam and found to be negigible. The
fraction of nonassociated clusters should remain constant as the particle rate
increases, as long as the pattern recognition remains efficient and there is
no significant increase in the number of clusters on a particular plane. This
quantity is plotted in figure 7 as a function of particle rate, where the rate
is determined from the telescope track reconstruction and timestamps. Up to a
rate of 5 MHz/cm2, corresponding to the maximum that the SPS can deliver, the
rate of nonassociated clusters is constant, indicating that the telescope
track reconstruction efficiency is not significantly degraded.

##  7 Summary

A high speed telescope based on the Timepix3 ASIC has been constructed. This
paper presented the mechanics, data acquisition, slow controls, and
performance figures. The simultaneous ToT and ToA measurements of the Timepix3
offers a fast, simple and robust pattern recognition and track reconstruction.
The use of a charge-weighted clustering algorithm and a track-based alignment
procedure provide residuals of the order of 4 $\,\upmu\rm m$ for each
telescope plane. The pointing resolution at the DUT position, in the centre of
the telescope, is determined to be $1.69\pm 0.16$ $\,\upmu\rm m$. A time
resolution of 350 ps is achieved for reconstructed tracks traversing eight
telescope planes. No deterioration of the telescope performance has been
observed to a rate of 5 MHz/cm2.

##  8 Acknowledgements

We would like to thank the Medipix3 collaboration and especially Michael
Campbell and Jerome Alozy for providing the Timepix3 assemblies for the
telescope. We also express our gratitude to our colleagues in the CERN
accelerator departments for the excellent performance of the PS and SPS. We
gratefully acknowledge the financial support from CERN and from the national
agencies: CAPES, CNPq, FAPERJ (Brazil); the Netherlands Organisation for
Scientific Research (NWO); The Royal Society and the Science and Technology
Facilities Council (UK).

## References

  * [1] R. Ballabriga, M. Campbell, and X. Llopart, Asic developments for radiation imaging applications: The medipix and timepix family, Nucl. Instrum. Meth. A878 (2018) 10
  * [2] K. Akiba et al., Charged particle tracking with the Timepix ASIC, Nucl. Instrum. Meth. A661 (2011) 31, arXiv:1103.2739
  * [3] K. Akiba et al., The Timepix Telescope for High Performance Particle Tracking, Nucl. Instrum. Meth. A723 (2013) 47, arXiv:1304.5175
  * [4] T. Poikela et al., Timepix3: a 65k channel hybrid pixel readout chip with simultaneous toa/tot and sparse readout, Journal of Instrumentation 9 (2014), no. 05 C05013
  * [5] LHCb Collaboration, LHCb VELO Upgrade Technical Design Report, Tech. Rep. CERN-LHCC-2013-021. LHCB-TDR-013, 2013
  * [6] CERN, The proton synchrotron, https://home.cern/science/accelerators/proton-synchrotron
  * [7] CERN, The super proton synchrotron, https://home.cern/science/accelerators/super-proton-synchrotron
  * [8] J. Visser et al., SPIDR: a read-out system for Medipix3 & Timepix3, JINST 10 (2015), no. 12 C12028
  * [9] B. van der Heijden et al., SPIDR, a general-purpose readout system for pixel ASICs, Journal of Instrumentation 12 (2017), no. 02 C02040
  * [10] D. Cussans et al., A readout system for a cosmic ray telescope using Resistive Plate Chambers, JINST 8 (2013) C03003
  * [11] P. Instrumente, Models m403.42s (translation) and m-060.2s (rotation), http://www.physikinstrumente.com
  * [12] Festo, Model reference egsl-bs-55-200-5p, https://www.festo.com/
  * [13] Keithley, Model 2410 smu, http://www.tek.com/keithley
  * [14] M. Clemencic et al., Recent developments in the LHCb software framework Gaudi, J. Phys. Conf. Ser. 219 (2010) 042006
  * [15] J. Mościcki et al., Ganga: A tool for computational-task management and easy access to grid resources, Computer Physics Communications 180 (2009), no. 11 2303
  * [16] J. Jakubek et al., Pixel detectors for imaging with heavy charged particles, Nucl. Instrum. Meth. A591 (2008) 155
  * [17] M. Vicente Barreto Pinto, K. Carvalho Akiba, and E. Ribeiro Polycarpo Macedo, Caracteriza o do TimePix3 e de sensores resistentes radia o para upgrade do VELO, 2016.  Presented 04 Sep 2015
  * [18] V. Blobel, Software alignment for tracking detectors, Nucl. Instr. Meth. A566 (2006), no. 1 5