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Facolta di Scienze Matematiche, Fisiche e Naturali

Laurea Magistrale in Fisica

First prototype of a trackingsystem with “artificial retina” for

fast track finding

Relatore: Prof. Fernando Palombo

Correlatore: Dr. Nicola Neri

Marco Petruzzo

Matricola n◦ 791581

A.A. 2013/2014

Codice PACS:

07.05.Hd

29.40.Gx

First prototype of a tracking

system with “artificial retina” for

fast track finding

Marco Petruzzo

Dipartimento di Fisica, Universita degli Studi di Milano,

Via Celoria 16, 20133 Milano, Italia

A.A. 2013-2014

Contents

Introduction 1

1 Physics Motivations 3

1.1 CP symmetry and its violation . . . . . . . . . . . . . . . . . . . 3

1.2 CP violation in the Standard Model . . . . . . . . . . . . . . . . 4

1.2.1 The CKM matrix . . . . . . . . . . . . . . . . . . . . . . . 7

1.3 CP violation in heavy flavor physics . . . . . . . . . . . . . . . . . 9

1.3.1 B factories . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.3.2 High energy hadron colliders . . . . . . . . . . . . . . . . . 11

1.4 Flavor oscillations and CP violation . . . . . . . . . . . . . . . . . 14

1.5 Fast track finders . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

1.6 Pattern recognition in Associative Memory devices . . . . . . . . 18

1.6.1 Silicon Vertex Trigger at CDF . . . . . . . . . . . . . . . . 20

1.6.2 Fast Tracker at ATLAS . . . . . . . . . . . . . . . . . . . . 22

2 Tracking system prototype with “artificial retina” 24

2.1 The artificial retina algorithm . . . . . . . . . . . . . . . . . . . . 24

2.1.1 Inspiration from neurobiology . . . . . . . . . . . . . . . . 24

2.1.2 Track parameters definition . . . . . . . . . . . . . . . . . 26

2.1.3 Retina response . . . . . . . . . . . . . . . . . . . . . . . . 27

2.1.4 Hardware implementation of the artificial retina . . . . . . 29

2.2 Telescope Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.2.1 Telescope module . . . . . . . . . . . . . . . . . . . . . . . 33

2.2.2 Telescope Layout . . . . . . . . . . . . . . . . . . . . . . . 36

2.3 Retina Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . 37

2.3.1 Data Acquisition system . . . . . . . . . . . . . . . . . . . 39

2.3.2 TEL62 board . . . . . . . . . . . . . . . . . . . . . . . . . 41

1

CONTENTS 2

3 Design and simulation of the prototype system 47

3.1 Sbt software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3.1.1 Main functionalities of the Sbt software . . . . . . . . . . . 47

3.2 Optimization of the telescope layout . . . . . . . . . . . . . . . . 48

3.2.1 Test of the system with cosmic rays . . . . . . . . . . . . . 49

3.2.2 Expected rate of the cosmic rays . . . . . . . . . . . . . . 49

3.3 Optimization of the artificial retina parameters . . . . . . . . . . 51

3.3.1 Sharpness of the retina response . . . . . . . . . . . . . . . 52

3.3.2 Track parameters determination . . . . . . . . . . . . . . . 53

3.3.3 Optimization of the retina response . . . . . . . . . . . . . 55

3.3.4 Threshold value for the retina response . . . . . . . . . . . 56

3.4 Tracking performances . . . . . . . . . . . . . . . . . . . . . . . . 58

3.4.1 Resolution for single track events . . . . . . . . . . . . . . 58

3.4.2 Retina response in presence of background . . . . . . . . . 61

3.4.3 Efficiency and purity as a function of the threshold . . . . 63

3.4.4 Efficiency and purity as a function of the grid step . . . . . 64

3.5 Perspectives for the future - Artificial retina with time information 66

3.5.1 Redefinition of the retina algorithm . . . . . . . . . . . . . 66

3.5.2 Simulation of the retina using the time information . . . . 67

4 Testbeam at CERN 71

4.1 Testbeam setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

4.1.1 Reference telescope . . . . . . . . . . . . . . . . . . . . . . 71

4.1.2 Layout of the electronics logic . . . . . . . . . . . . . . . . 72

4.1.3 Reconstruction of tracks from TimePix3 telescope . . . . . 74

4.2 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

4.2.1 Hit resolution of the DUT . . . . . . . . . . . . . . . . . . 76

Conclusions 78

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

Introduction

In high energy physics experiments at colliders the total number of interactions is

very high while some interesting phenomena can represent just a small fraction of

the entire cross section. The trigger system identifies and selects the events of

interest to be used for higher level of processing and to be stored for subsequent

analysis. The event selection is based on the properties of the event itself. In flavor

physics the presence of a detached vertex is a strong signature of the production

of a particle containing b or c quarks. Because of their lifetimes of O(1ps), these

particles can travel away from the primary vertex enough to be measured with a

tracking system before decaying to lighter particles. The usual way to recognize a

detached vertex is based on the reconstruction of displaced tracks and real-time

tracking systems are used for the event selection. A trigger system based on

track reconstruction is also referred to as vertex trigger or track trigger. A track

trigger system is characterized by its efficiency , the throughput (the frequency

at which the events are processed) and the latency (the delay for taking trigger

decisions). Another important feature is the quality of the reconstructed tracks

to be compared to the offline results. A strategy to achieve high efficiency, high

throughput and low latency is to use a highly parallelized algorithm, based on

fast electronics. An example of a hardware vertex trigger is the Silicon Vertex

Trigger (SVT) of the Collider Detector at Fermilab (CDF). This device is capable

to reconstruct tracks online, thanks to the use of a custom-made processor, the

Associative Memory (AM). The AM compares the hits from the tracking system

to several pre-calculated patterns simultaneously providing the track candidates

to be fitted. The evolution of this concept will be used by ATLAS in the Fast

Tracker (FTK) device during the Run II of LHC, starting in 2015.

In this thesis we discuss the design and the simulation of the first prototype of a

tracking system using an “artificial retina” for fast track finding, implemented on

commercial field-programmable-gate arrays (FPGA) electronics. The retina algo-

rithm is inspired by the neurobiological low-level mechanism of visual recognition

in mammals. It is based on massively parallel calculation of the response of an

array of cells, in which different tracks “receptors” are stored, and covering the

1

CONTENTS 2

entire parameter space in which tracks are defined. By interpolating the response

of adjacent cells, it is possible to obtain good tracking performance while keeping

the number of cells within manageable limits.

The prototype system consists of a telescope made of single-sided silicon strip

sensors. In my thesis work I simulated the telescope and the artificial retina using

a C++ software, in order to study the response of the system and optimize its

design. In particular we have optimized the geometry of the tracking system, the

distribution of the array of cells in the track parameter space and the response

of each cell. The resolution on the track parameters obtained using the retina

algorithm are comparable with the offline results based on a χ2 fit determination.

The retina architecture has been designed and is currently being implemented

in Altera Stratix III FPGA. The retina system is modular and can be designed

to work with large tracking devices at high rates (up to 40 MHz) with a latency

below 1µs [1]. The prototype discussed in this thesis represents the first working

device made in hardware.

We will discuss the physics motivation for a real-time track trigger in Chapter 1.

The Retina algorithm, the implementation of FPGA electronics and its application

to the telescope will be described in Chapter 2. Details about the simulation of the

system and the settings used in the final configuration will be discussed in Chapter

3. Perspectives for the retina algorithm for the future, including applications to

ultrafast silicon detectors will be discussed in Section 3.5.

During my thesis activity I participated to a testbeam for the upgrade of the

tracking detector of the LHCb experiment. The software that we developed for

the simulation of the retina prototype telescope has been used to reconstruct the

testbeam events and perform studies on a detector under test. A brief description

of this work will be given in Chapter 4.

Chapter 1

Physics Motivations

In modern experiments at high-energy hadron colliders, powerful real time tracking

systems are needed to reconstruct and quickly select potentially interesting events

for higher level of processing, and finally permanent storage for subsequent analysis.

This issue is particularly challenging at experiments like LHCb, at the Large

Hadron Collider, that aims to reconstruct flavor events where there are no easily

identifiable event characteristics that can be used for preselection, like total

transverse energy, missing transverse energy or leptons with high transverse

momentum. This means that all events need to be tracked at the full LHC

bunch-crossing rate of 40 MHz. In particular, real time tracking systems cover an

important role on the study of CP violation helping in the selection of interesting

events from an overwhelming background.

1.1 CP symmetry and its violation

CP symmetry is perhaps the discrete symmetry which has drawn more exper-

imental and theoretical attention for several reasons: besides its fundamental

significance and its connection to time reversal symmetry, through the CPT theo-

rem, it is the most striking case of a fundamental symmetry which is violated in

nature by a very small amount, and its detected manifestations have been rather

limited, even within the realm of phenomena governed by the weak interactions.

Moreover any deviation from the already small predicted value can be interpreted

as a new physics effects hidden in the loop diagrams. Through loop we can

investigate scale of energy inaccessible directly now or even in the near future.

When the first experimental indications showed that parity symmetry was not

universally valid [2], but was violated in processes governed by weak interactions,

it was rather difficult to accept that nature actually distinguishes left from right

at a very fundamental level. Such uneasiness was however quickly mitigated by

3

CHAPTER 1. PHYSICS MOTIVATIONS 4

the suggestion that the left-right symmetry might just be implemented with the

addition of the operator C (inversion of all intrinsic quantum numbers of involved

particles) to the operator P (inversion of spatial coordinates). Left-right symmetry

would indeed be somehow restored as CP symmetry.

CP symmetry fell, in the 1964, only 7 years after observation of the P violation [11].

The observation of neutral long-lived K mesons decay in both two and three pions

states showed that not all interactions are symmetric under CP transformation.

The measurement of a O(10−3) branching fraction for the K0L → π+π− was the

first evidence for CP violation.

After 30 years of series of experiments, in 1999 the first direct CP violation evi-

dence was established, still in neutral kaon states, by the NA48 [3] collaboration.

In 2001 the evidence of the direct CP violation was also established by the KTeV

[4] collaboration. It directly concerns the decay amplitudes of two CP conjugate

states, and confirms the theory for which the CP violation is an universal property

of the weak interaction.

1.2 CP violation in the Standard Model

Since the first experimental evidence of CP invariance violation, considerable

efforts to describe it into a coherent theoretical environment have been performed.

They significantly have contributed to build the Standard Model [5] (SM), that is

the theoretical and experimental environment which actually better describes the

nature at the smallest scale of fundamental interactions.

CP violation is linked to the appearance of complex factors in the Lagrangian,

and it is therefore useful to consider where such terms can appear in a non-trivial

way in the Lagrangian of the SM.

Since CP violation has been observed only in weak processes, we start by consid-

ering the part of the Lagrangian density of the SM :

L = L(G) + L(F ) + L(QG) + L(Y ) ,

L(G) contains the kinetic terms for the gauge vector bosons, of the form:

L(G) = −1

4W (a)

µν W(a)µν − 1

4BµνB

µν (1.1)

W (a)µν = ∂µW

(a)ν − ∂νW

(a)µ + gϵabcW

(b)µ W (c)

ν (1.2)

Bµν = ∂µBν − ∂νBµ (1.3)

in which the field strengths W(a)µν of the three SU (2) gauge boson W (a) (a=1,2,3,

coupling constant g) and the filed strength Bµν of the U (1) gauge boson B


(coupling constant g′) appear. These terms are necessarily real and thus cannot

induce CP violation.

The quarks are arranged in left-handed SU (2) doublets

QLi=

ULi

DLi

, (1.4)

and right-handed SU (2) singlets:

URi, DRi

, (1.5)

with

U ≡ {u, c, t}, D ≡ {d, s, b} .

The kinetic terms have the form:

L(F ) = iQLiγµ∂µQLi

+ iURiγµ∂µURi

+ iDRiγµ∂µDRi

+ . . . , (1.6)

and the interaction terms

L(QG) =− gQLiγµσa2QLi

W (a)µ − g′Y (QL)QLi

γµQLiBµ (1.7)

+ g′Y (UR)URiγµURi

Bµ + g′Y (DR)DRiγµDRi

Bµ ,

where σa are the Pauli matrices and Y (QL) = 1/6, Y (UR) = 2/3, Y (DR) = −1/3

is the weak hypercharge of the quarks. The Y values for the different fermions

are assigned in such a way to obtain a pure vector neutral current interaction

term corresponding to the electromagnetic current:

L(QG) =− g√2

JµCCW

+µ + J†µ

CCW−µ

(1.8)

− g

cos θWJµNCZµ − g sin θWJ

µEMAµ ,

where the field W+ = W (1)−iW (2)√2

annihilates a W+ boson, W− = W+†, and the

neutral fields are

Z = cos θWW(3) − sin θWB A = sin θWW

(3) + cos θWB , (1.9)

where the weak mixing (Weinberg) angle is tan θW ≡ g′

g, with g sin θW = e, the

magnitude of the electron charge. Here

JµCC = ULi

γµDLi, (1.10)

JµNC =

1

2

ULi

γµULi−DLi

γµDLi

− sin2 θWJ

µEM , (1.11)

JµEM =

2

3U iγ

µUi −1

3Diγ

µDi , (1.12)


are the weak charged, weak neutral, and electromagnetic (EM) (neutral) quark

currents, respectively. It can be checked explicitly that the hermicity of Eq. (1.8)

requires the coupling constants g, g’, e to be real quantities, so that also here no

CP violation can be incorporated.

Finally, the interaction of the quarks and leptons with Higgs field, introduced to

give masses to them and to the gauge bosons, is accounted for by the Yukawa

term and the most general form is

L(Y ) = −G(U)ij QLi

φ0

−φ−

URj

−G(D)ij QLi

φ+

φ0

DRj

+ h.c. (1.13)

where G(U−D) are n× n matrices. The spontaneous symmetry breaking give the

mass terms

−G(U)ij vULi

URj−G

(D)ij vDLi

DRj+ h.c. , (1.14)

where ⟨φ0⟩vac = v is the non zero expectation value of the Higgs field. The

appearance of coupling constants which are now matrices in flavor space means

that the down-type quark which couples to a particular up-type quark in the

interaction terms (see Eqs. (1.10),(1.11),(1.12)) is in general not the same which

couples to it in the mass terms.

As masses are usually more important in the dynamics of elementary particles

than their weak interactions, the mass terms are made diagonal rather than the

interaction terms. Passing to a matrix notation in flavor space {Ui}, {Di} → U ,D,

we can rotate the quark basis

U(m)L,R = S

(U)L,RUL,R, D

(m)L,R = S

(D)L,RDL,R , (1.15)

where S(U,D)L,R is a unitary matrix. The U (m),D(m) fields are identified as the states

of definite mass and the mass terms (1.14) become diagonal in this basis

−vU (m)

L S(U)L G(U)S

(U)†R U

(m)R − vD

(m)

L S(D)L G(D)S

(D)†R D

(m)R + h.c. (1.16)

= muu(m)L u

(m)R +mdd

(m)

L d(m)R + . . .

The diagonalization in Eq. (1.15) has no effect on neutral currents

JµNC =

1

2

ULγ

µUL +DLγµDL

− sin2 θW

2

3UγµU − 1

3DγµD

=1

2

U

(m)

L γµU(m)L +D

(m)

L γµD(m)L

− sin2 θW

2

3U

(m)γµU (m)

− 1

3D

(m)γµD(m) , (1.17)

which remain diagonal in the new fields due to the unitary of S(U,D)L,R ; processes in

which quark flavor changes but charge does not, for example s→ d transitions,


only occur at second order in the weak interactions, as required by the experimental

observation. In the expression for the charged weak currents

JµCC = ULγ

µDL = U(m)

L γµS

(U)L S

(D)†L

D

(m)L (1.18)

a non trivial unitary matrix appears

VCKM ≡ S(U)L S

(D)†L , (1.19)

called the Cabibbo-Kobayashi-Maskawa (CKM) matrix [6] [7], which measures the

mismatch between the matrices which diagonalize the U and D quark mass term.

The appearance of the matrix V CKM with complex elements opens the possibility

of having CP violation; however this will only occur if the matrix cannot be made

real with any choice of arbitrary phase factors.

1.2.1 The CKM matrix

The matrix VCKM appearing in (1.19) is explicitly written as

VCKM =

Vud Vus VubVcd Vcs VcbVtd Vts Vtb

(1.20)

Here the Vij are the couplings of quark mixing transitions from an up-type quark

i = u, c, t to a down-type quark j = d, s, b. In the SM the CKM matrix is unitary

by construction, as we have seen in Section 1.2. This is the expression of two

experimental observation:

• weak decays universality ⇒

i=u,c,t VixV∗ix =

V †V

xx

= 1,

• the absence of Flavor Changing Neutral Currents (FCNC).

The elements of the CKM matrix exhibit a pronounced hierarchy. While the

diagonal elements are close to unity, the off-diagonal elements are small. The

CKM matrix is usually expressed in terms of the Wolfenstein parametrization

which can be understood as an expansion in λ = |Vus| ≈ 0.2. It reads up to

order λ3

VCKM =

1− λ2/2 λ Aλ3(ρ− iη)

−λ 1− λ2/2 Aλ2

Aλ3(1− ρ− iη) −Aλ2 1

+O(λ4) . (1.21)

Transitions within the same generation are governed by the CKM matrix elements

of O(1), those between the first and the second generation are suppressed by


CKM factors of O(10−1), those between the second and the third generation are

suppressed by O(10−2), and transitions between the first and the third generation

are suppressed by CKM factors of O(10−3).

The magnitudes |Vij| of the CKM matrix elements can be measured using the

following tree-level processes:

• |Vud|: nuclear beta decay;

• |Vus|: K → πℓν;

• |Vcd|: ν production of charm from valence d quarks;

• |Vcs|: charm-tagged W decays and semileptonic D decays;

• |Vcb|: exclusive and inclusive b→ cℓν;

• |Vub|: exclusive and inclusive b→ uℓν;

• |Vtb|: t→ bℓν.

The unitary of the CKM matrix results into a set of 12 equations, consisting of

6 normalization and 6 orthogonality relations. The former involve the sums of

squared moduli i

|Vij|2 = 1, (1.22)

which however (being real) bear no information on CP violation. The latter can

be represented as 6 triangles in the complex plane, all having the same area.

However, only two of those are non-squashed triangles, having angles of the same

order of magnitude. They are defined by the relations:

VudV∗ub

(ρ+iη)Aλ3

+VcdV∗cb

−Aλ3

+ VtdV∗tb

(1−ρ−iη)Aλ3

= 0 , (1.23)

V ∗udVtd

(1−ρ−iη)Aλ3

+V ∗usVts −Aλ3

+ V ∗ubVtb

(ρ+iη)Aλ3

= 0 . (1.24)

At λ3 level of approximation, the two orthogonality relations agree with each

other. Therefore these relations describe the same triangle in the (ρ, η) plane

shown in Fig. 1.1 , which is usually referred to as the unitarity triangle of the

CKM matrix. Angles of unitarity triangle are usually called α, β, γ.

All the 6 orthogonality relations must be proved, and if any of them fails to be

verified by experiments then some new physics must be present. The study of

several, different physics processes have provided measurements of CP asymmetries

in nature. Precise measurements of CKM parameters are required for a stringent

test of the SM explanation of the CP violation. Fig. 1.2 shows the global fit of

the unitarity triangle from a combination of experimental results [8].


Figure 1.1: Rescaled unitarity triangle

Figure 1.2: Global CKM fit in the (ρ, η) plane.

1.3 CP violation in heavy flavor physics

While CP violation might have a role in leptonic interactions as well, the most

experimentally accessible field is that of quark interactions. Experimental efforts

to study CP violation had covered the decades separating its first evidence from

nowadays, interesting many aspects of high energy, astroparticle and cosmological

physics. An important field of investigation is represented by flavor physics at

accelerating machines, and in particular by the beauty and charm sectors. In

particular, due to its connection with the 3-generation structure of the matrix, the

heavier quarks that are still able to form bound states (bottom and charm) play

a central role. Luckily, the large mass of these quarks also helps in allowing some

simplifying approximations in performing theoretical calculations of the relevant


hadron dynamics. Past experiments on beauty and charm physics have provided

important contributions to the understanding of the CP violation, and to the

determination of the CKM matrix parameters. At the same time, current and

future experiments, such as LHCb at the LHC collider and Belle II at SuperKEKB

machine, will be able to largely improve our knowledge on CKM parameters

thanks to a huge production of b and c hadrons, resulting in a collection of

very large samples of interesting physics processes. The b hadrons represent

particularly interesting systems to study CP violation. First, they contain the b

quark, belonging to the third quark generation and therefore characterized by the

possibility to decay to quarks of both first and second generations of the first or

second generation. This allows reaching larger CP violation effects than in kaon

systems. Moreover, the larger mass of the b quark compared to the s quark one

makes kinematically available many decay modes, offering multiple experimental

possibilities to study CP violating observables. Even having a smaller mass,

charmed hadrons equally represent very interesting systems, and they are the

only system in which up-type quark interactions can be studied, which might in

principle have a separate dynamics from down-type quarks. However, the SM

predicts a very small amount of CP violation in this sector (. 0.1%).

Over years, numerous experiments were dedicated to b and c hadron studies,

following different approaches. Two deeply different but complementary environ-

ments are represented by B factories and by high energy hadron colliders.

For these reasons, flavor physics represents a particularly promising and interesting

sector to deeply study CP violation and search for non SM physics. However, the

presence of multiple available decay channels results in small branching fractions

of individual processes, and high statistic samples are required.

1.3.1 B factories

B factories are e+e− colliders, operating at the mass of the Υ(4S) which decays

more than almost exclusively into BB pairs (where B = B0 or B+). Operating

at an energy calibrated to the Υ(4S) production, just above the open beauty

threshold, avoids the presence of fragmentation products and imposes kinematic

constraints resulting in background reduction. Pile-up events are typically absent

and track multiplicity is typically ∼ 12 tracks per event. However, the cross-section

of BB production is limited to σ(bb) ∼ 1 nb.

At a symmetric B -factory (colliding beams with the same energy), such as CESR

at Cornell, the center-of-mass (CM) frame is at rest in the laboratory system. The

two B mesons obtained from the decay of a Υ(4S) are produced almost at rest

and they fly off in opposite directions with momenta of 335 MeV/c (βγ = 0.06).


The average decay length of a B0 meson at this energy is only ∼ 30 µm, which

cannot be easily resolved with vertex detectors. At higher energies (such as LEP)

the measurement would become possible but the background would be higher and

the important advantages of correlated production would be lost.

With an asymmetric B -factory, with different energies for the two beams, two

advantages would arise:

• the boost result in increased decay lengths thus allowing its measurement

• the CM frame would be moving in the laboratory, and the two B mesons

would fly off in the same direction (for a boost larger than the B momentum

in the CM), so that the measurement of their decay positions would give

information directly on the decay time difference, without requiring an

accurate knowledge of the production point.

BaBar and Belle experiments operated at e+e− asymmetric B factories (see Section

1.3.1), with CM energy of 10.58 GeV corresponding to the Υ(4s) mass peak. BaBar

operated at the PEP-II collider at SLAC in California and accumulated about

530 fb−1 of data between 1999 and 2008. PEP-II collided 9.0 GeV e− and 3.1

GeV e+ head-on, corresponding to a CM boost of βγ = 0.56 in the direction of

the e− beam, which corresponds to an average separation of 260 µm between

the decay vertices of the two B mesons. Belle operated at the KEKB collider at

KEK in Japan and accumulated about 1040 fb−1 of data between 1999 and 2010.

KEKB collided 8.0 GeV e− and 3.5 GeV e+ with a ±11 mrad crossing angle and

a CM boost of βγ = 0.425. In this environment the average separation of the

two B is 200 µm. The distance between the two B mesons allows to determine

the time-interval between the two decays with sufficient precision to measure

time-dipendent CP violation asymmetries, as shown in Fig. 1.3 [9] [10].

1.3.2 High energy hadron colliders

The last most important hadron colliders are Tevatron and LHC.

The Tevatron started the operations in 1987 and completed the data taking in

2011. It reached the maximum CM energy of 1.96 TeV with an instantaneous

luminosity of 4.31 × 1032 cm−2 s−1 in pp collisions. CDF and D0 experiments

operated at the Tevatron and are multipurpose experiments, and the geometry

surrounds the interaction region. Their goals include the study of the production

and decay of heavy particles such as the top and bottom quark, the W± and the

Z0 bosons.

The LHC at CERN started the operation in 2009 (2012), colliding pp beams

at a CM energy of about 7(8) TeV with instantaneous luminosity of about


Figure 1.3: Left: Belle flavor-tagged ∆t distribution (top) and raw

CP asymmetry (bottom) for the B0 → (cc)K0S CP -odd sample (left)

and the B0 → J/ψK0L CP -even sample (right). The distribution are

background subtracted. Right: BaBar flavor-tagged ∆t distributions

(a,c) and raw CP asymmetries (b,d) for the B0 → (cc)K0S CP -odd

sample (top) and the B0 → J/ψK0L CP -even sample (bottom). The

shaded regions represent the fitted background.

3.7(5.0)× 1033 cm−2 s−1. The next period of data taking, starting in 2015, will

be at a CM energy of 13(14) TeV with a nominal luminosity of 1 × 1034 cm−2

s−1. For optimal data taking and event reconstruction, the luminosity at LHCb

experiment is locally controlled by displacing the beams in the vertical direction

to yield L = 2− 5× 1032 cm−2 s−1. The LHCb experiment, operating at the LHC,

is a dedicated b physics experiment that features a forward magnetic spectrometer

with a polar angle coverage of approximately 15 to 300 mrad and a pseudo-rapidity

range of 1.9 < η < 4.9. The reason is that in the LHC environment, the bb pairs

are produced at small angle with respect to the beam direction, in the forward or

in the backward direction, and with relatively high momentum.

Hadron colliders have much larger cross-section for b and c quarks production.

The dominant production process for b hadrons is the non-resonant inclusive bb

production, with typical values at Tevatron (pp collisions) and LHC (pp collisions),

integrated on the entire solid angle

σ(pp→ bbX,√s = 1.96TeV) ∼ 80µb , (1.25)

σ(pp→ bbX,√s = 7TeV) ∼ 250µb , (1.26)


which are relatively large compared to e+e− machines. The CM energy available

at hadron colliders allows the production of all b hadrons species: B0 and B+

mesons (as at the B factories), but also B0s , B

+c mesons and b baryons. The typical

βγ Lorentz boost of produced b hadrons are larger compared to B factories. This

results in larger decay lengths, which allow probing shorter scales in heavy flavor

time evolution and helping in the suppression of prompt background. However,

at hadron collisions the bb cross-section is about three order of magnitudes lower

than hadron-hadron inelastic cross-section:

σ(pp inelastic,√s = 7 TeV) ∼ 70mb , (1.27)

resulting in high suppressed signal to background ratio. Because of the limited

bandwidth available for storing data, this makes it necessary tracker and trigger

systems which operate in real time, capable to discriminate interesting events from

the huge light-quark background and therefore to select high purity signal sample

to store. Events in hadron colliders are also more complex than at B factories,

resulting in more difficult reconstruction of b hadrons decays and requiring higher

granularity detectors. Indeed, in most hard interactions only one constituent

(valence or sea quark, or gluon) of the colliding hadron undergoes an hard scattering

against a constituent of the other colliding hadron: this is the leading interaction

that may produce a bb pair. Others hadron constituents rearrange in color neutral

hadrons, which may have transverse momentum sufficient to enter the detector

acceptance, resulting in the so named underlying event. In the underlying event

multiple hard scattering interactions may occur between the partons consisting

the same pair of colliding hadrons. Fragmentation of all quarks and gluons in the

event represents an important source of track multiplicity. Finally, when beams

collide, multiple hard interactions may occur between their hadrons, resulting in

pile-up events. Each hard interaction introduces related fragmentation processes

and underlying events.

Similar arguments are valid for charmed hadrons, although characterized by even

higher production cross section:

σ(pp→ ccX,√s = 7 TeV) ∼ 6 mb . (1.28)

Starting from 2015, the LHC will run at higher center-of-mass energy of 13 and

14 TeV, exploiting greater production cross sections of charm and beauty pairs:

σ(pp→ bbX,√s = 14 TeV) ∼ 500µb , (1.29)

σ(pp→ ccX,√s = 14 TeV) ∼ 10mb . (1.30)

even if with an increased production of background processes:

σ(pp inelastic,√s = 14 TeV) ∼ 100 mb . (1.31)


Figure 1.4: Angular distribution in three mass ranges for events with

cos θ > 0.9995. The one in the K region mass (in the middle) shows a

peak at cos θ = 1. This was the first indication of KL → π+π− decay.

1.4 Flavor oscillations and CP violation

As already mentioned in Section 1.1, the observation of the process KL → π+π−

was the first indication of indirect CP violation. In Fig. 1.4 is represented the

event distribution of the famous experiment at Brookhaven [11], that made the

discovery. After 30 years of series of experiments, in 1999 was established the

first evidence of direct CPV, by the NA48 collaboration and later, in 2001, by the

KTeV collaboration, still in neutral kaon states. It directly concerns the decay

amplitudes of two CP conjugate states

Γ(K0S → π0π0)/Γ(K0

S → π+π−)

Γ(K0L → π0π0)/Γ(K0

L → π+π−)≈ 1 + 6Re

ε′

ε

(1.32)

where ε′ indicates the amount of direct CP violation and ε the amount of CP

violation in mixing. The result

Re

ε′

ε

= (1.67± 0.26) · 10−3 ⇒ ε′ = 0 , (1.33)


Figure 1.5: Evolution of the measurement of ϵ′/ϵ in the Kaon decays

over 30 years of efforts.

implies that CP violation is present in mixing as well as in the decay, albeit with

smaller rate than in the mixing and the evolution in time of this measure is shown

in Fig. 1.5 . The consequence is that CP violation may occur also in the decay of

charged particles.

Huge experimental efforts have been dedicated to extend the CP violation study

on other systems than kaons. Evidence for B0 −B0oscillation was found in 1987

by the ARGUS experiment at the e+e− collider DORIS-II located at DESY [12].

The evidence consisted of a single fully reconstructed decay into B0B0 (both

semileptonic decays) from B0B0pairs produced at the Υ(4s). A three standard

deviation excess of events in which a fully reconstructed neutral B meson was

accompanied by a “wrong sign” high-energy lepton was obtained. CP violation in

sector other than kaon was first observatied in B0 → J/ψKs decays at BaBar and

Belle experiments, see Fig. 1.3 [9] [10]. The CP violating asymmetry is caused by

the interference of decay amplitudes with B0 −B0flavor mixing amplitudes, with

different strong and weak phases.

In 2006, CDF obtained the first observation of flavor oscillations in the B0s −B

0

s

meson system whose frequency measurement is shown in Fig. 1.6 [13]. The

B0s −B

0

s oscillations are very fast compared to the B0−B0system, i.e. ∆ms/Γs =

26.49± 0.29 to be compared with ∆md/Γd = 0.770± 0.008, and a time-dependent

analysis is required for the extraction of the mixing parameters. In 2013 the LHCb

collaboration announced the discovery of CP violation in the B0s decays (Fig. 1.7)

with ACP (B0s → K−π+) = 0.27± 0.04± 0.01 [14]


Figure 1.6: (Upper panel) The measured amplitude values and uncer-

tainties versus the B0s −B

0

s oscillation frequency ∆ms. (Lower panel)

The logarithm of the ratio of likelihoods for amplitude equal to zero

and amplitude equal to one, Λ = log[LA=0/LA=1(∆ms)], versus the

oscillation frequency. The dashed horizontal line indicates the value of

that corresponds to a probability of 1% in the case of randomly tagged

data.

In the charm sector (D0−D0system) 5σ deviation from the no-mixing hypothesis,

from a single measurement, was achieved for the first time, as shown in Fig. 1.8,

by the LHCb collaboration [15] at the end of 2012. Albeit the D0 −D0mixing

had already been accepted by the community due to the combination of all the

measurements previously done, the confirmation from a single measurement was

an important test. The mixing in the D0 −D0system is very suppressed due to

GIM ( Glashow-Iliopoulos-Maiani) mechanism [18] in the loop. This is the reason

why it has been discovered later with respect the other systems. No CPV has

been discovered since it is very suppressed in the SM (. 0.1% is expected).

1.5 Fast track finders

Fast track finders are of fundamental importance for triggering efficiently on

interesting physics processes. They rely on fast pattern recognition and simplified

track fitting techniques. The pattern recognition identifies the candidate tracks,

from a collection of hits, before the track fit. This process is typically serialized

and solved by trials and errors.


Figure 1.7: Invariant mass spectra for Bs0 → Kπ reconstructed events

at LHCb. ACP (B0 → K+π−) and (c, d) ACP (B

0s → K−π+). Panels

(a) and (c) represent the K+ invariant mass, whereas panels (b) and

(d) represent the K−π+ invariant mass.

A simple example of pattern recognition for straight tracks identifies a track road

connecting one hit in the first sensor to one hit in the last sensor. For each of the

intermediate layers, if the position of the hit is inside the track road, this is added

to the track candidate. If the number of hits is greater than the minimum required

points then we have found a track candidate. This process must be iterated for all

the possible track roads, whose total number is the product of the hits on first and

last plane. In general the execution time is proportional to a power of the number

of hits. This feature can be problematic in a trigger application because if the

pattern recognition takes too long some events can be lost. In Fig. 1.9 different

track roads ending on the same hit are shown. The red (solid) line correspond

to a track candidate, while the others are rejected because of the low number of

points.

More advanced pattern recognition techniques are based on the concept of “tem-

plates”, a precomputed set of hit configurations corresponding to real tracks,

stored in a database (“pattern bank”). Hits coming from the detector are com-

pared to the database in real time to look for matching patterns.

We would like to point out that analyzing different combinations in sequence can

represent a bottleneck in the track finding. Examining the combinations in parallel

is the key feature of the Fast Track Finder devices described in the following.


τ/t0 2 4 6 20

R

3

3.5

4

4.5

5

5.5

6

6.5

7

310×

Data

Mixing fit

Nomixing fit

LHCb

Figure 1.8: Decay-time evolution of the ratio R of wrong-sign D0 →K+π− to right-sign D0 → K−π+ yields with the projection of the

mixing allowed (solid line) and no-mixing (dashed line) fits overlaid.

Figure 1.9: Example of different trials for a straight line pattern

recognition. The (solid) line corresponds to a candidate track, the blue

(dashed) lines represent unsuccessful trials.

1.6 Pattern recognition in Associative Memory

devices

For sake of simplicity we discuss the working principle of the Associative Memory

(AM), applied to the reconstruction of 2D straight tracks. We consider, as example,

a series of 5 detectors and divide each layer in nbins bins along one directions, with


nbins smaller than the number of channels of each detector. A charged particle

crossing all the detectors fires in general one bin per layer, as shown in Fig. 1.10.

Each bin is identified by a coordinate and we define a pattern as a set of bin

Figure 1.10: Example of different tracks corresponding to different

patterns.

coordinates corresponding to a possible track. Since the bin size is greater than

the detector resolution, many tracks in a little region of the track parameter

space can match the same pattern. If on one hand the resolution is artificially

degraded, on the other hand the number of possible patterns is strongly reduced,

down to ∼ n2bins. All the patterns corresponding to tracks crossing the layers

are calculated from simulations and the complete set is called pattern bank. The

AM is a particular kind of content addressable memory (CAM) [20] in which the

pattern bank is stored, the hits from the detector are compared to the patterns

and for valid patterns the addresses of the matching hits are output.

Different subsets of the pattern bank are stored in the AM chips, present on a

board (AM board), that receives the hits information from the detectors. Every

incoming signal is routed to all the patterns, which in parallel determine whether

there is a match. The operation is iterated for all the hits and the pattern

recognition is complete as soon as the last hit is read. The time needed to perform

the pattern recognition is independent from the size of the pattern bank and it is

equal to the time needed to read the hits from the detector. The valid patterns

are output by the AM sequentially in order to perform the track fitting. A pattern

is valid if all its coordinates have at least one correspondence with the measured

hits. The AND circuit corresponding to a pattern is also referred as road. In Fig.

1.11 we show an example of a set of hits activating one of the possible roads.

Because of the coarser resolution of the found patterns, it is not possible to directly


Figure 1.11: Example of a set of fired hits (red), matching the road j.

The road i is not matched.

use them to get the track parameters. A linearized track fitting [21] is applied to

the hits with the full resolution. Since a pattern corresponds to a limited area of

the track parameter space, it represents a constraint and precalculated coefficients

are used to determine the track parameters. This method allows to simplify the

computation and to reduce the time for the calculation.

Examples of systems using the AM are the Silicon Vertex Trigger of the Collider

Detector at Fermilab, and the Fast TracKer of the ATLAS experiment.

1.6.1 Silicon Vertex Trigger at CDF

The Silicon Vertex Trigger is part of the Level 2 decision system of the CDF

three-level trigger [19]. Level 1 and Level 2 are completely implemented in hard-

ware. Level 3 is implemented in software. The CDF trigger provides a strong

data reduction through fast identification of distinctive signal signatures, many

of them are based on the track reconstruction of fast charged-particles in the

bending plane of the spectrometer. The event rate is reduced from 2.5 MHz

(Tevatron bunch crossing frequency) to 30 KHz in the Level 1, and up to 300 Hz

in the Level 2. The trigger system uses the information from the silicon vertex

detector (SVXII) [22] and the central drift chamber COT [23]. The Level 1 trigger

requires 2 tracks in the drift chambers, that are reconstructed by the eXtremely

Fast Track processor (XFT) [24]. The XFT reconstructs 2-dimensional tracks

(in the plane transverse to the beam axis) and provides the tracks and hits to

the rest of the trigger chain. The tracks are matched to the silicon hits from the

SVXII. The Level 2 requires at least a 120µm impact parameter. The impact

parameters is defined as the distance from a secondary track to the primary vertex

of interaction, as shown in Fig. 1.12. At Level 3 a full software confirmation is


Figure 1.12: Definition of the impact parameter of the track in a decay

with secondary vertex.

performed and the rate is reduced to 75 Hz. The SVT provides the reconstruction

of tracks with 35 µm impact parameter resolution. The full tracking is performed

in ∼ 15µs, and would require ∼ 0.1s via software. This is possible thanks to

an highly parallelized/pipelined architecture, in particular using the AM and

performing the track fit in fast FPGAs.

Figure 1.13: Scheme of the SVXII detector. Left: longitudinal view.

Right: the modular structure with 5 concentric layers and 12 angular

wedged is shown.

The geometry of the detector is symmetric. The SVX is made of 6 longitudinal

blocks and each block is made of 5 concentric layers. The SVX can be divided

in 12 angular wedges, as we can see in the right part of Fig. 1.13. Each wedge


corresponds to a 30◦ slice and is processed by a dedicated hardware. The coin-

cidence of the COT and the hits from the SVXII is required to start the track

reconstruction using an AM system.

The planes are divided in programmable width bins, typically 250− 700µm, while

the XFT tracks are swum to the outer radius of the SVX, and considered like an

extra (virtual) layer. The typical bin size is 3mm.

A set of 32K most probable patterns is computed offline with a MonteCarlo pro-

gram and loaded in the AM pattern bank. At the end of this process a linearized

track fit is performed.

1.6.2 Fast Tracker at ATLAS

The Fast Tracker[25] at ATLAS experiment will be part of the Level 2 hardware

trigger. A precise measurement of the impact parameter allow to perform b-

tagging or to identify decay modes with b quarks in the final state. It is based on

the AM pattern recognition as SVT. Some technical features and the hardware

are different from SVT, but the track reconstruction method in substantially

unchanged.

Figure 1.14: Scheme of the ATLAS tracker

The detector coverage will be initially limited to the ATLAS barrel region, and

then it will be expanded to the whole geometrical range covered by the ATLAS

tracking system. The Inner Detector is composed by 12 concentric layers. Only 8

layers are used, allowing 1 missing layer.

The geometry is symmetric and allows to divide the FTK system in 16 angular


wedges (22.5◦ plus 10◦ overlap), to parallelize the processing. The total number

of patterns compared by the FTK is ∼ O (109). Each detector layer is divided in

bins, here called Super Strips. A Super Strip made by ∼ 24× 36 pixels or ∼ 24

strips. The instantaneous luminosity at LHC is L = (1− 3)1034cm−2s−1, with a

bunch-crossing rate of 40 MHz. This result in track multiplicity of O(100) and

many pile-up events. FTK will accept Level 1 triggers at 50-100 KHz and will

provide tracks at O(1KHz) to Level 3 trigger. The main difference with the SVT

is the use of variable resolution patterns (3 to 6 bits). Changing the resolution of

a bin corresponds to take an equivalent bin of different width. This feature allows

more flexibility in the construction of the pattern bank.

An example of variable resolution patterns is given in Fig. 1.15, where different

size bins are used and allow to reduce the number of patterns, as shown in the

central and right part.

Figure 1.15: Variable resolution patterns. The same set of tracks

matches different a different number of patterns, depending on the

resolution of the size of the bins.

Chapter 2

Tracking system prototype with

“artificial retina”

We describe the design of the first prototype of a tracking system with artificial

retina for fast track finding. In particular we describe the retina algorithm, the

telescope design and the retina architecture. The artificial retina is inspired by the

mechanism that underlies the early stages of visual-information processing in the

primary visual cortex of mammals and it is based on the extensive parallelization

of data distribution and pattern recognition algorithm.

The tracking system consists of a telescope based on 8 single-sided silicon sen-

sor, the readout electronics and the data acquisition system (DAQ). The retina

algorithm is implemented using commercial FPGAs.

2.1 The artificial retina algorithm

2.1.1 Inspiration from neurobiology

The artificial retina for high energy physics was proposed in 2000 [16]. It is inspired

by the low-level mechanism used by the eye to recognize straight edge, as pointed

out by D.H. Hubel and T.N. Wiesel [17]. In 1959 they performed experiments on

several cats, aimed at the investigation of visual recognition of objects in space.

The neural response to the stimuli from the retina was demonstrated to depend

on the shape and orientation of specific objects.

Each neural receptor receives the stimuli from a defined region of the retina

(receptive field). Hubel and Wiesel measured the electric signal received by the

receptors, when the cats were shown spotlights on different areas of the receptive

field. Each area provides an excitatory or inhibitory stimulus when hit by the

spotlight. They also showed that if both excitatory and inhibitory regions are

24

CHAPTER 2. TRACKING SYSTEM PROTOTYPEWITH “ARTIFICIAL RETINA”25

stimulated, they interact in a mutually antagonistic way, providing a weaker signal

with respect to the case when only excitatory regions are stimulated. For this

reason, when the cats were shown straight edges, the strength of the measured

signal was different, depending on the edge position and orientation inside the

receptive field. In Fig. 2.1 is shown the electrical response of a neural receptor to

different light spot orientations as measured by Hubel and Wiesel, taken from the

original article in Ref. [17] Hence, the brain can establish a two-way relationship

Figure 2.1: Electrical response of a neural receptor to a rectangular

light spot oriented in various directions. The response is maximal for

one of the proposed orientations.

between the strength of the neural receptors signals and the parameters of the

observed line. In this way it can evaluate the information relative to the shown

edge.


2.1.2 Track parameters definition

We briefly describe the telescope layout in order to define the track parameters

used in the retina algorithm.

Let’s consider a telescope with 8 single-sided silicon strip detectors perpendicular

to the z axis, as shown in Fig. 2.2 . The x coordinate is measured by the detector

in the range [−Lx/2, Lx/2], where Lx is the dimension of the sensor along the

direction perpendicular to the strips.

Each cluster at layer k is described by the coordinates (zk, xk). We define a

cluster as the average position of hits from adjacent strips. In particular we use an

arithmetic mean to evaluate the position. The cluster position is then defined by

xclust =1

N

Ni=1

xi,hit, (2.1)

where N is the number of adjacent hits.

The z coordinate of the clusters is given by the nominal position of the sensor.

z

x

Figure 2.2: layout of the telescope

If (zf , xf) and (zl, xl) are the coordinates of the clusters on the first and last

telescope detectors, respectively, we define (x−, x+) and (z−, z+) according to

x± =xf ± xl

2, (2.2a)

z± =zf ± zl

2, (2.2b)

where (z−, z+) are constant terms depending on the telescope geometry and

(x−, x+) are defined as the track parameters. The equation of a 2D track is

x(z) = x+ + x−z − z+

z−. (2.3)


The domain of possible tracks within the geometrical acceptance in the (x−, x+)

space is defined by the following relations|x− − x+| ≤ Lx

2,

|x− + x+| ≤ Lx

2.

(2.4)

2.1.3 Retina response

Let’s consider a grid of uniformly distributed cellular units in the (x−, x+) space.

The distance between different cells is defined as ∆x (grid step) and it is assumed

to be identical along the x− and x+ axes. Each cellular unit (x−i , x+j ) is associated

Figure 2.3: Cellular unit (i,j) and corresponding track receptors in the

(z,x) space

to a set of track receptors placed on the telescope layers, corresponding to the

intercepts of the track defined by the (x−i , x+j ) parameters, as visualized in Fig.

2.3 . The position of the track receptor at layer k is given by

xijk = x+j + x−izk − z+

z−.

The response (weight function) of a cellular unit is evaluated comparing the

receptor position to the position of the clusters measured on the telescope layers.

In order to define the weight function we first define

sijk = xk − x+j − x−izk − z+

z−, (2.5)

as the distance between the measured cluster and the track receptor at layer k.

The response of a cell to a single cluster is defined as

Wijk =

exp− s2ijk

2σ2

if |sijk| ≤ 2σ,

0 if |sijk| > 2σ.(2.6)


where σ is a constant value that is in general greater than the grid step and has

to be optimized for optimal response. A Gaussian response field determines the

cellular unit excitation as defined in the previous equation and shown in Fig. 2.4.

sijk

Wijk

σ

Figure 2.4: Response field of a track receptor to a cluster. The receptor

is shown in blue (circle) and the cluster position is shown in red

(rectangle).

The total weight function is the sum of all the responses of the track receptors,

defined as

Wij =Nk=1

Wijk, (2.7)

where N is the total number of clusters.

The Wij function is evaluated in parallel for all the cellular units.

A reconstructed track is identified by a local maximum of the weight function.

The value of the maximum is usually required to be greater than a threshold value

(thr). The track parameters are determined by interpolating the weights evaluated

for (imax, jmax) and the neighbor bins along x− and x+ axes, as shown in Fig. 2.5.

For each track parameter, the interpolation is achieved using a Gaussian function

and the track parameters are reconstructed according to

x−reco = x−i max + δx−, (2.8a)

x+reco = x+j max + δx+, (2.8b)


where δx− and δx+ are defined by

δx− =∆x

2·ln

Wi−1 j

Wi j− ln

Wi+1 j

Wi j

lnWi−1 j

Wi j+ ln

Wi+1 j

Wi j

, (2.9a)

δx+ =∆x

2·ln

Wi j−1

Wi j− ln

Wi j+1

Wi j

lnWi j−1

Wi j+ ln

Wi j+1

Wi j

, (2.9b)

for (i, j) = (i, j)max.

In Fig. 2.5 we show a graphical example of the interpolation method. The track

parameter is given by the center of the interpolating function.

Figure 2.5: Example of interpolation along the x+ axis. A Gaussian

function is used to interpolate the maximum weight and the weight of

the neighbor cellular units.

Details about the chosen values for ∆x, σ, thr will be discussed in Chapter 3.

2.1.4 Hardware implementation of the artificial retina

Here we describe a general hardware implementation of the artificial retina. A

scheme of the architecture is shown in Fig. 2.6. It consists of three different

modules: the switch, the cellular engines and the track fitter.

The artificial retina receive the clusters from the detectors. The aim of the switch

is to deliver the signals only to the cellular units with expected non zero response.

The cellular engines correspond to the hardware implementation of one or multiple

cellular units and provide the calculation of the weight function. In the end,

the track fitter determines the track parameters using the interpolation method

discussed in Sec 2.1.

Switch The clusters need to be distributed to the cellular engines in real time.

The response of a cellular unit to a cluster is considered to be non zero only if


Figure 2.6: General architecture of the artificial retina with the switch,

a pool of cellular engines and the track fitter unit.

|sijk| ≤ 2σ. This means that a given cellular engine must receive the cluster signal

only from a subset of (zk, xk) positions. Viceversa a cluster must be delivered only

to the cellular units that satisfy the relationxk − x+i − x−jzk − z+

z−

≤ 2σ.

This is achieved using a switch network, that delivers the signals to the proper

cellular units in parallel. By using the switch we optimize the flux of data to be

sent from the detectors to the array of cellular engines.

Before describing the details of the implementation of the switch we introduce

some definitions. We define a group as a physical area on each detector, without

any overlap. It corresponds to a certain number of adjacent clusters. In fact,

since the position of a cluster is calculated by an arithmetic mean, it can assume

only a discrete number of values. Wee divide each layers in Ngroups then we

need log2(Ngroups) bits to identify each group and log2(Nlayers) bits are needed

to identify the layer. In this scheme a cluster position corresponds to one group


only. We define a region as a set of cellular units, covering part of the space of

parameters, without any overlap between regions.

The switch is a programmable logic that accepts clusters as input, reads the

address of the corresponding group and delivers a copy of the signal to a certain

number of regions. Clusters from the same group are delivered to the same regions.

All the cellular engines in the a region receive the same signal. For each group,

the map of the regions precomputed and stored for each group in Look-Up Tables

(LUT) inside the switch logic. The switch is composed of a network of nodes. The

2-way sorter represents the elementary block of the switch network. It has two

2d 2d

2m 2m

0

0

1

1

2x2

Figure 2.7: Scheme of the 2-way sorter. Two LUTs are implemented

in the 2-way dispatchers (2d).

inputs and two outputs and is composed of two dispatchers (2d) and two mergers

(2m). The inner connections are shown in Fig. 2.7. Each 2-way sorter compares

the group address to a LUT, that contains the pre-computed data paths associated

to every possible incoming signal. The value returned by the comparison with

the LUT is a 2 bit string that identifies if the signal is to be forwarded to zero,

one or both the mergers. Signals coming to one merger are serialized and sent

to the output. An “ad hoc” design of the network connections allow to build an

ninputs × noutputs modular switch, where ninputs is the number of lines from which

the switch receives the clusters and depends on the particular implementation,

and noutputs corresponds to the number of regions we have defined. An example of

4× 4 switch network, made of four 2-way sorters is shown in Fig. 2.8 .


Figure 2.8: Example of 4x4 switch network composed of four 2-way

sorters.

Cellular Engine A cellular engine can be identified with a cellular unit. De-

pending on the particular implementation one engine can provide the weight

calculation for different cellular units. The logic structure of a cellular engine is

Figure 2.9: Logic structure of the cellular engine

shown in Fig. 2.9. For each incoming (zk, xk) cluster signal, Wijk is calculated

using different LUTs. A LUT accepts the x address (the part of the cluster address

that identifies the x position in the layer) and returns the precomputed value of xk.

The resolution of this LUT depends on the number of possible cluster positions.

In particular the value is given by log2(2 nstrips) . Recalling the definition in Eq.

(2.5), sijk can be written as

sijk = xk − fij(zk) (2.10)

where

fij(zk) = x+j + x−izk − z+

z−. (2.11)


A LUT accepts the z address (the number of the layer) and returns the value of

fij(zk). Since fij(zk) depends on (x−i , x+j ), a different LUT is necessary for each

cellular unit and |sijk|/(2σ) is calculated from the obtained values. At the end a

LUT accepts this value and returns the value of Wijk. If |sijk|/σ > 2 the returned

value is zero.

An accumulator sums the evaluated response to the previously calculated responses.

After all the responses have been processed, the evaluation of the weight function

(Wij) is complete.

All the engines work in parallel. Once the weight function has been evaluated, for

each cellular unit (Wij > thr) the value is compared to the first neighbor bins. If

a local maximum is identified, the coordinates of the cell are output to the track

fitter and the interpolation method is applied.

Track fitter The track fitter receives the values of the weight function of the

local maxima and its first neighbors along the x− and x+ coordinates. Two

independent evaluations are peformed to reconstruct the track parameters x−recoand x+reco, according to Eq. (2.8) and Eq. (2.9). The logarithmic terms of the

equation are calculated using a LUT, in order to improve the speed performances.

At the end the couple of track parameters (x−, x+)reco of the identified tracks,

determined through the interpolation, are sent to a PC and stored to disk.

2.2 Telescope Design

The telescope is made of 8 single-sided silicon detectors and two plastic scintillators.

The coincidence signal of the scintillators is used as input trigger for the readout

electronics of the silicon sensors. Eight aluminum modules hosts the sensors. A

model of the telescope is shown in Fig. 2.10.

2.2.1 Telescope module

In Fig. 2.11 one telescope module is shown. It consists of an aluminum frame and

hosts a silicon sensor, a TT Hybrid board, and the pitch adapter to connect the two

components. The telescope layout is shown in Fig. 2.10, while the single module

is shown in Fig. 2.11 The sensor is an ST Microelectronics OB2 single-sided strip

detector and was designed for the CMS tracker [26]. It is p+-on-n type and is AC

coupled. The dimension of the active area is 93.9mm ×91.6mm (LxH) and the x

coordinate is measured along L. Each sensor has 512 strips, the pitch is 183µm

and the thickness is 500µm. A schematic of the sensor is shown in Fig. 2.12.

The silicon detector is connected to a front-end hybrid board (TT Hybrid), that


Figure 2.10: Scheme of the telescope in 0◦ − 180◦ configuration for 2D

track reconstruction.

Figure 2.11: Scheme of a single module of the telescope. The module

hosts the silicon sensor, the pitch adapter and the TT Hybrid board.

hosts 4 Beetle chips. Two models of TT Hybrid (K,M) will be used. The only

difference between K and M model are the physical dimensions, so all the telescope

modules are equivalent. In Fig. 2.13 both the hybrids are shown. The M model in

the left part of the picture is 2mm longer than the K model on the right. The TT

Hybrid boards are used in the LHCb experiment for the readout of the Trigger

Tracker (TT) stations [29]. The sensors used in the TT stations are similar to the

STM OB2, but they have been produced by Hamamatsu Photonics. The Beetle

chip is custom ASIC [27] that provides the analog readout of 128 channels. The

chip multiplexes 32 channels on a single analog output, for a total of 16 analog


Figure 2.12: Schematic of the STM OB2 sensor.

Figure 2.13: Picture of the TT Hybrid front-end boards. M model on

the left and K model on the right.

outputs per plane. For each channel the chip features a low-noise charge sensitive

preamplifier and a CR-RC shaper with programmable shaping time. An analog

pipeline is present with a programmable latency of up to 160 cycles. The ADC

sample rate is 80 Msps (mega-samples persecond), while the maximum Beetle chip

read out frequency is 40 MHz (the LHC bunch-crossing frequency). The maximum

accepted trigger rate by the Beetle chip is 1.1 MHz to perform dead-timeless

readout within 900ns per trigger.


The pitch of the Beetle chip is 40.24µm and is internally adapted to 112µm pitch

the TT Hybrid board. A flex polyimide kapton pitch adapter has been designed

to connect the sensor to the TT Hybrid (183µm to 112µm). A schematic is shown

in Fig. 2.14.

Figure 2.14: Schematic of the pitch adapter. The detector is connected

to the top. The TT Hybrid is connected to bottom.

2.2.2 Telescope Layout

The telescope layout is shown is Fig. 2.10. The final configuration will have

alternate 0◦ and 180◦ oriented modules, in order to reduce the distance between

them and increase the geometrical acceptance. This configuration allows to

reconstruct 2D tracks only. It will be also possible to use an alternate 0◦ − 90◦

configuration to reconstruct 3D tracks, as shown in Fig. 2.15.

The z axis, by definition, passes through the barycenter of the sensors, placed

orthogonally to it. All the sensors are parallel.

The distance between the planes is set to

d = 0.8cm. (2.12)

The active volume of the scintillator is 15×15×1 cm3. The distance from the first

scintillator to the closest silicon detector is set to 2.62cm. The other scintillator is

positioned at 5.0cm from the last silicon detector.


Figure 2.15: Scheme of the telescope in 0◦ − 90◦ configuration for 3D

track reconstruction.

The z axis direction points to the ground. The x axis is defined orthogonally to

the length of the strips so the sensors measure the (z, x) position of the hits.

2.3 Retina Architecture

We describe here the hardware implementation of the artificial retina for the case

of the prototype under development. The schematic is shown in Fig. 2.19.

The space of (x−, x+) track parameters is represented in Fig. 2.16. The length of

the diagonals is Lx, and it is identical to the dimension of the silicon sensor. This

area is divided into 4 regions corresponding to 4 different FPGAs.

As visually represented in Fig. 2.17, the FPGA area is divided in a grid of 4×4

regions. In each region there are 16 engines, each one processing the data of 2

cellular units (cells). In this configuration the cellular units are equally distant

along the the x−, and x+ directions. The four FPGA areas have some overlap

in such a way that the cell with local maximum weight and its neighbors are

contained in one FPGA area. In this case, all the information to calculate the

track parameters resides in a single FPGA.

The cells distance between adjacent cells is set to

∆x =Lx

56. (2.13)


X-

X+

+Lx /2

+Lx /2- Lx /2

- Lx /2

Figure 2.16: Space of (x−, x+) parameters divided into 4 FPGA areas

FPGA 2 FPGA 3

FPGA 1

Cell 0

Cell 1

FPGA 4

(a) Regions (b) Engines (c) Cells

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Figure 2.17: Division of an FPGA area in regions, engines, cellular

units. Left: a FPGA area is divided in 16 regions. Center: a region

covered by 16 engines. Right: an engine corresponds to 2 cellular units.

This value is evaluated considering a quarter of the tracking area. The length of

the diagonal is Lx/2. We want to cover this length using 14 engines, because we

need a “border” of engines outside this area. Each engine contains 2 cellular units.

Then we obtain

∆x =Lx

2

1

14

1

2=Lx

56. (2.14)

The ∆x value, depends on the number of cellular units. This number depends, in

turn, on the amount of available resources. In particular we will see in Chapter

3, the resolutions of the reconstructed track parameters improves for decreasing

values of ∆x.

Let’s consider the case of a track with (x−, x+) parameters at the border of a

FPGA area. The overlapping region is limited to two adjacent cells along the x−

and x+ coordinates, in order to avoid ambiguities in the track reconstruction. In


Fig. 2.18 is shown the case where a cell with maximal weight is at the border of

FPGA1 and a local maximum cannot be identified, while it can be reconstructed

in FPGA0.

FPGA 0

FPGA 1

X+

Weight

Figure 2.18: Example of local maximum of the weight response in the

overlapping region between FPGA0 and FPGA1. Track parameters

are reconstructed in the FPGA 0.

In order to solve possible ambiguities we define the conditions for the identification

of a local maximum. A local maximum is identified if the value of the weight

function is greater or equal than the values of the right/top-right/top/top-left

neighbor cells, and if it is strictly greater than the values on the left/bottom-

left/bottom/bottom-right cells.

In this way, if two adjacent cells have the same weight value, only one would be

identified as a local maximum.

2.3.1 Data Acquisition system

The data acquisition system (DAQ) is composed of four DAQ boards. The DAQ

board is based on Xilinx Kintex 7 FPGAs and has been specially designed and

produced for this project [28]. A board is capable to readout 1024 channels

simultaneously at the rate of 1.1 MHz. A total of 4 DAQ boards is needed to read

the telescope. A scheme of the logic is shown in Fig. 2.20.

The analog signals from two sensors are received from the TT Hybrid boards,

through a total of 32 lines. Each line carries the signal from 32 adjacent strips.

Multichannel 12-bit ADCs (analog-to digital converter) with high speed serial

outputs have been used. The serialized signals are then processed using a Xilinx

Kintex 7 FPGA (commercial FPGA). First the signals are de-serialized by the

ISERDES units. Then a programmable zero suppression algorithm is applied: the

input data are compared to a predefined threshold for data decimation and rate

reduction. A simple clustering algorithm is applied by the cluster units: a cluster


Figure 2.19: Scheme of the artificial retina architecture for the proto-

type system.

Figure 2.20: Block diagram of the DAQ board.

is here defined as a maximum of 5 adjacent strips with over threshold signals. The

center of the cluster is calculated as the arithmetic mean of the strip positions

and its value can coincide with the center of a strip or with the middle position


between two strips. A total of 1023 discrete positions are possible (512 for the

strip centers, 511 for the interstrip positions). 10 bits are necessary to express

the x coordinate; 3 bits are needed to identify the detector plane. Therefore the

cluster position (zk, xk) is defined by a 13 bits address.

In principle a cluster can produce a non zero weight in cellular units that reside

in any of the 4 FPGA areas depending on the (z, x) coordinates. The cellular

units in one FPGA area receive the cluster signals only from one DAQ board, as

shown in Fig. 2.19. The DAQ board implements 12 Gbps (giga-bit per second)

bidirectional serial links to interconnect all the four boards for horizontal data

exchange. A 32× 4 switch (first level switch) is present in each DAQ board to

deliver an incoming signal to any of the other DAQ boards or the FPGA of the

TEL62 board

First level switch We described the general structure of a modular switch

network in Sec. 2.1. The first level switch is implemented using two 16× 16 and

two 2 × 2 sorters as shown in Fig. 2.21. The cluster units of the first and the

16x16 16x16

2x2

0 15 16 31

01 01

0 1

0 1

2x20 1

2 3

Figure 2.21: Scheme of the first level switch. The 32 × 4 sorter is

composed of two 16× 16 sorters and two 2× 2 sorters.

second sensor send the signals to the 16 × 16 sorters and only 2 of the output

lines of the 16× 16 sorter are connected to the subsequent 2× 2 sorters.

In this way a cluster can be distributed to any of the 4 FPGA areas.

2.3.2 TEL62 board

The TEL62 board has been developed for the NA62 experiment at CERN [30].

It is a very efficient solution for the acquisition and processing of signals from

multichannel detectors and it is back compatible with the TELL1 board, used in

LHCb.


Figure 2.22: Picture of the TEL62 board.

A picture of the TEL62 board is shown in Fig. 2.22.

The retina architecture is implemented in a fully pipelined design on the TEL62.

The TEL62 board has 4 Altera Stratix III FPGAs corresponding the 4 FPGA

areas. No high-speed communication buses are present for the horizontal data

exchange between the four FPGAs. The cell responses (weight) from different

FPGAs cannot be used for track parameters calculations; only weights from the

same FPGA can be interpolated. This determines the need for the interconnection

between the DAQ boards, the implementation of the first level switches and the

overlapping regions.

Second Level Switch For each FPGA area, a second sevel switch is imple-

mented in the system. The inputs correspond to the 4 pairs of detectors read

by the DAQ boards, while the 16 output correspond to the FPGA regions. The

switch network consists of eight 4× 4 sorters, where some lines(dashed) are not

connected, as shown in Fig. 2.23. For a nicer view, not all the lines connecting

the first and second row of 4× 4 sorters are drawn. Each 4× 4 sorter is made by

four 2-way sorters. An example of 4× 4 sorter has been shown in Fig. 2.8.

We will now describe the connections between the 4× 4 sorters, since this infor-

mation is useful to simplify the routing map of the clusters, stored in the LUTs.

A 4× 4 sorter is made by four 2-way sorters, organized in two rows. Outputs from

the top-left 2-way block are connected to the left inputs of the second row blocks.

Outputs from the top-right block are connected to right inputs.

The 4× 4 sorters are organized in two rows. Outputs from the i-th 4× 4 sorter

(first row) are connected to the i-th input of each 4 × 4 second row block. In

particular, this is shown for the top-left 4× 4 sorter, in Fig. 2.23.


4x4

4x4

4x4

4x4

4x4

4x4

4x4

4x4

16x16

2x2

2x2

2x2

2x2

2x2

2x2

2x2

2x2

2x2

2x2

2x2

2x2

2x2

2x2

2x2

2x2

2x2

2x2

2x2

2x2

2x2

2x2

2x2

2x2

2x2

2x2

2x2

2x2

2x2

2x2

2x2

2x2

2x2

0 1 2 3

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Figure 2.23: Scheme of the Second Level Switch. Red (dashed)

line/blocks are not used

As we already defined, each 2-way sorter has two 2-way dispatchers, that can

route the signal to zero, ore both the mergers, and every dispatcher contains a

LUT for the comparison of the incoming signal and the determination of the data

path. Since some dispatchers are not used in the 4× 16 switch network, a total of

28 LUTs is needed.

We will now discuss the implementation of the LUTs in the 2-way sorter. In

particular, we will treat the 2-way sorters row-by-row. The cluster position is

defined by a 10 + 3 bits (respectively for x and z ) address. The group number is

defined by the 5 most significant bits of the x address. This means that we are

considering groups of 32 adjacent cluster positions.

The evaluation of the LUTs has been performed using a script implemented with

the Mathematica software. We remind that the LUT values of a 2-way sorter are

2 bit strings the identify to which output the signal has to be forwarded.

For each group we determine to which regions the signal must be delivered and

we build a 16 bit ordered string (Service String): if a region receives the signal

the bit value is 1, otherwise it is 0. An example of the construction of the Service

String is shown in Fig. 2.24.

The 2 bit LUT values of all the 2-way dispatchers can be determined from the

corresponding Service String, using logic rules implemented in the Mathematica

script.

In Fig. 2.25 is shown the rule to evaluate the LUT values stored in a dispatcher

in the first row of 2-way sorters. In particular, looking at the structure of the


0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Reg 0

Reg 1

Reg 2

Reg 3

Reg 4

Reg 5

Reg 6

Reg 7

Reg 8

Reg 9

Reg 1

0

Reg 1

1

Reg 1

2

Reg 1

3

Reg 1

4

Reg 1

5

0 0 1 0 0 1 0 0 1 1 0 0 0 01 1

Second Level Switch Outputs

16 bits string

Map of "activated" regions

Figure 2.24: Example of the construction a Service String from the

map of the activated regions. The blue (filled) regions receives the

cluster signal and the corresponding bit is set to 1.

connections of the 16× 16 switch network, a dispatcher in the first row, selects if

a signal has to be routed to zero, one or two blocks of 8 regions. The LUTs of

0 0 1 0 0 1 0 0 1 1 0 0 0 01 1Service String

for a group address{ {

OR OR

1 1 LUT value for 2-way splitter in the

first row of 2-way sorter

Figure 2.25: Example of evaluation of LUT entry for a 2-way dispatcher

in the first row of 2-way sorters. The OR function is applied to the

first and last 8 bits of the Service String corresponding to the group

address.

the dispatchers in the second, third and fourth row of 2-way sorter are evaluated

applying different logic rules to the previously evaluated Service String.

Once the cluster signal comes to a region, all the 16 cellular units evaluate the

weight Wijk.

A cellular engine provides the calculation of the weight for two adjacent cells. We


already described the general implementation of the cellular engine in Sec.2.1,

and the scheme is shown in Fig. 2.9. The value of fij(zk) is returned by a 3× 16

bits LUT, that accepts the 3 bits z address. A 10× 16 LUT accepts the 10 bits x

address and provides the value of xk.

|sijk/(2σ)| is calculated and compared to a 10 × 16 bits LUT that returns the

evaluation of Wijk. An accumulator is used to evaluate the weight function by

summing the Wijk contributions.

The value of σ is chosen to be

σ = 1.1 ∆x. (2.15)

The threshold (thr) value for the identification of a local maximum is set to

thr = 6.9. (2.16)

The values for σ and thr have been chosen according to the results obtained from

the simulations that are discussed in Chapter 3, aimed to optimize the quality of

the track reconstruction.

The interpolation method is applied to all the local maxima (and neighbor) cellular

units using the Eq. (2.9) and Eq. (2.8). The argument of the logarithmic terms

is limited to the [0, 1] range and is evaluated using a 10× 16 bit LUT to improve

the speed performances.

The track parameters are then sent from the track fitter to a PC and are stored

to disk.

Latency of the system The DAQ boards can accept the trigger at a maximum

rate of 1.1 MHz that corresponds to the maximum trigger rate accepted by the

Beetle chip.

The FPGAs in the DAQ boards and in the TEL62 operate at a frequency of 200

MHz. We remind that the first level switch is implemented in the DAQ boards,

while the second level switch is implemented in the TEL62. The latency of the

retina response is represented in Table 2.1 and is below 100 clock cycles which

corresponds to 0.5µs at 200MHz clock frequency.

Each 2-way sorter needs two clock cycles to compare the incoming signal to the

LUT in the 2-way dispatcher, and one cycle in the 2-way merger. This information

allows to calculate the latency of the switches. In particular the first level switch

latency is 15 clock cycles and the latency of the second level switch is 12 cycles.

The cellular engines evaluate the weight using different values returned by the

LUTs or by arithmetic operations.

Also in the track fitter some values are directly calculated in the FPGA while

some are returned by LUTs, like the evaluation of the logarithmic terms.


Latency of the retina

Task Clock cycles

First level swtich 15

Second levele switch 12

Engine 15

Track fitter 30

Total <100

Table 2.1: Latency of the retina hardware. The total value is below

100 clock cycles.

Chapter 3

Design and simulation of the

prototype system

The geometry of the telescope and the design of the artificial retina have been

optimized using Monte Carlo simulations. In some cases the parameters are limited

by technical constraints, like the minimum mechanical distance between planes or

the total available FPGAs resources. The Sbt (Software for beam test) software,

developed in the past for testbeam analysis, has been adapted to simulate the

retina response. The Sbt software allows to define the telescope geometry, to

simulate the multiple scattering of the particles with the material and reconstruct

the generated tracks. The retina algorithm has been implemented for 2D track

reconstruction.

3.1 Sbt software

The Sbt package is a C++ software, that uses ROOT libraries, developed for

simulation and reconstruction of beam test events by Marco Bomben, Nicola Neri

and John Walsh. I adapted the software in order to reconstruct tracks with the

retina algorithm and introduced other changes to the code in order to simulate

the telescope prototype.

3.1.1 Main functionalities of the Sbt software

Sbt allows to configure the geometry of telescope with N tracking detectors and

one or multiple DUTs. Different types, materials, dimensions and positions/orien-

tations can be configured for any of the detectors. In particular, pixel, single-sided

strip and double-sided strip detectors can be used simulated. Depending on

the type of the detector, different clustering algorithms and pattern recognition

47

CHAPTER 3. DESIGN AND SIMULATION OF THE PROTOTYPE SYSTEM48

algorithms can be used.

It is also possible to set different parameters for the events simulation, like the

number of tracks per event, the number of noise hits, the type of particles and

their energy. Different particle guns are implemented to generate tracks as in

a beam test environment or to simulate the cosmic ray angular distribution of

particles, as we did in this work.

The simulation generates the list of the digitized channel signals for each track to

be reconstructed.

The track reconstruction consists of different steps. The information of the hits is

reconstructed from the digitized channel signals (digis). A predefined threshold is

applied for background suppression, then a clustering algorithm forms clusters

of adjacent hits. Two reconstruction algorithms can be used. The first, that we

will refer to as offline algorithm is based on a pattern recognition algorithm to

identify the track candidates and the track parameters are determined by simple

χ2. The second is the retina algorithm, as previously defined.

At the end of the track reconstruction process, all the events are saved in a ROOT

file. The use of the ROOT output files allows either quick and easy access to the

data or more advanced analysis.

3.2 Optimization of the telescope layout

Before optimizing the telescope layout we need to define some constraints on

the geometry. As shown in Fig. 3.1, the barycenter of each planes lies on the z

axis and sensors are parallel to each other and perpendicular to the z axis. The

z

x

Figure 3.1: Scheme of the layout of the prototype telescope where d is

the distance among planes. The planes are parallel to each other and

perpendicular to the z axis.


distance among the planes, d, is constant and has been minimized in order to

increase the angular acceptance of the telescope improving the track resolution,

as discussed in the following sections. The telescope has been designed to host a

detector in the middle for prototype sensor tests (detector under test, DUT), but

this solution is not discussed here.

3.2.1 Test of the system with cosmic rays

This telescope will be able reconstruct tracks from cosmic ray particles. The test

with cosmic rays allows to verify the functionalities of the system and prove the

working principle. Eventually, the prototype will be tested on a beam to study

the response at higher rates, up to 1.1MHz. The intensity of cosmic rays at sea

level, over an horizontal surface is approximately Icosmic = 1.67 · 10−2cm−2s−1 [31].

The approximate angular distribution for 3 GeV muons is

dN

d cos θ= ∝ cos2 θ (3.1)

where θ is the azimuthal angle measured with respect to the z axis. The distribution

is shown in Fig. 3.2 as a function of the polar angle θ. The ratio between the

Figure 3.2: Polar plot of the normalized angular distribution vs. the

polar angle θ.

number of particles crossing the entire telescope and the number of particles

interacting on the first layer is defined as the geometrical acceptance. We want to

keep this value as high as possible, since the expected rate is quite low. Obviously

this means that we have to minimize the distance d between the planes.

3.2.2 Expected rate of the cosmic rays

We generated 3GeV muons according to the cosmic rays angular distribution,

represented in Eq. (3.1). For different values of d we generated a set of 10000

tracks and we evaluated the geometrical acceptance as a function of the plane


Figure 3.3: Geometrical acceptance vs. d. The acceptance decreases

for increasing distance d.

distance. The results are represented in Fig. 3.3. As expected the acceptance

increases when reducing the distance d.

The mechanical design of the telescope has been optimized in order to minimize

the distance between the planes, achieving a value of d=8cm , determined by

the space for readout electronics and the cables. The corresponding geometrical

acceptance is about ϵ8p = 0.448.

In order to evaluate the expected rate of cosmic rays, we have to consider the

presence of the scintillators. We performed a similar simulation for the final setup.

Here the geometrical acceptance is defined as the ratio between the number of

tracks crossing both scintillators and planes, and the number of tracks crossing

the first scintillator. The dimension of the scintillator area is 15× 15cm2. The

distance from the first scintillator to the closest silicon detector is set to 2.6275cm.

The other scintillator is positioned at 5.0225cm from the last silicon detector. The

obtained value is

ϵ10p = 0.157. (3.2)

Taking in account that the ϵ10p and ϵ8p refer to different surface values, the

expected rate as for cosmic rays is

R = Icosmic ϵ10p Ascint = 0.59Hz. (3.3)

The trigger is given by the coincidence of the signals of scintillators. Since the area

of the scintillators is wider, the number of tracks crossing the 8 silicon layers is

lower than the number of triggers and their ratio is determined from the simulation

to be

ϵcoinc = 0.616. (3.4)


3.3 Optimization of the artificial retina param-

eters

The artificial retina response has been simulated with the Sbt software with the

goal to study and optimize its performance. The grid of cellular units is modelized

as a 2D histogram, using the TH2 ROOT class. The coordinates of the center each

bin correspond to the track parameters of the cell. The bins are distributed along

the x− and x+ axes and the bin width ∆x is identical for both the directions; the

grid covers a (Lx+2∆x)× (Lx+2∆x) square in the space of track parameters. Lx

is the dimension of silicon sensor and its values is Lx = 9.4cm. Only bins within

the detector acceptance, which satisfy the following conditions, are considered,|x−i − x+j | ≤ Lx+2∆x

2,

|x−i + x+j | ≤ Lx+2∆x2

.(3.5)

These bins are represented inside the red frame in Fig. 3.4.

0

1

2

3

4

5

6

7

X -[cm]

-4 -3 -2 -1 0 1 2 3 4

X +

[cm

]

-4

-3

-2

-1

0

1

2

3

4

Figure 3.4: Event display of the artificial retina for a track in the

geometrical acceptance.

In the Monte Carlo simulation the process is not parallelized and the hits are

assumed to be delivered to the appropriate cells without modeling the switch

functionalities. For each cluster, the Wijk function is evaluated for all the bins

inside the area defined in Eq. (3.5) and summed over all the cluster k in order

to evaluate the weight function Wij. We require the condition |sijk| < 2σ to be

satisfied for the evaluation of Wijk, as defined in Eq. (2.6) .


3.3.1 Sharpness of the retina response

It has been shown that σ is the width of the Gaussian function that describes the

receptor response field. It determines the sharpness of the retina response and it

a parameter that has to be tuned.

Let’s consider a cluster of hits in the (x−, x+) space, where (zk, xk) identifies a

bundle of lines, defined by

sk := xk − x+ − x−zk − z+

z−= 0.

If we consider a different cluster (zm, xm), the corresponding line intersects the

first bundle in one and only one point in the (x−, x+) space, as shown in Fig.

3.5. The coordinates of the interception correspond, to the track parameters.

If we consider multiple clusters from a track, all the corresponding lines in the

I

Figure 3.5: Intersections of bundles of lines in the (x−, x+) space corre-

sponds to track coordinates. In the are shown two lines, corresponding

to two clusters, intersecting in one point.

parameters space (x−, x+) will intercept in one point, within the uncertainty due

to the effect of multiple scattering and the finite detector resolution.

In Fig. 3.6 we show the weight function for a track crossing the planes telescope:

each “line” represents one of the bundles defined by the clusters position.

For a single track, all the weights must sum up in the same region of the parameters

space, producing one local maximum. In particular this condition is satisfied if

σ ≥ (σx)MS ⊕ (σx)Res,

where (σx)MS is the uncertainty on the track intercepts due to the multiple

scattering and (σx)Res is the error introduced by the finite resolution of the

detector. This requirement can be interpreted as a lower limit on the σ value.


Figure 3.6: W (x−, x+) for a reconstructed track

Since in the artificial retina the weight function is not continuous, but is evaluated

by a discrete set of cellular units we need to set σ & ∆x in order to have a local

maximum cell with non negligible response.

3.3.2 Track parameters determination

The parameters of the reconstructed tracks are determined by interpolating the

weight function with a Gaussian function along the x− and x+ coordinates. This

is motivated by the definition of the Wij function as the sum of different Gaussian

contributions. The distribution of the weight Wij can be approximated by the

sum of Gaussian functions with identical width and mean. The natural choice for

interpolating the cell values along x+ is a generic Gaussian function, the x+reco is

determined according to Eq. (2.8) and Eq. (2.9).

The x− profile near (x−i , x+j )max can be approximated as the sum of Gaussian

functions with different widths but identical means. When using a Gaussian inter-

polation, this introduces a systematic error on the reconstructed x−reco parameter.

The (x−reco−x−gen) deviation has been evaluated using a Mathematica script, where

x−gen represents the parameter of the generated track. The deviation depends

linearly to ∆x and is inversely proportional to the σ/∆x ratio. The deviation

depends also on the (x−gen − x−i ) distance, where xi is the center of the cell.

In Fig. 3.7 we show the behavior of (x−reco − x−gen)/∆x as a function of σ/∆x and

(x−gen − x−i ).


Figure 3.7: Behavior of the systematic error as a function of the

distance between the generated track parameter and the center of the

local maximum cell as a function of the σ/∆x ratio.

In Fig. 3.8 the residual (x−reco−x−gen)/∆x vs. (x−gen−x−i ) is shown, for σ/∆x = 1.1

.

The maximum deviation isx−reco − x−gen

max

≃ 0.013.

Figure 3.8: Behavior of the systematic error as a function of the

distance of between the generated track parameter and the center of

the maximum weight cell, for σ/∆x = 1.1.

The resolution depends linearly on ∆x, that should be minimized. In the case this

value is not tunable because is fixed by the available FPGAs resources. A possible

strategy to remove the systematic error is to tabulate the offset as a function of

δx− (see Eq. (2.9) in a Look-Up Table and use these values to correct the track

parameters evaluation.


3.3.3 Optimization of the retina response

We want to optimize the tracking resolution of the retina assuming the ∆x value

is fixed by the available FPGA resources,

∆x = 0.168cm.

Moreover, we requireσ

∆x> 1,

to be able to interpolate the weight function using neighbor cells. Experiments

with 10000 tracks have been simulated for different σ/∆x values. The cosmic ray

distribution has been used and the polar angle θ has been limited to the maximum

angle of reconstructable tracks in the geometrical acceptance. This is valid also

for the next simulations. No threshold has been set for the identification of the

local maximum of the weight function.

x∆/ σ1 1.2 1.4 1.6 1.8 2 2.2

m]

µR

eso

lutio

n [

0

5

10

15

20

25

30

35

40

45

50

Res)gen

X

reco

(X

Res)gen

+X

reco

+(X

Figure 3.9: Resolution on x− and x+ track paramters as a function of

σ/∆x

For each configuration the residual distributions of (x−reco−x−gen) and (x+reco−x+gen)

have been measured, where (x−, x+)gen represents the track parameters of the

generated track. The width of the residuals distributions vs. σ/∆x are shown in

Fig. 3.9.

The x+ resolution does not depend on the σ value, while the resolution for x−

slightly improves for increasing values of σ/∆x. This is the effect of the systematic

error introduced by the Gaussian interpolation method.

In principle increasing the value of σ we obtain better resolutions. This is valid

only if there are no noise hits or multiple tracks. In fact if we consider two

cluster of hits in the same plane, increasing the value of σ prevents to distinguish

clusters associated to different tracks. In Fig. 3.10 we show the sum of two


Gaussian functions with different means. If the relative distance between the

clusters is |xk − xm| ≤ 2σ, the contributions Wijk sum up in a function with a

single maximum.

-3 -2 -1 1 2 3Σ

0.5

1.0

1.5

Weight

-3 -2 -1 1 2 3Σ

0.2

0.4

0.6

0.8

1.0

1.2

Weight

-3 -2 -1 1 2 3Σ

0.2

0.4

0.6

0.8

1.0

Weight

Figure 3.10: Sum of Gaussian functions with identical σ and distance

of 1σ (left), 2σ (center), 3σ (right) between the mean values.

We also note that noise hits or hits from multiple tracks can contribute to increase

the value and can modify the shape of the weight function. The magnitude of this

effect depends also on the number of tracks and noise hits per event and would

affect the resolution of the track parameters, the reconstruction efficiency and the

purity.

We decide to set the ratio at σ/∆x = 1.1, as defined in Eq. (2.15). We will

show in Section 3.4 that adopting this choice we can obtain resolutions on track

parameters comparable to the offline results.

3.3.4 Threshold value for the retina response

Let’s discuss here the definition the threshold value for the identification of a local

maximum of the retina response. So far we have discussed the case of one track

passing through all the telescope planes. In this case it is not necessary to set

a threshold, because we have only one local maximum. If we consider a more

general situation we can have different cases, for example:

• One track with some missed hits.

The local maximum value Wij is lower than the one corresponding to a track

with all the hits.

• Multiple tracks.

There are different local maxima. We want to identify the maxima corre-

sponding to the generated track and reject the fake maxima.

• One or multiple tracks with noise hits.

Noise hits can produce local maxima.

In Fig. 3.11 we show the weight function for 8 hits belonging to a track plus a noise

hit in the first layer. Several local maxima are present, but only one corresponds


0

1

2

3

4

5

6

7

X -[cm]

-4 -3 -2 -1 0 1 2 3 4

X +

[cm

]

-4

-3

-2

-1

0

1

2

3

4

Local Maximums

Figure 3.11: Retina response, Wij, for an event with a track plus a

noise hit in the first layer.

to the reconstructed track. Setting a proper threshold allows to identify only the

meaningful maxima. Other local maxima below the threshold will be rejected.

In order to optimize the value of thr to be chosen in the final configuration

Entries 4994

Maximum Weight6.8 7 7.2 7.4 7.6 7.8 80

5

10

15

20

25

30

35

40 Entries 4994

thr

Figure 3.12: Distribution of the maximum weight value for single track

events

(∆x = 0.168cm, σ/∆x = 1.1) we performed a simulation of 10000 single track

events (number of tracks crossing the first detector). For each event we require

a hit in each detector to be sure that the track crosses all the telescope and we

evaluate the weight function for the cellular units with maximal weight. The

distribution of the maximum of the weight function is shown in Fig. 3.12 and a

threshold value of thr=6.9 retains all the generated tracks.


3.4 Tracking performances

In this section we present the results obtained from the simulations using the

following retina parameters:

∆x = 0.168cm, σ/∆x = 1.1, thr=6.9 . We will reconstruct single track events,

and we will compare the track parameters resolution to the offline results based

on a χ2 fit.. Then we will discuss the tracking performance in presence of noise

hits for this configuration and alternative retina configurations.

3.4.1 Resolution for single track events

In Fig. 3.13 we show the residual distribution between the reconstructed and

generated track parameters.

xminus_reso

Entries 5001

Mean 0.6279

RMS 27.66

/ ndf 2χ 173.3 / 148

Constant 1.87± 99.09

Mean 0.3757± 0.6813

Sigma 0.32± 25.94

m]µ) [gen

xreco

(x

200 150 100 50 0 50 100 150 2000

20

40

60

80

100

120

xminus_reso

Entries 5001

Mean 0.6279

RMS 27.66

/ ndf 2χ 173.3 / 148


Mean 0.3757± 0.6813

Sigma 0.32± 25.94

Resolution

Offline X

xplus_reso

Entries 5001

Mean 0.306

RMS 19.89

/ ndf 2χ 213.1 / 122


Mean 0.2526± 0.1647

Sigma 0.22± 17.44

m]µ) [gen+x

reco

+(x

200 150 100 50 0 50 100 150 2000

20

40

60

80

100

120

140

160

180

200xplus_reso

Entries 5001

Mean 0.306

RMS 19.89

/ ndf 2χ 213.1 / 122


Mean 0.2526± 0.1647

Sigma 0.22± 17.44

Resolution+

Offline X

Figure 3.13: Distribution of (x−reco − x−gen) and (x+reco − x+gen) for offline

reconstructed tracks, fitted with a Gaussian function (red solid line).

5001 of the 10000 simulated events have been reconstructed in the geometrical

acceptance of the telescope. The track parameters have been reconstructed

using the offline and retina algorithm. The distributions for (x−reco − x−gen) and

(x+reco − x+gen) residuals have been measured and fitted with a Gaussian function,

for offline and retina reconstructed tracks,in Fig. 3.13 and Fig. 3.14, respectively.

We will call the widths of the Gaussian fit function σx− and σx+ (not to be

confused with σ, the width of the receptors response). These values correspond

to the resolution of the reconstructed track parameters. No correction have been

introduced to correct the systematic error due to the interpolation along the x−

coordinate. Moreover the logarithmic terms of Eq. (2.9) have been evaluated

simulating a 10 × 16 resolution LUT, simulating the engine calculation. This


xminus_reso

Entries 5001

Mean 0.5252

RMS 31.38

/ ndf 2χ 154.6 / 162


Mean 0.4334± 0.3773

Sigma 0.34± 29.86

m]µ) [gen

xreco

(x

200 150 100 50 0 50 100 150 2000

20

40

60

80

100

xminus_reso

Entries 5001

Mean 0.5252

RMS 31.38

/ ndf 2χ 154.6 / 162


Mean 0.4334± 0.3773

Sigma 0.34± 29.86

Resolution

Retina X

xplus_reso

Entries 5001

Mean 2.117

RMS 19.86

/ ndf 2χ 205.9 / 119


Mean 0.252± 1.989

Sigma 0.22± 17.45

m]µ) [gen+x

reco

+(x

200 150 100 50 0 50 100 150 2000

20

40

60

80

100

120

140

160

180

200xplus_reso

Entries 5001

Mean 2.117

RMS 19.86

/ ndf 2χ 205.9 / 119


Mean 0.252± 1.989

Sigma 0.22± 17.45

Resolution+

Retina X

Figure 3.14: Distribution of (x−reco − x−gen) and (x+reco − x+gen) for retina

track, fitted with a Gaussian function (red solid line). ∆x = 0.168cm,

σ = 0.185cm and thr = 6.9.

means that the logarithmic function has been evaluated for 210 values in the [0, 1],

and the returned value has a 16bits precision.

The x− and x+ resolutions for the offline reconstructed tracks are

(σx−)offline = (26.0± 0.3) µm, (3.6a)

(σx+)offline = (17.4± 0.2) µm. (3.6b)

The x− and x+ resolutions for the retina reconstructed tracks are

(σx−)retina = (29.9± 0.3) µm, (3.7a)

(σx+)retina = (17.4± 0.2) µm. (3.7b)

The obtained values for σx+ are comparable, while we obtain a better resolution

for σx− using the χ2 fit. This discrepancy is due to the systematic error introduced

by the interpolation method, that can be corrected by parametrizing the offset as

a function of the x− reconstructed value in a LUT.

Quadratic track receptor response We will briefly discuss an alternative

way to evaluate the weight function and extract the track parameters. In particular

we define the track receptors response using a quadratic function instead of a

Gaussian function. We will also redefine δx± used in the interpolation method

introduced in Eq. (2.8). We will refer to these value as (Wijk)quad and δx±quadwhile the sijk and Wij values don’t change respect to th definitions reported in


Eq. (2.5) and Eq. (2.6),

(Wijk)quad =

1− s2ijk

4σ2 if |sijk| ≤ 2σ

0 if |sijk| > 2σ, (3.8)

δx−quad =∆x

2· −Wi−1 j +Wi j+1

2Wi,j −Wi−1 j −Wi+1 j

, (3.9a)

δx+quad =∆x

2· −Wi j−1 +Wi+1 j

2Wi,j −Wi j−1 −Wi j+1

, (3.9b)

for (i, j) = (i, j)max.

Using this method the shape of the weight function nwithear the local maximum

can be approximated as a quadratic function along the x− and x+ coordinates.

Along the x+ it is the sum of N quadratic functions with the same widths, while

along the x− it is the sum of N quadratic functions with different widths, which

is also a quadratic function. We can then interpolate the weight maximum using

a quadratic function along x− and x+ without introducing any systematic error

on the track reconstruction.

In Fig. 3.15, we show the resolution of the x− and x+ track parameters, recon-

structed using the quadratic retina response and the interpolation method. The

xminus_reso

Entries 4983

Mean 0.6391

RMS 27.67

/ ndf 2χ 170.4 / 148


Mean 0.3766± 0.6812

Sigma 0.32± 25.96

m]µ) [gen

xreco

(x

200 150 100 50 0 50 100 150 2000

20

40

60

80

100

120

xminus_reso

Entries 4983

Mean 0.6391

RMS 27.67

/ ndf 2χ 170.4 / 148


Mean 0.3766± 0.6812

Sigma 0.32± 25.96

Resolution

Bilinear Response X

xplus_reso

Entries 4983

Mean 0.3196

RMS 19.86

/ ndf 2χ 212.2 / 122


Mean 0.2528± 0.1726

Sigma 0.22± 17.42

m]µ) [gen+x

reco

+(x

200 150 100 50 0 50 100 150 2000

20

40

60

80

100

120

140

160

180

xplus_reso

Entries 4983

Mean 0.3196

RMS 19.86

/ ndf 2χ 212.2 / 122


Mean 0.2528± 0.1726

Sigma 0.22± 17.42

Resolution+

Bilinear Response X

Figure 3.15: Distribution of (x−reco − x−gen) and (x+reco − x+gen) for single

track events, reconstructed using the retina algorithm with (Wijk)bilinearand δx±bilinear, and ∆x = 0.168cm, σ = 0.185cm and thr = 6.9.


obtained values are comparable with the offline resolutions.

(σx−)quad = (26.0± 0.3) µm, (3.10a)

(σx+)quad = (17.4± 0.2) µm. (3.10b)

This method represents a valid alternative to the Gaussian field receptor response

and can be considered for implementation in the hardware. However, the Gaussian

field allows a more general and flexible configuration of the retina response. For

example, if the |sijk| ≤ 2σ cut is not applied, the quadratic response becomes

negative outside this range and it is not limited, while the Gaussian response is

always positive and tends to zero for increasing values of |sijk|.

3.4.2 Retina response in presence of background

We analyze the behavior of the artificial retina in presence of background hits.

We will simulate single track events with different detector occupancy levels. The

detector occupancy is defined as the fraction of fired channels (hits) with respect

to the number of channels of the detector.

If the distance between two clusters is less than 2σ, the positions are not resolved

by the retina algorithm and they will contribute Wij affecting the track parameter

determination, worsening the resolution. The presence of background hits modifies

the weight function with potential impact also on the reconstruction efficiency, as

described in the following.

We will refer to a track that has been generated in the simulation and that

corresponds to a particle crossing the telescope as reconstructable track. A ghost

track is a fake track corresponding to a local maximum but not associated to a

reconstructable track.

The purity of the sample is the fraction of reconstructed tracks that corresponds

to reconstructable tracks.

P :=#rec.ble

#rec.ed

#rec.ed

, (3.11)

where #rec.ble is the number of reconstructable tracks and #rec.ed is the number of

reconstructed tracks.

Another effect of the noise hits is that we cannot reconstruct some of the recon-

structable tracks reducing the efficiency.

The efficiency is defined as the fraction of reconstructable tracks that are effectively

reconstructed.

ϵ :=#rec.ble

#rec.ed

#rec.ble

. (3.12)


We will refer to a reconstructable track that is also reconstructed by the artificial

retina as a good retina track. In particular we identify a track as a good track

applying if it satisfties:

• it is associated with a local weight maximum over threshold;

• the clusters are associated to the generated ones ( > 6/8 clusters), according

to the Monte Carlo information.

Efficiency and purity of the retina tracks have been evaluated using the simulations.

We show the results obtained for 10000 simulated tracks with 0.5% detector

occupancy using the nominal configuration, discussed before, for the telescope and

the retina. The number of reconstructable tracks within the detector acceptance

is 4900. The number of reconstructed tracks is 5318, while the good retina tracks

are 4892. The obtained values of efficiency and purity are

ϵ0.5% = 99.8%, (3.13a)

P0.5% = 92.9%. (3.13b)

In Fig. 3.16 the (x−reco − x−gen) and (x+reco − x+gen) distribution are shown. In

both the plots we observe a thin peak in the middle that corresponds to tracks

reconstructed in events with background hits far from the track clusters. Ghost

tracks are not included in the distributions. The root mean square (RMS) of the

xminus_reso

Entries 4892

Mean 2.075

RMS 248.7

m]µ) [gen

xreco

(x

1000 800 600 400 200 0 200 400 600 800 10000

20

40

60

80

100

120

140xminus_reso

Entries 4892

Mean 2.075

RMS 248.7

Resolution

Retina X

xplus_reso

Entries 4892

Mean 3.254

RMS 163.7

m]µ) [gen+x

reco

+(x

1000 800 600 400 200 0 200 400 600 800 10000

20

40

60

80

100

120

140

160

180

xplus_reso

Entries 4892

Mean 3.254

RMS 163.7

Resolution+

Retina X

Figure 3.16: (x−reco − x−gen), (x+reco − x+gen) distribution for reconstructed

tracks with 0.5% detector occupancy and ∆x = 0.168cm, σ = 0.185cm

and thr = 6.9.


distributions are,

(x−reco − x−gen)RMS = (248.7± 2.5)µm, (3.14a)

(x+reco − x+gen)RMS = (163.7± 1.7)µm. (3.14b)

The resolutions are not comparable to the values obtained using simulated events

without background hits. The same simulation has been repeated for 1% detector

occupancy. We obtained

ϵ1% = 99.9%, (3.15a)

P1% = 46.0%. (3.15b)

The efficiency value is almost unchanged, while the purity decreases for increasing

values of occupancy. In Fig. 3.17 the (x−reco − x−gen) and (x+reco − x+gen) residual

distributions are shown. The obtained RMS values are

xminus_reso

Entries 4948

Mean 10.6

RMS 360.3

m]µ) [gen

xreco

(x

1000 800 600 400 200 0 200 400 600 800 10000

10

20

30

40

50

xminus_reso

Entries 4948

Mean 10.6

RMS 360.3

Resolution

Retina X

xplus_reso

Entries 4948

Mean 2.331

RMS 261.9

m]µ) [gen+x

reco

+(x

1000 800 600 400 200 0 200 400 600 800 10000

10

20

30

40

50

60

70xplus_reso

Entries 4948

Mean 2.331

RMS 261.9

Resolution+

Retina X

Figure 3.17: (x−reco − x−gen), (x+reco − x+gen) distribution for good retina

tracks in presence of 1% detector occupancy and with ∆x = 0.168cm,

σ = 0.185cm and thr = 6.9.



As one could expect, the resolutions get worse for increasing levels of detector

occupancy.

3.4.3 Efficiency and purity as a function of the threshold

The threshold value has been set so far to maximize the efficiency for track

reconstruction in absence of background hits. As we have seen, the noise modify


the response of the weight function and in general increase its value. Using an

higher threshold we can reduce the number of ghost tracks, increasing the purity

of the reconstructed tracks. On the other hand some good tracks whose weight

value is below threshold will be rejected, reducing reconstruction the efficiency.

In Fig. 3.18 we show the efficiency and purity distribution for the nominal

configuration with 0.5% and 1% detector occupancy levels. Each point corresponds

to a different value of threshold, in the range [6.8, 8.4].

Efficiency0.4 0.5 0.6 0.7 0.8 0.9 1

Purity

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Efficiency vs. Purity

0.005 noise occupancy


Figure 3.18: Efficiency and purity as function of the threshold in the

range of values [6.8, 8.4] with ∆x = 0.168cm, σ = 0.185cm.

The value of the threshold has to be tuned according to the required performance

and track sample characteristics.

As an example, let’s consider a configuration with thr > N , where N is the number

of planes. In this case all events with low noise, or noise hits distant from the

track hits (enough to not modify the shape and position of the maximum), will

be rejected. This means that we are discarding the higher quality tracks. An

optimal choice of the threshold depends on the kind of selection of tracks we want

to perform, whether we want a high pure sample or a sample with high efficiency.

3.4.4 Efficiency and purity as a function of the grid step

As we already discussed, we will not perform an optimization of the ∆x parameter,

since it is fixed by the available resources of the FPGAs of the TEL62 board.

About 250 engines can fit on an Altera Stratix III FPGA, corresponding to 500

cellular units for a total of 1000 engines and 2000 cells in the TEL62 board hosting

4 FPGAs. However, in presence of background hits it is possible to improve the

resolutions for the track parameters and higher purity of the sample increasing

the number of cellular units, while keeping constant the value of σ/∆x. In this

way it is possible to better resolve the positions of the clusters and the localization

of the maximal weight.


We studied the case with a grid of 20200 cellular units, which is about ∼10 times

higher with respect to the nominal configuration. In this case ∆x = 0.0474cm,

σ = 0.0522cm and thr = 6.9. The simulated detector occupancy is 1% and we

obtain:

ϵ1% = 99.9%, (3.17a)

P1% = 95.3%. (3.17b)

The purity is much higher with respect to the result obtained in the nominal

configuration and the resolutions on x− and x+ are also improved. This is an

important result which demonstrates that allocating adequate FPGA resources

allows to improve the performance of the retina response, even in presence of

relative high background. In Fig. 3.19 the (x−reco−x−gen) and (x+reco−x+gen) residualdistributions are shown.

xminus_reso

Entries 4946

Mean 1.771

RMS 64.74

m]µ) [gen

xreco

(x

1000 800 600 400 200 0 200 400 600 800 10000

50

100

150

200

250

300

xminus_reso

Entries 4946

Mean 1.771

RMS 64.74

Resolution

Retina X

xplus_reso

Entries 4946

Mean 0.004334

RMS 42.17

m]µ) [gen+x

reco

+(x

1000 800 600 400 200 0 200 400 600 800 10000

50

100

150

200

250

300

350

400

xplus_reso

Entries 4946

Mean 0.004334

RMS 42.17

Resolution+

Retina X

Figure 3.19: (x−reco − x−gen) and (x+reco − x+gen) residual distribution

for good retina tracks with 1% detector occupancy, ∆x = 0.0474cm,

σ = 0.0522cm and thr = 6.9.

The RMS values are



In Fig. 3.20 we show the efficiency and purity plot for threshold in the range

of values [6.6, 8]. The detector occupancy levels are 0.5% and 1%. The purity is

always above 90%.


Efficiency0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Purity

0.9

0.91

0.92

0.93

0.94

0.95

0.96

0.97

0.98

0.99

1

Efficiency vs. Purity



Figure 3.20: Efficiency and purity as function of the threshold in

the range of values [6.8, 8.4], for 0.5% and 1% detector occupancy.

∆x = 0.0474cm, σ = 0.0522cm.

3.5 Perspectives for the future - Artificial retina

with time information

Here we discuss the possibility of the application of the artificial retina to a

tracking system using detectors capable to provide precise time information of the

hits with sub-ns resolution. An example of this kind of detector is represented

by the GigaTracker [32] developed by the NA62 experiment at CERN. The

sensor is an hybrid silicon pixel detector capable to provide the time of the hits

with a time resolution of about 200ps. Another example is represented by the

development of the UFSD [33] (ultra fast silicon detectors), that are foreseen

to reach time resolutions up to 20-30ps in the future. Combininig the time

information with a redefinition of the retina algorithm it is possible to heavily

suppress the contributions of background hits out of time, comparing the measured

time to the expected time of the track. Moreover, it is possible to reconstruct the

time information of the track with good precision even in presence of background

hits.

At high energy physics experiments at accelerators, where the expected time of

the interactions is defined by the bunch crossing frequency, this approach can be

applied as described in the following.

3.5.1 Redefinition of the retina algorithm

In order to use the time information of the clusters we have to modify the definition

of the weight. Let’s consider an hypothetical experiment with a bunch crossing

rate of 40MHz. This means that we have particle interactions every 25ns, and

assume that the longitudinal dimension of the interaction region is approximately


30cm. The time of the bunch crossing is synchronized with the clock of the

accelerator, so the time of the hits in the tracking system are expected to be

approximately in a time window [−0.5, 0.5]ns around the clock time, tclk, if we

approximate the speed of the particles with the speed of light.

In order to include the time of the clusters we redefine the weight introducing

a time dependent contribution. In particular we use a 3D grid of cellular units

to reconstruct the track parameters (x−, x+, t) of the tracks. Each cellular unit

evaluates the weight function for a different value of (x−i , x+j , tl). Here we provide

the definition of the weight

Wijlk =

exp− s2ijk

2σ2

exp

− t2lk

2σ2t

if |sijk| ≤ 2σ and |tlk| ≤ 2σt

0 if |sijk| > 2σ or |tlk| > 2σt, (3.19)

where tlk is defined as

tlk = tl − tk, (3.20)

and σt is the width of the receptor Gaussian field of the response, as a function of

time for the k -th cluster. The weight function is defined as

Wijl =N−1k=0

Wijlk. (3.21)

The (x−, x+) interpolation strategy has been defined in Eqs. (2.8), (2.9) and it is

valid. The interpolation for the t direction is calculated according to

treco = tl max + δt (3.22a)

δt =∆t

2·lnW−1

W0− lnW+1

W0

lnW−1

W0+ lnW+1

W0

, (3.22b)

for W0 = W(i,j,l) max,W±1 = W(i,j,l±1) max,

where treco is the reconstructed time of the track, tl max is the time at the local

maximum, δ is the interpolation offset with respect to the maximum and ∆t is

the time difference between adjacent receptors along the t axis.

3.5.2 Simulation of the retina using the time information

Here we present the simulation of single track events with 1% detector occupancy

using the time information of the hits in the retina. We consider a telescope


composed by 8 planes, the first sensor is placed at z = 0cm and the last is placed

at z = 28cm. The distance between adjacent detectors is 4cm for all the planes.

We consider a set of 10000 tracks, and the starting point of the track is fixed at a

distance of 10cm (in z ) from the first detector. The beam profile is Gaussian with

a width of 0.1cm. The azimuthal angle (from the z axis) is Gaussian distributed

and the width is set to σθ = 0.1rad. The time of the tracks is Gaussian distributed

and centered in t = tclk with the width set to 0.5ns.

The time of the track hits is generated according to the distance between the

starting point and the planes, and assuming that the particles travel at the speed

of light. A Gaussian error of 0.1ns is applied, to simulate the time resolution of

the detector. The noise hits are uniformly distributed in time over a 25ns interval.

In our model the 3D grid is composed by three 2D grids of (x−il , x+jl) cellular units,

as shown in Fig. 3.21. We set t0 = tclk and t±1 = tclk ± 1.33ns, so the grid

covers the time interval [−2, 2]ns. The width of the Gaussian field of the receptor

response to the time of the hit is set to σt = 1.5ns. The threshold value has been

set to thr = 6. Using these values we expect to find the local maxima only in the

Figure 3.21: Scheme of the three 2D time layer

central layer, then we limit the search of the maxima to the cells in this layer. In

Fig. 3.22 the response of the retina is shown in two cases, in the left plot, no time

information has been used, while in the right plot the time information has been

used to reconstruct the same simulated event. The contribution of the background

to the retina response is heavily suppressed in the second case.

The obtained values for efficiency and purity are

(ϵ1%)time = 96.7%, (3.23a)

(P1%)time = 92.5%. (3.23b)


0

1

2

3

4

5

6

7

X

4 3 2 1 0 1 2 3 4

X +

4

3

2

1

0

1

2

3

4

0

1

2

3

4

5

6

7

X

4 3 2 1 0 1 2 3 4

X +

4

3

2

1

0

1

2

3

4

Figure 3.22: Response of the retina to a track with 1% detector

occupancy. Left: no time information is used. Right: time information

is used with 100ps time resolution.

to be compared with the corresponding values obtained without using the time

information (ϵ1%)no time = 99.9% and (P1%)no time = 18.9%.

The distribution of (treco − tgen) is shown in Fig. 3.23. The obtained resolution

for the time of the track is better than the time resolution of the measured hits,

σtime = (53.4± 1.1)ps. (3.24)

In Fig. 3.24 we show the (x−reco − x−gen) and (x+reco − x+gen) distributions for

TimeX_resoEntries 5762Mean 0.5985RMS 77.6

/ ndf 2χ 40.14 / 34Constant 3.8± 185.1 Mean 0.97± 1.45 Sigma 1.13± 53.43

) [ps]gentimereco

(time500 400 300 200 100 0 100 200 300 400 5000

20

40

60

80

100

120

140

160

180

200

TimeX_resoEntries 5762Mean 0.5985RMS 77.6

/ ndf 2χ 40.14 / 34Constant 3.8± 185.1 Mean 0.97± 1.45 Sigma 1.13± 53.43

Retina Time Resolution

Figure 3.23: Time resolution for the retina tracks with 1% detector

occupancy, fitted with a Gaussian function (solid red line).


tracks reconstructed using the time information. The solid line represents the

distributions for single track events with 1% detector occupancy, compared to the

distributions for track events without noise. The obtained RMS values are



NO_NOISE

Entries 5887

Mean 0.9351

RMS 70.62

m]µ [gen

Xreco

X1000 800 600 400 200 0 200 400 600 800 10000

100

200

300

400

500

600

700NO_NOISE

Entries 5887

Mean 0.9351

RMS 70.62

0.01_NOISE

Entries 5762

Mean 2.805

RMS 160.4

NO_NOISE

Entries 5887

Mean 0.9351

RMS 70.62

0.01_NOISE

Entries 5762

Mean 2.805

RMS 160.4

0 noise

0.01 noise

residualminusXNO_NOISE

Entries 5887

Mean 0.4377

RMS 55.19

m]µ [gen+

Xreco+

X1000 800 600 400 200 0 200 400 600 800 10000

100

200

300

400

500

600

700

800

NO_NOISE

Entries 5887

Mean 0.4377

RMS 55.19

0.01_NOISE

Entries 5762

Mean 0.3125

RMS 107.1

NO_NOISE

Entries 5887

Mean 0.4377

RMS 55.19

0.01_NOISE

Entries 5762

Mean 0.3125

RMS 107.1

0 noise

0.01 noise

residualplusX

Figure 3.24: (x−, x+) resolution for retina tracks with no background

hits (red) and 1% detector occupancy (blue).

This simple example demonstrates the relevance of adding the precise time infor-

mation of the clusters to the retina that improves the performance in presence of

background hits.

This technique based on the precise time information of the hit might allow appli-

cations to online track triggers in experiments at very high luminosity with non

negligible detector occupancy, while keeping the FPGA resources at manageable

levels.

Chapter 4

Testbeam at CERN

During the period of my thesis I contributed also to the test of the prototype

silicon sensor of the upgrade of the LHCb experiment at CERN, in particular

for the Upstream Tracker [34] . The testbeam activity was held at the Proton

Synchrotron from July 25th to August 6th, 2014. The goal of the testbeam was

mainly to verify the functionalities of the reference telescope based on TimePix3

sensors [35], for the first time operated on beam, the setup of the data acquisition

of the detector under test (DUT), and the software for event reconstruction.

The readout of the DUT was performed using the ALIBAVA data acquisition

system [36], a commercial system for characterization of silicon microstrip detectors.

The front-end electronics is based on 2 Beetle chips, capable to read out 256

channels.

The tracks have been reconstructed using the Sbt software used for the simulation

presented in this thesis, that I modified in order to read the files containing the

telescope hits and the files from the ALIBAVA system, containing the DUT hits

information.

My contribution to the testbeam activity was also focused on the control of the

data quality and analysis of the data on the DUT. I will give a description of the

testbeam setup, then I will present some results obtained during the testbeam

period.

4.1 Testbeam setup

4.1.1 Reference telescope

The reference telescope is composed by 8 TimePix3 sensors, two scintillators

providing the trigger signal for the DUT, and the ALIBAVA system for the

readout of the DUT. The telescope has been developed and provided by the LHCb

71

CHAPTER 4. TESTBEAM AT CERN 72

collaboration. The sensor has 256 × 256 pixels and the physical dimension is

14× 14mm2. The pixel size is 55× 55µm2 .

The telescope is divided in two arms. Planes in the upstream arm are nominally

rotated by −9◦ about the x axis and by 9◦ about the y axis. Planes in the

downstream arm are rotated respectively by 9◦ about the x axis and by 9◦ about

the y axis, as shown in Fig. 4.1. Further corrections to the alignment of the

telescope have been provided.

The DUT is a single-sided strip silicon detector: the dimension of the active area is

1.024×1.1cm2, the strip pitch is 80µm and the thickness is 250µm. The sensor has

131 strips but only 113 are connected to the Beetle chip. The DUT is orthogonal

to the z axis and measures the position of the hits along the x coordinate. Firstly

it was placed downstream of reference telescope, then it was positioned between

the two arms and in the following we will refer to this configuration. In this case

it is possible to obtain better resolutions on the intercepts of the tracks on the

DUT.

In Fig. 4.1, we show the layout of the telescope with the DUT in the center.

Side view

Upper view

DU

TD

UT

z

z

x

y

Figure 4.1: Testbeam telescope and DUT layout scheme with the DUT

in the center.

4.1.2 Layout of the electronics logic

The readout of the telescope and the DUT is performed using two separate data

acquisition systems, then the data are matched offline according to the time infor-


mation of the hits and the timetag of the scintillators coincidence. The ALIBAVA

is designed for the characterizations of silicon sensors, using a radioactive or a

laser source and does not provide the timetag of the hits. The ALIBAVA system

can not record all the particle interactions since the internal time needed for the

readout of the sensor and to send the information to the PC is of order of ms.

During this periods the system is busy and all signals are lost.

By the way, to perform the analysis, we need a one to one correlation between

hits in the DUT and the tracks. This is possible if the number of events recorded

by the ALIBAVA is equal to the number of triggers set to the telescope. This is

achieved using a particular layout for the electronics logic, as shown in Fig. 4.2.

Scint. Trigger

Alibava

system

Busy signal

Coincidence

Unit

Inversion

of

the signal

OUT

Trigger (to telescope)

Figure 4.2: Layout of the electronics logic

The ALIBAVA has an output that provides the busy signal of the system. The

busy signal is positive when the system is not able to record, otherwise is zero.

A logic unit is used to electrically invert the signal, then the NOT OUT signal

is used as output from the unit. In such a way the signal is zero if the system

is busy and negative when the system is ready to record and it can be used to

inhibit the scintillators signal (scintillator trigger). In fact, the NOT OUT signal

is used in coincidence with scintillators signal (scintillator trigger) to produce

the trigger signal to the reference telescope. The output is split and sent to the

reference telescope, to save the trigger timetag, and to the ALIBAVA system as

trigger input.

Let’s describe the use of this logic with a simple example. If a signal comes from

the scintillators when the ALIBAVA is busy, the NOT OUT of the electrically

inverted busy signal is zero, and the coincidence unit outputs a zero signal. In

this case no trigger is sent to the telescope.

The configuration has been tested using a pulse generator to simulate the scin-

tillator trigger and a scaler, to verify the setup; the number of trigger coincides

with the number of recorded data, up to a 10MHz rate. The number of impinging

particles from the PS was of the O(KHz).


4.1.3 Reconstruction of tracks from TimePix3 telescope

The TimePix3 telescope is data driven and works in triggerless mode. Each

detector continuously records the stream of pixel hits and the data are written to

different files for the different planes. Each pixel data contains the position, the

time and the charge information of the pixel hit. The telescope can receive the

trigger from the logic described in the previous section and saves the trigger time

in a separate file.

I adapted the Sbt software in order to read the telescope data. The file contains

the time ordered hits from the sensors and the trigger times. For each trigger, we

look for all the telescope hits inside a tunable time window around the trigger

time. The width of the time windows has been set to 60ns. When all the the

telescope hits in the time window have been read, we identify the hits in the DUT

and we build an event.

At that point we look for adjacent hits for each sensor and we build the clusters.

The position of the cluster is calculated by weighting each hit with its measured

charge. This is valid either for the pixel and strip detectors.

For each combination of clusters in the first and last telescope sensor, we identify a

3D track road and we require at least 7 aligned space points, within some tolerance

(track road width). The track road width is set to 1mm and is useful to reject

inconsistent candidate tracks. Once the track candidates have been identified, a χ2

fit is applied and the information is stored in a ROOT output file for subsequent

analysis.

4.2 Data analysis

We give some examples of data analysis on the DUT for a run with 10000 trigger

counts.

The z positions for the telescope planes are shown in Tab. 4.1. The reconstruction

has been made using the alignment positions provided by the VELO group that

was responsible for the reference telescope. The VELO is the vertex locator

detector of the LHCb experiment.

Telescope and DUT Positions

Det0 Det1 Det2 Det3 DUT Det4 Det5 Det6 Det7

z[cm] 0.0 3.3 6.4 9.8 29.05 42.1 45.2 49.0 52.5

Table 4.1: Positions of the telescope and DUT planes along z.


In Fig. 4.3 is shown the distribution of the cluster size in the DUT, for cluster

associated with reconstructed tracks in the telescope. The cluster size is defined as

the number of adjacent strips that compose the cluster. The track are impinging

the DUT at 0◦ angle with respect to the nominal axis and the cluster size is small,

1 or 2. In Fig. 4.4 we show the ADC distribution of the clusters for clusters

htemp

Entries 5507Mean 1.316RMS 0.5676

ClustSize0 1 2 3 4 5 6 7 8 9 10

0

500

1000

1500

2000

2500

3000

3500

4000

htemp

Entries 5507Mean 1.316RMS 0.5676

Cluster Size

Figure 4.3: Distribution of the cluster size for the DUT.

reconstructed in the DUT sensor. The threshold for the background suppression

has been set to ADC=20. The left peak is produced by the background hits, while

the right peak corresponds to the Landau most probable value.

adcEntries 5351

Mean 54.12

RMS 25.42

ADC0 20 40 60 80 100 120 140 160 180 200

0

50

100

150

200

250

300

350

400

450

adcEntries 5351

Mean 54.12

RMS 25.42

Pulse height distribution

Figure 4.4: Distribution of ADC of the clusters. The left peak corre-

sponds to background hits or partially reconstructed clusters.

In Fig. 4.5 the charge distribution is shown for clusters in the DUT with cluster

size greater than 1. The contribution of the background is suppressed and it is

possible to identify the Landau distribution.


adcEntries 1558

Mean 69.88

RMS 28.88

ADC0 20 40 60 80 100 120 140 160 180 200

0

20

40

60

80

100

120

140

160

180

200

adcEntries 1558

Mean 69.88

RMS 28.88

Pulse height distribution

Figure 4.5: Distribution of ADC of the clusters for cluster size > 1.

We have just shown some examples of the information that can be extracted from

the reconstructed events. The analysis of the test beam data is in progress and

these are preliminary results that guarantee the good quality of the data.

4.2.1 Hit resolution of the DUT

The intrinsic resolution of the hits can be measured using the information of

the track intercepts on the DUT and the reconstructed clusters in the DUT. We

calculate the intersection of the reconstructed tracks with the DUT and evaluate

the distribution of the residual on the DUT, defined as (xDUT −xtrk), where xDUT

is the cluster position and xtrk is the intercept position.

ResidualEntries 7433

Mean 0.001198

RMS 29.07

/ ndf 2χ 19.44 / 26


Mean 0.3792± 0.5517

Sigma 0.42± 21.15

m]µ [trackXDUTX100 80 60 40 20 0 20 40 60 80 1000

50

100

150

200

250

ResidualEntries 7433

Mean 0.001198

RMS 29.07

/ ndf 2χ 19.44 / 26


Mean 0.3792± 0.5517

Sigma 0.42± 21.15

Figure 4.6: Distribution of the (xDUT − xtrk)

In Fig. 4.6, the distribution of the (xDUT − xtrk) residual is shown. It has been


fitted with a Gaussian function in the range [−35, 35]µm in order to estimate the

core component. The value of the width is

σ2residual = (21.2± 0.4)µm (4.1)

The distribution represents the sum of different effects: the uncertainty on the

extrapolated tracks (σtrack), the effect of the multiple scattering (σMS) and the

uncertainty on the reconstructed hit (σhit).

In order to evaluate the the intrinsic resolution σhit of the hit, we need to subtract

the other contributions from the obtained residual, using the equation:

σ2hit = σ2

residual − σ2track − σ2

MS . (4.2)

The multiple scattering contribution can vary according to the geometrical setup

and the thickness of the DUT. It has been evaluated with a simulation for the

proposed configuration. The estimate of the value is σMS = (3.9± 0.1)µm, while

the uncertainty value σtrack is evaluated from the covariance matrix of the χ2

track fit. If the track is parametrized as x = Ax +Bxz, we write the covariance

matrix as

V =

σ2A covAB

covAB σ2B

.

and evaluate σtrack =σ2A + 2 z covAB + z2σ2

B = (1.9±0.1)µm , for zDUT=29.05mm.

The obtained value for the intrinsic resolution is:

σhit = (20.7± 0.4)µm ,

where the error is statistical only.

The expected hit resolution for a silicon strip sensor is σhit =pitch√

12= 80√

12µm =

23.1µm. This value is consistent with the measured resolution of the hit, consid-

ering that we have clusters with 1 or 2 hits.

Further analysis is in progress within the LHCb UT group.

Conclusions

Real-time trackers and trigger systems play a fundamental role on modern experi-

ment at high-energy hadron colliders. In flavor physic experiments the interesting

signals are highly suppressed by the background and high precision measurements

are very challenging. However, the presence of a displaced vertex is a strong

signature of the production of a particle with b or c quarks, and the use of real-time

tracking system is crucial to select potentially interesting events for higher level

of processing or for subsequent analysis.

In this thesis I studied the design of the first prototype of a tracking system

based on an innovative approach for track reconstruction, inspired by the low level

mechanism of the visual recognizing in mammals, the so-called “artificial retina”

algorithm. The algorithm is highly parallelized and provides the track parameters

reconstruction interpolating the analogic response of an array of cellular units,

corresponding to different precomputed tracks, covering the entire space of track

parameters. No pattern recognition is needed since the retina algorithm provides

the identification of the tracks and determines the track parameters.

A prototype telescope composed of 8 planes of silicon detectors is currently

under construction representing the first prototype of tracking system with artificial

retina [37]. The artificial retina is implemented on commercial FPGAs (Altera

Stratix III) on the TEL62 board, in a fully pipelined design and can reconstruct

tracks up to a frequency of 1.1 MHz .

At a first stage the prototype will be tested with cosmic rays in order to demonstrate

the functionalities of the system and the working principle of the algorithm. At a

later stage it could be tested at higher rates in a beam test environment.

The total latency of the artificial retina, including the latency of the DAQ system

is below 1µs.

The artificial retina consists of a switch, a pool of cellular engines, and the

track fitter. The switch is needed to deliver the hit information from the read

out electronics to a proper set of cellular engines with expected non negligible

response. The switch has been designed as a modular network of 2-way sorters.

Each 2-way sorter receives an address through 2 inputs and forwards the signal to

78

CONCLUSIONS 79

one or both the outputs, according to the comparison of the cluster address to a

LUT. The LUTs contains the precomputed data path of each possible incoming

signal. An “ad hoc” configuration of the network has been used to design the

First Level Switch integrated in the DAQ boards and the Second Level Switch

implemented in the artificial retina.

A cellular engine contains the precomputed parameter of a track and provides the

evaluation of the weight function, an analog response (weight function) based on

the distance of the measured hits from the track stored in the cell. The weight

function is maximal in presence of a candidate track. The track fitter interpolates

the weight function of the local maximum and the neighbor cells and provides the

calculation of the track parameters.

The hardware implementation of the system is discussed in this thesis, the engine

design and the optimization of a grid of 2048 cellular units.

During my work I programmed the LUTs of the switch for routing of the

signals, developing a script with the Mathematica software.

I implemented the retina algorithm in a C++ software to simulate the tracks

of the telescope and evaluate the performance of the artificial retina. The design

of the telescope has been optimized to increase the geometrical acceptance for

cosmic rays. I also optimized the design of the artificial retina to improve the

resolution on the track parameters.

The quality of the reconstructed tracks in absence of noise hits is comparable

with the results obtained with the offline analysis. In particular, for the nominal

configuration of the prototype we obtained

(σx−)retina = (29.9± 0.3)µm ,

(σx+)retina = (17.4± 0.2)µm ,

to be compared with the results obtained from an offline analysis

(σx−)offline = (26.0± 0.3)µm ,

(σx+)offline = (17.4± 0.2)µm .

I studied the performances for different retina configurations and also the

behavior of the system in presence of background hits.

The artificial retina is affected by the presence of the background. I investigated

some possible strategies to better deal with this effect and mitigate the contribution

of the background. I simulated an artificial retina with ∼20000 cellular units

and we demonstrated that increasing the number of cells improves the quality of

the reconstructed tracks and the purity of the sample in presence of background.

Thanks to the modular design of the artificial retina this possibility can be achieved

CONCLUSIONS 80

simply increasing the FPGA resources.

A Fast Track Finder has been designed and proposed for the upgrade of the LHCb

experiment [1].

I also analyzed possible applications of the retina using detectors with precise

time information of the hit and demonstrated that by introducing a time dependent

contribution to the weight function it is possible to heavily suppress the effect of

background hits not in time with the track.

During the period of my thesis I also participated to a testbeam at CERN for

the test of the prototype detectors for the upgrade of the tracking system of the

LHCb experiment. I contributed to the setup of the data acquisition system, the

data taking, and the offline analysis using the Sbt software, providing a prompt

response of the quality of the data and preliminary results for the prototype sensor

characterization.

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