Atmospheric Calibration of the Fluorescence …personalpages.to.infn.it/~tonachin/phdthesis.pdfLHC,...

Universita degli Studi di Torino

Dipartimento di Fisica Sperimantale

Dottorato di Ricerca in Fisica Fondamentale, Applicata ed Astrofisica

XX ciclo

Aurelio Siro Tonachini

Atmospheric Calibration of the

Fluorescence Detectors with the LIDAR

System of the Pierre Auger Observatory

Coordinatore del Dottorato Supervisore

Prof. Stefano Sciuto Dott. Roberto Mussa

Anni accademici: 2004 − 2007

Settore scientifico di afferenza: FIS/04

i

Contents

Introduction 1

1 Cosmic Ray Physics. 3

1.1 Main Characteristics of Cosmic Rays . . . . . . . . . . . . . . . . . . . . . 6

1.1.1 Energy Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.1.2 The GZK Cutoff . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.1.3 Acceleration Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . 10

1.2 The Origin of Ultra High Energy Radiation . . . . . . . . . . . . . . . . . 12

1.2.1 Possible Astrophysical Sources of UHECR . . . . . . . . . . . . . . 14

1.2.2 Non-acceleration Origin of CR above 1020 eV . . . . . . . . . . . . 17

1.3 UHECR Astronomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2 The Pierre Auger Observatory 23

2.1 Extensive Air Showers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.1.1 The Electromagnetic Cascade . . . . . . . . . . . . . . . . . . . . . 25

2.1.2 Lateral Distribution Function . . . . . . . . . . . . . . . . . . . . . 26

2.1.3 Longitudinal Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.1.4 Fluorescence Light Production . . . . . . . . . . . . . . . . . . . . . 29

2.1.5 Atmospheric Attenuation by Molecules and Particulate . . . . . . . 31

2.2 Overview of the Previous Experiments . . . . . . . . . . . . . . . . . . . . 36

ii CONTENTS

2.2.1 AGASA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

2.2.2 HiRes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

2.3 The Auger Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

2.3.1 The Southern Site . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

2.3.2 Surface Array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

2.3.3 Fluorescence Detectors . . . . . . . . . . . . . . . . . . . . . . . . . 44

2.4 Atmospheric Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

2.4.1 Balloon Launches Program . . . . . . . . . . . . . . . . . . . . . . . 47

2.4.2 Weather Stations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

2.4.3 Horizontal Attenuation Monitor . . . . . . . . . . . . . . . . . . . . 48

2.4.4 FRAM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

2.4.5 Aerosol Phase Function Measurement . . . . . . . . . . . . . . . . . 49

2.4.6 IR Cloud Cameras . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

2.4.7 CLF and XLF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

2.4.8 Lidars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

3 The Elastic Lidars.

An Atmospheric Monitoring Network 55

3.1 Lidar Hardware and Data Acquisition . . . . . . . . . . . . . . . . . . . . . 56

3.1.1 Mount . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.1.2 Laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.1.3 Mirrors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

3.1.4 Photomultiplier and Digitization . . . . . . . . . . . . . . . . . . . 59

3.1.5 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

3.2 Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

3.2.1 Current Status . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

3.2.2 Typical Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

3.2.3 Shoot-the-Shower . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

CONTENTS iii

3.3 The Lidar Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

3.3.1 Starting Up and Shutting Down the Lidars . . . . . . . . . . . . . . 69

3.3.2 The Programs for Operating the Lidars . . . . . . . . . . . . . . . . 69

3.3.3 The Software for the Online Monitoring . . . . . . . . . . . . . . . 79

3.4 T3 Processing in Detail . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

3.5 Observations: June 2005 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

3.6 Conclusions and Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . 85

4 Lidar Analysis Framework 87

4.1 An Introduction to Lidar Analysis . . . . . . . . . . . . . . . . . . . . . . . 87

4.1.1 Reduction of Noise and Signal Distortion . . . . . . . . . . . . . . . 88

4.1.2 Matching Analog and Photon Counting Traces . . . . . . . . . . . . 90

4.1.3 Some Useful Equations . . . . . . . . . . . . . . . . . . . . . . . . . 90

4.2 LDA: Lidar Data Analysis Framework . . . . . . . . . . . . . . . . . . . . 92

4.2.1 Framework Classes . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

4.2.2 A Simple Example . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

4.3 Access from the Web . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

4.4 Database Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

5 Horizontal Runs Analysis 103

5.1 Determination of the Overlap Function . . . . . . . . . . . . . . . . . . . . 104

5.1.1 Understanding the Overlap shape with a Simulation . . . . . . . . . 105

5.1.2 Overlap Function from Horizontal Runs . . . . . . . . . . . . . . . 106

5.2 Aerosol Horizontal Attenuation Length . . . . . . . . . . . . . . . . . . . . 110

5.2.1 About Measurement Uncertainties . . . . . . . . . . . . . . . . . . . 110

5.2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

6 Detecting Clouds with Lidars 115

6.1 Cloud detection algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

iv CONTENTS

6.2 Atmospheric Parameters and their Use . . . . . . . . . . . . . . . . . . . . 120

6.3 Summary Plots of the Last Years . . . . . . . . . . . . . . . . . . . . . . . 122

7 Aerosol Optical Depth Determination with a Multiangle Method 125

7.1 Methods for Obtaining the Optical Depth . . . . . . . . . . . . . . . . . . 126

7.1.1 Klett’s Far-End Solution . . . . . . . . . . . . . . . . . . . . . . . . 126

7.1.2 Solution for a Two-Component Atmosphere . . . . . . . . . . . . . 129

7.1.3 Optical Depth Solution . . . . . . . . . . . . . . . . . . . . . . . . . 133

7.1.4 Multiangle Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

7.2 Analysis Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

7.2.1 Multiangle Analysis with Discrete Scans . . . . . . . . . . . . . . . 139

7.3 Results and Comparison with CLF . . . . . . . . . . . . . . . . . . . . . . 145

Main Topics for Future Work 149

A Database Tables 151

1

Introduction

Cosmic rays were discovered at the beginning of 20th century, more than ninety years ago,

and the questions about their real origin and even, at the very high energies, about their

nature are still unsolved. A new generation of experiments is going to study cosmic rays

at the highest energies detected, and nowadays the Pierre Auger Southern Observatory

plays the leading role in this field. The observatory, sited in Argentina and now near-

ing completion, was designed to adopt two different detecting techniques: extensive air

showers, generated by the interaction of high energy cosmic rays with our atmosphere,

are simultaneously observed at ground by a large array, that covers an area of about

3000 km2, and by fluorescence detectors, installed at the boundaries of the array, which

are sensible to fluorescence light emitted at the passage of these particle showers through

atmosphere.

The atmospheric medium on one side acts as a calorimeter, in which cosmic ray cas-

cades develop and reveal themselves by the emission of a weak light detectable only during

moonless nights; on the other side atmosphere represents an attenuating medium as well,

absorbing and scattering the fluorescence light, which is travelling from its source to the

detectors. Both aspects are seriously considered by the Auger Collaboration, and the

latter one is the main subject of my thesis.

My dissertation starts with an overview of cosmic ray physics, and continues with a

detailed description of the Pierre Auger Observatory, with a particular attention to all

2 CONTENTS

the atmospheric monitoring devices (see Chapters 1 and 2). The following chapters are

dedicated to my PhD activity with a system of elastic lidars.

Chapter 3, after describing all the components that make up our lidars, presents how

they are used during the normal data taking. In this field, my main effort concerned the

design and the development of a software package able to control lidars remotly, to check

constantly their operation, and to order lidars to sample the atmosphere along the paths

of the most important showers.

Chapter 4 starts talking about lidar raw signals, their features and their problems,

and how I decided to treat them in my following analyses. This chapter presents also the

framework that I designed in order to make it possible to perform any kind of analysis

starting from our lidar raw signals. The framework is conceived to be simple and light

enough to use it also for an online fast analysis, flexible enough to run over any kind of

scan or sequence of them.

Chapters 5, 6, 7 describe my analyses of lidar scans, in the order they are actually

executed. Horizontal scans revealed their importance for knowing atmospheric properties

at ground and constantly checking the alignment of the receivers. Clouds are now detected

with a new algorithm designed by myself, and results are shown in Chapter 6. Light

attenuation by atmosphere is the topic of the last chapter: there are presented different

techniques, focusing in particular on the multiangle method, whose results are shown in

comparison with another atmospheric monitoring device, the CLF.

3

Chapter 1

Cosmic Ray Physics.

Cosmic ray research started almost 100 years ago. The studies that led to the discovery

were a cross between physics, environmental and material sciences. After the discovery

of radioactivity it was observed that the air is being ionized at a relatively high rate.

The measurements showed that every second 10 to 20 ions were generated in a cubic

centimeter of air. At that time, the main question was whether this radiation was a

property of the air or a product of the natural radioactivity of the Earth. The ionization

was measured with electroscopes at different heights in towers (including the Eiffel tower)

in order to study the penetration power of this radiation, but the results were inconclusive.

The breakthrough occurred just before the First World War, when Hess in Austria and

Kohlhorster in Germany decided to make measurements from balloons.

It was Wednesday the seventh of August, 1912, when Victor Hess, 29, flew with a

black and orange balloon, named Bohmen (German for Bohemia), up to 5350 meters.

4 Cosmic Ray Physics.

Inflation was complete and the Aeroclub members disconnected hoses from hydrogen

tanks on some wagons nearby. Captain Wolfgang Hoffory, the pilot, walked around the

outside of the basket inspecting the sand-filled ballast bags hanging from its perimeter.

Shouting final orders to the ground crew he swung effortlessly aboard. He was a veteran

of many ascensions and had, in fact, piloted Dr. Hess on a number of flights during the

previous months. But none went as high as he hoped to rise today [38]. Hess measured

Figure 1.1: On the left, a drawing of the ascent of the Bohmen. On the right, measurements

made from the Bohmen show that above 4 km the ionization rose rapidly indicating that “rays

of very great penetating power are entering our atmosphere from above” [38].

the strength of the ionizing radiation with ionization chambers. A ionization chamber

consists of a gas filled enclosure between two conducting electrodes. By measuring the

rate at which the leaves collapse one can determine the strength of the ionizing radiation.

His results are shown in Figure 1.1: the increase with altitude demonstrated that the

ionization must be caused from above.

5

During the next two years Kohlhorster confirmed Hess’ results with his flights that

reached altitude of 9 km. Millikan improved the detection technology and started mea-

suring the ionization with instruments that were lowered in mountain lakes. Since the

total thickness of atmosphere corresponds to only about 10 m of water, Millikan believed

that his measurements in water will determine better the absorption length of the cosmic

radiation. Millikan first used “cosmic rays” to describe this type of radiation, and thus

created the current name of the field.

A lot of progress was made in the following decades. Cosmic ray research concen-

trated on the high energy physics properties of these particles. Most of the discoveries of

new particles before 1950 were made in measurements of cosmic ray interactions. New

experimental techniques, such as nuclear emulsion stacks and counters, made possible an

explosion of new discoveries. In 1939 Pierre Auger discovered the existence of extensive

air showers by studying coincidences in a system of 3 counters [5]. The progresses in QED

became important for the theory of electromagnetic showers, which was fully developed

by 1940. In the 1950s and 1960s the fast progress of the particle accelerators attracted

most of the high energy physicists, while cosmic ray researchers started to study higher

energies. The characteristics of hadronic interactions became much better known, and

the analysis of cosmic ray data improved significantly. Direct measurements of cosmic

rays from balloons and satellites led to a good knowledge of the chemical composition of

cosmic rays.

The rapid development of cosmic ray acceleration theories led to the birth of several

models, appeared almost simultaneously in the late 1970s, that described the cosmic

particle acceleration at astrophysical shocks. Some years later, with the advent of X-ray

and γ-ray astronomy, a new challenge started: cosmic ray physicists started looking at

the exact direction from which high energy particles arrive at Earth. The ambition for the

development of cosmic ray astronomy led to the current operation of the third generation

of telescopes.


During the last 15 years many particle physicists became very interested about the

origin and nature of the highest energy cosmic rays. LHC, the next generation accelerator,

will study particle interactions at an equivalent laboratory energy of about 4 × 1017 eV,

while cosmic rays of energy exceeding 1020 eV have been detected.

After more than ninety years from their discovery, the questions about the origin and

the nature of cosmic rays are still unsolved. The new generation of experiments will offer

the chance to find new clues to solve this difficult enigma.

1.1 Main Characteristics of Cosmic Rays

1.1.1 Energy Spectrum

The cosmic ray (CR) flux falls is a steeply falling function of energy, and ranges in

energy from 106 eV up to 1020 eV (see Figure 1.2). In this range the flux changes of

about thirty orders of magnitude, following approximately a power law of the type E−α.

The fact that a power law exists over many decades is decisive in restricting possible

acceleration mechanisms, since the source of cosmic rays must be such as to generate a

power law spectrum. The power index α has slight but important variations: the first is

at Ek ≃ 3 · 1015 eV, where it changes from ∼ 2.6 to about 3 (this zone is called the knee);

a second change happens around Esk ≃ 4 ·1017 eV, where the flux steepens and the power

index becomes α = 3.3 (the second knee); at an energy Ea ≃ 5 · 1018 eV the flux flattens

again to α ≃ 3 forming a sort of ankle. Around 1014 eV direct observations run out of

statistics; nevertheless, the showers of secondary particles created in the interaction of the

primary CR with the atmosphere are extensive enough to be detectable from ground. This

change of detection techniques complicated the comprehension of the first knee feature.

The ankle feature, instead, was first discussed in detail by the Fly’s Eye experiment.The

situation at the high end of the CR spectrum is so far inconclusive and represents the

main topic of the recent strong increase of theoretical and experimental activities in the

1.1 Main Characteristics of Cosmic Rays 7

ultra high energy cosmic ray (UHECR) physics. The present data seem also to reveal a

steepening just below 1020 eV, but past experiments detected more events than expected

from an extrapolation of the GZK “cutoff” at ∼ 1020 eV (see Chapter 2). This is perhaps

the most puzzling and hence interesting issue related to UHECR studies, because this

kind of cutoff is expected at least for extragalactic nucleon primaries, independently of

the production mechanism.

1.1.2 The GZK Cutoff

When Penzias and Wilson in 1965 discovered that the noise in their antenna was not due

to a technical problem and announced the discovery of the cosmic microwave background

(CMB) radiation, a new era of cosmology started. The existence of CMB strongly supports

the big bang theory and the related processes of nucleosynthesis.

It is now proven that the CMB has a perfect blackbody spectrum with temperature

of 2.73 K. The best estimate of the temperature is 2.725 ± 0.002 K. The microwave

background is universal and isotropic. The anisotropy of its temperature is on the 10−5

level.

Greisen, Zatsepin, and Kuzmin predicted that high energy nuclei would interact with

the CMB and lose energy. This process would cut off the cosmic ray spectrum and, even

if CR particles were accelerated to higher energy, they would not be able to surviveduring

their propagation from their source to us. This prediction is called GZK cutoff (from their

names). Let us consider, for example, a proton interacting with a photon of the CMB.

This interaction can result in production of pions,

p + γCMB → p + π0 ,

p + γCMB → n + π+ . (1.1)

In the Lab system the square of the CM energy is

s = m2p + 2Epǫ (1 − βp cos θ) , (1.2)


Figure 1.2: The cosmic ray spectrum.

where ǫ is the energy of the photon and θ the angle between the two particles. In face to

face collisions (cos θ = −1) and for the average energy of the CMB (6.34 · 10−4 eV) the

threshold energy becomes

Ep =mπ0

4ǫ(2mp + mπ0) ≃ 6.8 · 1019 eV . (1.3)

another energy loss process is the production of electron-positron pairs. This is an


electromagnetic process in which the photon generates a pair in the proton nuclear field.

The proton threshold energy is much lower, since only two electron masses have to be

added to the proton mass in the CM system. For face to face collisions the threshold is

about 4 · 1017 eV. The proton energy loss per interaction is small, about 0.001 Ep.

Nuclei heavier than protons have also another way to loose energy: their interaction

with CMB can led to photodisintegration. The nucleus absorbs the photon and forms an

excited state, which decays releasing one or two nucleons.

Figure 1.3: Energy dependence of the proton energy loss length from pion photoproduction,

pair production (marked BH), and the total energy loss length Lloss in Mpc (thick line). The

dashed line shows the proton interaction length in the CMB, λpγ , and the dotted line shows

the neutron decay length.

Propagation of UHE Protons in the Universe

In order to study the effect of CMB on the propagation of protons in the Universe, it is

convenient to find the relation between the proton mean free path λpγ in the CMB and


the proton energy Ep [51]. The mean free path (in cm) is defined as:

λ−1pγ (Ep) =

1

8E2p

∫∞

ǫthr

dǫn(ǫ)

ǫ2

∫ smax

smin

ds(s − m2

p

)σpγ(s) , (1.4)

where ǫ is the photon energy (in eV) and n(ǫ) is the photon number density in units of

cm−3 eV−1, smin is the square of the minimum center of mass energy (mp + mπ0)2, and

smax = mp + 4Epǫ, assuming that βp = 1. With the same assumption, the threshold

photon energy is given by:

ǫthr =smin − m2

p

4Ep

. (1.5)

The mean free path reaches a minimum at about 5 · 1020 eV (see Figure 1.3).

For energy above 1020 eV the photoproduction energy loss dominates, and above 8 ·1020 eV the energy loss length is almost constant at about 15 Mpc.

1.1.3 Acceleration Mechanisms

There are basically two types of acceleration mechanisms considered in connection to cos-

mic ray acceleration: direct acceleration of charged particles by an electric field; statistical

acceleration (Fermi acceleration) in a magnetized plasma. In the first case, the electric

field in question can be due, for example, to a rotating magnetic neutron star (pulsar),

or a (rotating) threaded by magnetic fields. For several reasons, the direct acceleration

mechanisms are not widely favored: a major disadvantage of this mechanism is that it is

difficult to obtain the characteristic power law trend of the CR spectrum in any natural

way. It has been pointed out, however, that a power law spectrum does not necessary

point to Fermi acceleration, but can be the result of a fractional gain in energy of a few

particles accompanied by a significantly large fractional loss in the number of remaining

particles.

The basic idea of the statistical acceleration mechanism originates from a paper by

Fermi [20] in 1949. Even though the average electric field may vanish, there can still

be a net transfer of kinetic energy of moving magnetized plasma to individual charged


particles (called “test particles”) in the medium, due to repeated collisionless scatterings

(“encounters”) of the particles either with randomly moving inhomogeneities of the tur-

bolent magnetic field or with shocks in the medium. Fermi’s original paper [20] considered

the first case, i.e., scattering with randomly moving magnetized plasma. In this case, even

if a test particle can gain or lose energy at each encounter, there is on average a net gain

of energy after many encounters. Let us consider a cloud with infinite mass and velocity

vcl, and, for simplicity, a particle entering the cloud at speed of light. Its mass could be

neglected and its energy is therefore E0 ≃ p0c. The particle scatters many times in the

magnetic turbulence end eventually comes out in a direction collinear and opposite to its

initial direction (see Figure 1.4).

Figure 1.4: A depiction of Fermi’s idea of particle acceleration by scattering in magnetized

clouds. Only the case when the particle trajectories are collinear with the cloud velocity are

shown.

The particle energy in the cloud frame is:

E∗

0 = γcl (E0 + βclp0) , (1.6)

where βcl = vcl/c and γcl = (1 − β2cl)

−1/2. The energy of the particle E1 at the time it

exits the cloud will be:

E1 = γcl (E0 + βclp∗

0) = E0 · γ2cl (1 + βcl)

2 . (1.7)


The particle gained an amount of energy ∆E. The relative gain is:

∆E

E=

E1 − E0

E0= γ2

cl (1 + βcl)2 − 1 . (1.8)

The original Fermi’s idea is nowadays called second order Fermi mechanism, because

the average fractional energy gain is in this case proportional to β2cl. Therefore, this

mechanism is not a very efficient acceleration process.

A more efficient process is instead given by encounters of particles with plane shock

fronts. The shock ahead of an expanding supernova remnant is formed because the ex-

pansion velocity of the remnant vR is much higher the sound speed of the interstellar

medium. The shock runs ahead of the expanding remnant with velocity vS, which in turn

depends on vR and the ratio of specific heats of the shocked and unshocked media. If the

interstellar medium at the shock is ionized, the shock velocity vS ≃ 4/3 vR. The strength

of the shock is characterized by the compression ratio R,

R ≃ vS/vR

vS/vR − 1. (1.9)

For a ionized medium, R = 4. In shock acceleration, the average fractional energy gain

of a particle per encounter is of first order in the relative speed between the shock front

and the isotropic-CR frame. It is thus much faster than the original Fermi acceleration

mechanism. In addition, the supernova shock velocity is much higher than the average

velocity of molecular clouds. As a result shock acceleration is orders of magnitude more

efficient, and correspondingly much faster. Recent calculations show that the maximum

energy achievable with shock acceleration is close to 5 · 105 GeV.

1.2 The Origin of Ultra High Energy Radiation

While attempting to find sources of ultra high energy cosmic rays, a natural approach is to

extend the models that explain acceleration of galactic cosmic rays and look for brighter

1.2 The Origin of Ultra High Energy Radiation 13

and larger astrophysical objects. In addition, these sources should not be too far away,

otherwise the energy losses on propagation would imply an extremely large luminosity.

Figure 1.5: Hillas plot [27] showing the size and magnetic field strength of sites that can

accelerate protons and iron nuclei to an energy of 1020 eV.

The minimum requirement for an acceleration site is the containment of the accelerated

cosmic rays inside the acceleration volume. A relation between the maximum energy

achieved by a CR and the main features of the acceleration site is given by:

Emax = γeZBR , (1.10)

where B is the magnetic field strength and R is its linear dimension. Hillas developed

this requirement including also the effect of the average velocity of the scattering centers

βsc and obtained the condition:

BR > 2E/Zβs , (1.11)


where B is in µG, R in parsec, E in PeV, and Ze is the charge of the accelerated parti-

cle [27].

In Figure 1.5 a graph that illustrates this requirement and the possible sources of

UHECR is shown. Sites that can in principle accelerate particles to an energy above

1020 eV are on the upper right-hand part of the graph. There are only four objects that

might be able to accelerate protons to that energy: high magnetic field neutron stars with

surface magnetic field exceeding 1013 G and linear dimension of 10 km, active galactic

nuclei (AGN), lobes of giant radio galaxies, and Gpc shocks in the extragalactic medium.

1.2.1 Possible Astrophysical Sources of UHECR

Following the Hillas plot, let us give a brief description of the possible sources of ultra

high energy cosmic rays.

Shocks Resulting from Structure Formation

Very large scale shocks with a dimension exceeding 10 Mpc, generated by gravitating

structures during the continuous process of clustering, could be a source candidate of

UHECR [45]. The maximum energy achievable at such shocks depends on the shock size.

Assuming an intergalactic field B0 ∼ 10−9 G, for 10 Mpc and larger shocks with average

magnetic fields of the order of 1 µG the maximum energy can exceed 1020 eV. However, if

one balances the loss rate due to pion production on the CMB with the acceleration rate

at the shock, it follows that these losses limit the maximum energy for protons to about

4.5 · 1019 eV.

Clusters of Galaxies

Average magnetic fields of 5 µG and extension up to 500 kpc have been observed in

clusters of galaxies. According to Eq. 1.11, these sites could accelerate CRs to energies


well above 1020 eV. However, the large sizes of these clusters consequent energy losses

limit the maximum energy achievable to about 1019 eV.

Radio Galaxies

Hot spots of FR (Fanaroff-Riley) II type galaxies represent another possible source of

UHE cosmic rays. FR II type galaxies are giant radio galaxies that exhibit two jets going

in opposite directions. The hot spot is the termination shock of the jet in its propagation

in the extragalactic medium. The extension of these jets and their hot spots may reach up

to 100 kpc. It has been estimated that magnetic fields at the hot spot exceed 10 µG, that

means that protons may be accelerated to about 1021 eV. The energy loss is not expected

to be significant. These elements classify radio galaxies as one of the most attractive

candidates for UHECR acceleration.

Active Galactic Nuclei

Active Galaxies are believed to be supermassive black holes surrounded by an accretion

disk. The accretion disk is composed of a hot gas made from stars that have been torn

apart by the tremendous tidal forces exerted by the black hole. Through a poorly under-

stood mechanism the black hole emits beams of high energy particles along its rotation is,

perpendicular to the disk. All active galactic nuclei (AGN) could in principle be good ac-

celerators for the ultra high energy cosmic rays. The two main regions of acceleration are

the environment of the black hole and the hot spots (in case of FR II jets). However, the

maximum energy achievable by protons during their residence time in these accelerators is

about 1017 eV. Alternatively, protons leaving the nucleus with an energy of 108 GeV can

be reaccelerated all along the jet, reach 1011 GeV at the hot spot, and then escape [26].

If so, extragalactic jets could be the main accelerators of UHECR. It is difficult anyway

that particles can reach such energies with usual Fermi processes.


Gamma Ray Bursts

The phenomenology of GRBs, bursts of 0.1 MeV-1 MeV photons lasting for a fraction

of second up to hundreds of seconds, suggests that the observable effects are due to

dissipation of the kinetic energy of a relativistically expanding wind, a fireball, whose

primal cause is not yet known. It is now proven that the GRBs are of cosmological origin

(at average redshift z = 1) and that they originate in jets. The main constraints that a

relativistic wind needs to satisfy in order to allow proton acceleration to > 1020 eV are: (1)

the magnetic field energy density should exceed a few percent of the relativistic electron

energy density; (2) the wind Lorentz factor should exceed ∼ 102. As explained in [58],

these constraints are independent of the acceleration process. The similarity of these

constraints and the ones imposed on wind parameters, based on independent physical

considerations by γ-ray observations, were the basis for association of GRB and UHECR

sources.

Colliding Galaxies

Colliding galaxies are also a suitable candidate for the acceleration of UHECR. The move-

ment of galaxies through clusters, as well as galaxy-galaxy collisions, produce large-scale

shocks easily visible at radio frequencies. A shock of dimension ∼ 30 kpc for the colliding

galaxies and a shock field of about 20 µG could provide conditions for acceleration above

1020 eV.

Quiet Black Holes

The hypothesis is that UHE protons can be accelerated at the event horizon of spin-

ning massive black holes associated with currently non-active galaxies. This suggestion

is an alternative to the presence of powerful astrophysical systems in our cosmological

neighborhood. The model requires 109M⊙ black holes within 50 Mpc from our Galaxy.


Pulsars

Pulsars are the smallest objects in the Hillas plot that could accelerate protons to the

highest energies. In this case, models do not usually use shock acceleration, rather di-

rect acceleration in the strong electrostatic potential drop induced at the surface of the

neutron star. Since in this case the UHECR would be of galactic origin, this suggestion

deletes all the problemsrelated to UHECR propagation through extragalactic distances

and consequent energy losses.

1.2.2 Non-acceleration Origin of CR above 1020 eV

The acceleration scenarios presented in the previous section are grouped in the so-called

“bottom-up” models. The acceleration to energies above 1020 eV is considered a very

unlikely process since it requires strong conditions and extremely favorable parameters.

These difficulties led to the development of “top-down” theories, which gather exotic

particle physics models. The basic idea is that the observed cosmic rays are the result of

the decay of extremely massive X particles, whose masses are as high as 1025 eV. There are

two distinctive features that characterize all top-down models: a flat injection spectrum

and a particle composition different from the bottom-up scenarios. In acceleration models

the accelerated particles injected in the intergalactic medium are protons, higher mass

charged nuclei, or neutrons created in interactions in the source medium. In top-down

models, instead, the massive X particles decay into a chain of all known elementary

particles with nucleons and mesons as final products. The more aboundant mesons decay

into neutrinos and electrons or into γ-rays depending on their charge. As a result, the

injection fluxes of γ-rays and neutrinos exceed the nucleon fluxes by a factor of about 30,

except at energies close to the X mass.

Top-down models always have a flatter injection spectrum because of properties of the

QCD fragmentation functions. The flat E−2 acceleration spectrum is the dividing line


between all shock acceleration models that have such or steeper power law spectra, and

top-down models, that have flatter ones. More recent studies of the fragmentation process

tend to modify the injection spectrum, which results anyway to be flatter that the ones

associated to acceleration scenarios.

Figure 1.6: Differential γ-ray (dashed lines) and nucleon (solid lines) spectra multiplied by

E3 from a particular top-down model and different magnet field values [51].

While neutrino spectra do not change during propagation, nucleon and γ-ray spectra

are strongly affected by interactions with the CMB. The main process for photons is the

pair production γγ −→ e+e−, whose threshold energy is m2e/ǫ/(1 − cos θ), where ǫ is

the energy of the background photon and θ is the angle between the two photons. At

higher energy other processes such as double pair production start dominating. These

interactions initiate the development of electromagnetic cascades: electrons and positrons

suffer inverse Compton (IC) scattering on the radiation field and boost these photons

to very high energies. Moreover, for such high energies the CMB is no longer the only

important background: the extragalactic radio background becomes important as well.

1.3 UHECR Astronomy 19

The injection spectra are thus heavily modified. Even though at injection the γ-rays

dominate the nucleons, at relatively modest distances from injection the nucleons could

be much more abundant, as shown in Figure 1.6 which refers to a particular top-down

model. At injection the photon spectrum dominates by about a factor 10 the nucleon

one; at energies close to those observed at Earth the nucleon spectra dominate in this

particular model.

Top-down models are generally divided in two main classes: one related to topological

defects, such as magnetic monopoles or cosmic strings, and another related to cold dark

matter. Monopoles are point-like topological defects that may have been produced in the

earliest phases of the evolution of the Universe. A monopole and an antimonopole can

form a bound state and then annihilate. Cosmic strings, instead, are one-dimensional

topological defects, whose mass can be as high as 3 · 1010M⊙ per parsec length. There are

many models which identify cosmic strings as UHECR sources: superconducting strings

that generate ultra high energy packages when their electric current reaches a critical

value; ordinary strings can emit X particles at their cusps, or during their intersection

and final stages of evolution. There are also hybrid models where monopoles are connected

with strings.

The second class of top-down scenarios studies the decay of quasi-stable massive X

particles produced in the early Universe. these particles must have a lifetime comparable

with Hubble time. They may (or may not) be a substantial part of dark matter. The

maximum energy achievable in this case is also the mass of the X particle. For further

details about top-down models, see the review by Bhattacharjee & Sigl [6].

1.3 UHECR Astronomy

The influence of galactic and extragalactic magnetic fields on charged particle propagation

is a topic which is very interesting for the possibility of doing UHECR astronomy. UHECR


astronomy depends also on chemical composition of UHE cosmic rays: if magnetic fields

can be neglected, proton primaries are expected to form small-scale clustering of UHECR

arrival directions; on the other hand, for nuclei with higher electric charge Ze, deflection

in the galactic magnetic field (GMF) alone decrease a small-clustering signal even at the

highest energies observed. The effect the galactic magnetic field on UHECR propagation

is studied for three different GMF models in [28].

Figure 1.7: Deflection maps for three different models of GMF, with a rigidity of 4·1019 V. The

deflection scale is in degrees, and the maps refer to the direction as observed at the Earth [28].

1.3 UHECR Astronomy 21

In particular, the authors observed that the GMF might be used as a natural spec-

trograph for UHECR, thus helping in source identification, restricting the GMF models,

obtaining a beater knowledge of primary chemical composition. An important consid-

eration is that GMF effects cannot be neglected even for 1020 eV protons, especially for

trajectories along the Galactic plane or crossing the GC region. However, with the present

knowledge about Galactic magnetic fields, a correction for deflections is very hard, since

magnitude as well as direction of deflections are very model-dependent.

Figure 1.7 shows how particles with a rigidity E/Ze = 4 · 1019 V are deflected by the

GMF. The Galactic magnetic field has been shown to have both regular and turbulent

components. The regular component is thought to have a spiral structure reminiscent

of the Galactic arms with one or more reversalstoward inner (and probably also outer)

Galaxy and a magnitude of order ∼ 3 µG in the vicinity of the Earth. Protons with

energy 4 · 1019 eV can be deflected in the regular GMF by ∼ 5◦. The random compo-

nent of GMF, instead, causes a spread of arrival directions of UHECR around the mean

position, thus potentially destroying important information about the actual location of

the sources. Under particular conditions on the magnetic field, it may also lead to the

“lensing” of cosmic rays. Observationally, the magnitude of the random component of

GMF is comparable to the magnitude of the regular one. However, deflections of CR in

the random field are expected to be considerably smaller, of a factor 0.03-0.3 [53].

Extragalactic magnetic fields (EGMFs) may also deviate UHE cosmic rays. So far,

evidences of the presence of EGMFs have been found only in galaxy clusters. These

are provided by the observation of extended synchrotron radio halos of galaxy clusters

and from Faraday rotation measurements (RMs) of polarized radio sources sited within

the clusters or in their background. The strength of the Intra Cluster magnetic fields

(ICMFs) are estimated to be about 0.1 − 1 µG in a region of about 1 Mpc around the

cluster centroid where the field is assumed to be uniform. Assuming that ICMFs have a

cellular structure with cell size ∼ 10 kpc the local field strength is estimated to be in the


range 1 − 10 µG.

Figure 1.8: Deflection maps for protons with arrival energy of 4 · 1019 eV (upper figure) and

1 · 1020 eV (upper figure) [18].

Simulations of the magnetic field structure in the nearby Universe have been performed

recently by [18]. These simulations are able to reproduce a number of observations, the

most relevant being RMs in galaxy clusters. From these, it is possible to estimate an upper

limit to the expected deflections of extremely high energy cosmic rays, which has been

done for protons with arrival energy of 4 · 1019 eV and 1 · 1020 eV (see Figure 1.8). Even

under pessimist conditions, the predicted deflections of UHE protons result to be almost

undetectable. This would mean that a detailed study of deflections of UHE primaries in

the Galactic magnetic field becomes particularly important.

23

Chapter 2

The Pierre Auger Observatory

The low rate of ultra high energy cosmic rays requires detectors with large collecting

areas. As anticipated in the previous chapter, in fact, a direct detection of the CR is not

possible anymore. The atmosphere is indeed a large area UHECR detector, as each of

these energetic particles, colliding with it, creates extensive air showers (EAS) of charged

particles. On average, a typical vertical shower has a footprint on the ground with a

radius of about one kilometer, while the longitudinal extent in atmosphere is around 10

kilometers. There are two main techniques for detecting EAS: the first requires an array

of widely spaced particle detectors on the ground; another possibility is the observation of

the fluorescence light emitted by the passage of charged particles through the atmosphere.

The big disadvantage of the fluorescence detection is the duty cycle, that is about 10%

since fluorescence light can be detected only during clear moonless nights.

To understand the origin of ultra high energy cosmic rays, a good knowledge of the

24 The Pierre Auger Observatory

energy, the atomic mass, and the arrival direction of each particle is needed. The indirect

measurements made necessary by the low flux of these particles makes acquiring such

information extremely difficult. Shower measurements are always incomplete. Surface

detectors measure particle densities sparsely and at one altitude only, while shower particle

densities randomly fluctuate around expected values for a CR of a certain mass and

energy. Thus even a perfect measurement would not uniquely determine the properties

of the primary particle that initiated the shower; conclusions can be given only on a

statistical point of view. Furthermore, surface detectors measurements are based on high

energy interaction models, which are used to compute the expected particle densities for

a given primary particle. Any such model is an extrapolation from known interaction

properties at lower center-of-mass energies. Consider, for instance, that the collision of

a 1019 eV primary with air has a center-of-mass energy one order of magnitude bigger

(and even more) than LHC ones. Uncertainties in the hadronic interaction model imply

uncertainties in the interpretation of the footprint of an EAS.

Fluorescence measurements, on the other hand, are much less dependent on extrapo-

lation and give a more reliable evaluation of the primary particle energy. This is obtained

directly by the amount of energy deposited by the shower in atmosphere. However, there

are also difficulties related to these measurements. The most important source of sys-

tematics is the fluorescence light yield (see Section 2.1.4), though, once well known, can

be used for all fluorescence measurements. The other source of systematics is related to

atmospheric transparency: even if its contribution is lower, it needs a continuous moni-

toring. In Section 2.4 all the instruments used to monitor the atmosphere in the Pierre

Auger Observatory are presented.

In the next section the previous recent experiments are described, and their results

are compared. In Section 2.3 a detailed description of the Pierre Auger Observatory is

found. A section apart is dedicated to the intensive atmospheric monitoring performed

in the Auger Project.

2.1 Extensive Air Showers 25

2.1 Extensive Air Showers

Before going into details on the design of more recent experiments, let us introduce the

fundamental parameters, related to the extensive air showers (EAS), which allow to mea-

sure indirectly the most energetic cosmic rays. EAS, generated by the impact of a cosmic

ray, can be studied at the surface (at different altitudes), from the space or beneath the

earth. The quantities that are usually measured are: the lateral distribution function, i.e.,

the particle density as a function of the distance from the shower axis of the charged parti-

cles in the EAS; the lateral distribution of Cherenkov light produced by the EAS particles

in the atmosphere; and the longitudinal development of the shower in the atmosphere,

that is the number of ionizing particles as a function of atmospheric depth.

The time distribution of particles arriving at the surface as well as the Cherenkov light

pulse rise time and width carry information about the longitudinal development of the

shower. Nevertheless, this method is somewhat model dependent. The only direct way of

studying the longitudinal development is to observe the atmospheric fluorescence related

to the passage of an EAS.

2.1.1 The Electromagnetic Cascade

As a first approximation, one can imagine that the EAS generated by the interaction of

a primary particle behaves as if only electromagnetic processes were important. Let us

assume, for example, that an incident photon of energy E0 travels in atmosphere for a

distance R before creating an electron-positron pair. The two secondary particles carry

half of the photon energy. After another distance R, each of them will bremsstrahlung

and produce a photon of average energy E0/4. The electromagnetic shower will grow in

this way, and at a distance nR there will be 2n secondary particles, each with an average

energy E0/2n. This process stops when the particle energy goes below the critical energy

Ec, at which the dominant energy loss is by ionization rather than bremsstrahlung. At


that point the shower have reached its maximum: the total number of secondary particles

is thus given by the primary energy E0 divided by the critical energy Ec. From the

previous considerations, it is easy to show that the number of distances R required to

achieve the shower maximum is given by the expression:

n = ln(E0/Ec)/ln2 . (2.1)

The depth of the shower maximum, Xmax, thus has a logarithmic dependence on the

energy of the incident particle. The number of particles at the shower maximum, instead,

is linearly dependent on the primary energy.

This simple result is applicable to hadronically initiated showers as well, even if the

distribution of interaction points of the hadronic shower depends on σp−air and the atomic

number of the primary particle. The proportionality between the number of particles at

the shower maximum and the primary energy still holds. The predicted number of charged

particles at the shower maximum shows a small model sensitivity - less than 3% between

QGSJET-II, QGSJET-I, and SIBYLL 2.1 [46].

2.1.2 Lateral Distribution Function

A very important observable is the spatial distribution of particles at a given detection

altitude, because ground arrays techniques use the particle density distributions of EAS

to estimate the primary energy, fitting the so-called lateral distribution function (LDF).

This distribution, observed in a plane perpendicular to the shower axis at some depth

in the atmosphere, is mainly determined by electron multiple scattering , since the elec-

tromagnetic component is by far the dominant one in real EAS. The lateral distribution

function derived for an electromagnetic cascade by Nishimura and Kamata, and later

developed by Greisen, is the well-known NKG formula, given by:

ρ(r) =Ne

r2m

Γ(4.5 − s)

2πΓ(s)Γ(4.5 − 2s)

(1 +

r

rm

)s−4.5 (r

rm

)s−2

, (2.2)


where s is the age of the electromagnetic shower, Ne is the total number of electrons in

the shower, and rm is the Moliere radius. The age parameter, s = 3/[1 + 2ln(E0/Ec)/t]

(where t =∫∞

zρatmdz/X0 and X0 is the radiation length in air), characterizes the actual

stage of the shower development, and is equal to unity at the shower maximum. For

hadronic showers, the experimental average lateral distribution is well represented by the

NKG equation with effective age of 1.25.

Muon Lateral Distribution Function

The number of muons in a shower is 50 to 100 times smaller than the number of electrons

near the shower axis, while it becomes the dominant component at distances of one

kilometer. At ground level and for large zenith angles the muonic component of an

EAS becomes dominant, reaching a maximum at 75◦, after which it decreases slightly.

Therefore, the study of muon density distributions at all zenith angles becomes very

important. the muon component is directly coupled to the hadronic component of the

EAS and reflects more directly than the electromagnetic component the properties of the

initial hadron. An NKG-type lateral distribution function, empirically derived by Greisen,

is given by:

ρµ(r) ≃ Nµ

(r

rG

)−0.75 (1 +

r

rG

)−2.5

, (2.3)

with rG = 320 m.

2.1.3 Longitudinal Profile

The longitudinal profile is defined as the development of the shower in atmosphere in

terms of number of particles as a function of atmospheric depth X. The evolution of the

EAS is usually well approximated by the Gaisser-Hillas function,

Ne(X) = Nmax

(X − X0

Xmax − X0

) (Xmax−X0)λ

· exp

[(Xmax − X0)

λ

], (2.4)


which has been deduced for a proton-induced electromagnetic shower. In this function, X0

id the point of initial interaction and λ = 70 g/cm2 is the interaction length. The dominant

component of the shower is given by the electromagnetic particles, which account for 99%

of the total number of particles: it is made up of electrons, positrons, and photons, which

carry about 85% of the total energy. The remaining 15% of energy is mainly carried by

muons and pions.

The energy carried by the electromagnetic component of an EAS is subsequently

calculated by integrating the longitudinal profile, as follows:

Eem =Ec

Xr

∫Ne(X)dX , (2.5)

where Ec ≃ 81 MeV is the critical energy, Xr = 37 g/cm2 is the radiation length of

electrons in air, and X is the atmospheric depth.

Since the Gaisser-Hillas function does not take into account any hadronic component,

in order to estimate the energy of the primary CR a correction factor must be applied.

A relevant parameter, related to the development of the shower, is clearly Xmax and

its variation in function of the primary energy and composition. The elongation rate, i.e.,

the change of mean shower maximum depth in atmosphere in energy is defined by:

Del =dXmax

d lnE. (2.6)

The trend of Xmax is studied because it depends (on average) on the chemical composition

of incident cosmic rays. Lighter cosmic rays, such as protons, penetrate deeper in atmo-

sphere, resulting in a larger Xmax; on the contrary, heavier particles such as iron, induce

EAS which develop earlier in atmosphere. Another important feature is that fluctuations

of Xmax for showers generated by heavy nuclei are smaller than for showers created by

lighter nuclei. According to Monte Carlo simulations, the mean Xmax for iron and proton

primaries differ by about 90-100 g/cm2.


Figure 2.1: Average longitudinal shower profiles for vertical proton and iron showers of

1019 eV obtained with different simulations. The red line represents the average atmospheric

depth of the Pierre Auger Observatory.

2.1.4 Fluorescence Light Production

As an EAS propagates through atmosphere, its charged particles deposit energy in air

by excitation and ionization of air molecules. Some of these molecules, during the fol-

lowing de-excitation, emit fluorescence light isotropically. The major components of the

atmosphere are N2 (78.08%), O2 (20.95%), Ar (0.93%), and each of them influences the

emission of fluorescence light in different ways. The spectrum of fluorescence light in

comprised for 82.4% between 300 and 430 nm, where several peaks of strong emission are

found (see Figure 2.2).

The main fluorescence light is produced by de-excitation of 2 electronic states of the

nitrogen molecule, namely the second positive (2P) band system and the first negative

(1N) system of N+2 .


Figure 2.2: Spectrum of absolute fluorescence yield of nitrogen in air between 300 and 430 nm

measured with a spectrometer [40].

Three processes of excitation of N2 are involved [31]:

1. Direct excitation: the energy deposited in air excites nitrogen molecules, giving as

a result an excited state (1N) of N+2 and two electrons,

N2 + e → N+∗

2 + e + e .

Fluorescence light will then be released by the excited N+2 .

2. Excitation via secondary electrons: high energy particles of an EAS ionize nitrogen

molecules producing several lower energy electrons. This electrons, in turn, are able

to excite N2 molecules to their 2P state with a resulting electron spin change,

N2 + e(↑) → N∗

2 + e(↓) .

3. Excitation via Auger electrons: some ionization processes, releasing a K-electron,

lead to the emission of a second electron (Auger effect). As in the previous case,

these are in turn able to excite N2 molecules. However, this effect has a cross section

one order of magnitude lower than the cross sections of the previous processes.


In air, optical emission of nitrogen molecules is affected by competing processes, such as

collision with other molecules.

Argon is involved in fluorescence emission as well. The reaction Ar + e → Ar∗ has the

largest cross section for Ar(3P2). This followed by Ar∗ + N2 → Ar + N∗

2. Thus, the energy

is mainly transferred from argon to nitrogen by secondary electrons rather than direct

collisions. The net contribution of argon to the production of light, anyway, is estimated

to be less than 1%. However, argon emits directly fluorescence light at a wavelength

around 310 nm. Its contribution is anyway negligible. The UV-fluorescence emission

by O2 is negligible too; oxygen mainly acts as a collisional quencher, decreasing the air

fluorescence yield [12].

Fluorescence yield is one of the biggest systematic uncertainties in the energy recon-

struction by fluorescence light detection. Different experiments, such as AIRFLY [15] and

MACFLY [16], are attempting to describe the pressure dependence of the FLY on air

pressure, in order to be able to estimate the fluorescence light emission induced by an

EAS.

2.1.5 Atmospheric Attenuation by Molecules and Particulate

Another effect that has to be taken into account while measuring the emitted fluorescence

light is the atmospheric attenuation, which affects the light traveling between its source

and the detector. Molecules and aerosols can either absorb or scatter fluorescence light,

causing a decrease of the detected light intensity. Whereas light scattering redistributes

any light energy in the atmosphere, light absorption converts the light energy to internal

energy of the absorbing molecules and eventually transfers it to the surrounding gas as

heat.


Light Scattering by Molecules (Rayleigh Scattering)

It can be shown that, ignoring depolarization effects and temperature and pressure ad-

justments, the molecular angular scattering coefficient in the direction θ with respect to

the incident light at wavelength λ is given by:

βθ,mol =π2 (m2 − 1)

2N

2N2s λ4

(1 + cos2 θ

), (2.7)

where m is the real part of the index of refraction, N is the number of molecules per

unit volume at the existing pressure and temperature, and Ns is the number density

of molecules at standard conditions (Ns = 2.547 × 1019 cm−3 at Ts = 288.15 K and

Ps = 101.325 kPa). The term (1 + cos2 θ) assumes isotropic air molecules.

Integrating Eq. 2.7 over all the solid angle, one can obtain the molecular volume

scattering coefficient as:

αmol =

∫ 2π

φ=0

∫ π

θ=0

βθ,mol sin θ dθ dφ =8π3 (m2 − 1)

2N

3N2s λ4

. (2.8)

The intensity of molecular scattering is thus sensitive to the wavelength of the incident

light: the scattering is proportional to λ−4. Therefore, it is negligible in the infrared

region of the spectrum and dominates scattering in the UV region. The real part of the

refractive index can be found from the relation:

108 (ms − 1) = 8342.13 +2406030

130 − ν2+

15997

38.9 − ν2, (2.9)

where ms is the real part of the refractive index for standard air at temperature Ts = 15◦C,

pressure Ps = 101.325 kPa, and ν = 1/λ (expressed in µm−1). The value of ms for the

spectral region of interest is thus approximately 1.00028. the effect of temperature and

pressure on the refractive index is described by:

(m − 1) = (ms − 1)

(1 + 0.00367 Ts

1 + 0.00367 T

)P

Ps

, (2.10)

where m is the real part of the refractive index at temperature T and pressure P [37].


From Eqs. 2.7 and 2.8 it follows that the molecular phase function Pθ,mol, normalized

to 1, is given by:

Pθ,mol =βθ,mol

αmol=

3

16π

(1 + cos2 θ

). (2.11)

From this, it follows that the molecular phase function is symmetric with respect to

the incident direction of the incoming light, that is, it is the same value 3/8π for the

backscattered light (θ = 180◦) and for the light scattered in forward direction (θ = 0◦).

The molecular cross section σmol is the ratio:

σmol =αmol

N=

8π3 (m2 − 1)2

3N2s λ4

, (2.12)

where N is the molecular density. This parameter represents the fraction of incoming

light that is scattered by one molecule in all directions when the molecule is illuminated.

Raman Scattering

Although the Rayleigh scattering in atmosphere represents the dominant mode of molec-

ular scattering, it is also possible for the incident photons to interact inelastically with

molecules: a small fraction of light is scattered by excitation. Scattered photons are

shifted in frequency by an amount that is unique to each molecular species. The Raman

scattering cross section depends on the polarizability of the molecules. The incident pho-

ton can excite molecules to a higher energy state. The subsequent deexcitement results in

scattered photons with less energy by an amount of vibrational transition energies. This

allows the identification of scattered light from specific molecules in the atmosphere. Wa-

ter vapor and nitrogen molecules, for instance, cause shifts that are respectively 3652 cm−1

and 2331 cm−1.

The Raman effect can be explained in a completely classical way. When two particles

with opposite charges e are separated by a distance r, the resulting electric dipole moment

is p = er. As an example, heteronuclear diatomic molecules, such as NO or HCl, must

have a permanent electric dipole because one atom is more electronegative than the other.


In contrast, homonuclear diatomic molecules, such as O2 or N2, will not have a permanent

dipole moment because of their symmetric charge distribution. Anyway, all atoms and

molecules have a nonzero polarizability even if they have no permanent dipole moment.

When an external oscillating electric field E = E0 sin (2πνextt) is applied to any

molecule, a dipole moment p is induced in it. The induced dipole will be proportional to

the field strength, p = αE, where α is called the polarizability of the molecule. For most

molecules of interest, the polarizability is assumed to vary linearly with the separation

distance between the nuclei:

α = a0

(dα

dr

)δr , (2.13)

where δr is the distance between the nuclei. For a molecule that is oscillating harmonically

the distance between the nuclei is δr = r0 sin (2πνvt), where r0 is the maximum oscillation

amplitude, and νv is the frequency at which the molecule is oscillating in absence of an

external electric field. In presence of an external electric field, instead, the induced dipole

moment p becomes:

p = α0E0 sin (2πνextt) + E0r0

(dα

dr

)sin (2πνextt) sin (2πνvt) , (2.14)

which can be rewritten as:

p = α0E0 sin (2πνextt)

+

(E0

2

)r0

(dα

dr

){cos [2π (νext − νv) t] + cos [2π (νext + νv) t]} . (2.15)

The first term of Eq. 2.15 represents the elastic (Rayleigh) scattering, which occurs at the

excitation frequency νext. The second term represents the Raman scattering, that occurs

at the Stokes frequency νext − νv and at the anti-Stokes frequency νext + νv. Thus on each

side of the laser frequency there may be emission lines that result from inelastic scattering

of photons caused by molecular vibrations in the scattering material.


Light Scattering by Particulates (Mie Scattering)

As the particulate size increases with respect to the wavelength of the incident light, the

nature of scattering changes dramatically. In this case, one may visualize the scattering

process as an interaction between waves that wrap themselves around and through the

particle itself, sometimes constructively interfering, sometimes destructively. Mie was

the first who attempted to describe this scattering in 1908 by considering the scatterers

as spherical. Figure 2.3 depicts the shape of the aerosol phase function for particles of

different sizes, considering the Mie approximation. The size is expressed in terms of a

dimensionless parameter φ = 2πρ/λ (where λ is the incident wavelength and ρ the particle

radius).

Figure 2.3: The angular distribution of scattered light intensity for three particles with

different size parameters φ. As the scattering parameter increases, the scattering in the forward

direction also increases.

It is often useful to know a simple approximation of the wavelength dependence of

atmospheric particulate scattering. The Angstrom coefficient, γ, is a parameter that


describes this approximated dependence. The coefficient is defined by the relation:

αaer =const

λγ. (2.16)

For real atmosphere, γ ranges from γ = 4 (for purely molecular scattering) to γ = 0 (for

scattering in fog and clouds). Because γ is obtained by an empirical fit to experimental

data rather than derived from scattering theory, the use of a specific value of γ is limited

to a restricted spectral range or certain atmospheric conditions.

Light Absorption by Molecules and Particulates

Depending on the wavelength of the incident light, atmospheric particulates and molecules

can also act as light-absorbing species. The main atmospheric gases that absorb light in

the ultraviolet, visual, and infrared regions of spectra are water vapor, carbon dioxide,

oxygen, and ozone. Absorbing particles are characterized by a complex index of refraction

m, which has has a real and an imaginary component: the first part is related to refraction

properties (commonly known as “index of refraction” n); the imaginary one is related to

the absorption properties of the medium.

Following Mie scattering theory, an expression can be written for the absorption coef-

ficient in a unit volume filled by absorbing species. Considering species of the same size

and type, the absorption coefficient is given by:

αabs = Nπρ2Qabs , (2.17)

where Qabs is the absorption efficiency factor, ρ is particle radius, and N is the number

of absorbing particles per unit volume.

2.2 Overview of the Previous Experiments

The first pioneering researches started more than 40 years ago with the ground array

of Volcano Ranch, where the first cosmic ray with an energy of about 1019 eV was

2.2 Overview of the Previous Experiments 37

detected [41]. This experiment was subsequently followed by the SUGAR array [60],

Haverah Park [39], and Yakutsk [19]. The more recent results came from AGASA

and HiRes (the evolution of Fly’s Eye fluorescence telescopes). The collecting areas

of giant ground arrays range from 100 km2 (AGASA) to thousands of km2 (Telescope

Array and Pierre Auger observatories). While the Fly’s Eye fluorescence detector had an

aperture of about 100 km2sr, the newer experiments adopting the fluorescence technique,

namely HiRes, Telescope Array, and the Pierre Auger Observatory, have one order of

magnitude higher time-averaged collecting areas. Table 2.1 shows a comparison of the

most important features of each experiment.

Experiment Location Technique Area

Volcano Ranch New Mexico array of scintillation counters 1 km2

SUGAR Australia array of scintillation counters 100 km2

Haverah Park UK array of Cherenkov detectors 12 km2

Yakutsk Russia array of scintillation counters,

Cherenkov detectors, underground

muon detectors

20 km2

Fly’s Eye Utah 2 fluorescence detector sites —

AGASA Japan scintillators, muon detectors 100 km2

HiRes Utah 2 fluorescence detector sites —

Table 2.1: Previous experiments with their main features.

2.2.1 AGASA

The Akeno Giant Air Shower Array (AGASA) is a large surface array sited in Japan. It

consists of 111 scintillation counters (surface detectors), deployed over an area of about

100 km2 at an average altitude of about 670 meters a.s.l., and 27 detectors under ab-

sorbers (muon detectors) [2]. The detectors, connected with a pair of optical fibers, have

nearest-neighbor separation of about 1 km. AGASA was designed to study the cosmic ray


spectrum between 1016.5 and 3 · 1018.5 eV. The detection technique adopted was based on

the measurement of the muon component in the EAS. Muons with energies around 1 GeV

are ,in fact, one of the most important observables in extensive air showers. The total

number of muons Nµ attenuates more slowly with atmospheric depth than that of elec-

trons, Ne, after their maximum development. Since Nµ is much smaller than Ne the use

of this technique requires a large surface detector area. Another drawback is that Nµ is

quite sensitive to the model of hadronic interactions and chemical composition of primary

cosmic rays. The determination of the energy of the primary particle is extracted from

the measurement of the charged-particle density at 600 m from the core, S(600), which

is weakly dependent on primary composition and the stage of shower development [25].

The relation adopted for converting S(600) to primary energy has been so far evaluated

from Monte Carlo simulations up to 1019 eV, and is:

E = 2.21 · 1017S0(600)1.03 eV , (2.18)

where S0(600) is the S(600) value per m2 for a vertical incident shower [52]. The currently

assigned energies of AGASA events have an accuracy of ±25% in event-reconstruction

resolution and ±18% in systematic errors around 1020 eV. The AGASA group claims that

there are surely events above 1020 eV, and the measured spectrum, which covers more

than five decades up to a few times 1020 eV, does not show a GZK cutoff.

2.2.2 HiRes

Hi Resolution Fly’s Eye (HiRes) is an enhancement of the first air fluorescence detector,

named Fly’s Eye, located at Dugway (Utah). As the previous detector, HiRes is formed

by two independent sites completed respectively in 1997 and 1999. These 2 detector sites,

HiRes I and HiRes II, were spaced 12.6 km apart. These sites took data independently,

allowing monocular and stereo analyses. The small phototubes, which made up each eye,

had a resolution of 1 × 1 degree on the sky ( to bee compared with 5 × 5 degrees of

2.2 Overview of the Previous Experiments 39

Fly’s Eye). The fluorescence light emitted during the transit of an EAS is kept by the

photomultiplier tubes (PMTs), resulting in a characteristic pattern of pixel triggers. Air

fluorescence detectors record the PMT signal amplitude as a function of time and this

information, after appropriate calculations and corrections, can be used to obtain the

longitudinal shower profile.

Air fluorescence needs to be carefully calibrated since the energy of a shower, while

calorimetrically retrieved, depends on the absolute gain of the detector and atmospheric

conditions. The two HiRes sites have been built on hills, above the bulk of aerosol haze

in the atmosphere. Therefore little effort was made to understand the aerosol content of

the atmosphere: a set of steering lasers was used for this scope [1]. The need to have

a more robust and redundant system of atmospheric monitoring in Auger was inherited

from the HiRes experience (see Section 2.4).

Figure 2.4: Cosmic ray spectra measured by HiRes and AGASA. In the AGASA spectrum

there is no evidence of a GZK feature, while this is present in HiRes results.

While the most recent results of the AGASA collaboration disfavor any GZK suppres-

sion for cosmic rays above 1019.6 eV, the monocular-mode energy spectra of HiRes I and

HiRes II support the existence of a GZK feature. In Figure 2.4 a direct comparison of


the spectra obtained by the two experiments is shown. Before drawing any conclusion,

one has to take into account the poor statistics available so far. The need of a bigger

observatory is therefore unavoidable to understand the highest part of the spectrum. Fur-

thermore, a big effort to dominate the systematic errors (which are quite large in both

AGASA and HiRes) is needed.

2.3 The Auger Project

The Pierre Auger Observatory (PAO), born in 1992 from an idea of Jim Cronin and Alan

Watson, was conceived to solve all the open question about ultra high energy cosmic rays.

This ambitious aim will be feasible thanks to the main unique features of this cosmic ray

observatory:

1. Full sky coverage: with two sites, one in the northern hemisphere and one in the

southern one, the PAO will be able to see any part of the sky. This will be extremely

important for the identification of CR sources.

2. Large collecting area: the detection area is about 3200 km2 for the southern site,

which is close to completion. In the first design, the northern site was exactly a

copy of the southern one, but the latest plans are conceiving it even larger.

3. Hybrid technique: in order to diminish the uncertainties, the PAO adopts 2 different

techniques to study the development of EAS, namely a surface array of Cherenkov

detectors, and a system of fluorescence detectors observing the whole collecting area.

This huge challenge is supported by a worldwide collaboration of more than 300 scientists,

working on several fields, from the technological side to purely physical aspects. The

several peculiarities of this observatory are explained in details in the following sections.

2.3 The Auger Project 41

2.3.1 The Southern Site

Auger South is sited at Malargue, in the Argentinian province of Mendoza. The area

is relatively flat, at an altitude of 1400 meters a.s.l.; as required by the fluorescence

technique, the atmosphere has a low pollution, allowing a good visibility. The light

pollution created by the town is low as well. At the same time, the area has all the

infrastructures required by the observatory.

Figure 2.5: A schematic view of the Pierre Auger Observatory.

The southern site is made of a surface array of 1600 water tanks, each one separated

from its neighbors by 1.5 kilometers. At the borders of the vast area covered by the array,

there are 4 fluorescence detector (FD) sites. Each site has a field of view of 180×30 degrees,

looking inside the surface array area.


2.3.2 Surface Array

The Surface Detector (SD) array is made up of water Cherenkov detectors. Each of these

has a cylindrical structure, with a surface of 10 m2 and a height of 1.2 m. The entire

volume is filled with purified water, and observed by 3 photomultiplier tubes of 200 mm

diameter placed on the top every 120◦. The height corresponds to 3.5 radiation lengths

in water, sufficient to absorb at least 90% of electrons and photons passing through it.

The internal surface is lined with a reflective coat, in order to reflect Cherenkov light to

the tubes. Each detector has an independent power supply, based on a solar panel and a

battery. The data communication is handled by a GSM-like transceiver, which sends and

receives data from the nearest FD site. The absolute timing is provided to each tank by

a Global Positioning System (GPS) receiver. Figure 2.6 shows an SD tank.

Figure 2.6: Picture of and SD tank.

Signals picked up by the photomultipliers are read by six 10-bit Flash ADCs running

at 40 MHz. The digitized signals are then processed by a programmable logic device

board, where the first triggers are implemented (T1-T2) [24]. The T2 trigger requires the


fulfillment of at least one of the two following conditions:

• a simple threshold trigger (TH), which requires the coincidence of 3 PMTs signals

above 3.2 Vertical Equivalent Muon (VEM). This is meant to select large and fast

signals, which could correspond either to high energy EAS very close to the tank or

to the muonic component in horizontal showers;

• a time-over-threshold trigger (ToT), which requires the coincidence of 2 PMTs whose

traces have 10 bins above 0.2 VEM within a 3 µs sliding window. This is intended

to select small signals spread in time, corresponding either to high energy distant

showers, or to low energy ones. The ToT rate per tank is about 1.5 Hz.

When a tank satisfies both conditions, only the latter is marked. Signals are then sent to

the central building (CDAS), where a third level trigger is implemented. This is an OR

operation between:

• a 3-fold condition (labeled as TOT in the CDAS), which requires the coincidence

within a time window ∆t (depending on the distance) of 3 tanks passing the ToT

condition;

• a 4-fold condition, named 3C2&4C4, which requires the coincidence, within a time

window depending on the tank distance, among 4 tanks having passed any T2

condition;

• a further 3-fold condition, named 3C1H, which requires 3 aligned tanks which pass

any T2;

• an external condition, labeled as FD, generated by a fluorescence detector, when in

operation.

As it was shown during the design study, fluctuations in the shower signal, in the

energy range of interest of the Auger Observatory, have a broad minimum near 1000 m


from the core. Accordingly, S(1000), the signal at 1000 m from the shower axis, is used

as the basic parameter from which an estimate of the primary energy can be made. The

relation between the energy in EeV and S(1000), measured in VEM, currently adopted

is:

E = 0.12 ·(S(1000)

√1 + 11.8(sec θ − 1)2

)1.05

EeV . (2.19)

Thus, in a vertical EAS produced by a primary of 10 EeV, the signal at 1000 m from the

core is 67.5 VEM [14].

2.3.3 Fluorescence Detectors

Each Fluorescence Detector is formed by 6 sub-units, called mirrors or telescopes, which

have a field of view of 30◦ × 30◦. In each telescope, a 3.5 × 3.5 m2 spherical mirror

focuses the light entering through the diaphragm on the camera, which is made of 440

hexagonal photomultiplier tubes (pixels) arranged on a spherical surface. The mirror and

the camera surface are concentric; the camera is positioned at a distance from the mirror,

which corresponds to one half of the radius of the spherical mirror itself.

The trace of an EAS is seen by the camera as a luminous spot traveling at the speed

of light. The spot aberration is reduced by the presence of the diaphragm, resulting in a

spot angular size of 0.5◦, 1/3 of the pixel field of view.

In order to increase the collecting efficiency without deteriorating the image quality,

an additional corrector ring has been installed around the diaphragm. it is segmented in

24 UV-transmitting glass plates, with an outer radius of 1.10 meters. To reduce the night

sky background, a UV filter is applied on the diaphragm. A picture of a telescope and a

scheme of the FD are shown in Figure 2.7.

Shape and duration of the signal seen by a single pixel depends on the geometry of

the EAS, while the signal intensity depends on both the shower evolution and its distance

from the detector. Vertical showers falling near the detector produce fast signals, while

larger signals are generated by inclined showers which fall far away from the detector.


Figure 2.7: The Fluorescence Detector plan (top view) on the left, and a picture of a single telescope

on the right: the corrector ring, and the camera are clearly visible.

Typically, the signal duration varies from less than 100 ns to a few microseconds.

PMT signals are collected by a set of 20 front-end boards, each one reading a column

of 22 pixels. The sampling frequency of 10 MHz allows to have a very fine sampling of

the longitudinal profile of an EAS, considering that in 100 ns a shower traverses less than

4 g/cm2 of atmosphere. Candidate shower tracks, whose signal intensities pass the first

trigger, are compared to 108 pattern configurations (grouped in 20 classes), like the masks

shown in Figure 2.8. This is called “Second Level Trigger” (SLT). Only tracks with at

least 4 pixels corresponding to one of these pattern survive.

There is a third, more sophisticated, trigger (T3) which implements a fast reconstruc-


Figure 2.8: Main pattern configurations making up the Second Level Trigger (SLT).

tion of the shower with geometrical and time fits. Pixels which give a big contribution

to the χ2 are rejected. Tracks with more than 4 pixels left are then considered as good

showers. When a shower passes also this trigger, a T3 signal is sent to CDAS and to

atmospheric monitoring devices, such as lidars.

Fluorescence Detectors need an accurate calibration in order to do a precise conversion

from ADC counts to the corresponding photon flux. Absolute and relative calibration

are thus performed. The absolute calibration is performed by placing a 2.5 m diameter

calibrated light source (nicknamed “Drum”) at the FD aperture [9], and repeated about

once a year. This end-to-end calibration treats the FD as a black box, and thus includes

all the possible effects, such as filter transmission, mirror reflectivity, PMT efficiencies

and gains, and so on. On the other side, there is a faster and simpler relative calibration,

which monitors the temporal performance of the pixels, mirrors and aperture components.

This calibration is run every night before and after the data taking.

2.4 Atmospheric Monitoring

One of the most important sources of uncertainties related to fluorescence measurements

is the estimation of the atmospheric effects on light propagation through atmosphere. The

Pierre Auger Observatory has seriously taken this issue into account, designing a complex

2.4 Atmospheric Monitoring 47

and redundant system of atmospheric monitoring devices.

2.4.1 Balloon Launches Program

Several launches of automatic radiosondes bound to helium-filled balloons have created a

monthly database containing average pressure, density, and temperature profiles. These

data allow to create average extinction coefficient profiles related to the molecular com-

ponent of the atmosphere, and a precise conversion between altitude and atmospheric

depth as well. Malargue monthly models go from 1.2 km up to 30 km a.s.l. in steps of

200 m [30]. The balloon launch trajectories are shown in Figure 2.9, while the average

molecular attenuation coefficient at ground is shown in Figure 2.10. This is used by lidar

measurements, as it will be shown in Chapters 5 and 7.

Figure 2.9: Balloon launch paths above the

PAO. The different colors mark different cam-

paigns.

MonthJan Feb Mar Apr May Jun Jul Ago Sep Oct Nov Dec

]-1

(0)

[km

mol

α

0.059

0.06

0.061

0.062

Figure 2.10: Variation of the molecular atten-

uation coefficient at ground, retrieved by bal-

loon launch measurements, as a function of time

(month by month).


2.4.2 Weather Stations

there are 5 weather stations, one for each fluorescence site, and another one near the

central laser facility (CLF, which will be described in Section 2.4.7). They monitor relative

humidity, temperature, wind speed and direction, pressure, and solar radiance at ground.

These measurements are executed automatically during the whole day and night. This

information is used both to monitor the weather situation during the FD data acquisition,

and to monitor the detector performances as a function of weather conditions.

2.4.3 Horizontal Attenuation Monitor

The Horizontal Attenuation Monitor (HAM) is a device for studying the wavelength

dependence of light scattering. The HAM system, consists of a DC light source, located

at the FD site of Coihueco, and a receiver, located at the FD site of Los Leones. The

DC light sources emit a broad spectrum of wavelengths including in the 300-400 nm

range, where Fluorescence Detectors are sensitive. The light detectors consist in UV

enhanced CCD arrays at the focus of 15 cm diameter mirrors. A filter wheel in front of

the CCD sensor allows to select different wavelengths, namely 365, 404, 436, and 542 nm.

A measurement of the horizontal attenuation length for these wavelengths is performed

every hour during FD operation [13]. The attenuation of light by aerosols as a function

of the incident wavelength is typically parametrized by the power law:

τ(λ) = τ(λ0) ·(

λ0

λ

)γ

, (2.20)

where the reference wavelength is λ0 = 355 nm, and γ is the so-called Angstrom exponent

of the dependence (γ ≈ 4 for molecular scattering).

2.4.4 FRAM

The FRAM, Ph(=F)otometric Robotic Atmospheric Monitor, is an optical telescope

equipped with a CCD camera and a photometer. By observing automatically a set of


selected stars and a calibration source, the wavelength dependence of the attenuation is

derived. Furthermore, the integral vertical aerosol optical depth can be extracted.

The narrow-field pointing CCD camera has a resolution of 752×580 pixels and a field

of view of 7′ × 5′. It is mainly used for the fine centering of a star into the field of view of

the 1′-diameter photometer. For wavelength dependence measurements, the FRAM has

a set of narrowband filters, having central wavelengths at 340, 365, 394, and 412 nm [54].

2.4.5 Aerosol Phase Function Measurement

The Aerosol Phase Function (APF) light sources, in conjunction with the Fluorescence

Detectors, are designed to measure the aerosol phase function on an hourly basis during

FD data taking. There are 2 APF monitors installed, one at Coihueco, the other one at

Los Morados.

Each APF building contains light sources which operate at different wavelengths in the

region of interest (between 300 and 400 nm), in order to study the wavelength dependence

of the aerosol phase function. The light beam is provided by a broadband Xenon flash

lamp source, which produces horizontal shots in the field of view of the nearest FD (see

Figure 2.11.

The aerosol phase function is extracted by using a modified version of the Henyey-

Greenstein function,

Pa(θ) =1 − g2

4π

[1

(1 + g2 − 2gµ)3/2+ f

3µ2 − 1

2 (1 + g2)3/2

], (2.21)

where θ is the scattering angle with respect to the beam direction, µ = cos θ, g is an asym-

metry parameter equal to the mean cosine of the scattering angle, and f is a fit parameter

used to tune the relative contribution of the forward and backward scattering [57]. An

example of the APF analysis is shown in Figure 2.12.


Figure 2.11: Schematic top view of an APF shot

acquired by the Fluorescence Detector.

Figure 2.12: Example of APF data fit, where

the aerosol contribution is visible.

2.4.6 IR Cloud Cameras

Since clouds are a major obstacle to fluorescence light propagation, it is extremely impor-

tant to have a precise knowledge of the cloud coverage during and after the data taking.

Infrared cloud cameras, installed above each FD building, take continuously IR images

of the sky, creating a full sky picture every 15 minutes, and images of the FD field of

view with a higher frequency. These steerable cameras have a field of view of 46◦ × 35◦.

Pictures are then processed in order to identify cloud contours, and associate the covered

areas to the corresponding FD pixels. The IR camera information, put together with

LIDAR cloud height measurements (Chapter 6), allows to know precisely the position of

cloud layers, and the cloud coverage of each FD pixel, at a given time.


2.4.7 CLF and XLF

The Central Laser Facility (CLF) is placed in the middle of the SD array, at distances

that range from 26 to 39 km from FDs. This instrument produces laser pulses with a

wavelength of 355 nm, a pulse width of 7 ns, and a maximum energy around 7 mJ. The

laser beam is scattered by molecules and aerosols present in atmosphere, and thus can be

detected by FDs. For every hour of FD operation, several hundred laser shots are fired in

different directions and with different energies. CLF shots are used for many purposes,

such as for testing the geometrical reconstruction and the mirror alignment of the FDs,

or checking the hybrid reconstruction by injecting a fraction of the laser light with a fiber

into a nearby SD tank.

Figure 2.13: VAOD(h) obtained by hourly summed CLF laser profiles. The plot on the left

shows in green the mean CLF profile, which is compared to a reference profile (in red). On

the right, the resulting optical depth profile as a function of altitude is shown (thick black line)

between two error curves (thin black lines).

Its main purpose is, anyway, the study of light attenuation in air. Every hour, the ver-

tical CLF shots are processed in order to extract a vertical aerosol optical depth (VAOD)


profile as a function of height. the CLF estimates the aerosol content using an iterative

procedure that does not require absolute photometric calibrations of the laser beam and

the FDs. A reference laser profile Iref(h) taken during very clean night is used, instead,

to extract a first estimation of the optical depth,

τi(h) = − ln I(h) − ln Iref(h)

1 + csc ǫ(h), (2.22)

where ǫ(h) is the elevation angle to the track point at altitude h. By deriving the optical

depth, the aerosol attenuation coefficient αi(h) is obtained. This is then used to iteratively

correct the light profile for aerosol scattering. At the end of iteration, the final α(h) is

then integrated to obtain the VAOD.

Systematic uncertainties are due to FD and laser calibration, and determining the

aerosol-free reference profile. In addition, variations of laser profiles during an hour are

taken into account to estimate the error bars. Figure 2.13 shows an example of VAOD

profile extracted by CLF measurements.

A new laser facility, called XLF, identical to the CLF, has been recently installed.

This new system is indicated in Figure 2.5.

2.4.8 Lidars

In addition to CLF and XLF, the observatory employs 4 steerable elastic lidars (one for

each FD site). The name “lidar” stands for light detection and ranging. Their main tasks

are:

1. the evaluation of the cloud coverage, the measurement of the lowest cloud layer

height, and its mean light attenuation;

2. an estimation of the horizontal aerosol attenuation;

3. the calculation of hourly based VAOD profiles;

4. the determination of additional information related to the most energetic EAS.


Since the laser facilities and the lidar are completely independent and adopt different

techniques to retrieve the optical properties of atmosphere, the two measurements are

completely uncorrelated. In addition, at the Los Leones FD site, a Raman lidar test

system is installed. This system allows not only to detect aerosols, but also to measure

the relative concentration of N2 and O2 in atmosphere. The elastic lidar system is the

main topic of my thesis, and it will be described in details in the next chapters.

55

Chapter 3

The Elastic Lidars.

An Atmospheric Monitoring Network

As we have seen in the previous chapter, the Pierre Auger Observatory has an extensive

program to monitor the atmosphere within the FD aperture and measure atmospheric

attenuation and scattering properties in the 300 to 400 nm sensitivity range of the FDs.

Within this system, a central role is played by a system of four elastic ∗ backscatter lidar

stations, one at each fluorescence site. The system is currently under construction, with

three out of four stations fully operating. At each lidar station, a high-repetition UV

laser sends short laser light pulses into the atmosphere in the direction of interest. The

backscattered signal is detected as a function of time by photomultiplier tubes at the foci

∗Here, the term elastic refers to the light scattering process. In elastic lidar applications, the return

signal is measured at the same wavelength as the original laser signal.

56The Elastic Lidars.


of parabolic mirrors. Both the laser and the mirrors are mounted on a steering frame that

allows the lidar to cover the full azimuth and elevation of the sky.

During each hour of FD data taking, the four lidars perform a routine scan of the sky

over each FD. The data provide information about the height and coverage of clouds as

well as their depth and opacity, and the local aerosol scattering and absorption properties

of the atmosphere. In addition to this routine operation, the lidar system is used for real

time monitoring of the atmospheric homogeneity between the FDs and selected cosmic

ray events. For example, if a high energy “hybrid” event is observed with the SD and

one or more FDs, the routine scan is interrupted and, within 2 to 4 minutes of the event

detection, the lidar scans the atmosphere in the vicinity of the air shower reported by

the FD. This procedure is called ”shoot-the-shower” (StS), and allows for a rejection of

events where the light profile from the track is distorted by clouds or other aerosol non-

uniformities that are not characterized well by the average hourly aerosol measurements.

Both light reflection and opacity can distort the light profile.

In this Chapter the design and standard operation procedure of the lidar system is

described. It is organized as follows. Section 3.1 describes in detail the current lidar hard-

ware. In Section 3.2, the daily operating procedure is summarized, including a description

of the routine scan and the shoot-the-shower operation. In Section 3.3, a detailed descrip-

tion of the software that controls the lidar system is given. The last Section is dedicated to

an overview of the online monitoring software, and the integration of the lidar information

in it.

3.1 Lidar Hardware and Data Acquisition

Since March 2006, three of the four lidar stations of the Pierre Auger Observatory have

been operational. The first lidar was installed at the Los Leones site in March 2002 and

started data taking soon after, mainly to test the impact on FD operations and define

3.1 Lidar Hardware and Data Acquisition 57

optimal running conditions. The lidar at the Coihueco site began operation in March

2005, and the lidar at the Los Morados site started operation in March 2006. The fourth

FD at Loma Amarilla is currently taking data; the corresponding lidar is expected to be

completed by December 2007. A schematic diagram of a lidar station is shown in Fig. 3.1.

Fig. 3.2 shows a photograph of the Los Leones lidar setup.

3.1.1 Mount

Each lidar station has at its core a fully steerable alt-azimuth frame built originally for the

EAS-TOP experiment [3]. Two DC servomotors steer the frame axes with a maximum

speed of 2◦/s. The absolute pointing direction is known to 0.2◦ accuracy.

The frame is mounted on a 20′ shipping container and is protected from the weather

by a fully retractable motorized cover during periods when the lidar is not operating.

Frame-steering and cover movements are controlled by an MC-204 motion controller from

Control Techniques, which allows the system to be operated both locally at the site and

remotely via Ethernet. This unit has a flash memory (EPROM ) in which the programs

for moving the frame and the cover are stored. These programs are witten in a modified

version of the well-known Basic, called Trio BASIC. More details about the programs can

be found in [50]. MC-204 is connected to a local Unix machine through an RS-232 serial

port.

3.1.2 Laser

Each mount is equipped with a UV laser source and mirrors for the detection of the

backscattered light. The choice of a laser for the lidar system is dictated by the following

requirements: the wavelength of the laser has to roughly match the dominant wavelength

of air fluorescence photons; the laser power should be low to minimize interference with the

FD; and the repetition rate should be high to reduce data collection time. Los Leones lidar

has been initially equipped with a Nd:YAG laser manifactured by Big Sky Technologies,



LASER

351 nm

MIRROR

=80 cm, =41 cmF j

LICEL

TR40-160

PCI-AT

DIO-32

LIDAR DAQ

FD DAQ

FD

DA

Q V

ET

O

LA

SE

R T

RIG

GE

R

TR

IGG

ER

RE

Q.

HV

SIGNAL

LA

SE

R S

YN

C-

TR.

Figure 3.1: Schematic diagram of the Pierre Auger Observatory lidar system. Each lidar

telescope uses a set of three Φ = 80 cm diameter parabolic mirrors with a focal length of

ϕ = 41 cm.

Figure 3.2: The Los Leones lidar system. Pictured are the 3 mirrors and the box which

houses the high frequency laser. The laser shoots from the box in the direction of the field of

view of the mirrors.

Inc. [7]. This laser operates with a repetition frequency up to 20 Hz, and a pulse energy up

to 7 mJ, depending on the wavelength. The emitted wavelength can be choosen among


1064, 532, 355, and 266 nm. Despite the fact that its third harmonic meets perfectly

our requirements, falling near one of the main peaks of the nitrogen fluorescence line

spectrum, the maximum pulse energy is too high and causes a lot of interference, while

at lower energies the signal-to-noise ratio is too poor to perform a good measurement of

the optical depth. Moreover, instabilities of the signal intensity have been observed while

moving the frame. For these reasons, the lidars are now operated with diode pumped

solid state lasers of type DC30-351 manufactured by Photonics Industries [47]. This laser

generates the third harmonic of Nd:YLF at 351 nm and is operated at a repetition rate

of 333Hz and a per-pulse energy of roughly 100 µJ. The laser wavelength of 351 nm is at

the center of the nitrogen fluorescence line spectrum, which extends from about 300 nm

to 400 nm, with three main spectral lines at 337 nm, 357 nm and 391 nm [29].

3.1.3 Mirrors

For the collection of the backscattered light, each lidar telescope uses a set of three

Φ = 80 cm diameter parabolic mirrors with a focal length of ϕ = 41 cm (see Fig. 3.1).

The mirrors were produced using BK7 glass coated with aluminum, and the reflective

surface is protected with SiO2 coating to ensure the necessary surface rigidness as well

as good UV transmittance. The average spot size at the focus is 3 mm FWHM. Each of

the mirrors is mechanically supported by a Kevlar frame which is in turn fixed to the

telescope frame using a three point system. This allows fine adjustment of the field of

view direction to ensure collinearity of the mirrors and the laser beam.

3.1.4 Photomultiplier and Digitization

A Hamamatsu R7400U-03 photomultiplier is used for backscatter light detection. Each

mirror has its own photomultiplier, so each lidar telescope comprises three independent

mirror/photomultiplier systems. The photomultiplier reaches a gain of 2 × 106 at the

maximum operation voltage of 1000 V. The default voltages for our photomultipliers are



770 V and 850 V for the farthest mirror, which correspond respectively to gains of 3× 104

and 7 × 104 (see Figure 3.3). To facilitate the light collection from the mirror, the whole

active 8 mm-diameter photomultiplier window is used.

Figure 3.3: Photomultiplier gain characteristics.

Background is suppressed by the means of a broadband UG-1 filter with 60% trans-

mittance at 353 nm and FWHM of 50 nm. The use of far more selective interference

filters is unfortunately not possible because the extreme speed f/0.5 (ϕ/Φ ≃ 0.5) of the

mirrors leads to a large spread of possible incident angles. As interference filters are

very sensitive to the light impact angle, light has to hit the filter almost orthogonally, or

else the transmitted wavelength can shift considerably. However, one must bear in mind

that the lidar is constructed to operate during FD data taking, which is only possible on

moonless nights. A simple absorption filter is therefore sufficient for effective background

suppression.


Due to our specific design requirements, a rather long (12m) signal cable between the

photomultipliers and digitizers has to be used. To minimize the signal dispersion as well

as RF interference, UVF-303 series military standard cables are used.

The signals are digitized using a Licel TR40-160 three-channel transient recorder. For

analog detection the signal is amplified and digitized by a 12 bit 40MHz A/D converter

with 16 k trace length (current mode). At the same time a fast 250MHz discriminator

detects single photon events above a selected threshold voltage (photon counting mode).

A combination of current and photon counting measurement is used in the subsequent

analysis to increase the dynamic range of the whole system. The Licel recorder is operated

using a PC-Linux system through a National Instruments digital input-output card (PCI-

DIO-32HS) with the Comedi interface within the ROOT framework.

3.1.5 Trigger

The lidar is connected to the FD data acquisition (FD DAQ) system by means of three

optical fibers. Whenever the lidar system wants to start a measurement, a trigger request

is issued to the FD DAQ. In response, a logic pulse of frequency 333 Hz is generated by

the FD GPS clock and transmitted to the laser, which fires a single laser pulse for every

trigger. The frequency of 333 Hz corresponds to the maximum acquisition rate of the

digitizer for the given memory depth (16 k) and sample rate (40 MHz). The lidar DAQ

is triggered by the laser synchronization signal generated at every successful laser shot.

Whenever the lidar direction of measurement comes close or into the FD field of view, a

veto signal which prevents FD data acquisition can be generated.

The lidar DAQ software is organized in several layers to allow remote or unattended

operation as well as integration into the central Auger DAQ system. A run-control pro-

gram sends the hardware settings and run parameters to the DAQ program through a

communication server. The DAQ program controls the Licel and photomultiplier settings

(tube gain via high voltage level, photon scaler discriminator level), triggering system,



telescope steering and cover operation. Through the DAQ program, the user also controls

the shooting directions and the number of laser shots per shooting angle. Current and

photon counting traces are summed for 1000 laser shots in the Licel, stored in a ROOT

file and sent to the online analysis framework for monitoring.

3.2 Operation

3.2.1 Current Status

The lidar stations were designed to be operated remotely from the observatory’s central

campus in Malargue. There, a computer is used to centralize the operation and issue all

the startup commands to the three existing lidar stations and also to monitor the quality

of the data being collected.

The remote operation of systems with this level of complexity presents a number of

challenges. In order to achieve a safe handling of the telescopes, various software routines

and hardware devices have been installed to monitor the performance and status of lidar

operations. These monitoring subsystems include programs used to collect weather related

information (mainly rain and wind speed data). The presence of ambient light and the

status of the power supply are monitored as well. In the occurrence of an external event

such as rain that could jeopardize the lidar equipment, these subsystems assume control

of the station by parking the telescope and closing the cover.

3.2.2 Typical Operation

Lidar operation starts at astronomical twilight. After the telescope cover is opened, an ini-

tialization procedure is executed to calibrate the incremental encoders used to determine

the telescope position.

A webcam located in the interior of the telescope cover is used to confirm visu-

3.2 Operation 63

ally that these tasks are executed correctly. In this way, before starting a run, the

operator has information about the status of the telescope in real time and about the

weather conditions at each site through the information being sent to the lidar web site

(http://lidar.auger.org.ar).

Figure 3.4: A typical night of lidar shooting activities at Coihueco, shown in an azimuthal

equatorial projection of the sky. Depicted are the coordinates for the lidar automatic shooting

strategy, which comprises: discrete sweeps for atmospheric parameter estimation; continuous

sweeps for cloud detection; horizontal shots toward the Central Laser Facility (CLF) for cal-

ibration; and shoot-the-shower scans to probe the tracks of important showers viewed by the

fluorescence detector (FD). The Coihueco FD field of view is shown in gray. The light blue and

light red points have been recently removed, in order to decrease the induced deadtime of the

FD.

Following initialization, the system enters an operational mode called AutoScan. In

AutoScan mode, the telescope performs a cycle of steering scripts unless otherwise in-

terrupted until the end of the night. When the laser is fired, the telescope position is

determined by the coordinates contained in these scripts. There are five main steering

strategies: four making up the AutoScan pattern and a fifth, shoot-the-shower, that from



time to time interrupts the AutoScan. These strategies are discussed below, and Fig. 3.4

shows, in an azimuthal equatorial projection of the sky, the firing pattern for a typical

night of lidar activities at Coihueco.

1. Continuous scans: In this scan, the telescope is moved between two extreme posi-

tions with a fixed angular speed while the laser is fired. The telescope sweeps the

sky along two orthogonal paths with fixed azimuthal angle, one of which is along

the central FD azimuth (90◦). Along both paths, the maximum zenith angle is 45◦.

The continuous sweeps are constrained to take 10 minutes per path from start to

finish. Along each path, the lidar performs on the order of 100 measurements with

1000 shots per measurement. The purpose of these scans is to provide useful data

for simple cloud detection techniques and to probe the atmosphere for horizontal

homogeneity. An example of the data produced by this kind of scan is shown in

Fig. 3.5.

2. Discrete scans: In this scan, the telescope is positioned at a set of particular coor-

dinates to accumulate larger statistics at a few locations. As indicated in Fig. 3.4,

these measurements are performed at 6 discrete zenith angles for 4 different azimuth

angles, and directly overhead (zenith angle 0◦). In order to reduce the amount of

deadtime of the relative fluorescence detector induced by the lidar, the 2 points

that fall in the field of view of the FD have been recently removed. To accumulate

large statistics, 12 measurements are performed at each location. Each measure-

ment consists of 1000 laser shots run at 333Hz. The combined duration of the two

discrete sweeps is about 30 minutes. The data obtained in this mode are useful to

determine the vertical distribution of aerosols in the atmosphere, and to study the

measurement uncertainties.

3. Horizontal and CLF shots: In this mode, the laser fires horizontally towards the

location of the CLF. 1000 laser shots per measurement are performed. The data

3.2 Operation 65

collected in this scanning mode are used to detect low-lying aerosols and also to

determine the horizontal attenuation between the CLF and the FD telescopes for

comparison with measurements made by other atmospheric monitoring systems.

The total duration of about 3 minutes has been lately shorten to only 8 seconds by

removing two out of three points.

4. Vertical shots: In this mode, the laser shots vertically for 5 minutes. In this way,

the data collected allow a high precision measurement of the vertical aerosol opti-

cal depth with an inversion technique, such as Klett’s or Fernald’s. methods (see

Chapter 7). This scan is present only at Los Leones, and its analysis is meant to

study systematics and make comparisons with Raman lidar results.

5. Shoot-the-Shower (StS): This rapid response mode is used to measure the atmo-

spheric attenuation in the line of sight between the FD telescopes and a detected

cosmic ray shower. This scanning mode suspends any of the previously mentioned

sweeps. It will be described in further detail in section 3.2.2.

A complete scanning cycle, excluding StS, takes about 60 minutes to complete. All

scans are therefore performed on an hourly basis. The maximum length of a lidar running

night depends on the length of astronomical twilight and varies over the course of the year

from less than five hours during the summer to almost fourteen hours during the winter.

As shown in Fig. 3.4, some shooting positions are very close to or inside the field of view

of the FD telescopes. In order to prevent the detection of a large number of spurious FD

events generated by the lidar shooting activity, buffer zones have been delimited around

the FD fields of view. Every time the laser is fired inside this buffer zone, the FD DAQ

is inhibited in order to avoid any interference. This is accomplished by sending a veto

signal from the lidar to the FD when the laser is ready to fire. The total FD deadtime

introduced by all lidar operations is less than 2 %.



-3

-2

-1

0

1

2

3

4

Distance [m]-6000 -4000 -2000 0 2000 4000 6000

Hei

gh

t [m

]

0

1000

2000

3000

4000

5000

6000

7000

Figure 3.5: Result of a typical continuous lidar scan. Shown is the intensity of backscattered

light as a function of height and horizontal distance to the lidar station at (0,0). A cloud layer

around 5 km height is clearly visible in this scan.

3.2.3 Shoot-the-Shower

A primary design requirement of the lidar system is that it probes the atmosphere along

the tracks of cosmic rays observed by the FDs. This function, called shoot-the-shower

(StS), exists to recognize unusual and highly localized atmospheric conditions in the

vicinity of individual air showers of high interest. The showers of primary interest for StS

are hybrid events, because these are used to set the energy scale of the surface detector

[42]. Stereo events, due to their high energies and typically large distances from the FDs,

are also of interest for atmospheric probing. Conditions that can affect FD observations

at different times of the year include the presence of low and fast clouds, and low-level

aerosols due to fog, dust, or land fires.

The basic operation of StS is depicted in Fig. 3.6. The axis of a cosmic ray air shower,

when projected onto the field of view of an observing air fluorescence detector, defines a

plane called the shower-detector plane, or SDP. When a lidar station shoots the shower,

3.2 Operation 67

it performs a series of laser shots within this plane, determining the atmospheric trans-

mission between the shower segment and the FD. For a given shower, up to 60 pointing

directions with 1000 laser shots per pointing are allowed, all within the FD field of view.

Lidars receiving StS requests from CDAS automatically stop the default shooting

operation (AutoScan), move to the FD field of view, initiate the StS, and then resume

the AutoScan when StS is complete. If the lidar receives an StS request while shooting

another shower, the request is pushed into a queue for later processing. In the next

paragraph, a detailed description of the software that controls the whole acquisition is

presented, with a particular attention to the code that handles the StS.

Both to minimize the FD deadtime introduced by StS and to collect StS of particular

interest, the lidar software cuts on the number of SD tanks participating in the event,

Figure 3.6: The geometry of shoot-the-shower (StS). The lidar station at a fluorescence

detector site initiates shots in the shower-detector plane within the zenith field of view of the

FDs (approximately 0 ◦ to 30 ◦ in elevation). Up to 60 pointing directions, with 1000 laser shots

per pointing, are allowed per StS.



which is a rough measure of the primary cosmic ray energy. This cut reduces the number

of requests to several per FD site per night. A further reduction in the rate is achieved

by rejecting events caused by known artificial light sources in the detector, such as other

lidar stations and the CLF. In addition, the intensity of the high-repetition laser means

that the lidar must carefully avoid incidents of cross fire into other unvetoed FDs during

StS. Therefore, angular windows in azimuth and in zenith are defined around each FD;

the lidar is forbidden from entering these windows during StS.

The operation of StS in the field of view of the photomultiplier cameras raises the issue

of possible long term effects on the phototubes themselves. Although FD data acquisition

is inhibited during StS, the photomultipliers continue to operate at high voltage during

their exposure to powerful nearby laser shots. However, since the shooting rate is one

to two shots per FD per night, the effect of the StS is not significant in comparison to

other strong and persistent light sources. These sources include the typical night sky

background with its large number of bright stars, and heavy lightning activity during the

summer months. In addition, a comparison of tube noise directly before and after StS

events shows no significant effect of the shooting activity on the tube noise.

3.3 The Lidar Software

In order to turn on and off the lidars, perform regular scans, shoot the showers, and

handle exceptional situations a set of programs have been developed. The main purpose

is to provide some easy-to-use graphical interfaces for operating the lidars ( supported by

a detailed manual) to the end user, which could be even unexpert. In case of very serious

situations, instead, the user is supposed to call an expert, which is able to control the

telescope by using low-level applications. The expert has a good knowledge of both the

hardware and the software that controls directly all the hardware devices, especially the

basic commands to remote control an MC-204.

3.3 The Lidar Software 69

These can be divided into 3 categories: in the first one, the programs for turning on

and off all the devices and checking the lidar status are presented; the second category

collects all the software for running in AutoScan mode and shooting the shower; the last

category is made up of the programs that the operator has to use to follow the run, check

the lidar life parameters, and write down what happens.

3.3.1 Starting Up and Shutting Down the Lidars

The software for turning on and off the lidars talks directly with the hardware, namely

with the MC-204 and the remote power control (RPC). At the beginning of the shift,

the operator needs to turn on several devices, open the cover, and reset the frame. A

program called Lidar Power Control (lpc), shown in Figure 3.7, has a friendly grafical

user interface, that helps the operator turning on the MC-204, the light, the webcam,

and the laser. The laser is the most delicate part of the system: for this, its starting has

been made automatic with lpc. The same program is used at the end of the shift to turn

everything off.

Once the MC-204 is on, the cover and the telescope can be moved. The operator has

now to open the cover and reset the lidar frame. The C++ programs TelescopeOpenCover

and TelescopeReset do that, talking to MC-204 by using the TLSteer class. At the end

of the shift, the telescope needs to be parked again on the horizontal, and the cover must

be closed. These tasks are done with TelescopePark and TelescopeCloseCover. All these

steps are made easy by a detailed wiki manual and intuitive icons (Figure 3.8).

3.3.2 The Programs for Operating the Lidars

A shoot the shower scheme is fairly straightforward to implement in software, so long

as several constraints are kept in mind. For example, the rate of T3 events in each

fluorescence detector fluctuates between one every few minutes on clear nights to several



Figure 3.7: The Lidar Power Control.

Figure 3.8: All the lidar run programs are reachable from a window on the Lidar PC desktop.


per minute in poor weather. Most of these events are not proper air showers, so the StS

software must be able to immediately reject the majority.

run night0 2 4 6 8 10 12 14 16 18

StS

req

uest

s

0

10

20

30

40

Morados

run night0 2 4 6 8 10 12 14 16 18

StS

req

uest

s

0

10

20

30

40

Los Leones

run night0 2 4 6 8 10 12 14 16 18

StS

req

uest

s

0

10

20

30

40

Coihueco

Figure 3.9: Mono-hybrid StS rates in May 2005, showing the count of StS requests per night

without any cuts on the number of SD tanks (blank histogram) and with a five-tank cut (hashed

histogram).

In addition, even real event rates are high enough that shooting every shower is im-

practical. While the rate of stereo events is typically less than one per night, the number

of small hybrid events (∼ 1 EeV) can approach two to three per hour (see Fig. 3.9).

If the LIDARs were to shoot every observed hybrid event, they would spend the entire



night slewing and shooting low-energy showers, to the exclusion of the autoscan and the

more interesting large events. As a result, the software must be capable of at least some

additional cuts on shower size.

In order to shoot a shower, a LIDAR station must have access to T3 events from both

the ground array and the fluorescence detectors. These data are scattered among several

locations, such as log files on the RAID disk at CDAS, or TCP/IP messages sent from

the FD PCs running in the fluorescence buildings to the PCs working in the LIDAR sites.

The data must be merged in order to form T3 triggers and start the StS. Moreover, there

are currently three running LIDAR stations, with plans to bring up one more, and their

behavior must be coordinated — both among themselves and with the FD telescopes.

To meet all of these needs, the lidar software, responsible of running in the AutoScan

mode, checking the telescope life parameters, and shooting the showers, consists of several

client and server programs that communicate over network sockets. A depiction of the

physical layout of the software is shown in Figure 3.10.

In the StS setup, a group of “remote” clients located on the FD and LIDAR PCs

receive and process T3 events from the fluorescence telescopes, while a “local” client on

the CDAS PC irene monitors the T3 event logs of the SD. These clients send T3 data to

a TCP socket server running on irene, which then moves the data on to two other “local”

clients for triggering and display. When the trigger client makes the decision to shoot the

shower, it communicates this information back through the socket server to the LIDAR

PC. The remote client on the LIDAR PC is then responsible for stopping the normal

acquisition, steering the telescope, and initiating the StS.

The lidar software components are described in specific detail below, going from left

to right in Fig. 3.10.


3.3.2.1 FD Client

Monitoring of T3 events in the fluorescence data begins on an FD PC, where a client

program evb packages T3 data and sends them through a network socket to a PC at

the nearby LIDAR station. The evb program is written in C++ and uses socket classes

provided in ROOT [11].

For each T3 event, evb sends to the LIDAR PC a T3 event number, time in GPS

seconds and nanoseconds, the number of PMTs triggered by the event, and three angles

from the online monocular reconstruction: a (θ, φ) pair called SDPTheta, SDPPhi that

defines the normal vector of the shower-detector plane (SDP); and an angle SDPAngle

that measures the azimuth of the shower impact point with respect to East.

The evb client sends out new T3 events over a unidirectional channel to the LIDAR

PC; it does not receive information from the LIDAR.

Figure 3.10: Compositional layout of the LIDAR shoot the shower software, showing active

components (squares), storage (ovals), and communications channels (circles). Channels with

arrows are unidirectional. Remote and local clients that monitor T3 events are shown on the

left; local clients that process T3 data and display other events are drawn on the right.



3.3.2.2 LIDAR PC Software

The LIDAR PCs, running version 2.4 of the Linux kernel, house a collection of socket

clients and servers that split responsibility for T3 sending and receiving, geometric trig-

gering, and telescope hardware control. The programs most important for the StS, called

lfdserver and lrcgui, are shown in Fig. 3.10, along with the resources they read from

and write to.

Socket Server: lfdserver

The primary responsibility of the lfdserver program is to open a port for T3 events sent

by the FD client evb. Like evb, lfdserver is written in C++ using the ROOT socket

classes. It performs no real analysis, simply logging the arrival T3 events from the FD

and sending the data on to the lrcgui client. Users may actively monitor the status of

the connection to the FD PC by viewing the lfdserver event log. The program writes T3

data to another socket across a unidirectional channel.

Socket Client: lrcgui

The lrcgui client is perhaps the most important program in the StS T3 processing chain,

since it handles events moving in both directions: those arriving from the FD, and those

returning from the T3 trigger client running on irene. It is also, with a second client called

olvmonit, a user interface to the telescope hardware. Olvmonit will be described better

in the next section.

Like evb and lfdserver, lrcgui is written in C++, but unlike these programs, it is built

upon the open-source C++ toolkit Qt [55]. The code base for lrcgui is common to all

of the LIDAR stations. Differences in the operation of the sites — e.g., PMT voltages,

number of laser shots, etc. — are stored in local configuration files (written in XML) read

by lrcgui at run time.

During normal LIDAR operations, users concurrently initiate the autoscan and T3


search at each LIDAR station using the interface provided by lrcgui. The telescope status

is continuously printed for the user in a message window. If the LIDAR runner enables a

T3 search, lrcgui listens for T3 events on the output port opened by lfdserver. When a

T3 event arrives, the program makes basic geometry cuts using the provided monocular

angles. For example, events whose shower-detector planes are too horizontal, or whose

Figure 3.11: Behavior of the lrcgui client during autoscan and shoot the shower modes.



trajectory would require laser shots directly into another fluorescence detector, are thrown

out. A further cut is then made on the number of FD PMTs triggered by the shower.

For a T3 event that survives the geometry and threshold cuts, lrcgui evaluates a shoot

the shower trajectory for the LIDAR and stores it in an array. The event data is then sent

through a bidirectional channel to a socket server running on irene, where it undergoes a

time coincidence test with events coming from other FDs and the SD.

If the event is not in coincidence with another T3, a “T3 Rejected” message is sent

from the time coincidence client program back to lrcgui through the bidirectional channel.

At this stage the stored StS trajectory is simply thrown out, and lrcgui waits for the next

T3 from the lfdserver.

If the event is in coincidence with another T3, a “T3 Ok” message is sent to lrcgui

indicating that a hybrid or stereo shower trajectory needs shooting. At this point, lrcgui

halts the LIDAR autoscan, moves the telescope into the FD field of view, and initiates

the StS along the previously calculated and stored trajectory. Once the StS is complete,

lrcgui re-initializes the telescope axes, starts a new autoscan, and begins listening for the

next T3 event.

Since lrcgui is directly connected to the central server, it is also responsible of sending

any error message from the lidars to alert the operator.

3.3.2.3 CDAS PC Software

The remaining programs involved in every StS are located on the Linux PC irene in

CDAS. These include the surface detector monitor, a socket server, and two socket clients

that locally process and display T3 event data.

Socket Client: Surface Detector Monitor

The event monitor for the surface detector is relatively simple compared to the chain of

clients and servers used to handle FD events. This program, SDmon, is a compact socket


client written in C++/QT. In contrast to the previously described software, which is all

“remote,” SDmon runs “locally” on the Linux PC irene in CDAS.

Trigger data from the SD are saved in real time to an event log on the RAID array

in CDAS. The RAID disks are NFS-mounted on irene, meaning that SDmon simply has

to parse the local log files for T3 events. At present, the program checks for SD events

generated by the “TOT” algorithm (as opposed to FD-triggered events), and cuts events

with less than six water tanks. Those T3s which pass the tank number and algorithm

cuts are sent to a port opened by a socket server, the LIDAR Beholder, on irene.

Socket Server: LIDAR Beholder

The LIDAR data acquisition clients running on the LIDAR PCs and on irene communicate

with each other via a socket server called the LIDAR Beholder. This C++ program is

fairly simple, built on the QSocket class available in the Qt distribution. Its main functions

are simply to open a network port and to act as a switchyard for messages between the

various socket clients. It requires little to no input from the user.

Conveniently, the LIDAR Beholder maintains a numbered list of the clients currently

connected to its open port, allowing users to observe the connection status of every StS

client. In addition, all messages written by clients to their sockets are printed in a message

window, enabling straightforward debugging of communication problems.

Socket Client: T3 Listener

After lrcgui, the T3 Listener is perhaps the second-most important program in the StS

trigger chain. It is another socket client on irene, written in C++ using Qt. All T3 events

passing cuts made by the lrcgui and SDmon clients are sent through the LIDAR Beholder

to this program, where the final trigger decision — a coincidence measurement based on

the arrival times of the T3s — occurs.

In the Listener, newly received T3 events are compared during a fifteen second window,



Figure 3.12: LIDAR Beholder, showing the connected clients list (left) and messages window

(right).

allowing coincident events to arrive from the FD or SD. During this time period, new

events are stored and displayed in a table. The program examines the time coincidence of

events by examining the GPS nanosecond field recorded in the FD and SD. A maximum

of 0.2 ms is allowed for stereo coincidence, and 0.4 ms for a hybrid coincidence. Regardless

of the state of a given event, it is removed from the comparison table at the end of fifteen

seconds.

For those events passing the coincidence cuts, the Listener sends a message “T3 Ok”

back to the LIDAR Beholder, along with the name of the appropriate LIDAR client, so

the StS can begin. As described earlier, the message “T3 Rejected” is returned to the

LIDAR clients when events are not in coincidence. All events, passed or not, are pushed

into a second storage table for all received data after fifteen seconds. The hourly rates of

received and passed events are calculated by the program and displayed for review.


3.3.3 The Software for the Online Monitoring

One of the main technical challenges is the creation of a structure for the online monitor-

ing, which has to include all the detectors belonging to the observatory. This instrument

is especially necessary for the shifters, which follow the data taking, but is also designed

in order to be accessible from a remote computer, allowing all the PAO members to fol-

low the measurements and check the observatory status. This system is installed in a

dedicated machine, Moni, and is based on MySQL Version 5, php, and Javascript. All

the information is summarized in colored plots made with GnuPlot and JPGraph. The

latest version of MySQL has been adopted because it incorporates fundamental features,

such as replication and alarm handling. While the SD array life parameters arrive directly

to the central campus, the FD sites pick up data locally, and transer them to the cen-

tral campus only afterwards. The same logic is implemented in the database replication:

the master database running on Moni receives SD data directly, while the FD data is

replicated from the slave databases present in each remote site to master one [48]. The

database connections are depicted in Figure 3.14.

Since the lidars are located in each FD site, the logic is similar to the FD one. Nev-

ertheless, in order not to increase too much the replication processes, lidar data travel to

Moni as XML files, which are then processed locally.

Figure 3.13: T3 Listener received events window.



Among the lidar run programs, 3 of them are involved in the online monitoring:

olvmonit, iloview, and the LIDAR Beholder.

LIDAR Beholder

The LIDAR Beholder, besides working as a TCP/IP server, has another important task.

On the first sheet, it shows a list of alarm lights, to alert the operator in case something

is not working properly. There are four kinds of alarms for each site: the first two tell the

user if the acquisition and the online monitoring programs (lrcgui, ldaq and olvmonit)

are running; the last two lights, instead, are directly related to the telescope operation.

These lights become red if the telescope is not aligned anymore or it is blocked. These

two errors come from the MC-204, that sends them to lrcgui as a string message. Lrcgui

in its turn sends them to the LIDAR Beholder.

Figure 3.14: MySQL database storage and replication scheme.

3.4 T3 Processing in Detail 81

Olvmonit: Data Analyser and Database Filler

Every time a new event is collected and stored, olvmonit catches it, and performs a quick

analysis. The events is shown in a window, where the end user can decide to display the

signal (or the S function) versus distance, height, or time bin. The uesr can also zoom

the part of interest. In the window three signals appear, respectively in red, green, and

blue, representing the 3 tracks collected by the 3 different mirrors. Olvmonit measures

also the background and the variance of the analog and photon counting tracks, the peak

of the signal, and the range reached. It detects als possible clouds by using the algorithm

described in Chapter 6. The analysis is performed with the LDA framework described in

Chapter 4. This information is sent first to iloview, then it is also written in XML files

and sent to moni, where everything is stored in a MySQL database.

Socket Client: iloview

A socket client running at CDAS, iloview provides an extremely useful event display for

users. It combines results from all of the LIDAR stations in one place, allowing users to

easily visualize the LIDAR shooting trajectories, observe the variation of the PMT gains

during the shift, and watch an accumulating cloud display.

3.4 T3 Processing in Detail

As discussed earlier, the first T3 processing occurs in lrcgui, where a T3 notify from

lfdserver is received. The program first calculates the difference between the T3 event

time and the current time. If this number does not fall within a window of 10 minutes,

the incoming event is instantly rejected.

The software must also reject T3 events that originate from the various artificial light

sources on site. Hence, the next step is a comparison of the T3 nanosecond time with a set

of external artificial event sources, carried out by a function called VetoExternalSources.



At present, sources of artificial T3s include the three operating LIDARs at Los Leones, Los

Morados and Coihueco, the Central Laser Facility (CLF), and the Aerosol Phase Function

Monitor (APF). Each source can be identified by its unique combination of period and

time phase, defined by its position with respect to the FD. These values are shown in

Table 3.1.

External Source Period (ms) Phase (ms)

LIDAR Los Leones 3 0

LIDAR Los Morados 3 0

LIDAR Coihueco 3 0

CLF (mode 1) 1000 500

CLF (mode 2) 1000 250

APF 1000 0

Table 3.1: List of artificial event sources and their typical time values.

If an incoming T3 event passes the artificial source veto, the program performs a check

of the event geometry, calling the function PreProcessT3. Events are rejected if they are

too inclined (more than 65◦) or the given angles are incompatible. Otherwise the StS

path is calculated and the event is passed to T3 Listener through the socket connection.

The StS path contains up to sixty points, with an angular spacing of 1.5◦ between each

point. Since the LIDAR takes data in a given direction for four seconds, the maximum

amount of time spent for a StS is four minutes.

During the StS scan, it is possible that a LIDAR could shoot towards a FD site,

causing a large amount of self generated T3s. To prevent such an artificial boost in the

T3 rate, the LIDAR software defines forbidden areas around the FD directions. If a point

of the StS path falls in one of these regions, it is simply thrown out.

The forbidden regions are defined in terms of FD coordinates (θ, φ) by entries in the

3.4 T3 Processing in Detail 83

configuration file lrcgui.t3conf. An upper limit on θ is fixed to 80◦ for each region, while

a window (φ, ∆φ) is defined for every FD seen by each LIDAR station (see the tables

below). Each station sees three sites: one on the left, one on the center, and one on the

right.

LIDAR at Los Leones

Area φ (degrees) ∆φ (degrees)

LEFT (Coihueco) 48.9 20.0

CENTER (Loma Amarilla) 10.9 10.0

RIGHT (Morados) -30.0 20.0

LIDAR at Los Morados


LEFT (Los Leones) 59.3 20.0

CENTER (Coihueco) 9.9 10.0

RIGHT (Loma Amarilla) -35.3 20.0

LIDAR at Coihueco


LEFT (Loma Amarilla) 56.1 20.0

CENTER (Morados) 9.9 10.0

RIGHT (Los Leones) -42.0 20.0

Table 3.2: Forbidden regions around the FDs directions for LIDAR stations at Los Leones

and Coihueco as defined in lrcgui.t3conf.

After an event has passed all of the basic cuts, lrcgui sends it to the T3 Listener. When

lrcgui receives a ”T3 Ok” back from the T3 Listener, it calls the function ProcessT3, which



takes the previously calculated StS coordinates and sets the shoot the shower path.

3.5 Observations: June 2005

During the June 2005 LIDAR run, we completed the SD T3 monitor and implemented the

StS for hybrid events. During several clear nights in the middle of the run, the LIDAR

stations at Los Leones and Coihueco operated with T3 enabled, and both sites observed

hybrid and stereo events. To boost the event rate during testing, the SD monitor tank cut

was lowered to four tanks. The resulting data were presented at the Paris collaboration

meeting on 9 June.

One of the more impressive hybrid events, which occurred on 5 June near Los Leones,

is shown in Figs. 3.15, 3.16, and 3.17. As shown in the figures, this air shower triggered

a large number of tubes in mirrors 1 and 2 in the Los Leones FD, as well as thirteen

water tanks in the SD. The offline SD reconstruction estimated this event’s energy at

approximately 11 EeV.

Figure 3.15: Multi mirror hybrid event at Los Leones (GPS time: 802071849) viewed in FD

event display.

It should be clear from Fig. 3.17 that the Los Leones LIDAR station was able to shoot

the shower track with reasonable accuracy.

3.6 Conclusions and Perspectives 85

Figure 3.16: Multi-mirror hybrid event at Los Leones: water tanks triggered (left) and re-

construction using the LDF (right).

3.6 Conclusions and Perspectives

In this Chapter the lidar telescopes and all the software involved in the online data taking

and monitoring have been presented. Our software has been provided with a grafical

user interface, which simplifies its learning and use. The Shoot-the-Shower chain is quite

efficient, but since the lidars caused a big amount of T3 bursts in the StS operations,

bigger and bigger veto windows have been defined. The result is that most of the StS

tracks are incomplete and useless. The increasing interest in the StS technique leads

to find a smart solution to this issue. The common idea is to centralize more the lidar

management, receiving the T3 information and controlling the FD vetoes directly from

irene. This will allow to shoot the most important showers with all the involved lidars,

stopping the acquisition of the FDs which fall along the StS paths. The FD deadtime,

increased by the vetoes, could be reduced by shooting only the stereo-hybrid events.

This plan, however, requires to rewrite most of the software, especially lrcgui and ldaq,

and to integrate some of their functions in a unique centralized program, that handles all

the lidars together.



Figure 3.17: StS trajectory of the Los Leones multi-mirror event, displayed in the iloview

client. The z-value of each point represents the maximum PMT signal measured in that par-

ticular direction. The shaded region depicts the field of view of the Los Leones FD.

87

Chapter 4

Lidar Analysis Framework

4.1 An Introduction to Lidar Analysis

As mentioned above, the Licel module records backscattered light measurements in cur-

rent mode and photon counting mode. Current mode operation uses direct, high-speed

digitization of the signal from the photodetector. Its use maximizes the near-field spatial

resolution. However, it is only good for a few-kilometer range, where the signal to noise

ratio (SNR) is sufficiently high. As the signal decreases as the square of the distance,

photon counting is required in order to obtain information about the atmosphere at large

distances. On the other hand, the photon counting saturates in the near-field due to

limitations of the Licel. At distances less than 5 km from the lidar station, the light level

causes a rate greater than 10MHz and the deadtime starts to be an issue (≥ 5 %). How-

ever, the combination of current and photon counting mode covers the full dynamic range

of the return signal from near the detector out to a distance of 20-25 km. Fig. 4.1 shows

88 Lidar Analysis Framework

an example for a signal in current and photon counting mode.

distance from lidar [km]0 2 4 6 8 10

phot

on c

ount

rat

e [M

Hz]

1

10

210

310

410

510

Lidar Response

Deadtime Corrected Photon CountMerged Analog and Photon Signal

Figure 4.1: Signals from both current and photon counting mode. The figure shows the

backscatter signal up to 10 km distance from the lidar. As long as the photon counting trace is

saturated, only the current mode trace is used. When saturation becomes negligible the signal

in current mode is fused with the one in photon counting mode.

4.1.1 Reduction of Noise and Signal Distortion

Raw traces present noises and distortions that depend on many factors, and are specific

of each Licel module. Before doing any type of analysis, one needs to remove or at least

reduce these effects, which could otherwise deteriorate the final results.

A first problem that we have identified on some channels is represented by electronic

noises on the analog traces with frequencies that are multiples of the sampling frequency.

Let us remember that a sampling bin lasts 25 ns. The most evident noise has a period of

about 50 ns: this is easily removable by grouping bins by multiples of 2.

There are correlated noises with lower frequencies, that are visible only by summing a

certain number of consecutive tracks (using, for example, shots at the same angles taken

4.1 An Introduction to Lidar Analysis 89

with discrete scans). The periods of these noises are respectively equivalent to 1024, 2048,

8192 sampling bins, and their amplitudes and phases are constant and well defined. These

low-frequency noises are present only on the old Licel channels, namely Channel 1 and 2

at Coihueco, while in the new ones the signals are cleaner.

Another problem that has been investigated is related to the undershoot of the analog

traces. This is particularly evident at Coihueco, and has direct effects on analysis results.

In fact, while it is easy to see on the last part of the trace, where the backscattered signal

is null and the background presents a light slope of some hundredths of ADC counts,

its main contribution is where the signal is high. The distortion created by undershoot

causes an overestimation of the optical depth.

distance [m]25000 30000 35000 40000 45000 50000 55000 60000

Pow

er [A

DC

]

0

0.02

0.04

0.06

0.08

0.1

0.12

Coihueco - Background PMT 1

Figure 4.2: Analog trace affected by undershoot (in grey), and the same trace after the

correction (in red). The time constant used is tRC ≃ 9 · 106 s.

All these effects are in general removable with automatic algorithms, that are included

in the analysis framework.


4.1.2 Matching Analog and Photon Counting Traces

In order to combine the current and photon counting signals, the ratio of the two signals

is calculated. A range in which this ratio is almost constant is identified, usually when

the photon count rate is under 10MHz, and signals are merged in that region. In the

first kilometers this condition is not met due to the fact that the photon counting mode

saturates for high photon rates (see Fig. 4.1). Typically, the optimal merging region is

5-10 km from the detector, where both the current and photon counting signals are valid.

The algorithm that is responsible of glueing the traces works as follows. The analog

trace PADC(r) and photon counting trace PPC(r) are extracted from the ROOT file. The

photon counting trace is considered to be valid between 0.5 MHz and 10 MHz [43]. Above

this rate, the signal begins to saturate. Since the lower threshold of 0.5 MHz is never

reached, because the sky background noise is usually higher, the traces are cut when the

signals are less than 3 times the background fluctuations. In the range so defined, a good

linearity between photon counting and analog signals is supposed. Therefore, a graph

with photon counting trace versus analog trace is drawn (see Figure 4.3), and from the

fit to the points the ratio R and the shift K between the two traces are extracted. The

analog trace is subsequently converted in photon count units by using the relation:

Pan(r) =1

R(PADC(r) − K) . (4.1)

Pan(r) and PPC(r) are then fused where their ratio R′(r) is 1 within 2%, forming a unique

trace called P (r). At shorter distances, where PPC(r) is saturated, P (r) ≡ Pan(r).

4.1.3 Some Useful Equations

The derived signal can be parameterized by the so-called lidar equation:

P (r) = P0ct02

β(r)Aeff(r)

r2e−2τ(r) = P0

ct02

β(r)A

r2e−2

R r

0α(r′)dr′ , (4.2)

4.1 An Introduction to Lidar Analysis 91

PCP0.05 0.1 0.15 0.2 0.25

AD

CP

0

0.05

0.1

0.15

0.2

0.25

Figure 4.3: A graph showing the analog trace versus the photon counting trace in the range

of linearity. A fit to this points defines the 2 quantities R and K used to fuse the traces.

where P (r) is the signal received at time t from photons scattered at a distance r

from the lidar, P0 is the transmitted laser power, t0 is the laser pulse duration, β(r) is

the backscattering coefficient, τ(r) is the optical depth, α(r) is the extinction coefficient,

and Aeff(r) is the effective receiving area of the detector. Aeff(r) is proportional to the

overlap of the telescope field of view with the laser beam (shown in Fig. 4.4). Over the

range of distances where the laser beam and mirror viewing field only partially overlap,

it is possible to experimentally determine an overlap function from horizontal scans [61],

as it is described in Chapter 5.

The far limit rf of our range is defined as the distance at which the signal to noise

ratio is below 3σP , with σP =√

P . This value typically ranges between 20 and 25 km,


depending on the shooting direction and atmospheric conditions. In the region from r0

to rf , it is convenient to express the return signal as a function of distance r in terms of

a range-corrected and normalized auxiliary function, S(r):

S(r) = lnP (r)r2

P (rn)r2n

= lnβ(r)

β(rn)− 2τ(r; rn) . (4.3)

In this equation, P (r) is the signal at distance r, and τ(r; rn) is the optical depth cal-

culated in the range [rn, r]. The normalization distance rn is a fixed distance to normalize

P , chosen such that at rn, the entire signal is in the field of view of the mirrors.

As we will see in the next chapters, all our analyses start from Equations 4.2 and 4.3.

4.2 LDA: Lidar Data Analysis Framework

The data acquired by a lidar are stored in compressed ROOT files, with a header contain-

ing a run log and the current settings, and a tree giving access to all the events saved. Each

event is formed by 2 traces for each photomultiplier, one for the analog mode, the other

for the photon counting mode. Each event is the sum of N laser shots, depending on the

Figure 4.4: A diagram showing the overlap that occurs in our lidar system, where the laser

beam is emitted parallel and outside the field of view of the telescope.

4.2 LDA: Lidar Data Analysis Framework 93

laser shooting frequency, and the acquisition time. At present, with the high-frequency

laser running at 333 Hz, each event is formed by 1000 shots.

Every month thousands of events are created by the lidars. The need to monitor their

main parameters, to analyse them with different techniques, and to use the data obtained

from a scan to optimize the analysis of other ones forces to design a flexible framework,

which contains the basic functions to treat the signals in different ways.

The Lidar Data Analysis framework (LDA), currently at version 3.4, is based on C++

and MySQL [44], a powerful database used to store the prominent information of each

scan. One of the benefits of using a database like MySQL is the fact that it is possible

to create a web interface for checking the results. This interface is now available at the

address http://www.auger.to.infn.it/lidar/ and is described in details in Section 4.3.

4.2.1 Framework Classes

The framework is formed by several classes, to handle file lists, the file structure, the

tracks, and the atmosphere models.

CLidarFileReader. This is the class for reading the lidar ROOT files. Once a file has

been loaded, with this class one has access to all the information contained in the header,

namely the number of laser shots, the active photomultipliers, the starting time of the

run, and the run type. Moreover, one can select an event, know the shooting angles, and

extract the data as a CLidarRawData object.

CLidarRawData. An object belonging to this class has two traces, one for the analog

mode, the other for the photon counting mode. These can be filled either with data

contained in a file, or data created by the user. The object contains information like the

site name, the angles, the number of laser shots and so on.


CLidarData. This class, instead, can handle one trace only, but contains several op-

erators and functions to process the data. For example, one can sum a trace to another

one; concatenate two traces; cut a piece of a trace; make the derivative of a trace. Fur-

thermore, one can calculate the maximum range achieved by the lidar, or calculate the

average, find the maximum or the minimum of a trace. The trace can be anything: a

lidar signal, an attenuation profile, an aerosol optical depth, etc.

CLidarPower: This is a child of CLidarData, and contains functions which are typically

applied to a lidar signal:

1. MakeBinAverage: it groups consecutive bins, making the average of the values

contained;

2. Smooth: it smooths data performing a moving average.

CLidarSFunction: This is again a child of CLidarData, and is used for calculating the

S function, defined as in Eq. 4.3. S can be expressed either in function of distance or in

function of height.

CAtmosphereModel: This class is studied to model the molecular and aerosol trans-

mission in function of height. The molecular extinction coefficient is calculated by using

temperature, pressure, and density tables. These tables belong either to the US Standard

Atmosphere or to the monthly profiles obtained by the balloon launches at the Pierre

Auger Observatory [8]. Another way to get it is to model the molecular extinction coef-

ficient αm as:

αm(h) =1

Lme−h/h0

m , (4.4)


where Lm is the molecular attenuation length and h0m is the molecular scale height. The

aerosol extinction length, instead, is modeled by the following equation:

αa(h) =1

La

1, h < hx

e−(h−hx)/h0a , h > hx

. (4.5)

La is the aerosol attenuation length, hx is called mixing height, and h0a is the aerosol scale

height.

CAtmosphereModel can return a simulated power return signal (as a CLidarPower

object) or directly an extinction coefficient profile in function of height (as a CLidarData

object).

CDatabase: This class is used for establishing a connection to a MySQL database, with

a structure described in Section 4.4. There are several functions to fill the tables with the

analyzed data, and to retrieve the data stored for another analysis.

There are two classes more, COverlapFunction and CClouds, that are indispensable

in the lidar analysis. The first, used to calculate the overlap function, and to correct the

data for that, is discussed in details in Chapter 5, where the horizontal scan analysis is

presented; the last one is used for the cloud detection, and it is discussed in Chapter 6.

4.2.2 A Simple Example

As a simple example of the use of this framework, let us write portions of the code that fills

the lidar database with the run properties. This program, called RunWatcher, receives in

input a file list and the directory in which the files stay.

vector <string> rootFileNames;

if (!LoadFileList(argv[1],&rootFileNames)) {


return 1;

}

vector<string>::iterator iter;

for(iter = rootFileNames.begin(); iter != rootFileNames.end(); iter++) {

// Connect to database

CDatabase db(dbName,dbUser,dbPassword);

db.UseMySQL(useMySQL);

db.Connect();

db.SetUpdateFlag(updateDB);

// More code here...

}

Inside the loop, the program opens the run and reads the main properties. This is

done only by using a CLidarFileReader object.

// Open file

CLidarFileReader lfr;

stringstream ssName;

ssName.str("");

ssName<<eventsDirectory<<*(iter);

if (!lfr.OpenFile(ssName.str().c_str()))

{

cerr << "Unable to open root file \’"<<ssName.str()<<"\’"<<endl;

continue;

}


unsigned int runEvents=lfr.GetNEvents();

string sFN=*(iter);

if (runEvents<1 || runEvents>200)

{

db.SetGoodRun(sFN,false);

badFiles++;

continue;

}

lfr.SelectEvent(0);

int pmts=lfr.GetNActivePMTs();

unsigned long int gpsBegin,gpsEnd;

gpsBegin = lfr.GetGPSTime();

lfr.SelectEvent(runEvents-1);

gpsEnd = lfr.GetGPSTime();

Once the run properties have been defined, they are put into the database with

the command db.InsertRun(site,runNumber,runType,sFN,gpsBegin,gpsEnd). After

this, there is a loop over the events, to determine the offset, the variance of the offset,

and the peak of each signal.

CLidarRawData raw; // raw data

CLidarPower current; // signal from current mode

CLidarPower photon; // signal from photon counting

double curOffset,curErrorOffset;


double phoOffset,phoEerrorOffset;

CLidarPower p;

// loop over the photomultipliers

for (int m=0; m<pmts; m++)

{

raw=lfr.GetData(m,true,success);

current.CopyFromRaw(raw,CLidarData::CURRENT);

photon.CopyFromRaw(raw,CLidarData::PHOTON);

current.CalculateAverage(curOffset, curErrorOffset, uint(current.GetNData()*0.85),

uint(current.GetNData()));

photon.CalculateAverage(phoOffset, phoEerrorOffset, uint(photon.GetNData()*0.85),

uint(photon.GetNData()));

bool goodSignal;

p = GetGluedSignal(&lfr,m,BINAVG,&goodSignal);

SubtractOffset(&p);

int max=int(p.GetValue(p.FindMaximum(20,140)));

double lastGoodDistance = p.GetLastGoodBin()*p.GetDR(0);

db.SetEventProperties(sFN, m, ev, gpsBegin, lfr.GetZenith(), lfr.GetAzimuth(), max,

curOffset, curErrorOffset, phoOffset, phoEerrorOffset, lastGoodDistance);

}

4.3 Access from the Web

As mentioned above, all the results from the different lidar analyses are stored in a MySQL

database. This information is made available to the whole Auger Collaboration through a

web application, made with Php, Javascript, and the AJAX technology. The web interface

4.3 Access from the Web 99

is easily expandable, and presents on the top a menu with 3 sections: (1) Run by Run,

(2) Cloud Coverage, (3) α at Ground.

Run by Run: In this section, the whole run list is displayed (see Fig. 4.5). The desired

month and day can be selected by using a calendar on the left side. Other menus help

the user selecting the scan types and lidar sites he wants to be shown. A GPS search

is available too. On the main frame the runs are displayed: after a colored band, which

marks the different sites, the main properties, like the scan type, cloud coverage, and the

photomultipliers status are shown.

Figure 4.5: Run by run section of the web interface.


Each row can be expanded, clicking the “+” button on the left. More details appear,

like the starting and ending GPS times, the scan duration. Images coming from different

analyses, with their main results, follow, as shown in Figure 4.6. In particular, the cloud

detection program stores S function plots for each tube, the detected cloud plot, the

cloud coverage in function of height; the horizontal scan analysis stores there the overlap

function plots and the attenuation coefficient at ground measured by the different tubes;

the multiangle reconstruction program stores a graph of the aerosol vertical optical depth

(VAOD), compared with the CLF results when these are available.

Figure 4.6: Each row, once expanded, shows more details about the run. In this case, a

continuous scan displays information about the cloud coverage.

Even more detail are available: clicking on the button “Show Details”, a window

pops up, showing the main parameters variation in function of the event number (there

are many events in each run). This is useful for studying background variations, laser

stability, and optics alignment.

Shoot-the-Shower events are put in evidence with a light pink background color.

Events with all PMTs off, or with a bad alignment, are marked with a striped gray

background.

Cloud Coverage: This section shows the cloud coverage measured by the continuous

scans in function of time. Moreover, it shows the lowest cloud height. In this way it

4.3 Access from the Web 101

is possible to distinguish good clear nights from cloudy nights, where the fluorescence

analysis becomes more difficult. The user can choose to see the coverage situation either

for an entire month, or just for one night (hour by hour). The left panel allows also to

search a particular GPS time. In this case, the selected UTC hour is shown on the top,

and the corresponding night is plotted. Figure 4.7 shows an example of this page.

Figure 4.7: Cloud coverage section of the web interface.

α at Ground: In this section, daily or monthly plots of the total extinction coefficient

at ground are shown. As in the previous section, it is possible to select the desired month,

or even a single day. Again, on the left side, there is a GPS search form.

The daily plots show the results from the different lidar channels (respectively in red,

green, and blue), while a horizontal pink line show the molecular contribution αmol(0) at

ground. In the monthly plots, instead, the minimum and the maximum values are shown

for each night, respectively with a N and a H symbol (see Figure 4.8).


4.4 Database Structure

The MySQL database that hosts the run properties and the analysis results is formed by

several tables. LidarRunTab and LidarEventTab contain basic information of the scan

properties, while StSTab contain the data in the run log of the Shoot-the-Shower runs.

WeatherTab, HorizontalTab, and LayerTab are filled by the analyses of the horizontal,

continuous and discrete scans. Two tables are dedicated to the study of the uncertainties,

namely CurrentErrorTab for the analog tracks and PhotonErrorTab for the photon count-

ing tracks. The overlap functions, found by analysing horizontal events, are contained in

the OverlapTab. A description of the table fields is reported in Appendix A.

Figure 4.8: α at ground section of the web interface.

103

Chapter 5

Horizontal Runs Analysis

Every hour a horizontal run is performed. This consists in 3 events of 1000 shots in the

field of view of the Flourescence Detector. During this run, the lidar points towards the

CLF station. This means in terms of Zenith and Azimuth coordinates that Los Leones

lidar shoots at (-90,5), Coihueco lidar at (-90,-5), and Los Morados lidar at (-90,30).

The backscattered signal, collected by the mirrors and recorded by the Licel unit, can

be parameterized by the well-known lidar equation presented in Chapter 4 (see Eq. 4.2).

Let us rewrite it as:

P (r) = P0ct02

β(r)G(r)A0

r2e−2τ(r) = P0

ct02

β(r)G(r)

r2e−2

R r

0 α(r′)dr′ , (5.1)

where G(r) = Aeff(r)/A0 is the overlap function (also known as geometrical form factor),

and Aeff(r) is proportional to the overlap of the telescope field of view with the laser

beam (shown in Fig. 4.4). It is convenient for the horizontal scan analysis to express the

return signal as a function of range r in terms of the range-corrected and normalized

104 Horizontal Runs Analysis

auxiliary function, S(r), already presented in Chapter 4:

S(r) = lnP (r)r2

P (rn)r2n

= lnβ(r)

β(rn)− 2

∫ r

r0

α(r′)dr′ . (5.2)

Here the normalization distance rn, chosen such that the entire signal is in the field of

view of the mirrors (G(r) ≃ 1), is fixed to 4.5 km. Only in case the range is very low,

this distance could be changed to about 3 km, taking into account the risk of having an

incomplete signal. If we hypothesize the atmosphere to be horizontally homogeneous, we

expect the terms α and β of Eq. 5.2 to be constant at a given height. Therefore, for

horizontal shots the Eq. 5.2 becomes:

S(r) = −2αground(r − r0) . (5.3)

αground is the sum of the molecular and the aerosol extinction coefficients at ground. This

means that it is obviously measured at the level of each site: 1400 m a.s.l. at Los Leones

and Los Morados; 1700 m a.s.l. at Coihueco. The properties of the molecular atmosphere

is again extracted from the temperature, pressure, and density profiles database, used

also for the other analyses. In this way, the aerosol contribution can be extracted from

the measurement of αground.

5.1 Determination of the Overlap Function

In the range close to the lidar, where the laser beam does not intersect the field of view of

the receiving optics, no signal is obtained, so that here G(r) = 0. In the areas of complete

overlap, instead, G(r) is, generally, normalized to 1. Therefore, with the increase of r, the

overlap function ranges from 0 to unity. Let us call rg the distance where G(r) becomes

1 (with a tolerance of 5%). rg is not known a priori, because the shape of the overlap

function can change if the receivers are not perfectly aligned with the laser. Slight changes

of the overlap function can also occur while moving the lidar frame.

5.1 Determination of the Overlap Function 105

5.1.1 Understanding the Overlap shape with a Simulation

The misalignment of receivers with respect to the laser source directly influence the overlap

function shape. The expected overlap curve can be obtained with a raytracing simulation.

In our simulation program∗ one can modify the orientation of the receiver along an ideal

line that connects the receiver to the mirror center, as depicted in Figure 5.1, or along an

orthogonal direction. It is possible to put the PMT out of focus as well. The program

takes into account all the mechanical parts of the frame, including the PMT holder, that

makes a shadow on the receiver. This explains why G(r) never reaches unity. Let us rotate

the mirror from δθ = −5 (convergent strabismus) to δθ = +5 (divergent strabismus). The

result is shown in Figure 5.2.

Figure 5.1: Orientation of the receiver with re-

spect to the line that connects the laser source to

the mirror. The receiver in red has a convergent

strabismus, that corresponds to negative values

of δθ. The strabismus of the receiver in green is

divergent (δθ > 0).

Distance [m]0 200 400 600 800 1000 1200 1400 1600 1800 2000

G

0

0.2

0.4

0.6

0.8

1

° = -5θδ ° = -4θδ ° = -3θδ ° = -2θδ ° = -1θδ ° = 0θδ ° = 1θδ ° = 2θδ ° = 3θδ ° = 4θδ ° = 5θδ

Figure 5.2: The resulting overlap functions

are shown, adopting the same color and angular

conventions. The thick black line represents a

well aligned mirror. The distance between the

laser and the receiver used in this simulation is

120 cm.

The more the receiver has a convergent strabismus, the more its field of view intersects

the laser beam nearby. Going farther in detection range, part of the laser beam falls out

of the field of view. The resulting effect is a bump at shorter ranges, and an overlap

∗The raytracing program was originally developed by M. Horvat


function that decreases with distance. Therefore, the more the strabismus is convergent,

the more the signal appears attenuated (larger values of optical depth). On the contrary,

with a divergent strabismus the signal enters farther in the field of view. If the strabismus

is large the overlap tends to gradually increase with distance. The signal, thus, appears

less attenuated that it would be, causing an underestimated optical depth. It stands to

reason that the same effects can be caused by a laser strabismus.

5.1.2 Overlap Function from Horizontal Runs

The determination of the overlap function G(r) is extremely important for two main

reasons: G(r) is useful in order to correct the signals recorded in the continuous and

discrete scans in the short range; it is also a good indication of misalignment of the receiver

with respect to the laser, as we have seen in the previous section. The determination of

G(r) is done by applying the slope method [37, 17] on the horizontal scans. If we replace

in Eq. 5.2 the complete expression of P (r) given by Eq. 5.1, the result is:

Sexp(r) = lnP (r)r2

P (rn)r2n

= lnG(r)β(r)

G(rn)β(rn)− 2

∫ r

r0

α(r′)dr′ . (5.4)

As explained before, G(rn) ≃ 1. Since we are using horizontal shots, and our hypothesis

is that the atmosphere is horizontally homogeneous (see Eq. 5.3), this equation becomes:

Sexp(r) = ln G(r) − 2αground(r − r0) . (5.5)

Therefore, Eq. 5.3 represents the ideal condition in which all the beam is seen by the

receiving optics, while Eq. 5.5 is the real situation.

Once αground is calculated by a linear regression in a safe range in which G(r) ≃ 1, the

overlap function is extracted:

G(r) = eSexp(r)+2αground(r−r0) . (5.6)

If one wants to apply the method on non-horizontal scans, stronger conditions need to be

requested about the homogeneity of the atmosphere. It turned out that this is possible


distance [m]0 1000 2000 3000 4000 5000 6000 7000 8000

over

lap

-0.6

-0.4

-0.2

-0

0.2

0.4

0.6

0.8

Figure 5.3: A real signal (in grey) is compared to the expected signal (black line) in the case

in which G(r) = 1 over all the range. The expected signal is calculated with a linear regression

between 4 and 9 km.

distance [m]0 1000 2000 3000 4000 5000 6000 7000 8000 9000

over

lap

0

0.2

0.4

0.6

0.8

1

Figure 5.4: The overlap function is calculated by using Eq. 5.6. G(r) > 0.95 at a distance

of 1000 meters from the source.


during periods in which free convection is dominant in the lower atmospheric boundary

layer [61].

Time

Dis

tanc

e [m

]

0

500

1000

1500

2000

2500

3000

Time

Dis

tanc

e [m

]

0

500

1000

1500

2000

2500

3000

Time

Dis

tanc

e [m

]

0

500

1000

1500

2000

2500

3000

Figure 5.5: Distributions of rg in function of time for the three currently running lidars (in

order Los Leones, Los Morados, and Coihueco). The red, green, and blue curves correspond to

mirrors number 0, 1, and 2 respectively. The lidar at Los Leones has 2 mirrors only.

It can be interesting to know for each receiver the distance rg, where the overlap

function reaches unity within 5%. We choosed a period that goes from July 2006 to June

2007 to plot rg for all the currently running lidars. These distributions are shown in

Fig. 5.5. As one can see rg is not constant, but changes with time. The trends mean a

progressive misalignment of the mirrors. Below rg it is difficult to perform any analysis.


This means that between the ground and rg a kind of interpolation is needed. Since most

of the aerosol contribution comes from the first kilometers of the atmosphere, the more

rg is big the less the result one gets is precise. For this reason we choosed a threshold

Ts = 1.2 km. All the receivers that have rg more than this threshold are discarded. Ts is

shown in Fig. 5.5 with a thick black line. Due to this cut, there is a clear decrease of the

efficiency. Fig. 5.6 shows how the efficiency variates in function of the threshold Ts.

distance [m]gT0 200 400 600 800 1000 1200 1400 1600 1800 2000

Effi

cien

cy [%

]

0

10

20

30

40

50

60

70

80

90

100

distance [m]gT0 200 400 600 800 1000 1200 1400 1600 1800 2000

Effi

cien

cy [%

]

0

10

20

30

40

50

60

70

80

90

100

distance [m]gT0 200 400 600 800 1000 1200 1400 1600 1800 2000

Effi

cien

cy [%

]

0

10

20

30

40

50

60

70

80

90

100

Figure 5.6: Variation of the efficiency in function of the threshold Ts for the three currently

running lidars (in order Los Leones, Los Morados, and Coihueco). The red, green, and blue

curves correspond to mirrors number 0, 1, and 2 respectively. The black line represents the

efficiency of the system, with at least one of the mirrors with rg 6 Ts.


5.2 Aerosol Horizontal Attenuation Length

The aerosol attenuation of light can be described by a simple wavelength independent

model, which is based on two parameters only, known as the aerosol horizontal attenuation

length La and the aerosol scale height ha. This model is used in the CLF analysis made

in Napoli [4, 56]. The vertical aerosol optical depth (VAOD) τaer between the altitudes

h1 and h2 is here described by the following equation:

τaer(h2, h1) =

∫ h2

h1

αaer(h′)dh′

= −ha

La

[exp

(−h2

ha

)− exp

(−h1

ha

)]. (5.7)

Therefore, in this model the aerosol extinction coefficient αaer(h), whose integral gives

the VAOD, is modeled as:

αaer(h) =1

Laexp

(− h

ha

), (5.8)

that is the same expression found in Chapter 4 (Eq. 4.5 with hx = 0). The aerosol

extinction coefficient at ground (h = 0) is therefore αaer(0) = (La)−1. As explained at

the beginning of this Chapter, from the lidar measurements αground = αmol(0) + αaer(0)

is obtained. αaer(0) is then easily extracted, by subtracting the molecular contribution.

5.2.1 About Measurement Uncertainties

An important issue is the estimation of the uncertainties associated to αaer(0). These

could be caused mainly by these reasons: (a) the atmosphere is sometimes not homo-

geneous; (b) the optics are not collecting all the expected backscattered light; (c) the

source is not shooting on the horizontal.

The fact that atmospheric aerosols tend to be fairly homogeneously distributed in

the horizontal is verified scan by scan. In fact, the scatter of the S function around a

straight-line fit reflects how well the horizontal homogeneity hypothesis is met.

5.2 Aerosol Horizontal Attenuation Length 111

The second and the third reason are related to hardware problems. In fact, if the optics

are not collecting all the light, they could be out of alignment. As we have seen, this is

strongly related to the overlap function: if the strabismum of the system is divergent,

rg is big; instead, if it is convergent, the overlap function shows a peak. The more the

peak is high, the more the system is squinting. The last cause of uncertainty is a wrong

shooting direction: this can be caused either by a wrong alignment of the laser or a wrong

position of the lidar recorded by the encoders. While the first is less probable, because the

optics alignment procedure is done with the lidar shooting on the horizontal direction, the

correct reading of the encoders is checked during acquisition every time the lidar passes

near the Zero sensors.

In order to associate an error to the measurement of αaer(0), the region between 4

and 9 km is splitted in 6 subregions. For each one we perform a linear regression and

estimate the difference between the slope of the fit and αaer(0). This strategy will take

into account a possible non-homogeneous atmosphere, that will return a bigger error.

Time

]-1

(0)

[km

aer

α

0

0.02

0.04

0.06

0.08

0.1

0.12

Figure 5.7: The aerorol attenuation coefficient

at ground in function of time: Los Leones (blue

circles), Los Morados (red stars), Coihueco (green

triangles) are compared to αmol(0) (dashed line).

Time

10/1

11/1

12/1

13/1

14/1

15/1

16/1

17/1

18/1

19/1

20/1

21/1

22/1

23/1

24/1

25/1

26/1

27/1

]-1

(0)

[km

aer

α

0

0.02

0.04

0.06

0.08

0.1

0.12

Figure 5.8: A detail of the previous Figure,

namely January, 2007. A common trend of the

measurements is visible by the 3 sites.


5.2.2 Results

The measurements of αaer(0) made by the 3 sites between July 2006 and May 2007 are

shown in Fig. 5.7. For comparison, the value of αmol(0) is shown. If Figure 5.8, instead,

a zoom in on January, 2007 has been done for a better clearness. With the data collected

in the same time period, a plot containing the distributions of the aerosol attenuation

coefficient has been done (see Figure 5.9).

]-1(0) [kmaerα0 0.02 0.04 0.06 0.08 0.1 0.12

Ent

ries

0

20

40

60

80

100

120

140

160

180

200

220

Figure 5.9: The aerorol attenuation coefficient at ground distributions: Los Leones (in blue),

Los Morados (in red), and Coihueco (in green).

In this plots, the fact that the atmosphere is in general more transparent at Coihueco

stands immediately out. Despite this difference, explainable with the fact that Coihueco

stays about 300 meters higher than the other sites, it is also visible that all these distri-

butions have a peak around 0.02-0.03 km−1. This value, between one third and a half of

the mean molecular aerosol coefficient at ground, is equivalent to an aerosol horizontal

attenuation length La ≃ 40 km. In order to study the atmospheric uniformity over the

5.2 Aerosol Horizontal Attenuation Length 113

whole site, the results from the 3 lidars have been compared. Keeping in mind that the

lidars at Los Leones and Los Morados are at about the same altitude, while Coihueco is

around 300 meters heigher, we expect to find a stronger correlation between the first two

sites. In fact Fig. 5.10 highlights a correlation between Los Leones and Los Morados,

while the comparisons of these two sites with Coihueco do not show a clear correlation

with the higher site. However the air turns out to be more transperent at Coihueco with

respect to the other sites.

]-1(0) [kmaerαLos Leones 0 0.02 0.04 0.06 0.08 0.1 0.12

]-1

(0)

[km

aer

αC

oihu

eco

0

0.02

0.04

0.06

0.08

0.1

0.12

]-1(0) [kmaerαLos Morados 0 0.02 0.04 0.06 0.08 0.1 0.12

]-1

(0)

[km

aer

αC

oihu

eco

0

0.02

0.04

0.06

0.08

0.1

0.12

]-1(0) [kmaerαLos Leones 0 0.02 0.04 0.06 0.08 0.1 0.12

]-1

(0)

[km

aer

αLo

s M

orad

os

0

0.02

0.04

0.06

0.08

0.1

0.12

Figure 5.10: Correlation between the measurements of αaer(0) at the same times.

115

Chapter 6

Detecting Clouds with Lidars

As we have seen before, the backscattered signal is recorded in two different ways, current

mode and photon counting mode, and subsequently combined. This guarantees a longer

range, that can reach up to 25 km. The glueing of the two signals is performed in a valid

region of both signals, between the lower toggle rate (typical 0.5 MHz) and the upper

toggle rate (typical 10-12 MHz) [43].

Once we have the glued signal, described by Eq. 4.2, it is convenient for our purposes

to express S in function of the height h. Thus, Eq. 4.3 becomes:

S(h) =P (h)h2

P (hn)h2n

= lnβ(h)

β(hn)− 2τ(h; hn) sec(θ) . (6.1)

In this equation, P (h) is the signal at height h, τ(h; hn) is the optical depth calculated in

the range [hn, h], and θ is the lidar inclination angle from the zenith. The normalization

116 Detecting Clouds with Lidars

height hn is a fixed height to normalize P , chosen such that at hn, the entire signal is in

the field of view of the mirrors.

6.1 Cloud detection algorithm

Signals are processed in order to locate clouds in them, and in that case to measure their

properties. Clouds, in fact, are visible as strong localized scattering sources (see Figure

6.1). We describe now the algorithm that carries out this task, dividing it into logical

steps.

Figure 6.1: S(h) function. Clouds are visible

as echoes of the signal. The first cloud starts in

A, showing the maximum peak in B. Suddenly

a second cloud starts in C, showing a peak in D

and ending in E. The grey curve is a simulated

totally-molecular atmosphere.

Figure 6.2: Subtracting simulated S function

to the real one, we obtain S. End points C and

F are validated because S(C) and S(F ) are re-

spectively lower than S(A) and S(D).

6.1 Cloud detection algorithm 117

Step 1: Cloud spotting

The properties of the molecular atmosphere at the Pierre Auger Observatory site are

very well-known thanks to an extensive balloon-launching program which has produced a

detailed database including temperature, pressure, and density profiles over the site [8].

Data from these balloon flights have been used to create monthly models of the molecular

atmosphere at the Malargue site. In the lidar analysis we use these monthly models to

calculate a simulated signal reflected by a clear and 100 % molecular atmosphere, and we

subtract it to the measured signals as shown in Fig. 6.2. In this way, we obtain a new

function, called S(h), whose equation is:

S(h) = S − Smol

= S − ln

[βmol(h)

βmol(hn)

]+ 2τmol(h; hn) sec(θ)

= ln

[β(h)

β(hn)

βmol(hn)

βmol(h)

]− 2τaer(h; hn) sec(θ) . (6.2)

Afterwards the derivative of S(h), dS(h), is calculated (see Figure 6.3). The derivative

is obtained by taking each bin of S(h), and making a linear regression over a certain

number of bins around it. So far this number is fixed to 7, but in principle it can be

modified through a specific function. S(h) appears to be approximately constant before

the cloud. Therefore its derivative is around zero. Every time dS(h) goes above 3 standard

deviations from 0, a cloud candidate is found. Examples of starting points of clouds are

shown in the following Figures with an A and a D.

Step 2: Cloud thickness

In order to obtain the cloud thickness, the second derivative S ′′(h) of S is calculated. The

algorithm searches the first zero in S ′′(h) after point A where the value of S is less than

the value it assumes at the beginning of the cloud (point C1 in Figure 6.4). Then the


Figure 6.3: Points A and D are found by us-

ing the derivative of S(h). They represent the

beginnings of the first and of the second cloud

respectively. The peaks B and E coincide with

the first zeroes of S′ after A and E for whom S

is lower than S(A) and S(D).

Figure 6.4: In order to determine the end

points C and F of the clouds, the positions of

the first two zeroes of S′′ after the peaks are lo-

calized and averaged. These are shown in this

figure as C1 and C2 for the first cloud, F1 and F2

for the second one.

following zero is detected (point C2 in Figure 6.4), and the mean value of these positions

is identified as the end of the cloud. This point is marked in the Figures 6.1 and 6.2 with

a C. Therefore the thickness of the cloud is the difference in height between points C and

A, hC − hA. The same sequence is done for the next cloud, finding points F1 and F2, and

calculating F .

Step 3: Grouping and selection

In most cases the influence of a partial overlap of the second cloud causes a bad estimation

of the optical depth inside the first one. For this reason, we decided to group very near

clouds separated by less than 10 meters and calculate the total optical depth inside the

6.1 Cloud detection algorithm 119

whole layer. For example, clouds in Figure 6.1 are grouped and treated as a unique cloud

of thickness hF − hA.

Step 4: Comparison between two mirrors

In order to reduce the possibility of a wrong detection, clouds detected by two different

mirrors of the same lidar are compared, and only clouds detected by both are taken into

account and stored into a new array of clouds. This is obtained by building a mask for

each mirror, with a binning of 3.75 meters, where 0 represents clear sky, and 1 the presence

of a cloud. The starting point of the clouds is obtained by applying an AND operation

between the two masks. The ending point is obtained by applying an OR operation

instead. An example of this technique is shown through the scheme in Figure 6.5.

Figure 6.5: Clouds are found separately for 2 mirrors, and a mask is created for both mirrors. From

the comparison of the masks a cloud is found, and two clouds are discarded because they do not match.

The starting point of the cloud is found with an AND operation; the ending point is found with an OR

operation.

Figures 6.6 and 6.7 are an example of the usage of this technique. In the continuous


lidar scan (Figure 6.6), obtained by plotting S(h) as a function of shooting direction,

several clouds are visible in a height range that goes from 7.5 to 10 km. The result of the

cloud detection algorithm gives the plot shown in Figure 6.7, where the starting point of

the detected clouds is highlighted by a bright point.

Figure 6.6: Azimuth continuous scan taken

by the Coihueco lidar station (lidar-ch-20060922-

233921-R10555.root).

Figure 6.7: Detected clouds in the same scan.

Bright points identify the beginning of the cloud.

The colored scale is in arbitrary units.

6.2 Atmospheric Parameters and their Use

By using the algorithm presented in the previous section, useful information for other

studies can be derived. For instance, the determination of the height of the cloud layers

can be compared with the information coming from the cloud cameras. In this way, the

association of the height information to the layers detected in the field of view of the FDs

can increase our accuracy on the determination of the cloud coverage over the site.

Another use of the cloud coverage information is the further improvement of the de-

6.2 Atmospheric Parameters and their Use 121

termination of the FD exposure for aperture simulations [49]. From a combination of the

height of the lowest cloud layer and the cloud coverage, a quality paramenter can be set

in order to estimate the possibility of an acceptable detection efficiency. Moreover, a list

of cloud-free nights (note: it does not mean clean nights), or even cloud-free hours during

a night, can be done.

One can also subdivide the atmosphere in horizontal layers of a fixed height (e.g. 200

meters), and estimate the cloud coverage of each layer. The cloud coverage layer by layer

could be useful to select the nights in which clouds are very high (as they are in Figure

6.6), or to know the cause of a sudden decrease of the signal in the FD events at particular

heights. In Figures 6.8 and 6.9 an example of cloud coverage estimation is shown.

Figure 6.8: Azimuth continuous scan taken

by the Coihueco lidar station (lidar-ch-20060923-

044511-R10584.root) showing several cloud layers

at different heights. Heights are relative to the

lidar station altitude.

Coverage (%)0 10 20 30 40 50 60 70 80 90 100

Hei

ght a

.s.l.

(m

)

2000

4000

6000

8000

10000

12000

14000

16000

Cloud Coverage

Figure 6.9: From cloud detection, cloud cov-

erage is estimated for each horizontal layer. In

this plot, heights are relative to the sea level. the

Coihueco lidar station is situated at an altitude

of 1691.8 m a.s.l.

Once the lowest clouds have been identified, their effect on the light propagation is

estimated. The turbidity of a layer of thickness H can be described by a transmission


factor

T (H) = e−τ(H;0) , (6.3)

where τ(H ; 0) is the total optical depth.

Consider, for instance, a cloud at a height hA that ends at a height hF . From a lidar

scan, the auxiliary function S(h), given by Eq. 6.1, is obtained, and S(h) is calculated by

using Eq. 6.2. The difference between the values assumed by S(h) in hA and hF is:

∆S(hF ; hA) = ln

[β(hF )

βmol(hF )

βmol(hA)

β(hA)

]− 2τaer(hF ; hA) sec θ . (6.4)

At heights above 2 km from ground a quasi-molecular atmosphere can be assumed in

the proximity of clouds. Therefore, β ≃ βmol in hA and hF , and Eq. 6.4 becomes:

∆S(hF ; hA) ≃ −2τaer(hF ; hA) sec θ , (6.5)

where τaer(hF ; hA) is due to scattering and absorption of the light by the cloud. In

this way, the cloud optical depth can be estimated:

τaer(hF ; hA) ≃ −1

2∆S(hF ; hA) cos(θ). (6.6)

The lowest cloud layer properties, and the cloud coverage for each layer is obtained

run by run. Then, an averaged result is given for each hour of data taking. Lidar data

are stored in the MySQL database described in Chapter 4.

6.3 Summary Plots of the Last Years

As mentioned before, while the lidar at Coihueco is the first one that started a regular

data taking with the high-frequency laser, at Los Leones the prototype setup have been

replaced, and the lidar started taking data with the high-frequency laser in May, 2006

6.3 Summary Plots of the Last Years 123

(after two months considered as “commissioning time”); the third lidar, mounted at Los

Morados, started taking data in April, 2006, but the first 3 months were mainly again

dedicated to tests.

Figure 6.10: Data taking and analysed months for the 3 sites of Los Leones (LL), Los Morados (LM),

and Coihueco (CH). Not analysable months are painted in grey.

Cloud detection results with the low-frequency laser have been already presented

in [50], althouogh the detecting technique was rather different. The following plots show

the cloud coverage above the site for the last two years. Since many times cloud layers


above 10 km a.s.l. do not affect FD events, the cloud coverage is here shown without

considering clouds detected above this altitude.

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Clo

ud C

over

age

[%]

0

10

20

30

40

50

60

70

80

90

100

20062006

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Clo

ud C

over

age

[%]

0

10

20

30

40

50

60

70

80

90

100

20072007

Figure 6.11: Cloud coverage of the last 2 years for the 3 sites of Los Leones (blue), Los Morados (red),

and Coihueco (green).

125

Chapter 7

Aerosol Optical Depth Determination

with a Multiangle Method

Lidars are commonly used to extract the atmospheric extinction coefficient α(r), and thus

the optical depth τ(r), in many fields. As we have already underlined in Chapter 3, the

lidars have a leading role in the estimation of aerosol attenuation and scattering properties

in the Pierre Auger Observatory.

Unfortunately, the lidar equation (Eq. 4.2) contains more than one unknown value and

is thus undetermined. Hence additional hypotheses are needed to solve it. Many authors

attempted different approaches, whose main conditions, advantages, and drawbacks are

presented in the following sections. The the fundamentals of multiangle technique, which

is giving in our specific case the most stable results, are described in Section 7.1.4, while

its application on discrete scans is described in deep in Chapter 7.2.

126 Aerosol Optical Depth Determination with a Multiangle Method

7.1 Methods for Obtaining the Optical Depth

All elastic lidar inversion methods developed so far require one or more a priori assump-

tions that are chosen according to the particular atmospheric situation. The main dif-

ferences between these methods lie in the ways of determining the boundary conditions

and in the particular assumptions, such as a relationship between the attenuation and

the backscattering coefficients. There are three basic methods to solve the lidar equation

and find the optical depth [37]. These methods are as follows:

1. The slope method: this technique is used for homogeneous atmospheres. Since in

many cases atmospheric horizontal homogeneity is a reasonable, this method has

been used in the horizontal scans analysis, described in Chapter 5.

2. The boundary point solution: in this case, an a priori estimate of the extinction co-

efficient at a certain distance within the measurement range is used. This technique

is adopted for both homogeneous and inhomogeneous atmospheres.

3. The optical depth solution: in this method, used again in both homogeneous and

inhomogeneous atmospheres, the total optical depth is assumed or should be known.

Besides these, more complicated data processing techniques using multiangle mea-

surements have been developed. These methods, which are applied to a number of lidar

signals measured at different elevation angles, are based on the horizontal homogeneity

assumption, while no relation is needed between the attenuation and the backscattering

coefficients.

7.1.1 Klett’s Far-End Solution

From the lidar equation (Eq. 4.2), the S function is calculated, choosing the normalization

point such as the bakscattered signal is completely seen by the receiving optics. In this

7.1 Methods for Obtaining the Optical Depth 127

way, one of the unknowns, i.e. the laser intensity, is canceled. Let us rewrite the S

equation for simplicity:

S(r) = lnP (r)r2

P (rn)r2n

= lnβ(r)

β(rn)− 2

∫ r

r0

α(r′)dr′ . (7.1)

The remaining two unknown quantities, namely the attenuation coefficient α(r) and the

backscattering coefficient β(r), can be related by the following assumption of proportion-

ality:

β(r) ∝ α(r)k , (7.2)

where k is a constant value over the whole range. Although Eq. 7.2 is completely empirical

and has no theoretical grounds, in 1966 Fenn stated that such a dependence was valid

to within 20-30% over a broad spectral range of extinction coefficients, between 0.01 and

1 km−1. For relatively clear atmospheres, with extinction coefficients up to 1 km−1, the

constant k is, approximately 0.7, whereas for more turbid atmospheres with α > 1 km−1,

the constant k becomes ∼ 1.3 [36]. Replacing Eq. 7.2 into Eq. 7.1 one finds a Bernouilli’s

differential equation, with an existing analytical solution. It has been demostrated that a

forward inversion algorithm is numerically instable in most of the cases. Klett proposed

an stable alternative method, which procedes from a chosen far point rf to the near end

[32]. Subsequently, the attenuation coefficient turns out to be:

α(r; αf) =eS(r)/k

eS(rf )/k/αf + 2k

∫ rf

reS(r′)/kdr′

. (7.3)

This equation still depends on the value of αf assumed by the attenuation coefficient

at the far point. This value should be estimated either by an external source or by an

ad hoc assumption. If rf is sufficiently high, a reasonable assumption could be that at

that height the aerosol contribution is almost zero, letting α coincide with the molecular

attenuation coefficient αm. This value in turn could be estimated by using the dataset

provided by balloon launch champaignes over the Pierre Auger Observatory. The optical


depth τ(r) can be directly extracted from Eq. 7.3:

τ(r, r0, αf) =k

2ln

keSf /k + 2αf

∫ rf

r0eS(r′)/kdr′

keSf /k + 2αf

∫ rf

reS(r′)/kdr′

. (7.4)

As an exercise, let us apply the Klett’s method on a vertical scan taken by the lidar

at Los Leones. A vertical scan is formed by about 80 events, each one made up of 1000

shots. Summing together all the events one achieves a very good SNR. A signal from a

vertical scan is shown in Figure 7.1. By applying Eq 7.1 one finds the S function, shown

in Fig. 7.2 in comparison to the molecular S function expected.

Distance [m]

0 2000 4000 6000 8000 10000 12000 14000

Pow

er [A

DC

Cou

nts]

-210

-110

1

10

210

310

Figure 7.1: The mean backscattered signal, ob-

tained by averaging the 78 events of Run lidar-ll-

20070215-014916-R14821.root, taken by the lidar

of Los Leones.

Distance [m]1000 2000 3000 4000 5000 6000 7000 8000

S fu

nctio

n

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

Figure 7.2: Corresponding S function, com-

pared to the S function obtained by a pure molec-

ular atmosphere Smol(r).

The aerosol extinction coefficient in function of the altitude from the lidar is then

obtaining with the Klett’s method for 3 different values of the constant k, namely 0.7,

1.3 and an intermediate value of 1.0. The algorithm has been run from a far-end point

at 9 km above the lidar, where αaer has been forced to 0, down to hg ≃ 0.9 km where

the overlap function is almost equal to unity. From ground to hg, we performed an

interpolation between αground, measured with the nearby horizontal scans, and α(hg).

The molecular contribution has been subsequently subtracted. The results are shown in


Figure 7.3: in this particular case, the profile obtained with k = 1.3 is mainly negative,

meaning that the atmosphere is cleaner than what we expect; on the contrary, for k = 0.7,

αaer is still prominent above 7 km, and at height hg is significantly higher than the value

at ground; for the intermediate value of k, instead, αaer is substantially 0 above 7 km,

and the interpolation in the first range is in agreement with the slope of the attenuation

coefficient between 0.9 and 1.2 km. The vertical aerosol optical depth is then obtained

by an integration of αaer for the 3 configurations (see Fig. 7.4).

Distance [m]

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

]-1

[km

aer

α

-0.005

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04k=0.7

k=1.0

k=1.3

Figure 7.3: The aerosol attenuation coefficient

in function of height above the lidar obtained with

the Klett’s inversion method. The 3 profiles are

obtained by setting k respectively to 0.7 (black),

1.0 (red), 1.3 (blue).

Distance [m]

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

VA

OD

0

0.02

0.04

0.06

0.08

0.1

k=0.7

k=1.0

k=1.3

Figure 7.4: The vertical aerosol optical depth

(VAOD) obtained by integrating αaer. The inte-

gration steps measure 15 meters. The blue pro-

file (k = 0.7) is unphysical, while the black one

(k = 1.3) is overestimated.

Although Equation 7.4 has been used widely for both horizontal and slant direction

measurements, the critical problem of a proper choice of the constant k is still unsolved.

Moreover, k cannot be considered to be constant in real atmospheres.

7.1.2 Solution for a Two-Component Atmosphere

The basic idea of a two-component atmosphere solution assumes an atmosphere in which

neither the particulate component nor the molecular one can be ignored when evaluating


opical attenuation. Such an atmospheric situation is typical, for example, of clear or

moderately turbid air. Here the assumption of a single-component atmosphere, described

in the previous Section, is clearly poor.

The first lidar measurements in which such an approach was used for studying tropo-

spheric particulates were reported by Gambling and Bartusek [23] and Fernald et al. [22].

In the latter study, a general solution for a two-component atmosphere was given. Later,

in 1984, Fernald proposed a new calculation method based on the application of an a

priori assumption on particulate characteristics at some specific range [21]. Klett [33] and

Browell et al. [10] developed a boundary point solution based on analytical formulation,

making it possible to avoid some computational difficulties with Fernald’s solution. More

recent iterative procedures were presented by Weinman [59] and Kovalev [34, 35].

In a two-component atmosphere the attenuation and backscattering coefficients can

be written as:

α(r) = αaer(r) + αmol(r) ; (7.5)

β(r) = Πaer(r)αaer(r) + Πmol(r)αmol(r) . (7.6)

If the molecular attenuation coefficient αmol(h) is known, in order to solve the lidar equa-

tion it is necessary to estimate the backscatter-to-extinction ratios Πaer and Πmol. The

latter one depends on scattering and any absorption from the molecular component that

may be present, that is,

Πmol =βmol(r)

αmol(r) + κA,mol(r). (7.7)

The absorption term is cosidered as negligible at our operating wavelengths, thus, from the

Rayleigh’s scattering theory, Πmol reduces to a range-independent quantity, Πmol = 3/8π.

Let us now introduce a modified S function, defined as:

S(r) = S(r) + 2(F − 1)

∫ rf

r

αmol(r′)dr′ , (7.8)

where F = Πmol/Πaer. The lidar equation is then solved, giving a formula for the aerosol


attenuation coefficient which depends on F and on far-end assumptions:

α(r; F, αf) =e

eS(r)

eeS(rf )/αf + 2∫ rf

reeS(r′)dr′

, (7.9)

with αf = Fαmol(rf) + αaer(rf ). The optical depth is then expressed as:

τ(r; r0, αf) =1

2ln

[e

eS(r) + 2αf

∫ rf

r0e

eS(r′)dr′

eeS(r) + 2αf

∫ rf

reeS(r′)dr′

]+ (1 − F )

∫ rf

r0

αmol(r′)dr′ . (7.10)

Backscatter-to-Extinction Ratio

Various experimental investigations have shown that the backscatter-to-extinction vari-

ations could be very large in both time and space. For mixed-layer aerosols, this value

may vary, approximately, from 0.01 sr−1 for turbid atmospheres to 0.11 sr−1 for clean

ones and may be even as large as 0.2 sr−1 [37]. The selection of a reasonable value of the

backscatter-to-extinction ratio for a particular atmospheric condition is a very difficult

problem for practical elastic lidar measurements. This value can even change during the

night, not only because of a variation of the aerosol composition in air, but also because

its relationship with humidity. It has been demostrated, in fact, that humidity plays an

important role in particulate properties and thus in the backscatter-to-extinction ratio.

While absorbing or releasing water, their physical and chemical properties change, in-

cluding their size and index of refraction. In turn, these changes can affect the optical

parameters of particulates, such as scattering, backscattering and absorption.

A Method for finding the appropriate Fernald’s Ratio

The backscatter-to-extinction ratio is a fundamental parameter to be determined in any

two-component atmosphere model. This value has to be assumed a priori or extracted by

external measurements.

An extremely useful piece of information comes from the horizontal scan analysis:

we know the value of the aerosol attenuation coefficient at ground. Unfortunately, in


Distance [m]

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

]-1

[km

aer

α

-0.005

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04=0.025aΠ=0.108081aΠ=0.35aΠ

Figure 7.5: The aerosol attenuation coefficient

in function of height above the lidar obtained with

an iterative Fernald’s inversion method. The blue

and the black lines represent the boundary pro-

files; the red line is obtained ater 30 iterations.

Distance [m]

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

VA

OD

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09 =0.025aΠ=0.108081aΠ=0.35aΠ

Figure 7.6: The vertical aerosol optical depth

(VAOD) obtained by integrating αaer. As before,

the integration steps measure 15 meters. The red

curve is quite in agreement with the one obtained

with the Klett’s method.

the incomplete-overlap region the signal cannot be inverted. Therefore other additional

assumptions on the variation of αaer in the region between ground and rg are necessary.

In our method we decided to assume that the aerosol attenuation coefficient variation

from ground to rg is constant, and its derivative is the same we measure in the first 50

meters above rg. The best profile is obtained by our algorithm, performing a dichotomous

loop between two boundary profiles of α(r). These profiles coincide with a very clean

atmosphere and a turbid one. Between the values assumed by the extinction coefficient

at ground and at rg a linear interpolation is done. The difference d between the slopes in

the ranges [0, rg] and [rg, rg + ǫ], with ǫ = 50 m, is then associated to each profile. The

dichotomous loop is then performed, using d as the guiding parameter, whose value must

tend to zero, and changing the Fernald’s ratio between the boundary ratios. The loop

can have a fixed number of steps, or alternatively can be stopped when d is sufficiently

near to 0.

An example of the application of the iterative Fernald’s analysis is shown in Figures 7.5


and 7.6. The boundary profiles are in black and blue, while the red one is the result of

the dichotomous loop.

Since this method does not require shots at different angles, it should be adopted for

the analysis of the vertical runs and the Shoot-the-Shower scans. For the latter ones, since

they are very inclined, αaer cannot be assumed zero at the far point, but an estimation of

this should come from other measurements.

7.1.3 Optical Depth Solution

Another way to solve the lidar equation is to use the total transmittance over the lidar op-

erating range as a boundary value. As in the previous method, the optical depth solution

is based on the assumption that the backscatter-to-extinction ratio is constant over the

whole range. In clear and moderately turbid atmospheres, the total atmospheric trans-

mittance (or the total optical depth) may be found from an independent measurement

performed by a specific instrument. Some attempts have been done in Auger by using

the FRAM [54], but the accuracy of the measurements is not sufficient for our purposes

so far. Therefore the optical depth solution is here presented only for completeness.

In this method, the two-way transmittance T 2max over the lidar maximum range from

rg to rmax,

T 2max = e

−2R rmax

rgαaer(r′)dr′

, (7.11)

is used as a solution boundary value. The solution is derived by estimating T 2max and cal-

culating the integral Imax of the range-corrected signal Z(r) = P (r)r2 over the maximum

range from rg to rmax. It can be found [37] that the aerosol extinction coefficient profile

is given by

αaer(r) =0.5Z(r)

Imax

1−T 2max

− I(rg, r), (7.12)

where I(rg, r) is the integral of Z(r) over the range from rg to r. The optical depth solution

is quite stable, because, for real atmospheres, T 2max is a finite positive value comprised


between 0 and unity, so that the denominator of Eq. 7.12 is also always positive.

7.1.4 Multiangle Method

The difficulties in the selection of a boundary value presented in the previous methods

can be overcome with a multiple-angle measurement approach. Generally, in multiangle

measurements, the lidar scans the atmosphere in many angular directions at a fixed

azimuth, starting from the horizontal, and producing a two-dimentional image of the

sky known as a range-height indicator (RHI) scan. Due to the interferences of our lidar

source with the FD measurements, these scans are constrained outside the FD field of

view. The main assumption in the multiangle approach is to have a horizontally uniform

atmosphere with constant scattering characteristics at each altitude. This condition of

horizontal layering occurs during stable atmospheric conditions, generally at night.

Under the condition of horizontally invariant atmosphere, the optical depth in function

of height can be extracted directly from lidar multiangle measurements withour other

assumptions. The technique is therefore based on two main conditions. First it is assumed

that in any thin horizontal slice of the atmosphere the backscatter coefficient β(h) is

constant and does not change during the time required by a lidar to complete the scan.

In other words, if we consider N different slant paths with elevation angles θ1, θ2, ..., θN

(measured with respect to the zenith), the backscatter coefficient at a given altitude h

remains invariant,

β(h, θ1) = β(h, θ2) = ... = β(h, θN) = const . (7.13)

The horizontal uniformity is also applied to the extinction coefficient, which does not

depend on the particular shooting direction,

α(h, θ1) = α(h, θ2) = ... = α(h, θN) = const . (7.14)

If this condition is valid, the optical depth of each layer is inversely proportional to the

cosine of the elevation angle. Thus, it makes sense to rewrite the S function of Eq.4.3 in


terms of height h and a geometric factor ξ = 1/ cos θ = sec θ. The S function becomes:

S(h, ξ) = lnβ(h)

β(hn)− 2ξ

∫ h

hn

α(h′)dh′ = lnβ(h)

β(hn)− 2ξτ(h; hn) , (7.15)

where τ(h; hn) is the optical depth calculated in the range [hn, h], and the normalization

height hn is a fixed height to normalize the return signal, chosen such that at hn, the

overlap function is equal to unity. If we consider again N shots at different elevation

angles, it is evident that for a given height h all the terms of Equation 7.15 are constant

except for ξ. In an ideal atmosphere, the vertical optical depth τ(h; hn) is given by the

slope of the line passing through the points S(h, ξ1), S(h, ξ2),..., S(h, ξN) in the plane

(ξ,S). In Figures 7.7 and 7.8 an example obtained with simulated signals is shown. In

practice, the points in the plane (ξ,S) result more scattered due to the noise. Thus, given

N shots at different angles θ, one makes a linear regression of the S(h, ξi) values for each

height, obtaining a profile of the vertical optical depth.

Height [m]0 1000 2000 3000 4000 5000 6000 7000 8000 9000

S

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2 ° = 0 θ

° = 20 θ ° = 27 θ ° = 37 θ ° = 43 θ ° = 59 θ ° = 70 θ

Figure 7.7: S functions at 7 different elevation

angles in function of height. The normalization

point is at hn = 3 km.

)θsec(1 1.5 2 2.5 3

S

-0.6

-0.5

-0.4

-0.3

-0.2

Figure 7.8: At h = 4 km the values of S(h, θ) for

all the 7 elevation angles are plotted in function

of ξ = sec(θ). The slope of the line in grey gives

τ(hn, h).


About Uncertaintes and Applicability of the Multiangle Method

The necessary information can be in principle retrieved from a two-angle measurement,

that is, by making measurements only along two slant paths. Both two-angle and multi-

angle methods are anyway extremely sensible to measurement errors, especially when the

angular separation of the lidar shots is small. Let us consider, for example, two lidar shots

at the elevation angles θ and θ + ∆θ taken at the same time. The following equations are

thus obtained:

S(h, θ) = lnβ(h)

β(hn)− 2 sec(θ)τ(h; hn) ; (7.16)

S(h, θ + ∆θ) = lnβ(h)

β(hn)− 2 sec(θ + ∆θ)τ(h; hn) . (7.17)

The two equations are normalized at the same height hn, such as it is possible to calculate

the vertical optical depth. In fact, combining Eqs. 7.16 and 7.17, one obtains:

τ(hn, h) =1

2

[S(h, θ) − S(h, θ + ∆θ)

sec(θ + ∆θ) − sec(θ)

]. (7.18)

Using standard methods to propagate the uncertainties, and ignoring for simplicity the

covariance term, one obtains the following expression for the uncertainties in the optical

depth:

δτ(hn, h) =1

2[sec(θ + ∆θ) − sec(θ)]−1

√δS(h, θ)2 + δS(h, θ + ∆θ)2 , (7.19)

where δS(h, θ) and δS(h, θ + ∆θ) are the relative uncertaintes in the S functions of

Eqs. 7.16 and 7.17. It is straightforward that when the angular separation ∆θ tends

to zero, the factor in brackets of Eq. 7.19 does the same; accordingly, the uncertainty

δτ(hn, h) tends to infinity. This means that the two-angle method is extremely sensitive

to the measuremet errors on the signals when the angular separation between consecutive

shots is small. The term in brackets acts as a magnification factor of all the errors

originating from signal noise, receivers nonlinearity, optical misalignments, and so on.

7.2 Analysis Strategy 137

A possible violation of the condition in Eq. 7.13 leads to a similar forumla, where it

appears the same magnification factor. Therefore, a small ∆θ causes again an explosion

of the uncertaintes in the optical depth. On the other hand, an increase in ∆θ increases

the distance between the measured scattering volumes at height h. This may weaken or

invalidate the horizontal homogeneity assumption. Thus the measurement uncertainty

increases both for small and large angular separations ∆θ.

To complicate the situation, the basic assumption of horizontal homogeneity in thin

spatially extended horizontal layers may often be incorrect for real atmospheres: local

aerosol plumes or clouds not only cause a wrong estimation of the optical depth at the

height where they lay, but also will influence the measurement accuracy for all higher

altitudes. Before performing a multiangle analysis on a scan, it is therefore essential to

test determine the spatial location of the heterogeneous areas.

7.2 Analysis Strategy

Taking into account the considerations of the previous section, a robust analysis starategy

which handles all the different situations has been designed. It consists in a chain of C++

programs, using the LDA classes presented in Chapter 4, and partially introduced in the

previous chapters. A main program, called lscan, scans an entire directory and lists all

the lidar ROOT files. After that, it calls sequentially 7 programs, that will run taking in

input the ROOT files listed (see Scheme 7.9).

The first program is called runFill. It simply takes the file list and catalogue the

ROOT files in a MySQL database. The files will be tagged as “Not Yet Analysed”. The

next program is RunWatch. This time the ROOT files are opened and their contents

are read. The main properties of the tracks, namely the signal peak, the offset and its

variance, are checked and saved in the database. Moreover, the run properties, such as

the scan type, its duration and the log, are stored in order to complete the list in the


database. At this point, one is aware of the number of potentially good files, and the

working photomultipliers for each run.

Figure 7.9: A depiction of the analysis chain. All the programs

are sequentially called by lscan and save information in a MySQL

database. A few options are read from a text file, settings.txt.

Afterwards, the horizontal scans are selected from the run list, and the horizontal scan

analysis, discussed in Chapter 5, is executed. A first program, called Hor, extracts the in-

formation related to the overlap function and the attenuation coefficient at ground. Then,

it checks the position of rg (the distance at which the overlap function is approximately

equal to unity) and the shape of the overlap function. With this information it decides

for each receiver whether it is sufficiently in focus or not. Since all the information com-

ing from the horizontal scans is subsequently used in the optical depth analysis, another

program, called CheckOverlap, takes in input each run file of the list, searches the nearest

horizontal scans taken within 1.5 hours from the starting time of the input file, and checks


the stability of the overlap function and the status of the receivers.

The last operation one has to perform before starting a multiangle analysis is to check

possible sources of heterogeneity in the atmosphere, namely aerosol or cloud spots and

layers. This is done by the program CloudFinder by using the method described in

Chapter 6.

Sampling the Atmosphere

As a standard for the Pierre Auger Observatory, the atmosphere is sampled in horizontal

layers above each Fluorescence Detector site. Each horizontal slice has usually a height of

200 meters (but in principle the database is flexible enough to allow any thickness). The

altitude of each atmosphere layer is understood above the sea level. The sampling rate of

the lidar DAQ has anyway a higher precision, which allows us to divide the atmosphere

in steps of 50 meters.

Furthermore, there is also a temporal sampling, which has usually a sampling of 1 hour.

In this time, around 2 discrete and 2 continuous scans are made on average. Therefore

the information stored in the final Offline database will be an average of the information

picked.

7.2.1 Multiangle Analysis with Discrete Scans

Considering the influence of the magnification factor of Eq. 7.19 on the uncertaintes in the

vertical optical depth, it stands to reason that the discrete scans are the most suitable for

a multiangle approach, because the angular separation of the shots in the continuous scans

is too small. Moreover, the discrete scans are designed to make several consecutiveshots

at each elevation angle: in this way the uncertainty δP of the averaged signals obtained

is lower.

Let us now describe in details all the steps that make up the multiangle analysis

program, MultiDisc. These can be divided in three sections: in the first one, the program


connects to the database and checks whether the run in input is analysable or not; in the

second one, the lidar signals are loaded, grouped by elevation angle, and averaged; in the

last section, the multiangle technique is applied and theresults from different mirrors are

matched.

Part 1: Preliminary Operations

In this part, MultiDisc checks if an overlap function profile is available in order to correct

the signals of the 3 (or 2) receivers. To do that, it connects to the database through a

dedicated class, and calls a function named GetMeanOverlap. This function returns an

overlap function object, if the profile is available.

The following step is an inspection of the photomultiplier states. The function

GetPMTState can return 4 states: on, off, low signal, bad overlap. All the photomultipliers

for which the function does not return on are discarded. Clearly, if no photomultiplier

survives, the run is skipped.

For all the passed receivers, the total attenuation coefficient at ground α(0) is loaded

from the database; the molecular part is subtracted, and, if the resulting aerosol contri-

butions are not negative, they are averaged. In order to know the molecular attenuation

coefficient, the molecular attenuation profile is loaded. This will be used again in the

third part.

The last check concern the cloud coverage: the function GetCloudyLayer returns the

height of the first layer which is covered by clouds for more than 20%. This will be a limit

for the analysis. In case this height is lower than the normalization height hn of the S

functions, the run is not analysed. The normalization height is tipically 3 km.

Part 2: Preparing the Signals

Afterwards, the signal tracks are read event by event; the photon counting and the analog

track of each event are matched to obtain a longer range; the stability of the signals are


checked to avoid sudden changes of intensity probably due to power instabilities of the

electric lines. The signals are cleaned from sampling noises and the small undershoot

(if there is any) is removed. The events are then grouped angle by angle: all the tracks

belonging to the same shooting direction are averaged, increasing in this way the SNR.

The averaged signals are then corrected in the low range for the overlap function. Once

the tracks are ready, the S functions are calculated (see Figure 7.10).

Height [m]0 1000 2000 3000 4000 5000 6000 7000 8000 9000

S

-2

-1.5

-1

-0.5

0

0.5

1

1.5

Figure 7.10: Real S functions at 7 different elevation angles in

function of height calculated from the zenith discrete scan lidar-

ch-20070110-224005-R12449.root taken at Coihueco. The green

line represents hg, where the overlap function is about 1 for all

the tracks.

Part 3: Obtaining the VAOD

At this point the program proceeds with the multiangle analysis: the atmosphere is ideally

subdivided in horizontal layers with a thickness of 50 meters; for each layer the values of

S(h, θ) of all the functions, calculated in the previous step, are put in a graph (sec θ,S);

a linear regression is made (see Figure 7.11), and the total optical depth τ(hn, hlayer) is


extracted. This operation is done for each correctly working photomultiplier.

It is fundamental to note that the vertical optical depth is the integral of the atten-

uation coefficient between two heights, the normalization height hn and the layer height

hlayer. This means that the curve of τ(hn, h) versus height will be zero at hn and negative

below the normalization height.

)θsec(1 1.5 2 2.5 3

S

-0.2

-0.18

-0.16

-0.14

-0.12

Figure 7.11: At h = 3.5 km the values of S(h, θ) for all the

elevation angles of run lidar-ch-20070110-224005-R12449.root are

plotted in function of ξ = sec(θ). As before, the slope of the line

in grey gives τ(hn, h).

The result that we want to obtain, instead, is the optical depth from ground τ(0, h),

τ(0, h) =

∫ hn

0

α(h′)dh′ +

∫ h

hn

α(h′)dh′ = τ(0, hn) + τ(hn, h) . (7.20)

Therefore, all the curve τ(hn, h) needs to be shifted by a factor τ(0, hn). The region of

uncomplete overlap, however, cannot be used to obtain a reliable profile even if the signals

are corrected by the overlap function. In fact, any little misalignment of the optics or the

laser during the telescope steering could change the shape of overlap curve: we decided,

therefore, to use the signals only where they are corrected for the overlap function at most


by 5%. The optical depth in the range between ground and hg must be deduced from the

horizontal measurements. Since we can calculate α(0) by analysing the horizontal scans

(see Chapter 5), we can make a linear interpolation between the attenuation coefficient

at ground and the mean value of it obtained in the first 300 meters above hg. The result

of this interpolation is like the ones shown in Figure 7.12.

Height [m]0 200 400 600 800 1000 1200 1400

VA

OD

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08Lidar VAODMolecular ODOverlap ~1Cloudy layer (>20%)

Height [m]0 200 400 600 800 1000 1200 1400

VA

OD

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07


Figure 7.12: Two examples of interpolation of the attenuation coefficient between ground and hg (green

line). The pictures show the final vertical aerosol optical depth (VAOD), which is the integral of αaer.

Above the green line, the points are the result of the multiangle analysis.

If there are more than one active mirror, the resulting vertical optical depth is the

average of the different profiles obtained. Once the resulting τ(hn, h) is calculated, the

molecular contribution,calculated by integrating αmol(h) (see Part 1) is subtracted, giving

the vertical aerosol optical depth (VAOD) with respect to hn as before.

Since the VAOD is theoretically the integration on a range of an always positive

quantity (the aerosol attenuation coefficient), its profile must be increasing monotonic.

Nevertheless negative values sometimes are present, due to random fluctuations of the

signals, little undetected inhomogeneities, or perhaps some differences between the in-

stantaneous molecular aerosol attenuation profile and the monthly average obtained by

the balloon measurements. These negative values are removed putting them to zero and

creating a sort of buffer that increases for negative values and decreases for the positive


ones. The main effect of the buffer is to force the new VAOD profile to follow in average

the old one, without the presence of small decreases.

An example of the final result of these operations is shown in Figure 7.13. In this

graph the VAOD profile (in black) is compared to the expected molecular optical depth

(in pink). The error bars are calculated for each mirror through a standard propagation of

the measurement uncertaintes and by the comparison of the results of 2 different receivers

of the same lidar.

Height [m]0 1000 2000 3000 4000 5000 6000 7000 8000 9000

VA

OD

0

0.05

0.1

0.15

0.2

0.25

0.3


Figure 7.13: The final result, V AOD(0, h), obtained by merging 2 mirrors and applying the zero

suppression on the attenuation coefficent profile (black curve wirh error bars). The profile is compared

to the molecular OD (pink curve).

In case of cloudy skies, the cloud detection information stored in the database is read

by the program, in order to stop the analysis below the first cloud layer. As for the

previous analyses, the lidar database is structured in order to contain the VAOD profiles

for each discrete scan. The Offline database, instead, requires a hourly information: since

a complete lidar Autoscan lasts about oue hour, all the discrete scan results contained in

each hour are combined in order to provide hour by hour a unique averaged profile. In

7.3 Results and Comparison with CLF 145

Figures 7.14 the evolution of the VAOD during two different nights is represented in 3D

colored plots.

time (hours)

22:00

23:00

0:00

1:00

2:00

3:00

height (200m steps)

20003000

40005000

60007000

8000

VA

OD

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

time (hours)

23:00

0:00

1:00

2:00

3:00

4:00

height (200m steps)

20003000

40005000

60007000

8000

VA

OD

0

0.02

0.04

0.06

0.08

0.1

Figure 7.14: Evolution of the vertical aerosol optical depth (VAOD) measured by a lidar in two different

nights. The first plot is the night of 13 January 2007 at Coihueco, the second is 23 December 2006 at

Los Morados.

7.3 Results and Comparison with CLF

The multiangle analysis is now regularly executed after the end of each monthly run on the

lidar data. The VAOD profiles, stored in the lidar MySQL database of the Torino Auger

server, are visible at the web page http://www.auger.to.infn.it/lidar/. The same data

are then stored in the local Offline database and periodically transferred to the master

database. Let us now consider the scheme in Figure 6.10: while the lidar at Coihueco has


been running correctly since the end of year 2005, only since July, 2006 all the 3 lidars

are running in their final configuration producing VAOD profiles. Hourly estimations of

the VAOD are also provided by the Central Laser Facility (CLF), which has been already

described in Chapter 2. Every quarter-hour its laser fires sets of 50 shots, and the number

of photons observed as a function of height by a Fluorescence Detector are averaged in

order to obtain a hourly signal profile Nobs(h). It is shown in [1] that, for vertical laser

shots, the VAOD can be approximated by:

τaer(0, h) = − lnNobs(h)

Nmol(h)[1 + csc φ]−1 , (7.21)

where φ is the angle with respect to the ground at which the detector receives the scattered

light, and Nmol(h) is a clear-night reference profile.

It is useful make a comparison between the two measurements, since the techniques

and the detectors are completely uncorrelated. The variable used to compare them is the

VAOD at hC = 4.5 km a.s.l., that is about 3 km above the observatory. Most of the

aerosols are usually confined below this height, and at the same time the measurement

ranges of both equipments are well above it.

A comparison of the 2 distributions of τ(0, hC) is shown in the figures 7.15, 7.16,

and 7.17 for the 3 sites. The data shown is relative to a period range that goes from July,

2006 to January, 2007. This is dictated by the fact that the latest CLF results are not

available so far.

Even if there is some correlation between the two measurements, more investigations

are necessary. The lidars and the CLF data of Los Leones and Los Morados seem to

be less correlated, while at Coihueco there are 2 classes: in the first one the lidar is

more in agreement with the CLF; in the second one the CLF is recording a more opaque

atmosphere.

7.3 Results and Comparison with CLF 147

CLF VAOD at 4.5 km a.s.l.0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

LID

AR

VA

OD

at 4

.5 k

m a

.s.l.

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

VAOD at 4.5 km a.s.l.0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Cou

nts

0

5

10

15

20

25

30

35

40Lidar

CLF

Figure 7.15: Los Leones

CLF VAOD at 4.5 km a.s.l.0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

LID

AR

VA

OD

at 4

.5 k

m a

.s.l.

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

VAOD at 4.5 km a.s.l.0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Cou

nts

0

5

10

15

20

25 Lidar

CLF

Figure 7.16: Los Morados


CLF VAOD at 4.5 km a.s.l.0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

LID

AR

VA

OD

at 4

.5 k

m a

.s.l.

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

VAOD at 4.5 km a.s.l.0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Cou

nts

0

10

20

30

40

50

Lidar

CLF

Figure 7.17: Coihueco

149

Main Topics for Future Work

Since three years ago, a lot of work has been done in order to make the remote acquisition

of the lidar system working stably. The software package in its last version allows a

complete control of these devices in an easy way, preventing in most cases the intervention

of an expert during the data acquisition. However, the software needs to be upgraded, as

we have already said in Section 3.6, to optimize the Shoot the Shower operation. Most

of the programs must be modified, thus creating a more centralized system which allows

to send simultaneous vetoes to more than on Fluorescence Detector. This topic needs

several months of development, with a first phase in which a simulated lidar system is

used, and a second phase of local installation and troubleshooting.

A better comprehension of the behavior of lidar signals and their dependence on

the optical alignment allowed us to set up an analysis chain, supported by a light and

stable framework, in which we used horizontal, discrete, and continuous scans to obtain

a lot of information from the atmosphere. The study of horizontal scans allowed to

check the alignment of the receivers, not only during the offline analysis, but also during

maintenance operations to prepare lidars for the following data acquisitions. Since optical

alignment is of primary importance for having good analyzable data, this alignment could

be constantly monitored during data acquisition, and a specific software tool should be

prepared to make these alignment faster.

Cloud detection is working without problems, finding clouds in all discrete, continuous,


and even Shoot-the-Shower scans. The integration of this information with infrared cloud

camera snapshots of the FD field of view is now under development. This will allow to

associate potentially cloud covered layers to fluorescence shower profiles, and optimize FD

analysis.

A multiangle technique has been applied to discrete scans to obtain a hourly estima-

tion of the vertical aerosol optical depth. This was made possible by using additional

information coming from horizontal and continuous scans: this stable analysis has been

compared to CLF measurements in order to start a study of the possible sources of sys-

tematics. In Chapter 7 is also presented a new iterative inversion technique that could be

applied in the future to Shoot-the-Shower scans.

151

Appendix A

Database Tables

LidarRunTab

Field Type Comment

LidarRunTabId Int Primary key

GoodRun Enum(’y’,’n’) Flag

EyeId Int(1) Lidar number

RunType Enum(...) Scan type (see Section 3.2.2)

RootFile VarChar(100) File name

GPSStart Int(9) Start time (GPS seconds)

GPSEnd Int(9) End time (GPS seconds)

PMT0 enum(...) Photomultiplier #0 state



152 Database Tables

LidarEventTab

Field Type Comment

LidarEventTabId Int Primary key

LidarRunTabId Int(6) Key

GPSStart Int(9) Start time of the event (GPS seconds)

Zenith Float Zenithal shooting angle

Angle Float Azimuthal shooting angle

MaxPMT0 Int(4) Peak (in ADC counts) in PMT #0



PedCurPMT0 Float Analog trace pedestal in PMT #0



PedPhoPMT0 Float Photon counting pedestal in PMT #0



SigmaCurPMT0 Float Analog trace pedestal variance in PMT #0



SigmaPhoPMT0 Float Photon counting pedestal variance in PMT #0



RangePMT0 Int(5) Maximum range (in meters) of PMT #0



153

StSTab

Field Type Comment

StSTabId Int Primary key


T3Id Int(4) T3 Id number

GPSsec Int(9) Arrival time, GPS seconds

GPSns Int(9) Arrival time, nanoseconds

SDPAngle Float Angle defining the SDP

SDPTheta Float Angle defining the SDP

SDPPhi Float Angle defining the SDP

HorizontalTab

Field Type Comment

HorizontalTabId Int Primary key


Alpha0PMT0 Float αground measured by PMT #0



ErrAlpha0PMT0 Float Error on αground for PMT #0



Chi2PMT0 Float χ2/d.o.f of the linear fit (PMT #0)



MaxAtBinPMT0 Float Position of the signal peak (in bins)



Version Int Version of the program hor

154 Database Tables

OverlapTab

Field Type Comment

OverlapTabId Int Primary key


Distance Int(4) Distance r from the source (in meters)

Overlap Float Overlap function G(r)

PMT Int(1) Photomultiplier number

LayerTab

Field Type Comment

LayerTabId Int Primary key


Height Int(5) Layer Altitude a.s.l. (in meters)

VAOD Float Vertical Aerosol Optical Depth

VAODError Float VAOD error

CloudCoverage Int(3) Layer cloud coverage (%)

AttenuationLength Float Attenuation Length (in km)

AttenuationLengthError Float Attenuation Length error

VOD Float Total vertical Optical Depth

VODError Float Total vertical Optical Depth error

VMOD Float Molecular Optical Depth (from model)

Version Int Version of the program multidisc

155

WeatherTab

Field Type Comment

WeatherTabId Int Primary key


CloudCoverage Int(3) Cloud coverage (%)

LowestCloudHeight Int(5) Height of the lowest cloud layer (in meters)

LowestCloudThickness Int(4) Thickness of the layer (in meters)

LowestCloudOd Float Optical depth of the layer

MaxHeight Int(5) Maximum height reached

Version Int Version of the program cloudfinder

157

Bibliography

[1] R. Abbasi et al., Techniques for Measuring Atmospheric Aerosols at the High Resolution Fly’s

Eye Experiment, Astroparticle Physics, 25 (2006), pp. 74–83.

[2] AGASA Collaboration, Official website, http://www-akeno.icrr.u-tokyo.ac.jp/AGASA/.

[3] M. Aglietta et al., The EAS-TOP Atmospheric-Cerenkov-Light Telescope and its Combined

Operation with the e.m. Detector, Il Nuovo Cimento C, 16 (1993), pp. 813–824.

[4] M. Ambrosio, C. Aramo, D. D’Urso, F. Guarino, and L. Valore, Evaluation of Atmospheric

Aerosol Concentration from CLF Data Analysis, GAP Note 2005-56.

[5] P. V. Auger, Extensive Cosmic-Ray Showers, Rev. Mod. Phys., 11 (1939), pp. 288–291.

[6] P. Bhattachargee and U. Sigl, Origin and Propagation of Extremely High Energy Cosmic Rays,

Phys. Rep, 327 (2000), pp. 109–247.

[7] Big Sky Laser Technologies, Inc., Official website, http://www.bigskylaser.com.

[8] J. Blumer et al. (for the Pierre Auger Collaboration), Atmospheric Profiles at the

Southern Pierre Auger Observatory and their Relevance to Air Shower Measurement, in Proc. 29th

Int. Cosmic Ray Conference, Pune, India, (2005).

[9] J. Brack, R. Meyhandan, and G. Hofman, Prototype Auger Absolute Calibration System:

Fluorescence Detector Calibration at Los Leones, GAP Note 2002-033.

[10] E. V. Browell, S. Ismail, and S. T. Shipley, Ultraviolet DIAL Measurements of O3 Profiles

in the Region of Spatially Inhomogeneous Aerosols, Appl. Opt., 24 (1985), pp. 2827–2836.

[11] R. Brun et al., ROOT: An Object-Oriented Data Analysis Framework, http://root.cern.ch.

[12] A. N. Bunner, cosmic ray detection by air fuorescence, Ph.D. Thesis, (1967).

158 BIBLIOGRAPHY

[13] R. Cester et al. (for the Pierre Auger Collaboration), Atmospheric Aerosol Monitoring

at the Pierre Auger Observatory, in Proc. 29th Int. Cosmic Ray Conference, Pune, India, (2005).

[14] A. Collaboration, Properties and Performance of the Prototype Instrument for the Pierre Auger

Observatory, Nucl. Instr. Meth. A, 523 (2004), pp. 50–95.

[15] A. Collaboration, Measurement of the Pressure Dependence of Air Fluorescence Emission In-

duced by Electrons, Astroparticle Physics, 28 (2007), pp. 41–57.

[16] M. Collaboration, Measurement of Air and Nitrogen Fluorescence Light Yields Induced by Elec-

tron Beam for UHECR Experiments, Astroparticle Physics (in press), (2007).

[17] S. W. Dho, Y. J. Park, and H. L. Kong, Application of Geometrical Form Factor in Differential

Absorption Lidar Measurement, Optical Review, 4 (1997), pp. 521–526.

[18] K. Dolag, D. Grasso, V. Springel, and I. Tkachev, Mapping Deflections of Extragalactic

Ultra High Energy Cosmic Rays in Magnetohydrodynamic Simulations of the Local Universe, Nucl.

Phys. B (Proc. Suppl.), 136 (2004), pp. 234–243.

[19] N. N. Efimov et al., The Energy Spectrum and Anisotropy of Primary Cosmic Rays at Energy

E0 > 1017 eV Observed in Yakutsk, in Astrophysical Aspects of the Most Energetic Cosmic Rays,

Nagano and Takahara, eds., 1991.

[20] E. Fermi, On the Origin of the Cosmic Radiation, Phys. Rev., 75 (1949), pp. 1169–1174.

[21] F. G. Fernald, Analysis of Atmospheric Lidar Observations: Some Comments, Appl. Opt., 23

(1984), pp. 652–653.

[22] F. G. Fernald, B. M. Herman, and J. A. Reagan, Determination of Aerosol Height Distribu-

tion by Lidar, J. Appl. Meteorol., 11 (1972), pp. 482–489.

[23] D. J. Gambling and K. Bartusek, Lidar Observation of Tropospheric Aerosols, Atmos. Environ.,

6 (1972), pp. 181–189.

[24] P. L. Ghia, The Compact 3ToT as SD Physics Trigger for Vertical θ < 60◦ Showers, GAP Note

2004-018.

[25] N. Hayashida et al., Muons (¿1 GeV) in Large Extensive Air Showers of Energies Between 1016.5

eV and 1019.5 eV Observed at Akeno, Journal of Physics G: Nuclear and Particle Physics, 21 (1995),

pp. 1101–1119.

BIBLIOGRAPHY 159

[26] G. Henry, G. Pelletier, P. O. Petrucci, and N. Renaud, Active Galactic Nuclei as High

Energy Engines, Astropart. Phys., 11 (1999), pp. 347–356.

[27] A. M. Hillas, The Origin of Ultra-High-Energy Cosmic Rays, Ann. Rev. Astron. Astrophys., 22

(1984), pp. 425–444.

[28] M. Kachelrieß, P. D. Serpico, and M. Teshima, The Galactic Magnetic Field as Spectrograph

for Ultra-High Energy Cosmic Rays, Astropart. Phys., 26 (2007), pp. 378–386.

[29] F. Kakimoto et al., A Measurement of the Air Fluorescence Yield, Nucl. Instr. Meth. A, 372

(1996), pp. 527–533.

[30] B. Keilhauer et al., Molecular atmosphere profiles for malargue, GAP Note 2005-021.

[31] , Impact of Varying Atmospheric Profiles on Extensive Air Shower Observation: Fluorescence

Light Emission and Energy Reconstruction, Astroparticle Physics, 25 (2006), pp. 259–268.

[32] J. Klett, Stable Analytical Inversion Solution for Processing Lidar Returns, Appl. Optics, 20

(1981), p. 211.

[33] J. D. Klett, Stable Inversion with Variable Backscatter/Extinction Ratios, Appl. Opt., 20 (1985),

pp. 211–220.

[34] V. A. Kovalev, Lidar Measurement of the Vertical Aerosol Extinction Profiles with Range Depen-

dent Backscatter-to-Extinction Ratios, Appl. Opt., 32 (1993), pp. 6053–6065.

[35] , Sensitivity of the Lidar Equation Solution to Errors in the Aerosol Backscatter-to-Extinction

Ratio: Influence of a Monotonic Change in the Aerosol Extinction Coefficient, Appl. Opt., 34 (1995),

pp. 3457–3462.

[36] V. A. Kovalev, G. N. Baldenkov, and V. I. Kozintev, Relationship Between Total Scattering

and Backscattering in the Atmosphere, Bull. Acad. Sci. U.S.S.R., Geoph. Ser., (1987), pp. 611–615.

[37] V. A. Kovalev and W. E. Eichinger, Elastic Lidar. Theory, Practice, and Analysis Methods,

Wiley ed., 2004, pp. 144–152.

[38] J. Kraus, A Strange Radiation from Above, Cosmic Search, 2 (1980), p. 20.

[39] M. A. Lawrence, R. J. O. Reid, and A. A. Watson, The Cosmic Ray Energy Spectrum Above

4 · 1017 eV as Measured by the Haverah Park Array, Journal of Physics G: Nuclear and Particle

Physics, 17 (1991), pp. 733–757.

160 BIBLIOGRAPHY

[40] G. Lefeuvre et al., Absolute Measurement of the Nitrogen Fluorescence Yield in Air between 300

and 430 nm, Nucl. Instr. Meth. A, 578 (2007), pp. 78–87.

[41] J. Linsley, L. Scarsi, and B. Rossi, Extremely Energetic Cosmic-Ray Event, Phys. Rev. Lett.,

6 (1961), pp. 485–487.

[42] J. Mattews and R. Clay, Atmospheric Monitoring for the Auger Fluorescence Detector, GAP

Note 2001-029.

[43] B. Mielke, Analog + photon counting, http://www.licel.com/analogpc.pdf.

[44] MySQL AB, Official website, http://www.mysql.com.

[45] C. A. Norman, D. B. Melrose, and A. Achterberg, The Origin of Cosmic Rays above 1018

eV, As. J., 454 (1995), pp. 60–68.

[46] S. Ostapchenko, QGSJET-II: Results for Extensive Air Showers, Nuclear Physics B (Proceedings

Supplements), 151 (2006), pp. 147–150.

[47] Photonics Industries International, Inc., Official website, http://www.photonix.com.

[48] J. Rautenberg et al. (for the Pierre Auger Collaboration), Online Monitoring of the

Pierre Auger Observatory, in Proc. 30th Int. Cosmic Ray Conference, Merida, Mexico, (2007).

[49] F. Salamida and S. Petrera, An End-to-end Calculation of the Auger Hybrid Exposure, GAP

Note 2007-002.

[50] G. Sequeiros, Lidar Technique for Atmospheric Monitoring in the Pierre Auger Observatory, PhD

thesis, 2006.

[51] T. Stanev, High Energy Cosmic Rays, Springer ed., 2004, pp. 225–231.

[52] M. Takeda et al., Energy Determination in the Akeno Giant Air Shower Array Experiment,

Astropart. Phys., 19 (2003), pp. 447–462.

[53] P. G. Tinyakov and I. I. Tkachev, Deflections of Cosmic Rays in a Random Component of the

Galactic Magnetic Field, Astropart. Phys., 24 (2005), pp. 32–43.

[54] P. Travnıcek et al. (for the Pierre Auger Collaboration), New Method for Atmospheric

Calibration at the Pierre Auger Observatory Using FRAM, a Robotic Astronomic Telescope, in Proc.

30th Int. Cosmic Ray Conference, Merida, Mexico, (2007).

[55] Trolltech, Qt 3.3 White paper, http://www.trolltech.com.

BIBLIOGRAPHY 161

[56] L. Valore, M. Ambrosio, C. Aramo, D. D’Urso, and F. Guarino, CLF Data Analysis:

Measurement of the Aerosol Concentration and Comparison with other Analyses, GAP Note 2007-

56.

[57] E. Visbal, S. BenZvi, B. M. Connolly, J. Matthews, M. Prouza, and S. Westerhoff,

First Analysis of Signals from the Auger APF Light Sources, GAP Note 2006-083.

[58] E. Waxman, Gamma-Ray Bursts: Potential Sources of Ultra High Energy Cosmic-Rays, Nucl.

Phys. B (Proc. Suppl.), 151 (2006), pp. 46–53.

[59] J. A. Weinmann, Derivation of Atmospheric Extinction Profiles and Wind Speed over the Ocean

from a Satellite-Borne Lidar, Appl. Opt., 27 (1988), pp. 3994–4001.

[60] M. M. Winn, J. Ulrichs, L. S. Peak, C. B. A. McCusker, and L. Horton, The Cosmic-Ray

Energy Spectrum Above 1017 eV, Journal of Physics G: Nuclear Physics, 12 (1986), pp. 653–674.

[61] Y.Sasano, H. Shimizu, N. Takeuchi, and M. Okuda, Geometrical Form Factor in the Laser

Radar Equation: an Experimental Determination, Applied Optics, 18 (1979), pp. 3908–3910.

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