Download Modeling a dual mirror Cherenkov telescope to analyse pointing

VU University Amsterdam
MSc Physics
Particle and Astroparticle Physics
Master Thesis
Modeling a dual mirror Cherenkov
telescope to analyse pointing precision
by
Gijsbert Tijsseling
1853562
August 2014
Supervisor:
Dr. David Berge
Daily Supervisor:
Arnim Balzer
Examiner:
Dr. Jacco Vink
Abstract
Modeling a dual mirror Cherenkov telescope to analyse pointing precision
by Gijsbert Tijsseling
The Cherenkov Telescope Array (CTA) is a fourth generation Imaging Atmospheric
Cherenkov Technique (IACT) telescope array currently in its prototyping phase. As
demonstrated by current experiments, such as H.E.S.S. or MAGIC, the IACT has enormous potential. CTA will succeed its predecessors in every aspect, e.g. energy range,
sensitivity, field of view or angular resolution. The array will include telescopes of three
different sizes. The Small Sized Telescope (SST) will assure an unrivalled coverage of the
high energy part of the electromagnetic spectrum (from 1 Tev to above 100 TeV). The
GATE CHEC Telescope (GCT) will use a dual mirror design to ensure low costs and a
large field of view (∼9◦ ) of the Cherenkov camera. The dual mirror design requires a
new pointing method for these type of telescopes which is currently under development.
Pointing refers to targeting a location in the sky as precise as possible. By using the
Cherenkov camera to measure starlight directly and compare the resulting images to
known star charts, a pointing precision below the required 7 arcseconds RMS can be
obtained. Extensive MonteCarlo simulations of the point spread function (PSF) and the
camera electronics are used to verify that the required precision can be achieved. This
includes various PSF models, multiple star fitting and the effect of the Earth’s rotation
during the fit. Results show that a PSF approximated by a Gaussian is not sufficient to
obtain the required precision and a more accurate PSF model is required. Preliminary
results of multiple star fitting look promising and show a precision of 12-13 arcseconds
RMS.
Contents
Abstract
i
Contents
ii
Introduction
1
1 Gamma Ray Astronomy
1.1 Cosmic Rays . . . . . . . . .
1.2 Gamma Rays . . . . . . . . .
1.3 Sources of Gamma Rays . . .
1.3.1 Supernova Remnants .
1.3.2 Pulsars . . . . . . . .
1.3.3 Galactic Centre . . . .
1.3.4 Active Galactic Nuclei
1.3.5 Galaxy Clusters . . .
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3
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2 Cherenkov Telescopes
2.1 Extensive Air Showers . . . . . . . . . . . .
2.1.1 Particle Showers . . . . . . . . . . .
2.1.2 Cherenkov Emission . . . . . . . . .
2.2 Imaging Atmospheric Cherenkov Technique
2.3 Current Experiments . . . . . . . . . . . . .
2.4 Cherenkov Telescope Array . . . . . . . . .
2.5 CTA SST . . . . . . . . . . . . . . . . . . .
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11
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3 Camera and Electronics
3.1 CHEC . . . . . . . . .
3.2 Electronics . . . . . .
3.3 ADC Slow Readout . .
3.4 Lab Setup . . . . . . .
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4 Pointing
4.1 Current Pointing Method . . . . . . .
4.2 Sources of Pointing Deviation . . . . .
4.2.1 Tracking Deviation . . . . . . .
4.2.2 Deformation of the Structure .
4.2.3 Inelastic Deformations . . . . .
4.2.4 Inaccuracies of Image Analysis
4.3 Dual Mirror Pointing . . . . . . . . . .
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5 MonteCarlo Simulations
35
5.1 Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
5.1.1 Telescope and Camera . . . . . . . . . . . . . . . . . . . . . . . . . 35
ii
iii
5.2
5.3
5.4
5.5
5.6
5.7
5.1.2 Starlight and NSB . . . . . . .
RooFit . . . . . . . . . . . . . . . . . .
Point Spread Function . . . . . . . . .
5.3.1 PSF of the H.E.S.S. Telescope
5.3.2 PSF Simulations for the GCT .
Moving a Star over the Camera . . . .
Rotation of the Earth . . . . . . . . .
Multiple Star Fitting . . . . . . . . . .
Discussion . . . . . . . . . . . . . . . .
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36
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49
Summary
51
Acknowledgements
52
Bibliography
53
Introduction
Astronomy is one of the first of the natural sciences. It can be traced all the way back
to the beginning of civilization. Artefacts have been found from the ancient Chinese,
Greeks and Babylonians describing observations of objects visible with the naked eye.
In these ancient times astronomy was used for counting days and creating calendars.
However, astronomy went through a revolution when the telescope was invented. Thanks
to this invention scientist were able to investigate weak sources, visible in the optical,
and astronomy could be used for astrometry and celestial navigation. After this big step
things moved quickly. New techniques were developed to research other parts of the
electromagnetic spectrum and we were able to learn about the Universe.
One of the most recent fields of interest is gamma-ray astronomy. This field focuses
on the upper end of the electromagnetic spectrum. Gamma-ray astronomy is strongly
connected to cosmic rays. Cosmic ray particles arrival directions are isotropic due to
their charged nature and interstellar magnetic fields which makes it impossible to identify
their source. Gamma rays, however, are not disturbed by deflection and can be traced
back in a straight line to their source of origin.
Cosmic rays were discovered in 1912 when Victor Hess observed that ionisation rates
increased with altitude [1] while the opposite was expected. The measurements were
done with balloon experiments carrying electrometers to an height up to 5300 meters.
He reported ”The results of my observation are best explained by the assumption that
a radiation of very great penetrating power enters our atmosphere from above.” Hess
could even discard the Sun as a possible source by comparing balloon flights at different
times during the day and throughout a solar eclipse. In 1936, Hess received the Nobel
Price in Physics for his research and this discovery. In 1920, Robbert Millikan referred,
for the first time, to this radiation from outer space as cosmic rays.
From the first discovery, scientist showed great interest in cosmic rays. Many more
experiments followed to investigate their nature and origin. After balloons, also satellite
and ground-based experiments were initiated to perform more in-depth research. In
parallel, there are initiatives focusing more on cosmic gamma ray detection. In 2004 the
H.E.S.S experiment was the first ground-based experiment to spatially resolve a source
of cosmic gamma rays [2]. There is still much to discover and improve in gamma-ray
astronomy and this is the motivation for CTA [3]. The CTA project is an initiative to
build the next generation ground-based very high energy (VHE) gamma-ray instrument.
By surpassing all current Cherenkov telescope experiments in sensitivity and precision,
1
2
it will provide a deep insight into the non-thermal high-energy universe and the origin
of cosmic rays.
To obtain the most accurate physics results, the true direction of the telescope must be
known as precise as possible. The systematic uncertainty CTA wishes to ascertain is
below 7 arcseconds for the position of a point like sources. This work will investigate a
newly proposed pointing method for the SST-2M telescope by performing MonteCarlo
simulation. Different models are tested to examine if the required 7 arcseconds can be
achieved.
Chapter 1
Gamma Ray Astronomy
Gamma-ray astronomy is an exceptional field in astronomy. By observing the universe
in one of the highest energy ranges (up to PeV) we can detect the most extreme events
occurring. At this moment, about 170 gamma ray sources have been detected1 . Objects
like stars produce radiation through thermal processes and the amount and energy of
this radiation is given by temperature. The most energetic radiation produced thermally
by extreme hot objects is about 10 keV. Radiation produced with more energy cannot
originate from these objects and must have another origin and production process. This
significant amount of gamma-ray flux is created by non-thermal processes such as cosmic
charged particle acceleration. As the flux is very low for these high energy photons, a
specialized detection method is required to observe gamma-ray sources.
1.1
Cosmic Rays
After the discovery of the cosmic rays by Hess, many experiments have analysed and
investigated this extraterrestrial radiation to determine its origin and composition. The
main components are protons, they make up 85% of all cosmic rays. Followed by 12% of
alpha particles and 1% of heavier elements and 2% electrons. Remarkable is the matter
antimatter ratio. Only 0.01% of the cosmic rays consist of antimatter [4]. This is an
indication for the matter-antimatter asymmetry in the Universe.
Figure 1.1 shows the energy spectrum of cosmic rays. The spectrum looks remarkably
featureless. To enhance the feutures, the spectrum is multiplied with E 2.5 . The spectrum
can mostly be described as a power law
dN
∼ E −γ
dE
(1.1)
The γ in Equation 1.1 represents the spectral index and is approximately 2.7. The power
spectrum shows two features. One at an energy of 3 − 4 · 1015 eV the spectrum steepens
to an index of γ ' 3. This is called the knee [5]. The second feature can be seen at
an energy of 3 · 1018 eV and is called the ankle. At 5 · 1019 the spectrum reaches the
1
See http://tevcat.uchicago.edu/ for all gamma ray sources
3
Chapter 1. Gamma Ray Astronomy
4
Greisen-Zatsepin-Kuzmin limit (GZK limit) [6]. This is the theoretical upper limit on
cosmic ray energy. The limit arises from protons interacting with the cosmic microwave
background (CMB). The mean free path is in the order of 50 Mpc. The knee indicates
the energy range where the galactic magnetic field cannot longer contain the energetic
cosmic rays and they diffuse out of the galaxy. A transition area follows between galactic
and extra-galactic cosmic ray particles. From the ankle is the extra-galactic particles will
dominate the energy spectrum. Cosmic ray particles with energies above the GZK limit
are unable to reach earth unless they originate from sources within ∼50 Mpc. However,
particles at these extreme high energies are sparse, resulting in limiting statistics and
inconclusive results.
The acceleration mechanisms of charged cosmic rays are still a subject of discussion. The
acceleration process of low energy particles can be explained by varying magnetic fields2 .
These magnetic fields are already present in normal stars and can accelerate particles
up to energies of 1011 eV. Acceleration of charged cosmic rays over 1011 eV require very
powerful magnetic fields which are present in extreme objects such as pulsars. One of
the most popular high energy acceleration model is Fermi acceleration [7]. The model
describes how particles can be accelerated by reflecting of a moving plasma cloud or
”magnetic mirror” (second order Fermi acceleration). This was later adapted for a
shock front model where particles would cross the shock front multiple times (first order
Fermi acceleration) [8].
1.2
Gamma Rays
Gamma-rays are electromagnetic radiation on the top end of the electromagnetic spectrum. See Figure 1.2. Photons with an energy over 100 keV are classified as gamma
rays. Gamma rays cover a wide energy range (from kev to beyond PeV) and are divided
in different sub ranges according to energy and their interaction qualities. A division,
including the primary detection method, is given by [10] as following:
• Low energy (LE) gamma rays. All gamma rays below an energy of 30 MeV are
qualified as LE gamma rays. Detecting LE gamma rays is done via Compton
scattering.
• High energy (HE) gamma rays. Photons between 30 MeV and 30 GeV. These
gamma rays are typically detected with satellite or balloon detectors
• Very high energy (VHE) gamma rays. Photons between 30 GeV and 30 TeV. VHE
gamma rays are best detected with Cherenkov telescopes.
2
∇ × E = −δB/δt
Chapter 1. Gamma Ray Astronomy
Figure 1.1: Cosmic ray energy spectrum from various experiments. Image shows the
so called knee, ankle and GZK region. The spectrum is scaled with E2.5 . Image from
[9].
Figure 1.2: The electromagnetic spectrum. Gamma-rays have the shortest wavelengths and highest frequency. Image from http://planck.caltech.edu/
5
Chapter 1. Gamma Ray Astronomy
6
• Ultra high energy (UHE) gamma rays. Photons between 30 TeV and 30 PeV. Best
detected by air shower arrays.
• Extremely high energy (EHE) gamma rays. All photons with an energy above 30
PeV. The EHE gamma rays are limited by the GZK cutoff and are only detectible
from sources within our own galaxy.
This work is focused on Cherenkov telescopes and will thus primarily be concerned with
VHE gamma rays
1.3
Sources of Gamma Rays
As described in Section 1.2, gamma rays cover a large energy range and will originate
from many different sources. A few of the sources capable of accelerating cosmic rays to
these energies will be described below.
1.3.1
Supernova Remnants
A Supernova is an extremely bright explosion of a massive star at the end of its life or of
a white dwarf exceeding the Chandrasekhar limit [11]. If a massive star runs out of fuel it
will undergo a core collapse causing a supernova from pair instability, the core exceeding
the Chandrasekhar limit, or photo disintegration [12]. At this moment, the core cannot
support itself as gravity exceeds the counter force of electron degeneracy pressure. The
core will collapse faster as heavy ions disintegrate but will eventually be stopped by the
neutron degeneracy pressure. The remaining matter will collapse on this incompressible
core and create an outgoing shockwave with energies of the order of 1041 joules [13].
This shock wave will expand and come in contact with the interstellar medium, forming
a forward shock front compressing and heating the interstellar medium. The interaction
of the shockwave also creates a reverse shock moving back into the supernova ejecta.
This compressed supernova ejecta is known as the supernova remnant. In the shock
fronts, particles are accelerated and create gamma radiation in the process.
The first direct evidence of SNRs accelerating cosmic particles is provided by observations of the Fermi LAT [14]. Figure 1.3 shows an image of the supernova remnant RX
J1713.7 and a schematic view of the shock wave.
Chapter 1. Gamma Ray Astronomy
7
Figure 1.3: TeV image of SNR RX J1713.7 (left). Image from [2]. And a schematic
view of shock wave from a SNR (Right). Image from http://astronomy.swin.edu.au.
1.3.2
Pulsars
After a supernova, as described above, there is a high possibility that the remaining core
will be a neutron star. A neutron star is a stellar
remnant that is formed due to a gravitational collapse. When the core exceeds the Chandrasekhar
limit, gravity overcomes electron degeneracy pressure causing the core to collapse even further. An
extreme compact object is left that is only supported by the neutron degeneracy pressure. The
radius decreases from ∼109 m of a star to ∼104 m
of a neutron star. Due to conservation of angular
momentum and magnetic flux the rotational period
of these objects is between a few milliseconds and
seconds and the magnetic field is in the range from
Figure 1.4:
A schematic view
0.1 T to 109 T. For pulsars, the magnetic axis is of a pulsar showing the magnetic
not aligned with the rotational axis. Electromagnetic radiation is emitted along the magnetic axis
field lines, the rotational axis and
the magnetic axis.
Image from
http://homepages.spa.umn.edu/
and this misalignment between rotational and magnetic axis causes the periodic flux variations, the so called lighthouse effect. See Figure
1.4 for a schematic view of a pulsar. Due to the rapid rotation there is also a strong
electric field capable of accelerating particles. As pulsars will mostly emit electrons and
positrons the gamma rays that are observed are most likely produced as synchrotron
radiation [15].
Chapter 1. Gamma Ray Astronomy
1.3.3
8
Galactic Centre
The galactic centre refers to the centre of our own galaxy. It is impossible to study the
galactic centre in visible light due to absorption by interstellar dust. However, the dust
becomes transparent for certain wavelengths such as radio and gamma rays. Figure 1.5
is an image of the galactic centre in radio. This area is also bright in gamma radiation
but it was unclear where this exactly originates from. By studying images in different
wavelengths there are a few potential sources emitting gamma-rays from (nearby) the
galactic centre:
• SGR A∗ : The super massive accreting black hole at the centre of our galaxy [16]
• SGR A East: a supernova remnant [17]
• G359.95 − 0.04: An energetic pulsar candidate [18]
• Dark matter: Gamma-rays due to dark matter self annihilation [19]
By increasing angular resolution and pointing precision the H.E.S.S. experiment was
able to exclude SGR A east. However, G359.95 − 0.04 and SGR A∗ are still compelling
candidates [20].
Figure 1.5: 90 cm VLA radio flux density map of the galactic center. The white
square shows the position of the SNR Sgr A East, the pulsar G359.950.04 is given by
the black triangle and Sgr A∗ is indicated by the intersection of the black lines. A and
B mark the positions of the maximum of the radio. The inner white circle denotes the
68% coincidence level of the gamma ray source, the white and black dashed line stands
for the 95% confidence level. Image from [20].
Chapter 1. Gamma Ray Astronomy
1.3.4
9
Active Galactic Nuclei
The universe is abundant with galaxies. Estimates run up to 170 billion in the observable universe [21]. Most of these galaxies contain at least one super massive black hole
at their center. These super masive black holes accumulate great amounts of matter via
accretion. In about 10% of the galaxies the accretion disk and jet forming will be so
luminous that they outshine the entire galaxy. Galactic Nuclei with this property are
called Active Galactic Nuclei (AGN). The intrinsic properties of AGN are high luminosity, variation of luminosity and primarily non-thermal emission in all wavelengths.
AGN are divided in subclasses according to their spectral properties. These subclasses,
however, are not per se identified with different objects but rather with the viewing angle of the object. Figure 1.6 shows a schematic view of the unified AGN model. ”Radio
quiet” AGN are divided in Seyfert 1 and Seyfert 2 AGN. These are, however, not interesting for VHE gamma-ray astronomy. About one out of ten AGN is ”radio-loud”. The
main characteristic of these AGN is the observable jet perpendicular to the accretion
disk. These jets contain shock fronts that can produce the detected VHE gamma rays.
Radio-loud AGN are devided into two types called ”Fanaroff-Riley Galaxies” type one
and type two (FR I and FR II) depending on the jet shape. If the jet is orientated along
the line of sight, the AGN is called a ”blazar”. Again a division is made here between
BL lac object and flat-spectrum radio quasars (FSRQ). BL lac objects have low emission peaks and high synchrotron frequencies ranging from infra-red to soft x-ray where
FSRQ have strong emission lines and low synchrotron frequency peaks. Apart from a
few exceptions, all AGN VHE-gamma ray sources are blazars. For a complete review of
all AGN subclasses and properties is given by [22].
AGN are very interesting as they are highly powerful particle accelerators and can be
used to study the intergalactic background photon field. Gamma-rays, while traversing
great distances, can interact with the photon field and undergo pair production (e+ /e− )
thus softening the observed spectrum [23].
1.3.5
Galaxy Clusters
The largest structures that are gravitational bound together in the Universe are galaxy
clusters. These clusters can consist from tens of galaxies up to thousands. By observing
non-thermal diffuse radio emission, galaxy clusters are found to be potential sources of
particle acceleration. Galaxy clusters are thought to be composed out of three main
components:
Chapter 1. Gamma Ray Astronomy
10
Figure 1.6: Schematic of the unified Active Galactic Nuclei model [22]. The classification depends on the viewing angle. Image from M. Menzel.
• Galaxies: In the visible spectrum only galaxies are observable. The mass fraction
of these galaxies is 1% in a galaxy clusters.
• Warm-hot intergalactic medium (WHIM): A plasma between galaxies of high temperature (KeV). The mass fraction of WHIM is 9% in a galaxy clusters.
• Dark matter(DM): Is not detected but is inferred by gravitational interactions.
The mass fraction of DM is 90% in a galaxy clusters.
Current theories predict that besides leptons, hadronic particles are present in galaxy
clusters. Here interactions with relativistic hadrons result in pions. The neutral particles
decay into gamma rays that could be observable here on Earth [24]. Also dark matter
self-annihilating can produce observable gamma rays [25].
Chapter 2
Cherenkov Telescopes
To observe gamma rays from outer space, there are different methods available. As
mentioned before, this work will focus on VHE gamma-rays. The primary detection
method here is using the atmosphere as a calorimeter and measuring the Cherenkov
light emitted by an air shower. This chapter will describe the extensive air showers, the
detection method, the current status of Cherenkov telescopes and the prospects of the
new planned facility the Cherenkov Telescope Array.
2.1
Extensive Air Showers
Whenever a cosmic ray reaches our atmosphere the particle will interact with an air
molecule and induce a particle shower of secondary particles.
2.1.1
Particle Showers
Here a distinction is made between photon (gamma-ray) induced showers and hadronic
induced showers.
Electromagnetic Showers
Showers induced by gamma rays or electrons are defined as electromagnetic cascades.
There are three main production and absorption processes within the atmosphere:
• Electron/positron (e− /e+ ) pair production by photons.
• Bremsstrahlung from electrons.
• Ionization of air molecules.
These processes dominate the longitudinal evolution of the cascade. A complete overview
is given by E. Segre [26]. The multi scattering of particles in the atmosphere determines
the lateral distribution of the shower.
11
Chapter 2. Cherenkov Telescopes
12
The number of particles in a cascade increase due to e− /e+ pair production and electron
bremsstrahlung. At the same time the energy per particles decreases. This exponential
decrease is given by Equation 2.1
X
< E >= E0 exp− Xr
(2.1)
Where < E > is the average energy per particle, E0 the initial energy of the primary
cosmic ray, X is the atmospheric depth and Xr is the characteristic radiation length.
The atmospheric depth can be written as
X(h) = X0 exp
− hh
0
(2.2)
Where h is the altitude in km, h0 = 8 km and X0 = 1013 g/cm2 . The particle shower
does not grow indefinitely. When particles reach an energy threshold, the ionization
of the atmosphere becomes a limiting factor. This energy threshold is named the critical energy Ec and for air is Ec ' 81 MeV. After decreasing to the critical energy,
absorption of particles dominates production processes and the cascade diminishes.
Heitler describes the cascade formation in
a simplified model [27]. Assuming a VHE
gamma-ray enters the atmosphere it will
initiate electron-positron pair production at
a hight around 10 km.
The electron-
positron pair are highly energetic and undergo
bremsstrahlung after a radiation length Xb .
The extremely energetic radiation generated
here will initiate pair production again after a
conversion length Xp and so on, creating a cascade of charged particles (e+ and e− ). A visual
representation of the Heitler model is given in
Figure 2.1. Here the characteristic radiation
length is
Xr ' Xp ' Xb
(2.3)
From this, the number of particles, N , in the
Figure 2.1: Heitler model of an electromagnetic cascade. Image from S. Schlenker.
cascade after n radiation lengths is given by
N = 2n
(2.4)
En = E0 2−n
(2.5)
And the energy per particle is
Chapter 2. Cherenkov Telescopes
13
The critical energy is reached after nmax radiation lengths: Enmax ' Ec . Inserting this
in Equation 2.5 and solving for nmax results in
nmax =
1
E0
ln
ln 2 Ec
(2.6)
Combining Equation 2.4 and Equation 2.6 gives the maximum number of particles in a
shower
Nmax '
E0
Ec
(2.7)
With the maximum of this shower at
Xmax = nmax · Xr =
Xr
E0
ln
ln 2 Ec
(2.8)
Hadronic Showers
Hadronic particles will experience weak and strong interactions. Their longitudinal development is determined by the nuclear interaction length λ . In most cases λ Xr and
they have large lateral momentum during strong interactions so the showers are longer
and wider than purely electromagnetic cascades.
Figure 2.2
shows a sketch of a hadronic
particle shower.
The develop-
ment process of hadronic showers is different than that of electromagnetic cascades.
The de-
velopment process is dependent
of hadron production, pion decay, de-excitation and muon decay. Pions cause the big lateral
spread as they obtain large hor-
Figure 2.2: Hadronic particle cascade. Image from M.
Hemberger.
izontal momentum. Charged pions decay into muons and neutrinos while π 0 decaying in hadronic showers create electromagnetic sub-cascades. Cherenkov light produced by these cascades can also be
measured with a Cherenkov camera. Figure 2.3 shows a MonteCarlo simulation of the
lateral development of an electromagnetic cascade and one of hadronic origin.
Chapter 2. Cherenkov Telescopes
14
Figure 2.3: The difference between a gamma ray and proton induced air shower.
Image from [28].
2.1.2
Cherenkov Emission
As the charged particles are extremely energetic, they can travel with a velocity higher
than the local velocity of light in the atmosphere (cair = c/nair ' 0.9997c). When this
happens, the charged particle will produce Cherenkov radiation [29]. A shockfront of light is emitted comparable to a
sonic boom.
See Figure 2.4 for a geo-
metric model of the shape and production of the Cherenkov radiation. Here a
particle travels with the velocity vp where
c
n
< vp < c with c being the velocity of
light in vacuum and n the refractive index of the medium. β is defined as β =
vp
c .
The path travelled in some time t by the
particle is given by βct and the produced
Cherenkov light is restricted to traverse a
distance of
c
n t.
Figure 2.4: Geometric model of Cherenkov radiation. Image from A. Horvath.
Due to geometric reasons
it is possible to calculate the openings angle of the created Cherenkov cone. This gives
Chapter 2. Cherenkov Telescopes
1
βn . For gamma-ray induced Cherenkov emission the opening
1◦ . This results in a ground area illuminated by Cherenkov light
15
cos θ =
angle is typical
about
with a radius in
the order of one hundred meters.
Figure 2.5: Simulated Cherenkov light pool of a shower from a primary gamma
ray(left) and proton (right). Image from K. Bernlöhr.
Figure 2.5 shows the difference between the Cherenkov light pool of a high energy photon
induced air shower and that of a proton. The cascade induced by the photon produces
an almost symmetric circle where the emission of the proton induced cascade clearly
shows the effect of the electromagnetic sub-cascades.
Cherenkov radiaton is different than typical emission spectra in the sense that it is a
continuous spectrum without any characteristic peaks. The emitted energy dE per unit
length and per unit of angular frequency(dxdω) is given by the Frank-Tamm Equation
[30]
dE =
c2
q2
µ(ω)ω(1 − 2 2
)dxdω
4π
v n (ω)
(2.9)
Where the particle has an electric charge of q, µ(ω) is the frequency dependent permeability, n(ω) is the frequency dependent refraction index of the medium, v is the speed
of the particle and c the speed of light in vacuum.
The spectrum of Cherenkov radiation has a maximum in the ultraviolet but due to
absorption and different forms of scattering in the atmosphere, the spectrum peaks at
around 330 nm and has a cut-off at about 200 nm. See Figure 2.6
Chapter 2. Cherenkov Telescopes
16
Figure 2.6: Differential spectrum of Cherenkov radiation at an altitide of 10 km and
dN 2
2 km. dxdλ
is given in arbitrary units. Image from W. Wilhelmi.
2.2
Imaging Atmospheric Cherenkov Technique
Ground based Cherenkov telescopes employ the Imaging Atmospheric Cherenkov Technique or IACT to detect gamma-rays by the Cherenkov light of the electromagnetic
cascade. Cherenkov images are analysed to answer three main question about cosmic
rays:
• What kind of particle was it?
• What was the energy?
• Where did the cosmic ray come from?
The flux of VHE gamma-rays drops to such an extent that space-based detectors become
insufficient in detecting gamma-rays due to their small collection area (∼m2 ). The
difference with IACT telescopes is that the Earth’s atmosphere is used as a calorimeter.
This results in a collection area of ∼0.2 km2 . This allows IACT telescopes to observe
VHE gamma-rays.
To measure the Cherenkov light, Cherenkov cameras are used. These cameras are built
up out of sensitive photon multipliers. With an intensity in the order of only 100
photons/m2 , depending on the energy of the gamma-ray and the altitude of the detection site, the Cherenkov emission is very faint. This requires a larger collection area
than just the focal plane of the Cherenkov camera. Therefore, large mirror structures
are used to focus the light on the camera. Figure 2.7 shows the main elements of an
air shower emitting Cherenkov light and the telescope for imaging. The telescope is
directed towards gamma ray source. The primary gamma-ray starts an air shower emitting Cherenkov light. This light is reflected and focused by the telescope’s mirror onto
the focal plane. As the shower develops, the produced Cherenkov light will arrive with
Chapter 2. Cherenkov Telescopes
17
Figure 2.7: Images representing an air shower emitting Cherenkov light and the
telescope for imaging. Image from S. Schlenker
different angles. This can be seen in the camera image. Longitudinal and lateral development of the shower will thus determine the image shape. For gamma-rays this
resembles an ellipse. Figure 2.8 shows a typical image of Cherenkov light induced by a
gamma-ray and a muon as seen by a Cherenkov camera.
The analyses of the images is based on the Hillas parameters. M. Hillas proposed
to define the image with only a few parameters [31]. See Figure 2.9 for a graphical
representation of the Hillas parameters. The assumption is that a shower image can
be parametrized by an ellipse. By analysing the width and length, the longitudinal
and lateral shower development can be deducted. The intensity of the ellipse gives
a measurement for the energy of the cosmic ray. The geometry of the shower can be
reconstructed by analysing the centre of gravity (maximum intensity) and the orientation
angle (Θ). By using this information a separation can be made between gamma-rays
and hadrons.
Chapter 2. Cherenkov Telescopes
18
Figure 2.8: Typical images of air showers as seen by the H.E.S.S. camera. With on
the left an image of a Moun and on the right a Gamma ray. Image from the H.E.S.S.
collaboration
Figure 2.9: Definition of the Hillas parameters. Image from [32].
In current experiments multiple Cherenkov telescopes work together (stereoscopic system) [33]. This is advantageous as this will increase sensitivity. A larger mirror area will
collect more photons. Furthermore, by using a central trigger system it is possible to
reject muons and local night sky background that would have triggered one telescope.
With less triggers the dead time is also reduced. In addition, stereoscopic systems have
an enhanced angular resolution by viewing the shower from various angles .
2.3
Current Experiments
At present, there are three IACT arrays operational. MAGIC [34], H.E.S.S. [35] and
VERITAS [36]. See table 2.1 for the details of the telescopes.
The MAGIC telescope array is located on La Palma, the VERITAS array in Arizona and
the H.E.S.S. experiment in Namibia. These Cherenkov telescopes have greatly improved
Chapter 2. Cherenkov Telescopes
Telescope
MAGIC
VERITAS
H.E.S.S.
Number of telescopes
2
4
5
19
Energy range
25 GeV - 30 TeV
50 GeV - 50 TeV
30 GeV - 100 TeV
Field of view
3.5◦
3.5◦
3.2◦ − 5.0◦
Angular resolution
0.08◦ − 0.17◦
0.1◦ − 0.14◦
0.08◦ − 0.14◦
Table 2.1: Details of current Cherenkov telescopes
specification
Mirror diameter
Energy range
Number of telescopes
LST
23m
10 - 500 GeV
4
MST
12m
0.1 - 10 TeV
20
SST
4m
1 - 300 TeV
70
Table 2.2: Details of the three different CTA telescopes. The number of telescopes is
for the southern array.
ground based gamma-ray astronomy. This lead to the discovery of many new gammaray sources and the ability to spatially resolve extended sources [2]. These discoveries
broadened our knowledge of cosmic non-thermal processes. However, there are still many
phenomena unexplained. To get a better understanding of the extreme processes in our
universe and explore different wavelengths there is a need for a higher precision and a
larger energy range. This will be realized with the Cherenkov Telescope Array
2.4
Cherenkov Telescope Array
The Cherenkov Telescope Array1 (CTA) is a planned facility of next generation Cherenkov
telescopes for measuring gamma-rays from space. CTA is a large collaboration (28 contributing nations and over 1000 scientists)and will serve as the first open observatory
in VHE gamma-ray astronomy. CTA will improve the sensitivity and the energy range
by an order of magnitude in comparison with current Cherenkov telescopes. Figure
2.10 shows this prospects and the comparison to the current gamma-ray telescopes. To
achieve the required energy range and sensitivity three different telescope types are under development. The Large Size Telescope (LST) [37], Medium Size Telescope (MST)
[38] and the Small Size Telescope (SST) [39]. See table 2.2 for some of the details2 . The
LSTs are needed for the lower energy range. As lower energy gamma rays produce a
smaller shower and thus less Cherenkov light a large collection area is needed. However,
the gamma-ray flux is higher so a smaller effective area can be used. For the gamma
rays in the medium energy range a smaller mirrors can be used. This reduces costs so
more MSTs can be build to cover a larger effective area. Finally the SSTs can be build
very small and in great numbers. Section 2.5 will discuss the SST in more detail.
1
2
http://www.cta-observatory.org/
As stated in the TDR document of May 2014.
Chapter 2. Cherenkov Telescopes
20
Figure 2.10: Sensitivity and energy range of CTA compared to the current telescopes.
Image from http://cerncourier.com/.
CTA will be build on two different sites. One on the Northern hemisphere, mostly for
extragalactic science, and one on the Southern hemisphere mostly for galactic science.
Candidates for the Northern site are Mexico, Arizona and Tenerife. For the Southern
site this is Chile and Namibia.
2.5
CTA SST
As mentioned above, CTA will be build with three different sized telescopes. The LST,
MST and SST. Most of the telescopes will be SSTs. This is possible as these are the
smallest and thus cheaper in construction. The SSTs will have a diameter of ∼4 m
and due to their large numbers they will give an unrivalled coverage of the universe in
gamma-rays from 1 TeV up to 300 TeV. As the flux of these high energy gamma rays
is very small, it is necessary to cover a large area to detect sufficient gamma rays. This
cannot be done by distributing a few telescopes over a large area. This is because every
shower induced by a gamma ray needs to be detected by multiple telescopes so photon
energy and direction can be reconstructed. This requires the great number of SSTs.
MonteCarlo studies show an optimal separation distance of 250 m [40].
The small sized telescope will be build in different models and this work is focused on
the GATE CHEC Telescope (GCT). This is a collaboration between the GAmma-ray
Chapter 2. Cherenkov Telescopes
21
Telescope Elements (GATE) and CHEC continuing under the name of the GATE CHEC
Telescope. The GATE collaboration will provide the dual mirror telescope structure and
CHEC will provide the Cherenkov camera. Figure 2.11 is a sketch of the GCT telescope.
Figure 2.11: Sketch of the GATE CHEC Telescope. Image from the SST Technical
Design Report May 2014.
The main difference with respect to standard Cherenkov telescopes is that the GCT is a
Schwarzschild-Couder dual mirror telescope. The dual mirror system will reduce plate
scale and allow for a large field of view (∼9◦ ) with a small and light weight camera which
will minimize costs.
The telescope has an altitude-azimuth mount. This allows a rotation and elevation angle
of 270◦ and 91◦ respectively. This new dual mirror system will require a new pointing
method which is described in Chapter 4.
Chapter 3
Camera and Electronics
The most complex part in building a Cherenkov telescope is the camera. The new
pointing method (as will be described in section 4.3) requires the Cherenkov camera to
be able to measure starlight. For these measurement, adjustments need to be made in the
design and electronics. Current Cherenkov cameras only require quick (∼nanosecond)
readout electronics which is not sufficient for starlight. For this, an additional readout
system is required in the order of 100 milliseconds. In the future this will be referred to
as the slow readout.
This chapter will give an overview of the camera design and the necessary adjustments
to incorporate a slow readout into the CHEC camera front end electronics.
3.1
CHEC
The Compact High Energy Camera (CHEC) is a camera development project within
CTA. The objective is to construct a Cherenkov camera for the dual mirror small sized
telescope (SST-2M). The project is a collaboration of the CTA-UK team with Dutch,
US and Japanese groups. At this moment, there ar two competing technologies for photomultipliers. For this, the collaboration will build two prototype CHEC cameras. The
first (CHEC-M) is based on multi-anode photomultipliers (MAPMs) and the second
(CHEC-S) is based on silicon photomultipliers (SiPMs). After completing the prototypes, extensive tests will conclude which one is most commendable.
The CHEC camera will have a field of view of 9◦ . The optical requirements need the
camera to have a curved focal plane. These requirements dictate a curvature radius of
1 m and a diameter of 35 cm. The focal plane will be instrumented with 32 photosensor
modules all containing 64 pixels.
The CHEC camera will provide full waveform information from every pixel. This will
allow useful information to be extracted from saturated pixels through pulse fitting.
22
Chapter 3. Camera and Electronincs
23
MAPM
The multi-anode photomultipliers is a single photon sensitive photodetector based on
current photomultiplier tube (PMT) technology. In contrast to PMTs, MAPMs can
measure the spatial distribution of intensity. The MAPM has a single photocathode
suplied with a high voltage. This is conected to multiple chains of dynodes leading to
a multi anode array. Here the dynode chain amplifies the initial photoelectrons and
preserves spatial information. A MAPM module can be seen as an array of PMTs in a
single housing with a single voltage supply. See Figure 3.1 for a schematic representation.
Figure 3.1: Schematics representation of the MAPM (left) and a schematic view of
the dynode model(right). Image from C. Joram.
For the CHEC-M prototype, 32 MAPMs of the H10966 series from Hamamatsu will form
the detector plane. The MAPM will measure 52 mm square with a photocathode area of
49 mm square. There is some space needed between the MAPMs (∼2 mm) resulting in
a maximum dead space of 5 mm. The photocathode material is bialkali and is covered
with borosilicate glass. The MAPMs have an wavelength range of 300 - 650 nm with a
peak wavelength is 400 nm. The average efficiency, taking the Cherenkov spectrum and
dead space into account, is ∼19% on-axis.
Chapter 3. Camera and Electronincs
24
SiPM
Silicon photomultipliers is a single photon appliance made from avalanche photodiodes
(ADPs) on a silicon substructure. When a photon is absorbed by silicon it can create a
electron-hole pair by freeing a valance electron and moving it to the conduction band.
By applying a reverse bias voltage, holes and electrons created in the p-n junctions
depletion region are moved towards the anode and the cathode respectively. By applying
an electric field > 5 · 105 V/cm the charge carriers gains enough kinetic energy to form
more electron-hole pairs. This will create an ionization cascade spreading through the
silicon. This process creates a measurable photocurrent and is called a Geiger discharge.
The current flow is then stopped by Quenching resistors. Finaly the bias voltage is reset
and the SiPM is ready for the next photon. See Figure 3.2 for the schematic of a SiPM
structure and of the Geiger mode.
Figure 3.2: Schematics representation of the SiPM pn structure(left) and a schematic
view of the Geiger mode. Image from http://www.sensl.com/.
SiPMs have the advantage that they require a much lower voltage suply (' 70V) than
normal PMTs. Furthermore, SiPMs have a linear dependency of gain versus supply
voltage and are almost independent of an external magnetic field. The SiPM tiles for
CHEC will also be from Hamamatsu and will be from the S12642-1616PA-50 series. The
SiPM will measure 51.4 mm square and will have 256 pixels of 3 × 3 mm2 . These will
be combined in groups of four te form 64 pixels of ' 6 × 6 mm2 for CHEC. A SiPM can
achieve a very high quantum efficiency (∼80%) but is more sensitive to cross talk and
has a temrature dependent gain.
3.2
Electronics
Figure 3.3 shows the schematics of the CHEC-M mechanical structure and TARGET
module.
Chapter 3. Camera and Electronincs
25
Figure 3.3: Schematics of the CHEC-M camera and TARGET module. Image from
[41]
• Photosensor module: CHEC-M and CHEC-S will consist of respectively 32 MAPM
or SiPM modules each housing 64 pixels. Every pixel will be ∼6 × 6 mm and this
corresponds to an angular size of ∼0.17◦ when installed on the GATE telescope
structure [41].
• Preamplifier module: The 4×16 channel pre-amplifier boards will be responsible for
the signal amplification and shaping. This will ensure an optimal camera readout
and trigger response. A low gain (∼8 × 104 ) is required for the slow readout due
to bright stars and night sky background light.
• Target module: The 4 × 16 channel TARGET module will receive the signal for
digitalisation and readout. It will also act as first level trigger.
• Backplane: The backplane will have 32 slots for all the TARGET modules. It will
provide a low voltage, triggering and route the signals from the TARGET modules
to the DACQ board.
• DACQ board: The DACQ board provides communication with the outside world
by routing data from the TARGET modules out of the camera. It will also accommodate the a central clock and event time stamping
• Mechanical structure: The camera support structure contains the cooling units
and completely encloses the camera to reject dust and moisture.
Chapter 3. Camera and Electronincs
26
The photosensors will be able to detect photoelectrons between 1 and ∼1000 within
nanoseconds. The preampliefers amplify and shape the incoming analogue signals from
the photosensor module as a full waveform. This will be shaped as best as possible for
triggering. The best shape is resolved by performing MonteCarlo simulations. Along the
preamplifiers there are 2 × 64 channels. One set for the fast readout for Cherenkov light
and one set for the slow readout. The slow readout is done via 4×16 channel multiplexers
to an ADC. The TARGET modules digitalise the amplified and shaped signal. The first
triggering will be performed here as well. This is done by summing up four pixels
bordering each other. This value is then discriminated. The signal continues to the
backplane where the camera triggering is performed. This demands two neighbouring
signals to arrive within a coincidence interval. The backplane will then route the data
to the DACQ boards. The DACQ board will output the data via fibres to a central
computer. A full description of the dataflow in the CHEC camera is given by [41].
See Figure 3.4 for the CHEC layout.
Figure 3.4: Schematics of the CHEC camera layout. Image from [41]
3.3
ADC Slow Readout
The analog-to-digital converter (ADC), for the slow readout, is designed to digitalise the
signal of the starlight readout. An ADC converts a continuous analog signal (voltage)
to a digital value. The ADC is located on the TARGET module and will receive its
signal from 4 × 16 channel multiplexers (MUX) on the pre-amp module. To measure
the performance, a test board is being developed in Leicester (See Figure 3.5). Here
Chapter 3. Camera and Electronincs
27
two multiplexers are connected to the ADC. For the communication with the outside
world (PC), a SPI interface is needed and for this a RaspberryPI1 board is used. A
RaspberryPI board is a pocket sized single board computer with an USB, Ethernet and
HDMI port. Furthermore, the board has low level peripherals in the form of a 2 × 13
pin expansion providing general input/output pins and access to SPI. By programming
a TCP/IP socket and writing a C program the test board can now be controlled by
a main PC. The program will set the MUX and read the ADC. Parameters are which
channels of the MUX should be read out, the number of samples and the time delay
between the samples. The program will then output the measurements of every channel
and display it. This can now be used to measure the level of noise and the response of
the slow readout ADC to confirm that it is working.
Figure 3.5: ADC test board in Leicester.
3.4
Lab Setup
Before constructing all GCT telescopes the camera and electronics need to be tested
thoroughly. First, all different components are tested on performance. To do this, a
lab setup is build to perform measurements in a controlled environment. Figure 3.6 is
a sketch of the lab setup currently under construction in Amsterdam. Here the normal
environment is simulated in a dark box. Two LEDs are used to simulate the night sky
1
http:/www.raspberrypi.org
Chapter 3. Camera and Electronincs
28
background and Cherenkov flashes. The light from these LEDs are combined through
a beam splitter and are diffused to create an uniform illumination. Another LED is
used to simulate starlight. This light is focused on the photomultiplier module(MAPM
or SiPM) mounted on the other side of the box. The module is connected to a preamplifier and a TARGET module. All electronic responses are closely monitored with
a LeCroy oscilloscope.
Figure 3.6: Schematics of the lab setup in Amsterdam. Courtesy of M. Bryan.
Once the test confirm the electronics comply with the requirements, a full operational
prototype will be used to continue with full field test of a complete camera.
Chapter 4
Pointing
Astronomical observations are rendered useless if it is not possible to assign an observation to a direction in the sky. Especially with gamma-ray astronomy, as the observation
time is very long, it is important to have a reproducible pointing direction.
Pointing is the ability to relate an observation to a location in the sky as precise as possible. By acquiring a high pointing precision it will be possible to expand our knowledge
on the processes of particle acceleration and cosmic ray production.
Figure 4.1: Radio image of M87 overlaid with the pointing precisions of the HEGRA
telescope system, the H.E.S.S. array and the prospect for CTA. Image adopted from
[42].
An example is given in Figure 4.1. Shown is the active galaxy M87 in radio. At the
centre is an AGN with extensive jets. As explained in Section 1.3.4 the jets are promising
regions for the acceleration of cosmic rays. The figure shows, besides the galaxy, the
pointing precision of the HEGRA telescope system (second generation IACT), the the
H.E.S.S. array (third generation IACT), and the prospects of the pointing precision of
CTA. The pointing precision for CTA will be accurate enough to really probe the jet
29
Chapter 4. Pointing
30
structure and acquire information about the origin of gamma rays in these jets. This
prospect is a grand motivation for improving pointing precision.
This chapter will give a short overview of the sources of pointing deviation. Furthermore,
it will give a description of the current pointing methods and the necessary adjustments
for the CTA SST.
4.1
Current Pointing Method
To get a better understanding of pointing, this section will describe the pointing method
based on the current implementation used by the H.E.S.S. telescopes.
The pointing method is similar to pointing methods in optical astronomy. By using
bright stars with known locations in the field of view (star locations in the Hipparcos
catalogue have an accuracy of 0.002 arcseconds [43]) it is possible to deduct the observation location in the sky. This is not possible with the current Cherenkov cameras as star
positions will be to inaccurate with the coarse photon multiplier pixels of the camera. In
addition, the readout electronics are based on nanosecond readouts for the Cherenkov
light and not on a few Hertz needed for starlight. However, by adding two additional
CCD cameras and reference LEDs to the telescope this method can still be applied.
See Figure 4.2 for a sketch of the two CCD
camera setup.
The central camera or
”LID CCD” is focused on the Cherenkov
camera. The LEDs on the edge of the
camera permit accurate measurements of
the camera position in reference to the reflected stars. Furthermore, the LID CCD
camera is used for mirror alignment and
measurements of the point spread function (PSF). The outer CCD camera or
”SKY CCD” is focused on infinity and its
purpose is to take unobstructed images of
the sky. The sky images will contain the
stars in the field of view used for pointing. The pointing deviation is defined as
the difference between a star position and Figure 4.2: Sketch of pointing setup with two
CCD cameras. Image from D. Berge
the camera centre. This is measured with
pointing runs. A pointing run is done by taking ten images with the SKY CCD camera
and two with the LID CCD. One showing the star near the centre of the camera, and
Chapter 4. Pointing
31
one with the eight positioning LEDs. During a pointing run the lid of the Cherenkov
camera must be closed. The lid is close to the focal plane so the focus changes from
10 km for the Cherenkov light to infintiy for the starlight. The LID CCD camera can
now take an image of stars in the field of view reflected on the lid. The SKY CCD
camera will take an image directly of the same part of the sky. This requires the two
CCD cameras to be perfectly aligned. This is done by mounting the CCD cameras on
the same steel beam so they are equally effected by deformations.
Figure 4.3: Mispointing of the SKY CCD camera. The stars are extracted from
the SKY CCD image and fitted to a known star chart so mispointing vector can be
constructed. Image from [32].
The points in the images taken with the SKY CCD are extracted and then fitted to the
positions of known stars in the field of view. The position and magnitude of stars can
be found in star charts from the Tycho and Hipparcos catalogue. By matching the SKY
CCD image to the star chart and comparing it to the image taken with the LID CCD
a mis-pointing vector is constructed (See Figure 4.3). This vector gives information of
the rotation and offset of the SKY CCD. The mis-pointing vector needs to be related to
the Cherenkov camera. This correlates to the offset of the image of the stars taken with
the LID CCD camera. From the LID CCD and the reference LEDs the centre of the
camera is also known and this can be related to the offset to determine the pointing of
the Cherenkov telescope. A complete review of the pointing method of H.E.S.S is given
by I. Braun [32].
Chapter 4. Pointing
4.2
32
Sources of Pointing Deviation
To understand the pointing of Cherenkov telescopes it is important to know where the
pointing deviation originate from. There are many sources contributing to ”errors”
in pointing. This section will focus on physical errors. These are errors caused by
misorientation of the whole telescope and deformations of the telescope structure itself.
Systematic erros are errors induced by the systems trying to correct for the physical
error.
4.2.1
Tracking Deviation
When tracking a source over the sky, small offsets and pointing inaccuracies will appear.
Shaft encoders are used to measure a given position. Small flaws in welds and the tracks
will cause small offsets. Systematic offsets can arise due to high velocities while tracking
objects near zenith. These shaft encoders have an accuracy in the order of one arcsecond.
4.2.2
Deformation of the Structure
The telescopes are big steel and or carbon fibre structures and cannot be seen as rigid
objects. Depending on the orientation and the altitude angle of the telescope the structure will deform due to gravity. These deformations are divided in elastic and inelastic
deformations. Elastic deformations are reproducible and are not dependent on the orientation history of the telescope. Three main parts of the telescope are affected by these
deformations:
• The mirror support structure
• The telescope masts
• The camera lid
The mirror support structure holds all the mirror facets. The masts holding the camera
are also connected to the support structure. Due to the weight of the mirror structure
and the gravitational pull on the masts the mirror facets will deform, changing the
position and shape of images on the focal plane.
The telescope masts support the Cherenkov camera. The deformation follow a cosine
function depending on the altitude of the telescope
δ(alt) = cos(alt)
(4.1)
Chapter 4. Pointing
33
Another deformation arises when opening and closing the camera lid. This operation
will shift the centre of gravity of the camera causing a small displacement of the camera
position. As pointing calibration runs are done with a closed lid and science runs with
an open lid this displacement should be taken into account.
4.2.3
Inelastic Deformations
Besides elastic there are also inelastic deformations. Here the orientation history of the
telescope results in an altered response.
This is known as hysteresis. A thorough
analysis has been done on the hysteris of
the H.E.S.S. telescopes [32] and the main
factor in these deformations is the highest
previous altitude of the telescope after the
park out. Figure 4.4 shows the effect of
the maximum previous park out altitude.
The effect is small for angles near zenith
but can build up to 20 arcseconds for a
previous maximum altitude of 40 degrees. Figure 4.4: Results of inelastic deformations.
The deviation in arcseconds is given with respect
For this reason, the telescopes are always to the previous park out position. Image from
[32].
parked out at zenith befor observations,
creating reproducible deformations.
4.2.4
Inaccuracies of Image Analysis
Pointing methods use cameras and stars and are influenced by errors caused by the
analysis routine for the spot extraction and the determination of the star position. These
errors depend on the spot extraction algorithm, fitting method, spot shape, intensity and
background levels. In order to get star positions, the spot extraction algorithm creates
a list of all spots visible in the picture. For CCD cameras of the H.E.S.S. telescopes this
is done with the eclipse software from N. Devillard [44].
4.3
Dual Mirror Pointing
As described in section 2.5 the GATE CHEC Telescope will be a dual mirror telescope.
This has a significant influence on the ponting method of the Cherenkov telescope.
Chapter 4. Pointing
34
Figure 4.5: Sketch of pointing setup for a single mirror and dual mirror telescope.
Image from D. Berge
In Figure 4.5 a sketch shows the difference between the structures and the effect on
pointing. Cherenkov and starlight will be reflected by the first mirror and then focused
by the second mirror on the Cherenkov camera. The star will be projected on the front
of the camera while the LID CCD is focused on the back of the camera. This eliminates
the possibility to use the LidCCD for pointing objectives1
For this dual mirror system a new pointing method was developed. In stead of using additional CCD cameras for pointing, the concept is to use the Cherenkov camera directly
to measure starlight.
For this scheme to work, it is of the utmost importance to reconstruct the star locations
as precise as possible from the Cherenkov camera. By comparing the reconstructed
star positions to a known star chart a pointing accuracy of 7 arcsecconds needs to be
achieved.
To realise this, the electronics and readout system of the camera have to be altered and
enhanced as described in Chapter 3.
An advantage is that there is no more need for dedicated pointing models. Another
benefit is omitting the off-line pointing runs. The pointing can be done in parallel with
the science data taking and could be used during a real time data analysis.
1
There are possibilities of placing a LidCCD camera in the secondary mirror but this is not preferable.
This will cause for more deformation and pointing models will have to take secondary mirror effects into
account.
Chapter 5
MonteCarlo Simulations
Before implementing the new pointing method on all the SST-2M, thorough lab tests
and simulations must be done to prove the concept. This work is focused on simulating
the Cherenkov camera, starlight and the night sky background (NSB) to investigate how
accurate the position of stars can be reconstructed and what procedures are necessary
to achieve the required pointing precision of 7 arcseconds.
This chapter will describe the required parameters of the telescope used for the MonteCarlo simulations, the program used for modelling and will elaborate on the point
spread function.
5.1
Specifications
Modelling the telescope, camera and stars requires an accurate knowledge of the parameters of the camera, telescope, NSB and starlight. For a comparison, the H.E.S.S. I
telescope is also added.
5.1.1
Telescope and Camera
In order to create a realistic MonteCarlo simulation, it is necessary to know the details
of the telescope structure, mirror and camera. This section will state all relevant parameters of both the GCT and the H.E.S.S. 1 telescope as shown in Table 5.1. Pixel size,
shape and the PSF are important to know in order to correctly simulate the starlight
as seen by the camera. This will determine how many pixels can be illuminated by one
star. The Mirror area is the area that collects and focusses the light on the camera,
mirror reflectivity indicates how many of the photons are reflected, Shadow of the structure indicates how many photons are blocked out and quantum efficiency indicate how
much of the remaining photons will be measured by the photosensors. The big range in
quantum efficiency for the GCT camera comes from the quantum efficiency of the two
prototypes.
35
Chapter 5. MonteCarlo Simulations
Parameters
Pixel shape
Pixel size
number of pixels
Total mirror area
mirror reflectivity
Quantum efficiency
Shadow of structure
On-axis PSF
36
H.E.S.S I [45, 46]
Hexagonal
0.16◦
960
108 m2
>80%
20-30%
10%
0.03◦
GCT [39, 41]
Square
0.17◦
2048
8.2 m2
>80%
35-80%
10%
0.05◦
Table 5.1: Specifications of the H.E.S.S and GCT telescope.
5.1.2
Starlight and NSB
Calculating the intensity of starlight and the night sky background is done with the
apparent magnitude equation given by Equation 5.1.
m − m0 = −2.5Log10
F
F0
(5.1)
Here m is the apparent magnitude, F the apparent flux, m0 and F0 are a reference
magnitude and reference flux.
Setting m − m0 = ∆m equation 5.1 can be rewritten to a variation in brightness.
∆m
F0
= 10 2.5 ' 2.512∆m
F
(5.2)
Increasing the magnitude by one results in a drop in brightness by a factor of 2.512. The
night sky background is calculated with respect to the starlight. A commonly used unit
for the brightness of the night sky is magnitudes per arcsecond squared. On potential
CTA sites the NSB will be in the order of magnitude 22 per square arcsecond [47].
Converting the pixel from degrees to arcseconds1 results in a pixel size of 374544 arcsec2
for the GCT camera. Relating the NSB to the pixel size of the GCT camera with the
apparent magnitude addition Equation given by Equation 5.3
mr = −Log2.512 (2.512−m1 + · · · + 2.512−mn )
(5.3)
Where mr is the resulting magnitude after adding mn magnitudes. In case of the GCT
camera this is
mr = −Log2.512 (374544 · 2.512−22 )
(5.4)
= 8.07
This corresponds to a NSB of magnitude 8 per pixel.
The brightness of all starlight and night sky background for the MonteCarlo study will
1
1 degree = 3600 arcseconds
Chapter 5. MonteCarlo Simulations
Math concept
Variable
Function
PDF
Integral
Math symbol
x
f (x)
F (x; p)
xmax
R
f (x)dx
37
RooFit class
RooRealVar
RooAbsReal
RooAbsPdf
RooRealIntegral
xmin
Space point
Addition
Convolution
→
−
x
f F (x) + (1 − f )G(x)
f (x) ⊗ g(x)
RooArgSet
RooAddPdf
RooFFTConvPdf
Table 5.2: Correspondence between mathematical concept and RooFit classes
be simulated using these Equations. As the goal is to determine the star position it is
sufficient to work with relative brightnesses. By setting an reference magnitude m0 = 8
not the absolute brightness will be used but the brightness relative to the night sky
background.
5.2
RooFit
This section will give an overview of the toolkit used to model the telescope and starlight
and perform the fits to measure the pointing precision. For this research the RooFit2
toolkit was used. RooFit is a ROOT library that implements a toolkit to model events
with a known distribution. These models, i.e pdfs, can be applied in a physics and
astronomical analysis. The created models can be used to generate toy MonteCarlo
data simulations, execute binned and unbinned maximum likelihood fits and provide
the desired plots for event studies. The RooFit library was originally designed for particle physics experiments (The BaBar experiment at SLAC in specific) [48] but due to
its open architecture it is also effective to analyse various types of experiments and the
corresponding data types.
The fundamental processes of RooFit is to implement models of data distributions.
Here all data entries qualify as discrete events in time. Furthermore, each event can be
associated with one or more observables. Common data distributions follow Poisson,
Gaussian or binomial statistics and the general modelling functions are all probability
density functions (PDFs).
The RooFit library is an object based environment using C++ classes to implement the
data modelling. The mathematical concepts in RooFit are rendered as C++ objects.
Table 5.2 shows the relation between mathematical concepts, their mathematical symbols and the corresponding RooFit classes.
2
http://root.cern.ch/drupal/content/roofit
Chapter 5. MonteCarlo Simulations
38
For the binned and unbinned fitting, RooFit is using MINUIT [49]. MINUIT is a computer program written in the 1970s for numerical minimization. It is designed to find the
minimum in an arbitrary multiparameter function. Different minimization algorithms
(MIGRAD, MINOS, HESSE, MINIMIZE and SIMPLEX) can be defined by the user
and the result will give best fit values, chi square value, parameter uncertainties, and
the correlation between parameters.
In this study the following Roofit PDFs were used:
• RooPolynomial. A polynomial PDF following f (x) =
imax
P
ai · xi . A polynomial
i=0
can be used to create a constant flat function.
• RooGaussian. A simple Gaussian PDF taking a variable x, a value for sigma and
a mean value as parameters. By multiplying two RooGaussians with RooProdPdf
a two-dimensional Gaussian PDF is formed.
• RooPoisson. A poisson PDF taking a varaible x and a mean as parameters. The
Poisson PDF is used for the background signal. The complete background signal
is created by convolving the PoissonPdf with the constant polynomial by using the
RooFFTConvPdf class.
• RooHistPdf. This creates a PDF from a multidimensional histogram. The distribution is normalised and takes a RooDataHist and a list of variables as argument.
RooDataHist can take a TH1, TH2 or TH3 histogram as argument and creates a
data histogram.
In this work MonteCarlo simulations have been done with RooFit to analyse star positions. The basic principle is shown in Figure 5.1. First, a model is created from PDFs
with the relevant parameters. This is done by creating a RooHistPdf from a custom
RooDataHist containing a simulated Point spread function. With toy MonteCarlo generation, a fake dataset is generated with the distribution of the model and a certain
binning. The data set is then fitted with the full PDF to acquire the relevant parameters. By repeating the process of data generation and fitting a distribution can be
obtained of the relevant parameters.
5.3
Point Spread Function
One of the important factors of determining the location of a star as precise as possible is
the point spread function (PSF). No image is a perfect representation of the real world.
All images are blurred to some extent. There are two main reasons. First, aberrations
Chapter 5. MonteCarlo Simulations
39
Figure 5.1: Concept of MonteCarlo study perfomed with RooFit. Image from W.
Verkerke
in the optical system will spread the image over a finite area. Second, diffraction effects
will also spread the image, even in a system that has no aberrations. The PSF models all
blurring effects and describes the system response for a point source. In mathematical
terms, the image seen by the detector is the convolution of the real image with the point
spread function. Convolution is described with Equation 5.5 and a representation is
given by Figure 5.2.
Z∞
(f ∗ g)(x) =
f (τ )g(t − τ )dτ
(5.5)
−∞
Here τ and x are the input and output parameters.
Figure 5.2: Image formed by the convolution of a two objects with the point spread
function of the system. Based on image from D. Lyon.
The PSF is the (normalised) image of a single point-like object. The quality of an
imaging system can be determined by the amount of blurring in the image. The image
construction is described by the linear system theory. Multiple images will be added
linear, with the final image being equivalent to the sum of the imaged objects.
Chapter 5. MonteCarlo Simulations
40
The factors contributing to the PSF of starlight are:
• Optical design (aberrations)
• Atmospheric seeing
• Detector characteristics
• Fabrication errors
• Surface smoothness
• Sterility of the optics (dust, grease, etc.)
• Deformations of the telescope structure
5.3.1
PSF of the H.E.S.S. Telescope
A first order approximation of the H.E.S.S. PSF is given by a two dimensional Gaussian
[45] where the RMS width of teh 2D−distribution is given by σ.
r80 =
p
ln(5)σ
(5.6)
with r80 is the radius containing 80% of the photons. r80 is dependent on the inclination
of the H.E.S.S. telescope and calibrated at an angle of 66◦ .
r80 (Θ) =
q
2
2
2
ref
f + d (sin Θ − sin Θ0 )
(5.7)
with ref f = 0.41 mrad, d2 = 0.96 mrad, Θ is the inclination angle in degrees and
Θ0 = 66◦ .
r80 also depends on the off-axis angle. This is given by
r80 (θ) =
q
rθ2 + d2θ θ2
(5.8)
with the on-axis width of the point spread function rθ = 0.41 mrad, dθ = 0.72 mrad
deg−1 represents the increase of the width per degree angular distance and θ is the ofaxis angle in degrees
Combining these equations gives a sigma for the Gaussian first order approximation of
the point spread function of H.E.S.S.
r80
1 q 2
σ=p
=p
ref f + d2θ θ2 + d2 (sin Θ − sin Θ0 )2
ln(5)
ln(5)
(5.9)
Chapter 5. MonteCarlo Simulations
41
Figure 5.3: PSF of H.E.S.S. telescope showing the effect of being off-axis. Image from
[45].
Figure 5.3 shows the PSF of the H.E.S.S. telescope drawn in a pixel of the Cherenkov
camera for reference. The effect of being off-axis with respect to the optical axis is
apparent.
Figure 5.4: PSF plus background simulated with RooFit and plotted on the H.E.S.S.
camera.
Figure 5.4 shows a simulated PSF of the H.E.S.S telescope modelled by RooFit. The
left image shows that the total PDF is build from a Gaussian PDF (Approximated as
described above) and background noise from the Poisson PDF. The total PDF is then
used to simulate data points. The simulated starlight is plotted on the right image as
would be seen by the H.E.S.S. Cherenkov camera. Note that with the H.E.S.S telescope
the PSF almost completely falls within one pixel of the camera. Determining the exact
position of a star will be inaccurate in such a case. This effect is described in Section
5.4
5.3.2
PSF Simulations for the GCT
Because of all the aberrations of the telescope described in Section 5.3 a two dimensional
Gaussian is only an approximation of the GCT and H.E.S.S point spread function. In
Chapter 5. MonteCarlo Simulations
42
order to create a more realistic model a more accurate PSF of the GCT telescope is
needed. To achieve this an advanced tray tracing program is used to simulate the point
spread function. The software used is Zemax3 and is able to create a PSF for every
location on the focal plane. Figure 5.5 shows an oversampled PSF created with Zemax
Figure 5.5: PSF of the GCT design created by a ray tracing program (left). The
same PSF plotted with RooFit (right). Courtesy of Remko Stuik.
(left) and the PSF plotted in RooFit (right). This PSF is 1.3 degrees off the optical axis
in both x and y direction. By inspection, it can be seen that the PSF is elongated along
the diagonal axis. By plotting the PSF in RooFit a faint halo even becomes visible.
This indicates that a Gaussian model does not perfectly represent the PSF.
Figure 5.6: A simulated point spread function with extra ring structure (left) and the
off-axis response of the PSF (right). Image adopted from R. Stuik and the SST TDR.
The point spread function can have many different shapes and structures. Depending on
its location and the degree off-axis substructures and secondary rings can form. Figure
5.6 (left) displays a Point spread function that is that is 2.1 and 3.8 degrees off-axis on the
3
http:/www.zemax.com
Chapter 5. MonteCarlo Simulations
43
x and y axis respectively. Here a clear substructure becomes visible. By combining data
from all point spread functions it is possible to determine the off-axis response. This is
shown in Figure 5.6 (right). This indicates
that an accurate knowledge of the PSF is
required to obtain a high accuracy in determining the position of a star. To investigate if it is sufficient to use one model to
fit star images at all locations in the focal
plane, an average PSF is constructed of
36000 different PSFs (all created with Zemax) evenly distributed in one quadrant
of the focal plane(Figure 5.7). This average PSF can be used to test if the required
precision can be achieved with one PSF
model.
5.4
Figure 5.7: Average PSF from 36000 PSFs.
Moving a Star over the Camera
To investigate how accurate the position of a star can be determined, depending on
its location with respect to the pixel boundaries, a star is simulated with a Gaussian
approximation of the point spread function. This star is then moved over a diagonal line
from the centre of the focal plane crossing 8 pixels. The simulated star is then fitted to
determine its position. Figure 5.8 shows a plot of the true mean of a star simulated on
the camera against its fitted mean. Here a pixel is made up out of ten arbitrary units
with 20 being the centre of the camera and 100 being the outer edge of the 8th pixels
off-axis. The lower plot shows the difference between the real and fitted mean of the
Gaussian. Notable is the almost step function like behaviour while moving along the
green line. This can be explained by the fact that stars near pixel boundaries can be
fitted much more accurately, because starlight will illuminate multiple pixels creating a
more accurate knowledge of the true location. Stars in the centre of a pixel will only
illuminate ∼1 pixel losing all the information of where the star is exactly in that pixel.
Furthermore a shift can be seen moving further off-axis which is due to the smearing
and the deformation of the point spread function. Hereby an offset is created.
To investigate the effects more accurately, starlight has been simulated over 36000 different locations on the camera. Every location has its unique simulated PSF. Every
simulated star is fitted with the Gaussian model and the true mean minus the fitted
mean is plotted in a histogram. This can be seen in Figure 5.9. Here an offset is created
Chapter 5. MonteCarlo Simulations
Figure 5.8: A simulated star is moved over the CHEC camera and every location is
fitted to determine the position. The deviation of the real position minus the fitted
position is plotted beneath. The vertical lines indicate pixel boundaries and the green
line indicates the ideal situation where real mean and fitted mean are equal.
Figure 5.9: All deviations plotted in a histogram with a RMS of 118.33 arcseconds.
44
Chapter 5. MonteCarlo Simulations
45
by the off-axis point spread functions. The total precision, for one quadrant, of this
method is a RMS of 118 arcseconds. This is clearly not sufficient for the required RMS
of 7 arcseconds. This means a more accurate method is needed to achieve the requirements. An improved method would be to use multiple stars in the field of view. Section
5.6 will describe this procedure.
5.5
Rotation of the Earth
Because the flux of gamma rays drops rapidly with increasing energy, observations of
sources require not only a large effective area but also long observation times. Observations in gamma-ray astronomy can take from several minutes up to many hours. When
observing over an entire night the effects of the rotation of the Earth should be taken
into account as the telescopes use an alt-azimuth mount. For the new pointing method
an extra effect should be investigated. While the fast readout for Cherenkov events is in
the order of nanoseconds, the slow readout for starlight is in the order of a few Hertz.
A risk arises that starlight will smear out over the camera if the readout is to slow with
respect to the rotation of the Earth.
The effect of rotation on the field of view is given by Equation 5.10
ṗ = ω0
cos φ cos A
cos a
(5.10)
Where ṗ is the time derivative of the parallactic angle, ω0 is the siderial rate (15 deg /hr),
φ is the latitude, A is the azimuth angle measured westwards from the south point
and a is the altitude measured zenithwards from the horizon. This coordinate system
is displayed in Figure 5.10. Sensitivity of Cherenkov telescopes reaches its maximum
Figure 5.10: Coordinate system for an alt-azimuth mounting on the southern hemisphere. Image from T. Carlson.
when observing near zenith because of the lower energy threshold. Rotation effects,
however, become stronger when close to zenith. With a zenith avoidence angle of 2.5◦
Chapter 5. MonteCarlo Simulations
the maximum rotation becomes ṗ =
46
ω0
cos 87.5
= 344 degree/hr = 344 arcsec/s. When the
slow readout for starlight operates at 10 HZ the effect of smearing is 34.4/612 = 0.05
pixel which is acceptable.
5.6
Multiple Star Fitting
Accuracy can be greatly boosted by fitting multiple star positions simultaneously in the
field of view. It is possible to get a prediction of the number of stars in the field of view.
99.9% of all stars up to a magnitude of 10
are accounted for in the Tycho Catalogue
Magnitude
Stars (total)
Stars (FoV)
order of the 8th magnitude this will be the
4
610
0.7
limiting magnitude.
5
1929
2.4
6
5946
7.4
7
17765
22.2
[50]. As the night sky background is in the
Nf ov
9·9
Ntot
=
360 · 180
(5.11)
With Nf ov the average number of stars in Table 5.3: For a certain magnitude the tothe field of view and Ntot the total number tal number of stars and the ◦expected number
of stars.
of stars on average per 9 field of view
Table 5.3 shows a list of usable magnitudes and the number of stars that are expected
in the field of view.
Figure 5.11: By comparing a set of stars measured with the cherenkov camera to a
known star map a offset and rotation angle of the camera can be obtained.
When taking an image from the sky (stars) the total set of stars can be offset by a 2D
vector and rotated around the centre of the camera. The offset can be expressed with
a transformation formula depending on a translation matrix, T, and a rotation matrix,
Chapter 5. MonteCarlo Simulations
47
R, given by
cos
φ
−
sin
φ
0
1
0
D
x T = 0 1 Dy , R = sin φ cos φ 0 0
0 0 1 0
1 (5.12)
With Dx and Dy being the translations in the x and y direction respectively and φ is
the rotation angle. The transformation formula is now given by
→
−0
→
−
P (x, y) = R · T · P (x, y)
(5.13)
Figure 5.11 shows the procedure of multiple star fitting. The method is to comparing a
set of stars, as seen with the Cherenkov camera, with stars on a known star chart. The
current pointing direction is known with some uncertainty so it is possible to determine
which stars will be in the field of view. With this knowledge, the relative distances
between stars is known and the whole set of stars can be compared to their known
positions from a star chart. This will result in an 2D offset vector and a rotation angle.
With only one star, a location in the sky can be determined but the rotation angle stays
unknown. With multiple stars this rotation angle can be determined. Another benefit
Figure 5.12: One quadrant of the GCT camera with 3 stars (and NSB) moving
through the field of view due to the rotation of the Earth. The time t is given in
minutes.
of multiple star fitting can be seen in Figure 5.12. While information about the exact
location is lost when the point spread function is completely contained within one pixel
there is a bigger chance that at least one star will be near the pixel edge for a precise
determination of its location. Here only the point spread functions of three stars are
projected on one quadrant of the GCT camera. An image is simulated every 10 minutes
taking into account the rotation of the Earth. The effect is that the stars rotate around
the center (0,0) of the camera. As seen in Figure 5.12, with three stars there is at least
Chapter 5. MonteCarlo Simulations
48
one star near the edge of a pixel every time illuminating at least two pixels. This will
result in a higher accuracy for the whole system.
Figure 5.13 shows a preliminary result of the multiple star fitting. Here the offset is
Figure 5.13: Preliminary result of the multiple star fitting procedure.
determined of 3000 different MonteCarlo simulations. The results show a RMS of ∼12
arcseconds for the x offset, a RMS of ∼13 arcseconds of the y offset and a RMS of 0.045
arcseconds for the rotation offset. Below are the fitting errors in the offsets. These
results are preliminary as the multiple star fitting algorithm is under construction.
Chapter 5. MonteCarlo Simulations
5.7
49
Discussion
In this work, MonteCarlo simulations have been done to investigate the accuracy of the
newly proposed pointing method for the SST-2M. This study has incorporated many
effects and properties of the telescope and camera. However, this is still a simplified
model. The camera in this study is an ideal camera and a number of aspects are not
taken into account. It is modelled as a complete uniform camera, no gaps are set between
the camera modules and their is no image distortion. Furthermore, variation in pixel
gain could be taken into account. These effects could negatively influence the pointing
precision.
As can be seen in this study, the PSF of the telescope is almost completely contained
within one pixel of the Cherenkov camera. This has the undesirable effect that the position determination of starlight is not so accurate when the star is near the centre of a
pixel.
A solution for this problem would be the
using smaller pixels or a ”worse” PSF.
Figure 5.14 shows the effect of different
sized PSFs. A small PSF (σ = 0.04◦ will
be contained completely within one pixel
most of the time and fitting the position
will only give an accurate measurement
on the pixel edge. A medium sized PSF
(σ = 0.06◦ ) will not yield an accurate location when near the centre but will become more accurate when moved closer to
a pixel boundary. A large PSF (σ = 0.08◦ )
will always be spread out over multiple
pixels and will so always give an accurate fit of the position. Besides creating a
large PSF, the same result can be accomplished by decreasing pixel size. However,
both methods are undesirable.
Smaller
pixel size will influence the detection of
Figure 5.14: The fitted position of a point
the weak Cherenkov light with not enough spread function approximated by a Gaussian
counts per pixel. Creating a worse PSF versus the real position. Performed with three
will result in a blurred image of the shower
jeopardizing the scientific measurements.
different values for σ. The vertical dashed lines
represent pixel boundaries.
Chapter 5. MonteCarlo Simulations
50
The result of imaging a star with the GCT camera is shown in figure5.15. Here the
difference can be seen between finely sampled psf (left) and the same psf as seen by
the GCT camera (right). The black horizontal and vertical lines indicate the pixel
boundaries. Here it shown that a star realy needs to be on a pixel boundary to illuminate
multiple pixels. This emphasizes the importance of multiple star fitting.
Figure 5.15: Very fine sampled PSF with black lines indicating pixel size GCT (left)
and same psfs as seen by the GCT camera (right). NSB is included in both images.
The preliminary multiple star fitting results are promising. However, the required 7
arcseconds is still not achieved. The fitting algorithm needs to be improved in order to
realise this. By analysing the results and the errors (Figure 5.13). One method would
be to apply cuts on the larger errors in the offset. By removing these offsets a higher
precision could be achieved. The effects of this should be further investigated to see how
much the precision can be improved.
Summary
To investigate the origin of cosmic rays and the cosmic non-thermal universe ground
based telescopes employing the Imaging Atmospheric Cherenkov Technique to observe
VHE gamma rays. The Cherenkov Telescope Array is a planned facility for next generation Cherenkov telescopes. To ensure a large energy range, three different telescope
sizes will be built. The dual mirror Small Size Telescope will be most sensitive for the
high energy range observing gamma rays between the 1 and 300 TeV.
In this work, a comprehensive MonteCarlo simulation study of the novel SST-2M pointing method was performed. This new pointing method is needed because the current
pointing methods do not work for a dual mirror telescope. In stead of using additional
CCD cameras the Cherenkov camera will be used directly to measure starlight. All
parameters of the GATE CHEC Telescope were analysed as well as the effects of night
sky background, Rotation of the Earth and multiple stars in de field of view.
A new algorithm was written in RooFit to perform MonteCarlo simulations. This was
used to simulate starlight from a point spread function approximated by a Gaussian.
These stars were simulated as seen by the Cherenkov camera so RooFit could fit the
star positions to investigate if the required pointing precision of a RMS of 7 arcseconds
can be achieved. As the point spread function can be fully contained within one pixel of
the Cherenkov telescope, determining the true position of the star is not very accurate
when located near the centre of a pixel. However, accuracy increases when a star is
located near a pixel edge. After fitting the position of a single star on more than 36000
different positions with a Gaussian model the precision turned out to be an RMS of 118
arcseconds which is unacceptable.
To increase precision more realistic point spread functions were created using the Zemax
ray tracing software. These PSFs were used to simulate more realistic stars and a model
was created from averaging 36000 PSFs which can be used to fit star positions.
At this moment, the RooFit algorithm is being extended to enable multiple star fitting.
With multiple star fitting a set of stars will be compared to a known star chart. With
this, it will be possible to determine the rotation angle and the offset of the system.
Another benefit of using multiple stars is the increased chance of at least one star being
at the edge of a pixel allowing accurate fitting. Preliminary results give an offset of
12-13 arcseconds RMS. Once the algorithm is improved, MonteCarlo simulations can be
done to investigate if the required 7 arcsecond RMS pointing precision can be achieved
with this method.
51
Acknowledgements
This last year has been a wonderful time for me working on my master research project.
I have learned so much on both science and the ways of a great collaboration. For this
I want to thank my supervisor, Dr. David Berge, who has guided me in my research
and given me the opportunity to grow and develop my research skills. I am profoundly
grateful to my daily supervisor, Arnim Balzer, who helped me throughout the project
and would patiently guide me through all my programming problems and frustrations. I
would also like to thank David Salek, Gabriele Sabato, Michael Muusse and Mark Bryan
with whom I could discuss the project during our weekly group meetings and Remko
Stuik from Leiden for his specific help on point spread functions. Furthermore, a special
thanks to Jon Lapington, Julian Thornhill, Jim Hinton and Richard White in Leicester
who helped and entertained me during my stay there. Last but not least, I would like
to thank my family and friends for all their support.
52
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