Modeling a Dual Mirror Cherenkov Telescope to Analyse Pointing Precision

Home , IACT

VU University Amsterdam

MSc Physics Particle and Astroparticle Physics

Master Thesis

Modeling a dual mirror Cherenkov telescope to analyse pointing precision

Gijsbert Tijsseling

1853562

August 2014

Supervisor: Daily Supervisor: Examiner: Dr. David Berge Arnim Balzer 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 enor- mous 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 3 1.1 Cosmic Rays ...... 3 1.2 Gamma Rays ...... 4 1.3 Sources of Gamma Rays ...... 6 1.3.1 Supernova Remnants ...... 6 1.3.2 Pulsars ...... 7 1.3.3 Galactic Centre ...... 8 1.3.4 Active Galactic Nuclei ...... 9 1.3.5 Galaxy Clusters ...... 9

2 Cherenkov Telescopes 11 2.1 Extensive Air Showers ...... 11 2.1.1 Particle Showers ...... 11 2.1.2 Cherenkov Emission ...... 14 2.2 Imaging Atmospheric Cherenkov Technique ...... 16 2.3 Current Experiments ...... 18 2.4 Cherenkov Telescope Array ...... 19 2.5 CTA SST ...... 20

3 Camera and Electronics 22 3.1 CHEC ...... 22 3.2 Electronics ...... 24 3.3 ADC Slow Readout ...... 26 3.4 Lab Setup ...... 27

4 Pointing 29 4.1 Current Pointing Method ...... 30 4.2 Sources of Pointing Deviation ...... 32 4.2.1 Tracking Deviation ...... 32 4.2.2 Deformation of the Structure ...... 32 4.2.3 Inelastic Deformations ...... 33 4.2.4 Inaccuracies of Image Analysis ...... 33 4.3 Dual Mirror Pointing ...... 33

5 MonteCarlo Simulations 35 5.1 Speciﬁcations ...... 35 5.1.1 Telescope and Camera ...... 35

ii iii

5.1.2 Starlight and NSB ...... 36 5.2 RooFit ...... 37 5.3 Point Spread Function ...... 38 5.3.1 PSF of the H.E.S.S. Telescope ...... 40 5.3.2 PSF Simulations for the GCT ...... 41 5.4 Moving a Star over the Camera ...... 43 5.5 Rotation of the Earth ...... 45 5.6 Multiple Star Fitting ...... 46 5.7 Discussion ...... 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 E2.5. The spectrum can mostly be described as a power law

dN ∼ E−γ (1.1) dE

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

1See 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 5

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/ 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 sup- ported 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. Electromag- field lines, the rotational axis and the magnetic axis. Image from netic radiation is emitted along the magnetic axis 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 8

1.3.3 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 9

1.3.4 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 classiﬁ- cation 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

h − h X(h) = X0 exp 0 (2.2)

2 Where h is the altitude in km, h0 = 8 km and X0 = 1013 g/cm . 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 crit-

ical 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)

And the energy per particle is −n En = E0 2 (2.5) 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

1 E0 nmax = ln (2.6) ln 2 Ec

Combining Equation 2.4 and Equation 2.6 gives the maximum number of particles in a shower E0 Nmax ' (2.7) Ec With the maximum of this shower at

Xr E0 Xmax = nmax · Xr = ln (2.8) ln 2 Ec

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 development process of hadronic showers is diﬀerent than that of electromagnetic cascades. The development process is dependent of hadron production, pion decay, de-excitation and muon decay. Pions cause the big lateral Figure 2.2: Hadronic particle cascade. Image from M. spread as they obtain large hor- Hemberger. izontal momentum. Charged pions decay into muons and neutrinos while π0 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 shock- front of light is emitted comparable to a sonic boom. See Figure 2.4 for a geometric 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 in-

vp dex of the medium. β is deﬁned as β = c . The path travelled in some time t by the particle is given by βct and the produced Figure 2.4: Geometric model of Cherenkov ra- Cherenkov light is restricted to traverse a diation. Image from A. Horvath. c distance of n t. Due to geometric reasons it is possible to calculate the openings angle of the created Cherenkov cone. This gives Chapter 2. Cherenkov Telescopes 15

1 cos θ = βn . For gamma-ray induced Cherenkov emission the opening angle is typical about 1◦. This results in a ground area illuminated by Cherenkov light 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. Bernl¨ohr.

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] q2 c2 dE = µ(ω)ω(1 − )dxdω (2.9) 4π v2n2(ω) Where the particle has an electric charge of q, µ(ω) is the frequency dependent perme- ability, 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 Tech- nique 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 19

Telescope Number of telescopes Energy range Field of view Angular resolution MAGIC 2 25 GeV - 30 TeV 3.5◦ 0.08◦ − 0.17◦ VERITAS 4 50 GeV - 50 TeV 3.5◦ 0.1◦ − 0.14◦ H.E.S.S. 5 30 GeV - 100 TeV 3.2◦ − 5.0◦ 0.08◦ − 0.14◦

Table 2.1: Details of current Cherenkov telescopes

speciﬁcation LST MST SST Mirror diameter 23m 12m 4m Energy range 10 - 500 GeV 0.1 - 10 TeV 1 - 300 TeV Number of telescopes 4 20 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 gamma- ray 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.

1http://www.cta-observatory.org/ 2As 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 ac- commodate 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

1http:/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 32

4.2 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 parked out at zenith befor observations, [32]. 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.

1There 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 Mon- teCarlo 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 36

Parameters H.E.S.S I [45, 46] GCT [39, 41] Pixel shape Hexagonal Square Pixel size 0.16◦ 0.17◦ number of pixels 960 2048 Total mirror area 108 m2 8.2 m2 mirror reﬂectivity >80% >80% Quantum eﬃciency 20-30% 35-80% Shadow of structure 10% 10% On-axis PSF 0.03◦ 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.

F m − m0 = −2.5Log10 (5.1) F0

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.

F0 ∆m ∆m = 10 2.5 ' 2.512 (5.2) F

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

−m1 −mn mr = −Log2.512(2.512 + ··· + 2.512 ) (5.3)

Where mr is the resulting magnitude after adding mn magnitudes. In case of the GCT camera this is −22 mr = −Log2.512(374544 · 2.512 ) (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

11 degree = 3600 arcseconds Chapter 5. MonteCarlo Simulations 37

Math concept Math symbol RooFit class Variable x RooRealVar Function f(x) RooAbsReal PDF F (x; p) RooAbsPdf xmax Integral R f(x)dx RooRealIntegral xmin Space point −→x RooArgSet Addition fF (x) + (1 − f)G(x) RooAddPdf Convolution f(x) ⊗ g(x) 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 sym- bols and the corresponding RooFit classes.

2http://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:

imax P i • RooPolynomial. A polynomial PDF following f(x) = ai · x . 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.

p r80 = 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◦ .

q 2 2 2 r80(Θ) = reff + d (sin Θ − sin Θ0) (5.7)

2 with reff = 0.41 mrad, d = 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

q 2 2 2 r80(θ) = rθ + dθθ (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 of- axis 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.

q r80 1 2 2 2 2 2 σ = = r + d θ + d (sin Θ − sin Θ0) (5.9) pln(5) pln(5) eff θ 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

3http:/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 Ze- max) 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 Figure 5.7: Average PSF from 36000 PSFs. model.

5.4 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 44

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. 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. Observa- tions 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

cos φ cos A p˙ = ω (5.10) 0 cos a

Wherep ˙ 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 46

ω0 the maximum rotation becomesp ˙ = 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) [50]. As the night sky background is in the order of the 8th magnitude this will be the 4 610 0.7 limiting magnitude. 5 1929 2.4 6 5946 7.4 9 · 9 N = N (5.11) 7 17765 22.2 fov 360 · 180 tot

With Nfov the average number of stars in Table 5.3: For a certain magnitude the total number of stars and the expected number the ﬁeld of view and Ntot the total number of stars on average per 9◦ﬁeld of view of stars.

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

1 0 Dx cos φ − sin φ 0

T = 0 1 D ,R = sin φ cos φ 0 (5.12) y

0 0 1 0 0 1

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

−→ −→ P 0(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 49

5.7 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 accom- plished 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 different values for σ. The vertical dashed lines will result in a blurred image of the shower represent pixel boundaries. jeopardizing the scientific measurements. 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.

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