Design, Implementation and Test of a new Feature Extractor for the ...

Design, Implementation and Test
of a New Feature Extractor
for the IceCube Neutrino Observatory
von
Marius Wallraff
Diplomarbeit in P H Y S I K
vorgelegt der
Fakultät für Mathematik, Informatik und
Naturwissenschaften
der Rheinisch-Westfälischen Technischen Hochschule Aachen
im
März 2010
angefertigt am
III. Physikalischen Institut B
Prof. Dr. Christopher Wiebusch

NewFeatu r eExtracto r

Abstract
The IceCube Neutrino Observatory at South Pole consists
of digital optical modules (DOMs) deep down in the
ice equipped with photomultipliers to capture Čerenkov
light induced by muons and other particles. These
DOMs digitize the analogue photomultiplier signals and
send the resulting waveforms to the surface. The large
amount of information has to be condensed for later particle
track and energy reconstructions.
This thesis presents a new framework – the NewFeatureExtractor,
NFE – to extract the arrival times and
the number of photons. Four algorithms have been implemented
in this framework to analyze different types
of waveforms. Their performance is tested by comparison
between simulated data and experimental data, and
by comparison with earlier algorithms, which are also
analyzed conceptually.

Contents
Abstract
List of Figures
List of Tables
i
vi
ix
1 Introduction 1
2 Neutrino Astrophysics 5
2.1 Neutrinos in Comparison with Other Messenger Particles . . . . . . . . . . 6
2.1.1 Photons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.2 Cosmic Rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.3 Gravitational Waves . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 Neutrino Production Processes . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.1 Nuclear Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.2 Thermal Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.3 Cosmic Ray Interactions . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3 Air Showers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3.1 Atmospheric Muons . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3.2 Atmospheric Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . 16
3 Neutrino Detection 17
3.1 Neutrino Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.2 Lepton Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2.1 Electron Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2.2 Muon Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2.3 Tau Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.3 Čerenkov Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4 The IceCube Neutrino Observatory 25
4.1 Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.2 Ice Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.3 Digital Optical Modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.4 Signal Digitization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.4.1 ATWD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.4.2 FADC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.4.3 SLC Chargestamps . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.5 Data Structure and Data Rate . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.6 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.6.1 DOMcalibrator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
iii

CONTENTS
5 Feature Extraction in IceCube 37
5.1 FeatureExtractor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
5.2 PulseExtractor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
5.3 SLCHitExtractor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
5.4 NewFeatureExtractor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
5.4.1 Main Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . 42
5.4.2 Program Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
5.4.3 Time Offset Constants . . . . . . . . . . . . . . . . . . . . . . . . . 44
5.4.4 Waveforms Without Pulses . . . . . . . . . . . . . . . . . . . . . . . 45
5.4.5 Pulse Merger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
6 Algorithms Implemented in NFE 47
6.1 Pre-evaluation Algorithm “Eva” . . . . . . . . . . . . . . . . . . . . . . . . 48
6.2 Extraction Algorithm “Simple” . . . . . . . . . . . . . . . . . . . . . . . . 49
6.3 Extraction Algorithm “BayesUnfold” . . . . . . . . . . . . . . . . . . . . . 50
6.3.1 Differences of FE’s and PE’s Implementations . . . . . . . . . . . . 54
6.4 Extraction Algorithm “SLCHE” . . . . . . . . . . . . . . . . . . . . . . . . 55
7 Performance Optimization 57
7.1 Calibration Using Monte-Carlo Data . . . . . . . . . . . . . . . . . . . . . 58
7.1.1 Pre-evaluation Algorithm "Eva" . . . . . . . . . . . . . . . . . . . . 58
7.1.2 Extraction Algorithm "Simple" . . . . . . . . . . . . . . . . . . . . . 62
7.1.3 Extraction Algorithm "BayesUnfold" . . . . . . . . . . . . . . . . . 65
7.1.4 Extraction Algorithm "SLCHE" . . . . . . . . . . . . . . . . . . . . 67
7.2 Verification Using Experimental Data . . . . . . . . . . . . . . . . . . . . . 71
8 Performance Tests 79
8.1 Extraction of Simple Pulses with “Simple” and “BayesUnfold” . . . . . . . 80
8.2 Extraction of Exotic Features . . . . . . . . . . . . . . . . . . . . . . . . . 90
8.3 Comparison with Other Feature Extractors . . . . . . . . . . . . . . . . . . 97
8.3.1 FeatureExtractor in Multi-Pulse Mode . . . . . . . . . . . . . . . . 97
8.3.2 FeatureExtractor in Single-Pulse Mode . . . . . . . . . . . . . . . . 112
8.4 SLCHitExtractor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
8.5 Runtime Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
9 Summary And Outlook 121
A Bayesian Unfolding 125
A.1 Formal Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
A.2 Adaption to IceCube’s Waveforms . . . . . . . . . . . . . . . . . . . . . . . 125
B Cascade Pulse Tagging 127
iv

CONTENTS
C Specific Problems and Anomalies 129
C.1 ATWD FADC Time Offset Caused Double Extraction . . . . . . . . . . . . 129
C.2 Implementation of the Second Single-Pulse Extraction Algorithm in FeatureExtractor
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
C.3 Missing Simulation of the daq_baseline in DOMsimulator . . . . . . . . . 130
C.4 Time Offset in SLCHitExtractor . . . . . . . . . . . . . . . . . . . . . . . . 130
Acknowledgements
Erklärung / Declaration
References
I
III
V
v

List of Figures
2.1 Differential particle flux for major cosmic ray components. . . . . . . . . . 8
2.2 All-particle cosmic ray energy spectrum from air shower measurements. . . 9
2.3 Second and first order Fermi acceleration. . . . . . . . . . . . . . . . . . . 10
2.4 Cosmic ray deflection angles near the GZK cutoff. . . . . . . . . . . . . . . 11
2.5 Total number of neutrinos produced in stars as function of star mass. . . . 13
2.6 Cosmic rays and neutrinos hitting the Earth. . . . . . . . . . . . . . . . . . 15
2.7 Vertical atmospheric muon and muon neutrino differential fluxs. . . . . . . 15
2.8 Zenith distribution of atmospheric muons and atmospheric muon neutrinos. 16
3.1 Neutrino nucleon cross-sections as a function of energy. . . . . . . . . . . . 18
3.2 Signatures of charged current interactions of neutrinos in Čerenkov media. 20
3.3 Depth development of electron initiated cascades. . . . . . . . . . . . . . . 20
3.4 Effective radiation length modified by the LPM effect. . . . . . . . . . . . . 21
3.5 Expected track length for muons and taus in Antarctic ice. . . . . . . . . . 22
3.6 Emission of Čerenkov radiation. . . . . . . . . . . . . . . . . . . . . . . . . 23
4.1 IceCube surface geometry with deployment season information. . . . . . . 26
4.2 Three-dimensional sketch of IceCube with DeepCore. . . . . . . . . . . . . 27
4.3 Effective scattering length and absorption length in deep Antarctic ice. . . 29
4.4 Sketch of an IceCube Digital Optical Module (DOM). . . . . . . . . . . . . 31
4.5 Waveforms illustrating the toroidal droop effect for OT and NT DOMs. . . 32
4.6 Comparison of different ATWD and FADC SPE shape parametrizations. . 34
5.1 Sketch illustrating FeatureExtractor’s two single-pulse extraction algorithms. 39
6.1 Sketch illustrating NFE’s pre-evaluation algorithm “Eva”. . . . . . . . . . . 48
6.2 Sketch illustrating NFE’s extraction algorithm “Simple”. . . . . . . . . . . 49
6.3 Sketch illustrating Bayesian Unfolding. . . . . . . . . . . . . . . . . . . . . 51
6.4 FE, PE, and NFE pulse definition algorithms for deconvoluted distributions. 53
6.5 Residual plot for the width parametrization used in “BayesUnfold”. . . . . 54
6.6 Sketch comparing NFE’s extraction algorithm “SLCHE” to SLCHitExtractor. 55
7.1 Two examples for waveforms with pulses extracted by NFE. . . . . . . . . 59
7.2 Two examples for waveforms with pulses extracted by NFE. . . . . . . . . 60
7.3 Two examples for waveforms with pulses extracted by NFE. . . . . . . . . 61
7.4 Time residuals of NFE extracted pulses for different “Simple” charge thresholds.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
7.5 Charge-time correlation of pulses from NFE extraction algorithm “Simple”. 65
7.6 Effects of “BayesUnfold”’s variable number of iterations – time residuals. . 68
7.7 Effects of “BayesUnfold”’s variable number of iterations – charges. . . . . . 69
7.8 Effects of “BayesUnfold”’s variable number of iterations – numbers of pulses. 70
7.9 Effects of “BayesUnfold”’s optimized deconvolution starting distribution. . 71
7.10 Time residuals and charges of “SLCHE” and NFE FADC pulses. . . . . . . 72
7.11 Time differences of ATWD and FADC NFE pulses for MC and experimental
data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
vi

LIST OF FIGURES
7.12 Ratio of total FADC and ATWD waveform charge for MC and experimental
data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
7.13 Charges of the first ATWD and FADC NFE pulses for MC and experimental
data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
7.14 Differences between the total charges of ATWD and FADC pulses for MC
and experimental data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
7.15 Comparison of ATWD and FADC pulses for MC and experimental data. . 77
8.1 Time residuals for the first pulses from simple MC waveforms extracted by
“Simple” and “BayesUnfold”. . . . . . . . . . . . . . . . . . . . . . . . . . . 81
8.2 Numbers of pulses from simple MC waveforms extracted by “Simple” and
“BayesUnfold”. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
8.3 Example for a waveform with a high baseline caused by incomplete simulation. 83
8.4 Effect of erroneous baselines on “Simple”’s and “BayesUnfold”’s numbers
of pulses from simple MC waveforms. . . . . . . . . . . . . . . . . . . . . . 84
8.5 Charges of the first pulses from simple MC waveforms extracted by “Simple”
and “BayesUnfold”. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
8.6 Differences between the total charges of all pulses from simple MC waveforms
extracted by “Simple” and “BayesUnfold”. . . . . . . . . . . . . . . . 86
8.7 Effect of erroneous baselines on “Simple”’s and “BayesUnfold”’s total charge
from simple MC waveforms. . . . . . . . . . . . . . . . . . . . . . . . . . . 87
8.8 Numbers of pulses from simple experimental waveforms extracted by “Simple”
and “BayesUnfold”. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
8.9 Differences between the total charges of all pulses from simple experimental
waveforms extracted by “Simple” and “BayesUnfold”. . . . . . . . . . . . . 89
8.10 Example waveforms to demonstrate NFE’s option EnforcePulse. . . . . . . 91
8.11 Example waveforms of exotic or difficult features. . . . . . . . . . . . . . . 92
8.12 Example waveforms of exotic or difficult features. . . . . . . . . . . . . . . 93
8.13 Example waveforms of exotic or difficult features. . . . . . . . . . . . . . . 94
8.14 Example waveforms of exotic or difficult features. . . . . . . . . . . . . . . 95
8.15 Example of a bright waveform from Markus Voge’s catalog. . . . . . . . . . 97
8.16 Time residuals of the first pulses extracted by FE and NFE from MC;
multi-pulse online-filtering settings. . . . . . . . . . . . . . . . . . . . . . . 98
8.17 Differences between the times of the first pulses extracted by FE and NFE
from MC and experimental data; multi-pulse online-filtering settings. . . . 100
8.18 Charges of the first pulses extracted by FE and NFE from MC and experimental
data; multi-pulse online-filtering settings. . . . . . . . . . . . . . . 101
8.19 Example waveforms for lower charges in NFE than in FE. . . . . . . . . . 102
8.20 Differences of the total charges of the pulses extracted by FE and NFE
from MC and experimental data; multi-pulse online-filtering settings. . . . 103
8.21 Example of saturated waveforms in different calibrations with pulses from
NFE and FE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
vii

LIST OF FIGURES
8.22 Numbers of pulses extracted by FE and NFE from MC and experimental
data; multi-pulse online-filtering settings. . . . . . . . . . . . . . . . . . . . 106
8.23 Time residuals of the first pulses extracted by FE and NFE from MC;
multi-pulse offline-processing settings. . . . . . . . . . . . . . . . . . . . . . 107
8.24 Charges of the first pulses extracted by FE and NFE from MC and experimental
data; multi-pulse offline-processing settings. . . . . . . . . . . . . . 108
8.25 Numbers of pulses extracted by FE and NFE from MC and experimental
data; multi-pulse offline-processing settings. . . . . . . . . . . . . . . . . . 109
8.26 Charge per pulse ratio of simulated data and experimental data for FE and
NFE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
8.27 Time residuals of the first pulses extracted by FE and NFE from MC;
single-pulse settings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
8.28 Charges of the first pulses extracted by FE and NFE from MC and experimental
data; single-pulse settings. . . . . . . . . . . . . . . . . . . . . . . . 114
8.29 Differences of the total charges of the pulses extracted by FE and NFE
from MC and experimental data; single-pulse settings. . . . . . . . . . . . . 115
8.30 Time residuals of pulses extracted by SLCHitExtractor and “SLCHE” from
MC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
8.31 Charges of pulses extracted by SLCHitExtractor and “SLCHE” from MC
and experimental data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
B.1 Tagging of pulses caused by cascades during muon propagation. . . . . . . 127
C.1 Comparison of FeatureExtractor’s documented and implemented second
single-pulse extraction algorithms. . . . . . . . . . . . . . . . . . . . . . . . 130
C.2 Effect of the simulation of the daq_baseline on extracted pulses. . . . . . . 131
viii

List of Tables
4.1 Overview over different digitizers resp. I3Waveform source types. . . . . . . 33
7.1 Default values used for pre-evaluation algorithm “Eva”. . . . . . . . . . . . 62
7.2 Default values used for extraction algorithm “Simple”. . . . . . . . . . . . . 62
7.3 Parameter values of the SPE pulse parametrizations employed. . . . . . . . 66
7.4 Default values used for the extraction algorithm “BayesUnfold”. . . . . . . 66
7.5 Default values used for extraction algorithm “SLCHE”. . . . . . . . . . . . 67
8.1 Runtimes for different feature extractors and datasets. . . . . . . . . . . . . 119
ix

LIST OF TABLES
x

CHAPTER I
Introduction

1 INTRODUCTION
Astronomy challenged and inspired mankind since prehistoric times. In its beginning,
it was strongly connected to astrology and served as basis for cults and religious beliefs.
With the introduction of agricultural techniques and the rise of great civilizations, many
practical applications emerged independently across the globe. Astronomy enabled the
creation of reliable calendars to forecast seasonal climate changes, provided means to
learn about the topography of Earth, allowed navigation on open sea, and more generally
motivated mathematical and scientific progress.
The ancient astronomers were limited to observations that could be undertaken with
their bare eyes. This did not change until Hans Lippershey invented the first known
telescope in 1608. Utilizing the light-gathering power of these new instruments, famous
astronomers like Galileo Galilei and Johannes Kepler soon made new discoveries and laid
the foundation for modern astronomy and astrophysics. During the following centuries
constant improvements to the instruments were made, but it was until the 19th century
that fundamentally new techniques were devised: Photography allowed precise long-time
observations, spectrography made it possible to analyze the composition and radial velocity
of distant objects. While especially the latter provided valuable new observables to
astrophysics, researchers were still depending on visible light. This limitation was eliminated
in the middle of the 20th century with the establishment of radio astronomy. In
the following decades, many parts of the electromagnetic spectrum were discovered to be
valuable means for the exploration of the visible universe, such as far and near infrared,
ultraviolet, X-rays, and gamma rays.
In parallel to this late development, Theodor Wulf, Domenico Pacini and Victor Hess
found the first strong evidences for extra-terrestial particles entering the Earth’s atmosphere,
the so-called cosmic rays. In the following decades, many experiments were conducted
to analyze the underlying mechanism, the composition and origins of these cosmic
rays, and a new field of physics was born: particle physics. Today, most particle physics experimentalists
work at accelerator experiments which allow high-precision measurements
in controlled environments and extremely high luminosities. However, cosmic rays remain
to be an interesting subject for both astrophysics and particle physics as they are both
astronomical information carriers complementary to electromagnetic radiation and reach
energies several orders of magnitude higher than those currently produced at particle
accelerators.
The advancement of detectors for the different branches of multi-messenger astronomy
and astroparticle physics has proven to be an important aspect of the efforts made
to understand the structure of matter and the Universe. This thesis is written in the
hope to be a small contribution to this endeavor by designing, implementing and finally
testing a new feature extractor for the IceCube Neutrino Observatory – the NewFeatureExtractor,
NFE. NFE is a package which analyses the recorded photomultiplier signals and
extracts the physics information; this is the number and arrival time of photons hitting
the photomultipliers.
2

Chapter 2 gives a short motivation and explains the basics of neutrino astrophysics
with its advantages and challenges. Chapter 3 goes more into detail and explains the
neutrinos’ interactions with baryonic matter, the propagation of the resulting particles
through matter and how these properties can be exploited for neutrino detection. Chapter
4 describes the IceCube Neutrino Observatory, with emphasis on its hardware and the
data acquisition. Chapter 5’s topic is feature extraction in IceCube. The three most
important existing feature extractor packages are introduced, and the design decisions for
NewFeatureExtractor are discussed. Chapter 6 illustrates the different algorithms used
by NFE; the corresponding performance optimization analyses are explained in chapter
7. Performance tests are presented in chapter 8. Finally chapter 9 gives a summary and
provides an outlook on future developments and tasks.
3

1 INTRODUCTION
4

CHAPTER II
Neutrino Astrophysics

2 NEUTRINO ASTROPHYSICS
2.1 Neutrinos in Comparison with Other Messenger Particles
Neutrino astronomy is one of the modern branches of observational astronomy. Most of
the early neutrino detectors were originally designed for astrophysics (e.g., the Homestake
experiment for measuring the solar neutrino flux) or particle physics (like KamiokaNDE
for the investigation of proton decay). Supernova SN1987A proved neutrino telescopes
to be valuable for both observational astronomy and astroparticle physics. Among other
applications, extra-terrestial neutrinos can be used to test astrophysical models and to
constrain values for neutrino properties which cannot be accessed directly by accelerator
experiments.
A big challenge is the very small cross-section of neutrino interactions (see section 3.1)
combined with a strong background of atmospheric particles caused by air showers (see
section 2.3). However, this small cross-section is also a major advantage of neutrino
astronomy as it allows to probe astrophysical regions obstructed by either foreground
objects or by the object itself. Furthermore, because of different production processes
neutrinos carry information that is complementary to that obtainable by other types of
telescopes, making neutrinos a valuable part of multi-messenger astronomy.
2.1.1 Photons
The electromagnetic spectrum offers much diversity in the obtainable data. The wavelength
λ is coupled with the photon’s energy E by
λ = c ν = hc
E
1.2398 eV m
≈ ,
E
where ν denotes the frequency of the wave; because of this, photons of different energies
interact with different objects. While for example visible light is absorbed by interstellar
dust, the dust grains reemit this light brightly in infrared frequency bands. The HI line –
also known as 21 centimeter line – is the spectral line corresponding to the hyperfine level
transitions of atomic hydrogen and can be observed by microwave telescopes. Because of
its small width its doppler shifts can be used to calculate velocity maps of the interstellar
medium. From roughly 200 keV upwards, gamma-ray observatories monitor the sky for
high-energy objects and events such as supernovae remnants, gamma-ray bursts or active
galactic nuclei (AGNs).
One major disadvantage of photons is their high scattering and absorbtion probability.
In many wavebands, parts of the sky are obstructed by interstellar matter, especially by
formations known as dark nebulas such as the Great Rift, or by the Galactic Center.
Furthermore, many parts of the spectrum are absorbed by the Earth’s atmosphere, raising
the need for extra-terrestial detectors, which are however limited in mass and thereby
not suitable for ultra-high-energy surveys as the low flux at these energies requires large
effective areas.
6

2.1 Neutrinos in Comparison with Other Messenger Particles
2.1.2 Cosmic Rays
Hadronic cosmic rays are massive particles originating from outer space. Their composition
is energy dependent; at low energy about 90% of the particles are protons, 9% are
helium nuclei and the rest consists of heavier nuclei, neutrons and anti-protons (see figure
2.1).[3] Cosmic Rays also have leptonic components; e.g., about one additional percent
consists of electrons. Depending on the definition used, neutrinos and gamma rays are
also included. For the rest of this section, ”cosmic rays“ is used synonymously for charged
hadronic cosmic rays unless stated otherwise.
Cosmic rays can be divided into two categories: Primary cosmic rays are directly emitted
from astronomical objects such as stars, supernovae or AGNs, while secondary cosmic
rays emerge from collisions between primary ones and interstellar matter.Some elements
such as Li, Be, B, F, Sc, and V (which are rare in stars because no stable isotopes are
generated during stellar nucleosynthesis) as well as anti-protons are unlikely to be primary
cosmic ray particles. However, during propagation the composition changes because of
nuclear interactions. Thus, the abundance of the aforementioned particles can be used
to differentiate between the two categories and thereby to learn about the interstellar
medium.
The energy spectrum of cosmic rays above 10 GeV follows an at least twofold broken
power law:
dN
dE ∝ E−α ,
with different spectral indices α at different energy regions. Between about 10 GeV and
the so-called knee at about 4·10 6 GeV, the spectral index is 2.68 ± 0.02[4], between the
knee and the disputable second knee near 3·10 8 GeV it is 3.02 ± 0.03[5], from there up to
the ankle at 5·10 9 GeV its value is 3.16 ± 0.08[5] and at even higher energies it flattens
to 2.81 ± 0.03[6]. Above the GZK cutoff energy of 5·10 10 GeV the spectrum is assumed
to steepen dramatically because of interactions of the cosmic rays with cosmic microwave
background photons,
p + γ → ∆ + → p + π 0 and
p + γ → ∆ + → n + π + .
The nucleons emerge with about 80% of the initial proton energy, the effective mean free
path is of the order of 13 Mpc.[7] Recent HiRes and Auger results show strong evidence
for a cutoff, however it is unresolved if this is caused by the GZK effect.[6]
Low energy cosmic rays up to about 10 GeV are modified by solar flares. The origin
of high-energy cosmic rays is unknown. Top-down models propose them to be decay
products of topological defects formed in the very early universe; however, these models
7

2 NEUTRINO ASTROPHYSICS
Figure 2.1: Differential particle flux for the major cosmic ray components.[1] Shown are the
ten elements which have the highest abundance in the solar system.[2]
8

2.1 Neutrinos in Comparison with Other Messenger Particles
10 5
Knee
E 2.7 F(E) [GeV 1.7 m −2 s −1 sr −1 ]
10 4
Grigorov
JACEE
MGU
TienShan
Tibet07
Akeno
CASA/MIA
Hegra
Flys Eye
Agasa
HiRes1
HiRes2
Auger SD
Auger hybrid
Kascade
10 3 10 14 10 15
2nd Knee
Ankle
10 13 10 16 10 17 10 18 10 19 10 20
E [eV]
Figure 2.2: All-particle cosmic ray spectrum at high energies from air shower measurements,
weighted with E 2.7 . The shaded area was probed by direct measurements.[1]
are disfavored because they predict a photon flux that has already been ruled out by
EGRET and Auger.[8] Bottom-up models on the other hand explain high-energy cosmic
rays by acceleration of lower energy ones, e.g., by processes called Fermi acceleration.
Second order Fermi acceleration relies on the random elastic scattering of charged particles
at moving magnetic inhomogenities such as sparse plasma clouds, see figure 2.3. If the
particle enters the inhomogenity head-on and is reflected, its energy increases. Likewise it
loses energy if it is reflected at a receding inhomogenity, but assuming a random velocity
distribution this is less likely to happen. The resulting relative energy gain per reflection
as a function of the entry angle θ 1 , the exit angle θ 2 and the cloud’s speed v c ≡ cβ c for
relativistic particles (β p ≈ 1) is
ξ := ∆E
E = 1 − β c cos(θ 1 ) + β c cos(θ 2 ) − βc 2 cos(θ 1 ) cos(θ 2 )
− 1. (2.1)
1 − βc
2
Averaging equation (2.1) over θ 1 and θ 2 leads to
ξ = 1 + 1 3 β2 c
1 − β 2 c
− 1 = 4 3 β2 c + O(β 4 c ). (2.2)
The speed of galactic plasma clouds is only of the order of β c = 10 −4 , therefore second
order Fermi acceleration is too ineffective to explain the highest energy cosmic rays.[3]
This does not apply to first order Fermi acceleration: Instead of considering plasma clouds,
first order Fermi acceleration takes place at large and sufficiently plain shock fronts such as
9

2 NEUTRINO ASTROPHYSICS
E + DE
E + DE
v g
v s
q 2
q 1
v c
q 2
q1
plasma
cloud
E
E
upstream
(unshocked)
downstream
(shocked)
Figure 2.3: Left: Second order Fermi acceleration at magnetic plasma clouds.
Right: First order Fermi acceleration at shock fronts.
those originating from supernovae (see figure 2.3). If a shock front traveling at β s through
resting unshocked plasma (upstream) accelerates the plasma to β g < β s (downstream),
equation (2.1) holds for particles passing the shock front from the upstream side as their
average speeds adapt to the average speed of the shocked plasma after enough elastic
scattering processes, with β c := β g . As the particles are now on average comoving with
the shocked plasma, they will gain the same amount of energy by a second crossing of the
shock front, with the unshocked plasma approaching at β g in the shocked plasma’s rest
frame. Averaging over the angles yields
ξ = 1 + 4 3 β g + 4 9 β2 g
1 − β 2 g
− 1 = 4 3 β g + O(β 2 g). (2.3)
First order Fermi acceleration is substantially more efficient than the second order variant
not only because of ξ being proportional to the first order of β g but also because of larger
average speeds (β g ≈ 10 −1 ) and higher repetition rates – the same shock front can be
passed many times.
The escape probability can be estimated as P esc = 4(β s − β g ).[3] Using this, the
expected spectral index for non-relativistic shocks at the source is
α = P esc
ξ
+ 1 ≈ 3(β s − β g )
β g
+ 1. (2.4)
For strong shocks in a monatomic gas or plasma this evaluates to α ≈ 2.[3] For highly
relativistic shocks, the spectral index approaches 2.3.[9] The observed cosmic ray spectrum
with α ≈ 2.7 can be understood with (first order) Fermi acceleration if the effect of the
propagation is considered: Certain propagation models such as the leaky box model predict
a softening of the spectrum because higher energy particles are more likely to escape the
galaxy in which they are accelerated.
Cosmic rays with energies up to the knee are assumed to originate from galactic accelerators
such as supernovae remnants, while ultra-high energies above the ankle are
10

2.1 Neutrinos in Comparison with Other Messenger Particles
Figure 2.4: Ratio A of the sky with cosmic ray deflection angle δ > δ th at 4·10 10 GeV, extrapolated
to the propagation distance d = 500 Mpc under the assumption that
A(δ th , d) = A 0 (δ th · ( d 0
d
) α ). Between 70 Mpc and 110 Mpc, α equals 0.8, however it
might drop to lower values because the magnetic field’s orientation differs between
galaxy filaments.[10]
attributed to extra-galactic sources which still have to be determined. The spectral softening
in the “lower leg” energy region might be explained by propagation models or cut-off
energies as mentioned above. The transition between galactic and extra-galactic cosmic
rays remains unknown.
Cosmic rays are interesting messenger particles because they carry information about
the composition of their sources (primary cosmic rays) and the properties of interstellar
matter (secondary cosmic rays). However, only ultra-high-energetic cosmic rays can be
used to directionally locate the source objects: Primary cosmic rays are charged, thus
they are subject to electro-magnetic deflection. A particle’s gyroradius is given by
r = p ⊥
qB ≈ 3.3 m E e T
GeV q B
(2.5)
with p ⊥ being the particle’s momentum perpendicular to the magnetic field ⃗ B. For most
parts of the sky, the average deflection angle for particles near the GZK cutoff does not
exceed a few degrees over at least 500 Mpc, see figure 2.4.
11

2 NEUTRINO ASTROPHYSICS
2.1.3 Gravitational Waves
The carrier of the gravitational force called graviton has not yet been directly detected
and might never be due to fundamental difficulties such as extremely small cross-sections,
very low fluxes and a very strong neutrino background.[11] Still, gravitation can be used
for astronomical means by searching for gravitational waves, which are distortions of the
spacetime traveling at the speed of light. They can only be emitted by sources with timedependent
quadrupole or higher-order moments in their stress-energy tensor; candidates
are closely rotating or colliding objects such as neutron stars or black holes.
Up to September 2009 no gravitational waves have been identified, but competitive
upper limits have been published by various earth-bound detectors.[12] Space-based detectors
such as LISA are planned to extend the observed frequency range within the next few
decades. Compared to neutrino observatories, they are more limited concerning the possible
source objects, but they can deliver complementary information and provide tests for
general relativity and possibly other models of gravity. Both gravitational waves and neutrinos
are able to propagate through regions that are not transparent to electro-magnetic
radiation.
2.2 Neutrino Production Processes
2.2.1 Nuclear Processes
Stars in their nuclear fusion phase continously produce large numbers of neutrinos. For
stars with masses from 2 up to at least 20 solar masses (M ⊙ ), the total number of neutrinos
produced by fusion until the end of the helium burning phase in the core of the star is
approximately proportional to the star’s initial mass (figure 2.5). Later fusion phases
that can occur in stars heavier than 4 solar masses contribute only about one additional
tenth to this number as none of the main processes besides the silicon burning require
proton-neutron-conversions or similar weak interactions.[14]
Some neutrinos originate from processes with well-defined initial states and two-body final
states such as electron capture. These neutrinos are emitted at discrete energies, while
others are produced with many-body final states (e.g. by beta decay) and have continuous
energy spectra. Independent of this, their highest energies are of the order of some MeV
because this is the typical energy scale of nuclear processes.
2.2.2 Thermal Cooling
In addition to the neutrinos directly produced by nuclear fusion, the extreme temperatures
and densities inside stars allow the emmitance of thermal or cooling neutrinos by vari-
12

{1{
2.2 Neutrino Production Processes
10 58
pp chain
CNO cycle
10 57
Neutrinos
10 56
10 55
− − ignition of He burning
____ end of He burning
10 54
1 10
M/Mo
Figure 2.5: Total number of neutrinos produced until the ignition (dashed line) and until the
end (solid line) of the helium burning phase in population I stars as a function of
the initial star mass in solar masses.[13]
ous processes.[15] The resulting neutrinos’ energies directly depend on the temperature.
Silicon burning is the last and hottest fusion phase and takes place at about 3.5·10 6 K;
stars below about 4 M ⊙ never reach the last fusion phases but instead gravitationally
collapse to white dwarfs when their fuel is burnt and heat up to well over 100·10 6 K.[16]
Proto-neutron stars’ core temperatures can approach 1·10 12 K for a couple of seconds,
quickly cooling down to below 100 GK. Using this information and the Boltzmann constant
k B = 86.17 eV/MK, the cooling neutrinos’ energies can be estimated to almost never
exceed several MeV.
2.2.3 Cosmic Ray Interactions
The most probable source of high-energy (> 1GeV) neutrinos are interactions of cosmic
rays. Various reaction channels exist, among the most important are those with charged
pion production
p + p → X + π +
p + p → n + ∆ ++ → n + p + π +
p + p → p + ∆ + → p + n + π +
p + n → p + ∆ 0 → p + p + π −
p + γ → ∆ + → n + π + 13

2 NEUTRINO ASTROPHYSICS
and for higher energies those with kaon production.
The resulting mesons themselves decay quickly by
K + → µ + + ν µ (63.55%)
K + → π + + π 0 (20.66%)
K + → π + + π + + π − (5.59%)
K + → π 0 + e + + ν e (5.07%)
K 0 S → π + + π − (69.20%)
K 0 L → π ± + e ∓ + ( ν ) e (40.55%)
K 0 L → π ± + µ ∓ + ( ν ) µ (27.04%)
K 0 L → π + + π − + π 0 (12.54%)
π + → µ + + ν µ (99.99%).
Only decay modes with likely neutrino output and branching ratio ≥ 5% have been listed,
modes for negatively charged particles exist correspondingly.[17] The neutrino production
efficiency is lower in regions of high density because the particles might interact with other
particles before they decay.
The decay of charged pions to electrons is highly suppressed in favor of the decay to
muons because the latters’ helicity can be changed by boosts more easily. The muons
almost exclusively decay into electrons by µ + → e + + ν e + ν µ . Tau neutrino production
is dominated by the decay of D s
± mesons, which themselves have a low production crosssection.
Therefore, the ratios between the expected neutrino flavors near the interaction
point can be roughly estimated to be ( ( ν ) e : ( ν ) µ : ( ν ) τ) = (1 : 2 : 0).
2.3 Air Showers
High energy cosmic rays and gamma rays which enter the Earth’s atmosphere generate
a large amount of particles in form of atmospheric cascades called air showers, see figure
2.6. Particularly important are atmospheric muons and atmospheric neutrinos. Their
understanding is vital for all neutrino telescopes; they pose both signal for some analyses
and the major background source for the others.
The reactions discussed in section 2.2.3 can also occur in the upper atmosphere. The
energy spectrum for atmospheric muons and neutrinos follows a power law of E −3.7 at
lower energies; the reason is that a meson’s probability to interact with the atmosphere
instead of decaying increases with the meson’s lifetime τ = γτ 0 ∝ E. At high energies a
prompt decay component from charmed mesons supervenes, hardening the spectrum to
the primary cosmic ray spectrum of E −2.7 (figure 2.7).[19]
14

339298621 5634138942
01234 563416249522.3 Air Showers
Figure 2.6: Two extraterrestial muon neutrinos (dashed lines, entering from the left) and two
cosmic rays hitting the Earth. One neutrino passes undetectable, the other interacts
inside the detector. The upper air shower produces an atmospheric neutrino
which is detected and an atmospheric muon which is absorbed by the Earth, the
lower air shower’s atmospheric muon is detected.
±
pand K decay
±
pand K decay
secondary decay
prompt charmed
meson decay
prompt charmed
meson decay
secondary decay
Figure 2.7: Vertical atmospheric muon (left) and muon neutrino (right) differential fluxs
(including anti-particles) weighted with E −3 . Dashed lines indicate alternative
models.[18]
15

2 NEUTRINO ASTROPHYSICS
2.3.1 Atmospheric Muons
Events Passing
10 8 40
10 7
35
10 6
30
10 5
25
10 4
20
15
10 3
10
10 2
5
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 0 -1 -0.9 -0
Despite their short mean lifetime of about
2.2 µs, high-energetic muons produced in
the upper atmosphere at a height of typically
20 km can reach the Earth’s surface
because of the time dilation or length contraction
(depending on the frame of reference)
explained by special relativity. With
their high penetration potential which is
further discussed in section 3.2.2 they are
a major component of the background for
neutrino telescopes. This background can
be significantly reduced by “looking downwards”,
i. e. zenith angle cuts, as muons –
cos(θ)
in contrast to neutrinos – are not able to
pass more than a few kilometers through Figure 2.8: Zenith distribution of atmospheric
ÙÖ ÄØ Ì muons ÞÒØ (solid) ÒÐ and×ØÖÙØÓÒ atmospheric Ó ÅÆ ØÖ
the Earth; see figure 2.8.
ÖÓÑ ÓÛÒÓÒ Ó×Ñ muon neutrinos ÖÝ ÑÙÓÒ׺ (dashed), Ì × simulated
ÒÐfor ×ØÖÙØÓÒ IceCube’s Óprecursor
ÙÔÛÖ ÖÓÒ×ØÖÙØ
ÐÒ ×ÓÛ× ØÖ
ÊØ Ì ÞÒØ
2.3.2 Atmospheric Neutrinos
ÒØ× Ø ×ØØ×ØÐ AMANDA.[20] ÔÖ×ÓÒ Ó Ø ØÑÓ×ÔÖ ÒÙØÖÒÓ ×Ñ
For most analyses, atmospheric neutrinos are background. Except for their energy spectrum
which differs from the expected signal spectrum, they are fundamentally indistinguishable
from neutrinos of extraterrestial origin. However, down-going atmospheric
neutrinos can be tagged by searching for coincident muons in the detector.[21]
10 4 Data
Atmospheric MC
10 3
Downgoing MC
10 2
10
1
0 2.5 5 7.5 10 12.5 15 17.5 20 22.5 25
Analyses which involve atmospheric neutrinos as signal include neutrino oscillation
studies. For those, atmospheric neutrinos are of special interest because of their long
baselines (up to the diameter of Earth) compared to reactor neutrinos or artificial neutrino
beams from particle accelerators, making these measurements complementary.
10 -1
Quality Cut
Data / MC
6
5
4
3
2
1
0
0 2.5
ÙÖ ÚÒØ ÕÙÐØݺ ÄØ È××Ò ÖØ× Ó ÚÒØ× ÓÚ
ÖÓÙÒ Å¸ ØÑÓ×ÔÖ ÒÙØÖÒÓ Å Ò ÜÔÖÑÒØРغ
ÖØÓ Ø»Åº
16
¿¼

CHAPTER III
Neutrino Detection

3 NEUTRINO DETECTION
Figure 3.1: Cross-sections for scattering of neutrinos (solid) and antineutrinos (dashed) from
isoscalar nucleons 1 at energies between 10 3 GeV and 10 12 GeV. The results are
based on HERA particle distribution function measurements and have been extrapolated
above 10 7 GeV (CTEQ4-DIS).[22][23]
3.1 Neutrino Interactions
Neutrinos are electrically neutral leptons with spin 1 . They only interact via weak and
2
gravitational forces and come in three weak eigenstates called flavors, named after the
charged lepton with which the respective neutrino eigenstate can interact by a charged
current interaction.
According to the Standard Model, neutrinos are massless particles; however it is widely accepted
that this is not accurate since many experiments verified the existence of neutrino
oscillations, which can occur because the neutrino mass eigenstates are pairwise different
and not congruent with the weak eigenstates.
Because of their low cross-sections, neutrinos can travel over huge distances through ordinary
matter almost without attenuation up to very high energies (figure 3.1). Not until
about 10 6 GeV, the Earth’s core starts to become opaque to neutrinos.
The relevant processes involving neutrinos are neutral current (NC) and charged current
(CC) interactions.
Neutral current interactions – i.e., interactions which are mediated by a Z 0 boson – are
1 The particle distribution function (PDF) of an isoscalar nucleon (an hadronic single state with isospin
I = I 3 = 0) is the arithmetic mean between those of a proton (I 3 = + 1 2 ) and a neutron (I 3 = − 1 2
), or
half the PDF of a deuteron, which is the true isospin singlet. As we can neglect electrical charges, it is a
good approximation of the average nucleon PDF.
18

3.2 Lepton Propagation
the same for the three flavors and constitute about 10% of the charged current crosssections.[22]
The most important NC interactions are those with the nucleons N because
they have much larger cross-sections than interactions with the matter’s electrons:
ν a + N → ν a + X, a ∈ {e, µ, τ}
X is the hadronic rest of the nucleon which will trigger a hadronic cascade. The neutrino
escapes with a large fraction of its initial energy.
Charged current interactions are mediated by W ± bosons and differ for the different flavors
mainly in the produced leptons a ± . As above, interactions with the nucleons make up the
largest part:
ν a + N → a − + X
ν a + N → a + + X
The initial direction of the lepton is well aligned with the neutrino’s track; the average
angle mismatch can be estimated as ψ = 0.7° · ( )
10 3 GeV 0.7.[24]
E ν
For both NC and CC up to about 10 7 GeV, the cross-sections for antineutrinos are below
their neutrino counterparts because of the valence quark distribution. This effect becomes
negligible for higher energies where the PDFs are dominated by sea quarks (and gluons,
which, however, do not interact via the weak force).
Gravitational effects can largely be ignored. Highly relativistic neutrinos independent
of their mass are subject to gravitational lensing just as photons; in fact, they can even
be lensed stronger by certain objects as they are able to pass most electromagnetically
opaque regions without absorption.[25]. However, in most cases the angle of deflection is
very small compared to the angular resolution of current neutrino telescopes.
The probability for a detector signal being caused by direct gravitational interactions is
negligible in the Standard Model but increases under assumptions such as the existence
of compact extra dimensions. In the latter case, one could expect an increased ratio of
elastic scattering (at impact parameters b larger than the Schwarzschild radius r S ) and
cascades without primary lepton through black-hole creation (at b < r S ).[26]
3.2 Lepton Propagation
The charged lepton produced in charged current interactions is the most important signature
for most types of neutrino detectors. Common to all flavors is the hadronic cascade at
the interaction point, which contains roughly 40% of the neutrino energy. The signatures
of the primary leptons inside the detector vary for the different flavors (see figure 3.2).
19

3 NEUTRINO DETECTION
hadronic
cascade
electromagnetic
cascade
Èerenkov radiation
e
Figure 3.2: Sketch illustrating the signatures of charged current interactions of neutrinos in
Čerenkov media as described in sections 3.2 and 3.3. Note that every hadronic
cascade also has an electromagnetic component.
Figure 3.3: Depth development of electron initiated cascades in numbers of particles vs. depth
in units of radiation lengths in ice. Shown are simulated curves for the sum of
electrons and positrons (blue), the excess of electrons (red), and theory predictions
(dashed, Approximation-B) at 1, 10, and 100 TeV (down to up).[27]
20

3.2 Lepton Propagation
Figure 3.4: Effective radiation length λ ∼ = X LPM modified by the LPM effect.[28]
3.2.1 Electron Propagation
Electrons in dense matter quickly lose energy through bremsstrahlung. The generated
photons convert to new electrons and positrons via pair production, resulting in an exponential
growth of the particle number until the photons’ energies fall below 2m e and the
leptons’ energy falls below the threshold at which ionization losses become dominating,
called critical energy. For ice, this cricital energy is E e crit = 81 MeV.[29] Since the photon
and electron free mean paths are of the same order of magnitude, the shower depth X at
a given initial energy E 0 up to about 1 PeV can be approximated by
X = X 0 log 2
( E0
E crit
)
with the radiation length X 0 (36.08 g/cm 2 in ice). As the cascade is highly boosted
and therefore directed, its length can be estimated to be L = 2Xρ, where ρ is the
density of the material. ( For deep Antarctic ice (ρ = 0.924 g/cm 3 ), this evaluates to
E e
)
L = 0.67 m log 0
2 81 MeV , which is of the order of 10 m.
Starting at about 1 PeV the radiation length X 0 has to be replaced by the effective
radiation length X LPM to take account for the LPM effect: The formation length for
bremsstrahlung and pair production interactions increases with the particle’s energy, resulting
in the suppression of these interactions and therefore in significantly longer cascades
(about 200 m at 10 EeV, see figure 3.4).[28]
3.2.2 Muon Propagation
Because of the muon’s higher mass m µ = 207m e , its energy loss due to bremsstrahlung is
much smaller. Up to the critical energy (E µ crit ≈ 500 GeV in ice) ionization losses are most
important, at higher energies electron pair production and radiation losses dominate. The
21

3 NEUTRINO DETECTION
expected track length l/km
50
40
30
20
10
muon
tau
0
10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9
initial energy E 0 /GeV
Figure 3.5: Expected track length for muons and tau particles in Antarctic ice according to
the models explained in section 3.2.1 and section 3.2.2.
total energy loss is approximately given by
− dE
dx
= a + bE, (3.1)
where a(E) is the ionization loss given by the Bethe-Bloch equation and b(E)E a parametrization
for the higher-energy processes; both parameters are fairly constant for
E > E µ crit.[30] For ice, this yields approximately
− dE
dx = 0.25 GeV/m + 4.3·10−4 E/m, [31]
leading to an expected track length of L = 2300 m · ln ( )
1 + E 0
E (figure 3.5), which is
µ
crit
small compared to the length a muon can travel in its mean decay time at its critical
energy, l µ ≈ 3 Mm. Since the energy losses are stochastical, actual values vary, and often
much energy is lost at once, triggering a cascade along the muon track. The scattering of
high-energy muons is negligible.[31]
3.2.3 Tau Propagation
Much heavier than muons (m τ = 16.8m µ ), tau particles lose even less energy when propagating
through matter. Equation (3.1) holds for them as well, with a being very similar
and b ≈ 3.6·10 −5 /m.[31] Because of the tau’s short mean lifetime τ τ = 0.29 ps, their detector
signature is determined by the hadronic cascade at the neutrino interaction point
and the decay of the tau which usually triggers a second cascade. The branching ratio for
τ − → µ − + ν µ + ν τ is 17.4%, the remaining decays spawn at least one electron or charged
22

3.3 Čerenkov Detectors
C
Figure 3.6: Sketch illustrating the emission of Čerenkov radiation (blue) by a superluminal
particle (track in red).
meson.[17] The interaction points are seperated by the tau decay length l τ = 49 m · E0
PeV
(figure 3.5). Up to a few PeV, the resulting cascades overlap and are indistinguishable.
For higher energies, both cascades are seperated and connected by a faint Čerenkov track,
forming a characteristic signature called double bang (illustrated in figure 3.2). If one of
these cascades lies outside the detector volume, the resulting signature is called lollipop
(resp. inverted lollipop).
3.3 Čerenkov Detectors
One of the most effective methods to detect neutrinos is the use of Čerenkov radiation.
Čerenkov radiation is emitted whenever a charged particle travels through dielectric matter
(the Čerenkov medium) at a speed v = βc higher than the material’s phase speed of
light c m = c , where n denotes the material’s refractive index (n = 1.32 for ice). The
n
particle travelling through the medium polarizes the surrounding atoms, which emit light
when they return into equilibrium. If the speed of the particle exceeds c m , the interferences
become constructive and a wave front of light is sent out at a distinctive angle
θ C = arccos (n −1 β −1 ) called Čerenkov angle (see figure 3.6). The light’s spectrum is continous
and its intensity is approximately linear in frequency, resulting in a blue appearance
to the human eye. At x-ray frequencies the spectrum is cut-off as the refraction index
becomes smaller than one.
The rate of emitted photons can be calculated with the simplified Frank-Tamm formula:
∫
dN
dx = λmax
2παz 2 (
1 − 1 )
dλ, (3.2)
λ min λ 2 n 2 β 2
where α ≈ 1 is the fine-structure constant and z the particle’s electric charge. The
137
wavelength range given by λ min . . . λ max is determined by the optical properties of the
23

3 NEUTRINO DETECTION
Čerenkov medium.
Čerenkov media have to be transparent for blue to ultraviolet light. Additionally, for
neutrino detection they need to have reasonably high density and be available cheaply in
large quantities. Air is not sufficiently dense, so neutrino interactions in air are rather
unlikely; it can still be used for air shower detectors. H 2 O, both liquid or solid, is well
suited for large detectors. Deep and clear lake or sea water generally involves less scattering
(up to a factor of 10[32]) but higher absorption (about factor 2) than bubble free ice.
Additional challenges for water neutrino telescopes are the variable environment and a
strong background of bioluminescence from various lifeforms as well as radioactive decays
of unstable isotopes such as 40 K.[33][34] The optical properties of deep Antarctic ice will
be examined in section 4.2.
24

CHAPTER IV
The IceCube Neutrino Observatory

4 THE ICECUBE NEUTRINO OBSERVATORY
4.1 Layout
The IceCube Neutrino Observatory is a combined air shower and neutrino detector located
at the Amundsen-Scott South Pole Station at the geographic South Pole. It consists of
three main parts, InIce, DeepCore, and IceTop (figure 4.2):
InIce is an underground Čerenkov detector which uses about one cubic kilometer of
Antarctic ice as neutrino interaction and Čerenkov medium, making it the World’s largest
neutrino detector at the time of writing. In its final configuration, it will consist of 80
long cables called strings with 60 digital optical modules (DOMs) each. The strings are
lowered into hot-water-drilled holes in the ice sheet, with the lowest DOMs positioned
around 2450 meters below the surface and a vertical spacing of about 17 m, adding up
to 1000 m of instrumented length. After deployment of each string, the water inside the
hole refreezes, making recovery and maintenance impossible but also optically coupling
the DOM to the surrounding ice. The horizontal spacing between the strings is approximately
125 m in a hexagonal pattern, spanning approximately one square kilometer across
(figure 4.1). Because of this geometry and the ice properties elaborated in section 4.2,
InIce’s lower energy threshold is about 100 GeV.
Figure 4.1: IceCube surface geometry with distances between the strings; the lighter a circle’s
color, the earlier the string has been deployed. Black circles are strings scheduled
for deployment in summer 2010/2011, small dots are IceTop tanks.[35]
26

4.1 Layout
Figure 4.2: Three-dimensional sketch of IceCube, with DeepCore marked in green. Also shown
are the dust layer at (2000 . . . 2100) m depth (see section 4.2), the ground below
the ice sheet at about 2850 m depth, and an image of the Eiffel Tower for size
comparison.[36]
27

4 THE ICECUBE NEUTRINO OBSERVATORY
DeepCore is a low-energy extension to this detector. Located at its lower center, it consists
of 6 extra strings with 60 high-efficiency DOMs each (section 4.3). In contrast to the
standard strings, they are more densly instrumented in two groups of 10 and 50 DOMs
each with an inner-group spacing of 10 m and 7 m respectively, and a gap of 257 m between
the two groups to take advantage of the clear ice in these regions (section 4.2). These
strings have been deployed in a half-sized hexagon centered at standard string 36. The
two standard strings 79 and 80 have not been deployed at their original positions and have
been proposed to be installed inside the DeepCore volume to make it even more densly
instrumented. The energy threshold of the combined InIce+DeepCore detector will be
around 10 GeV. In its task as low-energy extension, DeepCore supersedes IceCube’s now
decomissioned precursor, the Antarctic Muon And Neutrino Detector Array (AMANDA),
which took data from 1994 to 2009 and which was integrated into IceCube in 2005.
IceTop is an air shower Čerenkov detector which in its final configuration will comprise
of 160 polyethylene tanks at the ice sheet’s surface which encompass each a volume of
2.5 m 3 of bubble-free ice observed by two DOMs. It will be capable of reliably detecting
air showers with a primary particle energy threshold of about 150 TeV.[37] Besides conducting
interesting experiments by itself, it is planned to use it for background rejection
in neutrino analyses.
For this thesis InIce and DeepCore form the relevant part of IceCube as IceTop uses
its own feature extraction algorithms. Therefore “InIce+DeepCore” and “IceCube” will
be used interchangeably in the following chapters if not stated otherwise.
In the Antartic winter, temperatures regularly fall below −65 °C, rendering impossible
the operation of most machines. Because of this, IceCube had different string configurations
for data-taking during the months in which deployment had to be suspended.
Construction of Icecube began with one experimental string during 2005, followed by eight
additional ones in the 2005-2006 Antarctic summer. This configuration – following the
same naming scheme as the later ones – was called IC9. Together with the thirteen strings
deployed during the summer of 2006-2007, it formed IC22. During the next summer eighteen
strings were added, resulting in the detector configuration IC40. In the summer
between 2008 and 2009 eighteen more standard strings and one DeepCore string were
deployed (IC58+1 or IC59), as well as twenty during the 2009-2010 deployment season
(IC73+6 or IC79). With DeepCore already completed, the final detector will be fully
available in 2011.
4.2 Ice Properties
IceCube’s and especially DeepCore’s geometry are heavily influenced by the properties
of the Antarctic ice. The experiment’s location was chosen because of the deepness and
purity of the naturally available ice and because of the good infrastructure provided by
28

4.2 Ice Properties
Figure 4.3: Inverse effective scattering length (left) and inverse absorption length (right) vs
depth in deep Antarctic ice measured with pulsed sources at different wavelengths.
A, B, C and D denote major dust peaks. Values for deep ice (below D) might be
overestimated, see section 4.2.[39]
the Amundsen-Scott South Pole Station.[38] The two most important optical properties
are the effective scattering length λ e and the absorption length λ a .
The scattering length λ s for IceCube is defined as the mean free path between scattering
processes. The average angle between the unscattered path and the scattered path is
〈cos(θ)〉 ≈ 0.94 ≫ 0. Because of this, the effective scattering length is defined as
λ e := λ s
n ∑
i=0
〈cos(θ)〉 i
n→∞
−−−−→
λ s
1 − 〈cos(θ)〉 .
This is an estimate for the length after which a beam of light has become fairly isotropic.[39]
The scattering inside the upper ice layers is dominated by microscopic trapped air bubbles.
Because of the enormous pressure at high depths, the bubbles are compressed steadily until
at about 1400 m scattering at dust particles begins to prevail (figure 4.3). Below, there
are regions of higher dust concentrations which have been designated as dust peaks A to
D. The same structures have been identified by ice core measurements in other regions
and correlate well with cold periods (stadials) during the current interglacial period of
the current ice age. The strongest of those peaks – peak D, also known as the dust layer
– is approximately 65000 years old and features very short effective scattering lengths of
less than 10 m; because of this, DeepCore was designed with DOMs above and below this
region, but without DOMs within.
The absorption length – defined as the length after which the light intensity has
dropped by a factor of e −1 – is significantly higher than the effective scattering length
(about 100 m compared to about 30 m, see figure 4.3). At green wavelengths the main
contribution is the absorption by the ice itself; at shorter wavelenghts dust particles
dominate and the dust peaks can be identified accordingly.
29

4 THE ICECUBE NEUTRINO OBSERVATORY
The deep ice starting at 2100 m below the dust layer has not yet been studied as well
as above because the ice properties were calculated mostly based on data measured with
AMANDA. Only three AMANDA strings reached below the dust layer, the deepest being
string 11 with a maximum depth of 2136 m. As well-defined light signals are needed for
this type of measurement, various calibrated light sources have been used: AMANDA
optical modules (OM s) had diffusor balls attached which were coupled with a frequency
doubled Nd-YAG laser at the surface; two nitrogen lasers were deployed near the center
of the detector; eight OMs were equipped with flasher boards containing six blue LEDs
each, and one string was equipped with ultraviolet LED flasher boards for every OM.
Additionally to these pulsed light sources, two continous sources with wider spectrum
were deployed inside the ice.
All IceCube DOMs contain similar flasher boards with twelve LEDs each, see section
4.3. Recent IceCube measurements have shown that the deep ice might be clearer than
previously thought, with λ e ≈ 50 m and λ a ≈ 200 m at blue wavelengths (405 nm).
The resulting propagation length λ p acts as damping constant in the fluence development
of light sources in the diffuse regime, i.e., after a few scattering processes:
λ p :=
√
λe λ a
3
with
F (d 5λ e ) ∝ 1 d e− d
λp .[39]
4.3 Digital Optical Modules
The main task of IceCube’s DOMs is to capture Čerenkov light and to convert it into
digitized waveforms, which are then sent to the surface. They consist of a photomultiplier
tube (PMT), a flasher board, a mainboard containing most of the electronics, a delay
board, and a high-voltage board, housed inside a 32.5 cm diameter glass pressure sphere.
The photomultiplier is embedded into RTV (room temperature vulcanizing) silicone gel
to optically couple it to the glass, and it is shielded against Earth’s magnetic field by a
cage of mu-metal (figure 4.4).
The flasher board lies in the DOM’s upper hemisphere with six pairs of blue (405 nm)
LEDs mounted outwards in 60° intervals. Each pair consists of one LED on the lower side
of the board mounted horizontally and one LED on the upper side tilted approximately
40° upwards. As pointed out in section 4.2, the flashers can be used to determine or
validate ice properties and to calibrate the detector.
The high-voltage board is required to power the PMT. The PMT’s signal is decoupled
by a toroidal transformer instead of a capacitor; the circuit’s low capacity of about 5 pF
compared to the about 1 µF needed for a conventional capacitor coupling reduces the risk
of discharges damaging the mainboard and delivers a more stable long-time signal quality
as capacitors degrade over time. Furthermore, tests have proven the transformer coupling
30

4.3 Digital Optical Modules
Figure 4.4: Sketch of an IceCube Digital Optical Module (DOM).[40]
to better filter out the power supply’s noises. However, as the transformer acts as high-pass
filter, it causes droop: The signal’s voltage falls off right after the initial peak, distorting
the waveform and making it undershoot the former baseline. This effect depends strongly
both on the surrounding temperature T and on the toroid used. DOMs built before
2006 – called old toroid DOMs or OT – are highly affected by droop, while new toroid
DOMs (NT) are almost unaffected (figure 4.5). The individual toroid types are known
and the temperatures can be measured with an on-board sensor; therefore the droop can
be corrected for during calibration (section 4.6.1), using the dual-tau parametrization[42]
in which the DOM’s transient response ˜δ(t) to a signal δ(t) is modelled as
˜δ(t) = δ(t) − N
(
4.3 e − t
τ 1
− 3.3 e − t
τ 2
)
, τ 1 (T ) := t 1 +
t 2
, τ
1 + e − T 2 := 0.75 τ 1 .
Tc
The parameters N, t 1 , t 2 , and T C have to be determined empirically. While the NT
DOMs significantly reduce the droop problems, they also possess differently shaped, wider
waveforms (figure 4.6), which is important for feature extraction, i. e., the analyzation of
the waveforms captured by the DOMs, see section 5.
The delay board features a high-quality serpentine circuit that delays the throughgoing
signal for 75 ns. Only two of the three signal paths are delayed, a third path leads
to the trigger system to decide whether to launch this DOM, i.e., to digitalize waveform
31

4 THE ICECUBE NEUTRINO OBSERVATORY
Figure 4.5: Waveforms illustrating the toroidal droop effect for OT (upper) and NT (lower)
DOMs, showing an uncalibrated (raw) waveform on the left and the corresponding
droop-corrected one on the right. For the OT graphs 100 waveforms have
been averaged, the NT graphs show an individual waveform; both were taken at
−55 °C.[41]
and to check for local coincidence, see section 4.4.3. The trigger threshold is typically set
to 0.25 PE (photoelectron charges).
From the remaining two paths, one is distributed among three amplifiers (×16, ×2 and
×0.25) which supply the analog transient waveform digitizer (ATWD, section 4.4.1) with
data, and the other one supplies the fast analog digital converter (FADC, section 4.4.2).
Last but not least, the PMT itself is relevant for feature extraction as it is the component
which generates the signal. It is a Hamamatsu R7081-02 with a diameter of 25 cm
and a peak quantum efficiency of 25% around 410 nm. It houses ten dynodes leading to
a gain factor of about 10 7 and has a dark count rate below 400 Hz between −60 °C and
0 °C, mostly caused by 40 K decay in the glass. The DeepCore high-efficiency DOMs differ
in that they have an improved photocathode, leading to a higher quantum efficiency of
up to 33%.[43]
Three effects can lead to erroneous pulses: Photons may bypass the photocathode and
directly hit the first dynode ahead of the electrons, triggering an early electron cascade
from there on. Despite missing one multiplication process, these prepulses exceed a signal
32

4.4 Signal Digitization
Table 4.1: Overview over different digitizers resp. I3Waveform source types.
source n bins T bin T total resolution U satu
ns ns bit mV
ATWD ch0 128 3.3 422 10 100
ATWD ch1 128 3.3 422 10 800
ATWD ch2 128 3.3 422 10 7500
FADC 256 25 6400 10 70
SLC 3 25 75 10 70
strength of 0.25 PE for about 0.5% of all 50 PE pulses at 25 °C according to measurements
by Hamamatsu.[44] They typically occur 32 ns prior to the real pulse.[45]
Late pulses can occur if photoelectrons are backscattered at the first dynode. If they hit
the first dynode at the second approach, they will trigger a pulse which lags behind by up
to 66 ns, which is twice the transit time between photocathode and first dynode, or even
more for multiple backscattering. Their typical rate is 1.5% for pulses as above.
Finally, afterpulses are caused by ionized molecules of the remaining gas or luminescence
photons from the dynodes hitting the photocathode. They typically occur for 2.0% of
the aforementioned pulses and are frequently found a few microseconds after the real
pulse.[44][46]
4.4 Signal Digitization
The two digitizers ATWD and FADC mentioned in section 4.3 act as different sources for
raw waveforms. These raw waveforms still show undesirable characteristics such as droop,
and have to be calibrated before they can be used for feature extraction, see section 4.6.1.
The most important parameters of these digitization circuits are listed in table 4.1.
4.4.1 ATWD
The analog transient waveform digitizer is an application-specific integrated circuit (ASIC)
located on the DOM’s mainboard. Three amplifiers feed the PMT signals into three of
the ATWD’s input channels, leading to different saturation voltages U satu . If a trigger
condition is met, channel 0 – the one with the lowest gain – is digitized first. All channels
feature a resolution of 10 bit ̂= 1024 counts, i.e., discrete values; if the maximum value of
one of the first two channels exceeds 768 counts, the next higher channel is digitized as
well. For channel 2, U satu = 7.5 V is greater than the PMT’s maximum voltage of 5 V, so
all ATWD channels together span the full dynamic range of the PMT. The combination
33

4 THE ICECUBE NEUTRINO OBSERVATORY
q / PE
0.3
FeatureExtractor
NFE ATWD OT
NFE ATWD NT
NFE FADC
0.2
0.1
0 5 10 15 20
bin
Figure 4.6: Comparison of ATWD and FADC single photoelectron (SPE) waveform shape
parametrizations used in different feature extractors. The three NFE parametrizations
are based on a study by Christopher Wendt.[47] Note that the bin length
differs for ATWD and FADC, so the shapes are not to scale time-wise.
of the different channels is performed by the IceCube software module DOMcalibrator
either on a bin-to-bin or on a global waveform basis depending on the configuration; the
three channels’ combined effective resolution is about 14 bit.
The average waveform shape of a single photoelectron (SPE) signal depends on the DOM’s
toroid, see figure 4.6.
The conversion time amounts to 29 µs during which the ATWD can not capture further
waveforms. To compensate for these dead times, the mainboard contains two different
ATWD chips called ATWD-A and -B, processing the signal alternatingly. This significantly
reduces the dead time: When a DOM is triggered (launched), both the FADC and
one of the ATWD chips start capturing. The DOM can not be retriggered until the FADC
has done capturing; it is ready again after 6.45 µs (section 4.4.2). If the DOM is launched
again in the remaining 22.55 µs during which the ATWD chip is digitizing the waveform,
the FADC will start capturing together with the other ATWD chip.[46]
4.4.2 FADC
The fast analog digital converter has a larger bin length resulting in a coarser but longer
digitized waveform (table 4.1). Its main usage is to capture features which are too late or
too long to appear in the ATWD waveform(s).
The FADC’s time resolution is not sufficient to resolve SPE-like PMT features. Because
34

4.5 Data Structure and Data Rate
of this, a 180 ns pulse shaper is used to broaden the input signals. The widening allows
to estimate the feature’s arrival time with sub-bin precision by the distribution of the
captured charge in several bins. The FADC has negligible dead time (two clock cycles
equaling 50 ns), and is the digitizer used to provide SLC charge stamps.[46]
4.4.3 SLC Chargestamps
Prior to the IC59 data taking season in 2009, DOMs were only read out in case of multiple
DOMs fulfilling a hard local coincidence (HLC) condition: To reduce data caused by noise,
a DOM’s ATWD and FADC waveforms were only transmitted to the surface if one of the
neighboring or – depending on the configuration – one of the next-to-neighboring DOMs
also triggered within one microsecond.
Since IC59, DOM launches that do not fulfill HLC are kept irrespectively if other DOMs
triggered HLC during a small time window. To reduce the amount of data caused by these
so-called soft local coincidence (SLC) launches, SLC charge stamps are stored instead of
full ATWD and FADC waveforms. These charge stamps are condensed FADC waveforms;
instead of 256 bins they contain only the highest of the first 16 bins and its two direct
neighbors. In most cases, this will yield a concave waveform (in which the middle bin will
be the highest one), but in some cases FADC bin 0 or 15 might hold the maximum. In
these cases, the value of bin -1 (which can and will be accessed by the DAQ) resp. bin 16
might be even larger, leading to an irregular SLC charge stamp in which the middle bin
is not the highest.[48]
The comparatively low saturation voltage of the FADC does not hamper SLC charge
stamps because of two reasons: First the brightness required to saturate FADC would
almost inevitably trigger nearby DOMs and consequently HLC, and secondly there is
a third trigger condition called self-local coincidence, fully launching every DOM with
exceptionally strong PMT signals independently of HLC.[46]
4.5 Data Structure and Data Rate
The start times of DOMs fulfilling a HLC condition are sent to the IceCube Laboratory
on the surface and analyzed by triggers. If they meet the specified criteria of at least
one trigger condition, the launches are aggregated into an event. All waveforms inside an
event are calibrated, features are extracted and used by different algorithms to quickly
reconstruct a muon track or a cascade, which is then assessed by different online-filters.
If at least one of these filters decides that this event is worth to be kept, it remains in the
data stream which is written into binary .i3 files that are sent to northern hemisphere
collaboration members per satellite for offline-processing. Additionally all data is recorded
on tapes. Up to several hundreds successive .i3 files are summarized into a single detector
run normally lasting about 8 h, during which the detector configuration is assumed to be
constant.
35

4 THE ICECUBE NEUTRINO OBSERVATORY
A DOM’s in-ice data rate for HLC launches is about 10 Hz, its SLC launch rate
corresponds to the dark count rate of about 300 Hz. The rate of events passing the
triggers (global trigger rate) is of the order of 4000 Hz, the global filter rate lies below
100 Hz.
4.6 Software
The IceCube software is built within a highly modular framework called IceTray[49]. Data
processing of all kinds is organized serially in one-way streams. IceTray itself provides
base classes for modules (e. g. I3Module) and services (I3Service), frames (I3Frame)
which are the containers in which all data belonging to an individual IceCube event is
saved, a definition of physical units (I3Units), Python scripting support and much more.
Various projects can be loaded to provide further functionality by adding modules and
services, such as dataclasses as standardized interface for various IceCube specific objects,
DOMcalibrator for waveform calibration (section 4.6.1), tools for filtering, visualization
as well as feature extraction and reconstruction. The NewFeatureExtractor (NFE, I3NFE)
presented in this thesis is one of these projects.
IceTray and selected projects are bundeled to form different meta-projects which facilitate
easy installation of software environments for specialized tasks such as online-filtering,
simulation (IceSim), reconstruction (IceRec), or analysis (e. g. Offline-Software).
The software is written in C++ almost exclusively, however since IceTray v3 was released
in 2009, modules can be written in Python as well, which was previously only used for
steering scripts.
4.6.1 DOMcalibrator
Calibration encompasses many different processes in both the detector maintenance and
data taking processes. This section deals with the waveform calibration conducted by the
IceCube software module DOMcalibrator (I3DOMcalibrator).
The DOMcalibrator’s tasks are to convert the raw waveforms (I3DOMLaunchs) captured
by the PMT in units of counts to calibrated waveforms (I3Waveforms) in units of mV with
a near-zero baseline, to combine the three ATWD channels, and to compensate for known
signal distortions and time delays.
Per-DOM values for the signal transit time, a baseline offset and the gain are obtained by
monthly DOMCal detector runs and stored in an online database among other important
information such as droop correction parameters (see section 4.3). For use in offlineprocessing,
GCD files (geometry, calibration, detector status) belonging to individual
runs (or simulated datasets) are used instead.[41]
36

CHAPTER V
Feature Extraction in IceCube

5 FEATURE EXTRACTION IN ICECUBE
Feature extraction in IceCube refers to the analysis of digitized calibrated waveforms.
It aims for the determination of the number and time distribution of photons
observed by IceCube’s DOMs. The main challenge is to deconvolute the PMT’s and in
case of FADC the pulse shaper’s smearing functions with robust and efficient algorithms.
Dataclasses provides two classes for the feature extraction output: the I3RecoHit and
the I3RecoPulse.
An I3RecoHit stores information about time and source. It was designed to represent
a single photon triggering the PMT and therefore corresponds to a deposited charge
of exactely 1 PE. Similar hits were used in AMANDA’s reconstruction chain, however
in IceCube hits are largely deprecated in favor of pulses; of the four feature extraction
modules presented in this thesis, only FeatureExtractor and SLCHitExtractor support
hits.
I3RecoPulse also provides information about time and source, but additionally stores
the deposited charge in units of PE and the width of the pulse, thereby offering more
information, which depends less on design decisions; for example I3RecoHit creation is
ambigious in case of three distinct but close 0.7 PE features because their total charge
corresponds to only two hits, or in case of a single 1.5 PE feature.
Both classes offer a data member called hitID whose purpose is not well-defined. For
all four feature extraction modules presented in this thesis, it redundantly reflects the
hit’s or pulse’s position in their respective series 2 . This hitID is put to better use in
merged I3RecoPulseSeries as it can be used to trace back a pulse, see section 5.4.5.
All of the series of one event are finally organized in a STL map using their DOM
and string numbers combined in OMKeys as key value. The resulting I3RecoHitSeries-
Map/I3RecoPulseSeriesMap can then be accessed by other modules and services further
down the data stream.
For the following chapters, let w i , i = 0 . . . L, be the values of the bins of a given
calibrated waveform, with L = 127 for ATWD, L = 255 for FADC and L = 2 for SLC.
5.1 FeatureExtractor
The FeatureExtractor (I3FeatureExtractor, FE) mainly written by Dmitry Chirkin[50]
is the feature extraction module currently used for IceCube ATWD and FADC waveforms.
Developement began in 2003 for fat-reader, an alternative IceCube software suite. A first
release for IceTray under SVN 3 control was made in 2005 for the use with data from
2 Series is IceCube’s name for standard C++ STL vectors that contain related objects such as all
hits/pulses extracted from a single DOM for a distinct event.
3 SVN aka Subversion is the version-control system used for the central IceCube source code repository.
38

sum of all bins above
baseline + error
extrapolation of
maximum slope
to baseline
width
width:
half of the number
of bins above
first pulse‘s half
maximum height
threshold
5.1 FeatureExtractor
parabola fit to maximum bin
charge:
parabola maximum
× pulse width
extrapolation of first
local maximum slope
above threshold
to baseline
charge:
sum of all bins
extrapolation of
maximum slope
to baseline
width:
proportional to
charge / maximum
threshold
width
Figure 5.1: Sketch illustrating FeatureExtractor’s first single-pulse extraction algorithms to
left and its second one to the right. Shown is a part of a calibrated waveform in
arbitrary units; baseline correction has been omitted for reasons of clarity.
x
x
IceCube’s first deployed string. Since then, new algorithms and options were added to
the module. It is used for practically all physics analyses up to early 2010.
For ATWD the FeatureExtractor offers two single-pulse extraction algorithms that
define at most one pulse per waveform as well as two more sophisticated multi-pulse
x
extraction algorithms; for FADC it uses a fifth algorithm.[50]
x
x
x
The first single-pulse algorithm extracts only one pulse given by the largest feature
in the waveform, and its corresponding charge, see figure 5.1. It searches the maximum of
the waveform’s slopes ∆w i := w i+1 −w i from the beginning up to the waveform’s maximum
bin w max (or to the first saturated bin if any). The intersection of the extrapolation of this
slope with the baseline is used to define the leading-edge time. The algorithm then fits a
parabola through the waveform’s maximum and its two surrounding bins; the difference
between the position of the maximum and the leading-edge time from above defines the
width of the pulse. This width multiplied with the parabola’s maximum defines the charge
of the pulse.
This is a very fast algorithm, but it lacks robustness. For a given waveform, the maximum
of the waveform’s slopes does not neccessarily belong to the feature with the highest
amplitude; this might be due to overlapping features where one feature’s tail flattens
the next feature’s leading edge, due to binning effects, or due to statistical fluctuations.
In these cases, the extracted width and thereby the extracted charge can be extremly
overestimated, and the time does not match the largest feature. Also, for most track
reconstruction methods the first feature’s time is more valuable than the time of the
largest feature, because it is least affected by scattering. Therefore it is disadvantageous
to extract only the maximum pulse’s leading edge time as done by this algorithm.
To make it more robust, the algorithm can be configured to use the second single-pulse
algorithm’s charge estimate instead; however, the whole algorithm is largely superseded
by the second single-pulse algorithm.
39

5 FEATURE EXTRACTION IN ICECUBE
The second single-pulse algorithm extracts the time of the first feature’s leading
edge along with the waveform’s total integrated charge. Precisely, it searches for the
first local maximum of the ∆w i for all consecutive pairs (w i , w i+1 ) above a configurable
threshold and computes the position of baseline-crossing of its extrapolated slope. The
pulse’s charge q is defined as sum over all waveform bins, and the width is defined by
q
const·
w max
as illustrated in figure 5.1 (contradicting to the documentation[50], see section
C.2).
Like the first single-pulse extraction algorithm, this second one is fast, however it is
not robust regarding prepulses (see section 4.3): As prepulses are rare and only have
a small amplitude, they normally have little impact on reconstruction and might not
even pass the trigger or extraction threshold. However, for many-PE features they can
cause a comparably tiny peak ahead of the large feature. In these cases, the algorithm
attributes the whole charge to the prepulse, potentially increasing its weight in the later
track reconstruction heavily.
Because of its speed and the low rate of prepulses the algorithm is nonetheless well-suited
for online-filtering, for which it is currently used.[51]
The first multi-pulse algorithm is the sophisticated but time-consuming ROOTfit
algorithm. Using libraries of the eponymous ROOT framework[52], it fits increasing numbers
of SPE-like pulses to the waveform until either the χ 2 -measured goodness of the fit
does not increase anymore, or until the maximum number of pulses has been reached.
FeatureExtractor’s SPE pulse shape parametrization is
w(t) = q ((
1 − e
−τ 2) e −τ + w d (t) ) , (5.1)
c 1
(
√ ( ( ( ))
w d (t) = −c 2 e −c 3 τ
1 − e −τ − 1 πe 1 2
2 erf τ +
1
2) ) − erf 1
, τ = t−t 0
,
2
σ
where q, t 0 , and σ are fitting-parameters for the pulse’s charge, leading-edge time, and
width, respectively; erf denotes the error function, and c 1 . . . c 3 are constants. The term
w d is an approach to deal with droop; if it is to be included, the droop correction in
DOMcalibrator has to be disabled. The parametrization is shown in figure 4.6 with the
values used in the second multi-pulse algorithm (q = 1 PE, t 0 = 0, σ = 2 ns), and with
the droop correction term disabled (i.e., c 2 = 0).
This algorithm is neither recommended nor maintained anymore, and it is too slow for
large-scale reconstruction.
The second multi-pulse algorithm is based upon the method of Bayesian Unfolding.
Being reasonably fast and capable of determining photon arrival times in complex
features, it is used for practically all analyses that rely on multi-pulse extraction, e. g.,
cascade reconstruction and offline-processing muon track reconstruction.[51]
40

5.2 PulseExtractor
An algorithm using the same underlying method is implemented in the NewFeatureExtractor
NFE developed within this thesis. Therefore the method and the differences between
the two implementations are discussed in section 6.3.
The FADC algorithm is a multi-pulse algorithm similar to the second single-pulse
ATWD algorithm: It searches the waveform from start to end for a local slope maximum
of pairs (w i , w i+1 ) with w i+1 above threshold and extrapolates the resulting line to the
baseline to define the pulse’s time. For the calculation of the charge it sums up the bin
contents from i+1 on until either a bin is below the threshold or until a bin is higher than
its predecessor after the feature has fallen below half its previous maximum value, in both
cases excluding the determining bin. The width is defined as the number of bins summed
up. The algorithm then continues searching for the next pulse. Incomplete pulses at the
end of waveforms are not extracted.
Besides the obvious tasks of a feature extractor, FeatureExtractor also performs some
waveform calibration tasks such as baseline finding, transit time correction, or droop
correction. While the employed methods were superior to the ones used in DOMcalibrator
at the time of their introduction, the good quality of recent DOMcalibrator versions
caused most of these features to become obsolete. Their remaining in the code impairs
its readability[53], introduces an overload to the maintenance of the code and increases
the risk of misconfiguration.
5.2 PulseExtractor
PulseExtractor (I3PulseExtractor) is a rewritten and condensed version of FeatureExtractor.
Created mainly by Dmitry Chirkin and Christopher Wendt in 2009, the only
algorithm it includes is a modified variant of the original FeatureExtractor’s Bayesian
Unfolding algorithm. This algorithm can be applied to both ATWD and FADC if the
module is run in different instances. The module does not offer configuration options
besides names of the input and output objects.[54]
The PulseExtractor’s advantages are easy maintainability and high ease of use at the
expense of adaptivity and extraction performance (see section 6.3.1).
5.3 SLCHitExtractor
The SLCHitExtractor (I3SLCHitExtractor) was written in 2009 by Andreas Groß to be
the first module to extract hits from SLC charge stamps, which are recorded since IC59.
The algorithm defines the pulse time as t = t 0 + (i max − 1) · T bin − c 1
w imax−1
w max
− c 2 , where t 0
41

5 FEATURE EXTRACTION IN ICECUBE
denotes the charge stamp’s startTime and thereby the time corresponding to w 0 , whereas
i max denotes the bin with the highest value, w max ; this is illustrated on the right side of
figure 6.6. The charge is defined as q = wmax
c 3
.
The constants c 1 and c 3 are obtained by comparison of SLCHitExtractor’s pulses for SLC
charge stamps generated from full FADC waveforms with FeatureExtractor’s pulses. The
time offset c 2 has been abandoned recently in the belief that it was caused by a general
ATWD FADC time offset, which has been taken care of in DOMcalibrator; see appendix
C.4 for further discussion.[55]
5.4 NewFeatureExtractor
The NewFeatureExtractor (NFE) – written by the author of this thesis – is the latest of
the four feature extractors covered in this document and constitutes its main topic.
NFE is special in that it employs multiple algorithms for the same event, choosing an
approriate algorithm according to the waveform’s complexity; this concept is explained in
section 5.4.2. The algorithms themselves are discussed in chapter 6.
5.4.1 Main Characteristics
Well-documented code conforming the IceCube Coding Standards 4
Documentation for IceCube users and developers alike exists in form of wiki pages and
an internal report created out of passages of this thesis. It contains general information
about the project’s structure and the employed algorithms. Further in-detail information
for developers is found in doxygen mark-up source code comments that explain class
structures including purpose of methods and data members, and in standard C++ inline
comments explaining programming decisions and purpose of small code passages. The
project also provides example scripts to make the use of this project as easy as possible.
Focus on the main task of feature extraction
NFE relies on the waveforms being calibrated prior by DOMcalibrator or any other module.
It intentionally does not aim to improve for example the baseline level, but instead the
author communicated potential shortcomings of other modules to the respective authors.
This preserves IceTray’s data flow concept and prevents double treatment of problems or
other unintended side-effects later in the reconstruction chain. This also results in simpler
configuration of NFE.
4 http://software.icecube.wisc.edu/OFFLINE-SOFTWARE-V02-02-03/codingstandards.html
42

5.4 NewFeatureExtractor
Ease of use
To make the transition from other feature extractors to NFE as easy as possible without
sacrificing configurability and flexibility, all NFE modules and services require only a minimum
of configuration. This is implemented by reasonable default values which give good
results under almost all circumstances. Thoroughly tested defaults also help minimizing
unintentional misconfigurations.
Modular code organization
The code is organized into IceTray modules and services with specific purposes to improve
readability, expandability and possible bug tracking. Modular organization also allows the
creation of unit tests to thouroughly check passages of code. While initially providing good
means to test the code for errors during development, the main advantage of unit tests
is their ability to test the code for bugs introduced later by seemingly unrelated code
changes. The tests together with the provided example scripts are run prior to releasing
new versions of the project or of meta-projects containing it.
High performance
NFE is intended to succeed FeatureExtractor and SLCHitExtractor not only for offlineprocessing,
i.e., processing of stored data in the Nothern Hemisphere, but also for onlineprocessing,
for which performance is a major issue. Besides choosing efficient algorithms,
a new approach was taken in using different algorithms for different types of waveforms;
this is elaborated in section 5.4.2.
5.4.2 Program Structure
Most of IceCube’s DOM launches are caused by single photons whose corresponding waveforms
are considerably regular. To take advantage of this, the NFE framework allows
to use different extraction algorithms for waveforms of varying complexity. The time
saved during the extraction of simple waveforms can be spent for sophisticated and timeconsuming
algorithms to improve the results for more complex waveforms. Additionally,
this allows to use algorithms which excel in extracting certain waveforms but fail for other
waveform categories, or to use the same algorithm with different settings for different categories.
To decide which algorithm to use for a given waveform, a pre-evaluation algorithm is initially
called to quickly assess the waveform. Depending on the results, the NFE framework
(i.e., the module I3NFE) passes the waveform and all relevant data to the extraction algorithm
configured for this category. Currently, three categories have been implemented,
but this number can be expanded; they are simple for ATWD or FADC waveforms with
simple waveforms, complex for all remaining ATWD and FADC waveforms, and slc for
SLC charge stamps; the classification of these categories lies in the responsibility of the
43

5 FEATURE EXTRACTION IN ICECUBE
pre-evaluation algorithm (e. g. “Eva”, section 6.1).
All algorithms are implemented as services and inherit from a common pre-evaluation or
extraction algorithm base class. This modular design – inspired by the IceCube reconstruction
framework gulliver by David Boersma[56] – simplifies maintenance and facilitates
easy implementation of new algorithms without breaking existing code.
NFE’s framework is also responsible for calculating the gain constant needed to translate
waveforms in mV to waveforms in units of photoelectron charges (PE). Providing this
gain constant to the algorithms allows to define thresholds independently of hardware or
firmware thresholds that might change between different firmware or simulation software
versions. This eliminates one reason for recalibration of configuration settings; in addition
PE are more practical for setting thresholds as they are closer related to the physics processes.
The same approach was taken in PulseExtractor, while FeatureExtractor defines
thresholds in fractions of the trigger’s SPE discriminator threshold.
The exact conversion factor for the translation of mV to PE is T bin (g · Z · e) −1 . The average
PMT gain g (SPEmean) and the DOM’s impedance Z (FrontEndImpedance), which
is dominated by the toroid, are provided by either the GCD file or the online database.
Another non-obvious task for the framework is to optionally add an extra-info series
map and an algorithm-info series map to the frame. Those objects mirror the
I3RecoPulseSeriesMap’s structure, which means that for every pulse of every DOM with
entries in the pulse map these objects contain one integer each. The extra-info integer is
a bit mask containing information about whether the pulse was cut off in the beginning,
cut off in the end, or if it was saturated. The latter information is obtained from DOMcalibrator’s
StatusCompounds which are added to calibrated waveforms but are largely
ignored by other feature extractors. The algorithm-info contains the unique ID of the
algorithm that was used to extract the corresponding pulse.
To keep the code simple and to offer more configurability when needed, all data sources
(ATWD, FADC and SLC, resp. all different calibrated waveform series) are attached to
different instances of the I3NFE module. Algorithm instances (services) can be used by an
unlimited number of modules. The resulting pulse series maps can optionally be merged
into a single map by the pulse merger (section 5.4.5).
5.4.3 Time Offset Constants
One drawback of the application of different feature extraction algorithms within the
same event is the need for the introduction of time offset calibration constants. Those are
required to align the pulses to the same start time independently of the algorithm and
data source used. The two major objections against these constants are that they might
require maintenance and that they should ideally not be required.
The first objection only arises for features of different sources, specifically features which
44

5.4 NewFeatureExtractor
occur in both ATWD and FADC. It can be mitigated by deducing the time offsets from
well-calibrated waveforms so that they only compensate offsets introduced by the algorithms,
but not by a potentially imperfect calibration.
The second objection only holds under the assumption that SPE pulses are sufficiently
similar for all sources. Even if a single method could be used for all sources, the different
pulse shapes would require subsequent alignment (see figure 4.6).
5.4.4 Waveforms Without Pulses
Waveforms might not contain any features which pass a given threshold. NFE provides
three alternatives to deal with this situation: DOMs without pulses can either be excluded
from the pulse series map, or they can be added with an empty pulse series, or NFE can
force the algorithms to extract at least one pulse, respectively NFE can pass the waveform
to an algorithm which is capable of finding at least one pulse if enforced.
The important difference between the first two alternatives is that they lead to different
values for the per-event quantity NChan – i.e., the number of DOMs hit during the given
event, often used for energy estimation and quality cuts –, because it is defined as the
number of entries in the pulse series map. Therefore, the underlying question is if one is
to trust the hardware trigger or the feature extraction to decide whether a DOM was hit.
The physical implications of this choice have to be discussed in a larger scale than it is
possible in this thesis.
5.4.5 Pulse Merger
The pulse merger (I3NFEPulseMerger) is a stand-alone IceTray module designed to join
up to three pulse series maps into a single one. Usually these maps correspond to the different
pulse sources ATWD, FADC and SLC individually extracted by NFE, but differing
usage is supported.
The input maps are arranged by priority; by default, ATWD has the highest priority and
SLC has the lowest. The primary map is copied completely, pulses from the other two
maps are added successively if they don’t overlap with pulses from higher priority input
maps – they may, however, overlap with pulses from the same input map. An extra time
window can be configured to be required between the ending (defined as start time plus
width) of one pulse and the start of another pulse to reduce the probability of double
extraction, i.e., extraction of the same feature by different sources (compare appendix
C.1).
The NFE pulse merger differs from similar modules in that it supports merging of maps
with extra-info and algorithm-info.
45

5 FEATURE EXTRACTION IN ICECUBE
46

CHAPTER VI
Algorithms Implemented in NFE

6 ALGORITHMS IMPLEMENTED IN NFE
maximum
threshold
x
feature
threshold
x
x
Figure 6.1: Sketch illustrating NFE’s pre-evaluation algorithm “Eva”. If a waveform only contains
features like the first one, it is evaluated as simple; however if it contains
features which are too long, too high, or too close together, the whole waveform is
classified to be complex.
x
Up to now, one pre-evaluation algorithm (“Eva”) and three extraction algorithms have
been implemented. Of the latter three, “Simple” was designed mainly for the waveform
category of the same name, “BayesUnfold” is capable of handling well all types of ATWD
and FADC waveforms, and “SLCHE” extracts SLC chargestamps
x
exclusively; all four
algorithms are part of the default configuration
x
of the NewFeatureExtractor.
Currently “BayesUnfold” is the only algorithm capable of finding at least one pulse per
waveform if enforced (see section 5.4.4), so it needs to be used if EnforcePulse is set;
to accomplish this, a special EnforceAlgorithmServiceName can be set, which is only
necessary if “BayesUnfold” is not used for either simple or complex waveforms.
6.1 Pre-evaluation Algorithm “Eva”
As pointed out in section 5.4.2, the purpose of pre-evaluation algorithm is to quickly assess
a waveform and to decide whether it belongs to the simple, complex, or slc category.
The pre-evaluation algorithm “Eva” accomplishes this by four simple checks:
If a calibrated waveform’s source is SLC, it is directly assigned to the slc category. An
ATWD or FADC waveform is scanned once; if its features are either too high, too long
or too close together, the waveform is marked as complex (see figure 6.1). More precisely,
if one waveform bin’s value w i exceeds the threshold w max , or if l max successive bins
exceed the threshold w feat , or if the gap between bins exceeding w feat is smaller than the
allowed minimum distance of d min bins, then the scanning is stopped and the waveform is
categorized as complex.
The four parameters w max , w feat , l max , and d min can be configured individually for
48

6.2 Extraction Algorithm “Simple”
quadratic interpolation for leading edge times
linear interpolation for trailing edge times
charge:
sum over bins above
feature threshold
plus boundary bins
detection threshold w ,
detect
rejects flat features
widths
feature threshold w , feat
defines feature bounds
Figure 6.2: Sketch illustrating NFE’s extraction algorithm “Simple”. In the shown waveform,
three pulses are identified. The charge compensation has been omitted for reasons
of clarity. Note that “Simple” was not designed for complex features like the third.
ATWD and FADC to take into account the different characteristics of these two sources.
6.2 Extraction Algorithm “Simple”
The extraction algorithm “Simple” is a fast threshold based algorithm particularly suitable
for simple features. To define a feature, a threshold w feat is used. Starting at the
waveform’s beginning, the algorithm searches for bins exceeding w feat . If it finds one in bin
i, the potential pulse’s leading edge time t is defined as the time t parab where a parabola
through the points (i − 1, w i−1 ) to (i + 1, w i+1 ) crosses the threshold w feat plus a quadratic
charge compensation term and a constant time offset:
⎧
t = t parab − t q + t offset with
⎨c P0 (q − c P1 ) 2 for q < c P1 ,
t q =
⎩0 otherwise,
(6.1)
with charge q and configurable constants c P0 and c P1 . While using a parabola for interpolation
mainly improves the time resolution at a given charge level, the charge compensation
term accounts for the fact that smaller pulses cross the threshold later, so they are not
redundant (compare section 7.1).
If the waveform starts with a bin surpassing the threshold (i. e., i = 0), t parab in equation
(6.1) is not well-defined and gets replaced by t lin , which is the time of the intersection of
w feat with the linear extrapolation of the slope between the points (0, w 0 ) and (1, w 1 ). If
t lin is more than 10 ns ahead of the waveform’s start time t 0 , it is replaced by t 0 because
it has to be assumed that the waveform starts well within a feature and the extrapolation
could be too far off. Analogously, if the threshold is passed by the last bin (i = L), t parab is
replaced by t lin defined by the last two points, (L−1, w L−1 ) and (L, w L ). Lastly, this linear
fallback method is used with the points (i − 1, w i−1 ) and (i, w i ) if the parabola’s point of
49

6 ALGORITHMS IMPLEMENTED IN NFE
intersection lies more than one bin length away from bin i, i. e., if |t parab − iT bin | > T bin ; if
this happens, it must be due to numerical instability which arises for nearly colinear points
(catastrophic cancellation). It remains to be an open task to rearrange the equation used
to determine t parab to become more stable; this should be possible using Viète’s formulae,
but it will not improve the algorithm because the fallback method is well-suited in case
of colinear points.
The time calculation based on the intersection with the threshold w feat instead of the
baseline w = 0 was chosen to reduce the impact of waveform binning effects; extrapolations
down to the baseline possess a greater lever and thereby larger error potential than
interpolations between two known points of a relatively smooth curve. A disadvantage is
the crossing point’s obvious dependence on the pulse charge, or the need for two constants
to compensate for it.
The trailing edge time t end is required to calculate the width t − t end of the pulse;
“Simple” defines it as the point of threshold crossing determined by a linear interpolation
between the points (i+j −1, w i+j−1 ) and (i+j, w i+j ), where bin i+j is the first one to fall
below w feat for j > 0. No further corrections are applied because the achieved precision
for the width is sufficient. If the waveform ends prematurely, the waveform’s ending time
is taken instead and the pulse is marked as cut off in the extra-info series.
The pulse’s charge is defined as the total charge contained in the bins i − 1 to i + j,
q = ∑ i+j
k=i−1 w k. A potential charge related to a non-zero baseline is not substracted as
NFE explicitly relies on a correct baseline from DOMcalibrator.
If a pulse is added to the pulse series depends on whether the feature passes a second
threshold w detect and whether q ≥ q min . These two criteria can be disabled by setting
w detect = w feat and q min = 0, respectively. However having at least one of them active
allows w feat to be set to a substantially lower value without erroneously extracting baseline
fluctuations (see figure 6.2).
The two thresholds and the two charge compensation constants can be set individually
for ATWD and FADC, the time offset constant can be set for ATWD OT, ATWD NT
and FADC, and q min is the same for all sources, leading to a total of twelve configuration
parameters.
6.3 Extraction Algorithm “BayesUnfold”
“BayesUnfold” (BU ) uses the method of Bayesian Unfolding described by G. D’Agostini
in his paper A multidimensional unfolding method based on Bayes’ theorem.[57] It is also
employed in FeatureExtractor and PulseExtractor; this section explains the implementation
in NFE, section 6.3.1 shows the differences to FE’s and PE’s implementations, and
appendix A gives a more formal approach to the unfolding itself.
50

6.3 Extraction Algorithm “BayesUnfold”
Figure 6.3: Sketch illustrating Bayesian Unfolding as employed in FE, PE and NFE; see text
for description. Note that the deconvoluted waveform is not drawn to scale, the
unfolding is charge conserving.
The underlying idea behind unfolding techniques is to undo smearing and distortion
effects caused by the experiment’s hardware. Afterwards,
x
x it is easier to reconstruct the
arrival times of photons at the photocathode.
Besides the calibrated waveform to extract, the unfolding algorithm requires samples of
generic SPE pulses in the same binning. It then deconvolutes the waveform iteratively,
moving the charge into those bins in which SPE-like pulses with the given charge must
have occured to cause the actual waveform with maximum probability. An illustration
for this is given in figure 6.3: The waveform to the left side is the superposition of five
SPE-like features, the deconvoluted distribution to the right side is a histogram of the
same length and total charge, but the charge has been moved to the bins at the beginnings
of the individual features. For more details, see appendix A.
x
Starting Distribution One of the unfolding method’s parameters is the starting distribution
for the deconvoluted distribution, u i, 0 , i = 0 . . . L. As D’Agostini points out,
the method “gives the best results (in terms of its ability to reproduce the true distribution)
if one makes a realistic guess about the distribution that the true values follow, but,
in case of total ignorance, satisfactory results are obtained even starting from a uniform
distribution”.[57]
The SPE samples are zero everywhere but in a small region behind the position of the
hit. Because of this, a combination of an uniform distribution with the shifted waveform
provides a good initial guess:
u i, 0 = 1 2
w tot
L + 1 2 w k, k := (i + 1) mod L, w tot = ∑ w i (6.2)
The shift of one bin length is introduced to minimize a possible bias to later pulse times
and to speed up the unfolding, because the charge always needs to be shifted to the
beginning of the features. The uniform term is preserved because the algorithm can not
increase bin contents which are zero at any time during the deconvolution process, and
does so only slowly for very low bins contents.
51

6 ALGORITHMS IMPLEMENTED IN NFE
Number of Iterations An important parameter of the algorithm is the number of
iterations n iter . Steering the number of iterations adaptively can both reduce computation
time and improve the quality of extraction for “tricky” waveforms by giving them more
CPU time and thereby more iterations.
Moreover, terminating the unfolding procedure at the right time is the suppression of the
method’s inherent amplification of statistical fluctuations (positive feedback). D’Agostini
suggests to smooth the deconvoluted distribution after every iteration step to both speed
up the convergence and to decrease the amount of artifacts. However, this does not seem
to be applicable in this case since the target deconvolution should be spiky. 5
The “BayesUnfold” algorithm in NFE employs a conjunction of two stopping conditions:
Both the change of the highest bin and the sum of all bins above half the pulse charge
threshold q min must be small for two successive iteration steps (with the constraint n iter ≥
10):
max ({u i, ñ })
max ({u i, ñ−1 }) < ∆u min
∧
∑
i: u i, ñ > 0.5 q min
u i, ñ
∑
i: u i, ñ−1 > 0.5 q min
u i, ñ−1
< 0.3 ∆u min ∀ ñ ∈ {n iter−1 , n iter }
(6.3)
Both conditions depend only on relatively few bins which reduces the impact of the aforementioned
fluctuations. The first condition ensures that the highest pulse is extracted
precisely, and with it the other pulses as they received as many iterations. The second
condition ensures that no charge associated to pulses is lost. The factor of 0.3 has been
determined empirically during this thesis, using the unit test’s extra output for idealized
pulses. Additionally, a maximum number of iterations n max can be specified.
Pulse Definition When the unfolding procedure ends after n iter iterations, the features
in the deconvoluted distribution u i := u i, niter have to be extracted to define the pulses.
“BayesUnfold” uses three subsequent bins to define a pulse (figure 6.4). This is motivated
by two facts: First, even in an ideal case, SPE-pulse-like features have to be unfolded into
two subsequent bins in a deterministic ratio if they occured at a different time than that
of a bin – i.e., “between” two bins. Secondly, only a finite number of iterations (∼ 30) is
conducted, so SPE-pulse-like features whose charge should have been moved into a single
bin in fact end up in this main bin and the surrounding ones.
The deconvoluted distribution is scanned from its beginning to its end. If for a given i u i
exceeds 0.5 q min , “BayesUnfold” checks whether u i+1 > u i ; if so, i is incremenetd by one.
The three bins defining a pulse are u i−1 , u i , and u i+1 . The algorithm then checks whether
the third bin u i+1 should be accounted completely to the current pulse’s charge q or if it
5 It might be worthwhile to try out advanced smoothing methods, e. g. a multi-resolution Savitzky-
Golay filter as described in http://www.er.ams.eng.osaka-u.ac.jp/Paper/2006/Norbert06a.pdf.
52

6.3 Extraction Algorithm “BayesUnfold”
Figure 6.4: Sketch illustrating the algorithms used by the different feature extractors to define
pulses out of the unfolded distribution; areas of the same color belong to a single
pulse. Dark dashed lines indicate the charge thresholds, light dashed lines indicate
the threshold boundaries in which the pulse definition does not change.
left: NFE; middle: FE/PE with the same threshold;
right: FE/PE with a higher threshold; striped areas apply to FE only.
needs to be shared with a later pulse (see figure 6.4):
⎧
q = u i−1 + u i + f u i+1 with
⎨ u i
u
f := i +u i+2
u i+2 ≥ min ({u i , u i+1 })
⎩1 otherwise
If the total charge q exceeds q min , the pulse is accepted (i.e., written to the series) and
fu i+1 is substracted from bin i + 1 to prevent the charge from being accounted twice.
The pulse’s leading edge time is defined according to the charge distribution:
(
t = t i + T bin −
u i−1
+ f
u i−1 + u i
)
u i+1
u i + u i+1
The pulse width T is obtained by a charge-dependent parametrization of the SPE pulse
parametrization’s width at a height of 0.05 PE per bin:
T = T bin max ({1, c T1 ln (c T2 q − c T3 )}) (6.4)
The constants c T1 , c T2 , and c T3 are hard-coded for ATWD OT, ATWD NT, and FADC
respectively. The parametrization error is usually well below 1%, see figure 6.5. At the
beginning and at the end of the waveform, the algorithm switches to linear calculations
and marks pulses as cut off.
In summary, “BayesUnfold” offers three configuration parameters: the maximum number
of iterations, the stopping parameter ∆u min , and the charge threshold q min . Other
parameters, such as the SPE pulse samples, the width parametrization, and the time
offsets are hard-coded, but can easily be changed.
53

6 ALGORITHMS IMPLEMENTED IN NFE
0,01
relative error DT / T
0
−0,01
−0,02
2 4 6 8 10 12 14 16 18 20
q / PE
NFE ATWD OT
NFE ATWD NT
NFE FADC
Figure 6.5: Residual plot comparing the width parametrizations used in “BayesUnfold” to the
true SPE pulse parametrizations’ widths in dependence of the pulse’s charge.
6.3.1 Differences of FE’s and PE’s Implementations
FeatureExtractor and PulseExtractor both use the same SPE pulse parametrization (shown
in figure 4.6) which differs significantly from NFE’s; they do not discriminate between old
toroid and new toroid DOMs. The unfolding and pulse definition algorithms of FE and
PE are identical except for their handling of pulses below the threshold and the FeatureExtractor’s
time refinement: FeatureExtractor uses the time obtained from one of its
single-pulse extraction algorithms to replace the time of the nearest Bayesian Unfolding
pulse.
Both extractors conduct a fixed number of unfolding iterations (20) and define pulses
by two bins compared to the three bins per pulse used by NFE. Because of this, they
tend to split up features into many pulses and therefore require a comparably high charge
threshold to reduce the splitting. The only difference with non-negligible impact between
the FE and PE algorithms is how they handle charge in unfolded bins that fall below this
threshold. While PulseExtractor omits them and thereby loses some of the pulses’ charge,
FeatureExtractor compares the sum of all pulses’ charges to the charge computed by the
selected single-pulse extraction algorithm (preferably the second one, as it computes the
total charge which is needed here) and multiplies every pulse’s charge with this ratio to
ensure that the waveform’s charge is conserved. The difference between these two methods
is depicted as striped areas in figure 6.4.
The advantage of FeatureExtractor’s method is that no pulse charge is lost, the disadvantage
is an increased sensitivity to wrong baselines, e. g. those caused by faulty droop
correction. A disadvantage common to FE and PE is that the high threshold causes
a shift in the pulse’s time if from a pulse originally consisting of two bins only one is
incorporated, because the time depends on the charge’s center of gravity.
54

6.4 Extraction Algorithm “SLCHE”
parabola through all three points
time: point of maximum + offset
charge: const × area below parabola
width: parametrization T(q)
time: pre-maximum bin + const × ratio of
maximum bin value to predecessor bin value
charge: const × maximum bin value
width: three bin lengths
Figure 6.6: Sketch comparing NFE’s extraction algorithm “SLCHE” (left) to SLCHitExtractor
(right). Shown are three different digitizations of the same SPE-like feature (dashed
brown lines), the third being an irregular chargestamp.
6.4 Extraction Algorithm “SLCHE”
“SLCHE” – named after the SLCHitExtractor on which it was based originally – is an
exclusive SLC extraction algorithm. For regular charge stamps, i. e., those in which
the middle bin w 1 is the highest (section 4.4.3), the algorithm computes the position of
the maximum of the parabola defined by the three points (0, w 0 ) . . . (2, w 2 ), as well as
the area A enclosed by it and the baseline. To calculate the pulse time, the time t pmax
corresponding to the parabola’s maximum is shifted by a constant negative time offset
t offset :
t = t pmax + t offset , with t pmax = t 0 + T bin
−3w 0 + 4w 1 − w 2
−2w 0 + 4w 1 − 2w 2
.
The charge is computed by q = c q A, where c q is a configurable constant. It is used to
estimate the original feature’s width, employing the parametrization in equation (6.4)
and thereby exploiting that full FADC waveforms and SLC chargestamps have the same
shape. Figure 6.6 visualizes this algorithm at the two leftmost chargestamps.
Irregular waveforms are not necessarily concave (see section 4.4.3), therefore the calculations
of t pmax and A fail for them. Also, two or more photons hitting a DOM with
a small delay could cause waveforms that are approximately flat, leading to erroneously
high charge estimates.
Because of this, a fallback method is implemented:
t = t i + t offset , and q = c q
〈 A
w 1
〉
w i ,
55

6 ALGORITHMS IMPLEMENTED IN NFE
with i = 0 if w 0 > w 1 , and otherwise i = 2 if w 2 > w 1 or w 0 + w 2 ≥ 1.8 w 1 . 〈 〉
A
w 1
denotes
the mean A to w 1 ratio for regular charge stamps, determined empirically.
This fallback charge calculation is equivalent to the regular charge calculation 〈 performed 〉 in
SLCHitExtractor and could be expressed with a single constant ˜c q = c A
q w 1
. However,
the more complicated looking formulation with two multiplicative constants decouples
these constants and thereby simplifies configuration. Apart from c q , 〈 〉
A
w 1
, and toffset ,
there are no other configuration constants.
56

CHAPTER VII
Performance Optimization

7 PERFORMANCE OPTIMIZATION
Prior to the design of the algorithm, many waveforms were studied by eye (e.g., figure
7.1, visualized using a custom IceTray Python module and matplotlib) to get a feeling
for pulse shapes, baseline fluctuations, and potential problems arising with the feature
extraction. Most of the hard-coded and default parameters were based on this experience
and proved sustainable and robust under further investigation.
Important performance observables for the feature extraction are the time difference
∆t between the photon hitting the DOM and the extracted pulse, the charge per pulse,
the number of pulses, the total charge per waveform, and the number of waveforms in
which no pulse is found. Measurements of these observables have been conducted using
custom Monte-Carlo datasets simulated for the calibration of NFE. These datasets (2595
and 3071) include the Monte-Carlo hit information which is usually discarded after the
waveform simulation. This allows to directly evaluate the time resolution.[58][59] If not
stated otherwise, plots are based dataset 3071. Unfortunately, all simulated datasets
include erroneous data caused by bugs partly found as a consequence of this thesis; this
includes high baselines for ATWD and wrong impedances in the GCD files, see appendix
C.3. The impact of these bugs is discussed in the appropriate sections. Independently,
the calibrations and tests presented here will be repeated when fixed datasets become
available.
After all parameters were fixed, the measurements were repeated with experimental data
to verify the parameters’ correctness.
7.1 Calibration Using Monte-Carlo Data
The time offsets (section 5.4.3) of all algorithms have been adjusted to comply with pulses
extracted by “BayesUnfold” from ATWD new toroid waveforms, as the author assumes
them to be the most reliable pulses on average. A constant common time offset of all
algorithms to Monte-Carlo hits is irrelevant as long as it is of the order ten nanoseconds;
it does not affect the track reconstructions as this only depends on time differences between
pulses, and it is far too small to affect later high-level analyses. The policy chosen is to
extract the pulse start times instead of the Monte-Carlo hit times, which are about 11 ns
too late in comparison and roughly tag a SPE pulse’s maximum, see figure 7.1, figure 7.2,
and figure 7.3.
7.1.1 Pre-evaluation Algorithm “Eva”
First, the parameters of the pre-evaluation algorithm “Eva” and thereby the categorization
of waveforms were adjusted, as the performance of other algorithms depends on them.
They were determined using individual waveforms such as those in figure 7.1; they have
been verified using the SPE parametrizations employed in “BayesUnfold” (equation (7.1),
figure 4.6).
58

7.1 Calibration Using Monte-Carlo Data
ATWD (blue) and FADC (red) amplitudes / PE
ATWD (blue) and FADC (red) amplitudes / PE
0.99
NFE_ATWDPulses
OMKey(5,41)
0.4
0.3
0.2
0.1
0.0
14900 15000 15100 15200 15300 15400 15500 15600 15700
NFE_FADCPulses
time / ns
0.4
0.8
0.88
0.57
0.3
0.2
0.1
0.0
14900 15000 15100 15200 15300 15400 15500 15600 15700
NFE_ATWDPulses
OMKey(12,33)
1.51
0.58
1.64
0.73 0.70
0.60
0.6
0.4
0.2
0.0
13400 13500 13600 13700 13800 13900 14000 14100 14200
NFE_FADCPulses
time / ns
0.8
0.6
0.4
0.2
1.60
1.93 0.69 0.61 1.92
1.58
0.74
0.0
13400 13500 13600 13700 13800 13900 14000 14100 14200
Figure 7.1: Two examples for calibrated ATWD (blue, narrow) and FADC (red, wide) waveforms;
only a part of the FADC waveform is shown. Pulses are indicated by dashed
full-length vertical lines with the charge q given at top of the lines in units of PE;
horizontal bars indicate the pulse widths. Lines in the upper image each correspond
to ATWD pulses, lines in lower image to FADC.
Large solid or dotted ticks at the bottom axis indicate Monte-Carlo hit information
if available.
59

7 PERFORMANCE OPTIMIZATION
ATWD (blue) and FADC (red) amplitudes / PE
ATWD (blue) and FADC (red) amplitudes / PE
0.8
0.7
1.63
NFE_ATWDPulses
0.6
0.5
0.4
0.3
0.2
0.1
0.0
OMKey(69,33)
17500 17600 17700 17800 17900 18000 18100 18200 18300
NFE_FADCPulses
time / ns
0.8
1.60
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.8
0.6
0.4
0.2
0.0
0.8
0.6
0.4
0.2
17500 17600 17700 17800 17900 18000 18100 18200 18300
1.51
0.58
1.64
0.73 0.70
NFE_ATWDPulses
0.60
13400 13500 13600 13700 13800 13900 14000 14100 14200
NFE_FADCPulses
time / ns
1.60
0.74
1.93 0.69 0.61 1.92
1.58
OMKey(12,33)
0.0
13400 13500 13600 13700 13800 13900 14000 14100 14200
Figure 7.2: Two examples for calibrated ATWD (blue, narrow) and FADC (red, wide) waveforms;
only a part of the FADC waveform is shown. Pulses are indicated by dashed
full-length vertical lines with the charge q given at top of the lines in units of PE;
horizontal bars indicate the pulse widths. Lines in the upper image each correspond
to ATWD pulses, lines in lower image to FADC.
Large solid or dotted ticks at the bottom axis indicate Monte-Carlo hit information
if available.
60

7.1 Calibration Using Monte-Carlo Data
ATWD (blue) and FADC (red) amplitudes / PE
0.15
0.10
0.05
0.00
0.05
0.15
0.10
0.05
0.00
0.05
0.28
NFE_ATWDPulses
OMKey(11,54)
67400 67500 67600 67700 67800 67900 68000 68100 68200
NFE_FADCPulses
time / ns
0.17
67400 67500 67600 67700 67800 67900 68000 68100 68200
NFE_ATWDPulses
OMKey(87,37)
ATWD (blue) and FADC (red) amplitudes / PE
1.0 0.95 1.44
0.8
0.6
0.4
0.2
0.0
67600 67800 68000 68200
NFE_FADCPulses
time / ns
1.0 0.78 1.18 2.50 1.03
0.8
0.6
0.4
0.2
0.0
67600 67800 68000 68200
Figure 7.3: Two examples for calibrated ATWD (blue, narrow) and FADC (red, wide) waveforms;
only a part of the FADC waveform is shown. Pulses are indicated by dashed
full-length vertical lines with the charge q given at top of the lines in units of PE;
horizontal bars indicate the pulse widths. Lines in the upper image each correspond
to ATWD pulses, lines in lower image to FADC.
Large solid or dotted ticks at the bottom axis indicate Monte-Carlo hit information
if available.
61

7 PERFORMANCE OPTIMIZATION
Table 7.1: Default values used for pre-evaluation algorithm “Eva”.
parameter name in code value
ATWD
FADC
w max SimpleThreshold 0.40 PE 0.60 PE
w feat FeatureThreshold 0.08 PE 0.10 PE
l max FeatureMaxLength 6 bins 5 bins
d min FeatureMinDistance 4 bins 3 bins
Table 7.2: Default values used for extraction algorithm “Simple”.
parameter name in code value
ATWD
FADC
w feat FeatureThreshold 0.04 PE 0.08 PE
w detect DetectionThreshold 0.04 PE 0.08 PE
q min minCharge 0.15 PE 0.15 PE
c P0 QTCorrelationP0 1.6 ns 17.722 ns
c P1 QTCorrelationP1 1.7 1.2345
t offset NT DeltaTNewToroid −0.57 ns −10.03 ns
t offset OT DeltaTOldToroid −1.83 ns −10.03 ns
The values were adjusted in such a way that narrow and well-seperated SPE-pulse-like
features up to 1.5 PE in the spikiest possible binning are still considered to be simple
(table 7.1). This is tailored to the extraction algorithm “Simple” as it is not capable of
splitting features, for example to account a feature’s tail to the associated peak if it is
superimposed by another feature. While SPE features with charges as high as 1.5 PE are
quite common (e.g., figure 7.1, first pulse in DOM 12-33, or figure 7.2, DOM 69-33), very
similar features can be caused by two or more coincident photons (thid pulse in DOM
12-33); however as long as those are sufficiently close in time, this does not contradict a
pulse’s definition.
7.1.2 Extraction Algorithm “Simple”
The extraction algorithm “Simple”’s feature thresholds w feat were set sufficiently high not
to be surpassed by baseline fluctuations. For lower feature thresholds, the charge threshold
q min would still reliably prevent individual random fluctuations to be extracted as
pulses. However, fluctuations at the beginning of a real feature could impede the leading
edge detection.
62

7.1 Calibration Using Monte-Carlo Data
10 7
10 6
width: 0.81 0.81
mean: 11.19 11.20
10 5
10 4
entries
10 3
10 2
10 1
10 0
10 -1
40 20 0 20 40
t MC −t pulse /ns
10 7
10 6
width: 0.81 0.81
mean: 11.19 11.20
10 5
10 4
entries
10 3
10 2
10 1
10 0
10 -1
40 20 0 20 40
t MC −t pulse /ns
Figure 7.4: Distribution of the time residuals of NFE extracted pulses for different charge
thresholds; shown is the time difference between the first Monte-Carlo hit and the
first extracted pulse per waveform.
Blue areas are NFE with default settings (q min = 0.15 PE), green lines to the
left have q min = 0.2 PE for algorithm “Simple”, and green lines to the right have
q min = 0.25 PE. Red lines indicate Gaussian fits to all bins (excluding underflow
and overflow), with its width and its mean specified in the plot.
63

7 PERFORMANCE OPTIMIZATION
Tuning of the threshold q min requires a decision about whether some more false pulses outweigh
a better detection capability for very small pulses. Generally, early falsely detected
pulses (false pulses) can have a relatively high impact on the later track reconstruction,
however the number of false first pulses extracted using the current low q min = 0.15 PE
is deemed to be acceptable: For the about 4.1 million waveforms evaluated in figure 7.4,
only about 200 first pulses precede the expected time by more than 10 ns. For this optimization
it has to be considered that increasing the threshold only marginally reduces
the number of false pulses, but has a relatively high impact on true pulses:
For the sample in figure 7.4, q min = 0.2 PE eliminates about 50 early false pulses of about
23 million pulses in total, but almost triples the number of instances where the first hit
was missed. This is seen by the underflow bin, which rise from about 11000 entries to
about 31000 entries; q min = 0.25 PE eliminates additional 10 early false pulses at the cost
of more than 40000 additional missed first hits. In general, an as low as possible setting
is preferrable.
In cases where only one feature is present inside the waveform, the option EnforcePulse
in conjunction with “BayesUnfold” could be used to extract the pulse nonetheless if it
is missed; however, the rising of the plateau at the top in figure 7.4 with increasing q min
shows that often other features are extracted instead, preventing the extraction of the
valuable first feature (possibly direct primary lepton Čerenkov light).
This calibration will be repeated with future new Monte-Carlo data, because a significant
fraction of the fake pulses seems to be caused by artifacts from an incomplete simulation,
see figure C.2 in appendix C.
By default the detection threshold is disabled (w detect = w feat ). A different setting
would hamper the detection of very flat features like those seen in figure 7.3 for DOM
11-54, and q min is sufficiently suppressing noise hits as can be seen at the low fake pulse
rate discussed above.
The parameters c P0 and c P1 for the charge-time correlation compensation term t q in
equation (6.1) were obtained by a fit to the two-dimensional charge-time histograms in figure
7.5. While the agreement is not perfect, especially for very low charges, the quadratic
model is robust, and the fit lies within the natural scattering of the distribution. For the
analyzed dataset, the time resolution measured by a Gaussian fit to the distribution seen
in figure 7.4 (excluding the underflow bin) improves from 1.04 ns to 0.81 ns for ATWD
and from 4.68 ns to 3.34 ns for FADC.
The double structure in figure 7.5 also shows that the ATWD time distribution is heavily
influenced by the erroneous GCD information (geometry, calibratoin, detector status;
section 4.6.1), which prevents correct categorization of old toroid and new toroid DOMs.
The time resolution will probably improve further as soon as this general calibration problem
is fixed. A rough estimate of this bug’s impact can be obtained by extracting pulses
exclusively from old toroid DOMs because much fewer NT DOMs are reported to have
an old toroid than the other way around. The Gaussian width is 0.68 ns in this case.
The same test applied to FADC pulses yields no improvements in time resolution because
64

7.1 Calibration Using Monte-Carlo Data
20
20
15
9000
15
9000
7500
7500
10
10
t MC −t pulse /ns
5
6000
4500
t MC −t pulse /ns
5
6000
4500
0
3000
0
3000
5
1500
5
1500
10
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
q pulse1
0
10
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
q pulse1
0
25
2000
25
2000
t MC −t pulse /ns
20
15
10
5
0
1750
1500
1250
1000
t MC −t pulse /ns
20
15
10
5
0
1750
1500
1250
1000
5
750
5
750
10
500
10
500
15
250
15
250
20
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
q pulse1
0
20
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
q pulse1
0
Figure 7.5: Charge-time correlation of pulses from NFE extraction algorithm “Simple” only;
left: uncorrected, right: default c P0 and c P1 ; top: ATWD, bottom: FADC.
the toroid’s effect is smeared out by the pulse shaper. Nevertheless, further tests will be
undertaken to check if it can be worthwile to differentiate between FADC OT and NT as
soon as improved Monte-Carlo datasets become available.
7.1.3 Extraction Algorithm “BayesUnfold”
As pointed out in section 6.3, “BayesUnfold” requires generic templates of SPE pulses in
the same binning as of the waveforms. Basis for these samples was Christopher Wendt’s
parametrization, calculated from flasher run data (figure 4.6):[47]
w SPE (t) = a 1
(
e
−a 2 t+a 3
+ e a 4t−a 5
) −8
, (7.1)
with the parameter values specified in table 7.3. With the given parametrization, the time
offsets of both the binning and the parametrization itself are still arbitrary. The binning
was chosen not to be shifted against the arbitrary offset of the parametrization. For
ATWD NT/OT the samples start at bin 1 and end with bin 12 and 11, respectively; the
FADC sample reaches from bin 2 to the end of bin 10. These selections include 99.47%,
65

7 PERFORMANCE OPTIMIZATION
Table 7.3: Parameter values of the SPE pulse parametrization employed, and
of the pulse width parametrization, equations (7.1) and (6.4).
parameter
value
ATWD NT ATWD OT FADC
a 1 4.422419 mV 4.240862 mV 8.793769 mV
a 2 0.6537139 ns −1 0.7588095 ns −1 0.8369602 ns −1
a 3 0.1049991 0.0743131 0.3809843
a 4 0.08669082 ns −1 0.09235075 ns −1 0.13469828 ns −1
a 5 0.01385802 0.00904426 0.06131466
T bin · c T1 6.46351 ns 5.96069 ns 29.9302 ns
c T2 30.856 PE −1 31.983 PE −1 53.063 PE −1
c T3 4.8980 4.5038 6.3877
Table 7.4: Default configuration values and hard-coded parameters
used for the extraction algorithm “BayesUnfold”.
parameter name in code value
n max maxIterations
minRelativeChange
40
0.012 PE
speThreshold
0.25 PE
∆u min
q min
ATWD
FADC
L SPE NT NewToroid::speLength 11 8
L SPE OT OldTOroid::speLength 10 8
t offset NT NewToroid::timeOffset 0 ns 6.66 ns
t offset OT OldToroid::timeOffset −1.82 ns 6.66 ns
66

7.1 Calibration Using Monte-Carlo Data
Table 7.5: Default values used for extraction algorithm “SLCHE”.
parameter name in code value
c q chargeCalibConst 1.1584
〈 A
w 1
〉
· Tbin meanParabolaArea 53.09 ns
t offset slcDeltaT −50.14 ns
99.43%, and 99.60% of the SPE pulses’ charges, yet they are sufficiently short to permit
unfolding with high CPU efficiency.
The parameters for the termination condition in equation (6.3) for the number of
iterations were obtained from idealized SPE pulses using the unit test’s extra output
(option -as), and are listed in table 7.4. Comparisons between results with fixed and
variable numbers of iterations show that the time resolution improves slightly (2%) for
the latter, see figure 7.6; it also tends to extract more charge per pulse (figure 7.7) and in
total . In general the extraction of more charge is not necessarily advantageous because
it might originate from a wrong baseline. However, in this case it can be assumed that
the extra charge belongs to the pulses and got lost because the unfolding was stopped
too early. Thus the adaptive stopping condition is considered to be worthwile, see also
section 8.5.
Nevertheless, the extraction results could probably be further improved by fine-tuning: As
an example, the number of pulses per waveform shown in figure 7.8 decreases on average
when using a fixed n iter = 20, and it decreases further for n iter = 30. This indicates that a
significant fraction of the extra pulses which are extracted with the default settings might
be caused by excessive splitting.
After the termination conditions were optimized during development, the improvement
gained by using the optimized starting condition instead of a flat one mostly vanished.
The gain is only 0.8 iterations instead of 3 before optimization, see figure 7.9. Still, the
optimized starting condition is kept as there are no drawbacks.
7.1.4 Extraction Algorithm “SLCHE”
For the calibration of the paramters of “SLCHE”, the algorithm has been applied to
Monte-Carlo SLC charge stamps for which full waveforms were available. The results
were compared to pulses extracted with one of the other algorithms. Despite of ATWD
waveforms providing a better time resolution, FADC pulses were chosen for the comparison
in order to minimize systematical errors due to differences between ATWD and FADC,
as SLC charge stamps are generated from FADC waveforms. Also, only waveforms from
DOMs which did not fulfill the hard local coincidence condition were used to get a more
67

7 PERFORMANCE OPTIMIZATION
10 7
10 6
width: 0.81 0.83
mean: 11.11 11.07
10 5
10 4
entries
10 3
10 2
10 1
10 0
10 -1
40 30 20 10 0 10 20 30 40
t MC −t pulse /ns
10 7
10 6
width: 0.81 0.80
mean: 11.11 11.12
10 5
10 4
entries
10 3
10 2
10 1
10 0
10 -1
40 30 20 10 0 10 20 30 40
t MC −t pulse /ns
Figure 7.6: Plots illustrating the effects of “BayesUnfold”’s variable number of iterations. Both
simple and complex ATWD waveforms have been extracted together by BU.
Shown are the distributions of the time residuals for the default BU (variable n iter ,
〈n iter 〉 = 19.8; blue areas), and for BU with a fixed number of iterations (green
lines; n iter = 20 on the top, n iter = 20 on the bottom). Red lines indicate Gaussian
fits to all bins (excluding underflow and overflow).
68

7.1 Calibration Using Monte-Carlo Data
500000
width: 0.34 0.34
mean: 0.91 0.90
400000
300000
entries
200000
100000
0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
q pulse1
500000
width: 0.34 0.34
mean: 0.91 0.91
400000
300000
entries
200000
100000
0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
q pulse1
Figure 7.7: Plots illustrating the effects of “BayesUnfold”’s variable number of iterations. Both
simple and complex ATWD waveforms have been extracted together by BU.
Shown are the distributions of the charges of first pulses extracted by the default
BU (variable n iter , 〈n iter 〉 = 19.8; blue areas), and for BU with a fixed number of
iterations (green lines; n iter = 20 on the top, n iter = 20 on the bottom). Red lines
indicate Gaussian fits to all bins (excluding underflow and overflow).
69

7 PERFORMANCE OPTIMIZATION
10 7
10 6
width: 0.37
mean: 0.04
10 5
10 4
entries
10 3
10 2
10 1
10 0
10 -1
10 5 0 5 10 15 20
∆n pulses
10 7
10 6
width: 0.36
mean: 0.09
10 5
10 4
entries
10 3
10 2
10 1
10 0
10 -1
10 5 0 5 10 15 20
∆n pulses
Figure 7.8: Plots illustrating the effects of “BayesUnfold”’s variable number of iterations. Both
simple and complex ATWD waveforms have been extracted together by BU.
Shown are the distributions of the differences between the numbers of pulses extracted
by the default BU (variable n iter , 〈n iter 〉 = 19.8) and BU with a fixed
number of iterations (n iter = 20 on the top, n iter = 20 on the bottom). Positive
values correspond to more pulses for default BU.
70

7.2 Verification Using Experimental Data
40000
0cm
60000
35000
30000
25000
50000
40000
entries
20000
entries
30000
15000
20000
10000
5000
10000
0
10 15 20 25 30 35 40
number of iterations
0
10 15 20 25 30 35 40
number of iterations
Figure 7.9: Effects of “BayesUnfold”’s optimized deconvolution starting distribution:
Shown is the distribution of the number of iterations n iter for complex waveforms
from ATWD (left) and FADC (right) for the default starting distribution (solid
lines) and a uniform one (dashed lines).
specific sample for the calibration.
The resulting parameter values are listed in table 7.5. An illustration of the good agreement
between FADC and SLC in both time and charge can be seen in figure 7.10.
7.2 Verification Using Experimental Data
After all parameters have been adjusted to work well with simulated data, most analyses
were repeated using experimental data to verify both the correctness of these parameters
and the correctness of the simulation itself. The dataset used is run 113587 (IC59, 2009-
04-21), filtered to level 1 which means that it contains the events that passed the online
filtering.
The timing tests can not be repeated without modification because the true hit information
is not available for experimental data. Instead, the relative time distribution
for different sources (e.g., ATWD and FADC) can be compared to the one obtained from
Monte-Carlo simulations.
The results of this test can be seen in figure 7.11. The small time misalignement of
about 4 ns between the pulses from ATWD and FADC can be attributed to a time offset in
the experimental dataset itself, caused by an old DOMcal version. This offset is compensated
for in DOMcalibrator by manually shifting FADC waveforms by the recommended
value of −15 ns. Still, the Monte-Carlo dataset already uses the new DOMcal version for
which the problem was fixed; therefore, it is deemed to be more trustworthy. Final time
offset calibration values for NFE will be obtained using future IC79 Monte-Carlo data,
which can be verified by future IC79 experimental data.
71

7 PERFORMANCE OPTIMIZATION
10 7
10 6
width: 3.04 2.25
mean: 10.70 10.69
10 5
10 4
entries
10 3
10 2
10 1
10 0
10 -1
80 60 40 20 0 20 40 60
t MC −t pulse /ns
300000
width: 0.34 0.33
mean: 0.78 0.78
250000
200000
entries
150000
100000
50000
0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
q pulse1
Figure 7.10: Distributions of the time residuals and charges of “SLCHE” (green lines) and
FADC (blue areas) pulses from the same waveforms, with the latter extracted by
NFE with EnforcePulse set.
72

7.2 Verification Using Experimental Data
250000
width: 3.12
mean: 0.39
200000
150000
entries
100000
50000
0
6 4 2 0 2 4 6
∆t pulse /ns
250000
width: 3.68
mean: -3.46
200000
150000
entries
100000
50000
0
10 8 6 4 2 0 2
∆t pulse /ns
Figure 7.11: Distributions of the time differences of ATWD and FADC NFE pulses for Monte-
Carlo (top) and experimental data (bottom). Positive values indicate earlier
times in the FADC.
73

7 PERFORMANCE OPTIMIZATION
1200
1000
Old Toroid DOMs
New Toroid DOMs
total
350000
300000
Old Toroid DOMs
New Toroid DOMs
total
800
250000
entries
600
400
entries
200000
150000
100000
200
50000
0
1 0 1 2 3 4
FADC charge / ATWD charge
0
1 0 1 2 3 4
FADC charge / ATWD charge
Figure 7.12: Ratio of the total (integrated) charges of the ATWD waveform and the corresponding
fraction of the FADC waveform.
Left side: simulated dataset 3071; right side: experimental dataset L1 113587.
The distributions of the charge of the first pulse for ATWD and FADC disagree significantly
between Monte-Carlo data and the experimental data (figure 7.13): Most importantly
the mean values for Monte-Carlo differ by more than 0.1 PE while those for
experimental data seem to be well aligned. This is likely a problem of the simulation:
The ratio of the total (integrated) charge of the ATWD waveform and the corresponding
fraction of the FADC waveform differs largely between Monte-Carlo and experimental
data, see figure 7.12. A part of this disagreement can be attributed to a bug in the
daq_baseline simulation, see appendix C.3 and figure C.2.
Considered individually, the first ATWD and FADC pulses’ charges match well for experimental
data. The tails in the FADC charge distributions towards values higher than
2 PE can be explained by the FADC’s inferior time resolution; the separation of features
that can be distinguished as SPE-like in ATWD is often rendered impossible in FADC,
so multiple-PE features are more likely.
The distributions of the differences between the cumulative charge of all ATWD and
all FADC pulses per waveform in figure 7.14 support the hypothesis of a wrong simulation;
while the differences peak at 0 PE for experimental data, Monte-Carlo contains on
average about 0.14 PE more charge in ATWD than in FADC.
The distributions show tails towards high FADC charges similar to the tails already observed
in the distributions of the charges of first pulses (see above); however, in the
cumulative distributions they do not originate from inseparable pulses because it is irrelevant
if the charge is distributed between multiple pulses. Instead, they are caused by late
pulses that are present in the FADC waveform, but not in the ATWD waveform. Evidence
for this is the shallow secondary peak whose distance to the main peak is approximately
one mean FADC SPE charge for either Monte-Carlo or experimental data respectively.
The bottom plots in figure 7.15 show the distributions of the number of pulses per
waveform; they can not be compared directly because the datasets differ too much: The
74

7.2 Verification Using Experimental Data
500000
width: 0.36 0.36
mean: 0.93 0.81
400000
300000
entries
200000
100000
0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
q pulse1
600000
width: 0.39 0.43
mean: 0.90 0.94
500000
400000
entries
300000
200000
100000
0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
q pulse1
Figure 7.13: Distributions of the charges of the first pulses of ATWD (blue areas) and FADC
(green lines) NFE pulses for Monte-Carlo (top) and experimental data (bottom);
red lines indicate Gaussian fits.
75

7 PERFORMANCE OPTIMIZATION
90000
80000
width: 0.11
mean: 0.14
70000
60000
entries
50000
40000
30000
20000
10000
0
1.5 1.0 0.5 0.0 0.5
∆q pulses
160000
140000
width: 0.11
mean: -0.02
120000
100000
entries
80000
60000
40000
20000
0
1.5 1.0 0.5 0.0 0.5
∆q pulses
Figure 7.14: Distributions of the differences between the total charges of all ATWD and FADC
NFE pulses per waveform for Monte-Carlo (top) and experimental data (bottom).
Positive values indicate higher charges in ATWD; red lines indicate Gaussian fits.
76

7.2 Verification Using Experimental Data
10 7
10 6
10 5
10 4
entries
10 3
10 2
10 1
10 0
10 -1
0 50 100 150 200
n pulses
10 7
10 6
10 5
10 4
entries
10 3
10 2
10 1
10 0
10 -1
0 20 40 60 80 100 120 140 160
n pulses
Figure 7.15: Distributions of the numbers of ATWD (blue areas) and FADC (green lines) NFE
pulses for Monte-Carlo (top) and experimental data (bottom).
77

7 PERFORMANCE OPTIMIZATION
particle energy in the simulated dataset follows an E −1 neutrino energy spectrum (although
the dataset is untriggered, favoring low-energy events with few pulses), while the
experimental dataset follows the atmospheric muon energy spectrum of E −3.7 .
Still the plots are plausible: The triple peak structure in the Monte-Carlo ATWD and
the small break around bin 128 in FADC originate from fully illuminated waveforms, i.e.,
waveforms with “BayesUnfold”’s maximum number of pulses; 64 for ATWD and 128 for
FADC 6 . Higher entries and the third peak respectively originate from DOMs which were
launched twice because of ongoing events (see section 4.4.2).
Despite the problems arising due to the insufficient simulation, the comparisons of
ATWD data with FADC data are promising; the important features are qualitatively
understood, and the agreements are expected to improve with the next release of the
simulation software.
6 Technically, “BayesUnfold” can extract 128 pulses from ATWD and 256 from FADC. However, an
appropriate waveform is extremly unlikely.
78

CHAPTER VIII
Performance Tests

8 PERFORMANCE TESTS
8.1 Extraction of Simple Pulses with “Simple” and BU
The use of the algorithm “Simple” instead of “BayesUnfold” (BU) for pulses that have been
classified as simple by the pre-evaluation algorithm (see section 6.1) not only improves
NFE’s CPU efficiency (see section 8.5), but also improves the extraction results because
“Simple” only needs to extract those waveforms for which it was designed. “Simple”’s
lower charge threshold allows the algorithm to find more small true pulses while extracting
slightly less false pulses than BU in the same simple sample.
The leftmost bin of figure 8.2 shows that “Simple” does not have ATWD waveforms
without pulses compared to about 100000 for BU; the latter corresponds to 1.1% of all
tested waveforms. In FADC, there are 221 compared to about 170000, which corresponds
to 1.3% of all tested waveforms. Furthermore, the lower plateau to the left side in the
distribution of the time residuals of the first pulses in figure 8.1 indicates that the number
of first true features missed in favor of a later pulse is lower by about a factor of 5 in
ATWD; it is at the same level for “Simple” and BU in FADC. The time resolution of
“Simple” measured by a Gaussian fit to the peak (figure 8.1) is worse than that of BU by
a factor of 4% resp. 8%; this trade-off is deemed to be acceptable because the decline is
small compared to a waveform bin length.
The average number of pulses extracted by “Simple” is slightly larger compared to BU
(figure 8.2). The reason is that while “Simple” is not able to split features into multiple
pulses, its charge threshold is lower (0.15 PE vs. 0.20 PE). The inability to split can be
considered advantageous in this case because simple pulses are SPE-like enough to not
require splitting, and excessive splitting is not desired.
The large number of waveforms with more than ten pulses from “Simple” is caused by the
missing simulation of the daq_baseline (see appendix C.3). An example for a waveform
with extraordinarily high baseline caused by this bug can be seen in figure 8.3. Figure 8.4
shows the same distribution as figure 8.2, but with “Simple”’s detection threshold w detect
set to “Eva”’s feature threshold w feat = 0.08 PE. Due to this change the excessive pulses
are cut away at the cost of losing many true pulses from waveforms with a more normal
baseline: The number of waveforms without pulses increases from 0 to almost 200000
(leftmost bin).
The charge of the first pulse extracted by “Simple” is about 2% higher for ATWD and
about 2% lower for FADC on average than the charge of the first BU pulse, as can be
seen in figure 8.5; this is considered to be good agreement.
Finally, the difference of the total pulse charges extracted per waveform by both algorithms
peaks near to zero and features a small width of 0.1 PE if the pulses caused by
the incomplete simulation are cut away, compare figure 8.6 to figure 8.7.
These results will change slightly for new Monte-Carlo datasets which incorporate
the simulation of the daq_baseline; however significant deviations from the predicted
80

8.1 Extraction of Simple Pulses with “Simple” and “BayesUnfold”
10 7
10 6
width: 0.73 0.76
mean: 10.99 11.09
10 5
10 4
entries
10 3
10 2
10 1
10 0
10 -1
40 20 0 20 40
t MC −t pulse /ns
10 7
10 6
width: 2.85 3.08
mean: 11.16 10.82
10 5
10 4
entries
10 3
10 2
10 1
10 0
10 -1
80 60 40 20 0 20 40 60
t MC −t pulse /ns
Figure 8.1: Distribution of the time residuals of the first pulses extracted from simple Monte-
Carlo waveforms by “BayesUnfold” (blue areas) and “Simple” (green lines): Shown
is the difference between the Monte-Carlo hit time and the time of the first pulse;
red lines indicate Gaussian fits; top: ATWD, bottom: FADC.
81

8 PERFORMANCE TESTS
10 7
10 6
10 5
10 4
entries
10 3
10 2
10 1
10 0
10 -1
0 5 10 15 20 25
n pulses
10 7
10 6
10 5
10 4
entries
10 3
10 2
10 1
10 0
10 -1
0 5 10 15 20 25 30 35 40
n pulses
Figure 8.2: Distribution of the numbers of pulses extracted from simple Monte-Carlo waveforms
by “BayesUnfold” (blue areas) and “Simple” (green lines); top: ATWD,
bottom: FADC.
82

8.1 Extraction of Simple Pulses with “Simple” and “BayesUnfold”
ATWD (blue) and FADC (red) amplitudes / PE
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
1.30
NFE_ATWDPulses_bu
10400 10600 10800 11000 11200
NFE_ATWDPulses_simple
time / ns
1.33
0.18
0.65
0.16
0.35
0.27 0.16
0.39
0.41 0.48 0.18 0.21
0.23
0.37 0.18
10400 10600 10800 11000 11200
0.35
OMKey(9,55)
Figure 8.3: Example waveform for an erroneously high baseline caused by incomplete simulation.
Dotted lines indicate ATWD pulses extracted by “BayesUnfold” (top) and
“Simple” (bottom), with charge given in units of PE.
83

8 PERFORMANCE TESTS
10 7
10 6
10 5
10 4
entries
10 3
10 2
10 1
10 0
10 -1
0 2 4 6 8 10 12 14
n pulses
Figure 8.4: Effect of erroneous baselines on the distributions of the number of pulses extracted
from simple Monte-Carlo waveforms by “BayesUnfold” (blue areas) and “Simple”
(green lines). The excessive pulses caused by high baselines were cut away by a
higher feature threshold in “Simple”; compare to figure 8.2.
84

8.1 Extraction of Simple Pulses with “Simple” and “BayesUnfold”
1000000
width: 0.32 0.35
mean: 0.90 0.92
800000
600000
entries
400000
200000
0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
q pulse1
900000
800000
width: 0.32 0.34
mean: 0.81 0.79
700000
600000
entries
500000
400000
300000
200000
100000
0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
q pulse1
Figure 8.5: Distribution of the charges of the first pulses extracted from simple Monte-Carlo
waveforms by “BayesUnfold” (blue areas) and “Simple” (green lines); red lines
indicate Gaussian fits; top: ATWD, bottom: FADC.
85

8 PERFORMANCE TESTS
10 7
10 6
width: 0.07
mean: -0.08
10 5
10 4
entries
10 3
10 2
10 1
10 0
10 -1
10 5 0 5 10
∆q pulses
10 7
10 6
width: 0.09
mean: -0.03
10 5
10 4
entries
10 3
10 2
10 1
10 0
10 -1
10 5 0 5 10
∆q pulses
Figure 8.6: Distribution of the differences between the total charges of all pulses extracted
from simple Monte-Carlo waveforms by “BayesUnfold” and “Simple”: Positive
values correspond to higher values in BU; red lines indicate Gaussian fits; top:
ATWD, bottom: FADC.
86

8.1 Extraction of Simple Pulses with “Simple” and “BayesUnfold”
10 7
10 6
width: 0.10
mean: -0.02
10 5
10 4
entries
10 3
10 2
10 1
10 0
10 -1
10 5 0 5 10
∆q pulses
Figure 8.7: Effect of erroneous baselines on the distribution of the difference between the total
charges of all pulses extracted from simple Monte-Carlo waveforms by “BayesUnfold”
and “Simple”; positive values indicate higher total charges for BU; the red
line indicates a Gaussian fit. The excessive pulses caused by high baselines were
cut away by a higher feature threshold in “Simple”; compare to figure 8.6.
87

8 PERFORMANCE TESTS
10 7
10 6
10 5
10 4
entries
10 3
10 2
10 1
10 0
10 -1
0 2 4 6 8 10 12 14 16 18
n pulses
Figure 8.8: Distribution of the numbers of pulses extracted from simple experimental ATWD
waveforms by “BayesUnfold” (blue areas) and “Simple” (green lines). Experimental
data is unaffected by the daq_baseline bug, compare to figure 8.2.
88

8.1 Extraction of Simple Pulses with “Simple” and “BayesUnfold”
10 7
10 6
width: 0.08
mean: -0.08
10 5
10 4
entries
10 3
10 2
10 1
10 0
10 -1
10 5 0 5 10
∆q pulses
Figure 8.9: Distribution of the differences between the total charges of all pulses extracted
from simple experimental ATWD waveforms by “BayesUnfold” and “Simple”:
Positive values correspond to higher values in “BayesUnfold”; the red line indicates
a Gaussian fit. Experimental data is unaffected by the daq_baseline bug, compare
to figure 8.6.
89

8 PERFORMANCE TESTS
distributions are not expected because the distributions of total charge and number of
pulses for experimental data (in which this bug does not occur) show virtually no excessive
pulses; compare figure 8.2 to figure 8.8 and figure 8.6 to figure 8.9.
If some of the excessive pulses will remain in the new data regardless, either “Simple”’s
detection threshold or “Eva”’s feature threshold will be adjusted; lowering the latter helps
because then the affected waveforms will be marked as complex, and BU is more robust
towards an increased baseline as can be seen in figure 8.3.
8.2 Extraction of Exotic Features
The extraction of exotic features can be examined best by manually checking individual
waveforms; otherwise problems might be concealed by the higher statistics of normal
waveforms. Also, certain tests are hard to automatize, e. g., timing distributions of nonfirst
pulses, because the assignement of pulses to Monte-Carlo hits is not trivial.
Figure 8.10 shows an example for the performance of NFE for very small features: Normally
NFE does not extract any pulses because only the middle bin of the ATWD feature
exceeds “Simple”’s threshold w feat , therefore the extracted charge is about 0.12 PE < q min .
With EnforcePulse set, the feature is then relayed to “BayesUnfold” which first tries to
extract pulses normally. If this fails, BU defines a pulse centered at the deconvoluted
distribution’s maximum bin and accepts it regardless of its charge.
Most of the time, this works well: The only difference between the blue distribution in
figure 7.4 and green distribution in figure 8.16 is that for the latter EnforcePulse is set.
The number of waveforms for which the first extracted pulse is more than 50 ns away
from the Monte-Carlo hit is reduced from about 11000 to about 5000 (underflow bin).
The drawback is an increased number of false early pulses; an example for this can be
seen in figure 8.10: The ATWD feature is extracted successfully, but the FADC pulse (for
which EnforcePulse was set independently) might be caused by noise.
Final quantitative tests can only be conducted when simulations with proper baselines
become available (see appendix C.3).
Besides many randomly chosen waveforms like the ones shown in figure 7.1, a small
catalogue of exotic features provided by Markus Voge[60] was examined, along with other
waveforms from the same dataset; see figure 8.11 to figure 8.15.
For comparison, FeatureExtractor’s pulses are also shown.
Figure 8.11, top (DOM 50-24):
Noise artifacts such as this one appear in experimental data relatively often ( 1%); both
feature extractors are robust concerning this effect; it might however interfere with FE’s
charge calculation as single pulse’s charge seems to be overestimated – extraction by eye
yields about 0.38 PE, NFE finds 0.35 PE, FE 0.60 PE.
90

8.2 Extraction of Exotic Features
NFE_MergedPulses
OMKey(47,48)
ATWD (blue) and FADC (red) amplitudes / PE
0.15
0.10
0.05
0.00
0.05
0.15
0.10
0.05
0.00
0.05
19100 19200 19300 19400 19500 19600 19700 19800 19900
FE_Pulses
time / ns
0.23
19100 19200 19300 19400 19500 19600 19700 19800 19900
ATWD (blue) and FADC (red) amplitudes / PE
0.15
0.10
0.05
0.00
0.05
0.15
0.10
0.05
0.00
0.05
0.15
0.15
NFE_MergedPulses
OMKey(47,48)
19100 19200 19300 19400 19500 19600 19700 19800 19900
FE_Pulses
time / ns
0.23
19100 19200 19300 19400 19500 19600 19700 19800 19900
Figure 8.10: Example waveforms to demonstrate NFE’s option EnforcePulse, shown is a
waveform with pulses (dotted lines with charges in PE) extracted by NFE (upper
image each) and FE (lower image each):
Top: default NFE (EnforcePulse = False);
bottom: same settings bar EnforcePulse = True for both ATWD and FADC.
91

8 PERFORMANCE TESTS
ATWD (blue) and FADC (red) amplitudes / PE
0.30
0.25
0.20
0.15
0.10
0.05
0.00
0.05
0.30
0.25
0.20
0.15
0.10
0.05
0.00
0.05
0.35
NFE_MergedPulses
OMKey(50,24)
9900 10000 10100 10200 10300 10400 10500 10600 10700
FE_Pulses
time / ns
0.60
9900 10000 10100 10200 10300 10400 10500 10600 10700
NFE_MergedPulses
OMKey(18,4)
ATWD (blue) and FADC (red) amplitudes / PE
0.8
0.6
0.4
0.2
0.0
0.8
0.6
0.4
0.2
0.38
1.10
0.76
1.45
15500 15600 15700 15800 15900 16000 16100 16200 16300
FE_Pulses
time / ns
0.32
0.82
0.40
0.69
0.83
0.63
0.31
1.51
1.44
0.0
15500 15600 15700 15800 15900 16000 16100 16200 16300
Figure 8.11: Example waveforms of exotic or difficult features from IC59 experimental run
113912, partially from Markus Voge’s catalog of exotic waveforms. All waveforms
are shown with default NFE merged pulses (ATWD+FADC; top) and FE pulses
(IC59 multi-pulse online-filtering settings; bottom), indicated by dotted lines with
the charge given in units of PE.
92

8.2 Extraction of Exotic Features
ATWD (blue) and FADC (red) amplitudes / PE
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0.60
0.81
0.51
0.70
0.52
1.02
NFE_MergedPulses
0.94
0.65
0.59
9900 10000 10100 10200 10300 10400 10500 10600 10700
FE_Pulses
time / ns
0.54
0.45 0.42
0.40
0.710.34
0.34
0.47
0.22
0.81
0.24
0.67
0.41
0.20
9900 10000 10100 10200 10300 10400 10500 10600 10700
1.18
OMKey(54,1)
ATWD (blue) and FADC (red) amplitudes / PE
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.79
0.92
0.44
1.43
1.41
0.45
NFE_MergedPulses
OMKey(54,2)
10000 10100 10200 10300 10400 10500 10600 10700
FE_Pulses
time / ns
0.36
1.62
0.48
0.72
1.02
10000 10100 10200 10300 10400 10500 10600 10700
Figure 8.12: Example waveforms of exotic or difficult features from IC59 experimental run
113912, partially from Markus Voge’s catalog of exotic waveforms. All waveforms
are shown with default NFE merged pulses (ATWD+FADC; top) and FE pulses
(IC59 multi-pulse online-filtering settings; bottom), indicated by dotted lines with
the charge given in units of PE.
93

8 PERFORMANCE TESTS
ATWD (blue) and FADC (red) amplitudes / PE
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
1.00
0.32
0.28
NFE_MergedPulses
1.15
18300 18400 18500 18600 18700 18800 18900 19000 19100
FE_Pulses
time / ns
0.7 0.24
0.6
0.5
0.4
0.3
0.2
0.1
0.0
1.03
0.35
0.91
0.46
0.23
OMKey(47,51)
18300 18400 18500 18600 18700 18800 18900 19000 19100
ATWD (blue) and FADC (red) amplitudes / PE
0.5
0.4
0.3
0.2
0.1
0.0
0.5
0.4
0.3
0.2
0.1
0.0
0.26
1.32
NFE_MergedPulses
OMKey(65,13)
11300 11400 11500 11600 11700 11800 11900 12000
FE_Pulses
time / ns
1.08
11300 11400 11500 11600 11700 11800 11900 12000
Figure 8.13: Example waveforms of exotic or difficult features from IC59 experimental run
113912, partially from Markus Voge’s catalog of exotic waveforms. All waveforms
are shown with default NFE merged pulses (ATWD+FADC; top) and FE pulses
(IC59 multi-pulse online-filtering settings; bottom), indicated by dotted lines with
the charge given in units of PE.
94

8.2 Extraction of Exotic Features
ATWD (blue) and FADC (red) amplitudes / PE
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.25
0.58
0.44
1.35
NFE_MergedPulses
17500 17600 17700 17800 17900 18000 18100 18200 18300
FE_Pulses
time / ns
0.75
1.62
0.36
OMKey(83,17)
17500 17600 17700 17800 17900 18000 18100 18200 18300
NFE_MergedPulses
OMKey(38,48)
ATWD (blue) and FADC (red) amplitudes / PE
0.4
0.19
0.65
0.45
0.3
0.2
0.1
0.0
18000 18100 18200 18300 18400 18500 18600 18700 18800
FE_Pulses
time / ns
0.4
0.3
0.2
0.1
0.0
0.39
0.34
18000 18100 18200 18300 18400 18500 18600 18700 18800
Figure 8.14: Example waveforms of exotic or difficult features from IC59 experimental run
113912, partially from Markus Voge’s catalog of exotic waveforms. All waveforms
are shown with default NFE merged pulses (ATWD+FADC; top) and FE pulses
(IC59 multi-pulse online-filtering settings; bottom), indicated by dotted lines with
the charge given in units of PE.
95

8 PERFORMANCE TESTS
Figure 8.11, bottom (DOM 18-04):
This waveform was included in Markus Voge’s initial catalog because the first feature
was not extracted properly with the offline-reconstruction settings of FeatureExtractor
(see section 8.3.1); in its online-filtering settings that are shown here, FE extracts this
feature without problems, but tends to split SPE-like features excessively. NFE’s results
are reasonable.
Figure 8.12, top (DOM 54-01):
In this example, both extractors miss the tiny feature at 10 100 ns. Extraction by eye
yields about 0.1 PE.
Figure 8.12, bottom (DOM 54-02):
For this ATWD waveform, both extractors agree well. The ExclusionTime introduced
in FeatureExtractor to prevent double extraction (see appendix C.1) circumvents the
extraction of the FADC feature present in NFE.
Figure 8.13, top (DOM 47-51):
Here both extractors recognize the first feature as multi-PE hit with a small charge in
the first peak (perhabs a prepulse). The middle feature is extracted by NFE exclusively
despite the fact that it technically lies below FE’s charge threshold: FE splits the last
feature into three parts of which one only contains 0.23 PE – the missed feature contains
about 0.28 PE.
Figure 8.13, bottom (DOM 65-13):
This is an example for a very small first feature. It is extracted by NFE, but not by
FE. Also, NFE extracts more charge from the late ATWD feature (1.32 PE instead of
0.26 PE); extraction by eye yields well about 1.2 PE.
Figure 8.14, top (DOM 83-17):
Another example for a small early feature. Again it is missed in FeatureExtractor, but
here the missing charge is distributed among the extracted pulses.
Figure 8.14, bottom (DOM 38-48):
The first ATWD feature was too small to be recognized by one of the extractors; however
in contrast to FE, NFE’s PulseMerger is capable of appending FADC pulses at times
where ATWD waveforms are available if they do not clash with ATWD pulses.
Figure 8.15 shows a typical bright waveform, i. e. a waveform with high integrated
charge. The two feature extractors give roughly comparable results besides FeatureExtractor’s
more pronounced pulse splitting. Noteworthy is the gap between the end of the
ATWD waveform and the first FADC pulse for FE; the amount of charge lost due to this
is estimated by eye to about 7.6 PE of which NFE extracts 5.6 PE.
One idea for a more quantitative analysis for bright waveforms is to compare the original
waveform to a waveform generated based on the extracted pulses, for example with a
96

8.3 Comparison with Other Feature Extractors
ATWD (blue) and FADC (red) amplitudes / PE
5
4
3
2
1
0
5
4
3
2
1
0.79 1.27 1.43
1.07 1.12 0.74
0.74
2.05
0.71
1.82
1.79
3.12 1.42
0.50
1.82
1.98
0.90
3.68
0.62
0.63
0.45
0.64 2.56 1.88 0.69
4.84
0.39
0.48
0.49
1.20 1.66
2.48 3.20 0.40
0.95
1.66
2.05
0.71
1.12
1.81
NFE_MergedPulses
4.31
1.30
15400 15600 15800 16000 16200
FE_Pulses
time / ns
1.81 0.66 1.07
1.15
0.86 0.44 0.51
0.68 1.20
0.48
0.56 0.75 0.77 1.13 1.71 0.81 0.95
0.74 0.65
1.27
0.72 0.54
0.79
0.84
0.73
0.60
0.43
0.67
0.56
0.64
0.77
0.84
0.81
0.35 0.72
1.63
0.85
0.79
1.04
0.70
0.77 0.80
1.27
0.68
0.57
1.55
0.49
1.34 0.78
0.48
0.36 2.23 1.29 0.69
2.31 0.84 0.74
0.57
1.07
0.71
0.63 0.62
1.21
0.60
1.63 1.05
0.74
OMKey(26,10)
2.25
0.81
1.11
2.0
0
15400 15600 15800 16000 16200
Figure 8.15: Example of a typical bright waveform from Markus Voge’s IC59 exotic waveform
catalog. It is shown with default NFE merged pulses (ATWD+FADC; top) and
FE pulses (IC59 multi-pulse online-filtering settings; bottom), indicated by dotted
lines with the charge given in units of PE.
Kolmogorov-Smirnov test, however this has yet to be done systematically.
Reliable extraction of features where FeatureExtractor has difficulties bodes well; however
this is no guaranty for bug free and unproblematic operation. Therefore tests such as
these must be continued in future to identify problems of NFE or to discover unexpected
changes in the low-level reconstruction chain.
8.3 Comparison with Other Feature Extractors
The comparison of NFE’s results to that of other feature extractors is informative concerning
deficiencies of either of them. Knowledge of these deficiencies is important for
further improvements and for the study of systematical errors in low-level reconstruction.
8.3.1 FeatureExtractor in Multi-Pulse Mode
FeatureExtractor is the extractor used for ATWD and FADC waveforms in the IC59
online-filtering and offline-processing. The ability to test it with an independent project
is one of the main benefits of having multiple feature extractors.
The tests were conducted using both FE’s IC59 multi-pulse online and offline settings[51].
The former will be discussed in detail; afterwards, the differences of the offline-processing
97

8 PERFORMANCE TESTS
10 7
10 6
width: 1.23 0.81
mean: 0.53 11.19
10 5
10 4
entries
10 3
10 2
10 1
10 0
10 -1
40 20 0 20 40
t MC −t pulse /ns
Figure 8.16: Distributions of the time residuals of the first pulses extracted by FE (multi-pulse
online-filtering settings, blue area) and NFE (with EnforcePulse set, green line)
from Monte-Carlo data; red lines indicate Gaussian fits.
settings will be explained.
For better comparability, NFE’s option EnforcePulse was set because the analog is set
for FE. Both extractors are configured to extract features in both ATWD and FADC.
IC59 online-filtering settings
The distribution of the time residuals in figure 8.16 shows that NFE has a better time
resolution (Gaussian width of σ NFE = 0.81 ns instead of σ FE = 1.23 ns). NFE extracts
19 fake early pulses instead of a single one for FeatureExtractor from about 4.1 million
waveforms in total. This is balanced by the fact that for NFE only about 5500 first pulses
do not match the first Monte-Carlo hit, while this happens in about 90000 waveforms for
FeatureExtractor; this can be seen in the histogram entries in the lower plateau and the
underflow bin to the left of figure 8.16.
The time offset of about 11 ns between NFE’s pulses and Monte-Carlo hit times and
the absence of such an offset in FeatureExtractor’s pulse times is explained by the fact
that FeatureExtrator is used with its option PMTTransit set to 2 to have it subtract the
PMT transit time. By design NFE relies on DOMcalibrator’s time calibration instead,
98

8.3 Comparison with Other Feature Extractors
see section 7.1. This time offset can clearly be seen in the figures in section 8.2.
The distribution of the differences between the times of the first pulses for Monte-Carlo
data (figure 8.17) has a Gaussian width of σ ∆ = 0.91 ns. Assuming the individual times
to follow Gaussian distributions, this yields a correlation coefficient
ρ = σ2 FE + σ 2 NFE − σ 4 ∆
2σ FE σ NFE
= 0.74,
which is an encouraging result for both extractors because the distributions’ widths themselves
are significantly smaller than the ATWD waveform bin length (T bin = 3.3 ns).
In contrast to NFE, FeatureExtractor is not sensitive to the daq_baseline bug explained
in section 7.2 and appendix C.3 because of its own implementation of baseline
correction. Therefore, the mean of the charges of the first pulse extracted by FeatureExtractor
is the same for Monte-Carlo and experimental data, although it is further away
from 1 PE compared to NFE, see figure 8.18.
Moreover, FE’s distributions of the first charges are closer to a Gaussian distribution for
very low pulse charges. However, in a random sample of 37 waveforms for which NFE extracted
less than 0.2 PE for the first pulse, 11 of these pulses were caused by features that
were missed by FE in favor of a later feature. The remaining 26 pulses were extracted
from the only distinct feature of each waveform, triggering the extractors’ methods to
extract at least one pulse. For almost all of these features FE’s charges were between
50% and 100% higher than those of NFE, while the latter approximately agreed with the
charges extracted by eye; see figure 8.19 for an extreme example. The reason for this
effect might be that FE often raises the baseline and then scales up the pulse charge to
match the waveform’s integraged charge as described in section 6.3.1. Thus, despite the
strange shape of the distribution in figure 8.18, the charges of the first pulses extracted
by NFE are plausible.
The distributions of the differences of the cumulative charge of all pulses per waveform
between FE and NFE in figure 8.20 show a higher correlation between the extractors (i.
e., smaller width) for simulated data than for experimental data. The estimation of the
correlation coefficient using the fitted Gaussian distributions fails as it yields ρ = 1.02
and ρ = 1.01, respectively.
The distributions peak near 0 PE, but show tails with extreme values in both directions.
These deviations are partly due to problems with the calibration of saturated ATWD waveforms;
the IC59 online-filtering settings of DOMcalibrator have the SaturationLevel set
to 1022; this means that DOMcalibrator switchs to higher ATWD channels only for bins
that reach the digitizer’s maximum value. However, because of noise waveforms often fluctuate
to slightly lower values even if the channel is saturated. This leads to very uneven
waveforms of which one can be seen in figure 8.21. Setting the level lower (for example to
a value of 900) solves the problem; this was already done for the IC59 offline-processing
and is planned for future uses as well.[61]
Besides these calibration problems, the tails in figure 8.20 towards higher charges from
99

8 PERFORMANCE TESTS
900000
800000
width: 0.91
mean: -10.59
700000
600000
entries
500000
400000
300000
200000
100000
0
16 14 12 10 8 6 4
∆t pulse /ns
900000
800000
width: 1.15
mean: -10.16
700000
600000
entries
500000
400000
300000
200000
100000
0
16 14 12 10 8 6 4
∆t pulse /ns
Figure 8.17: Distributions of the times of the first pulses extracted by FE (multi-pulse onlinefiltering
settings) and NFE (with EnforcePulse set). Positive values correspond
to later times for FE; red lines indicate Gaussian fits.
Top: Monte-Carlo data; bottom: experimental data.
100

8.3 Comparison with Other Feature Extractors
600000
width: 0.29 0.36
mean: 0.81 0.93
500000
400000
entries
300000
200000
100000
0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
q pulse1
700000
600000
width: 0.31 0.39
mean: 0.81 0.89
500000
entries
400000
300000
200000
100000
0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
q pulse1
Figure 8.18: Distributions of the charges of the first pulses extracted by FE (multi-pulse onlinefiltering
settings, blue area) and NFE (with EnforcePulse set, green line); red
lines indicate Gaussian fits.
Top: Monte-Carlo data; bottom: experimental data.
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8 PERFORMANCE TESTS
ATWD (blue) and FADC (red) amplitudes / PE
ATWD (blue) and FADC (red) amplitudes / PE
0.30
0.25
0.20
0.15
0.10
0.05
0.00
0.05
0.30
0.25
0.20
0.15
0.10
0.05
0.00
0.05
0.4
0.3
0.2
0.1
0.0
0.4
0.3
0.2
0.1
0.0
0.16
NFE_MergedPulses
OMKey(3,16)
11800 12000 12200 12400 12600
FE_Pulses
time / ns
0.42
11800 12000 12200 12400 12600
NFE_MergedPulses
OMKey(47,40)
0.16
0.61
9800 10000 10200 10400 10600
FE_Pulses
time / ns
0.88
9800 10000 10200 10400 10600
Figure 8.19: Examples for waveforms in which NFE (upper image each) extracts significantly
less charge than FE (lower image each). Pulses are indicated by dotted lines with
the charge given in units of PE.
102

8.3 Comparison with Other Feature Extractors
10 7
10 6
width: 0.12
mean: -0.09
10 5
10 4
entries
10 3
10 2
10 1
10 0
10 -1
40 20 0 20 40
∆q pulses
10 7
10 6
width: 0.26
mean: 0.03
10 5
10 4
entries
10 3
10 2
10 1
10 0
10 -1
40 20 0 20 40
∆q pulses
Figure 8.20: Distributions of the differences between the total charges of all pulses extracted
by FE (multi-pulse online-filtering settings) and NFE (with EnforcePulse set).
Positive values correspond to higher charges for FE; red lines indicate Gaussian
fits.
Top: Monte-Carlo data; bottom: experimental data.
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8 PERFORMANCE TESTS
ATWD (blue) and FADC (red) amplitudes / PE
ATWD (blue) and FADC (red) amplitudes / PE
100
80
60
40
20
0
100
80
60
40
20
0
100
80
60
40
20
0
100
80
60
40
20
0
23.41
331.57
9.02
1.78
41.98
17.79
3.14
15.52
6.35
20.62
12.33
12.98
7.66
4.37
6.01
5.26
6.21
NFE_MergedPulses
8.02
2.92
0.76
1.55
1.59
6.23
1.22
0.29
12000 12100 12200 12300 12400
FE_Pulses
time / ns
30.68
25.61
44.67
250.20
55.18
12000 12100 12200 12300 12400
0.36
0.75
NFE_MergedPulses
1.87
0.26
0.49
18.26
42.32
3.07
29.75
4.40
0.54
419.15
8.75
0.84 6.51
0.51
23.47
5.40
140.35 14.61 9.05
1.71 1.37 0.94 0.53
6.37 1.71
60.92
17.12
10.35
0.44 2.05
8.16
34.48
0.39
6.37
1.21
OMKey(37,26)
12000 12100 12200 12300 12400
FE_Pulses
time / ns
43.88
26.38
118.37
147.56
134.07
109.03
75.19
12000 12100 12200 12300 12400
1.55
0.45
0.42
0.79
0.88
0.74
0.89
1.44
1.06
OMKey(37,26)
0.98
1.80
0.79
Figure 8.21: Example of saturated waveforms with pulses from NFE (upper image each) and
FE (lower image each). Pulses are indicated by dotted lines with the charge
given in units of PE. The waveforms have been calibrated with the IC59
online-filtering settings for DOMcalibrator (top) and its offline-processing settings
(SaturationLevel = 900, bottom), respectively.
104

8.3 Comparison with Other Feature Extractors
NFE (negative values) are mostly caused by saturated waveforms; for those, FeatureExtractor’s
option TinyThreshold causes pulses below 5% of the charge of the highest pulse
to be ignored. This can be seen in figure 8.21, where FE does not accept pulses during
most of the waveform. TinyThreshold is set to zero in the IC59 offline-reconstruction
settings.[51]
The tails towards higher charges from FE are probably caused by FADC waveforms that
are heavily affected by droop. FE successfully employs its own methods to correct for
this effect. This has to be investigated further with the aim to include these methods in
DOMcalibrator.
FeatureExtractor often produces many more pulses in ATWD waveforms because it
defines a pulse from two bins or from one bin of its deconvoluted distribution while NFE
uses three bins each, see section 6.3.1: FE extracts up to 127 pulses per ATWD waveform,
while NFE usually extracts 64 at most. For FADC on the other hand FeatureExtractor
extracts comparatively few pulses because its FADC algorithm is not capable of splitting
long features, while NFE usually extracts up to 128 pulses from a saturated FADC waveform.
This can be verified in figure 8.22, where the FE’s distribution for Monte-Carlo has its
first bend at about 150 pulses per waveform and then quickly falls off, whereas NFE has
a first bend at about 50 pulses per waveform, but does not fall off quickly because of high
numbers of FADC pulses. Very high numbers of pulses in Monte-Carlo data are caused
by DOMs which were launched twice; in current experimental data, first launch cleaning
cuts away waveforms from later launches.
In summary, FeatureExtractor finds less pulses on average because of its FADC algorithm,
and also because TinyThreshold rejects low pulses in very bright waveforms.
IC59 offline-processing settings
The recommended settings for IC59 offline-processing have been used in connection
with the recommended settings for DOMcalibrator, i. e., SaturationLevel = 900.[62][51]
For FeatureExtractor, the changes are:
• ADCThreshold = 1.1 −→ ADCThreshold = 1.8
The charge threshold to decide whether to accept a pulse or not was increased to
take account for a recent change in the DOMs’ discriminator thresholds. The effect
of this change is that for pulses that were previously split excessively now many
fractions fall below the threshold; this results in a higher charge per pulse because
the remaining pulses are rescaled (see section 6.3.1). The drawbacks are a higher
number of missed pulses and more unphysical redistribution of charge between pulses
of the same waveform.
105

8 PERFORMANCE TESTS
10 7
10 6
10 5
10 4
entries
10 3
10 2
10 1
10 0
10 -1
0 50 100 150 200 250
n pulses
10 7
10 6
10 5
10 4
entries
10 3
10 2
10 1
10 0
10 -1
0 50 100 150
n pulses
Figure 8.22: Distributions of the numbers of pulses extracted by FE (multi-pulse onlinefiltering
settings, blue area) and NFE (with EnforcePulse set, green line).
Top: Monte-Carlo data; bottom: experimental data.
106

8.3 Comparison with Other Feature Extractors
10 7
10 6
width: 0.90 0.81
mean: 10.18 11.19
10 5
10 4
entries
10 3
10 2
10 1
10 0
10 -1
40 20 0 20 40
t MC −t pulse /ns
Figure 8.23: Distributions of the time residuals of the first pulses extracted by FE (multipulse
offline-processing settings, blue area) and NFE (with EnforcePulse set,
green line) from Monte-Carlo data; red lines indicate Gaussian fits.
107

8 PERFORMANCE TESTS
600000
width: 0.32 0.36
mean: 0.88 0.93
500000
400000
entries
300000
200000
100000
0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
q pulse1
600000
width: 0.35 0.39
mean: 0.96 0.90
500000
400000
entries
300000
200000
100000
0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
q pulse1
Figure 8.24: Distributions of the charges of the first pulses extracted by FE (multi-pulse offlineprocessing
settings, blue area) and NFE (with EnforcePulse set, green line); red
lines indicate Gaussian fits.
Top: Monte-Carlo data; bottom: experimental data.
108

8.3 Comparison with Other Feature Extractors
10 7
10 6
10 5
10 4
entries
10 3
10 2
10 1
10 0
10 -1
0 50 100 150 200 250
n pulses
10 7
10 6
10 5
10 4
entries
10 3
10 2
10 1
10 0
10 -1
0 50 100 150 200
n pulses
Figure 8.25: Distributions of the numbers of pulses extracted by FE (multi-pulse offlineprocessing
settings, blue area) and NFE (with EnforcePulse set, green line).
Top: Monte-Carlo data; bottom: experimental data.
109

8 PERFORMANCE TESTS
• ExclusionSize = 5 −→ ExclusionSize = 1
This parameters governs the deadtime between ATWD and FADC in units of FADC
bin lengths during which no FADC pulses are accepted because their ATWD counterpart
might already have been extracted (double extraction, see appendix C.1);
it was largely overestimated in the old settings. The consequence of this change is
higher total charge and more accurate extraction performance.
• TinyThreshold = 0.05 −→ TinyThreshold = 0.00
TinyThreshold was originally introduced to prevent the extraction of pulses from
droop artifacts and prepulses. However, it hampers the accurate extraction of waveforms
(see figure 8.21) and can cause direct hits to be ignored. This was judged to
be more important, so the threshold was disabled. The results are more accurate
extraction and higher total charge, because the charge attributed to pulses which
do not pass TinyThreshold is forfeit.
• PMTTransit = 2 −→ PMTTransit = -1
This parameter influences the timing distribution by adding a time offset and correcting
for a correlation between the PMT voltage and the pulse time; however,
observed individually, disabeling the correction improves the time resolution measured
by the Gaussian width from 1.23 ns (not shown) to 0.90 ns (figure 8.23).
The offline-processing settings increase FeatureExtractor’s average charge per pulse
towards 1 PE (figure 8.24: 0.88 PE for Monte-Carlo and 0.96 PE for experimental data
instead of 0.81 PE for each in figure 8.18). However, the new settings also approximately
double the number of missed first pulses to about 177000 in 4.1 million waveforms (4.3%),
see figure 8.23. Besides, the time resolution increases from 1.23 ns to 0.90 ns.
The total number of pulses (figure 8.25) decreases slightly because of the lower ADCThreshold,
and there are more waveforms with exeptionally high numbers of pulses ( 100) because
of the disabled TinyThreshold.
In total, the changes were carefully compiled by many people and provide for an improvement
upon the older online-filtering settings, yet they also increase the number of
missed pulses and do not generally improve the charge per pulse:
A related test originally conducted by Juanan Aguilar[63] compares the agreement of the
ratio of charge per pulse between realistically simulated data (CORSIKA) and current
experimental data. The results can be seen in figure 8.26. The simulated data uses the
old discriminator thresholds, so it has to be extracted with ADCTreshold = 1.1 (onlinefiltering
settings). In contrast, the experimental data was taken with the new thresholds,
so the offline-processing settings are recommended; the ratio for experimental data is
shown for both FeatureExtractor settings.
As expected, the agreement is better for the offline-processing settings of FeatureExtractor,
however it is worse for ratios near 0.3 PE per pulse.
For NFE, the agreement is good for regions of high abundance. The disagreement for
110

8.3 Comparison with Other Feature Extractors
10 6
10 5
exp data (Run114060), onl.
exp data (Run114060), offl.
corsika (1628), onl.
10 4
entries
10 3
10 2
10 1
10 0
10 -1
1.0 0.5 0.0 0.5 1.0 1.5 2.0
log 10 (q tot PE −1 / n pulses )
10 6
10 5
exp data (Run114060)
corsika (1628)
10 4
entries
10 3
10 2
10 1
10 0
10 -1
1.0 0.5 0.0 0.5 1.0 1.5 2.0
log 10 (q tot PE −1 / n pulses )
Figure 8.26: Charge per pulse ratio for simulated data (dotted line) and experimental data
(solid lines) for FE (top, online and offline settings) and NFE (bottom, default
settings).
111

8 PERFORMANCE TESTS
10 7
10 6
width: 1.23 0.81
mean: 0.55 11.19
10 5
10 4
entries
10 3
10 2
10 1
10 0
10 -1
40 20 0 20 40
t MC −t pulse /ns
Figure 8.27: Distributions of the time residuals of the first pulses extracted by FE (singlepulse
settings, blue area) and NFE (with EnforcePulse set, green line) from
Monte-Carlo data; red lines indicate Gaussian fits.
low charges is probably caused by the missing simulation of the daq_baseline; the disagreement
for ratios higher than 3 PE per pulse has to be examined. Both datasets have
been extracted using the same (default) settings; NFE is not directly influenced by DOM
discriminator threshold changes because all thresholds are defined in units of PE.
8.3.2 FeatureExtractor in Single-Pulse Mode
NFE’s results were also compared to FeatureExtractor’s IC59 single-pulse extraction results
because this was the mode of operation for the IC59 online-filtering muon track
reconstruction; FE is configured to use its second single-pulse extraction algorithm and
to only extract ATWD waveforms.[51] For best comparability, EnforcePulse was set for
NFE and no FADC pulses were extracted; still NFE’s distributions shown in this section
closely resemble those in section 8.3.1 because the missing FADC pulses barely affect the
first pulse.
The distribution of the time residuals of the first pulses (figure 8.27) for FE is similar
to those obtained by FE in its multi-pulse mode; this is not surprising because FE uses
the single-pulse extraction time to replace the time of the Bayesian Unfolding pulse closest
112

8.4 SLCHitExtractor
to it (section 6.3.1), and the single-pulse extraction algorithm extracts the first feature if
can find. The distribution of the time residuals shows more early fake pulses; however,
the shapes and widths of the distributions of the time differences between FE and NFE
are effectively the same (±0.01 ns, not shown).
In figure 8.28, the distributions of the charges of the first pulses have a strong tail
towards high values because of the algorithm’s inability to split features. Furthermore
they are less stable regarding the transition from Monte-Carlo to experimental data: Their
mean increases from 0.87 PE to 1.04 PE, and the tail becomes significantly stronger for
experimental data; this is probably caused by the wrong charge simulation (figure 7.12)
and the datasets’ different energy spectra.
The distribution of the differences of the total charge per waveform for simulated data
in figure 8.29 reveals an on average higher total charge for NFE, despite the fact that
FE calculates the integrated charge; this is due to the wrong baseline simulation, which
is often fixed by FeatureExtractor’s own baseline correction algorithm. For experimental
data, FE’s integrated charge is higher than NFE’s charge because the latter is extracted
from features only.
8.4 SLCHitExtractor
SLCHitExtractor is currently used for the IC59 SLC charge stamp extraction, which
motivates tests of its performance and its use as a benchmark for NFE; see appendix C.4.
SLCHitExtractor’s time resolution is better than “SLCHE”’s with a Gaussian width
of 1.91 ns instead of 2.25 ns, see figure 8.30; both of them have better resolutions than the
(more flexible) NFE default combination of FADC algorithms (∼ 3 ns, figure 7.10), and
both resolutions are well below even one ATWD waveform bin length, so both are deemed
to be excellent.
SLCHitExtractor’s pulse times match those of FE’s ATWD pulses (if FE’s transit time
correction is activated), “SLCHE”’s instead match the time of NFE’s FADC pulses (see
section 7.1.4).
The charge distribution of SLCHitExtractor is less stable than that of “SLCHE” (figure
8.31); it shifts by 0.07 PE between Monte-Carlo and experimental data. It also shows an
unexplained excess in its 0.8 PE bin. Compared to “SLCHE” the mean of the distribution
is closer to 1 PE because it was calibrated to match the distribution of FeatureExtractor
in its offline-reconstruction settings.[64] Correspondignly, “SLCHE” matches the average
FADC charge extracted by NFE from simulated data.
113

8 PERFORMANCE TESTS
500000
width: 0.38 0.36
mean: 0.87 0.93
400000
300000
entries
200000
100000
0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
q pulse1
300000
width: 0.51 0.39
mean: 1.04 0.90
250000
200000
entries
150000
100000
50000
0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
q pulse1
Figure 8.28: Distributions of the charges of the first pulses extracted by FE (single-pulse settings,
blue area) and NFE (with EnforcePulse set, green line); red lines indicate
Gaussian fits.
Top: Monte-Carlo data; bottom: experimental data.
114

8.4 SLCHitExtractor
10 7
10 6
width: 0.13
mean: -0.06
10 5
10 4
entries
10 3
10 2
10 1
10 0
10 -1
40 20 0 20 40
∆q pulses
10 7
10 6
width: 0.22
mean: 0.14
10 5
10 4
entries
10 3
10 2
10 1
10 0
10 -1
50 40 30 20 10 0 10 20 30
∆q pulses
Figure 8.29: Distributions of the differences between the total charges of all pulses extracted
by FE (single-pulse settings) and NFE (with EnforcePulse set). Positive values
correspond to higher charges for FE; red lines indicate Gaussian fits.
Top: Monte-Carlo data; bottom: experimental data.
115

8 PERFORMANCE TESTS
10 7
10 6
width: 1.91 2.25
mean: -0.03 10.70
10 5
10 4
entries
10 3
10 2
10 1
10 0
10 -1
80 60 40 20 0 20 40 60
t MC −t pulse /ns
Figure 8.30: Distributions of the time residuals of the first pulses extracted by SLCHitExtractor
(blue area) and NFE’s “SLCHE” (green line) from Monte-Carlo data; red
lines indicate Gaussian fits.
116

8.4 SLCHitExtractor
700000
600000
width: 0.43 0.33
mean: 0.96 0.78
500000
entries
400000
300000
200000
100000
0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
q pulse1
1400000
1200000
width: 0.46 0.35
mean: 1.03 0.79
1000000
entries
800000
600000
400000
200000
0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
q pulse1
Figure 8.31: Distributions of the charges of the first pulses extracted by SLCHitExtractor
(blue area) and NFE’s “SLCHE” (green line); red lines indicate Gaussian fits.
Top: Monte-Carlo data; bottom: experimental data.
117

8 PERFORMANCE TESTS
8.5 Runtime Performance
NFE was designed to be viable for real-time online processing. Since computing capacity
at the South Pole is limited, efficient algorithms and data structures were used to generate
fast code.
The profiler callgrind/KCacheGrind was used to analyze the code. As expected,
the most CPU time consuming part is “BayesUnfold”; the fraction of the time spent
at this algorithm for ATWD with default NFE settings is 94.5% for E −1 Monte-Carlo
data, and 89.6% for experimental data. Of this time, “BayesUnfold”’s unfolding method
GetUnfolding() takes the highest share by far (93.9% of the total time for Monte-Carlo,
89.0% for experimental data). Thus, the focus in code optimization was on this unfolding
method.
Most of the remaining time (4.8% resp. 9.8%) is spent at I3Frame::Get() to read in
the input data, where calibration informations constitute the largest share of the time
requirements (> 80%).
For “BayesUnfold”’s GetUnfolding(), the number of calls to expensive functions or
operands such as double::/ was minimized and temporary objects were avoided if possible.
The use of the iterative stopping condition saves roughly 10 iterations on average
(see section 7.1.3) while it costs less than 10% of the CPU time to check the breaking
conditions for every iteration. Another tweak for BU was the introduction of templated
structs containing the source specific parameters from table 7.3 in form of static constants;
this allows the compiler to optimize the code more effectively and led to a gain in
speed of about 19%.
In comparison with other feature extractors, NFE shows superior runtime performance,
mostly because of the use of multiple algorithms, see table 8.1. The systematically shorter
times for experimental data are caused by its softer energy spectrum, since low-energy
events offer less waveforms to extract.
Switching from FeatureExtractor to NFE for online processing would reduce the average
3.76
time required per event to about ≈ 35% and hence would free up many of the
8.47+2.24
20 . . . 25 CPUs currently needed for feature extraction at the South Pole. If future muon
track reconstruction scripts still employ algorithms that depend on integrated charge, a
small and fast module can easily be created to join all pulses of each waveform.
118

8.5 Runtime Performance
Table 8.1: Runtimes for different feature extractors and datasets; errors are about ±3%.
Module Sources runtime per event
Simulated data,
Dataset 3071
t ms −1
Experimental data,
Run 113587, L1
t ms −1
FE multi-pulse ATWD+FADC 33.89 8.47
FE single-pulse ATWD 7.89 2.24
PE ATWD 18.49 5.39
PE FADC 37.89 10.66
SLCHitExtractor SLC < 0.50 < 0.27
NFE ATWD 4.19 1.21
NFE FADC 9.06 2.55
NFE ATWD+FADC 13.25 3.76
NFE SLC < 0.50 < 0.27
NFE PulseMerger — ≪ 0.50 ≪ 0.27
NFE EnforcePulse ATWD 4.21 1.19
NFE EnforcePulse FADC 9.45 2.61
NFE EnforcePulse ATWD+FADC 13.87 3.77
NFE BU only ATWD 20.13 5.70
NFE BU only FADC 30.21 8.30
119

8 PERFORMANCE TESTS
120

CHAPTER IX
Summary And Outlook

9 SUMMARY AND OUTLOOK
Within this thesis a new feature extraction package for recorded photomultiplier signals
in the IceCube Neutrino Observatory at South Pole was developed. Its task is to search
the waveforms captured by the digital optical modules for signals caused by photons.
This information is made available to other software modules by extracting it from the
waveforms’ features into pulses.
Existing feature extractor algorithms have been analyzed conceptually and with respect
to their performances. A concept for a new feature extractor was designed and key
characteristics were defined: The new feature extractor – called NFE – should have modular,
maintainable and well-documented code, it should be easy to use, flexible enough
to cover all feature extraction demands, it should be reasonably fast, and provide good
extraction performance in terms of miss rate, noise rate, and charge and time resolutions.
A new technique of dynamically choosing an appropriate algorithm according to the
waveform’s complexity was designed and implemented. The implemented algorithms are
“Eva” to quickly decide which extraction algorithm to use on the waveform, “Simple”
to extract pulses from waveforms with exclusively SPE-like features, “BayesUnfold” to
extract complex features, and “SLCHE” to extract pulses from SLC chargestamps. The
free parameters of these algorithms were calibrated using simulated datasets.
The performance of the new feature extractor was tested under various conditions.
The technique of dynamically choosing an appropriate algorithm proved to be successfull;
it improves the extraction quality and drastically speeds up the process. Testing NFE
with individual waveforms yields good results, in many cases NFE seems to perform better
than the currently used FeatureExtractor especially at small features.
Several characteristic distributions of resulting quantities for different feature extractors
were both tested individually and compared to each other. NFE’s distributions are promising
and support the positive impression gained from the individual waveform checks. Finally,
the CPU efficiency was found to be significantly superior to that of other feature
extractors.
On March the 1 st , 2010, NFE passed the collaboration’s code review with positive
remarks. As a consequence the project will be officially released soon after all comments
have been incorporated. Fortunately, a new version of the simulation meta-project with
various bugfixes will be released soon and can be used to verify or recalibrate the free
parameters of NFE’s algorithms; this is required as errors in the current simulated datasets
affect feature extraction.
For now, some open issues remain: More tests have to be conducted concerning saturated
waveforms. Especially the effect of transistor droop in the optical modules has to be
adressed; droop correction is already performed by the software module DOMcalibrator,
however sometimes droop effects remain. The original FeatureExtractor seems to employ
a powerful method of further repair waveforms, which could probably be implemented
into DOMcalibrator after exhaustive tests.
122

Another open issue are tests with flasher runs. Usually, experimental data does not offer
information about true hit times, so one has to rely on simulated datasets, accepting systematical
errors. Flasher runs offer an alternative because the time at which the flasher –
i. e., a light source inside the detector – was activated is well-known. Therefore they can
be used to verify the parameter settings and to check the extraction performance.
Furthermore, NFE lacks pybindings, i. e., an interface to directly access the algorithms
from a possibly interactive Python session. Pybindings can be useful for the verification
of the low-level reconstruction and will be part of a future release.
With its release, NFE will be open for analyses by the collaboration to decide whether it
should replace or complement the existing feature extractors in the official reconstruction
data chain. Regardless of this decision, much was learned about IceCube’s low-level
reconstruction, and some improvements were made.
123

9 SUMMARY AND OUTLOOK
124

APPENDIX A
Bayesian Unfolding
A.1 Formal Approach
Formally, one considers as given a histogram whose n E entries n Ei are interpreted as
numbers of effects E i which are caused by a not necessarily equal number n C of causes C j .
With n tot := ∑ n Ei one can define the probability for effect E i to occur as P (E i ) := n E i
n tot
.
Furthermore, the probability for a certain C j to cause each of the effects is given by
P (E i |C j ).
By applying Bayes’ Theorem, one obtaines
P (C j |E i ) = P (E i|C j ) · P (C j )
∑
j P (E i |C j ) · P (C j )
Using this and the pairwise disjointness of the E i , one can compute the probabilities
P (C j ) t+1 = ∑ i
P (C j |E i ) t · P (E i ) = ∑ i
P (E i |C j ) · P (C j ) t
∑k P (E i |C k ) · P (C k ) t
P (E i ) ∀ t ∈ N
iteratively, which then can easily be transformed into the most probable numbers of causes
that occured, n Cj = P (C j ) · n tot .
A.2 Adaption to IceCube’s Waveforms
The entries of the waveform (with negative values set to zero) are the numbers of effects
n Ei , the numbers of causes n Cj correspond to the charge (actually ∆t times charge, but
∆t is constant and can be considered later on) belonging to a pulse originating in bin j,
using the same binning for both effects and causes and therefore n C = n E .
P (E i |C j ) denotes the normalized single photo electron (SPE) pulse shape which for ATWD
is given by Christopher Wendt’s parametrization[47] (see section 7.1.3)
f : R ≥0 → [0, 1] : t ↦→ c
(
e − x−x 0
b 1 + e x−x 0
b 2
) −8
.
125

A
BAYESIAN UNFOLDING
According to this parametrization, the first L bins contain over 99.4% of the pulse’s
charge, therefore the computation can be significantly sped up by omitting most addends
of both sums:
P (C j ) t+1 =
j+L−1 ∑
i=j
P (E i |C j ) · P (C j ) t
∑ ik=i−L+1
P (E i |C k ) · P (C k ) t
P (E i )
Computation can further be accelerated by saving S m := P (E m |C 0 ) ≡ P (E m+j |C j )
instead of calculating P (E i |C j ) for all values of j; the resulting equation is
P (C j ) t+1 =
j+L−1 ∑
i=j
S i−j · P (C j ) t
∑ ik=i−L+1
S i−k · P (C k ) t
P (E i )
Finally, as we are interested in n Cj , we cancel out n tot :
n Cj , t+1 = n Cj , t
j+L−1 ∑
i=j
S i−j · n Ei
∑ ik=i−L+1
S i−k · n Ck , t
126

APPENDIX B
Cascade Pulse Tagging
This thesis’ initial topic was to tag pulses originating from cascades to reconstruct locations
of strong stochastic energy losses at muon propagation, with the aim to improve
both energy reconstruction and track reconstruction (see figure B.1).
This turned out to be impractical because of low Čerenkov luminosity, prepulses, and
too much scattering, but also demonstrated some limitations of FeatureExtractor such as
excessive pulse splitting (section 6.3.1), which were one of the motivations for the creation
of NFE. The low-level work also revealed two of the bugs found during the work on this
thesis.
U
U
t
DOM
t
particle track
Čerenkov cone
U
cascade light
t
Figure B.1: This thesis’ initial topic and one of the motivations to create NFE: Tagging of
pulses caused by cascades during muon propagation. If the waveforms were as
clear as the idealized ones in this illustration, cascades could be located and used
for direction and energy reconstruction refinement.
127

B
CASCADE PULSE TAGGING
128

APPENDIX C
Specific Problems and Anomalies
Many aspects of this thesis required checks of low-level observables or single waveforms,
owing to which several previously unknown problems or anomalies were found in the
projects involved. Some of those relevant to this thesis are explained below; this is by no
means meant to be offensive.
C.1 ATWD FADC Time Offset Caused Double Extraction
Up to very recent versions of the calibration tool DOMcal, there was a time offset between
the ATWD and FADC waveforms of about 15 ns for experimental data and 34 ns
for simulated data. This did not only corrupt the late (i. e. FADC) pulse times, but also
caused pulses extracted by FE just preparatory to the end of the ATWD waveform to
be extracted again in the FADC waveform, effectively doubling their impact because FE
automatically merged all ATWD pulses with all FADC pulses found outside the AWTD
waveform’s timespan.
This double extraction problem was solved by the respective projects’ authors by introducing
a time shift in DOMcalibrator and an exclusion time window in FE (25 ns by
default), during which no FADC pulses are extracted right after the end of the ATWD
waveform.
C.2 Implementation of the Second Single-Pulse Extraction Algorithm
in FeatureExtractor
The implementation of the second single-pulse extraction algorithm in FeatureExtractor
(section 5.1) differs from the documentation that ships with the source code[50] and from
its depiction in presentations[53] (figure C.1).
The pulse width is not determined by the number of bins that pass half of the first pulse’s
amplitude, but by a constant multiplied with the extracted charge, and divided by the
maximum entry of the waveform.
More importantly, the charge is not defined as charge above threshold, but as total integrated
charge which includes baseline fluctuations: In the IC59 settings[51], the baseline
is estimated by taking the average of the first three bins, and the resulting value is substracted
from all bins if it does not exceed a hard-coded threshold; still, time-dependent
129

sum of all bins above
baseline + error
C
extrapolation of
maximum slope
to baseline
SPECIFIC PROBLEMS AND ANOMALIES
width
width:
half of the number
of bins above
first pulse‘s half
maximum height
threshold
extrapolation of first
local maximum slope
above threshold
to baseline
width:
half of the number
of bins above
first pulse‘s half
maximum height
charge:
sum of all bins
above threshold
extrapolation of first
local maximum slope
above threshold
to baseline
width:
constant times
charge / maximum
charge:
sum of all bins
first pulse‘s half
maximum height
threshold
threshold
Figure C.1: Sketch illustrating
parabola fit to maximum bin charge:
the differences between
extrapolation
the
of firstdocumentation (left) and implementation
(right) parabola of FeatureExtractor’s maximum
local maximum secondslope
single-pulse extraction algorithm.
× pulse width
above threshold
Baseline detection has been omittedto for baseline reasons of clarity.
x
x
width:
proportional to
charge / maximum
charge:
sum of all bins
baseline shifts caused by droop or bad estimations due to the low statistics of the first
extrapolation of
three binsmaximum can cause
slope
deviations of the total charge.
to baseline
This behaviour might be responsible for the overestimation of the charge of low pulses
threshold
which is described in section 8.3.1 and illustrated in figure 8.19, because this algorithm is
width
used in FeatureExtractor’s multi-pulse settings x to obtain the total charge that is used to
rescale the pulses of its Bayesian Unfolding algorithm (see section 6.3.1).
x
x
x
C.3 Missing Simulation of the daq_baseline in DOMsimulator
If available, DOMcalibrator uses the daq_baseline stored in the calibration data to calculate
a waveform’s average baseline. Up to its current release however, DOMsimulator
does not simulate this baseline. This leads to an overcompensation by DOMcalibrator
and thereby to a wrong baseline (e. g., figure 8.3), which in turn affects the extracted
charge (figure C.2). Moreover, the pulse times are affected by the increased baseline, and
more fake pulses are extracted.
After being informed about an apparent mismatch between simulated and experimental
data baselines, the DOMsimulator’s and DOMcalibrator’s maintainer Stijn Buitink
quickly tracked and fixed the bug for the next release.
C.4 Time Offset in SLCHitExtractor
In its initial release, SLCHitExtractor had a hard-coded time offset calibration parameter
c 2 (see section 6.4), which was used to align SLCHitExtractor’s pulse times with FE’s
ATWD pulse times. It has been abandoned later when the ATWD FADC time offset was
fixed (appendix C.1), because the times matched well without this offset. However, this is
only true for FeatureExtractor’s FE59 online-filtering settings, or more precisely only for
130

C.4 Time Offset in SLCHitExtractor
40000
35000
Old Toroid DOMs
New Toroid DOMs
total
30000
25000
Old Toroid DOMs
New Toroid DOMs
total
30000
25000
20000
entries
20000
entries
15000
15000
10000
10000
5000
5000
0
1 0 1 2 3 4
FADC charge / ATWD charge
0
1 0 1 2 3 4
FADC charge / ATWD charge
30000
width: 0.32 0.31
mean: 0.98 0.81
30000
width: 0.32 0.31
mean: 0.92 0.81
25000
25000
20000
20000
entries
15000
entries
15000
10000
10000
5000
5000
0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
q pulse1
0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
q pulse1
10 7
10 6
width: 0.71 2.95
mean: 11.92 25.94
10 7
10 6
width: 0.70 2.95
mean: 11.78 25.94
10 5
10 5
10 4
10 4
entries
10 3
entries
10 3
10 2
10 2
10 1
10 1
10 0
10 0
10 -1
40 20 0 20 40
t MC −t pulse /ns
10 -1
40 20 0 20 40
t MC −t pulse /ns
Figure C.2: Effect of the simulation of the daq_baseline on pulses extracted with NFE; custom
simulation using 500 non-relativistic monopoles as light sources, the original
scripts were provided by Thorsten Glüsenkamp.
Left: data without baseline simulation; right: data with proper simulation.
Top row: ratio between the total ATWD integrated charge and the corresponding
FADC charge;
middle row: the first pulse’s charge per waveform for ATWD (blue area) and
FADC (green line);
bottom row: the first pulse’s time per waveform; the ATWD FADC time offset
was not applied.
131

C
SPECIFIC PROBLEMS AND ANOMALIES
pulses extracted with PMTTransit = 2 (section 8.3.1), and furthermore it is coincidence:
w
There is no reason why the time t = t 0 + (i max − 1) · 25 ns − c imax−1 1 w max
(section 6.4)
w
should match the true leading edge, because the term c imax−1 1 w max
only compensates for the
correlation (slope) between the ratio of the first two bins and the pulse time (which is
only well-defined for regular charge stamps). This time offset can be seen in the sketch in
figure 6.6, which is up to scale.
The total time offset of SLC pulses compared to FE’s ATWD pulses in IC59 offlineprocessing
data is composed of the about 11 ns between FE ATWD pulses for PMTTransit
= 2 and PMTTransit = -1, and the 15 ns caused by the original ATWD FADC time offset,
which was erroneously not applied to SLC charge stamps.
132

Acknowledgements
Without contributions of many people, writing this thesis would not have been possible.
First I would like to thank Prof. Dr. Christopher Wiebusch, who gave me the opportunity
to work on this highly interesting project. He invited me into his workgroup and
provided new ideas as well as neverending enthusiasm.
Special thanks go to Dr. David Boersma, whose great advice and invaluable experience
especially in software development and IceCube reconstruction made this project possible.
Moreover, I would like to thank Prof. Dr. Martin Erdmann for reviewing this thesis
as second referee.
Many thanks go to Anne Schukraft, Sebastian Euler, Matthias Schunck, Thomas
Krings, and Jan-Patrick Hülß for their extensive proof reading, and to them and the
rest of the IceCube Aachen workgroup for many interesting discussions, a great working
atmosphere and generally a good time. This particularly includes the Kinderzimmer in
both its former and its current lineup.
Special credits go to Thomas Krings, who shared his initial L A TEX templates to start
a common framework for future theses in Aachen. I would also like to thank Matthias
Schunk for the simulation of specialized Monte-Carlo datasets needed for tests and calibration,
and Thorsten Glüsenkamp for providing me with his simulation scripts.
Furthermore, many thanks go to the rest of the IceCube Collaboration, in particular
to Dmitry Chirkin, Christopher Wendt, Alex Olivas, Stijn Buitink, Andreas Groß, Cécile
Portello-Roucelle, Dennis Diederix, Markus Voge, and Fabian Clevermann for many interesting
discussions, and also to Thorsten Stezelberger from LBNL for his investigation
on the SLC firmware.
Finally I want to express my gratitude towards my family and my friends for their
enduring support!
I

Erklärung
Hiermit erkläre ich, dass ich die vorliegende Arbeit selbständig verfasst und keine anderen
als die angegebenen Quellen und Hilfsmittel verwendet habe.
Aachen, den 02. März 2010
Declaration
I hereby certify that this document has been composed by myself, and describes my own
work, unless otherwise acknowledged in the text.
Aachen, March the 2 nd , 2010
III

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XI