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\title{Innovative perspectives for seismic isolation of gravitational-wave detectors}
\author{Myself}
\date{}
\titlehead{A Thesis submitted for the degree of Philosophiae Doctor}
\publishers{School of Something\\University of Somewhere}

\begin{document}
\maketitle

\frontmatter

\chapter{Statement of originality}
Here I will certify that the work done is original from myself.

\chapter{Abstract}

A brief summary of the project goes here, with main results.

%dedica va qui

\chapter{Acknowledgements}

Here I need to acknowledge for any funding (UoB, RAS, IOP, Caltech).
%ricordati anche di ringraziare per l'estensione

\tableofcontents
\listoffigures
\listoftables

\chapter{Notations}
Useful notations, constants and formulas go here.\\
Speed of light:\\
$c = 3 \times 10^8$ m/s\\
Gravitational constant:\\
$G = 6,67 \time 10^{-11}$ Nm$^2$/Kg$^2$\\
Gravitational wave amplitude:\\
$h \sim 10^{-21} $ $1/\sqrt{Hz}$\\
Solar mass:\\
$M_{\odot} = 10^{33}$ g

\chapter{Acronyms}
AA = Anti-Aliasing\\
ADC = Analogue-to-Digital Converter\\
AEI = Albert Einstein Institute\\
aLIGO = Advanced Laser Interferometric Gravitational-wave Observatory\\
AI = Anti-Imaging\\
ASD = Amplitude Spectral Density\\
BRS = Beam Rotation Sensors\\
BS = Beam Splitter\\
BSC = Basic Symmetric Chamber\\
BH = Black Hole\\
CARM = Common Arm length\\
CDS = Control and Data System\\
CP = Compensation Plate\\
CPS = Capacitive Position Sensors\\
CS = Corner Station\\
DAC = Digital-to-Analogue Converter\\
DARM = Differential Arm Length\\
DCC = Document Control Center\\
DIFF2SE = Differential to Single-Ended\\
ETM = End Test Mass\\
ET = Einstein Telescope\\
FI = Faraday Isolator\\
FIR = Finite Impulse Response\\
HAM = Horizontal Access Module\\
HEPI = Hydraulic External Pre-Isolator\\
HoQI = Homodyne Quadrature Interferometer\\
HP = High Pass filter\\
HSTS = \\
IMC = Input Mode Cleaner\\
IMCL = Input Mode Cleaner Length\\
ISI = Internal Seismic Isolation\\
ITM = Input Test Mass\\
LHO = LIGO Hanford Observaotry\\
LLO = LIGO Livingston Observatory\\
LP = Low Pass filter\\
LSC = Length Sensing and Control\\
LVDT = Linear Variable Displacement Transformer\\
LVK = Ligo-Virgo-Kagra meeting\\
MCA = Mid-Course Assessment\\
MICH = Michelson length\\
MIT = Massachusetts Institute of Technology\\
ND = Neutral-Density (filter)\\
NPBS = Non-Polarizing Beam Splitter\\
NS = Neutron Star\\
OPL = Opltical Path Length\\
PBS = Polarizing Beam Splitter\\
PD = PhotoDiode\\
PR = Power Recycling\\
PRCL = Power Recycling Cavity Length\\
PSD = Power Spectral Density\\
QPD = Quadrant Position Device\\
RIN = Relative Intensity Noise\\
SC = Sensor Correction\\
SR = Signal Recycling\\
SRCL = Signal Recycling Cavity Length\\
STS = \\
TEC = Thermo-Electric Controller\\
UoB = University of Birmingham\\

\chapter{Structure of this thesis}
An introduction to frame the work and structure of the thesis go here.\\

STRUCTURE OF THESIS [DRAFT]\\

PART I: Gravitational astrophysics\\
Chapter 1: Gravitational waves and sources\\
Chapter 2: low frequency window and multimessenger astronomy\\
Chapter 3: Interferometry and Advanced LIGO\\

PART II: Lowering seismic noise\\
Chapter 4: Inertial sensors and optical levers\\
Chapter 5: Seismic isolation at LHO\\
Chapter 6: Laser stabilization for 6D seismic isolation\\

Appendix A: Assembling suspension chains for A+ at LHO\\
Appendix B: control loops\\
Appendix C: first GW detection

\mainmatter

\part{Gravitational-wave frontiers}
\include{GW}
\include{LF}
\include{LIGO}

\part{Lowering seismic motion}
\include{oplevs}
\include{CPSdiff}
\include{laserstab}

\appendix
\include{A}
\include{B}
\include{C}

\backmatter

\begin{thebibliography}{}

%chapt 1

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\bibitem{nar} J. V. Narlikar \textit{An introduction to Relativity}, Cambridge University Press, 2011

\bibitem{mag} M. Maggiore \textit{Gravitational waves - Vol. 1: Theory and Experiments}, Oxford University Press, 2013

%chapt 2

\bibitem{first} B. P. Abbott, \textit{Observation of Gravitational Waves from a Binary Black Hole Merger}, Phys. Rev. Lett. 116, 061102, 2016

%chapt 3

\bibitem{ligo} Advanced LIGO Systems Group, \textit{Advanced LIGO Systems Design}, DCC document T010075-v3, 2017

\bibitem{abb} B. P. Abbott et al, \textit{GW150914: The Advanced LIGO Detectors in the Era of First Discoveries}, Phys. Rev. Lett. 116, 131102, 2016

\bibitem{mar} D. Martynov et al., \textit{The Sensitivity of the Advanced LIGO Detectors at the
Beginning of Gravitational Wave Astronomy}

\bibitem{mat} F. Matichard et al, \textit{Seismic isolation of Advanced LIGO: Review of strategy, instrumentation and performance}, Class. Quantum Grav. 32 185003, 2015

\bibitem{lsc} K. Izumi, D. Sigg, \textit{Advanced LIGO: length sensing and control in a dual recycled interferometric gravitational wave antenna}, 2017 Class. Quantum Grav. 34 015001

%oplev

\bibitem{mca} C. Di Fronzo \textit{Optical sensors for improving low-frequency performance in GW detectors}, Mid-Course Assessment, University of Birmingham, 2018

\bibitem{poster2} C. Di Fronzo et al., \textit{Optical Lever for interferometric inertial isolation}, poster, LVC meeting, Maastricht 2018, https://dcc.ligo.org/LIGO-G1801693 

\bibitem{lantz} B. Lantz et al., \textit{Estimates of HAM-ISI motion for A+}, T1800066-v2, March 2018, https://dcc.ligo.org/LIGO-T1800066 

\bibitem{cooper} S. Cooper et al., \textit{Ham ISI model}, Technical note, University of Birmingham, March 2018, https://dcc.ligo.org/LIGO-T1800092

\bibitem{sina} S. M. Köhlenbeck, \textit{Towards the SQL Interferometer Length Stabilization at the AEI 10 m-Prototype}, PhD thesis, Gottfried Wilhelm Leibniz Universität Hannover, 2018

\bibitem{luise} L. KranzHoff for the AEI group, \textit{A novel vertical inertial sensor for with phasemeter readout}, poster, LVK September 2021

\bibitem{tuyen} D. Tuyenbayev, \textit{Extending the scientific reach of Advanced LIGO by compensating for temporal variations in the calibration of the detector.}, PhD thesis, University of Texas, 2017

\bibitem{venka} Venkateswara et al., \textit{Subtracting tilt from a horizontal-seismometer using a ground-rotation-sensor}, Bulletin of the Seismological Society of America (2017) 107 (2): 709-717

\bibitem{jones} R.V. Jones et al., \textit{Some developments and applications of optical levers}, 1961 J. Sci. Instrum. 38 37

\bibitem{agatzuma} K. Agatsuma, \textit{Optical lever for KAGRA}, GW monthly seminar at Tokyo, 2014

\bibitem{lantz2} B. Lantz et al. \textit{Review: Requirements for a Ground Rotation Sensor to Improve Advanced LIGO}, Bulletin of the Seismological Society of America, Vol. 99, No. 2B, 2009

\bibitem{collette} C. Collette et al. \textit{Review: Inertial Sensors for Low-Frequency Seismic Vibration Measurement}, Bulletin of the Seismological Society of America, Vol. 102, No. 4, 2012

\bibitem{clark} D. E. Clark, \textit{Control of Differential Motion Between Adjacent Avanced LIGO Seismic Isolation Platforms}, PhD thesis, Stanford University, 2013

\bibitem{aston} S. M. Aston at al., \textit{Update on quadruple suspension design for Advanced LIGO}, Class. Quantum Grav., 29 (2012) 235004 (25pp)

\bibitem{shapiro} B. Shapiro, \textit{Brief Introduction to Advanced LIGO Suspensions}, LAAC Talk, August 2014, https://dcc.ligo.org/LIGO-G1400964

%cpsdiff

\bibitem{proposal} C. Di Fronzo et al., \textit{Proposal for an experiment at LHO: Locking PRCL to IMCL}, proposal, 2019, DCC T1900656-v2

\bibitem{technote1} C. Di Fronzo et al., \textit{Reducing differential motion using CPS sensors}, technical note, 2019, DCC T1900777-v1

\bibitem{chiatalk} C. Di Fronzo, \textit{Reducing differential motion of Advanced LIGO seismic platforms to improve interferometer control signals}, talk, LVK September 2020

\bibitem{biscans} S. Biscans et al., \textit{Control strategy to limit duty cycle impact of earthquakes on the LIGO gravitational-wave detectors}, arXiv:1707.03466, 2017

\bibitem{kisseltalk1} J. Kissel, \textit{On Relaxing Our Demand for Single IFO Duty Cycle}, talk, 2019, DCC G1901125-v1

\bibitem{biscanstalk} S. Biscans, \textit{Global seismic control}, talk, GWADW 2019

\bibitem{biswas} A. Biswas et al., \textit{New methods to assess the impact of seismic events on LIGO detector duty cycle}, 2019, 	arXiv:1910.12143

\bibitem{kisselthesis} J. Kissel, \textit{Calibrating and improving the sensitivity of the LIGO detectors}, PhD thesis, 2010

\bibitem{adl2} LIGO Scientific Collaboration \textit{Advanced Ligo}, LIGO-P1400177-v5

\bibitem{kisseltalk2} J. Kissel, \textit{Advanced LIGO Active Seismic Isolation}, talk, 2011

\bibitem{technote2} C. Di Fronzo et al., \textit{Reducing differential motion of Advanced LIGO seismic platforms to improve interferometer control signals: block diagrams and maths}, technical note, 2020, DCC T2000108-v1

\bibitem{technote3} C. Di Fronzo et al., \textit{Reducing differential motion of Advanced LIGO seismic platforms to improve interferometer control signals:analysis of feasibility}, technical note, 2020, DCC T2000365-v2

\bibitem{lantztalk} B. Lantz, \textit{System-wide upgrades to improve the Seismic Isolation and control of detectors beyond A+}, talk, 2020

\bibitem{jenne} J. Driggers, \textit{Noise Cancellation for Gravitational Wave Detectors}, PhD thesis, 2016

\bibitem{llo} A. Pele' et al., \textit{ECR: Differential CPS and cavity offload}, proposal, 2019, DCC E1900330-v1

\bibitem{lantztech} B. Lantz et al., \textit{Estimates of HAM-ISI motion for A+}, technical note, 2018, DCC T1800066-v2

\bibitem{hammodel} S. Cooper et al., \textit{Ham ISI Model}, technical note, 2018


%6D

\bibitem{poster} C. Di Fronzo et al, \textit{A 6D inertial isolation system}, ET Symposium, 2019, poster, https://dcc.ligo.org/LIGO-G1900741

\bibitem{6d} C.M. Mow-Lowry, D. Martinov, \textit{A 6D interferometric inertial isolation system}, 2019 Class. Quantum Grav. 36, 24 

\bibitem{lisa} L Barsotti et al, \textit{Alignment sensing and control in advanced LIGO} 2010 Class. Quantum Grav. 27 084026

\bibitem{hoqi} S. Cooper et. al, \textit{A compact, large-range interferometer for precision measurement and inertial sensing}, 2018 Class. Quantum Grav. 35 095007

\bibitem{sam} S. Cooper, \textit{Breaking the Seismic Wall: How to Improve Gravitational Wave Detectors at Low Frequency}, PhD thesis, University of Birmingham, 2019

\bibitem{rio} $https://rio-lasers.com/1064-nm-laser-module/$

\bibitem{adj} $https://www.photonicsolutions.co.uk/upfiles/ADJUSTIKFiberLaserLG13Dec17.pdf$

\bibitem{mephi} $https://edge.coherent.com/assets/pdf/COHR\_ MephistoNPRO$

%appendix B

\bibitem{freise} Andreas Freise, \textit{The Next Generation of Interferometry: Multi-Frequency Optical Modelling, Control Concepts and Implementation}, Appendix B \textit{Control loops}, PhD thesis, 2003

\bibitem{wiki} https://en.wikipedia.org/wiki/Control-system

%appendix C

\end{thebibliography}

%ringraziamenti personali vanno qui

\end{document}