@@ -65,33 +65,16 @@ The optical levers can in principle reduce tilt motion below 1 Hz; the use of ca
%During my stay at LIGO Hanford site, I need to warmly thank Caltech for providing me accommodation and travel: this experience was very important for my studies.\\
%The completion of the work presented in this thesis would not have been possible without the action of the UoB, which accepted my application for an extension of my studies: the lockdown in 2020 stopped my lab work and the support of the UoB has been crucial to accomplish my project in the best way.\\
%\chapter{Grazie!}
%On a personal note, \textit{grazie} Conor for always being supportive, it was important in the hardest times! Grazie, with great respect.\\
%
%\noindent
%To my best friend here in the UK: \textit{grazie} Sam for your presence, your help, your effort to endure the enormous emotional baggage of this stubborn Italian one, who wanted to be your friend at all costs. I know it was not easy, I will not forget it.\\
%
%\noindent
%\textit{Grazie} to all my PhD colleagues who shared the stress and the fun of this experience with me. Riccardo, thanks for pushing me to go further, do better, stay stronger. George, thank you for the chess \& Czech classes, you opened my mind. Amit, your positivity is always contagious, thank you for sharing it!\\
%
%\noindent
%I really need to thank all the people on LIGO Hanford, who made me feel included and part of a great family. \textit{Grazie} Jenny, Jim, Rahul and Jeff B. for your infinite patience and for teaching me so much of LIGO; and I was very lucky to meet Dripta, an amazing housemate and friend, thank you for all the time you chose to share with me.\\
%\textit{Grazie} to my family in Seattle, zia Claudia, zio Carlo, Rossana \& Jim, Carla \& Wayne, who helped me to feel at home during my stay in the USA.
%
%\noindent
%To my friends in Italy: Vero \& Ludo, Alice \& Anna Paola, Martina, Francesca, Edo \& Nani, \textit{grazie} for your incredible will to stay close to me despite the 2000 km-distance.\\
%
%\noindent
%A mio nonno, zio Marco e zia Laura, zia Flora e zio Vincenzo, grazie per avermi riempito di affetto e di cibo, sono stati indispensabili.\\
%Ai miei genitori e a mia sorella, grazie per avermi sempre incoraggiato, ascoltato le mie lamentele e sopportato la distanza durante questi 4 anni cosi' importanti per me.
@@ -180,6 +172,7 @@ UoB = University of Birmingham\\
\backmatter
\begin{thebibliography}{}
\addcontentsline{toc}{chapter}{Bibliography}
%chapt 1
...
...
@@ -329,6 +322,26 @@ Beginning of Gravitational Wave Astronomy}
\end{thebibliography}
%\chapter*{Grazie!}
%Personal acknowledgements
%\addcontentsline{toc}{chapter}{Grazie!}
%On a personal note, \textit{grazie} Conor for always being supportive, it was important in the hardest times! Grazie, with great respect.\\
%
%\noindent
%To my best friend here in the UK: \textit{grazie} Sam for your presence, your help, your effort to endure the enormous emotional baggage of this stubborn Italian one, who wanted to be your friend at all costs. I know it was not easy, I will not forget it.\\
%
%\noindent
%\textit{Grazie} to all my PhD colleagues who shared the stress and the fun of this experience with me. Riccardo, thanks for pushing me to go further, do better, stay stronger. George, thank you for the chess \& Czech classes, you opened my mind. Amit, your positivity is always contagious, thank you for sharing it!\\
%
%\noindent
%I really need to thank all the people on LIGO Hanford, who made me feel included and part of a great family. \textit{Grazie} Jenny, Jim, Rahul and Jeff B. for your infinite patience and for teaching me so much of LIGO; and I was very lucky to meet Dripta, an amazing housemate and friend, thank you for all the time you chose to share with me.\\
%\textit{Grazie} to my family in Seattle, zia Claudia, zio Carlo, Rossana \& Jim, Carla \& Wayne, who helped me to feel at home during my stay in the USA.
%
%\noindent
%To my friends in Italy: Vero \& Ludo, Alice \& Anna Paola, Martina, Francesca, Edo \& Nani, \textit{grazie} for your incredible will to stay close to me despite the 2000 km-distance.\\
%Angela and Anna, \textit{grazie} for your presence and friendship in Birmingham.\\
%
%\noindent
%A mio nonno, zio Marco e zia Laura, zia Flora e zio Vincenzo, grazie per avermi riempito di affetto e di cibo, sono stati indispensabili.\\
%Ai miei genitori e a mia sorella, grazie per avermi sempre incoraggiato, ascoltato le mie lamentele e sopportato la distanza durante questi 4 anni cosi' importanti per me.
where W is the measured quantity, Y and Theta are the quantities we are interested in. Remembering that s = i$\omega$ in a steady-state situation, we have:
where W is the measured quantity, Y and $\Theta$ are the quantities we are interested in. Remembering that s = i$\omega$ in a steady-state situation, we have:
\begin{equation}
\centering
...
...
@@ -500,7 +500,7 @@ Summarizing, the prototype is ready for the test with the specifications listed
\begin{tabular}{c|lcl}
Beam size at QPD & w = 1 mm\\
Power at output & P = 3.5 mW\\
Displacement &$\Delta$ x = 2.22 $\times$ 10$^{-3}$\\
Displacement &$\Delta$ x = 2.22 $\times$ 10$^{-3}$m\\
