updates of thesis

main/A.tex

+\chapter{First detection}
+\label{A}
+
+On 14th September 2015 the two LIGO antennas observed for the first time a signal from a gravitational wave produced by the merger of two black holes. This was the very first time that a merger of such massive and elusive objects could be observed.\\
+The gravitational-wave signal has been named GW150914 and has been emitted by 2 black hole of masses of 36 $M_{\odot}$ and 29 $M_{\odot}$, which merged at a distance of 410 Mpc (z = 0.09)and produced a final BH of 62 $M_{\odot}$. The remaining 3 $M_{\odot}$ have been radiated in gravitational waves. Fig. \ref{gwsig} shows the signal detected from LIGO Hanford and LIGO Livingston.\\
+This detection has been the result of a wide scientific collaboration which efforts made possible a discovery that deserved the Nobel Prize in Physics in 2017 to the pioneers of gravitational wave hunting  \textit{'for decisive contributions to the LIGO detector and the observation of gravitational waves'}.
+
+\begin{figure}
+\centering
+\includegraphics[scale=0.7]{images/outreach.png}
+\end{figure}
+
+\begin{figure}[h!]
+\centering
+\includegraphics[scale=0.77]{images/GWsignal.png}
+\caption[First detection of a gravitatonal wave signal.]{First detection of a gravitational wave signal \cite{first}. The event is shown for both observatories at the time of observation 09:50:45 UTC on 14th September 2015. The top row is the gravitational wave amplitude for Hanford (H1) and Livingston (L1). In the L1 panel, there is a visual comparison of the two signals: the wave passe through L1 first, H1 signal (in orange) is shifted by the 6.9 ms of difference, and inverted due to their mutual orientation. The second row shows the consistency of the measured signal with expectations independently computed. Third row shows the residuals after subtraction of the measured time series and the numerical waveform. Bottom row is the same signal in frequency vs time, where it is evident the increase of frequency with time.}
+\label{gwsig}
+\end{figure}
+
+\begin{figure}
+\includegraphics[scale=0.8, angle=90]{images/logos.pdf}
+\end{figure}
\ No newline at end of file

main/B.tex

+\chapter{Control loops}
+\label{B}
+
+\section{Control theory}
+The theory of controls is a branch of science and technology which studies how to drive a given dynamical system. This is generally characterized by inputs and outputs and the former can be manipulated to obtain a desired output, which is chosen by a reference setpoint. The design and the technology involved depends on the system, but in general they imply a sensing section, a software section which can modify some features of the input and a feedback section to check that the manipulation of the input signal gave the output as set by the reference.
+\subsection{Principles: control loops}
+The collection of all the sections forms a control loop and controls the behaviour of a given variable under exam. Control loops can be:
+\begin{itemize}
+\item{Open-loop}: the control action is independent from the output.
+\item{Closed-loop}: the control action depends on the desired output conditions. This kind of loop uses feedback loops, that assure the process is correctly going on, i.e. the value of the variable under exam is that of setpoint.
+\end{itemize}
+
+\noindent
+In order to design a control loop, we need to build all the subsystems up: the main one is the \textbf{plant}, which is the physical parameter to be controlled; the plant is measured by one or more \textbf{sensors}, which detect a deviation (if any) in the signal from the reference setpoint. An error signal is then produced and processed by a \textbf{controller} into a correction signal that is sent to an \textbf{actuator}. The actuator applies the correction to the plant.
+
+
+\subsection{How to: block diagrams}
+Block diagrams are useful graphical instruments to describe, study and build a control loop. Each element of the control system is represented by a block and each block is joined by lines with arrows showing the sequence of controls. Following the logical steps stated before, we can then draw the block diagram of a basic system to be controlled:
+
+\begin{figure}[h!]
+\centering
+\includegraphics[scale=0.8]{images/block.png}
+\caption[Basic block diagram of a control loop.]{Basic block diagram of a control loop. The setpoint is injected as an input.}
+\end{figure}
+
+\noindent
+Every variable under interest at the output of each block can be evaluated by \textit{solving} the diagram.
+
+\section{Control analysis}
+Once the control loop has been schematically drafted, it needs to be finalized: the software section implies instructions. These are given by a computation of the transfer functions of the whole system, which gives the response in the frequency domain of the output to a given input. The computed (and measured) transfer function will then be modified with suitable filters to make the output adjust to the reference setpoint.
+\subsection{Transfer functions}
+Every dynamical system is characterized by equations of motion in the time domain. In order to study the system in the frequency domain, it is possible to apply a Laplace transform. So, for any function f(t) in the time domain, the Laplace transform is defined as:
+
+\begin{equation}
+\centering
+F(s) = \int e^{-st}f(t)dt
+\end{equation}
+
+\noindent
+where s = a + i$\omega$.\\
+A transfer function is defined as the ratio between the output and the input, in the frequency domain. For any input X(s) and output Y(s), the transfer function is:
+
+\begin{equation}
+\centering
+T(s) = \dfrac{Y(s)}{X(s)}
+\end{equation}
+
+\noindent
+and so the output is characterized by the product between the transfer function and the input signal in the Laplace domain, which is the Laplace transform of the convolution of the two functions in the time domain\footnote{An interesting demonstration of this statement can be found ....}.\\
+Since, in general, a function can be written as a product of polynomials, the transfer function is also in the form:
+
+\begin{equation}
+\centering
+T(s) = C \Pi_{i,j} \dfrac{(s-z_i)^j}{(s-p_i)^j}
+\end{equation}
+
+\noindent
+where z and p are the $i$th zeros and poles of the polynomial, of order $j$ and C is the amplitude. This form is useful to study the stability of the system:
+\begin{itemize}
+\item{Re(p) $<$ 0}: the system is asymptotically stable;
+\item{Re(p) = 0 with j = 1}: the system is marginally stable;
+\item{Re(p) = 0 with j $>$ 1 or Re(p) $>$ 1}: the system is unstable.
+\end{itemize}
+
+\noindent
+The gain of the system is defined as the radio between the amplitudes of the input and output, i.e. it's the absolute value of the transfer function:
+
+\begin{equation}
+\centering
+G = \dfrac{\mid Y(s)\mid}{\mid X(s)\mid} = \mid T(s)\mid
+\end{equation}
+
+\noindent
+and the phase is $\varphi$ = arg(T(s)).\\
+In the frame of control loops, the transfer function is given by the gain contributions of all the subsystems of the loop.
+
+\subsection{Phase and magnitude interpretation: the Bode plot}
+The Bode plot is a graph representing the response in frequency of the magnitude and phase of the system under exam. It is largely used to define the marginal conditions for the stability of the loop. The magnitude in expressed in dB = 20$\log_{10} (x)$ and it is computes as the absolute value of the transfer function:
+
+\begin{equation}
+\centering
+\mid T(s) \mid = \sqrt{T \cdot T^*}.
+\end{equation}
+
+\noindent
+The phase is expressed in degrees (deg) and it is comoputed as:
+
+\begin{equation}
+\centering
+\varphi =  -\arctan \left(\dfrac{ImT(s))}{Re(T(s))}\right).
+\end{equation}
+
+\noindent
+In the frame of loops, the closed-loop gain is given by:
+
+\begin{equation}
+\centering
+G_{CL} = \dfrac{G_{OL}}{1+G_{OL}},
+\end{equation}
+
+\noindent
+where G$_{OL}$ is the open-loop gain and also a pole for this relation. This means that if G$_{OL}$ = -1, G$_{CL}$ diverges and the loop is unstable. On the phase plot, we will have that $\varphi$ = -180$^{\circ}$. In general, when the trace on the phase plot approaches this value at certain frequencies, it means that the loop that we are building is unstable in that region.
+
+\subsection{Spectral density}
+Spectral densities are views of a signal in a frequency spectrum. It is a useful instrument to detect effects on the signal during processing, like peaks due to harmonics, or resonances. The physical parameter used in this study is the power spectral density, which measures the power of a signal as a function of frequency and has units of W/Hz$^{-1}$. When there is no direct power associated to the measurement (like in case of Volts) the units are in terms of the square of the signal per Hz. In some cases, an Amplitude Spectral Density (ASD), defined as the square root of the power spectral density, is used when the shape of the signal is quite constant; in this case the units are in the form of 1/Hz$^{-1/2}$ and the variations in the ASD will then be proportional to the variations of the signal itself.
+
+\subsection{Coherence}
+The coherence is a statistic relation between two signals or data sets x and y. It is defined as the ration between the cross spectral density of the two functions and the product of the spectral densities of each function:
+
+\begin{equation}
+\centering
+C_{xy}(f) = \dfrac{\mid S_{xy}(f) \mid ^2}{S_{xx}(f)S_{yy}(f)}.
+\end{equation}
+
+\noindent
+Coherence is a useful parameter to estimate the correlation between the two signals. In control loops, it can be used to verify how much the output can be predictable by the input. The values of the coherence lies between 0 and 1 and two signals are considered optimally correlated if their coherence approaches 1.
+
+\section{The French fry factory}
+\begin{figure}[h!]
+\centering
+\includegraphics[scale=0.35]{images/fries.jpg}
+\caption[The French fry factory.]{The French fry factory: basic principles of a control loop as explained by Dr. Jenne Driggers during a private conversation at LIGO Hanford. Original photo.}
+\end{figure}
+

main/LF.tex

+\chapter{The low frequency window}
+\label{LF}
+
+\section{Hidden GW sources}
\ No newline at end of file

main/LIGO.tex

@@ -139,7 +139,7 @@ The HAMs provide five levels of isolation, among which there is the Internal Sei
 
 \begin{figure}[h!]
 \centering
-\includegraphics[scale=1]{images/HAM.png}
+\includegraphics[scale=0.9]{images/HAM.png}
 \caption[Advanced LIGO HAM chamber design]{Schematic (a) and CAD model (b) of a HAM chamber \cite{mat}. Suspensions of auxiliary optics provide levels of passive isolation above 10 Hz. The ISI platforms where the suspensions live are optical tables actively isolated via low noise inertial sensors at low frequency ($\sim 0.1 Hz$). The hydraulic attenuators of the \textit{Hydraulic External Pre-Isolator} (HEPI) and the geophones gives isolation from ground motion.}
 \label{ham}
 \end{figure}
@@ -149,7 +149,7 @@ The BSCs have a similar design as the HAMs, but they have two stages of ISI to s
 
 \begin{figure}
 \centering
-\includegraphics[scale=1]{images/BSC.png}
+\includegraphics[scale=0.9]{images/BSC.png}
 \caption[Advanced LIGO BSC chamber design]{Schematic (a) and CAD model (b) of a BSC chamber \cite{mat}. The active isolation is similar to the one exposed for HAM chambers. The two ISIs provide two stages of isolation while and the suspensions  are design to be quadruple pendulums, for a total of seven levels of isolation.}
 \label{bsc}
 \end{figure}

main/LSCdiff.tex

+%\documentclass[a4paper,12pt]{book}
+%\usepackage[a4paper,top=2cm,bottom=2cm,left=2cm,right=2cm]{geometry}
+%\usepackage[utf8]{inputenc} 
+%\usepackage[english]{babel} 
+%\usepackage{graphicx}
+%\usepackage{subfigure}
+%\usepackage{array}
+%\usepackage{color}
+%\usepackage{colortbl}
+%\usepackage{verbatim}
+%\usepackage{lscape}
+%\usepackage{amsmath,amssymb}
+%\linespread{2}
+%%\title{CH.5 LSC signal optimization on LIGO}
+%\date{}
+%
+%\begin{document}
+\chapter{LSC signals optimization on LIGO}
+\label{LSCdiff}
+
+\noindent
+In the previous chapter I collaborated to enhance the performances of LIGO at low frequencies, modifying the software set up of the ISIs to reduce the motion of the chambers. As I anticipated, a consequence of this work could be the improvement of the LSC signals from LIGO cavities. Among them, DARM is particularly important, because it represents the gravitational wave signal. In this chapter I am going to show you how we tried to apply the new CPS configuration in order to obtain improvements in LSC signals at LIGO Hanford. This work has been performed during the 2019 commissioning break, in collaboration with LIGO Livingston Observatory.
+
+\section{LSC signals in LIGO cavities}
+Length to Signal Control is a crucial part of LIGO: as we know, gravitational waves can be seen by the interferometer if its sensitivity is high and stable enough. Optical signals in the cavities are very important in this frame: 
+
+\section{Optimization: LSC offloading}
+We saw that the cavities (and the optical signals) in LIGO are affected by the ISI motion, simply because they lie on them. Given the work done with the CPSs to suppress the ISI motion (described in the previous chapter), we should see an improvement on LSC signals. This is not immediate, though, nor trivial, because the optics are just set on the optical bench, without any communication with the ISI. The motion of the optics on the chambers due to other factors than seismic is not seen by the platforms: if we could connect this motion to the platform via software, this would make the optics and the platform more dependent on each other. This means that we can control the stabilization of the cavity lengths also with the ISIs.\\
+What we expect is a faster reach of locking and a longer state of lock of the interferometer during observing runs.
+
+\noindent
+This work has been performed on LIGO during the commissioning break between O3a and O3b observing runs, in October 2019. The reason of this choice is that we needed the interferometer to \textit{not} be observing, since we were going to modify some software structure of the instrument.\\
+
+\noindent
+During the commissioning break, we performed the experiment: through CPSs locking, we reduced the differential motion of HAM2 and HAM3 chambers and made them to move in sync. So they can be considered as a whole block. The IMC is entirely lying on HAM2 and HAM3, and it is straightforward to use it as a witness: to make this real, we need to feed the HAM2-HAM3 block with IMCL. This will lock the cavity signal to the HAM2-HAM3 block. The same feeding will be performed with PRCL, SRCL, DARM and MICH cavities, which optics lie on the other chambers, in and out the corner station. Fig. \ref{chamb} illustrates the chambers and the locations of the cavities.
+
+\begin{figure}[h!]
+\centering
+\includegraphics[scale=0.5]{images/chambs.jpg}
+\caption{Sketch of the blocks and the locations of the cavities.}
+\label{chamb}
+\end{figure}
+
+\noindent
+To lock the LSC signals to ISIs, we need to do something similar to what we did in the previous chapter: we need to connect via software two different set ups which do not talk to each other. We decided to start from the Power Recycling Cavity Lecgth (PRCL) because we locked HAM2 and HAM3 chambers, so it was natural to start to lock the cavities on the x axis. The same work is foreseen to be done for the other cavities: the very short period of time available during the commissioning break allowed us to modify only the software for PRCL, since the job involved the request of permissions to modify the structure of the interferometer and the synchronization with the job of other people working on different parts of LIGO. Moreover, during commissioning break, time is also used to work on the chambers, profiting of the out-of-lock mode. This means that, for every attempt of software modification, a locking trial was needed, to see if the new configuration of the instrument was giving better performances and, also, if it was affecting negatively other sides of the instrument. To try to lock LIGO, we needed people not to work besides the chambers. This was a huge and collaborative work, which involved many people on site, and their time.
+
+\paragraph{The Power Recycling Cavity Length (PRCL)}
+We need to connect the ISI to the cavity and to do it we need to know how the PR cavity works.
+
+\begin{figure}[h!]
+\centering
+\includegraphics[scale=0.7]{images/PRCLfeed.png}
+\caption{Block diagram of PRCL locked to ISI.}
+\label{prcl}
+\end{figure}
+
+\section{Beyond}
+
+%\begin{thebibliography}{9}
+%
+%\bibitem{phd} D. Tuyenbayev, \textit{Extending the scientfic reach of Advanced LIGO by compansating for temporal variations in the calibration of the detector.}, PhD thesis, University of Texas, 2017
+%
+%\end{thebibliography}
+%
+%\end{document}
\ No newline at end of file

main/main.tex

@@ -2,7 +2,7 @@
 \usepackage[a4paper,top=3cm,bottom=3cm]{geometry}
 \usepackage[T1]{fontenc}
 \usepackage[utf8]{inputenc} 
-\usepackage{palatino}
+\usepackage{bookman}
 \usepackage[english]{babel} 
 \usepackage{graphicx}
 \usepackage[font=small,hang]{caption}
@@ -14,7 +14,7 @@
 \usepackage{lscape}
 \usepackage{amsmath,amssymb}
 \linespread{2}
-\title{Innovative perspectives for seismic isolation of gravitational waves detectors}
+\title{Innovative perspectives for seismic isolation of gravitational-wave detectors}
 \author{Myself}
 \date{}
 \titlehead{A Thesis submitted for the degree of Philosophiae Doctor}
@@ -32,7 +32,7 @@
 
 A brief summary of the project goes here, with main results.
 
-\chapter{Introduction}
+\chapter{Structure of this thesis}
 An introduction to frame the work and structure of the thesis go here.\\
 
 STRUCTURE OF THESIS [DRAFT]\\
@@ -64,51 +64,75 @@ 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\\
 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\\
+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\\
+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\\
+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\\
+QPD = Quadrant Position Device\\
+RIN = Relative Intensity Noise\\
 SC = Sensor Correction\\
 SR = Signal Recycling\\
 SRCL = Signal Recycling Cavity Length\\
+TEC = Thermo-Electric Controller\\
+UoB = University of Birmingham\\
 
 \mainmatter
 
-\part{Gravitational astrophysics}
-
+\part{Gravitational-wave frontiers}
 \include{GW}
-
-\part{Detectors and seismic isolation}
-
+\include{LF}
 \include{LIGO}
-\include{oplevs}
-
-\part{Lowering seismic noise}
 
+\part{Lowering seismic motion}
+\include{oplevs}
+\include{CPSdiff}
+%\include{LSCdiff}
+\include{laserstab}
 
 \appendix
-%\include{A}
-%\include{B}
+\include{A}
+\include{B}
 
 \backmatter
 
@@ -136,6 +160,34 @@ Beginning of Gravitational Wave Astronomy}
 
 \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
 
+\bibitem{poster} \textit{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} $https://edge.coherent.com/assets/pdf/COHR\_ MephistoNPRO\_ WP\_ 9\_ 24\_ 19.pdf$
+
+\bibitem{phd} D. Tuyenbayev, \textit{Extending the scientfic reach of Advanced LIGO by compansating for temporal variations in the calibration of the detector.}, PhD thesis, University of Texas, 2017
+
+\bibitem{intro} B. Lantz et al., \textit{Estimates of HAM-ISI motion for A+}, T1800066-v2, March 2018, https://dcc.ligo.org/LIGO-T1800066 
+
+\bibitem{intro2} S. Cooper et al., \textit{Ham ISI model}, Technical note, University of Birmingham, March 2018, https://dcc.ligo.org/LIGO-T1800092
+
+\bibitem{ven} 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{mca} C. Di Fronzo \textit{Optical sensors for improving low-frequency performance in GW detectors}, Mid-Course Assessment, University of Birmingham, 2018
+
+\bibitem{poster} C. Di Fronzo et al., \textit{Optical Lever for interferometric inertial isolation}, poster, LVC meeting, Maastricht 2018, https://dcc.ligo.org/LIGO-G1801693 
+
 \end{thebibliography}
 
 \chapter{Acknowledgements}