final corrections

main/B.tex

@@ -151,6 +151,7 @@ C_{xy}(f) = \dfrac{\mid ASD_{xy}(f) \mid ^2}{ASD_{xx}(f)ASD_{yy}(f)}.
 \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.
 
+\newpage
 \section{The French fry factory}
 \begin{figure}[h!]
 \centering

main/CPSdiff.tex

@@ -50,7 +50,7 @@ Other ways to improve duty cycle is to increase the observable volume: this can
 \end{figure}
 
 
-
+\newpage
 \subsection{Differential motion between chambers}
 We have seen that among the noise sources which contribute to lock loss events there is the ground motion, including earthquakes and microseismic events. \\
 In particular, during O3 run, it was observed that the chambers in the corner station (CS) show differential seismic motion with respect to each other \cite{technote1}, because they move independently from each other with respect to ground. It is reasonable to think that if the chambers could have a synchronized motion, the whole interferometer would move following the ground motion, without being affected by it. This would in principle help the cavities to be stable and to maintain the resonance. In case of lock losses due to large earthquakes or high wind, stable resonance could be achieved in shorter times \cite{biswas}.\\
@@ -87,6 +87,9 @@ The Capacitive Position Sensors (CPS) measure the relative motion between two st
 \noindent
 One of the main differences between the behaviour of CPS IMCL and CPS PRCL is that the former is involving only the HAM chambers. Since HAM2 and HAM3 have a very good common motion, IMCL can be considered more stable with respect to PRCL, which instead involves also BSCs. Indeed, CPS PRCL is following only the BSCs, at frequencies below 0.03 Hz \ref{sus}.\\
 
+\noindent
+Fig. \ref{sus} shows the plots of PRCL and ICML as sensed by CPS projection to the suspension point. These projections indicate that reducing the differential motion as seen by the CPSs will help to reduce the residual motion seen by the optical cavities. We expect this to be effective in a range of frequencies between 0.1 and 0.5 Hz.\\
+
 \begin{figure}[H]
 \centering
 \includegraphics[scale=0.25]{images/ham2_ham3.PNG}\\
@@ -96,9 +99,6 @@ One of the main differences between the behaviour of CPS IMCL and CPS PRCL is th
 \label{diff}
 \end{figure}
 
-\noindent
-Fig. \ref{sus} shows the plots of PRCL and ICML as sensed by CPS projection to the suspension point. These projections indicate that reducing the differential motion as seen by the CPSs will help to reduce the residual motion seen by the optical cavities. We expect this to be effective in a range of frequencies between 0.1 and 0.5 Hz.\\
-
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.3]{images/CPS_SUSPOINT_IMCL.PNG}\\
@@ -107,6 +107,7 @@ Fig. \ref{sus} shows the plots of PRCL and ICML as sensed by CPS projection to t
 \label{sus}
 \end{figure}
 
+\newpage
 \section{Locking chambers via CPS}
 In the previous section we demonstrated that the CPSs are good sensors for differential motion and that they can be used to monitor the chamber motion at lower frequencies. That said, and remembering the aim of stabilizing the motion of the chambers making them moving in sync, it is possible to use the CPSs to lock HAM2 and HAM3 together, HAM4 and HAM5 together, BSCs in the Corner Station together and BSCs hosting the ETMs together (refer to Chapter \ref{LIGO} for the location of these chambers). This will stabilize the ISI differential motion with respect to a driving chamber.\\
 Since we saw that HAM2 and HAM3 show a very good common motion and that we can use the IMC as a witness of it, our first step is to lock the HAM2 and HAM3 chambers together by feeding HAM3 a calculated differential CPS signal. This is performed with an additive offset to the setpoint of the HAM3 isolation control loop \cite{technote2}.\\
@@ -150,10 +151,11 @@ $x_{p}$ & plant motion\\
 
 \noindent
 We can compute the signal $\textit{$d_{2}$}$ which will be the CPS offset to send to HAM3 chamber. In this case, HAM2 will drive HAM3 to follow its motion. Defining K = PC:\\
+
 \begin{equation}
 \centering
 \begin{split}
-d_{2} = x_{p_{2}} -  x_{g}\\
+&d_{2} = x_{p_{2}} -  x_{g}\\
 &= K[L_{2}(SN_{g} + Sx_{g} + d_2) + H_2N_{1_2} + H_2(x_g + d_2)] + Px_g - x_g\\
 &= KL_{2}S(N_{g} + x_{g}) + KL_{2}d_2 + KH_2N_{i_2} + KH_2x_g + KH_2d_2 + Px_g - x_g.
 \end{split}
@@ -321,8 +323,9 @@ Figure \ref{gs13_inj} shows the GS13 signal and its contributors.
 \label{gs13_inj}
 \end{figure}
 
+%\newpage
 \subsection{Blending filters}
-In order to compute the platform motion for the single chambers in isolation and, later, locked together via CPS, we need the low- and high- pass filters. Many possible blended filters have been found for different combinations of order of magnitudes and blending frequency: the plots in Fig. \ref{blend} show the velocity rms for every combination.
+In order to compute the platform motion for the single chambers in isolation and, later, locked together via CPS, we need the low- and high- pass filters. Many possible blended filters have been found for different combinations of order of magnitudes and blending frequency: the plots in Fig. \ref{blend} show the velocity rms for every combination.\\
 \noindent
 The best combination has been found computing the orders and the blending frequency which give the minimum of the cost. The optimized blending filter has been then built using the best values of \textit{l} and \textit{h} orders and blending frequency. The cost is given by:
 \begin{equation}
@@ -331,7 +334,7 @@ cost = \sqrt{\int((cps_{inj}\cdot LP)^2 + (T240_{inj}\cdot HP)^2)df}
 with a similar equation for the HAM chamber.\\
 Fig. \ref{cost} shows the cost and its rms obtained with the best blending filters for BSC and HAM chambers.
 
-\begin{figure}[H]
+\begin{figure}[h!]
 \centering
 \includegraphics[scale=0.45]{images/bscblend.png}
 \includegraphics[scale=0.3]{images/hamblend.png}
@@ -348,7 +351,7 @@ Fig. \ref{cost} shows the cost and its rms obtained with the best blending filte
 \end{figure}
 
 
-\subsection{Locking chambers}
+\subsection{Locking the chambers}
 With these elements, we can proceed with the analysis of the behaviour of the chambers when locked via CPS. We refer to HAM2 and HAM3 chambers, since in the previous sections we made the computations for them. We recall here that the equations we need are \ref{xp2}, \ref{d2}, \ref{xp3} and \ref{xp3xp2}, where $x_{p_{2}}$ is HAM2 platform motion, $d_{2}$ is the signal from HAM2 to send to HAM3 and $x_{p_{3}}$ is HAM3 motion when attached to HAM2 via CPS.
 
 \noindent
@@ -514,14 +517,14 @@ This block diagram has been solved with Mathematica in order to find the correct
 After every simulation which could possibly work for the system, we locked the interferometer and took a measurement of the PRM suspension point. The plot in Fig. \ref{prcltest} shows a comparison between the simulation and the actual measured PRCL signal: the outcome is positive because the two traces differ by only a factor of 2, which says that the crossover filter should be adjusted by a factor of 2 to match the real signal. This result has been obtained implementing the filter in Fig. \ref{prclfilter}. The test shows that the offloading works as expected and that the PRCL signal can be driven (and hence controlled) by the ISI.
 \begin{figure}[h!]
 \centering
-\includegraphics[scale=0.4]{images/PRM.png}
+\includegraphics[scale=0.6]{images/PRM.png}
 \caption[PRCL-ISI offloading test]{Best measurement of the PRCL signal with respect to the expected signal from the simulations: the two traces differ by a factor of 2.}
 \label{prcltest}
 \end{figure}
 
 \begin{figure}[h!]
 \centering
-\includegraphics[scale=0.45]{images/prcl_filter.png}
+\includegraphics[scale=0.65]{images/prcl_filter.png}
 \caption[PRCL-ISI crossover filter]{Open loop gain (OLG) crossover filter implemented at LHO for a measurement of PRCL signal in offloading conditions.}
 \label{prclfilter}
 \end{figure}
@@ -530,7 +533,6 @@ After every simulation which could possibly work for the system, we locked the i
 The new configuration proposed and tested has changed a crucial section of the structure of LIGO. This change might have consequences on other sides of the instrument, for example affecting other noise sources. A test about the effect of this configuration has been performed at LHO in 2020 by the LHO, LLO and Seismic teams. This test studied the impact of CPS differential controls on scattered light glitches on O3b run. The teams investigated the reason of an increase in the rate of glitches. The synchronized motion of the chambers with the ground could in principle make the instrument more sensitive to glitches (and other noise sources) which were hidden by the seismic and sensor noises. The study is showing that the configuration is not responsible for this increase, but there is an effect on the sensitivity of LIGO to glitches, when the configuration is activated. The complete study is exposed in details in the LHO logbook post \cite{lhotest}.\\
 This is an example of the impact of the CPS differential control on LIGO: it has been used to test the effect of wind in microseismic regions \cite{lhotest2} and further tests might help to understand the impact of less seismic motion on other noise sources.
 
-\newpage
 \section*{Conclusions}
 \addcontentsline{toc}{section}{Conclusions}
 This study is promising to provide a significant contribution to the improvement of LIGO LSC signals and the detector stability when it is running in observing mode. The tests at LHO demonstrated that the experiment succeeded in lowering the seismic motion of the platforms by a factor of 3 at low frequencies and that also the DARM signal benefited from it. The simulations have shown that it is possible to reduce the differential motion of the chambers by a factor of 3 in order of magnitude below 0.1 Hz. The test on the Power Recycling Cavity Length highlighted that the signal can be controlled by the ISI according with the software simulations.\\

main/LIGO.tex

@@ -210,7 +210,7 @@ In particular, DARM is exactly the gravitational wave signal and thus the most i
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.55]{images/lsc.png}
-\caption[LIGO LSC scheme.]{Cavity lengths involved in the sensing and feedback control for stabilization of resonators. The PRM is the Power Recycling Mirror, which summarizes the power recycling setup including three mirrors inside two chambers. The SRM is the same summary for the Signal Recycling.}
+\caption[LIGO LSC scheme.]{Cavity lengths involved in the sensing and feedback control for stabilization of resonators. The PRM is the Power Recycling Mirror, which includes the power recycling setup with three mirrors inside two chambers. The SRM is the same concept for the Signal Recycling cavity.}
 \label{lsc}
 \end{figure}
 

main/laserstab.tex

@@ -219,6 +219,7 @@ The performance of the setup depend strongly on the HoQIs because they are the s
 \subsection{Tested noise sources}
 There are several noise sources to take into account and that we tested and minimized: air currents and vibrations from electronics and cables have been reduced placing the optical setup into a foam box and moving the electronic devices suitably. The lasers have been left outside the box to avoid overheating inside, due to their heat dissipation. Cables have been isolated from the table and the breadboard by rubber feet.\\
 
+\newpage
 \paragraph{Offset/gain parameter matching}
 When aligning HoQIs, a significant contribution to the results was given by the fact that the fringes needed to be adjusted to match in gain and offsets: this was done via CDS and it provided one of the most important issues (and noise sources) during the tests. Imperfect fringe-visibility and parameter matching dominate the coupling from intensity to measured-phase, and we saw substantial improvements when these values were optimised. We had insufficient diagnostics to fix the issue, mainly because, to create fringes, the HoQIs needed to be mechanically shaken and tuned, and this could be done only manually and in dark room (to avoid room light to affect the offsets), providing imprecise results. We had no proper way to adjust the laser frequency without changing the intensity, and we had no way to adjust the intensity without changing the frequency. This made the offsets and gains change and pollute the measurements. The plots in Fig. \ref{parameters} show the difference between the row fringes generate while shaking HoQI1 and the ones generated after optimizing the parameters. We observed variations in the settings, which needed to be double-checked and readjusted before every measurement. This was an important issue that slowed the tests down and that it is worthy of further tests and data analysis.
 
@@ -230,6 +231,7 @@ When aligning HoQIs, a significant contribution to the results was given by the
 \label{parameters}
 \end{figure}
 
+\newpage
 \paragraph{Acoustic noise}
 The test in Fig. \ref{sound} shows that the setup is sensitive to acoustic noise: we injected a sound at 75 Hz and both HoQIs clearly detected it. Moreover, we found out that HoQI1 is detecting some noise around 22 Hz that HoQI2 is not able to sense: the two peaks in the figure are present in every condition of the laboratory and time of the day. The source of this noise is still under investigation: it could be a permanent sound in the lab non audible by humans. The fact that only HoQI1 can detect it could be due to its position with respect to the noise source: it might be closer to it than HoQI2. Imperfections in the optics and general setup of the HoQIs are also taken into account.\\
 
@@ -240,9 +242,10 @@ The test in Fig. \ref{sound} shows that the setup is sensitive to acoustic noise
 \label{sound}
 \end{figure}
 
+
 \paragraph{The role of the temperature}
 Temperature changes affected dramatically the measurements. The two lasers can be driven also via temperature modulation: this method has been used to move the beat-note peak along the frequencies and set it around 60 MHz, being this the setpoint we decided for it. However, both laser modules are sensitive to changes of the room temperature, which make the peak move out from the setpoint on large time scales (~hours): this affects long time measurements. The stabilization of the room temperature requires the use of the air conditioning, which in turn creates air currents visible by the setup below 10 Hz (Fig. \ref{ACtest} shows the difference between two tests taken with and without AC).\\
-Temperature changes are also responsible for deformations of metals; this induces noises into the HoQI platforms because of the different materials they are built of: temperature change induces differential expansion. In a rigid structure this creates stress and some of the bolted connections slide, introducing noise. This issue has been reduced by inserting rubber rings between the connections: this allows the baseplate to expand differentially without creating stress.\\
+Temperature changes are also responsible for deformations of metals; this induces noises into the HoQI platforms because of the different materials they are built of: temperature change induces differential expansion. In a rigid structure this creates stress and some of the bolted connections slide, introducing noise. This issue has been reduced by inserting rubber rings between the connections: this allows the baseplate to expand differentially without creating stress.
 
 \begin{figure}[h!]
 \centering

main/main.tex

@@ -20,7 +20,7 @@
 %\usepackage{setspace}
 %\usepackage{hyperref}
 %\mathrm
-\linespread{2}
+\linespread{1.5}
 \subject{A Thesis submitted for the degree of PHILOSOPHIAE DOCTOR}
 \title{Innovative perspectives for seismic isolation of gravitational-wave detectors}
 \author{Chiara Di Fronzo}
@@ -168,12 +168,19 @@ UoB = University of Birmingham\\
 \include{CPSdiff}
 \include{laserstab}
 
-\chapter*{Summary}
+\chapter*{Summary and future developments}
+\addcontentsline{toc}{chapter}{Summary and future developments}
 This thesis is intended to provide a contribution to the improvement of gravitational-wave interferometers in the lower frequency bandwidth (below 30 Hz). My PhD project then focussed on developing new devices and improving already existing control structures for this aim, through three different experimental works: the study of optical levers for sensing and reducing tilt motion, the modification of the control system of LIGO in order to improve the control of seismic motion on the platforms and the frequency stabilization of the laser surce for the 6D isolation system device.\\
 The optical lever can be in principle a good device to sense tilt motion over long lever arms. However, the noise budget indicated a small frequency window of good operation, while below 0.1 Hz the levers are limited by the ground motion along the z axis, but it opened the way to further tests to improve the technology: with a good sensing system of tilt motion, the addition of an actuation system able to reduce this noise will be crucially helpful to stabilize the suspension points of the optical chains and then of the whole cavity.\\
 The study on the CPS and LSC offloading is promising to provide a significant contribution to the improvement of LIGO LSC signals and the detector stability when it is running in observing mode. The tests at LHO demonstrated that the experiment succeeded in lowering the seismic motion of the platforms by a factor of 3 at low frequencies and that also the DARM signal benefited from it. The simulations have shown that it is possible to reduce the differential motion of the chambers by a factor of 3 in order of magnitude below 0.1 Hz. The test on the Power Recycling Cavity Length highlighted that the signal can be controlled by the ISI according with the software simulations.\\
-The results of the laser stabilization experiment showed that it is possible to stabilize the frequency of the laser source of the 6D device using the technology presented: a compact, easy to handle setup which makes use of small interferometers of the same type that are used inside the 6D sensor. With this technology, we managed to reach a frequency stabilization of 3.6 $\times$ 10$^3$ Hz/$\sqrt{Hz}$ at 1 Hz, without the need of installing the prototype in vacuum. This is already a promising result, but not yet sufficient for the requirements of 6D, especially below 1 Hz. This experiment requires further tests in vacuum in order to isolate the HoQIs and improve the performance.\\
-In conclusion, all the three experiments proposed in this thesis can provide an important contribution for the low frequency noise reduction and are worthy of further tests and developments, as demonstrated by the experimental results and the simulations. 
+The results of the laser stabilization experiment showed that it is possible to stabilize the frequency of the laser source of the 6D device using the technology presented: a compact, easy to handle setup which makes use of small interferometers of the same type that are used inside the 6D sensor. With this technology, we managed to reach a frequency stabilization of 3.6 $\times$ 10$^3$ Hz/$\sqrt{Hz}$ at 1 Hz, without the need of installing the prototype in vacuum. This is already a promising result, but not yet sufficient for the requirements of 6D, especially below 1 Hz. This experiment requires further tests in vacuum in order to isolate the HoQIs and improve the performance.
+
+\section*{Future developments}
+%\addcontentsline{toc}{chapter}{Acronyms}
+All the three experiments proposed in this thesis can provide an important contribution for the low frequency noise reduction and are worthy of further tests and developments, as demonstrated by the experimental results and the simulations.\\
+The optical levers and their performance under stimulation of vertical motion is a matter of studies at the AEI, and it would be ideal to fix the electronics and perform further tests with a lever arm of 10 m. This would be of great help to understand if optical lever can be useful to be installed on the platforms of the interferometers. A further analysis of the control system for reducing the tilt motion is required and it could be an ideal topic for another PhD project.\\
+The project developed at LIGO is currently in use, as highlighted in Chapter 5. It is straightforward to complete the job done there with more appropriate blending filters and fine tuning of the software design for locking the chambers: this work was due to 2020 or 2021, when I was supposed to go back to Hanford and conclude the work. However, it was not possible due to the pandemic. It would then be useful to go back when possible, or that another student into the fellowship program could bring the project to a final stage.\\
+The frequency stabilization of the lasers for the 6D isolation system requires another test in vacuum and, probably, independent tests on the single HoQIs to verify if there are internal defects. This is supposed to be studied at University of Birmingham. Since the setup is already built, the controller is designed and is working with good performance and it needs to be completed in order to be installed into the full 6D device, these further tests should be straightforward: an internship student or a Master's student could take care of this.
 
 \appendix
 \include{A}