updates

main/LIGO.tex

 \chapter{Interferometry and Advanced LIGO}
 \label{LIGO}
-Most of the work exposed in this thesis has been carried on in laboratories and on LIGO sites. In this chapter, I will briefly introduce interferometers and LIGO, and I will explain in details only the structures of LIGO that have been subject of study in this thesis work: this is essential to fully embrace the work exposed in Chapter \ref{CPSdiff} in particular, and in general for the devices described in the whole thesis. The information contained in this chapter will be often referred to throughout the thesis.
+Most of the work exposed in this thesis has been carried on in laboratories and on LIGO sites. In this chapter, I will briefly introduce interferometers and LIGO, and I will explain in detail only the structures of LIGO that have been the subject of study in this thesis work: this is essential to fully embrace the work exposed in Chapter \ref{CPSdiff} in particular, and in general for the devices described in the whole thesis. The information contained in this chapter will often be referred to throughout this thesis.
 
 \section{Interferometric detectors}
-The interaction of gravitation waves with two objects moving along the x axis produces effects on their distance $d = x_2 - x_1$ and hence the effect of the gravitational waves can be measured looking at the variation of the distance of the masses involved.\\
+The interaction of gravitation waves with two objects moving along the x axis produces effects on their distance $d = x_2 - x_1$ and hence the effect of the gravitational waves can be measured by looking at the variation of the distance of the masses involved.\\
 A method to do it is to measure the time light takes to travel from one mass to the other: this is the basic principle of the \textit{interferometer}.
 
 \begin{figure}[h!]
@@ -23,7 +23,7 @@ P_{out} = E^{2}_{0} \sin^2 [k(L_x - L_y)]
 \end{equation}
 
 \noindent
-where $E^{2}_{0}$ is the amplitude of the electric field generated by the laser source and k = $2\pi / \lambda$.\\
+where $E_{0}$ is the amplitude of the electric field generated by the laser source and k = $2\pi / \lambda$.\\
 We know that the effect of a gravitational wave is to modify the distance of two masses: in the case of the interferometer the path length difference in the arms is proportional to the gravitational wave amplitude $h$ \cite{mag}:
 
 \begin{equation}
@@ -51,7 +51,7 @@ P_{out} = E^{2}_{0} \sin^2 [k(L_x - L_y) + \Delta \phi].
 The amplitude of a gravitational wave is typically very small and corresponds to a variation of the arm length of the order of $\Delta L \sim 10^{-18}$ m. This means that, if we want to measure a considerable phase shift, the sensitivity of the instrument depends on the length of the arms.
 
 \paragraph{Fabry-Perot cavities}
-A useful way to increase the length of the arms is to make the laser beam travel back and forth into an optical cavity delimited by two mirrors, called \textit{Fabry-Perot cavity}: here, thanks to the multiple reflections, the optical path length will be longer. This process returns a longer optical arm length, proportionally to the quality factor of the cavity, which depends on the reflection coefficients of the two mirrors and it is called \textit{Finesse} (F):
+A useful way to increase the length of the arms is to make the laser beam travel back and forth inside an optical cavity delimited by two mirrors, called a \textit{Fabry-Perot cavity}: here, thanks to the multiple reflections, the optical path length will be longer. This process returns in a longer optical arm length, proportional to the quality factor of the cavity, which depends on the reflection coefficients of the two mirrors, named \textit{Finesse} (F):
 
 \begin{equation}
 \centering
@@ -67,22 +67,22 @@ which gives a phase shift:
 \end{equation}
 
 \noindent
-The higher is F, the higher is the effective length of the cavity and higher is the measureble phase shift.\\
+A larger F results in an increased effective cavity length, hence a larger measurable phase shift.\\
 
 \section{Advanced LIGO}
 
 The goal of this work is to provide a contribution to the improvement of one of the interferometric detectors in use at present time, based in the USA: the Advanced Laser Interferometric Gravitational-wave Observatory (aLIGO).\\
 
 \noindent
-The configuration of aLIGO is shown in Fig. \ref{aligo}: it is a Michelson interferometer provided with Fabry-Perot, power and signal recycling cavities and 4 km-long arms. The light source is a solid-state Nd:YAG laser of wavelength $\lambda$= 1064 nm, injected at a power between 5 - 125 W.\\
+The configuration of aLIGO is shown in Fig. \ref{aligo}: it is a Michelson interferometer adapted to include power recycling, signal recycling and 4km long Fabry-Perot arm cavities. The light source is a solid-state Nd:YAG laser of wavelength $\lambda$= 1064 nm, injected at a power between 5 - 125 W.\\
 \noindent
-The mirrors at the end of each arm, called End Test Masses (ETM), are made of fused silica and they are 34 cm $\times$ 20 cm in size and 40 kg in weight. A photodiode (PD) detects the power at the output. The optic able to split the injected beam into two parts along the arms is called Beam Splitter (BS) and it is placed at 45$^{\circ}$ between the arms.\\
+The mirrors at the end of each arm, called End Test Masses (ETM), are made of fused silica and they are 34 cm $\times$ 20 cm in size and 40 kg in weight. A photodiode (PD) detects the power at the output. The optic able to split the injected beam into two parts along the arms is called a Beam Splitter (BS) and it is placed at 45$^{\circ}$ between the arms.\\
 
 
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.9]{images/aligo.png}
-\caption[Advanced LIGO layout]{Advanced LIGO configuration as proposed in \cite{ligo}. As a second generation detector, it is provided with two Fabry-Perot resonant cavities in the arms, delimited by the Input Test Masses (ITM) and the End Test Masses (ETM), and two additional dual recycling cavities: the power recycling (PR) and the signal recycling (SR), which optics are all suspended. Compensation Plates (CP) take care of thermal effects occurring when high powers pass through the ITMs; mode cleaners in input and outputs keep the selected mode in resonance.}
+\caption[Advanced LIGO layout]{Advanced LIGO configuration as proposed in \cite{ligo}. As a second generation detector, it contains two Fabry-Perot resonant cavities in the arms, delimited by the Input Test Masses (ITM) and the End Test Masses (ETM), and two additional dual recycling cavities: the power recycling (PR) and the signal recycling (SR) cavities, whose core optics are all suspended to provide isolation from the environment. Compensation Plates (CP) take care of thermal effects occurring when high powers pass through the ITMs; mode cleaners in inputs and outputs keep the selected mode in resonance.}
 \label{aligo}
 \end{figure}
 
@@ -91,7 +91,7 @@ The instrument design is extremely intricate in all its details: this thesis wil
 There are two LIGOs in the USA, one in Hanford (WA) and one in Livingston (LA): some of the work that will be presented in the next chapters has been physically done in Hanford, in remote collaboration with Livingston team.
 
 \subsection{LIGO sensitivity and noise sources}
-The performance of LIGO in terms of how far in the Universe it can detect gravitational waves and from which sources depends on the sensitivity: this in turn depends on the quality of the technologies involved and on the limitation given by nature.
+The performance of LIGO, in terms of how far in the Universe it can detect gravitational waves and from which sources, depends on the sensitivity: this in turn depends on the quality of the technologies involved and on the natural limitations.
 Fig. \ref{sens} shows the sensitivity of LIGO during the first observation run and the main noise sources.
 
 \begin{figure}[h!]
@@ -118,11 +118,11 @@ Technical noises arise from electronics, control loops, charging noise and other
 
 
 \noindent
-This thesis focuses on the improvement of the seismic isolation system, which noises affect the inertial sensors placed on the suspension benches and the stabilization of the resonant cavities, which in turn limit the sensitivity of the detector in the low frequency bandwidth. The goal is to provide solutions to reduce seismic motion and improve the detector sensitivity.
+This thesis focuses on the improvement of the seismic isolation system. Seismic motion is measured using inertial sensors which are placed on the suspension benches. The residual motion effects the stability of the resonant cavities and limits the sensitivity of the detector in the low frequency band. The goal is to provide solutions to reduce seismic motion and improve the detector sensitivity.
 
 \section{LIGO seismic isolation system}
 \label{ligosei}
-Every optic needs to be stable with respect to seismic motion, because movements in the mirrors will cause unwanted displacement of the laser beam on the optical surface, resulting in noise during the laser travel into the cavities and then at the output. The main mirrors (test masses and beam splitter) are suspended from a stabilized bench and every suspension chain is placed in vacuum chambers called \textit{Basic Symmetric Chamber} (BSC). The auxiliary optics are placed on optical benches enclosed in the \textit{Horizontal Access Module} (HAM) chambers.
+Every optic needs to be stable with respect to seismic motion, because movements in the mirrors will cause unwanted displacement of the laser beam on the optical surface, resulting in noise during the laser travel into the cavities and then at the output. The main mirrors (test masses and beam splitter) are suspended from a stabilized bench and every suspension chain is placed in vacuum chambers called \textit{Basic Symmetric Chambers} (BSC). The auxiliary optics are placed on optical benches enclosed in the \textit{Horizontal Access Module} (HAM) chambers.
 
 \begin{figure}[H]
 \centering
@@ -136,7 +136,7 @@ The HAMs provide five levels of isolation, among which there is the Internal Sei
 \begin{figure}[h!]
 \centering
 \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.}
+\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 provides isolation from ground motion.}
 \label{ham}
 \end{figure}
 
@@ -151,7 +151,7 @@ The BSCs have a similar design as the HAMs, but they have two stages of ISI to s
 \end{figure}
 
 \paragraph{The sensors on the chambers}
-The devices dedicated to monitoring the seismic motion are inertial and displacement sensors, which are horizontal and vertical, according to the different motion they need to sense. Currently, no sensors for tilt motion are installed on the platforms. Actuators are paired to each sensors, for active isolation of the sensed noise. The vertical displacement sensors are called Capacitive Position Sensors and are placed between every stages of every chamber: they measure the relative motion between the platforms. These are the sensors we will use in Chapter \ref{CPSdiff}. The vertical and horizontal inertial sensors with the dedicated actuators are placed on the platforms, underneath the optical tables, measuring the seismic motion in the horizontal and vertical directions. The position and the use of these sensors are different for HAM and BSC chambers, depending on the number of stages and the presence of the suspensions. The calibration and the specific role of each sensor into the seismic isolation system can be found in \cite{kisselthesis}, with references to the covered range of frequencies in \cite{kisseltalk3}.\\
+The devices dedicated to monitoring the seismic motion are inertial and displacement sensors, which are horizontal and vertical, according to the different motion they need to sense. Currently, no sensors for tilt motion are installed on the platforms. Actuators are paired to each sensor, for active isolation of the sensed noise. The vertical displacement sensors are called Capacitive Position Sensors and are placed between every stage of every chamber: they measure the relative motion between the platforms. These are the sensors we will use in Chapter \ref{CPSdiff}. The vertical and horizontal inertial sensors with the dedicated actuators are placed on the platforms, underneath the optical tables, measuring the seismic motion in the horizontal and vertical directions. The position and the use of these sensors are different for HAM and BSC chambers, depending on the number of stages and the presence of the suspensions. The calibration and the specific role of each sensor into the seismic isolation system can be found in \cite{kisselthesis}, with references to the covered range of frequencies in \cite{kisseltalk3}.\\
 
 \begin{figure}[h!]
 \centering
@@ -165,19 +165,19 @@ Part of the work presented in this thesis focussed on the enhancement of the per
 Active isolation implies a sensing system of the noise to reduce and a control system to compensate the disturbance. Each platform includes relative position sensors, inertial sensors and actuators, working in all degrees of freedom.\\
 
 \noindent
-The control loop of a generic ISI stage on the X degree of freedom is  simplified in the block diagram in Fig. \ref{control}. The platform motion is the sum of the input disturbance and the contribution from the control signal and it is measured by relative position and inertial sensors. This motion is then low- and high-passed via filters suitably built to fit the requirements and tuned to obtain the best performances combining the best results of both filters. This technique is called \textit{blending}, and the frequency where the relative and the inertial sensors contribute at their best is called \textit{blend frequency}. The result of this blend is called \textit{super sensor}. The output of the super sensor feeds the feedback loop, where the actuators close the loop \footnote{A general overview of control loops theory is exposed in Appendix B}.\\
+The control loop of a generic ISI stage on the X degree of freedom is  simplified in the block diagram in Fig. \ref{control}. The platform motion is the sum of the input disturbance and the contribution from the control signal and it is measured by relative position and inertial sensors. This motion is then low- and high-passed via filters suitably built to fit the requirements and tuned to obtain the best performances combining the best results of both filters. This technique is called \textit{blending}, and the frequency where the relative and the inertial sensors contribute at their best is called the \textit{blend frequency}. The result of this blend is called the \textit{super sensor}. The output of the super sensor feeds the feedback loop, where the actuators close the loop \footnote{A general overview of control loops theory is exposed in Appendix B}.\\
 The sensor correction loop takes the ground motion signal from an inertial instrument, filtering it before adding it to the relative sensor signal. This filter is needed because the sum of the motions from the ground inertial and the relative sensors can in principle provide a measurement of the absolute motion of the platform. However, the ground sensors are affected by low frequency noise and need to be suitably filtered. 
 
 \begin{figure}[H]
 \centering
 \includegraphics[scale=0.65]{images/control.png}
-\caption[Control loop for a generic HAM-ISI]{Control loop of a generic HAM-ISI platform. Similar block diagrams can be applied for BSC-ISI platforms, including relative position sensors between the two stages of ISIs. \textbf{Green:} there is an inertial sensor measuring the ground motion along the x axis (GNDx), a Capacitive Position Sensor (CPS) measuring relative motions between the platform and the ground. Rotational sensors take care of tilt motion and GS13 are seismometers measuring seismic motion. Tilt and GS13 sensors are both placed on the platform. \textbf{Blue:} the Sensor Correction (SC) filter is typically a Finite Impulse Response (FIR) designed to provide required magnitude and phase match at 100 mHz (where isolation is needed). High- and low-pass filters (LP and HP) manipulate the signals from the low and high frequency sensors and are blended to form the super sensor, which output is sent to the control loop in \textbf{pink}. The overall corrected signal is then sent to the plant (\textbf{yellow}), which represents the processing phase for platform motion actuation.}
+\caption[Control loop for a generic HAM-ISI]{Control loop of a generic HAM-ISI platform. Similar block diagrams can be applied for BSC-ISI platforms, including relative position sensors between the two stages of ISIs. \textbf{Green:} there is an inertial sensor measuring the ground motion along the x axis (GNDx), a Capacitive Position Sensor (CPS) measuring relative motions between the platform and the ground. Rotational sensors take care of tilt motion and GS13s are seismometers measuring seismic motion. Tilt and GS13 sensors are both placed on the platform. \textbf{Blue:} the Sensor Correction (SC) filter is typically a Finite Impulse Response (FIR) designed to provide required magnitude and phase match at 100 mHz (where isolation is needed). High- and low-pass filters (LP and HP) manipulate the signals from the low and high frequency sensors and are blended to form the super sensor, whose output is sent to the control loop in \textbf{pink}. The overall corrected signal is then sent to the plant (\textbf{yellow}), which represents the processing phase for platform motion actuation.}
 \label{control}
 \end{figure}
 
 \section{LIGO Length Sensing and Control}
-Length sensing and control (LSC) is a crucial feature of LIGO because the cavities need to be stable in presence of resonance as long as possible. This requires feedback controls between optical resonators and low-noise sensing systems to avoid noise coupling into the gravitational-wave readout.\\
-There are several resonant cavities involved in this scheme, all important to guarantee the best performances on the sensitivity of the instrument. As we saw in Fig. \ref{aligo}, the resonators are the two Fabry-Perot cavities in the arms, the power recycling and the signal recycling cavities. The Fabry-Perot ones assure a higher sensitivity thanks to the beam bouncing into the cavity multiple times, increasing the time spent by the light into the arms and then the interaction time with a gravitational wave. The power recycling cavity is used to recover losses from power in the injection bench due to light reflected back to the laser source: this helps to increase the power travelling in each arm. The signal recycling cavity is placed at the output of the detector and is used to tune the detector to a specific observing bandwidth.\\
+Length sensing and control (LSC) is a crucial feature of LIGO because the cavities need to be stable and resonant for as long as possible. This requires feedback controls between optical resonators and low-noise sensing systems to avoid noise coupling into the gravitational-wave readout.\\
+There are several resonant cavities involved in this scheme, all important to guarantee the best performance on the sensitivity of the instrument. As we saw in Fig. \ref{aligo}, the resonators are the two Fabry-Perot cavities in the arms, the power recycling and the signal recycling cavities. The Fabry-Perot ones assure a higher sensitivity thanks to the beam bouncing inside the cavity multiple times, increasing the time spent by the light inside the arms and hence, the interaction time with a gravitational wave. The power recycling cavity is used to recover losses from power in the injection bench due to light reflected back to the laser source: this helps to increase the power travelling in each arm. The signal recycling cavity is placed at the output of the detector and is used to tune the detector to a specific observing bandwidth.\\
 
 \noindent
 The main disturbance affecting the stabilization of the resonators is the ground motion, acting on the position of the optics and that can not be reduced by the passive isolation systems below 1 Hz. This means that an active isolation and a feedback control are required.\\
@@ -211,7 +211,7 @@ 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 summarize the power reclycling 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 summarizes the power recycling setup including three mirrors inside two chambers. The SRM is the same summary for the Signal Recycling.}
 \label{lsc}
 \end{figure}