The amplitude of a gravitational wave is typically very small and corresponds to a variation of the arm length of the order of $\Delta L \sim10^{-18}$ 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 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):
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 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
...
...
@@ -117,7 +117,7 @@ Noises can be of fundamental, technical and environmental origin. Fundamental no
Technical noises arise from electronics, control loops, charging noise and other effects; environmental noises include seismic motion, acoustic and magnetic noises: these noises can be reduced once identified and carefully studied.\\
\noindent
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 affects 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.
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 affects 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 the coupling of seismic motion to the interferometer and improve the detector sensitivity.
\section{LIGO seismic isolation system}
\label{ligosei}
...
...
@@ -150,7 +150,7 @@ 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 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}.\\
The devices dedicated to monitoring and providing feedback 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
...
...
@@ -165,7 +165,7 @@ Active isolation implies a sensing system of the noise to reduce and a control s
\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 performance 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 given 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.
The \textit{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
...
...
@@ -215,8 +215,8 @@ In particular, DARM is exactly the gravitational wave signal and thus the most i
\end{figure}
\noindent
During the time at LIGO Hanford, some of the work has been devoted on the optimization of the time spent by cavities in resonance, using a new concept based on the communication between the optics and the platforms where they are placed.\\
During the time at LIGO Hanford, some of the work has been devoted to the optimization of the time spent by cavities in resonance (i.e. the duty cycle), using a new concept based on the communication between the optics and the platforms where they are placed.\\
\noindent
As we will see, time in stable mode is crucial to assure higher chances of detection of gravitational-wave candidates. Small disturbances during the operational mode can compromise the detector while observing, losing stabilization (locking). This means that operators need to spend time to lock the instrument again and reset it in observing mode, time that is precious and that could instead be spent detecting events.\\
As we will see, time in stable mode is crucial to assure higher chances of detection of gravitational-wave candidates. Small disturbances during the operational mode can compromise the detector while observing, losing stabilization (lock). This means that operators need to spend time to lock the instrument again and reset it in observing mode, time that is precious and that could instead be spent detecting events.\\
This work in particular intends to give a contribution to the improvement of the sensitivity and stabilization of LIGO at low frequencies.
The sensors dedicated to measure the seismic motion need to account for horizontal, vertical and tilt displacements in all degrees of freedom in order to be efficient: the technology for their improvement is currently pushing and competing on sensing as low seismic motion as possible. On an interferometric detector, seismic motion affects the stabilization of the supports where the optics lie. This produces unwanted noise at low frequencies (< 30 Hz), which reduces the sensitivity of the detector.\\
During the first year of my PhD studies, I investigated the use of optical levers to reduce tilt motion: a device has been built at UoB, and tested at the Albert Einstein Institute (AEI) in Hannover in June 2019.\\
The content of this chapter has been re-adapted from my MCA report \cite{mca}. A poster about this project has been presented at the LVK meeting in Maastricht (September 2018) \cite{poster2}.
The content of this chapter has been re-adapted from my Mid-term report \cite{mca}. A poster about this project has been presented at the LVK meeting in Maastricht (September 2018) \cite{poster2}.
\section{Inertial sensors affected by tilt-coupling}
There are many contributions affecting aLIGO sensitivity at low frequency. One of the most investigated is the tilt of HAM vacuum chamber of ISI platforms, which dominates above 1 Hz \cite{lantz}.\\
...
...
@@ -17,7 +17,7 @@ However, there is a possible way to measure angular displacements of the benches
\end{figure}
\paragraph*{Horizontal sensors}
One of the most important problems, in order to achieve good isolation, is the sensitivity of the horizontal sensors to rotation. If we could independently measure the rotation, we could calculate the true translation motion.\\
One of the most important problems, in order to achieve good isolation, is the sensitivity of the horizontal sensors to rotation. If we could independently measure the rotation, we could calculate the true translational motion.\\
\begin{figure}[h!]
\centering
...
...
@@ -94,7 +94,7 @@ Since we have a factor $\omega^2$ at the denominator, it has more contributions
When the seismometer is tilted, its sensitivity to angles increases as $g /\omega^2$. So, if we have some sort of seismic system measuring ground motion with horizontal seismometers, we could in principle measure this contribution and remove it by subtracting from the transfer function.
\paragraph*{Vertical sensors}
If we are dealing with vertical sensor, referring to Fig. \ref{v}, in presence of tilt we have:
If we are dealing with vertical sensors, referring to Fig. \ref{v}, in presence of tilt we have:
\begin{equation}
\centering
...
...
@@ -123,9 +123,9 @@ When the optic is tilted by an angle $\theta$, we have the situation illustrated
\end{figure}
\noindent
What if we have both horizontal and vertical seismometers on the same bench, as on aLIGO? In this case, we have two instruments that are sensitive to horizontal and vertical ground motion at the same time. When the bench is tilted, they are tilted at the same time of the same angle, but they are not affected in the same way, as we have seen, but we are not able to deduce the tilt motion at low frequency because of the limitations given by the sensors noises.\\
What if we have both horizontal and vertical seismometers on the same bench, as on aLIGO? In this case, we have two instruments that are sensitive to horizontal and vertical ground motion at the same time. When the bench is tilted, they are tilted at the same time of the same angle, but they are not affected in the same way, as we have seen, but we are not able to deduce the tilt motion at low frequency because of the limitations given by the sensor noises.\\
\noindent
If could measure both vertical and horizontal motions and decouple the contribution of the tilt for the horizontal one, we could know exactly the amount of corrections the actuators have to perform.\\
If we could measure both vertical and horizontal motions and decouple the contribution of the tilt for the horizontal one, we could know exactly the amount of corrections the actuators have to perform.\\
With optical lever systems we can measure the angle of the tilt, even if it is extremely small: in this way we could be able to directly measure the tilt angle $\theta$ and apply corrections to the horizontal sensor through a dedicated active system.\\
\noindent
...
...
@@ -139,7 +139,7 @@ The device described in this chapter should involve sensing and actuation for th
\end{figure}
\noindent
The purpose when thinking of interferometers is to help reducing the RX motion on the HAM chambers that propagates into the suspensions.
The purpose when thinking of interferometers is to help reducing the RX motion on the HAM chambers that propagates into the suspensions, proving a displacement of the suspension point and hence introducing noise in the cavities.
\section{Experiment design}
In order to understand the feasibility of the project in terms of performance, we have to estimate the noise budget and the sensitivity of the system.\\
...
...
@@ -165,7 +165,7 @@ When light is incident on the sensor, a photocurrent $I$ is detected by each qua
\begin{figure}[h!]
\centering
\includegraphics[scale=0.6]{images/quad.PNG}
\caption[QPD segmented details for beam position detection]{View of the segmented photodiode. Each quadrant Q receives a photocurrent which is the signal responsible for any displacement detection: depending on which quadrant is receiving more or less photocurrent, it is possible to derive the position of the beam onto the active area.}
\caption[QPD segmented details for beam position detection]{View of the segmented photodiode. Each quadrant Q receives a photocurrent which is the signal responsible for any displacement detection: depending on which quadrant is receiving more or less photocurrent, it is possible to derive the position of the beam on the active area.}
\label{j}
\end{figure}
...
...
@@ -377,7 +377,7 @@ T = 1.47 \times 10^{-12} \frac{W}{\sqrt{Hz}}.
\end{equation}
\subsection{Resolution}
Now that we have extracted the noise budget of our system, we can determine the sensitivity $\alpha$ of the sensor. This means that we want to know the efficiency of our system in measuring angles (in rad/$\sqrt{Hz}$).\\
Now that we have extracted the noise contributions to our system, we can determine the sensitivity $\alpha$ of the sensor. This means that we want to know the efficacy of our system in measuring angles (in rad/$\sqrt{Hz}$).\\
So, according to the block diagram in Fig. \ref{BD}, to obtain the angular measurement we have that:
\begin{equation}
...
...
@@ -418,7 +418,7 @@ In order to obtain a plot of the noise budget for the optical lever prototype, w
\end{itemize}
\noindent
The optical lever performance reported in \cite{sina} takes into account the motion along x axis, the spot displacement of the beam on the photodiode and the displacement of the photodiode itself.\\
The optical lever performance reported in \cite{sina} takes into account the motion along the x axis, the spot displacement of the beam on the photodiode and the displacement of the photodiode itself.\\
The differential Z motion is given by the difference between the z motion measured by the GS13 sensors on HAM4 and HAM5:
\begin{equation}
...
...
@@ -427,11 +427,11 @@ The differential Z motion is given by the difference between the z motion measur
\end{equation}
\noindent
The contribution from the GS13 needs to be manipulated to give rad/$\sqrt{Hz}$: this is done converting to measured velocity to displacement.
The contribution from the GS13 needs to be manipulated to give rad/$\sqrt{Hz}$: this is done converting the measured velocity to displacement.
\noindent
All the noise sources are divided by the lever arm, in order to obtain an estimation in radians.\\
A low pass filter (LP) at 1 Hz is applied to the BRS motion and a high pass filter (HP) is applied to the $\Delta Z$ motion at 0.1 Hz: we use the filters to estimate the motion, since we know that the measured signals are limited by noise where we are applying the filters.\\
Summing all the noise elements in quadrature, we have the total noise performance of the optical lever, which is shown in the plot in Fig. \ref{oplevnoise}: the plot shows that the improvements that optical levers can give are limited to a restricted range of frequencies and that they suffer the differential Z motion contribution below 0.1 Hz. Given the technical difficulties of developing and installing optical levers (see following sections), the effort would only be worthwhile if the Z motion was improved via better sensors.
Since all noises are independent from each other, summing all the elements in quadrature, we have the total noise performance of the optical lever, which is shown in the plot in Fig. \ref{oplevnoise}: the plot shows that the improvements that optical levers can give are limited to a restricted range of frequencies and that they suffer the differential Z motion contribution below 0.1 Hz. Given the technical difficulties of developing and installing optical levers (see following sections), the effort would only be worthwhile if the Z motion was improved via better sensors.
\caption[In vacuum QPD test: 30 mbar]{QPD signals during 30 mbar pressure conditions. It is noticeable a difference of two orders of magnitude with respect to the in-air condition. This is due to the reduced impact of air flows and dust on the beam path.}
\label{QPD}
\end{figure}
\noindent
The movement of South bench along z axis is used as a reference to monitor the bench adjustments with temperature variations. The variable under examination is displacement tested by a Linear Variable Displacement Transformer (LVDT).
The movement of the South bench along z axis is used as a reference to monitor the bench adjustments with temperature variations. The variable under examination is displacement tested by a Linear Variable Displacement Transformer (LVDT).
\subsection{Final vacuum set up}
The pressure has been set at 5 $\times$ 10$^{-3}$ mbar. What we expect is to find no variations in terms of the peaks we think are due to power fluctuations. Variations in LVDT trend can be due to temperature stabilization and related variations of pitch and yaw are then due to the more stable bench conditions (Fig. \ref{LVDT_FIN}).\\
The pressure has been set at 5 $\times$ 10$^{-3}$ mbar. What we expect is to find no variations in terms of the peaks we think are due to power fluctuations of the laser. Variations in LVDT trend can be due to temperature stabilization and related variations of pitch and yaw are then due to the more stable bench conditions (Fig. \ref{LVDT_FIN}).\\
\noindent
In this conditions, also the signals from the L4C seismometers and accelerometers (Watt's Leakage) placed on the Central bench have been measured (Fig. \ref{central}). The plots with the UoB electronics show that there is some leakage below 10 Hz, probably due to saturation, in the measurement of the accelerometers.\\
In this condition, also the signals from the L4C seismometers and accelerometers (Watt's Leakage) placed on the Central bench have been measured (Fig. \ref{central}). The plots with the UoB electronics show that there is some leakage below 10 Hz, probably due to saturation, in the measurement of the accelerometers.\\
\noindent
QPD performance is shown in the plots \ref{qpd_fin}. With AEI boxes we had expected results: no variations in the power fluctuation peaks and expected behaviour of pitch and yaw.\\
...
...
@@ -575,7 +575,7 @@ However, with UoB pre-amp the measurements do not seem consistent with what we e
\begin{figure}[h!]
\centering
\includegraphics[scale=0.25]{images/LVDT_T.PNG}
\caption[Different pre-amps test: bench LVDT motion]{Bench motion long z axis during the vacuum pump from 30 mbar to 5 $\times$ 10$^{-3}$ mbar pressure conditions. Pressure has been set at 30 mbar at first stage to let temperature to stabilize faster. The two-step vacuum procedure was a good idea: it accelerated the lowering of temperature by two times.}
\caption[Different pre-amps test: bench LVDT motion]{Bench motion along z axis during the vacuum pump from 30 mbar to 5 $\times$ 10$^{-3}$ mbar pressure conditions. Pressure has been set at 30 mbar at first stage to let temperature to stabilize faster. The two-step vacuum procedure was a good idea: it accelerated the lowering of temperature by two times.}
