@@ -25,7 +25,7 @@ Block diagrams are useful graphical instruments to describe, study and build a c
\end{figure}
\noindent
Every variable under interest at the output of each block can be evaluated by \textit{solving} the diagram. Referring to Fig. \ref{blockB}, solving a block diagram means solving the system of equations involving the variable under exam and each block. The product of the components of the block diagram give the total gain of the loop (see following sections).
Every variable of interest at the output of each block can be evaluated by \textit{solving} the diagram. Referring to Fig. \ref{blockB}, solving a block diagram means solving the system of equations involving the variable under exam and each block. The product of the components of the block diagram give the total gain of the loop (see following sections).
\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.
...
...
@@ -64,7 +64,7 @@ where z and p are the $i$th zeros and poles of the polynomial, of order $j$ and
\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:
The gain of the system is defined as the ratio between the amplitudes of the input and output, i.e. it's the absolute value of the transfer function:
\begin{equation}
\centering
...
...
@@ -84,7 +84,7 @@ The Bode plot is a graph representing the response in frequency of the magnitude
\end{equation}
\noindent
The phase is expressed in degrees (deg) and it is comoputed as:
The phase is expressed in degrees (deg) and it is computed as:
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.
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, this corresponds to$\varphi$ = -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$^{-1/2}$. 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.
Spectral densities are views of a signal in a frequency spectrum. It is a useful tool 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$^{-1/2}$. 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 ratio between the cross spectral density of the two functions and the product of the spectral densities of each function:
\chapter{Reducing differential motion of aLIGO seismic platforms}
\label{CPSdiff}
During 2019, I spent some months working on LIGO Hanford site (Washington, USA). This experience allowed me to be critically involved in the complicated life of a gravitational-wave interferometer. In particular, I was given the opportunity to study how to improve LIGO performances at low-frequency, focussing on the reduction of seismic motion of the platforms where the optics live.\\
In this chapter I will demonstrate how we can modify the software set up of LIGO in order to obtain different and possibly better performances for seismic motion stabilization, faster and longer locking mode and, ultimately, gravitational waves detections. The detailed computations included in this chapter are original and partially presented to the LIGO community and stored in LIGO DCC \cite{proposal}\cite{technote1} .\\
In this chapter I will demonstrate how we can modify the software set up of LIGO in order to obtain different and possibly better performances for seismic motion stabilization, faster and longer locking mode and, ultimately, more gravitational waves detections. The detailed computations included in this chapter are original and partially presented to the LIGO community and stored in LIGO DCC \cite{proposal}\cite{technote1} .\\
This work has been developed in collaboration with LIGO Hanford and LIGO Livingston laboratories, Stanford University, MIT and UoB and completed at UoB during 2020.\\
This chapter is partially including some technical notes I shared with LIGO collaboration and the contents of this study have been presented at conferences and workshops \cite{chiatalk}.\\
Essential information about the sections of LIGO involved in this study has been exposed in detail in Chapter \ref{LIGO}.
\section{Motivation: Duty cycle on LIGO}
Lock loss events are the main sources of preventing continuous observations for long periods of time: when light loses resonance in the cavities, a lock loss happens and the control system of the optical cavities are under effort to restore stabilization. This means that during lock loss the interferometer is no longer able to be stable and the observing time is interrupted \cite{biscans}.\\
Lock loss events are the main sources of preventing continuous observations for long periods of time: when light loses resonance in the cavities, a lock loss happens and the control systems of the optical cavities are under effort to restore stabilization. This means that during lock loss the interferometer is no longer able to be stable and the observing time is interrupted \cite{biscans}.\\
Duty cycle is one of the main topic where commissioners focus on before starting an observing run \cite{biscans}\cite{kisseltalk1}. It is needed not only to observe more gravitational waves, but also to identify noise sources and improve sensitivity \cite{biscanstalk}.\\
Since the number of detected events over a time period N(t) is proportional to the volume of Universe under observation V, the observing time t and the rate R of astrophysical sources that can occur in a certain volume:
...
...
@@ -40,7 +40,7 @@ N(t) = R\cdot V\cdot t,
\end{equation}\\
it can be seen that increasing the observing time towards a given direction, will increase the number of detected events.\\
\noindent
Other ways to spend time to improve duty cycle is instead to increase the observable volume: this can be achieved by spending time on hardware to improve sensitivity on a given frequency bandwidth \cite{kisseltalk1}.
Other ways to improve duty cycle is to increase the observable volume: this can be achieved by spending time on hardware to improve sensitivity on a given frequency bandwidth \cite{kisseltalk1}.
\begin{figure}[h!]
\centering
...
...
@@ -51,7 +51,7 @@ Other ways to spend time to improve duty cycle is instead to increase the observ
\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 motion with respect to each other \cite{technote1}. It is reasonable to think that if the chambers have a synchronized motion, the whole interferometer will move following the ground motion, and not being affected by it. This would in principle help the cavities to be stable and maintain resonance. In case of lock losses due to large earthquakes or high wind, stable resonance could be achieved in shorter times \cite{biswas}.\\
In particular, during O3 run, it was observed that the chambers in the corner station (CS) show differential motion with respect to each other \cite{technote1}. 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}.\\
On another side, reducing the differential motion between the chambers means to reduce a source of noise at low frequency (5-30 Hz), as we will show in the next section: this would improve the sensitivity of the interferometer.
\subsection{ISI stabilization}
...
...
@@ -67,7 +67,7 @@ In particular, CPS sensors are placed in every chambers at all stages: it is eas
The idea which should stabilize ISIs to follow the ground motion is to lock the chambers to each other, in order to make them move on a synchronized way, following a common motion given by a driver chamber (or block of chambers).
\paragraph*{Role of the mode cleaner}
We started our design on the chambers on the x arm. Along this direction, the Input Mode Cleaner (IMC) lies totally on HAM2 and HAM3 platforms: it can be used as a reference, or witness, of the motion between chambers, once they are locked together.\\
We started our design on the chambers on the X arm. Along this direction, the Input Mode Cleaner (IMC) lies totally on HAM2 and HAM3 platforms: it can be used as a reference, or witness, of the motion between chambers, once they are locked together.\\
%\begin{figure}[h!]
%\centering
%\includegraphics[scale=0.8]{images/IMC.png}
...
...
@@ -77,22 +77,22 @@ We started our design on the chambers on the x arm. Along this direction, the In
\noindent
In the next section we will demonstrate that CPS are good witnesses to sense differential motion and they also can be used to lock the chambers with each other.
In the next section we will demonstrate that CPS are good witnesses to sense differential motion and that they also can be used to lock the chambers with each other.
\section{Sensing differential motion via CPS}
The Capacitive Position Sensors (CPS) measure the relative motion between two stages of the isolation system. Referring to Fig. \ref{isi}, on HAM chambers they are are set between HEPI and ground, and between Stage 1 and HEPI. On BSC chambers they also measure the relative motion between Stage 1 and Stage 2. The plots is Fig. \ref{diff} show the differential motion seen by the CPS between BSC and HAM chambers: the sensors are reliable for this measurement, and they put in evidence that the HAM chambers have a more synchronized motion with respect to the motion between HAM and BSC and BSCs only. This means that the block of HAM chambers on x arm is more relatively stable and can be used as driver for the other chambers, with the mode cleaner acting as witness. We then projected the CPS of the x axis chambers to the suspension point in order to obtain PRCL and IMCL traces like as they would be sensed by the CPS. For BSCs, we decided to sum the contributions of the CPSs on stage 1 and stage 2 and to project this sum.
The Capacitive Position Sensors (CPS) measure the relative motion between two stages of the isolation system. Referring to Fig. \ref{isi}, on HAM chambers they are set between HEPI and ground, and between Stage 1 and HEPI. On BSC chambers they also measure the relative motion between Stage 1 and Stage 2. The plots in Fig. \ref{diff} show the differential motion seen by the CPS between BSC and HAM chambers: the sensors put in evidence that the HAM chambers have a more synchronized motion with respect to the motion between HAM and BSC and BSCs only. This means that the block of HAM chambers on X arm is more stable relatively to the other blocks and can be used as driver for the other chambers, with the mode cleaner acting as witness. We then projected the CPS of the X axis chambers to the suspension point in order to obtain PRCL and Input Model Cleaner Length (IMCL) traces like as they would be sensed by the CPS. For BSCs, we decided to sum the contributions of the CPSs on stage 1 and stage 2 and to project this sum to the suspension point.
\caption[CPS differential motion]{CPS differential motion between the HAM and BSC chambers along x axis. ISIs move in common, particularly in the same building. This can be confirmed by noting that the difference between two chambers is much lower than individual chambers.}
\caption[CPS differential motion]{CPS differential motion between the HAM and BSC chambers along X axis. ISIs move in common, particularly in the same building. This can be confirmed by noting that the difference between two chambers is much lower than individual chambers.}
\label{diff}
\end{figure}
\noindent
One of the main differences between the behaviour of CPS IMCL and CPS PRCL, is that the former is obviously 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 the only BSCs at frequencies below 0.02 Hz (\ref{sus}).\\
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 0.02 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.\\
...
...
@@ -106,10 +106,10 @@ Fig. \ref{sus} shows the plots of PRCL and ICML as sensed by CPS projection to t
\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 locking the HAM2 and HAM3 chambers together by feeding HAM3 a calculated differential CPS signal. This is done in practice with an additive offset to the setpoint of the HAM3 isolation control loop \cite{technote2}.\\
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}.\\
The block diagram in Fig. \ref{ham2b}, shows the structure of HAM2, where the signals from $d_{2}$ and $i_{2}$ represent the offsets given by CPS and inertial sensors \footnote{For a summary on control loops, general design and feature and how to solve a block diagram, refer to Appendix \ref{B}.}.\\
At low frequency the CPS noise is negligible because its contribution is about 10$^3$ times lower than the microseismic peak.\\
General block diagrams notations are listed in Tab. \ref{tab1}\\
General block diagrams notations used in the hereafter are listed in Tab. \ref{tab1}\\
\begin{table}[h!]
\centering
...
...
@@ -179,8 +179,9 @@ After some manipulations, and remembering that L$_2$ + H$_2$ = 1, we obtain:\\
The result in Eq. \ref{d2} is the signal to subtract to HAM3 in order to feed HAM3 a CPS differential motion; it is added to HAM3 as in the block diagram in Fig. \ref{ham3b} for HAM3. In the original configuration, without any feeding into HAM3, the block diagrams for both chambers would be identical. In this new configuration instead, there is no sensor correction and ground noise on HAM3 because they both come from the contribution from HAM2, which is the offset $d_{2}$ added to HAM3.\\
The result in Eq. \ref{xxp2} is the signal to subtract to HAM3 in order to feed HAM3 a CPS differential motion that is added to HAM3 as shown in the block diagram in Fig. \ref{ham3b}. In the original configuration, without any feeding into HAM3, the block diagrams for both chambers would be identical. With the provided feeding, instead, there is no sensor correction and ground noise on HAM3 because they both come from the contribution from HAM2, which is the offset $d_{2}$ added to HAM3.\\
\begin{figure}[h!]
\centering
\includegraphics[scale=0.8]{images/ham3B.PNG}
...
...
@@ -205,7 +206,7 @@ The differential motion will be:\\
which is what we expect to be the signal of the differential motion sensed by the CPSs. In order to see this signal, we need to put in practice the modifications of the filters involved in the loop, as shown in the following section.
which is what we expect to be the signal of the differential motion sensed by the CPSs. In order to see this signal, we need to implement the modifications of the filters involved in the loop, as shown in the following section.
\section{Analysis of feasibility}
The next step is to study how to modify the low and high pass filters in order to obtain the best performances from each one in the new configuration of the chambers \cite{technote3}. To do this, we are going to change the blending filters, i.e. those filters whose combination gives the best performance of the set low+high pass filters.\\
If by definition we have L+H=1, we can write it also as:
If by definition we have L+H=1, we can write it as:
According to the values of \textit{l} and \textit{h} we have different order of magnitudes of the binomials, which can be solved for the real part.\\
According to the values of \textit{l} and \textit{h}, we have different order of magnitudes of the binomials, which can be solved for the real part.\\
\noindent
In our case, we have two main contributions given by inertial sensors and the CPS. We will apply the high-pass filter to the GS13 and the low-pass one to the CPS.\\
To do this, we need that the specific contributions for each chamber are specified, with all the components well defined. For example, in the case of the CPS contribution, we need to define the tilt component, the CPS noise and the ground motion, which will take part into the platform motion as seen by the CPS sensor. This is because these components are independent from each other and will need to be summed in quadrature.\\
Besides, as we saw in the previous computations, we will need to apply filters: the Sensor Correction filter will be the one used on LIGO and shown in Fig. \ref{SC}; the high- and low- pass filters will be found through blending several possible filters across a certain number of \textit{l} and \textit{h} order of magnitudes, as introduced before. The best blended filter will be given by a combination of two \textit{l} and \textit{h} values at a specific blending frequency.\\
In our case, we have two main contributions given by inertial sensors and the CPS. We will apply the high-pass filter to the inertial sensors and the low-pass one to the CPS.\\
To do this, we need the specific contributions for each chamber to be specified, with all the components well defined. For example, in the case of the CPS contribution, we need to define the tilt component, the CPS noise and the ground motion, which will take part into the platform motion as seen by the CPS sensor. This is because these components are independent from each other and will need to be summed in quadrature.\\
Besides, as we saw in the previous computations, we will need to apply filters: the Sensor Correction filter will be the one used on LIGO and shown in Fig. \ref{SC}; the high- and low- pass filters will be evaluated through blending several possible filters across a certain number of \textit{l} and \textit{h} order of magnitudes, as introduced before. The best blended filter will be given by a combination of two \textit{l} and \textit{h} values at a specific blending frequency.\\
At the end of the analysis for each chamber (HAM and BSC) in isolation, we will connect the chambers via CPS and look at the results.\\
All this analysis has been performed through Matlab software.\\
...
...
@@ -271,15 +274,15 @@ All this analysis has been performed through Matlab software.\\
\end{figure}
\subsection{Contributions from CPS and inertial sensors}
To calculate the CPS signal contribution, we need the ground motion and we used the ITMY STS signal on X direction: this is going to be the same motion for every chamber, since there is only one sensor in the Corner Station to measure it, because it has been found that the ground motion is the same everywhere in the Corner Station. From this signal, we separate the contribution given by the tilt ($\theta_g$) from the microseismic frequency (0.08 Hz). Then we subtract the tilt to obtain the ground motion $x_g$ from the STS:\\
To calculate the CPS signal contribution, we need the ground motion and we used the ITMY STS signal on X direction. This is going to be the same motion for every chamber, since there is only one sensor in the Corner Station to measure it, because it has been found that the ground motion is the same everywhere in the Corner Station. From this signal, we separate the contribution given by the tilt ($\theta_g$) from the microseismic frequency (0.08 Hz). Then we subtract the tilt to obtain the ground motion $x_g$ from the STS:\\
\begin{equation}
x_g = STS - \theta_g.
\end{equation}\\
The CPS signal has been then computed summing in quadrature the contributions given by tilt, ground motion and CPS noise, and applying the sensor correction filter:\\
The CPS signal has been then computed summing in quadrature the contributions given by tilt, ground motion and CPS noise (N$_{cps}$), and applying the sensor correction filter:\\
Figure \ref{cps_inj} shows the CPS signal and all its contributions:
Figure \ref{cps_inj} shows the CPS signal and all its contributions.
\begin{figure}[h!]
\centering
...
...
@@ -289,7 +292,7 @@ Figure \ref{cps_inj} shows the CPS signal and all its contributions:
\end{figure}
\noindent
To calculate the platform motion of the BSC, we used data from the ITMX ISI along x direction. This is the signal from the T240 sensor. As before, we separate the tilt contribution ($BSC\theta_p$) from the signal and to obtain the inertial sensor contribution for the BSC chambers we sum in quadrature the contributions from tilt and T240 noise:
To calculate the platform motion of the BSC, we used data from the ITMX ISI along X direction. This is the signal from the T240 sensor. As before, we separate the tilt contribution ($BSC\theta_p$) from the signal and to obtain the inertial sensor contribution for the BSC chambers we sum in quadrature the contributions from tilt and T240 noise:
\begin{equation}
T240_{inj} = \sqrt{{BSC\theta_p}^2+{N_{T240}}^2}.
\end{equation}\\
...
...
@@ -332,7 +335,7 @@ The best combination has been found computing the orders and the blending freque
Fig. \ref{cost} shows the cost and its rms obtained with the best blending filters for BSC and HAM chambers.
\begin{figure}[h!]
...
...
@@ -344,29 +347,10 @@ Fig. \ref{cost} shows the cost and its rms obtained with the best blending filte
\end{figure}
\subsection{Locking 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 these chambers. We recall here that the equations we need are:
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. The differential motion was:
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
For the analysis of this section, we need to know which terms of these equations are coherent, in order to separate them from the incoherent ones, which will need to be summed in quadrature. Since we know that the ground motion is the same everywhere in the Corner Station, the terms involving $x_g$ are coherent. Noises are instead, by definition, independent from each other.\\
What we need to know is which terms of these equations are coherent, in order to separate them from the incoherent ones, which will need to be summed in quadrature. Since we know that the ground motion is the same everywhere in the CS, the terms involving $x_g$ are coherent. Noises are instead, by definition, independent from each other.\\
The previous equations then become:
\begin{equation}
\centering
...
...
@@ -386,7 +370,7 @@ Since L$_3$ = L$_2$ and H$_2$=H$_3$:
The plot in Fig. \ref{diffham} shows the differential motion of HAM2 and HAM3 in isolation, and Fig. \ref{cpsdiff} shows motions of the chambers when locked to each other and their differential motion. The improvement of the differential motion is evident below 0.1 Hz, but it is not convenient above this frequency: in this case, further studies of the blending filters involved could help to find a compromise.
The plot in Fig. \ref{diffham} shows the differential motion of HAM2 and HAM3 in isolation, and Fig. \ref{cpsdiff} shows motions of the chambers when locked to each other and their differential motion. The improvement of the differential motion is evident below 0.1 Hz, but it is not convenient above this frequency: further studies of the blending filters involved could help to find a compromise.
The computation of the differential motion between HAM2 and HAM3 in the conditions where the two ISIs are connected both via CPS and inertial sensors shows that there is no contribution from the sensor correction and from the ground noise.\\
Besides, it is worth notice that if L$_2$ = L$_3$, also H$_2$=H$_3$ by definition and the differential motion is:\\
Besides, it is worth notice that if L$_2$ = L$_3$, also H$_2$=H$_3$ by definition and then the differential motion is:\\
\begin{equation}
\centering
\begin{split}
...
...
@@ -467,9 +451,9 @@ which is exactly the solution that we would obtain if the differential motion wa
\section{Test on LIGO Hanford and LSC signals optimization}
During the 2019 commissioning break, in collaboration with LIGO Livingston Observatory, we tried to apply the new CPS configuration in order to obtain improvements in ISI motion and LSC signals at LIGO Hanford.\\
This test has been performed before the detailed analysis exposed previously and hence a more detailed and precise study for the choice of the blending filters involved is essential to get the expected enhancements; however the preliminary tests at LHO showed an improvement of a factor of 3 at 60 mHz (Fig. \ref{isitest}), as detected by the IMC sensors, and an encouraging result detected by DARM cavity below 0.1 Hz when all the chambers inside and outside the CS were locked (Fig. \ref{darmtest}).
This test has been performed before the detailed analysis exposed previously and hence a more detailed and precise study for the choice of the blending filters involved is essential to get the expected enhancements. However the preliminary tests at LHO showed an improvement of a factor of 3 at 60 mHz (Fig. \ref{isitest}), as detected by the IMC sensors, and an encouraging result detected by DARM cavity below 0.1 Hz when all the chambers inside and outside the CS were locked (Fig. \ref{darmtest}).
\noindent
This is an interested result that shows that with the implementation of the correct filters as shown in the analysis it is possible to reduce the differential motion of the platforms.\\
This is an interesting result that shows that with the implementation of the correct filters as shown in the analysis it is possible to reduce the differential motion of the platforms.\\
\begin{figure}[h!]
\centering
...
...
@@ -486,13 +470,13 @@ This is an interested result that shows that with the implementation of the corr
\end{figure}
\noindent
With this in mind, a positive consequence of this effect might be the improvement of the LSC signals from LIGO cavities. Among them, DARM is particularly important, because it represents the gravitational wave signal. It might be convenient to make the optics of the LS cavities, lying on the platforms and subjected to the ISI motion, be controlled by the ISI itself. This ideas has been developed and tested at LHO and is exposed in the following section.
With this in mind, a positive consequence of this effect might be the improvement of the LSC signals from LIGO cavities. Among them, DARM is particularly important, because it represents the gravitational wave signal. It might be convenient to make the optics of the LSC cavities, lying on the platforms and subjected to the ISI motion, be controlled by the ISI itself. This ideas has been developed and tested at LHO and is exposed in the following section.
\subsection{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, 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. Despite there is a sort of benefit as testified by Fig. \ref{darmtest}, the motion of the optics on the chambers due to other factors than seismic noise 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.\\
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, 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. Despite there is a sort of benefit as testified by Fig. \ref{darmtest}, the motion of the optics on the chambers due to other factors than seismic noise 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 Hanford during the commissioning break between O3a and O3b observing runs, in October and November 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.\\
This work has been performed on LIGO Hanford in October and November 2019, during the commissioning break between O3a and O3b observing runs. 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
To lock the LSC signals to ISIs, we need to do something similar to what we did with the HAM chambers: we need to connect via software two different setups which do not talk to each other. We decided to start from the Power Recycling Cavity Length (PRCL) because we locked HAM2 and HAM3 chambers, so it was natural to start to lock the cavities on the x axis.\\
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 of interest in this study.
...
...
@@ -504,10 +488,10 @@ Through CPSs locking, we reduced the differential motion of HAM2 and HAM3 chambe
\label{chamb}
\end{figure}
\noindent
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 the 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.
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. Moreover, during the 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. Despite these challenges, the results obtained are encouraging and validated the analysis of feasibility exposed.
\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 is going to communicate with the ISI (refer to Chapter \ref{LIGO} for details on the PR cavity). The block diagram in Fig. \ref{prcl} illustrate the simplified concept of the PR cavity connected to the ISIs of the block of HAM2 and HAM3 chambers.\\
We need to connect the ISI to the cavity and to do it we need to know how the PR cavity is going to communicate with the ISI (refer to Chapter \ref{LIGO} for details on the PR cavity). The block diagram in Fig. \ref{prcl} illustrates the simplified concept of the PR cavity connected to the ISIs of the block of HAM2 and HAM3 chambers.\\
The work done in this case is similar to the one done for the HAM chambers, except from the fact that a new filter needs now to be built in order to control how the ISI affect the motion of the PRC optics.
\begin{figure}[h!]
...
...
@@ -517,7 +501,7 @@ The work done in this case is similar to the one done for the HAM chambers, exce
\label{prcl}
\end{figure}
\noindent
This block diagram has been solved with Mathematica in order to find the correct crossover filters to add. The system was simulated via Matlab and includes information from calibration filter modules, PRM control filters, and HSTS models via the calibration filters. This is needed to simulate the addition of the ISI as a PRCL actuator. The aim is to offload low-frequencies to the ISI and hence we need to decide the best configuration of gains and offsets of the crossover filter.\\
This block diagram has been solved with Mathematica in order to find the correct crossover filters to add. The system was simulated via Matlab and includes information from calibration filter modules, PRM control filters, and HAM Small Triple Suspension (HSTS) models via the calibration filters. This is needed to simulate the addition of the ISI as a PRCL actuator. The aim is to offload low-frequencies to the ISI and hence we need to decide the best configuration of gains and offsets of the crossover filter.\\
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.
Most of the work exposed in this thesis has been physically done 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: 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, and I will often refer to the information contained in this chapter 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 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.
\section{Interferometric detectors}
The interaction of gravitation waves with two objects moving along the x axis produces effects on their distance $d = x_2- x_1$:
...
...
@@ -11,7 +11,7 @@ s \simeq d \left(1 + \frac{1}{2}h_+ \cos \left[\omega \left(t-\frac{z}{c}\right)
\end{equation}
\\
\noindent
So the effect of the gravitational waves can be observed on the distance of the masses involved. A method is to measure the time it takes for light to travel from one mass to the other: this is the basic principle of the \textit{interferometer}.
So the effect of the gravitational waves can be measured 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!]
\centering
...
...
@@ -21,8 +21,8 @@ So the effect of the gravitational waves can be observed on the distance of the
\end{figure}
\noindent
As shown in Fig. \ref{itf}, an interferometer is an instrument where a laser beam of wavelength $\lambda$ is split into two beams which propagate in two perpendicular arms of the same length. At the end of each arm, a mirror reflects the beam back to be recombined with the other one. The recomposed beam is then deviated to a power sensor.\\
If we consider the length of arms oriented to the x and y directions to be $L_x = L_y = L$, the power measured depends on the difference of path length travelled by the two beams:
As shown in Fig. \ref{itf}, an interferometer is an instrument where a laser beam of wavelength $\lambda$ is split into two beams which propagate in two perpendicular arms of the same length. At the end of each arm, a mirror reflects the beam back to be recombined with the other one. The recombined beam is then deviated to a photodiode.\\
If we consider the length of arms oriented to the x and y directions to be $L_x = L_y = L$, the power measured depends on the difference of path length between the two beams:
\begin{equation}
\centering
...
...
@@ -39,7 +39,7 @@ We know that the effect of a gravitational wave is to modify the distance of two
\end{equation}
\noindent
and so the key feature of this detector is that the beam coming from the recombination of the two ones that travelled in the arms brings a phase difference:
and hence the key feature of this detector is that the beam coming from the recombined beam brings a phase difference:
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 method to increase the length of the arms is to make the laser beam travel back and forth into a cavity delimited by two mirrors, called \textit{Fabry-Perot cavity}: here, the optical path length will be longer, due to the multiple reflections, and the field amplitude will increase due to constructive interference. This process returns a longer 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 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, and the field amplitude will increase due to constructive interference. 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):
\begin{equation}
\centering
...
...
@@ -78,10 +78,10 @@ The higher is F, the higher is the effective length of the cavity and higher is
\section{Advanced LIGO}
The ambition of this work is to give 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).\\
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 cavities, 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 instrument design is extremely intricate in its details: this thesis will provide technical information useful for the understanding of the work made on specific sections of aLIGO.
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 instrument design is extremely intricate in its details: this thesis will provide technical information useful for the understanding of the work made on specific sections of aLIGO.
\begin{figure}[h!]
\centering
...
...
@@ -96,7 +96,7 @@ There are two LIGOs in the USA, one in Hanford (WA) and one in Livingston (LA):
\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.
Fig. \ref{sens} shows the sensitivity of LIGO during the first observation run with the main noises shown.
Fig. \ref{sens} shows the sensitivity of LIGO during the first observation run and the main noise sources.
\begin{figure}[h!]
\centering
...
...
@@ -106,8 +106,8 @@ Fig. \ref{sens} shows the sensitivity of LIGO during the first observation run w
\end{figure}
\noindent
Advanced LIGO can be tuned to adjust the frequency band of detection: for each operational mode and detection frequency band there is a gravitational wave source candidate, typically mergers of neutron stars (NS-NS) and black holes (BH-BH).\\
Noise sources make LIGO blind in some frequency windows: technological limitations can be in principle overcome thanks to improvements in science, and this is what this present work is aiming to offer. The most important noise sources for LIGO are shown in the noise budget for LIGO Hanford (LHO) in Fig. \ref{lho}.
Advanced LIGO can be tuned to adjust the frequency band of detection: for each operational mode and detection bandwidth there is a gravitational wave source candidate, typically mergers of neutron stars (NS-NS) and black holes (BH-BH).\\
Noise sources make LIGO blind in some frequency windows: current technological limitations could be in principle overcome thanks to technological improvements, and this is what this present work is aiming to offer. The most important noise sources for LIGO are shown in the noise budget for LIGO Hanford (LHO) in Fig. \ref{lho}.
\begin{figure}[h!]
\centering
...
...
@@ -117,15 +117,15 @@ Noise sources make LIGO blind in some frequency windows: technological limitatio
\end{figure}
\noindent
Noises can be of fundamental, technical and environmental origin. Fundamental noises come from first principles, and they determine the ultimate design sensitivity of the instrument. They include thermal and quantum noise, and cannot be reduced without a major instrument upgrade. Quantum noises include shot noise of the sensors, causing power fluctuations, and radiation pressure forces, causing a physical displacement of the test masses. Thermal noise arises from the suspensions and the optical coatings and dominates in the 5-100 Hz frequency range.\\
Technical noises arise from electronics, control loops, charging noise and other effects that can be reduced once identified and carefully studied.\\
Environmental noises include seismic motion, acoustic and magnetic noises.\\
Noises can be of fundamental, technical and environmental origin. Fundamental noises come from first principles, and they determine the ultimate design sensitivity of the instrument. They include thermal and quantum noises, and they cannot be reduced without a major instrument upgrade. Quantum noise includes shot noise of the sensors, causing power fluctuations, and radiation pressure, resulting in a physical displacement of the test masses. Thermal noise arises from the suspensions and the optical coatings and dominates in the 5-100 Hz frequency range.\\
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, 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.
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 id to provide solutions to reduce seismic motion and improve the detector sensitivity.
\section{LIGO seismic isolation system}
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 journey 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 Chamber} (BSC). The auxiliary optics are placed on optical benches enclosed in the \textit{Horizontal Access Module} (HAM) chambers.
\begin{figure}[h!]
\centering
...
...
@@ -154,11 +154,11 @@ The BSCs have a similar design as the HAMs, but they have two stages of ISI to s
\end{figure}
\paragraph{Stabilizing the ISI}
Part of the work presented in this thesis focussed on the improvement of the performances of the active isolation system of the ISIs of both BSC and HAM chambers.\\
Part of the work presented in this thesis focussed on the enhancement of the performances of the active isolation system of the ISIs for both BSC and HAM chambers.\\
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; then this motion is 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 \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 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!]
...
...
@@ -170,13 +170,13 @@ The sensor correction loop takes the ground motion signal from an inertial instr
\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 bandwidth of observation.\\
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.\\
\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.\\
\noindent
The most important cavity lengths to keep stable are highlighted in Fig. \ref{lsc}; each length path between optics contributes to a specific signal monitored to keep the cavities in resonance. The signals are the Signal Recycling Cavity Length (SRCL), the Power Recycling Cavity Length (PRCL), the MICHelson (MICH), the Common Arm length (CARM) and the Differential Arm Length (DARM) and are described by the following relations between lengths:
The most important cavity lengths to keep stable are highlighted in Fig. \ref{lsc}; each length path between optics contributes to a specific signal monitored to maintain the cavities in resonance. The signals are the Signal Recycling Cavity Length (SRCL), the Power Recycling Cavity Length (PRCL), the MICHelson (MICH), the Common Arm length (CARM) and the Differential Arm Length (DARM) and they are described by the following relations between lengths:
In particular, DARM is exactly the gravitational wave signal and thus the most important to monitor and to keep stable.
In particular, DARM is exactly the gravitational wave signal and thus the most important one to monitor and to keep stable.
\begin{figure}[h!]
\centering
...
...
@@ -209,8 +209,8 @@ 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 focussed 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 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.\\
\noindent
As we will see, time in stable mode is crucial to assure higher chances of detection of gravitational-wave candidates and 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 (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.\\
This work in particular intends to give a contribution to the improvement of the sensitivity and stabilization of LIGO at low frequencies.
