@@ -53,7 +53,7 @@ Other ways to improve duty cycle is to increase the observable volume: this can
\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 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}.\\
In particular, during O3 run, it was observed that the chambers in the corner station (CS) show differential seismic motion with respect to each other \cite{technote1}, because they move independently from each other with respect to ground. It is reasonable to think that if the chambers could have a synchronized motion, the whole interferometer would move following the ground motion, without being affected by it. This would in principle help the cavities to be stable and to maintain the resonance. In case of lock losses due to large earthquakes or high wind, stable resonance could be achieved in shorter times \cite{biswas}.\\
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.
\footnotetext{For a full understanding of the legend, refer to Appendix C.}
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@@ -253,14 +253,14 @@ which is what we expect to be the signal of the differential motion sensed by th
\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 performance 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\footnote{This definition arises from the need to accounting for unconditional loop stability and noise contributions. For details about blending filters, refer to \cite{kisselthesis}.}, we can write it as:
If by definition we have L+H=1\footnote{This definition arises from the need to account for unconditional loop stability and noise contributions. For details about blending filters, refer to \cite{kisselthesis}.}, 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 orders of magnitude 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 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.\\
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@@ -303,7 +303,7 @@ Figure \ref{t240_inj} shows the T240 signal and its contributors.
\begin{figure}[h!]
\centering
\includegraphics[scale=0.3]{images/t240inj.png}
\caption[BSC contributions]{Plot of all the single BSC contributions computed from the inertial sensor involved in this chamber. We are certain that the T240 is dominated by tilt effects below 80 mHz, and by sensor-noise at higher frequencies: the $\theta_p$ contribution is the $T240_{inj}$ signal below 80 mHz. We interpolated these two bands together to determine an effective input disturbance from the T240.}
\caption[BSC contributions]{Plot of all the single BSC contributions computed from the inertial sensor involved in this chamber. We assume that the T240 is dominated by tilt effects below 80 mHz, and by sensor-noise at higher frequencies: the $\theta_p$ contribution is the $T240_{inj}$ signal below 80 mHz. We interpolated these two bands together to determine an effective input disturbance as witnessed by the T240.}
\label{t240_inj}
\end{figure}
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@@ -352,7 +352,7 @@ Fig. \ref{cost} shows the cost and its rms obtained with the best blending filte
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
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. We believe that the ground translation at low-frequencies is the same everywhere in the CS, and we already estimate the tilt separately, so the terms involving $x_g$ can be considered coherent. Noises are instead, by definition, independent from each other. The previous equations then become:
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. We assume that the ground translation at low-frequencies is the same everywhere in the CS, and we already estimate the tilt separately, so the terms involving $x_g$ can be considered coherent. Noises are instead independent from each other. The previous equations then become:
@@ -460,9 +460,9 @@ 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 the DARM signal below 0.1 Hz when all the chambers inside and outside the CS were locked (Fig. \ref{darmtest}).
\noindent
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. Some effects of this configuration have been testified even by IMCL, during a measurement in on/off offloading, reported in the LHO logbook post 52690. Other tests looking at the effect on the LSC cavities are reported in post 52729 of LHO logbook.\\
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. Some effects of this configuration have been testified even by IMCL, during a measurement in on/off offloading, reported in the LHO logbook post 52690. Other tests looking at the effect on the LSC cavities are reported in post 52729 of the LHO logbook.\\
\begin{figure}[h!]
\centering
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@@ -488,7 +488,7 @@ What we expect is a faster reach of locking and a longer state of lock of the in
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.
Through CPSs locking, we reduced the differential motion of HAM2 and HAM3 chambers and made them 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 to 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, whose optics are suspended 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.
\begin{figure}[h!]
\centering
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@@ -501,7 +501,7 @@ The same work is foreseen to be done for the other cavities: the very short peri
\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} illustrates the simplified concept of the PR cavity connected to the ISIs of the block of HAM2 and HAM3 chambers \footnote{Some insights about the shape of the transfer function of the suspensions are in Appendix C.}.\\
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.
The work done in this case is similar to the one done for the HAM chambers, except for 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.
\chapter{Laser stabilization for 6D isolation system device}
In this chapter I will introduce the 6D device, a new technology for inertial isolation. This project was presented to the scientific community at the 10th ET Symposium in 2019 \cite{poster}. My contribution to the development of this technique focused on the sensing side: a laser will be injected into the device and will need to be stabilized in frequency for a low-noise readout of the sensing system at lower frequencies. To do it, we propose a new technique based on compact interferometry.\\
\chapter{Laser frequency stabilization for 6D isolation system device}
In this chapter I will introduce the 6-Dimension (6D) device, a new technology for inertial isolation. This project was presented to the scientific community at the 10th ET Symposium in 2019 \cite{poster}. My contribution to the development of this technique focused on the sensing side: a laser will be injected into the device and will need to be stabilized in frequency for a low-noise readout of the sensing system at lower frequencies. To do it, we propose a new technique based on compact interferometry.\\
The experiment was built and tested in-depth: the laser stabilisation results were limited by excess noise in the sensors and many tests were made to identify and reduce noise. During these tests, it was determined that one of the devices was intrinsically noisier than the other.\\
This work was done entirely at UoB: the design of the project was conducted in 2020, while the experiment was built and tested from September 2020, when the University allowed the return to the laboratory, to July 2021.
\section{6D inertial isolation system overview}
The 6D inertial isolation system is a device based on a new technology under development at University of Birmingham and at Vrije Univestiteit in Amsterdam, which could enable detection of gravitational waves below 10 Hz \cite{6d}. We have already seen the importance for this frequency window to be opened (chap 2): this sensor could be installed on 2nd generation Earth-based interferometers, with major upgrades, on or under ground, allowing the different instruments to easily use the same device.\\
As the name reminds, the 6D investigates the motion of a reference mass in all 6 degrees of freedom, using 6 interferometers. In Fig. \ref{6d} it is shown a sketch of the design of the facility. \\
As the name reminds, the 6D system investigates the motion of a reference mass in all 6 degrees of freedom, using 6 interferometers. In Fig. \ref{6d} it is shown a sketch of the design of the facility. \\
\begin{figure}[h!]
\centering
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@@ -33,9 +33,9 @@ As the name reminds, the 6D investigates the motion of a reference mass in all 6
\noindent
All six degrees of freedom are simultaneously low-noise, reducing the cross-coupling affecting low force-noise measurements.\\
The reference mass, suspended from a single, thin, fused-silica fibre, provides supports in the vertical (Z) degree of freedom. An interferometric readout and control are used in all 6 degrees of freedom.\\
The major advantages is that this system can improve sensitivity, thermal noise, and tilt-to-translation coupling, providing isolation in all the degrees of freedom with the use of only one device. Currently aLIGO is seismically isolated by three seismometers and twelve geophones \cite{lisa}: the use of the 6D would replace three seismometers and six geophones on Stage 1 of the chambers.\\
The major advantages is that this system can improve sensitivity, thermal noise, and tilt-to-translation coupling, providing isolation in all the degrees of freedom with the use of only one device. Currently aLIGO is seismically isolated by three seismometers and twelve geophones \cite{lisa}: the use of the 6D device would replace three seismometers and six geophones on Stage 1 of the chambers.\\
\noindent
What we expect from 6D is isolation at low frequencies and reduction of fundamental noises: the thermal noise of the suspension is suppressed by the quasi-monolithic, fused-silica fibre; temperature gradients are kept under control thanks to the vacuum enclosure.\\
What we expect from the 6D system is isolation at low frequencies and reduction of fundamental noises: the thermal noise of the suspension is suppressed by the quasi-monolithic, fused-silica fibre; temperature gradients are kept under control thanks to the vacuum enclosure.\\
The expected performance is shown in Fig. \ref{6dsens}: the 6D isolator provides an improvement of the performance of more than two orders of magnitude with respect to what is possible with state of the art seismometers \cite{6d}.\\
The key point is to reduce the motion in order to limit the control noise and allow the bandwidth of control loops to be lowered. This is a goal set for a detector sensitive to low frequencies, and for which the 6D device can contribute \cite{yu}.
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@@ -124,7 +124,7 @@ To minimise airflows, the optical setup has been enclosed into a box made of foa
\paragraph*{Opto-mechanical design}
The optical layout is shown in Fig. \ref{las}: the two lasers have a twin optical layout. There is a Faraday Isolator (FI) at each output and then a 1 to 4 fibre beam splitter (BS) which separates the beam into 4 outputs of equal power: 3 outputs go into the vacuum chamber (for a total of 6 laser inputs, one for each 6D HoQI into the vacuum chamber). The remaining output is sent through a fibre coupler to a Schafter-Kirchhoff collimator and gives an output of about 1.2 mW for each laser; this proceeds freely on the breadboard towards a 1 inch, 10/90 (R/T) beam splitter: 10$\%$ of the light is sent to a fast DC coupled 125-MHz photoreceiver (PD) acted to sense the beat-note of the two lasers; two 1 inch mirrors deviate one of the two laser beams towards the transmitting surface of another 1 inch beam splitter, which combines the light from both lasers towards the photoreceiver; the other 90$\%$ of it is sent to the HoQIs, one for each laser. The optical path lengths (OPL) have been set to be equal, to assure the same beam size from both lasers at the photoreceiver.\\
The photoreceiver has strict constraints about the beam size and the input power: a focussing lens in front of the active area assures that the beam size is suitable to fit the 0.3 mm active area. Neutral density damping filters are added along the OPL, because the maximum input power of the device is 55 $\mu$W.\\
The whole optical setup lies on the bradboard and it is relatively easy to align because all the optomechanical components have been manufactured to make the beams out of the collimator to travel at the same height as HoQI components and the photoreceiver, so that there is no need of pitch tuning.
The whole optical setup lies on the breadboard and it is relatively easy to align because all the optomechanical components have been manufactured to make the beams out of the collimator to travel at the same height as HoQI components and the photoreceiver, so that there is no need of pitch tuning.
\begin{figure}[h!]
\centering
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@@ -134,7 +134,7 @@ The whole optical setup lies on the bradboard and it is relatively easy to align
\end{figure}
\paragraph*{HoQI design}
HoQIs for 6D laser stabilization have been built to fit the requirements, as shown previously: the adjustable arm-length mismatch is of 10 cm; the photodiodes have a bigger active area with respect to the one of the HoQIs inside the 6D vacuum chamber, because the laser spot size is larger than the one travelling into the 6D device. Moreover, this type of HoQI is independent from any inertial sensor, so both the arms end with mirrors on steering mounts, and instead of corner cubes use to for the A+ devices. Table \ref{hoqi} shows other small details that have been adapted for this experiment.\\
HoQIs for 6D laser stabilization have been built to fit the requirements, as shown previously: the adjustable arm-length mismatch is of 10 cm; the photodiodes have a bigger active area with respect to the one of the HoQIs inside the 6D vacuum chamber, because the laser spot size is larger than the one travelling into the 6D device. Moreover, this type of HoQI is independent from any inertial sensor, so both the arms end with mirrors on steering mounts, and instead of corner cubes used to for the A+ devices. Table \ref{hoqi} shows other small details that have been adapted for this experiment.\\
\begin{table}[h!]
\centering
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@@ -196,13 +196,13 @@ The beat-note receiver is 15 V powered and connected to a frequency counter, and
\label{cables}
\end{figure}
\noindent
The sensing and control system of the experiment is based on the HoQIs: the software code manipulating the HOQIs signal and driving the input modulation is written with Matlab Simulink and controlled by the CDS. The controller filter has been built taking into account all the features of the loop and implemented into the CDS: the filters are shown in Fig. \ref{filter}: their performance have been tested looking at the stability of the beat-note peak when each filter is switched on, and when they are on together as the full controller filter.\\
The lasers can then be controlled via input modulation through the feedback control loop built via the CDS, where HoQIs act as the sensors.
The sensing and control system of the experiment is based on the HoQIs: the software code manipulating the HOQIs signal and driving the input modulation is written with Matlab Simulink and controlled by the CDS. The controller filter has been built taking into account all the features of the loop and implemented into the CDS: the filters are shown in Fig. \ref{filter}: their performance has been tested looking at the stability of the beat-note peak when each filter is switched on, and when they are on together as the full controller filter.\\
The lasers can then be controlled via input modulation of the current feeding the lasers, through the feedback control loop built via the CDS, where HoQIs act as the sensors.
\begin{figure}[h!]
\centering
\includegraphics[scale=0.3]{images/filter.png}
\caption[Controller filter]{Bode plot of the controller filter installed into the CDS (green) and of the closed-loop expected gain when this filter is applied (magenta). This design should push the gain from below 0.1 Hz, assuring stability when applied at lower frequencies.}
\caption[Controller filter]{Plot of the controller filter installed into the CDS (green) and of the closed-loop expected gain when this filter is applied (magenta). This design should push the gain from below 0.1 Hz, assuring stability when applied at lower frequencies.}
\label{filter}
\end{figure}
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@@ -247,7 +247,7 @@ Temperature changes are also responsible for deformations of metals; this induce
\begin{figure}[h!]
\centering
\includegraphics[scale=0.3]{images/AConoff.png}
\caption[Test of the impact of AC on the frequency stability]{Test of the impact of AC on the frequency stability. From this plot the free running frequency measured by the beat-note is compared to the frequency measured when the setup is in loop in different AC conditions: the red trace shows a measurement taken when the AC was on, during the night: the AC creates air currents, and it is also responsible for changes in the temperature of the room and of the lasers, and it can induce dust in the OPL. All these contributions are affecting the setup below 10 Hz; the black trace shows the same test with no AC: below 10 Hz the trace is much quieter. The higher noise above 10 Hz is due to the fact that this test has been taken in daylight time, and HoQIs suffered the vibrations of the building. After this test we reduced the free space OPL between the optics were possible, filled the empty spaces of the box and reduced the free space between the last optic and the beat-note photoreceiver, to reduce air flows. All the following tests have been taken with AC off.}
\caption[Test of the impact of AC on the frequency stability]{Test of the impact of air conditioning (AC) on the frequency stability. From this plot the free running frequency measured by the beat-note is compared to the frequency measured when the setup is in loop in different AC conditions: the red trace shows a measurement taken when the AC was on, during the night: the AC creates air currents, and it is also responsible for changes in the temperature of the room and of the lasers, and it can induce dust in the OPL. All these contributions are affecting the setup below 10 Hz; the black trace shows the same test with no AC: below 10 Hz the trace is much quieter. The higher noise above 10 Hz is due to the fact that this test has been taken in daylight time, and HoQIs suffered the vibrations of the building. After this test we reduced the free space OPL between the optics were possible, filled the empty spaces of the box and reduced the free space between the last optic and the beat-note photoreceiver, to reduce air flows. All the following tests have been taken with AC off.}
\label{ACtest}
\end{figure}
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@@ -285,7 +285,7 @@ This test confirms that HoQI2 is in general noisier than HoQI1, especially above
\section{Laser stabilization: tests and results}
The tests have been performed measuring the stability of the beat-note peak around the 60 Hz setpoint: the frequency counter used for this measurements is a Keysight 53230A 350 MHz - 20 ps. The output of the fast photoreceiver is DC-coupled and can be directly connected to the counter. The measurements has been recorded on a USB drive: the data provided by the counter are in frequency (Hz).\\
Several tests have been taken in different conditions for noise hunting along the frequency range of interest, the best measurements are shown in Fig. \ref{test}. The tests with the heterodyne detection revealed that the system is very sensitive to the external noise sources described above and that the two HoQIs are nor robust and stable enough to assure the stability of the loop, despite the robustness of the controller filter. The solution for reducing these noises might be placing the HoQIs in vacuum.\\
Several tests have been taken in different conditions for noise hunting along the frequency range of interest, the best measurements are shown in Fig. \ref{test}. The tests with the heterodyne detection revealed that the system is very sensitive to the external noise sources described above and that the two HoQIs are not robust and stable enough to assure the stability of the loop, despite the robustness of the controller filter. The solution for reducing these noises might be placing the HoQIs in vacuum.\\
