@@ -61,3 +61,8 @@ The transfer function of the suspensions of the PRCL cavity illustrated in the b
\label{prclm1}
\end{figure}
%\section{CPS and LSC offloading tests at LIGO: some references}
%During the study for the CPS and LSC offloading exposed in Chapter 5, several tests and changes in the models of LHO and LLO have been carried on. The details of those tests are reported in the SEI, LHO and LLO logbooks: here some useful references are reported.
@@ -20,23 +20,22 @@ In this chapter I will introduce the 6D device, a new technology for inertial is
This work has been done entirely at UoB: the design of the project has been conducted in 2020, while the experiment has been 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 at 10 Hz and below\cite{6d}. We have already seen the importance for this frequency window to be opened (chap 2): this facility can be installed on Earth-based interferometers of every type, on or under ground, allowing the different instruments to easily use the same device.\\
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 0.1 Hz\cite{6d}. We have already seen the importance for this frequency window to be opened (chap 2): this facility can be installed on Earth-based interferometers of every type, 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. \\
\begin{figure}[h!]
\centering
\includegraphics[scale=1.2]{images/6d.png}
\caption[6D design.]{Sketch of the 6D device (Figure taken from \cite{6d}). The working principle is based on a isolated, suspended reference mass which is monitored by position sensors detecting the relative motion between the ground and the platform; actuators apply corrections to the platform and the whole apparatus is in vacuum.}
\caption[6D design.]{Sketch of the 6D device (Figure taken from \cite{6d}). The working principle is based on a isolated, suspended reference mass which is monitored by compact interferometers, detecting the relative motion between the mass and the platform; actuators apply corrections to the platform and the whole apparatus is in vacuum.}
\label{6d}
\end{figure}
\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 and a metal spring, provides supports in the vertical (Z) degree of freedom. An interferometric readout provides control in the X and Y tilting degrees of freedom.\\
The interesting advantage is that this system provides 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 interesting advantage is that this system provides 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.\\
\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.\\
We expect a reduction of the platform motion at aLIGO and the bandwidth of the control loop by a factor of about 5 \cite{6d}.\\
The expected performance is shown in Fig. \ref{6dsens}: at low frequency 6D isolator provides two order of magnitude better results with respect to the current devices. The time of observation is expected to be increased from 66\% to 81\% for each detector.\\
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 control noise will become negligible above 5Hz because the bandwidth for the control loops will be reduced to 0.5 Hz.
\begin{figure}[h!]
...
...
@@ -57,7 +56,7 @@ HoQI is a compact, fibre-coupled interferometer with high sensitivity and large
\label{hoqi1}
\end{figure}
\noindent
This device has been designed to sense motion at low frequency, with a sensitivity of 2 $\times$ 10$^{-14}$ m/ $\sqrt(Hz)$ at 70 Hz and 7 $\times$ 10$^{-11}$ m/ $\sqrt(Hz)$ at 10 mHz \cite{hoqi}. This is a result obtained when combining HoQI devices to inertial sensors to create an "interferometric inertial sensor" \cite{sam}. In the frame of compact devices, HoQIs are designed to be very small in size, so can can easily be attached to sensors. They are then ideal for 6D purposes, not only for their high sensitivity, but also for their small size.
This device has been designed to sense motion at low frequency, with a sensitivity of 2 $\times$ 10$^{-14}$ m/ $\sqrt(Hz)$ at 70 Hz and 7 $\times$ 10$^{-11}$ m/ $\sqrt(Hz)$ at 10 mHz \cite{hoqi}. This is a result obtained when combining HoQI devices to inertial sensors to create an "interferometric inertial sensor" \cite{sam}. In the frame of compact devices, HoQIs are designed to be very small in size, so they can easily be attached to sensors. They are then ideal for 6D purposes, not only for their high sensitivity, but also for their small size.
\noindent
The six HoQIs used for the 6D device need to be fed by a laser source that is sent into the vacuum chamber: my project focussed on this source, specifically how to stabilize it in frequency.
...
...
@@ -72,33 +71,35 @@ The laser chosen as source for 6D is a 1064 nm RIO ORION Laser Module (see Fig.
\label{rio}
\end{figure}
\noindent
What we want from this source is a low-noise readout for the HoQIs inside the 6D tank, and thus the laser source needs to be as low noise in frequency fluctuations as possible at frequencies below 1Hz, because this is the range of frequencies where the 6D isolator is aimed to detect and control seismic noise: we are going to use two Rio Orion laser modules to obtain a frequency stabilization suitable for 6D requirements. Constraints to these requirements are mainly given by the HoQIs. For 6D readout, HoQIs are built in such a way that the arm length mismatch is L$_{6D}$$<$ 3 mm. Limitations to this number are given by BOSEM size ($\pm$ 2 mm) and the ability to adjust it, once the devices are in vacuum. Another parameter to take into account is the noise of HoQIs, which is H = 6 $\times$ 10$^{-14}$ m/$\surd{Hz}$ at about 1 Hz \cite{hoqi}. Frequency fluctuations depend on both these parameters and we want it to meet the following requirement:
What we want from this source is a low-noise readout for the HoQIs inside the 6D tank, and thus the laser source needs to be as low noise in frequency fluctuations as possible at frequencies arond 10 mHz, because this is the range of frequencies where the 6D isolator is aimed to detect and control seismic noise: we are going to use two Rio Orion laser modules to obtain a frequency stabilization suitable for 6D requirements. Constraints to these requirements are mainly given by the HoQIs. For 6D readout, HoQIs are built in such a way that the arm length mismatch is as small as practically possible, e.g. L$_{6D}$$<$ 3 mm. Limitations to this number are given by BOSEM size ($\pm$ 2 mm) and the ability to adjust it, once the devices are in vacuum. Another parameter to take into account is the noise of HoQIs, which is H = 6 $\times$ 10$^{-14}$ m/$\surd{Hz}$ at about 1 Hz \cite{hoqi}. Frequency fluctuations depend on both these parameters and we want it to meet the following requirement:
\begin{equation}
\centering
\delta f_{6D}\ll f \times\frac{H}{L_{6D}}\simeq 5000 \frac{Hz}{\surd{Hz}}.
\delta f_{6D}\ll f \times\frac{H}{L_{6D}}\simeq 5000 \frac{Hz}{\surd{Hz}},
\end{equation}\\
\noindent
where f is the laser frequency.\\
The technique we are going to adopt to stabilize the laser in frequency, as anticipated, is to use HoQIs, because we can associate frequency fluctuations to fluctuations of arm length:\\
\begin{equation}
\centering
\delta f = \frac{\delta L}{L}\cdot f,
\label{df}
\end{equation}\\
and this arm length can belong to a HoQI placed on the optical bench. The use of compact interferometers to stabilize solid-state lasers in frequency is new and allows the whole set up to be small in size. This technique, in combination with cheap laser sources, makes the set up competitive with other more expensive products.\\
and this arm length can belong to a HoQI placed on the optical bench. The use of compact interferometers to stabilize the frequency of solid-state lasers without the use of cavity locking is new and allows the whole set up to be small in size. This technique, in combination with cheap laser sources, makes the set up competitive with other more expensive products.\\
We can then apply the same relation of. eq. \ref{df} to the arm length of the HoQI used for the laser stabilization, remembering that the requirement of $\delta$f $\ll$ 5000 Hz/$\surd{Hz}$ must remain valid. So, constraints to the arm length in this case are due also to the size of the bench and the whole set up.\\ We said we want a compact setup, but the arm length of this HoQI (say L$_{stab}$) can have a wider range of sizes to fit the requirement. For example, for L$_{stab}$ = 1 m we have:\\
\begin{equation}
\centering
\delta f_{stab} = f \times\frac{H}{L_{stab}}\simeq 16 \frac{Hz}{\surd{Hz}},
\end{equation}\\
which is still much lower than the threshold.\\
which is still much lower than the threshold of 5000 Hz/$\surd{Hz}$.\\
Since we want the setup to be as much compact as possible, we need to find the lowest possible L$_{stab}$ which gives an interesting $\delta f_{stab}$, compared to the current performances of RIO Orion and the best products available.\\
In the plot in Fig. \ref{perf} there is the analysis and comparison with two of the best products available.
\begin{figure}[h!]
\centering
\includegraphics[scale=0.3]{images/perf.png}
\caption[Analysis and comparison of RIO Orion laser with other products]{Analysis and comparison of RIO Orion laser with other products and with the configuration involving HoQIs.}
\caption[Analysis and comparison of RIO Orion laser with other products]{Analysis and comparison of RIO Orion laser with other products and with the configuration involving HoQIs. For an arm mismatch of 10 cm, $\delta f_{stab}$ is still below the threshold, being 168 Hz/$\sqrt{Hz}$, still fitting the 6D requirements.}
\label{perf}
\end{figure}
\noindent
...
...
@@ -114,7 +115,7 @@ Fig. \ref{free} shows a plot of the measured frequency noise of the Rio Orion la
\section{Experiment design}
The optical set up for the stabilization of the laser source is built on a 800 mm $\times$ 650 mm breadboard: this choice allows to adjust the position of the laser source easier when the light is sent to the 6D vacuum chamber. The setup includes two RIO Orion lasers with output power 12 mW each, and a double-check of the light signal through an optical heterodyne detection: the beat frequency is monitored to assure that the two light frequencies are as much similar as possible.\\
The frequency of the lasers is tunable via temperature and input modulation: in the first case, the Thermo-Electric-Controller (TEC) is driven by a software provided by the manufacturer, while in the second case the module can be integrated to any software code to apply a modulation voltage between +4 V and - 4 V.\\
The frequency of the lasers is tunable via temperature and input modulation: in the first case, the Thermo-Electric-Controller (TEC) is driven by a software provided by the manufacturer, while in the second case the module can be integrated to any software code to apply a modulation voltage between +4 V and - 4 V: the frequency tuning efficiency with this method is around 80 MHz/V, when a sinusoidal modulation is applied at 10 kHz. From specifications, the range of tuning spans between 50 and 100 MHz/V.\\
To minimise airflows, the optical setup has been enclosed into a box made of foam.
\paragraph*{Opto-mechanical design}
...
...
@@ -130,7 +131,7 @@ 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 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 a steering mirror. 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 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, instead of corner cubes use to for the 6D sensing technique. Table \ref{hoqi} shows other small details that have been adapted for this experiment.\\
\begin{table}[h!]
\centering
...
...
@@ -164,7 +165,7 @@ In Fig. \ref{chia} there is a photo of the HoQI built for this experiment.\\
\end{figure}
\noindent
The photodiodes are Hamamatsu S2386-8K and the optical layout is similar to the one shown in the figure \ref{hoqi1}: there are commercial 0.5 inch cubic beam splitters (three polarizing and 1 non polarising) mounted on custom cubic bases, two 0.5 inch mirrors on steering mounts, one 0.5 inch $\lambda$/2 waveplate and one 0.5 inch $\lambda$/4 waveplate, both mounted on a custom base allowing them to rotate for fine tuning. The whole optical set up is placed on a 75 mm $\times$ 200 mm $\times$ 10 mm baseplate.\\
The two HoQIs have been tuned to obtain the best fringe visibility, which is 0.8 for HoQI1 and 0.6 for HoQI2. The technique used to measure the fringe visibility is based on measured power on a sin vs cos plot, once the beams have been aligned to overlap in far field and produce interference, and tuning the steering mirrors for fine alignment and the waveplates for power adjustments (Fig. \ref{fringes}).
The two HoQIs have been tuned to obtain the best fringe visibility, which is 0.8 for HoQI1 and 0.6 for HoQI2. The technique used to measure the fringe visibility is based on measured power on a sin vs cos plot, once the beams have been aligned to overlap in far field and produce interference. The plot show a \textit{lissajous} figure, which can be tuned by improving the alignment with the steering mirrors and rotating the waveplates for power adjustments. When the adjustments are optimal (same power amplitude and in quadrature phase offset), the \textit{lissajous} is a circumference\footnote{For details about the characteristic equations of HoQIs and the working principle, refer to \cite{hoqi}.}. Fig. \ref{fringes} shows the sinusoids of the HoQI photodiodes after fringe visibility optimization.
\begin{figure}[h!]
\centering
...
...
@@ -174,8 +175,7 @@ The two HoQIs have been tuned to obtain the best fringe visibility, which is 0.8
\end{figure}
\section{AC-coupled control loop}
To acquire our data, we need to connect the HoQIs and the beat-note receiver to a data acquisition system. At UoB we have 3 CDS racks and one of them is dedicated to 6D. As shown in Fig. \ref{signals}, HoQIs will need a pre-amplifier, an Anti-Aliasing (AA) device and an Analog to Digital Converter (ADC) before connecting to CDS (Fig. \ref{signals}).\\
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 lasers can then be controlled via input modulation through a feedback control loop where HoQIs act as the sensors and feedback devices for frequency stability.
To acquire our data, we need to connect the HoQIs and the beat-note receiver to a data acquisition system. At UoB we have 3 CDS racks and one of them is dedicated to 6D. As shown in Fig. \ref{signals}, HoQIs will need a pre-amplifier, an Anti-Aliasing (AA) device and an Analog to Digital Converter (ADC) before connecting to CDS (Fig. \ref{signals}).
\begin{figure}[h!]
\centering
...
...
@@ -189,16 +189,17 @@ The beat-note receiver is 15 V powered and connected to a frequency counter, and
\begin{figure}[h!]
\centering
\includegraphics[scale=0.7]{images/cables.png}
\caption[Scheme of the electronics]{Detailed scheme of the electronics designed for this experiment. The different colors of the arrows represents different types of cables. Bacardi and Peapsy are the CDS and the computer controlling it, as we named them at UoB. Differential to single ended converters (Diff2SE) are needed because the CDS supports single ended outputs while the pre-amps are double ended. The Mokulab is the device used as an oscilloscope and/or as a spectrum analyser, connected to the beat-note fast photoreceiver. Green arrows indicate power supplies. The frequency counter can be connected to a computer to acquire data or a USB drive can be inserted to save data directly from the device. The temperature modulation requires the use of a software provided by the manufacturer and installed on computers. Each laser needs its own software connection. }
\caption[Scheme of the electronics]{Detailed scheme of the electronics designed for this experiment. The different colors of the arrows represents different types of cables. Bacardi and Peapsy are the CDS and the computer controlling it, as we named them at UoB. Differential to single ended converters (Diff2SE) are needed because the CDS supports differential outputs while the pre-amps are single ended. The Mokulab is the device used as an oscilloscope and/or as a spectrum analyser, connected to the beat-note fast photoreceiver. Green arrows indicate power supplies. The frequency counter can be connected to a computer to acquire data or a USB drive can be inserted to save data directly from the device. The temperature modulation requires the use of a software provided by the manufacturer and installed on computers. Each laser needs its own software connection. }
\label{cables}
\end{figure}
\noindent
Models of our system are designed with Symulink and the controller filters is designed using the tools provided by the CDS in Birmingham laboratory (Fig. \ref{filter}).
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: since we want a frequency modulation below 0.1 Hz and a robust and stable loop at the same time, we built the filter in three different steps. The first step is to run an AC filter with a pole at 0.01 Hz, at unity gain frequency 228 Hz, to AC-couple the feedback of the lasers. Then other two filters are added at lower and higher frequencies to stabilize the gain in the bandwidth we are interested in and make the whole loop stable. 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, where HoQIs act both as the sensors and feedback devices for the frequency stability.
\begin{figure}[h!]
\centering
\includegraphics[scale=0.3]{images/filter.png}
\caption[Controller filter]{Bode plot of the controller filter installed into the CDS (blue) and of the closed-loop expected gain when this filter is applied (red). Since we want to lower the frequency noise below 1 Hz, the filter has been designed with a pole at 0.1 Hz: this design should push the gain from below 10 Hz, with the maximum gain at 0.1 Hz, assuring stability.}
\caption[Controller filter]{Bode plot of the three-step controller filter installed into the CDS (green) and of the closed-loop expected gain when this filter is applied (magenta). Since we want to lower the frequency noise below 0.1 Hz, the filter has been designed with a pole at 0.1 Hz: this design should push the gain from below 0.1 Hz, assuring stability when applied at lower frequencies. The resulting controller filter is the product of the three different filters applied.}
@@ -471,7 +471,7 @@ The prototype and its own pre-amplifying electronics have been built at UoB (Fig
\section{Test at the AEI}
The aim of the collaboration was to test the optical lever prototype in vacuum. We used the South bench of the 10 m prototype at AEI in Hannover.\\
The device and part of its electronics have been adjusted in order to match the requirements for a measurements using the CDS and facilities at AEI.\\
The device and part of its electronics have been adjusted in order to match the requirements for a measurements using a Control and Data System (CDS) and facilities at AEI.\\
The pin configuration of the QPDs has been reset because the AEI electronics is set on a different one. It has been changed to the following:\\
