updates: oplev and cps diff

main/A.tex

-\chapter{First detection}
+\chapter{Assembling suspension chains for A+ at LHO}
 \label{A}
\ No newline at end of file
-
-On 14th September 2015 the two LIGO antennas observed for the first time a signal from a gravitational wave produced by the merger of two black holes. This was the very first time that a merger of such massive and elusive objects could be observed.\\
-The gravitational-wave signal has been named GW150914 and has been emitted by 2 black hole of masses of 36 $M_{\odot}$ and 29 $M_{\odot}$, which merged at a distance of 410 Mpc (z = 0.09)and produced a final BH of 62 $M_{\odot}$. The remaining 3 $M_{\odot}$ have been radiated in gravitational waves. Fig. \ref{gwsig} shows the signal detected from LIGO Hanford and LIGO Livingston.\\
-This detection has been the result of a wide scientific collaboration which efforts made possible a discovery that deserved the Nobel Prize in Physics in 2017 to the pioneers of gravitational wave hunting  \textit{'for decisive contributions to the LIGO detector and the observation of gravitational waves'}.
-
-\begin{figure}
-\centering
-\includegraphics[scale=0.7]{images/outreach.png}
-\end{figure}
-
-\begin{figure}[h!]
-\centering
-\includegraphics[scale=0.77]{images/GWsignal.png}
-\caption[First detection of a gravitatonal wave signal.]{First detection of a gravitational wave signal \cite{first}. The event is shown for both observatories at the time of observation 09:50:45 UTC on 14th September 2015. The top row is the gravitational wave amplitude for Hanford (H1) and Livingston (L1). In the L1 panel, there is a visual comparison of the two signals: the wave passe through L1 first, H1 signal (in orange) is shifted by the 6.9 ms of difference, and inverted due to their mutual orientation. The second row shows the consistency of the measured signal with expectations independently computed. Third row shows the residuals after subtraction of the measured time series and the numerical waveform. Bottom row is the same signal in frequency vs time, where it is evident the increase of frequency with time.}
-\label{gwsig}
-\end{figure}
-
-\begin{figure}
-\includegraphics[scale=0.8, angle=90]{images/logos.pdf}
-\end{figure}
\ No newline at end of file

main/C.tex

+\chapter{First detection}
+\label{C}
+
+On 14th September 2015 the two LIGO antennas observed for the first time a signal from a gravitational wave produced by the merger of two black holes. This was the very first time that a merger of such massive and elusive objects could be observed.\\
+The gravitational-wave signal has been named GW150914 and has been emitted by 2 black hole of masses of 36 $M_{\odot}$ and 29 $M_{\odot}$, which merged at a distance of 410 Mpc (z = 0.09)and produced a final BH of 62 $M_{\odot}$. The remaining 3 $M_{\odot}$ have been radiated in gravitational waves. Fig. \ref{gwsig} shows the signal detected from LIGO Hanford and LIGO Livingston.\\
+This detection has been the result of a wide scientific collaboration which efforts made possible a discovery that deserved the Nobel Prize in Physics in 2017 to the pioneers of gravitational wave hunting  \textit{'for decisive contributions to the LIGO detector and the observation of gravitational waves'}.
+
+\begin{figure}
+\centering
+\includegraphics[scale=0.7]{images/outreach.png}
+\end{figure}
+
+\begin{figure}[h!]
+\centering
+\includegraphics[scale=0.77]{images/GWsignal.png}
+\caption[First detection of a gravitatonal wave signal.]{First detection of a gravitational wave signal \cite{first}. The event is shown for both observatories at the time of observation 09:50:45 UTC on 14th September 2015. The top row is the gravitational wave amplitude for Hanford (H1) and Livingston (L1). In the L1 panel, there is a visual comparison of the two signals: the wave passe through L1 first, H1 signal (in orange) is shifted by the 6.9 ms of difference, and inverted due to their mutual orientation. The second row shows the consistency of the measured signal with expectations independently computed. Third row shows the residuals after subtraction of the measured time series and the numerical waveform. Bottom row is the same signal in frequency vs time, where it is evident the increase of frequency with time.}
+\label{gwsig}
+\end{figure}
+
+\begin{figure}
+\includegraphics[scale=0.8, angle=90]{images/logos.pdf}
+\end{figure}
\ No newline at end of file

main/CPSdiff.tex

@@ -23,7 +23,9 @@
 
 \chapter{Reducing differential motion of aLIGO seismic platforms}
 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 and in the following I am going to show you in detail how we can modify the software set up of LIGO in order to obtain a different and possibly better performance. This work has been developed in collaboration with LIGO Hanford and LIGO Livingston laboratories, Stanford University, MIT and UoB, and this chapter is partially including some technical notes I shared with LIGO collaboration.
+In this chapter and I am going to demonstrate in detail how we can modify the software set up of LIGO in order to obtain a different and possibly better performance. This work has been developed in collaboration with LIGO Hanford and LIGO Livingston laboratories, Stanford University, MIT and UoB.\\
+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.\\
+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.\\
@@ -46,7 +48,7 @@ Other ways to spend time to improve duty cycle is instead to increase the observ
 \end{figure}
 
 \subsection{Differential motion between chambers}
-It has been seen that among the noise sources which contribute to lock loss events there is the ground motion (CITA), including earthquakes and microseismic events. \\
+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. 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.\\
 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.
 
@@ -96,7 +98,7 @@ Fig. \ref{sus} shows plots of PRCL and ICML by CPS projection to suspoint. These
 \centering
 \includegraphics[scale=0.3]{images/CPS_SUSPOINT_IMCL.PNG}\\
 \includegraphics[scale=0.3]{images/CPS_SUSPOINT_PRCL.PNG}
-\caption[CPS suspoint projections]{CPS suspoint projections: IMCL and PRCL. The calibrated PRCL trace used as comparison has been de-whitened.}
+\caption[CPS suspoint projections]{CPS suspension point (suspoint) projections: IMCL and PRCL. The calibrated PRCL trace used as comparison has been de-whitened.}
 \label{sus}
 \end{figure}
 
@@ -137,7 +139,7 @@ $x_{p}$ & plant motion\\
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=1]{images/ham2B.PNG}
-\caption[HAM2 simplified block diagram]{HAM2 simplified block diagram.}
+\caption[HAM2 simplified block diagram]{Simplified block diagram for HAM2 chamber as it is at present on LIGO.}
 \label{ham2b}
 \end{figure}
 
@@ -180,7 +182,7 @@ The result in Eq. \ref{d2} is the signal to subtract to HAM3 in order to feed HA
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=1]{images/ham3B.PNG}
-\caption[HAM3 simplified block diagram with HAM2 offset]{HAM3 simplified block diagram for the new configuration: d$_{2}$ is the offset coming from HAM2.}
+\caption[HAM3 simplified block diagram with HAM2 offset]{Simplified block diagram for HAM3 in the new configuration where this chamber is now connected to HAM2: d$_{2}$ is the offset coming from HAM2.}
 \label{ham3b}
 \end{figure}
 \noindent
@@ -258,14 +260,14 @@ All this analysis has been performed through Matlab software.\\
 \centering
 \includegraphics[scale=0.3]{images/SCbode.png}
 \includegraphics[scale=0.3]{images/SC.png}
-\caption[Sensor correction filter]{Sensor correction filter.}
+\caption[Sensor correction filter]{The sensor correction filter as it is at present installed on LIGO. This filter is one of the contributors to take into account for when computing the blending filters.}
 \label{SC}
 \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 (cita!!). 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.
+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:\\
 \begin{equation}
@@ -276,12 +278,12 @@ Figure \ref{cps_inj} shows the CPS signal and all its contributions:
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.3]{images/cpsinj.png}
-\caption[CPS contributions]{CPS contributions.}
+\caption[CPS contributions]{Plot of all the single CPS contributions calculated. This computation is valid for all chambers, since CPSs are installed on all chambers and are subjected to the same working principle.}
 \label{cps_inj}
 \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 fro 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}\\
@@ -290,7 +292,7 @@ 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]{BSC contributions..}
+\caption[BSC contributions]{Plot of all the single BSC contributions computed from the inertial sensor involved in this chamber.}
 \label{t240_inj}
 \end{figure}
 
@@ -304,7 +306,7 @@ Figure \ref{gs13_inj} shows the GS13 signal and its contributors:
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.3]{images/gs13inj.png}
-\caption[HAM contributions]{HAM contributions..}
+\caption[HAM contributions]{Plot of all the single HAM contributions calculated for the inertial sensor involved in this chamber.}
 \label{gs13_inj}
 \end{figure}
 
@@ -336,7 +338,7 @@ 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 document we made the computations for these chambers. Reminding the equations we need:
+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. Reminding that the equations we need are:
 \begin{equation}
 \centering
 x_{p_{2}} = H_{2}N_{i_{2}} + L_{2}SC(N_{g} + x_{g}) - L_{2}x_{g},
@@ -369,14 +371,14 @@ d_{2} = \sqrt{(N_{i_{2}}{H_2})^2 +(\theta_g\cdot SC\cdot L_2)^2} + (x_g\cdot SC\
 \end{equation}
 
 \begin{equation}
-x_{p_{3}} = \sqrt{(N_{i_{2}}{H_2})^2 + [L_3\sqrt{(N_{i_{2}}{H_2})^2 +(\theta_g\cdot SC\cdot L_2)^2}]^2} + (x_g\cdot SC\cdot L_2 + x_g\cdot H_2)\cdot L_3 - (x_g\cdot L_3),
+x_{p_{3}} = \sqrt{(N_{i_{2}}{H_2})^2 + [L_3\sqrt{(N_{i_{2}}{H_2})^2 +(\theta_g\cdot SC\cdot L_2)^2}]^2} + (x_g\cdot SC\cdot L_2 + x_g\cdot H_2)\cdot L_3 - (x_g\cdot L_3).
 \end{equation}\\
 Since L$_3$ = L$_2$ and H$_2$=H$_3$:
 
 \begin{equation}
 x_{p_{3}} - x_{p_{2}} = |\sqrt{(L_2\cdot SC\cdot \theta_g\cdot L_2)^2 - (L_2\cdot SC\cdot \theta_g)^2} +(x_g\cdot SC\cdot {L_2}^2)-(x_g\cdot SC\cdot L_2)|.
 \end{equation}.\\
-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.
+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.
 
 \begin{figure}[h!]
 \centering
@@ -387,8 +389,8 @@ Plot in Fig. \ref{diffham} shows the differential motion of HAM2 and HAM3 in iso
 
 \begin{figure}[h!]
 \centering
-\includegraphics[scale=0.3]{images/cpsdiff.png}
-\caption[HAM chambers in CPS locking condition]{HAM chambers in CPS locking condition: the plot show the motion of each chamber, where HAM3 depends on HAM2, through CPS locking, and the differential motion between them.}
+\includegraphics[scale=0.5]{images/cpsdiff.png}
+\caption[HAM chambers in CPS locking condition]{HAM chambers in CPS locking condition: the plot shows the motion of each chamber, where HAM3 depends on HAM2, through CPS locking, and the differential motion between them. There is an improvement of the differential motion in the new configuration (purple trace) with respect to the situation in isolation (green dotted trace) below 0.1 Hz (highlighted by the grey area), but above this frequency it looks not convenient.}
 \label{cpsdiff}
 \end{figure}
 
@@ -454,12 +456,26 @@ x_{p_3} - x_{p_2} &= N_{i_3}H_3 - N_{i_2} H_2\\
 &= H(N_{i_3}-N_{i_2}),
 \end{split}
 \end{equation}\\
-which is exactly the solution that we would obtain if the differential motion was computed without any feeding.
+which is exactly the solution that we would obtain if the differential motion was computed without any feeding: this means that in this configuration the differential motion would be the same as in isolation condition.
 
-\section{CPS locking set up on LIGO}
+\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 so a more detailed and precise study for the choice of the blending filters involved is essential to get the expected improvements; however the preliminary tests at LHO showed an improvement of a factor of 3 at 60 mHz, 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.
 
-\section{Beyond: LSC signals optimization on LIGO}
-A positive consequence of this work might be the improvement of the LSC signals from LIGO cavities. Among them, DARM is particularly important, because it represents the gravitational wave signal. 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 LSC signals at LIGO Hanford.\\
+\begin{figure}
+\centering
+\includegraphics[scale=1.15]{images/isi_sup.png}
+\caption[ISI motion suppression]{Screenshot from LHO CDS showing a quick measurement with the chambers in the CS were locked: the witness is the IMC and we monitored also the ground motion to make sure that no important variations were happening at the moment of the measurement. The green traces represents the motion before the locking, while we took two measurement after the locking (blue and pink) to validate the test. \textbf{Left:} motion of the suspension point of the M2 and M3 optics (lying on HAM3 and HAM2 respectively). \textbf{Right:} ground motion and IMC cavity motion before (green) and after the locking mode (blue and pink).}
+\end{figure}
+
+\begin{figure}[h!]
+\centering
+\includegraphics[scale=1.2]{images/darm.png}
+\caption[DARM improvement with locked chambers]{Screenshot taken from LHO CDS when a quick measurement of DARM reaction to the lock of all the chambers has been taken. The result is encouraging because it shows an improvement of the signal below 0.1 Hz.}
+\end{figure}
+
+\noindent
+With the obtained results, a positive consequence of this work might be the improvement of the LSC signals from LIGO cavities. Among them, DARM is particularly important, because it represents the gravitational wave signal.
 
 \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. The motion of the optics on the chambers due to other factors than seismic 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.\\
@@ -476,10 +492,12 @@ Through CPSs locking, we reduced the differential motion of HAM2 and HAM3 chambe
 \label{chamb}
 \end{figure}
 \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. 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 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.
+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 made a quick computation (given the stretched timing) and 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.\\
+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 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.
 
 \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 works.
+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. 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.\\
+Te work done in this case is similar to the one done for the HAM chambers, except from the fact that a new filter need now to be built in order to control how the ISI affect the motion of the PRC optics.
 
 \begin{figure}[h!]
 \centering
@@ -489,4 +507,5 @@ We need to connect the ISI to the cavity and to do it we need to know how the PR
 \end{figure}
 
 \section*{Conclusions}
-
+Due to lack of time, it was not possible to take further measurements of ISI motion and LSC signals, especially with an accurate study of the blending filters. The study is however promising to be of great help in the improvement of the LSC signals of LIGO and its stabilization when in observing mode.\\
+LIGO Livingston site has also actuated a similar process, following the progression at LHO during 2019 collaboration and since the software skeleton of the new configuration has been built and installed on LIGO CDS, further studies and tests were due in 2020 to complete the last steps and test it fully on the interferometer. However the pandemic and the correlated travel restrictions have moved forward in the future the schedule for these tests.

main/main.tex

@@ -89,6 +89,7 @@ LHO = LIGO Hanford Observaotry\\
 LLO = LIGO Livingston Observatory\\
 LP = Low Pass filter\\
 LSC = Length Sensing and Control\\
+LVDT = Linear Variable Displacement Transformer\\
 LVK = Ligo-Virgo-Kagra meeting\\
 MCA = Mid-Course Assessment\\
 MICH = Michelson length\\
@@ -118,17 +119,16 @@ STRUCTURE OF THESIS [DRAFT]\\
 PART I: Gravitational astrophysics\\
 Chapter 1: Gravitational waves and sources\\
 Chapter 2: low frequency window and multimessenger astronomy\\
-
-PART II: Detectors and seismic isolation\\
 Chapter 3: Interferometry and Advanced LIGO\\
-Chapter 4: Inertial sensors and optical levers\\
 
-PART III: Lowering seismic noise\\
+PART II: Lowering seismic noise\\
+Chapter 4: Inertial sensors and optical levers\\
 Chapter 5: Seismic isolation at LHO\\
 Chapter 6: Laser stabilization for 6D seismic isolation\\
 
-Appendix A: first GW detection\\
-Appendix B: control loops
+Appendix A: Assembling suspension chains for A+ at LHO\\
+Appendix B: control loops\\
+Appendix C: first GW detection
 
 \mainmatter
 
@@ -145,6 +145,7 @@ Appendix B: control loops
 \appendix
 \include{A}
 \include{B}
+\include{C}
 %\appendix C on my work in LIGO labs
 
 \backmatter

main/oplevs.tex

@@ -32,7 +32,7 @@ When a rotation around the center of mass occurs, an additional term F$_{tilt}$
 \centering
 F_{tilt} = mg\sin\theta
 \end{equation}
-
+\bigskip
 \noindent
 where m is the mass and g = 9.8 m/s$^2$ is the gravitational acceleration.\\
 \noindent
@@ -98,12 +98,12 @@ If $\theta \ll$ 1, $\cos \theta \rightarrow$ 1: this means that the vertical sen
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.8]{images/vert.PNG}
-\caption[Tilting of vertical sensor]{Tilting of vertical sensor (Figure taken from \cite{ven}).}
+\caption[Tilting of vertical sensor]{Tilting of vertical sensor.}
 \label{v}
 \end{figure}
 
 \section{Optical levers}
-In general, an optical lever is a convenient device that makes use of a beam light and a position sensor to measure a small displacement and thus to make possible an accurate measurement of angles. This method is a very useful approach in sensitive non-contacting measurements. There is a light source, typically a laser, impinging on an optic reflecting the beam on a position device, which records any displacement of the beam, i.e. of the optic.\\
+In general, an optical lever is a convenient device that makes use of a beam light and a position sensor to measure a small displacement and thus to make possible an accurate measurement of angles. This method is a very useful approach in sensitive non-contacting measurements. A light source, typically a laser, impinges on an optic reflecting the beam on a position device, which records any displacement of the beam, i.e. of the optic.\\
 \noindent
 When the optic is tilted by an angle $\theta$, we have the situation illustrated in Fig. \ref{opt2}: if all the distances are known, we can compute the angle $\theta$.
 
@@ -432,19 +432,19 @@ The focussing lens of focal length 150 mm is inserted 10 cm before the photodiod
 \label{syst}
 \end{figure}
 \noindent
-The prototype and its own pre-amplifying electronics has been built at UoB (Fig. \ref{oplev20} and tested in air and in vacuum at the AEI.
+The prototype and its own pre-amplifying electronics has been built at UoB (Fig. \ref{oplev20}) and tested in air and in vacuum at the AEI.
 
 \begin{figure}
 \centering
-\includegraphics[scale=0.5]{images/OpLev20.jpg}
-\caption[Photo of the optical lever prototype]{Photo of the optical lever prototype as built at UoB.}
+\includegraphics[scale=0.55]{images/OpLev20.jpg}
+\caption[Photo of the optical lever prototype]{Photo of the optical lever prototypes as built at UoB. In this picture, the devices are not connected to electronics. Each platform hosts a laser source and a sensor. Each sensor is covered by a tube to avoid spurious light on the active area, and the focusing lens in placed at the suitable distance from it.}
 \label{oplev20}
 \end{figure}
 
 \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 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 pin configuration of the QPDs has been re-adjusted because the AEI electronics is set on a different one. it has been changed to the following:\\
+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:\\
 
 \begin{itemize}
 \item Q1: PIN 1 to PIN 1
@@ -454,17 +454,17 @@ The pin configuration of the QPDs has been re-adjusted because the AEI electroni
 \item BIAS: PIN 5 to PIN 4
 \end{itemize}
 \noindent
-Two adaptor cables have been build to connect the UoB boxes to the QPDs with the new pin configurations.\\
+Two adaptor cables have been built to connect the UoB boxes to the QPDs with the new pin configurations.\\
 \noindent
 To isolate the QPD, a small shield of plastic has been added to the QPD mount and the related metal screws have been changed with peek screws. Because of the presence of the new plastic layer, the height of all other components of the platforms has been adjusted.\\
-Every component has been vacuum-cleaned using an ultra-sonic bath: every mount was dis-mounted and then re-mounted after cleaning.
+Every component has been vacuum-cleaned using an ultra-sonic bath.
 
 \subsection{Installing the device}
 After cleaning, we installed the device into the South bench of the 10-m prototype. Due to the availability of the bench, only one fibre could be connected to one collimator; consequently, only one QPD has been connected.\\
 \noindent
 The lever arm has been set to be 20 cm: with the optical configuration foreseen for this lever arm the spot size on the photodiode is w $\simeq$ 1 mm. The power on that point is P = 3.5 mW.\\
 \noindent
-Summarizing, the prototype is ready for the test with the following specifications:\\
+Summarizing, the prototype is ready for the test with the specifications listed in Tab \ref{oplevspec}.\\
 
 \begin{table}[h!]
 \centering
@@ -478,6 +478,8 @@ Responsivity Si @ 1064 nm & $\rho$ = 0.2 A/W      \\
 Thermal noise             & Th = 21 nV/$\sqrt{Hz}$  \\
 Op-amp noise              & OP = 8,8 nV/$\sqrt{Hz}$
 \end{tabular}
+\caption{Specifications of the optical lever prototype tested at the AEI.}
+\label{oplevspec}
 \end{table}
 
 %\begin{table}[h!]
@@ -490,13 +492,13 @@ Op-amp noise              & OP = 8,8 nV/$\sqrt{Hz}$
 %\end{tabular}
 %\end{table}
 
-\subsection{Preliminary test in air}
-To test if everything was set in the best way, we performed a first measurement in air, using one of the AEI pre-amp boxes connected to the CDS. Fig. \ref{inair} shows the trend of Pitch, Yaw and Sum of the QPD quadrants.
+\paragraph*{Preliminary test in air}
+To test if everything was set in the best way, we performed a first measurement in air, using one of the AEI pre-amp boxes connected to the CDS. Fig. \ref{inair} shows the trend of pitch, yaw and the sum of the QPD quadrants.
 
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.3]{images/inair_test.PNG}
-\caption[OpLev test in air]{Preliminary test in air: the traces show the trend of the pitch, yaw and the sum of all QPD quadrants.}
+\caption[OpLev test in air]{Preliminary test in air: the traces show the trend of the pitch, yaw and the sum of all QPD quadrants (Q) as from the output of the pre-amp box built at UoB.}
 \label{inair}
 \end{figure}
 
@@ -538,33 +540,33 @@ The pressure has been set at 5 $\times$ 10$^{-3}$ mbar. What we expect is to fin
 \centering
 \includegraphics[scale=0.3]{images/LVDT.PNG}\\
 \includegraphics[scale=0.3]{images/ULVDT.PNG}
-\caption[Different pre-amps test: bench LVDT motion]{Bench motion long z axis at 5 $\times$ 10$^{-3}$ mbar pressure conditions. Blue curve is the trend measured by AEI pre-amp, red curve is measured with UOB pre-amp.}
+\caption[Different pre-amps test: bench LVDT motion]{Bench motion long z axis at 5 $\times$ 10$^{-3}$ mbar pressure conditions. Blue curve is the trend measured by AEI pre-amp, red curve is measured with UoB pre-amp.}
 \label{LVDT_FIN}
 \end{figure}
 \noindent
-In this conditions, also the signals from the L4C seismometers and accelerometers on Central bench have been measured.
+In this conditions, also the signals from the L4C seismometers and accelerometers placed on the Central bench have been measured.
 
 \begin{figure}[H]
 \centering
 \includegraphics[scale=0.3]{images/AEI_SOUTH.PNG}\\
 \includegraphics[scale=0.3]{images/UOB_SOUTH.PNG}
-\caption[Different pre-amps test: bench motion]{Motion of Central bench measured by L4Cs and accelerometers, with AEI and UOB pre-amps.}
+\caption[Different pre-amps test: bench motion]{Motion of Central bench measured by L4Cs and accelerometers, with AEI and UoB pre-amps. These plots highlights that the UoB electronics is not performing well (probably it is saturating) below 10 Hz.}
 \label{central}
 \end{figure}
 \noindent
-QPD performance are shown in the following pictures. With AEI boxes we had expected results: no variations in the power fluctuation peaks and expected behaviour of Pitch and Yaw with single quadrants.\\
-However, with UOB box (no. 0519) the measurements do not seem consistent with what we expected: despite the behaviour of each quadrant seems to follow the expected trend (even if differently from AEI trend), the curves of Pitch and Yaw do not match with the quadrants trend. We think that some non-linearities in UOB box could be the cause of the problem: this is still under investigation at UOB.
+QPD performances are shown in the following pictures. With AEI boxes we had expected results: no variations in the power fluctuation peaks and expected behaviour of Pitch and Yaw with single quadrants.\\
+However, with UoB box the measurements do not seem consistent with what we expected: despite the behaviour of each quadrant seems to follow the expected trend (even if differently from AEI trend), the curves of Pitch and Yaw do not match with the quadrants trend. We think that some non-linearities in UoB box could be the cause of the problem: this is still under investigation at UoB.
 
 \begin{figure}[H]
 \centering
 \includegraphics[scale=0.3]{images/AEI_QPD_TEST.PNG}\\
 \includegraphics[scale=0.3]{images/UOB_QPD_TEST.PNG}
-\caption[In vacuum QPD test]{QPD performance, with AEI and UOB pre-amps.}
+\caption[In vacuum QPD test]{QPD performance, with AEI and UoB pre-amps. There is an evident difference between the measurements taken with thw two different electronics: UoB electronics is under investigations to overcome the issue.}
 \label{qpd_fin}
 \end{figure}
 
 \paragraph*{Electronic noise}
-Noise measurements of CDS and unplugged electronics have been taken, to check if there could be issues related to it. However, they do not show any unexpected behaviour.
+Noise measurements of CDS and unplugged AEI electronics have been taken, to check if there could be issues related to it. However, they do not show any unexpected behaviour. The same measurement was not possible with UoB electronics because...
 
 \begin{figure}[H]
 \centering
@@ -573,21 +575,22 @@ Noise measurements of CDS and unplugged electronics have been taken, to check if
 \label{noise}
 \end{figure}
 
-\paragraph*{UOB and AEI comparison}
-The shot noise can be computed as:
-
-\begin{equation}
-\centering
-SN = \sqrt{\frac{2 \pi \hbar c P_0}{\lambda}},
-\end{equation}
-
-\noindent
-where P$_0$ = 3,5 mW is the output power, $\lambda$ = 1064 nm is the laser wavelength and c the speed of light. With the known parameters, we get:
-
-\begin{equation}
-\centering
-SN = 8,1 \time 10^{-11} \frac{W}{\sqrt{Hz}}.
-\end{equation}
+%\paragraph*{UOB and AEI comparison}
+%The shot noise can be computed as:
+%
+%\begin{equation}
+%\centering
+%SN = \sqrt{\frac{2 \pi \hbar c P_0}{\lambda}},
+%\end{equation}
+%
+%\noindent
+%where P$_0$ = 3,5 mW is the output power, $\lambda$ = 1064 nm is the laser wavelength and c the speed of light. With the known parameters, we get:
+%
+%\begin{equation}
+%\centering
+%SN = 8,1 \time 10^{-11} \frac{W}{\sqrt{Hz}}.
+%\end{equation}
 
 \section*{Conclusions}
-
+The measurements have shown that the device was problematic to calibrate due to issues probably related to electronics and due to the very short time of the visit it was not possible to take more in-depth tests. Other possible reasons to investigate might lie in the structure of the prototype: further tests might be useful to understand if the performances of the device can be improved by changing the position of the lens with respect to the QPD, and let the diode sit at the focus on the lens. This solution will concentrate the power and decrease the size of the beam.\\
+The device is currently not suitable for the purposes we tested for, but it opened the way to further tests to improve the technology.