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\title{Upgrade of the 40M Interferometer}
\author{R. Adhikari, Y. Aso, S. Ballmer, R. Bork, J. Miller, S. Vass, R. Ward, A. Weinstein}
%\date{${}$Date: 2007/09/30}
\ligodccnumber{T}{08}{0074}{00}{R} \ligodistribution{ISC Group}
%\ligodraft

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\begin{document}

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\section{Overview}
\label{sec:I}

This document describes the proposed upgrade of the 40m prototype interferometer 
at Caltech. Detailed background and motivation is given in Appendix~\ref{app:motive}.

The purpose of the upgrade is to match the properties of the 40m interferometer 
to the recent design of the Advanced LIGO interferometer~\cite{ISC:CDD} 
(T070247-00) and to enable more faithful prototyping of the real thing.

The following is a list of the major changes:
\begin{itemize}

\item Arm Cavity Finesse. The ITM transmission will be changed to match the 
      AdvLIGO finesse choice of 450 (T = 1.4\%)

\item Lightweight ITMs. In order to increase the effects of radiation pressure 
      we will replace the 1.25 kg MOS's with the 0.25 kg SOSs.

\item Modulation Frequencies. The 40m frequencies ($f_1$ = 33 MHz and $f_2$ = 166 MHz) 
      will be changed to match the AdvLIGO frequencies ($f_1$ = 9 MHz and $f_2$ = 45 MHz).
          
\item Recycling Cavities. The PRC and SRC will be made longer to accommodate 
      the lower modulation frequencies. This will be done by folding the cavities 
      using passively damped ANU tip/tilt suspended optics.

\item Mach Zehnder. The CDD shows that it is not necessary to have a Mach Zucker
      so we will remove the 40m Mach Zucker and go back to using serial modulation.

\item Controls Computers. All of the front end processors, ADCs, and DACs will be 
      replaced with AdvLIGO style hardware. There will be one or two central 
      multi-core computers with fiber links to remote ADC/DAC "blue-boxes". Custom 
      interface connectors will be made to connect the new digital controls with 
      the existing analog electronics.
          
\item Multi wavelength locking.  Investigate techniques to improve mean time to 
      lock: Multi-wavelength locking locking using dichroic optics (green, blue),
      frequency shifted PSL light injected through ETM or pick-off ports, PRN
      techniques.
          
\item Optical Levers. Test out fiber based OL distribution scheme? Not really necessary. 
      We should make sure to include whitening of all Oplev systems.
          
\item Wavefront Sensing. The 40m will continue to only have wavefront sensing for 
      the IMC. The full interferometer alignment will continue to be done by angular 
      dither demodulation.
          
\item Adaptive Noise Cancellation. There will be a few adaptive noise cancellation 
      machines to study the technique. This will require some new computers, 
      PEM sensors, shakers, etc.

\end{itemize}
          


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\clearpage
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\section{Descriptions of the Changes}
\label{sec:II}

\subsection{Modulation Frequencies}
The current modulation frequencies for the main interferometer are
(f$_1$ = 33~MHz \& f$_2$= 166~MHz). The modulation frequency for the
input mode cleaner is (f$_{MC}$ = 29.5~MHz). There are many practical
difficulties associated with using such high frequencies: small
photodiodes to reduce diode capacitance, increased dielectric losses
in the RF cables, incompatibility with the existing RF board layouts,
and incompatibility with the LIGO standard op-amp collection.

This experience led to a design choice (f$_1$ = 9~MHz and f$_2$ =
45~MHz) for Advanced LIGO utilizing a much lower frequency pair than
the previous design (f$_1$ = 9~MHz and f$_2$ = 180~MHz).


\subsection{Recycling Cavity Lengths}
The recycling cavity lengths will be made much longer than is current
(see Tables \ref{tab:params} and \ref{tab:oldparams}).  This will
require the installation of 2 folding mirrors per cavity. Since the
40m stacks do not give much seismic isolation in the control band
(reference?) we have chosen to install a variant of the ANU Tip-Tilt
mirrors to provide some isolation. In order to not have the added
complexity of controlling 4 more suspended optics, we will take
advantage of the inherent eddy current damping in the cages (reference
- add tip/tilt plots). We will also not install BOSEMs or coils in
these. They will be passively damped, uncontrolled folding
mirrors. The residual excitation at the Tip-Tilt free body modes is
small (the Q is ~2). Some basic Looptickle modeling shows that the 1/f
isolation provided by the Tip-Tilt mirrors is enough to bring the
noise from the recycling cavities to a level where it is below the
thermal noise in the arm cavity suspensions.

Figure~\ref{fig:RC2} and \ref{fig:RC3} show two possible layouts for the recycling 
cavities that are consistent with the
cavity length requirements (see section \ref{sec:III}). 

\begin{figure}[htbp!]
\begin{center}
  \includegraphics[width=1\linewidth,angle=0]{40m_opt_layout_Mark1_Pa-crop.pdf}
  \caption[layout1]
  {Possible way to fold both recycling cavities with 2 folding mirrors per cavity. The 
   power recycling cavity is shown in red, the signal recycling cavity in green.}
  \label{fig:RC2}
\end{center}
\end{figure}

\begin{figure}[htbp!]
\begin{center}
  \includegraphics[width=1\linewidth,angle=0]{40m_opt_layout_Mark2_Pa-crop.pdf}
  \caption[layout2]
  {Possible way to fold both recycling cavities with 3 folding mirrors for the power 
  cavity. The power cavity is shown in red, the signal cavity in green.}
\label{fig:RC3}
\end{center}
\end{figure}



\subsection{Mode Cleaner}
It will be made longer. The existing Input Mode Cleaner (IMC) length
is 13.548 m \cite{Kirk:Length} and is resonant with an 11.064~MHz RF
sideband. The new length will be 16.65 m, requiring a 3.1~m extension.
This can be accommodated in the 40m lab (see figure~\ref{fig:MC2}) by 
installing an extension tube between the existing tube and the 
MC2 chamber. This is expected to be a fairly simple operation.

We would have qualitatively the same prototyping experience whether we
used a 9 or 11 MHz sideband but since it is relatively easy and
inexpensive we feel that it is worth it to use the exact frequencies
in case there is something surprising to be learned about components,
RFI, etc.

\begin{figure}[htbp!]
\begin{center}
  \includegraphics[height=20cm]{mc2p.jpg}
  \caption[MC2 Tank]
  {View of the MC2 tank from around the MC1 chamber.}
\label{fig:MC2tank}
\end{center}
\end{figure}


\subsection{Arm Cavity Finesse}
The arm cavity finesse will be changed from 1200 to 450 to match the
new design~\cite{ArmFinesse}. This will require repolishing and
recoating the ITMs. We place no requirements on the thermal noise or
the polish and so we can afford to go with the cheapest / fastest
vendors (within reason). For the coating, we will require the
transmission of the ITM HR surface to be 0.014 +/- 0.002 and that the
differential transmission (T$_X$ - T$_Y$) be less than 0.001. This is
to prevent there being excess noise couplings which are qualitatively
beyond what we expect in Advanced LIGO.


\subsection{ITM Masses}
For the new ITMs we have the choice of either installing 2 MOSs or 2
SOSs.

There are 2 ITM MOS spares on hand and more than enough MCFM spares
that we can choose between them.

Installing SOSs will increase the effect of radiation pressure and
therefore require developing controls techniques which will be useful
in Advanced LIGO. We estimate that with SOS-ITMs, the longitudinal
optical spring can be made as high as 200 Hz in the detuned RSE
case. This seems, at this stage, like a potentially useful thing to
prototype and so we are planning to install SOS ITMs.


\subsection{Borkspace Revolution}

The current CPU power for the SUS and LSC FEs is undersized at the
40m. These processors frequently run over their time limit and fall
out of sync, requiring reboots of several systems. We therefore would
like to replace several of these with a single multi-core computer
(Sun Fire X4600 M2 AMD; 8 x 2.8 GHz Dual Core Opteron). Changing
from the VME crate style Pentiums to the commodity FE processor will
make the upgrade path easier in the future. There is also the significant
benefit of producing $\sim$7 spare VME processors for the observatories
during the Enhanced LIGO science runs.

We should put a table in here of all the FE computers, what they are,
how much time they take up, and how many ADC/DAC connections they
have, and how many signals they pass to where across the RFM net.

Figure~\ref{fig:SENDS} shows an example block diagram of what would
be prototyped at the 40m lab. This is also the proposed new DAQ
structure for Enhanced LIGO.


\subsection{Wavefront Sensing}

The 40m is the only place outside of the actual Advanced LIGO
interferometers that the full ASC-WFS system could be prototyped. The
iLIGO experience was difficult because of difficult to diagnose
problems in the WFS heads, demod boards, whitening boards, and
ADCs. On the optical side the WFS sensing matrix was often degenerate
and singular due to ill understood properties of the unstable power
recycling cavity and the Sigg-Sidles torque instabilities.

It will certainly be valuable to test out the full electronics chain
with realistic optical signals but the 40m optical plant is unlikely
to be a good prototype of the Advanced LIGO interferometer since the
40m arms will not be changed to approach the nearly unstable, confocal
geometry of Advanced LIGO.

Unless something unforeseen comes up, we will simply make the 40m
available as a lab to test the WFS electronics chain if it proves to
be convenient (e.g. by installing an Advanced LIGO WFS system on the
IMC). We will not setup a full IFO RF WFS system.

On the other hand, we will continue to commission the dither based
alignment system so as to have a useful bootstrap system when
commissioning the WFS in Advanced LIGO.


\subsection{Optical Levers}

Currently the 40m optical lever system serves to stablize the low
frequency (< 6 Hz) motion of the suspended optics. The lever lengths
are 1-3 meters long and use HeNe lasers. Due to geometrical
constraints the beams bounce off of fixed mirrors on the stacks on the
input and output paths. It is clear that the sensing noise of the
system is limited by bouncing off of the stack (f < 10 Hz) and from a
lack of whitening before the ADCs (f > 10 Hz).

The new design will use existing viewports, port mounted steering
mirrors, and simple telescopes with 2 inch optics to make 40m long
optical levers.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\newpage
\section{Looptickle Modeling}
\label{sec:III}
This section contains the results from a Looptickle / Optickle model.
It focuses on the zero-detuned mode that is going to be the main mode of AdvLIGO.

\subsection{Design parameters}
Table \ref{t:IFOConfig} summarizes the key design parameters. All cavity length are
optical path length numbers, i.e. they have not been corrected for the BS thickness.

\begin{table*}
\begin{center}
\begin{tabular}{lc}\hline\hline
%\multicolumn{2}{l}
%{{\bf Interferometer configuration}}\\ 
\textit{Quantity} & \textit{Value}  \\ \hline 
Input power       & $1~{\rm Watt}$  \\
Finesse           & $446$   \\
ITM transmission  & $0.014$ \\
PRM transmission (unchanged)  & $0.07$ \\
SRM transmission (unchanged)  & $0.07$  \\
Schnupp asymmetry & $0.050$  \\
$\rm l_{PRC}$     & $8.328~{\rm m}$  \\
$\rm l_{SRC}$     & $6.662~{\rm m}$  \\
Distance BS to ITMX & $2.025~{\rm m}$ \\
Distance BS to ITMY & $1.975~{\rm m}$ \\
Distance BS to PRM  & $6.328~{\rm m}$ \\
Distance BS to SRM  & $4.662~{\rm m}$ \\
$\rm l_{IMC}$ (round trip)     & $33.310~{\rm m}$ \\
$\rm l_{EX}$     & $38.55~{\rm m}$ 	\\
$\rm l_{EY}$     & $38.55~{\rm m}$    \\
Lower mod. frequency & 9~{\rm MHz}  \\
Upper mod. frequency & 45~{\rm MHz} \\
\hline\hline
\end{tabular}
\caption[Interferometer configuration]{
         Basic interferometer parameters. }
\label{t:IFOConfig}
\end{center}
\end{table*}


\subsection{Loop Designs}
No magic in this section. we aimed for a DARM UGF of 350~Hz, and auxiliary loop UGF's 
of 100~Hz. But neither of them are critical.

\subsection{Power / Signal Levels}
The table below shows the optical power at each port. No additional attenuators were 
included. The POP
beam assumes a PRC folding mirror with 1000~ppm transmission. A DARM offset of 40~pm 
was assumed. This gives $1.5~{\rm mWatt}$ of power on the DC detector. The offset can be increased
more, but the sensitivity will go down.

\begin{tabular}{lcccccccccccc}
\multicolumn{13}{l}{{\bf Optical Port Power in mWatt}}\\ \hline
FREQ (MHz)& -54.0& -45.0& -36.0& -28.8&  -9.0&   0.0&   9.0&  28.8&  36.0&  45.0&  54.0& Total \\ \hline
  REFL &   0.0&   0.2&   0.0&   0.0&   2.0&  26.8&   2.0&   0.0&   0.0&   0.2&   0.0&  31.2 \\
    AS &   0.0&   0.0&   0.0&   0.0&   0.0&   1.5&   0.0&   0.0&   0.0&   0.0&   0.0&   1.5 \\
   POP &   0.0&   0.0&   0.0&   0.0&   0.1&  17.6&   0.1&   0.0&   0.0&   0.0&   0.0&  17.9 \\
\end{tabular}

And the following table shows the RF power at each port in mWatt (both quadratures).

\begin{tabular}{lccccccc}
\multicolumn{8}{l}{{\bf RF power at ports in mWatt}}\\ \hline
FREQ (MHz)&  0.0&  9.0& 18.0& 36.0& 45.0& 54.0& 90.0 \\  \hline
   REFL   &31.17& 0.02& 4.01& 0.82& 0.01& 0.83& 0.35 \\
     AS   & 1.48& 0.01& 0.00& 0.00& 0.11& 0.00& 0.00 \\
   POP2   &17.91& 0.00& 0.24& 0.19& 0.00& 0.19& 0.03 \\
\end{tabular}

\subsection{Noise Subtraction}
Since the suspension thermal noise is dominant, we only need a modest amount of 
MICH subtraction to suppress the MICH noise below thermal noise. However, the 
couplings are the same as for AdvLIGO, and there is no reason not to implement 
the same subtractions.

\subsection{DARM Noise Budget}

The Looptickle model included the following noise sources:
\begin{itemize}
\item {\bf Quantum} or {\bf Shot Noise} from the loop itself, calculated by
  injecting vacuum noise at every open optical port.

\item {\bf Auxiliary length}: Shot Noise from the other loops, calculated by
  propagating the quantum noise in the other loops through the control system.

\item {\bf Seismic Noise}, This is an estimate (power law) for the noise at the 40m.
It includes coupling through the new Eddy-current damped recycling cavity folding mirrors.

\item {\bf Mirror Thermal} noise, estimate for 40m.

\item {\bf Suspension Thermal} noise, estimate for 40m.

\item {\bf Frequency Noise} incident on the input mode cleaner (i.e. input 
mode cleaner and common mode sensing noise are counted as shot noise from 
those length loops).  See figure \ref{fig:LaserNoise} for the assumed PSL noise level.

\item {\bf Intensity Noise} incident on the IMC.  The measured out-of-loop 
noise from the 40m ISS is $3 \times 10^{-8}$ from 80-3000~Hz.
See figure \ref{fig:LaserNoise} for the assumed PSL noise level.

\item {\bf Oscillator Phase Noise}.  See figure \ref{fig:LaserNoise} for the assumed PSL noise level.
The coupling does include the light passing through the IMC. 
Currently the estimate does not include potential noise added after the EOM/LO split.
The 40m lab currently uses IFR (Marconi) 2023 generators instead of Wenzel crystals for
signal generation. 

\item {\bf Oscillator Amplitude Noise}  See figure \ref{fig:LaserNoise} for the assumed PSL noise level.
Measurements of the iLIGO RF AM Stabilization box at the 40m~\cite{Valera:AM} show that the
AM noise stabilized EOM drive can be as low as $5 \times 10^{-8} \rm /\sqrt{Hz}$ above 10~Hz.

\end{itemize}

Figure \ref{fig:nbDARM} shows a noise budget for DARM.

\begin{figure}[htbp!]
\begin{center}
  \includegraphics[width=17cm,height=20cm]{DARM_noisebudget.pdf}
  \caption[nbDARM]{DARM noise budget.}
  \label{fig:nbDARM}
\end{center}
\end{figure}

\begin{figure}[htbp!]
\begin{center}
  \includegraphics[width=17cm,height=20cm]{LaserNoise.pdf}
  \caption[nbDARM]{Assumed noise at the IMC input. N = RIN for laser intensity noise,
                   radians for oscillator phase noise, dA/A for oscillator amplitude noise, and
                   Hz for laser frequency noise.}
  \label{fig:LaserNoise}
\end{center}
\end{figure}


\subsection{Optickle Sensing Matrices}
Tables~\ref{t:SensingMatrix100} and \ref{t:SensingMatrix1000} show the full sensing 
matrix at 100~Hz and 1~kHz.
We intend to used the same error signals as AdvLIGO, namely REFL\_I1 for CARM,
AS\_DC for DARM,  POP\_I1 for PRCL, POP\_Q2 for MICH and POP\_I2 for SRCL.
The 3-f signals for lock acquisition are easy to add, but were not yet modeled.
\input{sensingMatrix40m100Hz}

\input{sensingMatrix40m1kHz}

% ----------------------  IFO Diagram
\begin{figure}[!ht]
\begin{center}
\includegraphics[width=15cm]{IFO_diagram.pdf}
\caption{Def of LSC DOFs}
\end{center}
\label{fig:lsc-dia}
\end{figure}
% -----------------------------------------------------------------------

% =========================================================
\section{Lock Acquisition}
The duration of the lock acquisition process should be short enough
to not significantly impact the Detector availability for science
mode operation. In Acquisition mode there are no requirements on the
noise in the sensing systems (length or angle) in the GW band other than
what is required to prevent saturations during acquisition.

The low frequency (control band) angular fluctuations must be
consistent with small gain fluctuations in all LSC and ISC loops.

The present lock acquisition path at the 40m involves first locking
the interferometer with a non-negligible common arm offset which is
subsequently reduced to zero in a controlled manner.  The first stage
of this technique is statistical in nature, and is the most
significant contributor to the uncertainty in time required to acquire
lock.  This technique also introduces complications due to the
changing optical plant as the CARM offset is reduced.

We envisage developing an improved version of this path for
application to a broadband recycled 40m. Our approach will mirror that
covered in section 9 of \cite{ISC:CDD}. However, we do not plan to
implement a SPI at the 40m. We shall instead explore the possibilities
described in section~\ref{sec:auxsig}.This will involve two parallel
investigations:

\begin{itemize}
\item Control signals which are not affected by common arm offsets.

\item Independent control the arm cavity length at the nanometre level
  - allows one to hold the arms both on or off resonance and smoothly
  transition between these states.
\end{itemize}
 
We address each in turn:

\subsection{Harmonic Demodulation}

Simulations by L.~Barsotti show that error signals for the central
interferometer (PRCL,SRCL \& MICH) are available by demodulating the
reflected light at 3$f_1$ (PRCL, MICH) and 3$f_2$
(SRCL)\cite{ISC:CDD}. These signals are attractive as they present
little sensitivity to CARM detuning, while avoiding the complexity
introduced by doubly demodulating PD outputs.
\begin{figure}[!ht]
\begin{center}
\includegraphics[width=7.5cm]{3fsidebands.pdf}
\caption{The reflected signal demodulated at $3f_1$ is dominated by
  the beat between first and second order sidebands.}
\end{center}
\label{fig:3fsidebands}
\end{figure}

Consider the case of the $3f_1$ demodulation. These $3f$ signals arise
from the beat between the first and second order sidebands
($f_1SB1_{\pm}$ and $f_1SB2_{\mp}$) and between the carrier and third
order sidebands ($CR$ and $f_1SB3_{\pm}$) (figure~\ref{fig:3fsidebands}). 
The signal from the beat between sidebands is
generally much larger than that due to the carrier/$SB3$ beat as the
interferometer reflectivity for the third order sidebands is low. In
contrast, the second order sidebands are non-resonant in the recycling
cavity and hence provide a stable local oscillator in reflection which
is almost independent of optical parameters, interferometer resonances
and CARM offset. Figure~\ref{fig:3fsignals} shows a
comparison between $1f$ and $3f$ signals for various CARM offsets.

\begin{figure}[!ht]
\begin{center}
\includegraphics[width=17cm]{3fsignals.pdf}
\caption{A comparison between (simulated) science mode and lock
  acquisition signals for various CARM offsets. Left: PRCL, centre -
  MICH, right - SRCL. Parameters used are representative of AdvLIGO,
  we expect similar results at the 40m. Reproduced from p. 60 of
  \cite{ISC:CDD}}
\end{center}
\label{fig:3fsignals}
\end{figure}


Preliminary tests at the 40m using existing electronics have shown that MICH and
PRCL can be held on REFL31 (Reflected light demodulated at
$3f_1$=99MHz) I \& Q, respectively.

\subsection{Auxiliary signals}
\label{sec:auxsig}

To manipulate the arm cavities independently of the `standard' control
structure we require some means of separating the chosen readout
method from the usual PSL light. There exist a number of
options:

\begin{itemize}
\item {\bf Orthogonal polarizations}

  It is possible to inject orthogonally polarized light through any of
  the auxiliary ports and distinguish these signals by means of a
  polarizing beam splitter. To get a wide tuning range with this scheme
  we would need to use an auxiliary laser and tune its frequency
  by several~MHz. This scheme, as well as some of the following, would
  require the frequency stabilization of an external laser with respect to
  the PSL beam.

\item{\bf Frequency shifted PSL light}

  Better control of the arm length is achievable using a frequency
  shifted PSL pick-off. The shift would be in the hundreds of MHz
  regime and would likely be introduced by double-passing an
  AOM. Adjustment of the frequency shift via a VCO would give a wide
  tuning range and allow the arm to be swept to a resonance of the PSL
  light. A very similar scheme would be to use an external, tuneable
  laser as above.

\item {\bf Other wavelengths}

  The use of other wavelengths represents another valid option. A
  simple choice might be to double the PSL light to 532~nm. This beam
  benefits from the stabilisation of the PSL pump beam whereas other
  light sources must be independently stabilised.

  Use of a second wavelength would require dichroic coatings (both HR
  and AR). Recent explorations by S. Ballmer suggest that this type of
  coating can be achieved through small deviations from a 1/8, 3/8
  design.
  
  We should also take advantage of the dispersion in the bulk to achieve
  a split of this other color with respect to the 1064~nm beam.

\item{\bf Digital interferometry/ PRN}

  Phase modulated light, imprinted with pseudo random code is, when
  suitably demodulated, able to determine the positions of optics over
  a wide range without requiring any resonant phase
  shifts\cite{Bram:WhitePaper}\footnote{We do not discuss the
    suspension point interferometer mentioned in this reference as
    there are no plans to study this idea at the 40m}. We do not
  expect to investigate this technology independently but would like
  to host outside experiments (ANU).


\end{itemize}

Having a modulated beam one must decide where to inject it to create
useful signals\footnote{We are presently considering an actively
  stabilised fibre distribution system for transporting any
  secondary light source.\cite{Ye:fibres}}. Two ideas have been proposed:

\begin{itemize}

\item{\bf Injecting through ETM} From the ETM side the arm cavities
  are massively under coupled. This leads to small signal levels which
  are could easily be dominated by technical noise. Additionally, the
  light from the arm will enter the central cavities and efforts must
  be taken to minimize the coupling between the arm signal and other
  degrees of freedom. In this respect a second wavelength would be
  advantageous as the dispersion of fused silica may allow the
  separation of beams from the recycling cavities and the arm if the
  wedges are of appropriate size and orientation. Note: this wedge
  trick will not work for AdvLIGO since the beam sizes there are larger;
  we would have to use a beam reducer to split those beams.

\item{\bf Injecting through pick-offs} Similar to the above. Injecting
  through POX/POY gives an appreciable improvement in the signal to
  noise ratio since the arm cavities become over coupled with this
  topology. Coupling to the central interferometer is reduced. POP is
  also under consideration but is dependent on the layout of the
  stable recycling cavities.

\end{itemize}
% =========================================================

\section{Noise Diagnostics}
\label{sec:diag}
The following is a non-exhaustive list of diagnostic tests that we 
will do in order to verify our models of a DRFPMI with DC Readout.
As in the past, we expect the most useful parts of the noise coupling
measurements to be where we do not find agreement with the Optickle
model. Performance requirements for the AdvLIGO system are listed
in Section XXX of the ISC CDD~\cite{ISC:CDD}.



\subsection{Sensing and Control System Noise}
\subsubsection{Beam jitter coupling}
Band-limited noise injections on all of the interferometer optics
as well as the input beam to the interferometer and the OMC tip/tilt
steering mirrors. We will apply this noise in conjunction with low
frequency misalignments of the core optics in order to verify our
models of bilinear jitter coupling~\cite{Sigg:MM10}.

\subsubsection{Auxiliary Length Degrees-of-freedom}
The sensing and control of each auxiliary length degree-of-freedom
must be done in such a way that limits the coupling of their sensing
noise into the GW readout. We will check via standard swept sine
tests that the modeled transfer functions are correct and also do a
set of Monte-Carlo offset/noise tests as above to check our estimates
of allowable loop offsets.

\subsubsection{Frequency Stabilization}
Due to the short arm cavity lengths, we expect there not be a significant
frequency noise coupling in the 40m, even with low light levels on the
CARM/CM sensing detector(s). This can be compromised by scattering
and clipping noise in the MC/CM sensing chains but this also seems
controllable. There are frequency noise injection points available on these
servos.

\subsubsection{Laser Intensity Noise}
Laser intensity stabilization at the $5 \times 10^{-8} \rm /\sqrt{Hz}$ level
which is currently achieved seems copacetic and so we will not pursue an
AdvLIGO style Intensity Stabilization Servo (ISS). The existing system has
an injection point which can hooked up to the AWG.

\subsubsection{Modulation Source Noise}
Modulation/Oscillator noise is often tricky to model correctly and diagnose. The
baseline plan is to continue with the Marconi (IFR) generators even though they
have a much higher phase noise than the Wenzel OCXOs employed in iLIGO and
GEO600. The Marconi and the RF AM Stabilization circuit allow high bandwidth
modulation and straightforward wideband tuning range which are the {\it sine qua non}
of oscillator noise characterization.

\section{DC Readout System}

As Advanced LIGO will use the technique known as \emph{DC Readout}~\cite{pf:Talk03} for 
detection of the gravitational wave channel it is a crucial part of the global length 
sensing and control system, and thus needs to be tested in an integrated manner.  The current 
40\,m has a DC Readout system which consists of:

\begin{itemize}
\item A pair of piezo-electric tip-tilt steering mirrors (from Piezo-Jena) at the output 
      port of the interferometer.
\item A length adjustable (via New Focus picomotor), fixed mount, mode-matching telescope 
      with spherical mirrors.
\item A monolithic, four-mirror mode cleaning cavity with a finesse of 210 and a transmission 
      of approximately 90\%.  The body is made of copper.  The beam waist is 370 microns.
\item A pair of bare photodiodes (exposed to the vacuum) with an electronics amplification 
      package housed in a separate canister, all installed in the vacuum system atop a 
      seismic isolation stack.
\end{itemize}

As of this writing, the DC readout has not been demonstrated with a 
DR system. The program to study the PRFPMI with DC Readout was extended 
to support noise modeling for Enhanced LIGO. The system was designed to
work with the DRFPMI and it is expected to also work well with the 
upgraded system. The HOM susceptibility analysis was done assuming the
old system with the higher frequency sidebands and so it remains to be
determined if the existing low finesse OMC will be sufficient in isolating
the DC Readout photodiodes.

As the location and size of the arm cavity beam waist is not expected to change, all the 
installed components will function in the upgraded 40\.m interferometer.  However, desirable 
upgrades include, in order of priority:

\begin{itemize}
\item{\bf Photodetectors} The currently installed vacuum-compatible DC Readout photodetectors 
are a first prototype, and improvements have been made to the design for Enhanced LIGO.  The 
40\,m DC Readout system should be updated with a new photodetection chain with electronics 
similar to that being installed into Enhanced LIGO in order to lower the front end electronics
noise. This will require laying out a new board to fit inside the in-vacuum can which currently
contains the PD pre-amp.

\item{\bf OMC} A new output mode cleaner can be built and installed which matches the finesse 
              of the projected Advanced LIGO output mode cleaner, to provide a more faithful 
              representation. Another option is to swap mirrors to up the finesse of the existing
              copper OMC. We will wait to do some supporting calculations before going down
              that road.
              
\item{\bf Tip-Tilts} The piezo-electric steering mirrors can be replaced with suspended \
            tip-tilt mirrors, to more faithfully reproduce the situation in advanced LIGO.  
           Equipping these with curved mirrors could allow the removal of the fixed 
          mode-matching telescope. The baseline plan is to stay with the PZT mirrors.

\end{itemize}


\section{Squeezed Light Injection}
The 40m upgrade will allow for squeezed light/vacuum injection through the dark port via
the AS port Faraday Isolator. At this time we do not include the design of such a squeezer
but just leave the port open in case future squeezed light research indicates a need for
this kind of work.

\section{Adaptive Noise Cancellation}
Recent work~\cite{Pepper:SURF} has shown that there is some
promise in exploring active cancellation of environmental noise sources. The concomitant
technique of adaptive filtering has recently~\cite{Matt:AdaptiveTalk} been demonstrated
on a real time system in the 40m lab.

In order to pursue this we will have a dedicated front end system acquire many signals
including the PEM and SUS/ASC sensors. Some of the envisioned development includes:

\begin{itemize}
\item {\bf Seismic} Using the ultra-low frequency Wilcoxon accelerometers as well as a few
          seismometers (Ranger SS-1, Guralp CMG-40T, etc.) we will send signals to the
          longitudinal (POS) input of the suspensions
          to minimize fringe velocities for ease of lock acquisition. This will not lower the overall
          control signal amplitudes at the 40m nor reduce the amount of angular fluctuation but
          should ease locking efforts during the daytime.
          
          From our modeling we expect that optic angular fluctuations at the 40m and in AdvLIGO
          are dominated by length to angle cross-coupling in the suspensions and so it is not likely
          to be useful to attempt feed-forward cancellation of tilt at the 40m (although it should be
          useful for the AdvLIGO SEI system).
          
\item {\bf Acoustic} To explore higher frequency noise cancellation and reduce the noise in the
          100-1000~Hz band, we will install a set of microphones in the LSC sensing tables and the
          PSL and attempt to cancel some of the observed scattering/clipping noises. All of the
          ISC beam paths in AdvLIGO will be in-vacuum to avoid this effect but the technique may
          be useful to reduce unexpected couplings.
          
\item {\bf Magnetic} A set of magnetometers (Bartington or otherwise) will be installed to attempt
         subtraction of power line harmonics picked up in the sensing channels and from pickup
         in the test mass magnets. In AdvLIGO this technique may be useful to cancel pickup in the
         PUM (PenUltimate Mass) of the quad suspensions and the actual mirror of the triple
         suspensions of the beamsplitter and recycling cavity suspensions. Direct hardware based
         subtraction may reduce the bilinear noise which masks the Crab pulsar signal in iLIGO.
         
\item {\bf RF} A more speculative source of excess noise is direct coupling of RFI at the LSC
         modulation frequencies into the readout electronics. RF antennae with 
         modulators/demodulators will be installed to
         explore noise cancellation via this mechanism. 

\item {\bf LSC Corr} A potentially significant noise limit in AdvLIGO may be feedthrough of
         sensing noise from the aux. length loops. In order to achieve large cancellation factors
         of this noise we may be forced to use adaptive noise cancellation. We will build this into
         the LSC system at the 40m either directly or by hooking in a parallel process running the
         adaptive code.
\end{itemize}

The total list of sensors is still being determined but is likely to include a seismometer, several
accelerometers, microphones, magnetometers, and RF antennae. We will use the existing PEM
and PSL/IOO ADCU systems to acquire the slow channels. For all of the $\sim$100~Hz BW
cancellation we will require ADCs with less delay than the ICS-110B and therefore would hook
into the new acquisition system with General Standards ADCs.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{figure}[h]
 \begin{center}
  \includegraphics[width=17cm,angle=90]{SENDS.pdf}
 \caption[DAQ]{DAQ and Controls Diagram}
 \end{center}
 \label{fig:SENDS}
\end{figure}


% =================================================================


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\newpage
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\end{thebibliography}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newpage
\appendix

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{New Interferometer Parameters}
\label{app:params}

\renewcommand{\arraystretch}{1.4}
\begin{table}[!h]
\begin{center}
\begin{tabular}{lc}
\hline\hline
ITM Transmission & 0.014 \\
%
PRM Transmission & 0.07 \\
%
SRM Transmission & 0.07 \\
%\hline
ITM imbalance ($T_{ITMX} - T_{ITMY}$) & $T_{ITM} /50$\\
%\hline
Average round trip arm loss & 160 ppm \\
%\hline
Differential arm loss & 50 ppm \\
%\hline
Beamsplitter R/T imbalance & $\pm5 \times 10^{-3}$ \\
%\hline
Differential arm offset from dark fringe & 40 pm \\
%\hline
Arm Cavity finesse & 446 \\
%\hline
Output mode cleaner finesse & 250 \\
%
Power Recycling cavity length & 8.328 m \\
%
Signal Recycling cavity length & 6.662 m \\
%
Schnupp Asymmetry & 0.05 m \\
\hline\hline
\end{tabular}
\caption{Parameters used in the Optickle modeling. Shown are those
parameters that determine the laser and modulation source noise
couplings.} 
\label{tab:params}
\end{center}
\end{table}
\renewcommand{\arraystretch}{1}
% ----------------------------------------------------------------------------------------
\newpage
\section{Current (2007) Interferometer Parameters}
\label{app:oldparams}

\renewcommand{\arraystretch}{1.4}
\begin{table}[!h]
\begin{center}
\begin{tabular}{lc}
\hline\hline
ITM Transmission & 0.005 \\
%
PRM Transmission & 0.07 \\
%
SRM Transmission & 0.07 \\
%
ITM imbalance ($T_{ITMX} - T_{ITMY}$) & $T_{ITM} /11$\\
%
Average round trip arm loss & 160 ppm \\
%
Differential arm loss & 20 ppm \\
%
Beamsplitter R/T imbalance & $\pm5 \times 10^{-3}$ \\
%
Differential arm offset from dark fringe & 25 pm \\
%
Output mode cleaner finesse & 210 \\
%
Input mode cleaner finesse & 1500 \\
%
Input mode cleaner length & 13.547 m \\
%
Power Recycling cavity length & 2.15 m \\
%
Signal Recycling cavity length & 2.257 m \\
%
Schnupp Asymmetry & 0.452 m \\
%
\hline\hline
\end{tabular}
\caption{Measured parameters of the 40m interferometer as of March 2008. Shown are those
parameters that determine the laser and modulation source noise couplings.} 
\label{tab:oldparams}
\end{center}
\end{table}
\renewcommand{\arraystretch}{1}
% ----------------------------------------------------------------------------------------
\clearpage
\section{Interferometer Displacement Noise Spectrum}
\label{app:straintarget}

\begin{figure}[!ht]
\begin{center}
\includegraphics[width=17cm,height=16cm]{40.pdf}
\label{fig:lsc-dia}
\caption{Displacement noise from the 40m Bench model (in the ISC Modeling CVS).
                The quantum noise is shown for broadband and detuned RSE cases.}
\end{center}
\end{figure}


% #####################################################################
% ####################################################################
\clearpage
\section{Background and Motivation}
\label{app:motive}

Throughout the 1990's,
the 40m interferometer was used for developing and testing
elements of the Initial LIGO optical configuration and control scheme.
It was upgraded in 2001 - 2004 in order to test elements of the
(then conceived) Advanced LIGO optical configuration and control scheme,
as described in the ``Conceptual Design of the 40 meter Laboratory Upgrade
for prototyping a Advanced LIGO Interferometer'', T010115~\cite{40mcdr01}.
The main parameters of that upgrade are given in Appendix 
\ref{app:oldparams}.

The main goals of that upgrade were to learn how to control
a power-recycled Fabry-Perot Michelson (PRFPMI) suspended mass interferometer
with a signal recycling cavity (SRC) operated in 
detuned resonant sideband subtraction mode (RSE, forming a
dual-recycled FPMI, DRFPI)
(see Appendix C of \cite{40mcdr01}).
The Advanced LIGO design at the time called for the following
innovations in optical configuration and control:
(a) High finesse arm cavities ($\sim$1200) in order to reduce
the power required to circulate in the power recycling cavity.
(b) RSE to recover the high-frequency signal response
of the detector, ``detuned''
to optimize it for detection of binary neutron star
inspirals in the presence of other technical noise sources.
(c) A signal extraction scheme for controlling the
DRFPMI that employed a moderate Schnupp asymmetry and
two pairs of RF sidebands
with very different frequencies, in order to provide the
best contrast between the PRC and SRC length degrees of freedom
(9~MHz and 180~MHz for AdvLIGO, and 33~MHz and 166~MHz for the 40m testbed,
employing ``double-demod'' signals derived from the sidebands alone
to control the DRMI).
(d) A Mach-Zehnder to apply both pairs of sidebands in parallel,
eliminating ``sidebands on sidebands'' \cite{40m-sidebands}.
(e) DC readout for homodyne detection of the GW signal using
arm-filtered carrier light as the local oscillator.

By the end of 2005, the 40m team was able to acquire lock and control 
all five degrees of freedom of the DRFPMI, in detuned RSE \cite{40m-DRFPMI}.
By 2007, DC readout was demonstrated on a PRFPMI~\cite{40m-DCreadout}.

In the process, several issues were encountered:
(a) lock acquisition and control of high-finesse arm cavities
is very difficult, requiring the development of many tricks
to get robust signals during lock acquisition.
(b) The detuned signal cavity formed an optical spring
which complicated the dynamics of lock acquisition.
(c) High-frequency RF (greater than say, 50 MHz)
is hard to work with.
(d) Double-demod signals have poor SNR and the demod phases seem to
drift around excessively without obvious explanations.
(e) The Mach-Zehnder solution proved to have its own problems: intensity
noise and non-stationary RFAM.
(f) The VME-based control electronics architecture is a liability just as
it is for initial LIGO.

Partially in response to these observations, the AdvLIGO ISC 
group reconsidered high-finesse arm cavities \cite{ArmFinesse},
signal extraction schemes that make use of lower RF 
sideband frequencies \cite{ISC:CDD}, and continuing with serial
modulation as in initial LIGO.

It will be important to test this new scheme with a realistic,
suspended interferometer. The 40m lab is a near-ideal place to do this.

% :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
\begin{table}
\begin{center}
\begin{tabular}{|l|r|r|r|r|c|}\hline
Parameter                     &40m (1998)& LIGO 4K   & 40m(2002) & Adv LIGO & units \\ \hline
Carrier $\lambda$             & 514.5    & 1064.     & 1064.     & 1064.    & nm  \\
Transmissivity T(ETM)         & 1.2E-5   & 1.5E-5    & 1.0E-5    & 1.0E-5   &     \\
Transmissivity T(ITM)         & 0.00565  & 0.02995   & 0.005     & 0.005    &     \\
Transmissivity T(RM)          & 0.1375   & 0.0244    & 0.07      & 0.07     &     \\
Mode cleaner length           & 1.0      & 12.255    & 13.542    & 16.655   & m   \\
FSR$_{MC}$                    & 150.     & 12.23     &  11.07    & 9.00     & MHz \\
RF freq1 $f_1 = n_1 fsr_{mc}$ & 32.7     & 24.46     & 33.207    & 9.00     & MHz \\
Arm   Cavity $L_{arm}$        & 38.25    & 3999.     & 38.55     & 3999.    & m   \\
PR    Cavity $L_{PRC}$        & 2.294    & 9.191     & 2.257     & 8.328    & m   \\
PRM--BS      length           & 0.25     & 4.396     & 0.30      & 4.000    & m   \\
BS--ITMinline length          & 2.315    & 4.877     & 2.183     & 4.536    & m   \\
BS--ITMperpin  length         & 1.773    & 4.599     & 1.731     & 4.119    & m   \\
Schnupp Asymmetry length      & 0.542    & 0.278     & 0.451     & 0.416    & m   \\
Arm cavity pole freq          & 1814     &   91      &  1578     &   15     & Hz  \\
Arm Cavity Finesse            & 1080     &  205      &  1235     & 1235     &     \\
Rec Cavity Finesse            &   24     &  138      &    47     &   47     &     \\
Arm Cavity power gain         &  670     &  130      &   775     &  775     &     \\
Rec Cavity power gain         &    9     &   48      &  16.5     & 16.5     &     \\
mirror diameter               & 10.16    &    25.0   &    12.5   & 31.4     & cm  \\
mirror length                 &  8.89    &    10.0   &     5.0   & 13.0     & cm  \\
mirror mass                   &  1.58    &    10.8   &  1.35     &  40.0    & kg  \\
PRM ROC                       & flat     &  8700     &  348      &  8700    & m   \\
ITM ROC                       & flat     & 14540     & flat      & 14540    & m   \\
ETM ROC                       &   61     &  7400     & 57.375    &  7400    & m   \\
$n_1$                         &    -     &    3      &   3       &    1     &     \\
$n_2$                         &    0     &    1      &   0       &    0     &     \\
$n_3$                         &  7.84    &    652.13 &   8.05    &  239.61  &     \\  \hline
$n_4$                         &          &           &   0       &    0     &     \\
$n_5$                         &          &           &   5       &   21     &     \\
RF freq2 $f_2 = n_4 f_1$      &          &           & 166.033   & 180.0    & MHz \\
SR    Cavity $L_{SRC}$        &          &           & 2.151     & 9.148    & m   \\
SRM--BS length                &          &           & 0.200     & 3.821    & m   \\
RSE peak frequency            &          &           & 4000      &   300    & Hz  \\
Signal Cavity tune            &          &           &  0.235    &  0.038   & rad/($\pi/2$)\\
SRM ROC                       &          &           &  365      &   9000   & m   \\
\hline
\end{tabular}
\caption{
Historical comparison of several interferometers' design parameters:
the 40m in 1998 (recycling experiment),
the Initial LIGO 4K interferometers,
the 40m in 2002 (dual recycling for Advanced LIGO),
and the Advanced LIGO design circa 2002.
}
\end{center}
\label{tab:ancientparams}
\end{table}
% #######################################################################
% #######################################################################


%-----------------------------------------------------------------------------------------

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



\end{document}
