That's OK, but its best to use standard notation. The power recycling gain is defined as the power incident on the BS divided by the power incident on the PRM from the laser side. You should also compare it with the PRC gain that you expect from mirror transmissions.

 I've made snapshots of PR2, PRM, ITMY and ITMX mirrors. Power buildup recycling gain (POWER BS / POWER PRM) was equal to 3-4.

 We've looked at PR2 face camera when PRM, BS and one of the ITMs were aligned. We saw an extra beam at PR2 when ITMX was aligned (right plot). This spot stays on the PR2 when prcl is locked.

Then we looked at PR3 transmission mirror and saw that the main beam is not on the edge of the mirror. Secondary beam is clipping on the mirror mount of PR3 that we see on BS_PRM camera.

Measured beam spot positions:

"+" for pitch means that the beam is too high, "-" too low

"+" for yaw means that the beam is left if you look from the back, "-" is right

Beam spots were measured using x, y arm and prcl locking to the carrier.

I think the angle of incidence on TT inside BSC will be too large because of eddy current damping brackets. I've measured max possible angle of incidence

This means that we do not have too much range and there is a probability that 45 degree incident beam will start clipping. I think we should just cut off the central part of the bracket. We do not need it anyway, our eddy current damping due to corner magnets is good enough.

I've left the brackets near the laptop in the clean room.

Tonight we've noticed that ITMX local damping was kicking the optics. This happened because LR shadow sensor was not working. In ~30 minutes it started to work again. Evan and I were working on installation, moving and focusing cameras and locking prcl and mich. We've installed a camera on BSC and plugged it in to PSL_SPARE input.

I'm not sure that this can be correlated to ITMX LR shadow sensor behaviour.

 Yesterday I wanted to recenter Guralps. I turned them off, understood that would be able to center them because we do not have power cable to Guralp box from Tara yet and turned them back on.

I've switched Guralp cables and spectrums are fine now.

I've estimated max possible angle of incidence on TT if we allow 20mm tolerance for the beam size and 5 mm tolerance for spot location on the mirror. It turns out to be

alpha = 43 degrees

So we need to cut the central part of the bracket. Then the max possible angle of incidence will be

alpha = 63 degrees

We can start the vent on Monday and use TT with an old bracket for yaw damping and later during the week we can install the brackets after they will be baked.

What mode will you get if lock the cavity PRM - ITMY/ITMX/TEST MIRROR without PR2, PR3 and BS?

Is it possible to skip MC1, MC3 and lock the laser to this test cavity to make sure that this is not actuator/electronics noise?

 I wrote a small document on the application of LQG method to a Fabry-Perot cavity control.

 I think if we make MCL UGF higher then 20 Hz, arm cavity spectra will feel it. It might be possible to use a combination of feedback and feedforward control from ground seismometers. I made MCL UGF at 3 Hz to reduce 1 Hz motion of the pendulum; feedforward OAF subtracted the stack at 3.3 Hz. Once OAF converged, I blocked adaptation and the filter became static FIR. MC length RMS was reduced by a factor of 10 and arm cavity spectra was not affected at frequencies >20 and became better at low frequencies. We'll see if this enough.

On the attached plot red color shows MC_F with MC_L OFF, blue - MC_L is ON, green - MC_L and OAF are ON.

Then I locked PRCL (using AS_Q and REFL55_I) to carrier and aligned the cavity. Power RIN was 50-70% and 00 beam on the POP camera was moving significantly. BS oplev was shaking the optics at 5 Hz. I fixed it, but there should be something else as RIN was still high.

Jenne, Den

We suspect PRM shows significant length to angle coupling due to large oplev beam angle in yaw.  Tonight we locked PRCL with ITMs.

We could lock PRCL on carrier to power recycling gain of 15. Lock continued for a few hours but power rin RMS was 0.15.

We triggered and normalized on POP_DC. MICH gain was -1 (filters FM3-5), PRCL gain was -8 (filters FM2,4,5,6,9).

MC_L was OFF during locking.

MC down script is too slow to block MC_L when the cavity goes out of lock. As a result the loop strongly kicks MC2. We decided to make a threshold inside MCS model on MC TRANS that will block MC_L during lock loss. This is a lower threshold. Upper threshold can be slow and is implemented inside MC up script.

Fast threshold can be set inside MC2 POS. I did not correct MC2 top level medm screen as it is the same for all core optics.

Note: Fast trigger will also block ALS signal if MC loose lock.

Spectra of BS, PRM, ITMX, ITMY are attached with oplevs ON and OFF (in units of urad). Loops reduce RMS from ~2urad to ~0.3urad but phase margin should be increased. REF traces show loop OFF. <-- really?

Note how PRM pitch and yaw spectra are different in the frequency range 0.5 - 7 Hz; yaw is factor of 50 larger then pitch at 2 Hz.

I compared PCRL and XARM angular motions by misaligning the cavities and measuring power RIN. Divergence angles for both cavities I calculated to be 100 urad.

XARM pointing noise sums from input steering TTs, PR2 and PR3 TTs, BS, ITMX, ETMY.

PRCL noise - from input TT, PRM, PR2 and PR3 TT, BS, ITMX, ITMY.

I would expect these noises to be the same as angular motion of different optics measured by oplves is simular. We do not have oplves on TT but they are present in both passes.

I measured RIN and converted to angle. Sharp 1 Hz resonance at XARM pointing spectrum is due to EMTX, it is not seen by PRCL. Other then that XARM is much quiter, especially at 3 - 30 Hz.

As PRM  is the main difference in two passes, I checked its spectrum. When PRCL was locked I excited PRM in pitch and yaw. I could see this excitation at RIN only when the peak was 100 times higher then background seismic noise measured by oplev.

 I assume that pointing noise and dc misalignment couples 00 to 01 by a factor theta / theta_cavity

Inside the cavity 01 is suppressed by 2/pi*F*sin(arccos(sqrt(g_cav))).

For the XARM this number is 116 taking g-factor to be 0.32. So all pointing noise couples to power RIN.

Suppression factor inside PRC is 6.5 for g-factor 0.97. This means that 85% of jitter couples to RIN, I accounted for this factor while converting RIN to angle.

I did not consider translational motion of the beam. But still PRC RIN can not be explained by oples readings as we can see exciting optics in pitch and yaw. I suspect this RIN is due to PR3, as it can create stronger motion in yaw than in pitch due to incident angle and translational motion of the mirror. I do not have a number yet.

I made another estimation assuming that PRCL RIN is caused by translation of the cavity axis:

• calibrated RIN to translation, beam waist = 4mm
• measured PRM yaw motion using oplev
• estimated PR3 TT yaw motion: measured BS yaw spectrum with oplev OFF, divided it by pendulum TF with f0=0.9 Hz, Q=100 (BS TF), multiplied it by pendulum TF with f0 = 1.5 Hz, Q = 2 (TT TF with eddy current damping), accounted for BS local damping that reduces Q down to 10.

PRM and TT angular motion to cavity axis translation I estimated as 0.11 mm/urad and 0.22 mm/urad assuming that TTs are flat. We can make a more detailed analysis to account for curvature.

I think beam motion is caused by PR3 and PR2 TT angular motion. I guess yaw motion is larger because horizontal g-factor is closer to unity then vertical.

 I think it is too much. Incident power to IFO is 1.3 W. Even if we assume no losses and pick-offs on the path to the arms, we should get ~100 uW out of the cavity. I measured X and Y arms transmission to be 60 uW. Did you disable triggering during your measurement?

 We got granite bases today from the manufacturer. We plan to set them up on Wednesday, 8 am. Please note, there will be an installation mess at Xend, Yend and corner during ~4 hours. Let us know if you have any objections to do this at this particular time.

Installation locations are specified in elog 8270, scheme attached is valid except for Xend. Instrument will be installed on the place of nitrogen containers.

(  next to the wall at corner sout-east of the south end )

I modified our existing c1ass model to include alignment of input steering TT1 and TT2 for YARM and BS for XARM. Corresponding medm screens are also created.

Dithering:

ETM_PIT: frequency = 6 Hz, amplitude = 100 cnts
ETM_YAW: 8 Hz, 400 cnts
ITM_PIT: 11 Hz, 800 cnts
ITM_YAW: 14 Hz, 1200 cnts

These values were chosen by looking at cavity transmission and length signals - excitation peaks should be high enough but do not shake the optics too much.

Demodulation:

LO for each degree of freedom is mixed with cavity length and transmission signals that are first bandpassed at LO frequency. After mixing low-pass filter is applied. Phase rotation is chosen to minimize Q component

Sensing matrix:

8 * 8 matrix was measured by providing excitation at 0.03 Hz to optics and measuring the response in the demodulated signals. Excitation amplitude was different for each optics to create cavity transmission fluctuations of 25%

Though coherence was > 0.95 during the measurement for each element (except for TT -> Length signals), after inverting and putting it to control servo, loops started to fight each other. So I decided to try a simple diagonal matrix:

TT1_PIT -> ETM_PIT_TRANS, TT1_YAW -> ETM_YAW_TRANS, TT2_PIT -> ITM_PIT_TRANS, TT2_YAW -> ITM_YAW_TRANS,

ITM_PIT -> ETM_PIT_LENGTH, ITM_YAW -> ETM_YAW_LENGTH, ETM_PIT -> ITM_PIT_LENGTH, ETM_YAW -> ITM_YAW_LENGTH

And this matrix worked much better.

Control loops:

8 loops are running at the same time. UGF for input steering loops is 20 mHz, for cavity axis loops - 80 mHz. Slower loop is stronger at low frequencies so that cavity axis servo follows input steering alignment.

Results:

When I started experiment the cavity was misaligned, transmission was ~0.4. Servo was able to align the cavity in ~30 seconds. This time depends on mirrors misalignment as well as input optics and cavity axis misalignment relative to each other.

When servo converged I disturbed ETMY, ITMY, TT1 and TT2. Servo was able to compensate for this.

Excitation lines seen by transmission and length of the cavity are suppressed as shown on the attached as pdf figures.

Note:

Though the servo is able to align the cavity during my tests, this does not mean it will work perfectly any time. So please, if you lock, try to use the servo for alignment. If something goes wrong we'll fix it. This is better then to align IFO by hands every time.

Today Rana pointed out that our FSS slow servo is malfunctioning. It has been for a while that our laser temperature control voltage drifted from 0 to 10.

I looked at FSSSlowServo script that runs at op340m and controls the servo. Script disables the servo when MC transmission is less then FSS_LOCKEDLEVEL. But his value was set to 0.2 probably till reference cavity time.

This means that slow servo was not disabled when MC was unlocked. I changed this value to 7000.

Also I increased integral gain from 0.0350 to 0.215 such that fast control is always in the range 4.5 - 5.5

Tonight PRMI was locked on REFL55 I&Q for PRCL and MICH with POP110I as a trigger and power normalizer.

I could see power fluctuations and beam motion on the POP camera very much the same as for carrier. The difference is that carrier stays for hours while sidebands for a few minutes.

POP110:

I&Q analog gains were set to 15 dB. Relative phase was set to 25 degrees by looking at I and Q components when the cavity goes through the resonance. Q should be 0.

REFL55:

Phase rotation was measured by exciting PRM at 20 Hz and minimizing this line at REFL55_Q. I stopped at 33 degrees.

 RIN:

I compared power fluctuations of PRCL when it was locked on carrier (POP_DC) and on sidebands (POP110_I).

Time series of POP110_I during one of the locks

POP camera:

I've put 4 scripts into ASS directory for YARM alignment. They should be called from !Scripts YARM button on c1ass main medm screen.

Scripts configure the servo to align the cavity and then save computed offsets. If everything goes right, no tuning of the servo is needed.

Call TRANS MON script to monitor YARM transmission, then "ON" script for aligning the cavity, then "SAVE OFFSETS" and "OFF" for turning the servo off.

ON script:

• sets demodulation gains that I used during OL measuments
• sets LO oscillator frequency and amplitude for each optic
• sets demodulation phase rotation
• sets sensing matrix
• sets servo gains for each degree of freedom
• sets up limits for servo outputs
• gently increases the common gain from 0 to 1

SAVE OFFSETS script:

• holds servo outputs
• sets servo common gain to 0 and clears outputs
• reads old optics DC offsets
• computes new DC offsets
• writes new offsets to C1:SUS-OPTIC_ANGLE_OFFSET channel
• holds off servo outputs

OFF script:

• sets LO amplitudes to 0
• blocks servo outputs

Notes:

SAVE OFFSET script writes DC offsets to C1:OPTIC_ANGLE_OFFSET channel, not to _COMM channel!

LIMITS are set to 500 for cavity axis degrees of freedom and to 0.5 for input steering. Usually servo outputs is ~30% if these numbers. But if something goes wrong, check this for saturation.

DC offsets of all 8 degrees of freedom are written one by one but the whole offset of put at the same time. This works fine so far, but we might change it to ezcastep in future.

 To put everything in one place I add a final drawing of the base to this elog.

 Next time we continue with wiring and putting temperature and pressure sensors inside the box. Connector support plate drawing is attached. We'll have sensors inside the kit with STS-2 or Trillium as their connector is small enough (19 pin vs 26 pin for Guralps) that we can put an additional 4 pin lemo connecor (2 pins for each sensor). I think EGG.0B.304.CLL is good for this application. Temperature and pressure sensor we can by from omega.

 I attach the drawings for Guralp and T-240/STS-2 connector plates. Drawings contain all information about the screws, O-rings and connectors.

Basically, box mounting receptacle for seismometer cable is attached to the connector plate with 6-32 screws. Inside cable should be ~ 1m long and connect the plate with seismometer.

For T-240 realization we have an additional LEMO connector for temperature and pressure monitoring inside the station. We should buy sensors and plug them into some machine with slow controls.

LEMO connector has 9 pins. 4 will be used for temperature and pressure sensors and spare 5 can be used for future ideas.

Also I think it might be better to put two T-240 into isolation stations.

Jenne, Den

Today we worked on PRM angular servos and Y-arm ALS stabilization.

In the current PRMI angular control configuration two servos simultaneously drive PRM - oplev and POP ASC. We considered 2 ways to redesign this topology:

• once lock is acquired, turn on POP ASC servo that corrects oplev error signal
• turn off PRM oplev and turn on POP ASC  servo

The first option requires model rewiring so we started from the second one. We had to redesign POP ASC pitch and yaw servos for this because PRM TF has changed. Attached is servo OLTF.

This method worked out well and once PRMI is locked we turned off oplev servo with ramp of 0.5 sec and enable ASC POP servo with ramp of 1 sec.

Once PRMI was locked and ASC running we have turned off PRM angular local damping that presumably prevents us from bringing arms into resonance due to IR coupling to shadow sensors.

PRMI was stable using only ASC POP servo and we moved on to ALS. We found Y-arm beatnote and enabled control to ETMY.

Cavity was stabilized but not robust - we were loosing IR in a minute because green relocked to 01 mode with transmission equal to more than half of 00 mode. This is probably due to angle to length coupling of ETMY.

We were also loosing IMC during cavity stabilization. We made MCL servo and will tune it tomorrow looking at the arm spectrum as an OOL sensor.

I have calibrated ETMX and ETMY actuators and added a template armSpectra.xml into /users/Templates directory.

Template shows control and error signals of both arms. Procedure is standard: calibrate control to meters and match error based on UGF measurement. XARM UGF: 200 Hz, YARM UGF 210 Hz.

Noise level at high frequencies (>100 Hz) for YARM is 3*10^-15 and is factor of 3 better then for XARM. Servo gains are in the same ratio. I think there is less light on POX than on POY RF PD because I checked phase rotation and analog gain. I assume transimpedances are the same.

 It seems to me that current design of the common mode servo is already fine. Attached plots show common mode open and closed loop transfer function.

Frequency response of the servo is taken from the document D040180. I assumed coupled cavity pole to be ~100 Hz.

The only question is if our EOM has enough range. Boost 2 increases noise injection by 10 dB in the frequency range 20-50 kHz. Boost 3 has even higher factor.

I have modified/compiled/installed/restarted c1scx and c1scy models to include arm transmission QPDs in angular controls.

For initial test I have wired normalized QPD pitch and yaw outputs to ASC input of ETMs. This was done to keep the signals inside the model.

QPD signals are summed with ASS dither lines and control. So do not forget to turn off QPD output before turning on dither alignment.

Medm screens were made and put to medm/c1sc{x,y}/master directory. Access from sitemap is QPDs -> ETM{ X,Y} QPD

I had a look on x,y arms stabilization using ALS. Input green beam was misaligned and I was loosing 00 every few minutes. I vent on the floor and realigned green beams.

YARM alignemt was smooth - transmission increased from 0.4 to 0.85 with PSL shutter off.

XARM was tough. Steering mirrors did not have any derivatives when transmission power was 0.5. I walked the beam with piezos but got only 0.55. It seems that the input beam is mismatched to the cavity. When the transmission was 1 last time? Does anyone have a model of the xend table to compute mode matching?

Input green alignent was improved and I could keep arms stabilized for periods of ~30min - 1 hour. Still not forever.

I noticed that ALS_XARM and ALS_YARM servos have limiters of 6000 and control signal had high frequency components that were not rolled off as shown on the plot "ETMY_DRIVE". I have added a low pass filter that reduced RMS by factor of 5 and took 7 degrees of phase at UGF=150 Hz. Now margin is 33 degrees.

Then I excited ETMY longitudinally at 100 Hz and measured first and second harmonics of the YARM RIN. I got total DC offset of 0.3 nm. This means significant length coupling to RIN. First of all, "scan arm" script does not tune the offset very precise. I guess it looks at DC power, checks when cavity passes through symmetrical points of the resonance and takes the average. It is also useful to look at POX/POY and confirm that average is 0. Plot "ALS_RIN" shows comparison of YARM power fluctuations when it is locked using IR and stabilized using ALS. By manually correcting the offset I could reduce length coupling into RIN, coherence was ~0.1.

Cavity RMS motion also couples length to RIN. Plot "ALS_IR" shows YARM error signal. I also looked at POY signal (LSC-YARM_IN1) as an OOL sensor. At low frequencies POY sees only IMC length fluctuations converted to frequency. I have engaged MCL path and ALS error and LSC error signals overlaped. Cavity RMS motion is measured to be 200 pm.

Last time we designed MCL loop with UGF ~ 30 Hz and I think, it was hard to lock the arm because of large frequency noise injected to IFO.

This time I made a low bandwidth MCL loop with UGF=8 Hz. MCL error RMS is suppressed by factor of 10 and arms lock fine.

Attached plots show MCL OL, MCL error suppression and frequency noise injection to arms.

It is interesting that spectrum of arms increases below 1 Hz meaning that IMC sensing noise dominates in this range.

I did not include the loop into the IMC autolocker. I think it is necessary to turn it on only during day time activity and when beatnote is moving too much during arm stabilization.

Attached is matlab code that I used

 % IMC OL
G = zpk(-2*pi*8964, 2*pi*[-10; -10; -10; -1000; -274000], db2mag(242.5)) * ...
    tf([1 0.8*1.55e+05 3.1806e+10], 1);

% CARM PATH
CARM = G/(1+G);

% Common mode boosts
BOOST = zpk(-2*pi*4000, -2*pi*40, 1);
BOOST1 = zpk(-2*pi*20000, -2*pi*1000, 1);
BOOST2 = zpk(-2*pi*20000, -2*pi*1000, 1);
BOOST3 = zpk(-2*pi*4500, -2*pi*300, 1);

% Coupled cavity pole
CCPole = zpk([], -2*pi*100, 2*pi*100);

% Servo gain
Gain = db2mag(43);

% CARM OL with boosts
H = CARM * CCPole * BOOST * Gain;
H1 = H * BOOST1;
H2 = H1 * BOOST2;
H3 = H2 * BOOST3;

% Plot
% bode(H, H1, H2, H3, 2*pi*logspace(3, 5, 10000));
% bode(1/(1+H), 1/(1+H1), 1/(1+H2), 1/(1+H3), 2*pi*logspace(3, 5, 10000));

X,Y arms were stabilized using ALS and moved 5 nm from the resonance, PRMI was locked on sideband using REFL165 I&Q. POP angular servo was running; PRMI RIN was good (~2-3%)

During slow offset reduction I was sweeping MICH, PRCL and POP servos for instabilities due to possible optical gain variations, loops were fine.

I could reduce offset down to ~200 pm and then lost lock due to 60 Hz oscillations as shown on the attached plot "arm_offset"

Arms were stabilized with RMS comparable to the offset and power in arms was fluctuating from 3 to 45.

60 Hz line most probably comes from MICH. RMS is dominated by the power lines and is ~ 1 nm as seen on the plot "PRMI_CAL". I think this is too much but we need to do simulations.

When PRMI is locked on REFL 165 I&Q signals MICH rms is dominated by the 60 Hz line and harmonics. It comes from demodulation board.

To increase SNR ZFL-100 LN amplifier (+23.5dB) was installed in LSC analog rack. MICH 60 Hz and harmonics are improved as shown on the plot "mich_err"

I have also added a few resg at low frequencies. MICH rms is not 3*10^-10. In Optickle I simulated power dependence in PRC and ARMs on MICH motion. Plot is attached.

 I think we need to stabilize MICH even more, down to ~3*10^-11 . We can think about increasing RF amplifier gain, modulation index and power on BB PD.

CARM offset reduction was a little better today due to improved MICH RMS. Power in arms increases up to 15 and than starts to oscillate up to 70 and then PRMI looses lock.

Tomorrow we need to discuss where to put RF amplifier. Current design has several drawbacks:

• DC power for the amplifier is wired from a custom (not rack based) +15V power supply that was already inside the lsc rack and used for other ZFL-100LN
• BNC cables are used because I could not find any long SMA cables
• we would like gain of ~40 dB instead of 23.5 dB

Koji, Den

Some results and conclusions from tonight:

PRC macroscopic length is detuned. We measured REFL phases in carrier and sideband configurations - they are different by ~45 degrees for both 11 and 55 MHz sidebands. Additional measurement with phase locked lasers is required.

We got stable lock of PRMI+2arms with CARM offset of ~200 pm. We think this is the point when we should transition to 1/sqrt(TR) signals. We plan to rewire LSC model and also test CM servo with 1 arm during the day.

POP ASC OL shape changes when we reduce CARM offset probably due to normalization by sum inside the PD. Servo gets almost useless when PRMI power fluctuates by a factor of few.

SMA cables were made and installed for the REFL165 RF amplifier in lsc rack.

As a CM slow path test I locked free swinging yarm by actuating on MC length with bandwidth of 200 Hz. Crossover with AO is not stable so far.

I used xarm as an ool frequency noise sensor. MC2 violin mode is at 645 Hz, I have added a notch filter to LSC-MC2 bank.

Koji, Den

Procedure:

• lock yarm on IR, wire POY to CM input
• transition arm to CM length path by actuating on IMC
• increase AO gain for a stable crossover
• engage CM boosts

Result:

• arm can be kept on resonance and even acquired on MC2
• stable length / AO crossover is achieved
• high bandwidth loop can not be engaged because POY signal is too noisy and EOM is running out of range

We spent some time tuning CM slow servo such that fast path would be stable in the AO gain range -32db -> 29dB (UGF=20kHz) when all boosts are turned off and common gain is 25dB. Current filters that we use for locking are not good enough - AO can not be engaged due to oscillations around 1kHz. This is clearly seen from slow path closed loop transfer function. I will attach servo shapes tomorrow.

Attached plot "EOM" shows EOM rms voltage while changing AO gain from -10dB to 4dB. For UGF of 20kHz we need AO gain of 29dB.

It seems we can start using CM servo for CARM offset but the sensor should be at least factor of 30 better than POY. Add another factor of 10 if we would like to use BOOST 2 and BOOST 3.

Koji, Den

CM Servo with POY11 successfully engaged. UGF: ~15kHz.

Tonight we decided to repeat one arm locking using high-bandwidth CM servo. We low-passed AO signal to avoid saturations of the EOM. We tried different configurations that compromise between noise and loop phase margin and ended up with a pole at 30kHz. SR560 is used as a low-pass filter.

Another problem that we faced was big (~2.6V) electronic offset at the input of 40:4000 BOOST. Once engaged, cavity would be kicked out of lock. We calibrated this offset to be almost half linewidth of the cavity (~300pm). To avoid lock loss during engaging the boost we increased common mode gain to maximum (31 dB).

Measured OL is attached. UGF is 15kHz, phase margin is 60 degrees. We have also simulated evolution of loop shape during bringing AO path. Plot is attached.

The final procedure is

• set common gain up to 31dB, AO gain to 8dB, MC IN2 gain 10dB, CM offset 0.7V
• lock arm with CM slow path with bandwidth of 200 Hz
• enable AO path, gradually increase slow and fast gains by 12 dB
• enable boost

We did online adaptive filtering test with IMC and arms 1 year ago (log 7771). In the 40m presentations I can still see the plot with uncalibrated control spectra that was attached to that log. Now it the time to attach the calibrated one.

Template is in the /users/den/oaf

We've subtracted acoustic noise from PMC using 1 EM 172 microphone. We applied a 10 Hz high-pass filter to PMC length signal and 100,200,300:30,30 to whiten the signal.We used ~10 minutes of data at 2048 Hz as we did not see much coherence at higher frequencies.

We were able to subtract acoustic noise from PMC length in the frequency range 10-700 Hz. In the range 30-50 Hz error signal is less by a factor of 10 then target signal.

We aligned and locked Y arm for green:

• installed camera on PSL to monitor green transmission
• aligned green path on the ETMY table to see the beam on the PSL camera
• misaligned ETMY and aligned ITMY to see reflected beam on REFL PD
• installed green transmission PD on PSL
• aligned ETMY and locked YARM to 00 mode

I've switched error channel cable to output monitor. Whitening filter is need for scattering measurements.

We aligned accurately 00 green in yarm, changed voltage on PZT2 to see red flashing at TRY at the normalized level 0.2-0.3. The plan was to lock yarm using POY11 and green from other side, maximize red TRY by adjusting PZT2. But POY11 does not go out of the vacuum, so we adjusted TRY by flashing. 2 DOFs of PZT2 is not enough to match 4 DOFs of red beam so we adjusted both PZT2 and cavity mirrors. TRY flashing is 0.5-0.6 and green is still locking to 00 though its transmission is not maximized. We'll fix it later by adjusting input green beam.

Next we wanted to get red beam on TRX PD. Beam steering was done by BS only. We misaligned BS in pitch and excited BS angle motion by 1000 counts. We could see red beam moving on the wall of ETMX chamber. We moved it to ETMX mirror frame, estimated position of the mirror center and moved BS to this position. The beam should be approximately in the middle. For now we can not see red beam on the camera at ETMX table, more work is needed.

Today at 11:13 AM the stack of invacuum BS table was kicked and IFO misaligned. We adjusted PZT2 voltage by ~20 V in yaw such that IPPOS was restored. Then we could lock arms.

We've provided acoustic excitation using speakers on the AS table and saw that PSD of YARM feedback signal increased in the frequency range 50 - 100 Hz. Meanwhile, XARM feedback signal did not change. Moreover, YARM noise is much higher at these frequencies compared to XARM.

The problem was with YARM oplev servos. Both ITMY and ETMY produced noise to YARM length. ITMY oplev signal had a huge resonance at 55 Hz. We measured coherence with accelerometers, it was 0.8. It turned out that one of the mirror mounts was not fixed in the oplev path. When we fixed it, noise has gone.

Note: speakers were on AS table but mirror mounts could steel feel it on ITMY table.

Then we had a look on ETMY table. We saw a mirror on suspiciously long mirror mount that was used in the ETMY oplev path. We slightly kicked long mount with a small screwdriver and YARM control signal went up with resonance at 100 Hz.

 The problem was caused by low reflectivity of the mirror that splits MC reflected beam into two: first goes to trash, second - to WFS. Power before the mirror was 100mW, reflected beam that goes to WFS was 0.3mW. Using dataviewer we learnt that the beam intensity was ~5 times more in the past.

This happened because the mirror position was adjusted a few days ago. Its reflection depends on the angle of incidence and amount of light to WFS was significantly reduced. We could either increase the angle of incidence or use two mirrors with high reflectivity instead of this with high transmission.

We've chosen the second variant not to confuse anyone in future with non-45 degrees angles. We are now using one mirror with reflectivity 98% to direct most power to the trash while other 2% are directed using the second mirror to WFS path. We now have 0.7 mW on WFS1 and 1.3 mW on WFS2.

Then we adjusted WFS 

• blocked the beam and run scripts/MC/WFS/WFS_FilterBank_offsets to calculate offsets in the WFS servo
• aligned MC and centered beams on WFS 1 and 2
• provided excitation to MC1 at 5 Hz (400 counts) and adjusted I&Q phase rotation
• adjusted the gain and changed it in MC autolocker (reduced from 0.25 to 0.15 as we now have more power of WFS as before)

We were able to close the loops. The phase margin is too low though, we need to improve feedback filters.

We are now trying to understand why the coherence between SUS-X_SUSPOS_IN1 and SUS-X_SUSPOS_OUT is lost below 1 Hz for X = MC1, MC2, MC3, BS, ITMX, ITMY, ETMX, ETMY, SRM. It is OKEY only for PRM but the different filteres are used there. For PRM - 30:0.0 and Bounce Roll, for all others - 30:0.0 and Cheby. The transfer functions between these two signals plotted in foton and fft tools are also not the same.

If we switch off all the filters between these 2 signals, than the coherence is one. If one of the filters is switched on, everything is also fine. But if there are several present, than they filter the signal in unexpected way.

Moreover it seems that the coherence is dependent on the input signal. The coherence is better with local dumping than without.

follow up email from Dennis 5-13-2018. The last line agrees with the numbers in elog13821.

Basic Idea

The idea behind this study was that in several frequency ranges, there are spikes, or just dominant features, in the ASD of each of the sensors. I’ll model these noise sources as a signal  where  is a Nx1 matrix that describes how the single noise source couples into each sensor. Lets assume that this noise source is the dominant source of noise power in the sensors between  and . Then the band limited covariance matrix will have the following form.

 is the integral of the PSD of the noise source over the frequency band. We can use SVD of  to calculate the result of the PCA.  . Since  is a Nx1 dimensional matrix,  is a 1x1 matrix,  is a Nx1 matrix with a the singular value in the first component and 0’s in the rest, and  is a NxN matrix. The first column of  is equal to  up to a scalar. The result of the columns of  for an orthogonal basis for the space perpendicular to . Therefore, for prominent features in the ASD of the sensors, we can "zoom in" and do a PCA. The first principle component will tell us how the noise source is coupling into the sensor vector space. The rest of the principle components will define subspace orthogonal to the noise source. Therefore a virtual sensor designed in this orthogonal subspace will avoid the noise spike.

Test with simulated noise

The first test I did was to choose some S_n at random and a noise source ASD of  with = 1KHz. I started with the CSD of the unsupressed sensor data, , and calculated the CSD with the new simulated noise: . Attachement 1 shows the ASD of the unsuppressed sensors with this added noise. The second figure is zoomed in on the noise peak. The results of the PCA analysis are summarized by attachment 2. The first figure in attachment 2 shows the ASDs of the virtual sensors formed by the principle components of the PCA. The second figure zooms in on the 1Khz feature. The solid blue curves are the ASDs of the sensors and the dotted red lines are the PCA virtual sensors. This figure shows that the first PCA sensors clearly contains the noise spike but the other N-1 (7) PCA sensors are now flat over this frequency range.

Test with real noise

Attachements 3 and 4 show the same anaylsis done on a real noise feature in the sensors ASDS at ~180Hz and attachments 5 and 6 show the same for a ~640 Hz feature. Both tests show results consistent with the simulated noise test. These are the only tests I've performed thus far so I haven't found a feature yet that doesn't play well with this analysis. 

Conclusions

Virtual sensors could be designed to avoid particular noise spikes this way but a more optimal sensor could avoid multiple noise spikes by transitioning, as a function of frequency, between the othogonal subspaces defined by the PCA. Also, ths technique provides a measure of  up to a scaling. Perhaps this can allow for the origin of these noise features to be identified. 

After Yuta locked PRMI and measured the sensing matrix, I changed the input matrix to the following and measured the MICH and PRCL OLTFs.

              AS55Q           |      REFL11_I

MICH A:   0.99752413, 0.00247587

PRCL A:  -0.99752413, 0.99752413

This input matrix was calculated by taking the 2x2 submatrix of the AS55Q and REFL11_I components of the sensing matrix. I took the inverse and then scaled the first row by the MICH->AS55_Q sensing matrix element and likewise for the second row with the PRCL->REFL11_I sensing matrix element.

GPS time for data from lock with new input matrix: 1376274300 - 1376274400.

The OLTFs are saved in:

users/deven/PRCL_OLTF_8-16

users/deven/MICH_OLTF_8-16

This elog post refers to this previous post which details a PRMI lock where the sensing matrix and OLTFs for MICH and PRCL were measured. In addition, I grabbed the time series data during this lock from AS55, REFL11, REFL55, and REFL165 for I and Q demodulations from GPS time 1373763480 - 1373763560. During the lock, the MICH signal was normalized by POPDC, but I confirmed with Koji this didn't affect the data in the channels I used.

Channels I grabbed from:

x1 = "C1:LSC-AS55_I_ERR_DQ" #AS55_I
x2 = "C1:LSC-AS55_Q_ERR_DQ" #AS55_Q
x3 = "C1:LSC-REFL11_I_ERR_DQ" #REFL11_I
x4 = "C1:LSC-REFL11_Q_ERR_DQ" #REFL11_Q
x5 = "C1:LSC-REFL55_I_ERR_DQ" #REFL55_I
x6 = "C1:LSC-REFL55_Q_ERR_DQ" #REFL55_Q
x7 = "C1:LSC-REFL165_I_ERR_DQ" #REFL165_I
x8 = "C1:LSC-REFL165_Q_ERR_DQ" #REFL165_Q

I calculate (what I'm calling)the covariance matrix: COVAR(X) = [CSD(x_i,  x_j)]_i,j where X is the vector of measurements from each sensor and CSD is the cross spectral density. Each element is the CSD between two sensors and the diagonals are the PSD of each sensor. The ASDs of this data is shown in attachement 1.  

Attachement 4 depicts a block diagram I am using to represnt the feedback system. PC includes details of the control filters, actuators and mechanical plant. After this block, n_d represents displacement noise that enters in Y, the state of MICH and PRCL. S is the sensing matrix and M is the input matrix that fuses the sensors. n_s represnts all other noise on the sensors. Based on this model, the measured data form the sensors had this relation to the input noise sources: X = (I+SPCM₀)^-1(Sn_d+n_s), where M₀ is the input matrix used during the lock. COVAR(X) = COVAR( (I+SPCM₀)^-1(Sn_d+n_s) ) =  (I+SPCM₀)^-1COVAR(Sn_d+n_s)((I+SPCM₀)^-1)^H. These transfer functions take linear combinations of the frequency representations of the signals/noises so the PSDs and CSDs of the new signals get new cross terms based on the mixing. This is captured by maping the covariance matrix between the transfer function and its hermitian conjugate. This was used to remove the suppression by the feedback loop by mapping COVAR(X) with (I+SPCM₀). I define COVAR(X)_unsupressed = (I+SPCM₀)COVAR(X)(!+SPCM₀)^H =  (I+SPCM₀)(I+SPCM₀)^-1COVAR(Sn_d+n_s)((I+SPCM₀)^-1)^H(I+SPCM₀)^H  = COVAR(Sn_d + n_s). The ASDs of the unsuppressed noises in each sensor are shown in attachements 2 and 3. In 2, these ASDs are calibrated to meters by multiplying them by the recipricol of the sensing matrix coefficient mapping MICH to that sensor. In 3, the same is done for PRCL.

The theoretical closed loop performance of new M's can be calculated by mapping the COVAR(X)_unsuppressed by the closed loop transfer function for a signal injected at the sensors, X, to the fused sensors, Z. This TF is (I+MSPC)^-1M. Then, from Z the signals are mapped by (MS)^-1 to simulate the new ability to control and sense Y. As before, these transfer functions are used to map the covariance matrix. I define COVAR(Y) = [(MS)^-1 (I+MSPC)^-1M] COVAR(X)_unsuppressed[(MS)^-1 (I+MSPC)^-1M]^H. I have previouly tried using a transfer function from noise injected at the sensors directly to Y, but I don't think this captures the important dynamics since S and M are rectangular matricies. M maps from a vector space with dimension equal to the number of sensors(8 in this case) to dimension equal to the number of DoFs(2 in this case). Previously, I was using S^-1(I+SPCM)^-1 as the transfer function to map COVAR(X)_unsuppressed --> COVAR(Y) where S^-1 is the Moore-Penrose inverse of S. At low frequencies I think this can be equivalent for a class of M's, but all M dependence goes away for high frequencies when PC --> 0. On the other hand, we expect M to be very important at high frequencies since it determines what sensing noise enters the system. 

Attachements 5 and 6 show the theoretical ASD for MICH and PRCL with several choices of M as well as the open loop noise. These correspond to the square root of the diagonal elements of COVAR(Y). The M₀ curve shows the performance of the lock in which the data was taken. The calculation for this is the same as described above but M₀ was chosen to select AS55_Q for MICH and REFL11_I for PRCL. The MS=G₀ data was calculated by starting with the Moore-Penrose inverse of S, so that MS is diagonal, and scaling the rows to have the same MICH and PRCL gain as M₀. The top row of S^-1 was scaled by the MICH --> AS55_Q sensing matrix element and the bottom row by the PRCL --> REFL11_I sensing matrix element. The last matrix shown, MS=G_0 w/ noise fit is subject to the MS=G_0 constraint just described, but it was also fit to reduce noise entering the system at high frequencies. Above 1KHz, the noise is pretty white in all sensors. The ASDs for 1KHz to just below the cutoff frequency are shown in attachment 8. For these range of frequencies I used M*COVAR(X)_unsuppressed*M^H as a cost function to approximate the open loop sensing noise entering the fused sensors. I used scipy.optimize.minimize() to optimize M for this cost function with repsect to the MS=G_0 constraint that I assumed would be crucial for decent closed loop performance at low frequencie. This optimization was done at every frequency step, but the result was unsuprisingly pretty constant over the chosen frequency range so I averaged the elements of the matrix to make a constant matrix. This matrix is used to calculate the MS=G_0 w/ noise fit data.

Both matrices suggested show improvements in these calculations. The both rely on the sensing matrix, which has large uncertainties and is assumed to be frequency independent which may strongly hinder their performance in the real PRMI LSC system.

The matrices are given below. The order of the channel names above determines the order of the coefficients along each row. 

MS=G_0 matrix:
[ 0.06554358  0.89041025 -0.02285036 -0.08922597  0.0720552   0.00681149 -0.24507124 -0.15858639]
[  4.0546419   55.0763957   -0.46854116  -5.7461138    4.48030295 0.4226362  -15.15734417  -9.809963  ]
MS=G_0 w/ noise fit
[ 0.20865055  0.194148   -1.70063937 -7.07367426  0.04610331 -0.01614077 -0.10858281 -0.06099116]
[  12.91008472   12.00303754 -104.26878095 -437.86044383    2.82103162 -0.99588645   -6.71642619   -3.77348024]

Yehonathan, Paco, and Hiroki helped lock the interferomter into PRMI. While locked, the sensing matrix was calaculated with scripts/CAL/SensingMatrix/ReadSensMat.ipynb. Several of the matrix elements flipped sign from the previous matrix I've used: measured in described in this elog. The results are shown in attachement 1. The interferomter was locked with AS55_Q sensing MICH and REFL11_I sensing PRCL. Also, data was recorded from the following channels from 1375574090 - 1375574170 when the lock was stable.

x1 = "C1:LSC-AS55_I_ERR_DQ" #AS55_I
x2 = "C1:LSC-AS55_Q_ERR_DQ" #AS55_Q
x3 = "C1:LSC-REFL11_I_ERR_DQ" #REFL11_I
x4 = "C1:LSC-REFL11_Q_ERR_DQ" #REFL11_Q
x5 = "C1:LSC-REFL55_I_ERR_DQ" #REFL55_I
x6 = "C1:LSC-REFL55_Q_ERR_DQ" #REFL55_Q
x7 = "C1:LSC-REFL165_I_ERR_DQ" #REFL165_I
x8 = "C1:LSC-REFL165_Q_ERR_DQ"

The goal was to try both methods described in this elog about calculating new input matrices. However, there was only time to try the simplest which takes the Moore-Penrose inverss of the sensing matrix and rescaled the first row by the MICH --> AS55_Q sensing matrix element and the second row by the PRCL --> REFL11_I sensing matrix element. The matrix is given below.

[ 0.00024464  0.00237176  0.00955445  0.04220886 -0.0198488   0.0049371 -0.0044138   0.0001007 ]
[ 0.0009515   0.00924028  0.02669179  0.16685194 -0.07720723  0.01935389 -0.01722475  0.0003956 ]

There was only time to plug the matrix in and briefly close the loop and compare the error signals for MICH from the normal sensing matrix with AS55_Q and with the proposed virtual sensor. Lock was not achieved with the new sensors. A screen shot of the error signals are given in attachement 2. The fused error signal is in blue and the AS55_Q signal is in orange. The screen shot shows the error signal for the fused sensor is very different than AS55_Q: large high frequency fluctuations. Based on these results, I am going to use saved time series of the sensors to compute the error signals as functions of time for the data used in the last elog. I'm not sure whether to attribute the poor performance to the large uncertainties in the sensing matrix and the assumption that the sensing matrix is frequency independent or the noises on the sensors which weren't considered in the calculated of this input matrix.