1. Check: ASS for X arm seems not quite doing its job. ETMX has to be moved using sliders to obtain maximum TRX and the arm alignment was seen to be drifting.
ETMX ASC output was turned off for whatever reason. Switched it on, ASS is fine.
The following that went unnoticed from yesterday were recovered today:
1. ETMX and ETMY 'misalign' scripts weren't running. Troubleshooting showed slow machines c1auxex and c1auxey weren't responding. The machines were reset.
2. PRM oplev gains were zero. Gain values were set looking back at the burt files.
3. X end PZT power supplies were turned ON and set to 100V.
4. X end doubler temperature was reset to the last optimal value on elog (36.35 deg).
Some hitches that should be looked into:
2. Check: Status of other slow machines and burt restore whichever needs one.
Incidentally, while messing around with transfer functions and sensing matrix elements this evening, I was able to sideband lock straight onto REFL33 I&Q. The settings were all identical to Koji's ELOG, with the following differences:
REFL33 WHTN: 30dB demod phase +125.5deg (tweaked from 135.5 to minimize MICH in I)
REFL33I x +1.0 -> PRCL
REFL33Q x +3.0 -> MICH
MICH OFS 0 / Gain 1/ Limitter ON (Oscillations occurred at 1.3)
PRCL OFS 0 / Gain -0.04 / Limitter ON
MICH ITMX -1.0 / ITMY 1.0
PRCL PRM 1.0
[Manasa, Eric, Koji]
PRMIsb was locked with REFL165I&Q.
- Aligned the arms with ASS. The misaligned ETMX and ETMY
- Configured PRMIsb with IFO_Configure screen
- Immediately PRMIsb was locked with REFL55I&Q
- Checked the REFL165 phase in terms of the REFL165Q vs PRCL. It was already well adjusted at -82.5deg. We tuned the phase a bit more and got -83.5deg.
- With DTT, relative gain between REFL55I and REFL165I was measured. REFL165I is about x10 higher than REFL55I and has the same sign.
- The transition of PRCL with the input matrix was just easy.
- With DTT, relative gain between REFL55Q and REFL165Q was measured. REFL165Q is about x3 higher than REFL55Q and has the same sign.
- The transition of MICH was flakey, but after careful adjustment of the PRM alignment, ~10s lock was achieved. It seemed that the PRM alignment fluctuation
was bug enough to unlock the interferometer.
- Eric went into the lab and aligned all of the oplevs except for the SRM's one.
- Now the lock with REFL55 and also with REFL165 became more robust. Less MICH offset and darker AS port.
REFL55 WHTN: 45dB demod phase +45.0deg
REFL165 WHTN: 45dB demod phase -83.5deg
Input matrix: for acquisition:
REFL55I x 1.0 -> PRCL
REFL55Q x 1.0 -> MICH
Input matrix: PRCL Transition:
REFL55I x 1.0 + REFL165I x 0.0 -> x0.5 + x0.0 -> x0.5 + x0.05 -> x0.3 + x0.05 -> x0.2 + x0.05 -> x0.1 + x0.05 -> x0.0 + x0.05
Input matrix: MICH Transition:
REFL55Q x 1.0 + REFL165Q x 0.0 -> x0.5 + x0.0 -> x0.5 + x0.3 -> x0.3 + x0.3 -> x0.2 + x0.3 -> x0.1 + x0.3 -> x0.0 + x0.3
MICH POP110I 100up/10down / FM Trig FM2/3/9 35up 2down 5sec delay
PRCL POP110I 100up/10down / FM Trig FM2/3/6/9 35up 2down 0.5sec delay
MICH OFS 0 / Gain 1.3 / Limitter ON
PRCL OFS 0 / Gain -0.04 / Limitter ON
MICH PRM -0.2625 / BS 0.5
PRCL PRM 1.0
Recovery work: now arms are locking as usual
- FB is failing very frequently. Everytime I see red signals in the CDS summary, I have to run "sudo ntpdate -b -s -u pool.ntp.org"
- PMC was aligned
- The main Marconi returned to initial state. Changed the frequency and amplitude to the nominal value labeled on the unit
- The SHG oven temp controllers were disabled. I visited all three units and pushed "enable" buttons.
- Y arm was immediately locked. It was aligned using ASS.
- X arm did not show any flash. I found that the scx model was not successfully burtrestored yesterday.
The setting was restored using Mar 22 snapshot.
- After a little tweak of the ETMX alignment, a decent flash was achieved. But still it could not be locked.
- Run s/LSC/LSCoffset.py. This immediately made the X arm locked.
- Checked the green alignment. The X arm green is beating with the PSL at ~100MHz but is misaligned beyond the PZT range.
The Y arm green is locked on TEM00 and is beating with the PSL at ~100MHz.
Extending the previous model, I've closed a rudimentary CESAR loop in simulink. Error signals with varying noise levels are combined to bring a "cavity" to lock.
There are many things that are flat out arbitrary at this point, but it qualitatively works. The main components of this model are:
And it can lock!
Right now, all of the functions and noise levels are similar to the previous simulation, and therefore don't tell us anything about anything real...
However, at this point, I can tune the parameters and noise levels to make it more like our interferometer, and thus maybe actually useful.
As far as I know the system is running as usual. I had the IMC locked and one of the arm flashing.
But the other arm had no flash and none of the arms were locked before kunch time.
This morning Steve and I went around the lab to turn on the realtime machines.
Also we took the advantage of this opportunity to shutdown linux1 and nodus
to replace the extension cables for their AC power.
I also installed a 3TB hard disk on linux1. This was to provide a local daily copy of our
working are. But I could not make the disk recognized by the OS.
It seems that there is a "2TB" barrier that the disk bigger than 2.2TB can't be recognized
by the older machines. I'll wait for the upgrade of the machine.
Rebooting the realtime machines did not help FB to talk with them. I fixed them.
Basically what I did was:
- Stop all of the realtime codes by running rtcds kill all on c1lsc, c1ioo, c1sus, c1iscex, c1iscey
rtcds kill all
- run sudo ntpdate -b -s -u pool.ntp.org on c1lsc, c1ioo, c1sus, c1iscex, c1iscey, and fb
sudo ntpdate -b -s -u pool.ntp.org
- restart realtime codes one by one. I checked which code makes FB unhappy. But in reality
FB was happy with all of them running.
Then slow machines except for c1vac1 and c1vac2 were burtrestored.
Zach reported that svn was down. I went to the 40m wiki and searched "apache".
There is an instruction how to restart apache.
Out gassing plus leak rate 0.15 mTorr / hour
The pressure rose to 2.5 mTorr in 17 hours
V1 was opened at 1:56pm
VM2 opened at 2:10 so the RGA region is back to 1e-5 torr
I'm checking the status from home.
P1 is 8e-4 torr
nodus did not feel the power outage (is it APS supported?)
linux1 booted automatically
c1ioo booted automatically.
c1sus, c1lsc, c1iscex, c1iscey need manual power button push.
9:11pm closed PSL shutter, turned Innolight 2W laser on,
turned 3 IFO air cond on,
CC1 5.1e-5 torr, V1 is closed, Maglev has failed, valve configuration is " Vacuum Normal " with V1 & VM1 closed, RGA not running, c1vac1 and c1vac2 were saved by UPS,
(Maglev is not connected to the UPS because it is running on 220V)
reset & started Maglev.........I can not open V1 without the 40mars running...........
Rossa is the only computer running in the control room,
Nodus and Linux1 was saved by UPS,
turned on IR lasers at the ends, green shutters are closed
It is safe to leave the lab as is.
The 40m experienced a building-wide power failure for ~30 seconds at ~7:38 pm today.
Thought that might be important...
We should make screens like this for the LSC signals, errors, ALS, etc.
Please take a look at the table top with the flashlight before removing it. If it is dusty, wipe it down with dry lint free cloth in the box.
There is one box with flash light and wiper at AP, ETMY & ETMX optical tables.
I've been getting a simulation going with the eventual goal of simulating CESAR-type signals for CARM. So for I've only been using MIST, though I'm still thinking about what to do for a fully time domain approach. (For example, maybe a mixture of simulink and analytical equations? We'll see how painful that gets...)
Anyways, with the parameters I have for the 40m, I've set up a simulation, where I can do things like a "static" CARM scan.
(i.e. PRMI perfectly locked. Ask what different PDs see if the arms were just statically sitting at some CARM offset)
PDH signals are there in the REFL diodes. The coupled line width here looks smaller than the ~40pm number I've heard before, so I should check my parameters. (Likely culprit, I'm using nominal R and T for the arm cavities)
I've also done the slightly more sophisticated thing of looking at the transfer function from CARM motion to different PDs, at different CARM offsets. For TRX and REFLDC, these seem to match up qualitatively to some plots that Kiwamu has done for aLIGO, with frequencies shifted by the relative arm length factor of 100. (Q's left, K's right, Y-axis on mine are W/m with 1W input the IFO)
We can also look at the PDH diodes (revised from my initial post. Had an error in my code):
That's where I've gotten so far!
[ Manasa, Ericq and Steve ]
Vivitek D952HD with 186 hours installed.
I tried to repeat Koji's PRMI lock using REFL165I/Q. I was not able to lock PRMI stably. All I could get was momentary PRMI sb locks (few seconds) using AS55Q for MICH and REFL165Q for PRMI. I tried to transition MICH locks from AS55Q to REFL165I/Q and this did not work well; I lost even the momentary locks.
The demod phases for both AS55 and REFL165 were also very different.
AS55 WHTN: 21dB demod phase -78.7deg
REFL165 WHTN: 45dB demod phase -80.7deg
AS55Q x1.00 MICH
MICH POP110I 100up/10down / FM Trig FM2/3/6/7/9 35up 2down 5sec delay
PRCL POP110I 100up/10down / FM Trig FM2/3/6/9 35up 2down 0.5sec delay
MICH OFS 0.0 / Gain -10 / Limiter ON
PRCL OFS 0 / Gain -0.023 / Limiter ON
MICH ITMX -1.0 / ITMY +1.0
PRCL PRM 1.0
MC spot sposition script was ran
Found no notable beam position change before and after the earthquake
UR osem IR shield glass is pushed back. It came out of its clip holder. The magnet is free.
Atm2, UL & LL magnets centered poorly. Almost hinging on opposite sides.
UR & LR centered well. There have plenty of room to move in an earth quake.
It was little bit surprising to me but Rana's professorial rock'n roll excitation released its sticking on the unconfirmed thing by unconfirmed reason.
I aligned the Xarm manually and via ASS.
Now we are back in the normal state.
This recovery proceeder deserves a pattern
Note: IR shield glass position variations, Atm4
I am really, really happy to hear that it was just a sticking situation. Really happy.
I tried to take the photos of the magnets from outside. So far most suspicious was LL.
Otherwise, the magnets are OK.
(The SD magnet is the one with most reasonable response.)
Steve will try to take much more zoomed photo with Olympus. But the LL coil already showed some response in my observation in the morning.
Off again. Restarted ntp on fb.
I confirmed that we need to vent the chambers.
All of the mirrors have been aligned except for ETMX.
ETMX does not respond to the excitation by the UR and LR coils. Likely that the magnets are knocked off, or stuck in the coil.
PRM/SRM oplevs are too much off and can't be turned on. Need realignment of the beams on the QPDs.
- FB was down. FB restarted ("telnet fb 8087", then type shutdown)
- Aligned the MC mirrors.
- Aligned PRM. Look at the REFL. It was slightly mislisligned.
- AS has no beam. The Y arm was resonating with the green. So I determined that the TTs were the misaligned guys.
- Touched TT2 pitch with an increment of 0.1. Immediately the AS beam spot for ITMY was found. And the arm was resonating.
- The RM was further aligned. The bias sliders were saved and then the PRM was misaligned.
- Yarm was locked on TEM01. The ASS maximized the transmission for TEM01, and then the arm was locked on TEM00.
The ASS aligned the arm and TTs. These values were saved.
- Yarm was aligned and I can see the AS spot. So I believe the BS is still well aligned.
- Aligned the PRM to reduce the ghost beams.
- Moved the ITMX to have Michelson fringes properly.
- Also aligned the SRM.
- Now ETMX was checked. Played with the alignment biases to see if the mirror was sticking on the coils. The mirror can rock a little, but it did not come back.
- Then, checked each magnets. 0.8Hz 1000cnt signals were injected to each coils (cf. C1:SUS-PRM_**COIL_EXC) to see how the mirror could react.
The OSEM output and green spot on the ETMX cage were observed.
- Saw some response by actuating the UL, LL, SD coils.
- Saw no response from the UR and LR coils. They show the OSEM output of zero. Does this mean the magnets fell in the coils?
//Manasa// MC spot positions measured and they look alright with not much change from before the earthquake (attach)
We had our annual safety inspection today. Our SOPs are outdated. The full list of needed correction will be posted tomorrow.
The most useful found was that the ITMX-ISCT ac power is coming from 1Y1 rack. This should actually go to 1Y2 LSC rack ?
Please test this so we do not create more ground loops.
Annual crane inspection is scheduled for 8-11am Monday, March 17, 2014
The control room Smart UPS has two red extension cords that has to be removed: Nodus and Linux1
KroneCrane Fred inspected and certified the 3 40m cranes for 2014. The vertex crane crane was load tested at fully extended position.
It looks like that ETMX have 2 sticky magnets.
Asymptotic cooling of the mirror motion with CESAR was tested.
With ALS and the full control bandwidth (UGF 80-100Hz), the actuator amplitude of 8000cnt_pp is required.
Varying control bandwidth depending on the noise level of the signal, the arm was brought to the final configuration with the actuator amplitude of 800cnt_pp.
Q and I have started to...
As Koji suggested in his email this afternoon, we looked at how much actuator range is required for various forms of arm locking: (1) "regular" PDH lock aquisition, (2) ALS lock acquisition, (3) CESAR cooling.
To start, I looked at the spectra and time series data of the control signal (XARM_OUT) for several locking situations. Happily, when the arm is at the half fringe, where we expect the 1/sqrt(TRX) signal to be the most sensitive (versus the same signal at other arm powers), we see that it is in fact more quiet than even the PDH signal. Of course, we can't ever use this signal once the arm is at resonance, so we haven't discovered anything new here.
EricQ then made some violin plots with the time series data from these situations, and we determined that a limit of ~400 counts encompasses most of the steady-state peak-to-peak output from locking on the PDH signal.
[ericq: What's being plotted here are "kernel density estimates" of the time series data of XARM_OUT when locked on these signals. The extent of the line goes to the furthest outlier, while the dashed and dotted lines indicate the median and quartiles, respectively]
I tried acquiring ALS and transitioning to final PDH signals with different limiters set in the Xarm servo. I discovered that it's not too hard to do with a limit of 400 counts, but that below ~350 counts, I can't keep the ALS locked for long enough to find the IR resonance. Here's a plot of acquiring ALS lock, scanning for the resonance, and then using CESAR to transition to PDH, with the limit of 400 counts in place, and then a lockloss at the end. Even though I'm hitting the rails pretty consistently, until I transition to the more quiet signals, I don't ever lose lock (until, at the end, I started pushing other buttons...).
After that, I tried acquiring lock using our "regular" PDH method, and found that it wasn't too hard to capture lock with a limit of 400, but with limits below that I can't hold the lock through the boosts turning on.
Finally, I took spectra of the XARM_OUT control signal while locked using ALS only, but with different limiter values. Interestingly, I see much higher noise between 30-300 Hz with the limiter engaged, but the high frequency noise goes down. Since the high frequency is dominating the RMS, we see that the RMS value is actually decreasing a bit (although not much).
We have not made any changes to the LSC model, so there is still no smoothing between the ALS and IR signals. That is still on the to-do list. I started modifying things to be compatible with CARM rather than a single arm, but that's more of a daytime-y task, so that version of the c1lsc model is saved under a different name, and the model that is currently compiled and running is reverted as the "c1lsc.mdl" file.
I have modified the IFOconfigure scripts and the corresponding .req files for the X arm and Y arm in burt. I have also added configure scripts to save and restore LSC settings for locking the arms using ALS error signals.
The settings are yet to be saved and the scripts should also be checked if they are working as required.
Nic, Jenne, EricQ, and Koji should describe the demonstartion of CESAR achieved tonight.
Q and I have started to use the ALS slow servo for the end aux lasers while locking the arms using ALS. The servo prevents us from hitting the limits of the PZT range for the end lasers and a better PDH locking.
But keeping the servo ON causes the slow output to drift away making it hard to find the beat note everytime the arm loses lock. The extensive beat note search following the unlock can be avoided by clearing history of the slow servo.
Speaking of the whitening board, I had neglected to post details showing the the whitening was at least having a positive effect on the transmon QPD noise. So, here is a spectrum showing the effects that the whitening stages have on a QPD dark noise measurement like I did in ELOG 9660, at a simulated transmission level of 40 counts.
The first whitening stages gives us a full 20dB of noise reduction, while the second stage brings us down to either the dark noise of the QPD or the noise of the whitening board. We should figure out which it is, and fix up the board if necessary.
The DTT xml file is attached in a zip, if anyone wants it.
[Nic, Jenne, EricQ, and Koji]
We have used CESAR successfully to bring the Xarm into resonance. We start with the ALS signal, then as we approach resonance, the error signal is automatically transitioned to 1/sqrt(TRX), and ramped from there to POX, which we use as the PDH signal.
In the first plot, we have several spectra of the CESAR output signal (which is the error signal for the Xarm), at different arm resonance conditions. Dark blue is the signal when we are locked with the ALS beatnote, far from IR resonance. Gold is when we are starting to see IR resonance (arm buildup of about 0.03 or more), and we are using the 1/sqrt(TRX) signal for locking. Cyan is after we have achieved resonance, and are using only the POX PDH signal. Purple is the same condition as cyan, except that we have also engaged the low frequency boosts (FM 2, 3, 4) in the locking servo. FM4 is only usable once you are at IR resonance, and locked using the PDH signal. We see in the plot that our high frequency noise (and total RMS) decreases with each stage of CESAR (ALS, 1/sqrt(TR) and PDH).
To actually achieve the gold noise level of 1/sqrt(TR), we first had to increase the analog gain by swapping out a resistor on the whitening board.
The other plots attached are time series data. For the python plots (last 2), the error signals are calibrated to nanometers, but the dark blue, which is the transmitted power of the cavity, is left in normalized power units (where 1 is full IR resonance).
In the scan from off resonance to on resonance, around the 58 second mark, we see a glitch when we engage FM4, the strong low frequency boosts. Around the 75 second mark we turned off any contribution from 1/sqrt(TR), so the noise decreases once we are on pure PDH signal.
In the scan through the resonance, we see a little more clearly the glitch that happens when we switch from ALS to IR signals, around the 7 and 12 second marks.
We want to make some changes, so that the transition from ALS to IR signals is more smooth, and not a discrete switch.
Today we modified the CESAR block.
- Now the sign(X) function is in a block.
- We decided to use the linearization of the PDH.
- By adding the offset to the TR signal used for the switching between TR and PDH, we can force pure 1/sqrt(TR) or pure PDH to control the cavity.
True. But we first want to realize this for a single arm, then move onto the two arms case.
At this point we'll need to incorporate frequency dependence.
As part of our CESAR testing last night, we had a look at the noise of the 1/sqrt(TR) signal.
Looking at the time series data, while we were slowly sweeping through IR resonance (using the ALS), Rana noted that the linear range of the 1/sqrt(TR) signal was not as wide as it should be, and that this is likely because our SNR is really poor.
When a single arm is at a normalized transmission power of 1, we are getting about 300 ADC counts. We want this to be more like 3000 ADC counts, to be taking advantage of the full range of the ADC.
This means that we want to increase our analog gain by a factor of 10 for the low gain Thorlabs PDs.
Looking at the photos from November when I pulled out the Xend transmission whitening board (elog 9367), we want to change "Rgain" of the AD620 on the daughter board. While we're at it, we should also change the noisy black thick film resistors to the green thin film resistors in the signal path.
The daughter board is D04060, S/N 101. The main whitening board for the low gain trans QPD is D990399, RevB, S/N 104.
We should also check whether we're saturating somewhere in the whitening board by putting in a function generator signal via BNC cable into the input of the Thorlabs whitening path, and seeing where (in Dataviewer) we start to see saturation. Is it the full 32,000 counts, or somewhere lower, like 28,000?
Actually the gain was changed. From gain of 2 (Rgain = 49.4kOhm) to 20 (Rgain = 2.10kOhm), Corresponding calibration in CDS was also changed by locking the Xarm, running ASS, then setting the average arm power to be 1. Confirmed Xarm is locking. And now the signal is used for CESAR. We see emperically that the noise has improved by a factor of approximately 10ish.
The composite error signal
Very nice error signal. Still, I think we need to take into account the frequency shape of the transfer function TR -> CARM.
Two weeks ago (Feb 26) I took the "Q MON" output of the demodulator that sends its Q output to the MC servo board as the error signal, and connected it to an SR785, so we can occasionally monitor the error signal noise. (Also, I did not appropriately ELOG the fact I touched things...)
I'm working on an automated script to do the monitoring, but the wireless router that the SR785 is connected is wicked slow. I should run an ethernet cable to it...
I'm just figuring I'll look at the full span (~100kHz) spectrum every ten minutes, and compare it to some nominal spectrum from a known-good time, and the last few hours.
The nominal gain of the XARM for the POX11 error signal is 0.03 (instead of previous 0.3)
This is due to my increase of the gain in FM4 by 20dB so that we can turn of FM4 without changing the UGF when it is at 150Hz.
The YARM servo was not yet touched.
After making the CDS modification, CESAR was tested with ALS.
First of all, we run CESAR with threshold of 10. This means that the error signal always used ALS.
The ALS was scanned over the resonance. The plot of the scan can be found in EricQ's elog.
At each point of the scan, the arm stability is limited by the ALS.
Using this scan data, we could adjust the gains for the TR and PDH signals. Once the gains were adjusted
the threshold was lowered to 0.25. This activates dynamic signal blending.
ALS was stabilized with XARM FM1/2/3/5/6/7/9. The resonance was scanned. No glitch was observed.
This is some level of success already.
Next step was to fully hand off the control to PDH. But this was not successfull. Everytime the gain for the TR was
reduced to zero, the lock was lost. When the TR is removed from the control, the raw PDH signal is used fot the control
without normalization. Without turning on FM4, we lose 60dB of DC gain. Therefore the residual motion may have been
too big for the linear range of the PDH signal. This could be mitigated by the normalization of the PDH signal by the TR.
The LSC model was modified for CESAR.
A block called ALSX_COMBINE was made in the LSC block. This block receives the signals for ALS (Phase Tracker output), TRX_SQRTINV, TRX, POX11 (Unnormalized POX11I).
It spits out the composite ALS signal.
Inside of the block we have several components:
1) a group of components for sign(x) function. We use the PDH signal to produce the sign for the transmission signal.
2) Hard triggering between ALS and TR/PDH signals. An epics channel "THRESH" is used to determine how much transmission
we should have to turn on the TR/PDH signals.
3) Blending of the TR and PDH. Currently we are using a confined TR between 0 and 1 using a saturation module. When the TR is 0, we use the 1/SQRT(TR) signal for the control,
When the TR is 1, we use the PDH signal for the control.
4) Finally the three processed signals are combined into a single signal by an adder.
It is important to make a consideration on the offsets. We want all of ALS, 1/SQRT(TR), and PDH to have zero crossing at the resonance.
ALS tends to have arbitorary offset. So we decided to use two offsets. One is before the CESAR block and in the ALS path.
The other is after the CESAR block. Right now we are using the XARM servo offset for the latter purpose.
We run the resonance search script to find the first offset. Once this is set, we never touch this offset until the lock is lost.
Then for the further scanning of the arm length, we uused the offset in the XARM servo filter module.
Using Koji's mathematica notebook, and Nic's python work, I set out to run a time domain simulation of the error signal, with band-limited white noise added in.
Basically, I sweep the displacement of the cavity (with no noise), and pass it to the analytical formulae with the coefficients Koji used, with some noise added in. I also included some 1/0 protection for the linearized PDH signal. I ran a sweep, and then compared it to an ALS sweep that Jenne ran on Monday; reconstructing what the CESAR signal would have looked like in the sweep.
The noise amounts were totally made up.
They matched up very well, qualitatively! [Since the real sweep was done by a (relatively) noisy ALS, the lower noise of the real pdh signal was obscured.]
Given this good match, we were motivated to start trying to implement it on Monday.
At this point, since we've gotten it working on the actual IFO, I don't plan on doing much more with this simulation right now, but it may come in handy in the future...
In order to better understand how the composite signal would behave in the presence of noise, I decided to do a simple analysis of the cavity signals while sweeping through resonance.
My noise model was to just assume that a given signal has some rms uncertainty (error bars) and use linear error propagation to propagate from simple signals to more complicated ones.
I used the python package uncertainties to do the error propagation.
I assumed that the ALS signal, the cavity transmission, and the cavity PDH error signal all have some constant noise that is independent of the cavity detuning. Below is a sweep through resonance (x axis is cavity detuning in units of radians).
The shaded region represents the error on each signal.
Next I calculated the 'first order' calculated error signals. These being a raw PDH, normalized PDH, an inverse square root trans, and the normal ALS again. I tuned the gains so they match appropriately.
Here, one can see how the error in the trans signal propagates to the normalized and trans signals and becomes large are the fractional error in the trans signal becomes large.
Next I did some optimization of linear combinations of these signals. I told the code to maximize the total signal to noise ratio, while ensuring that the overall signal had positive gain. I did this again as a function of the cavity detuning.
Each curve represents the optimized weight of the corresponding signal as a function of detuning.
So this is roughly doing what we expect, it prefers ALS far from the resonance, and PDH close to the resonance, while smoothly moving into square root trans in the middle.
It's a little fake, but it gives us an idea of what the 'best' we can do is.
Finally I used these weights to recombine the signals into a composite, to get an idea of the noise of the overall signal. At the same time, I plot the weighting proposed by Koji's mathematica notebook (using trans and 1-trans, and a hard switch to ALS).
So as one can see, at least for the noise levels I chose, the koji weighting is not much worse than the 'optimal' weighting. While it is much simpler.
The code for all this is in the svn at 40mSVN/nicolas/workspace/2014-03-06_compositeerror
The ALS error (i.e. phase tracker output) is linear everywhere, but noisy.
The 1/sqrt(TR) is linear and less noisy but is not linear at around the resonance and has no sign.
The PDH signal is linear and further less noisy but the linear range is limited.
Why don't we combine all of these to produce a composite error signal that is linear everywhere and less-noisy at the redsonance?
This concept was confirmed by a simple mathematica calculation:
The following plot shows the raw signals with arbitorary normalizations
1) ALS: (Blue)
2) 1/SQRT(TR): (Purple)
3) PDH: (Yellow)
4) Transmission (Green)
The following plot shows the preprocessed signals for composition
1) ALS: no preprocess (Blue)
2) 1/SQRT(TR): multiply sign(PDH) (Purple)
3) PDH: linarization with the transmission (If TR<0.1, use 0.1 for the normalization). (Yellow)
4) Transmittion (Green)
1) Use ALS at TR<0.03. Use 1/SQRT(TR)*sign(PDH)*(1-TR) + PDH*TR at TR>0.03
2) Transmittion (Purple)
I don't know why, but as you can see in Steve's plot from earlier this morning, the PMC transmission has been going down significantly all weekend. The PMC refl camera was very bright. I tweaked up the alignment (mostly pitch), and now we're back to normal.
The IMC was having trouble staying locked all morning, and I'm hoping that this PMC adjustment will help - the MC already looks better, although it's only been a few minutes.