I simulated how the 3f signal is affected by the resonance condition of the arms.
To keep it simple, I only simulated a double cavity. The attached plot shows the result. In x there is the arm cavity detuning from resonance (in log scale to show what happens close to the 0 value). In the y axis there is the PRC detuning. So every vertical slice of the upper plot gives a PDH signal for a given arm detuning. The bottom plot shows the power build up inside the arm, which is dominated by the carrier.
The 3f signal is not perturbed in any significant way by the arm resonance condition. This is good and what we expected.
However, in this simulation I had to ensure that the 1f sidebands are not perfectly anti-resonant inside the arms. They are indeed quite far away from resonance. If the modulation frequency is chosen in order to make the 1f sidebands exactly ant-resonant, the 2f will be resonant. This screws up the signal: REFL_3f is made of two contributions of equal amplitude, one on the PRC sidebands resonance and the other on the PRC carrier resonance. When the arm tuning goes to zero, these two cancels out and there is no more PDH...
However, this is a limit case, since the frequency show match perfectly. If the modulation frequency is few arm line widths away from perfect anti-resonance, we have no problem.
Yes, the resonance of the 2nd-order sidebands to the IFO screws up the 3f scheme.
2f (~22MHz) and 10f (~110MHz) are at x 5.6 and x 27.9 FSR from the carrier, so that's not the case.
Could we also see how much gain fluctuation of the 3f signals we would experience when the arm comes into the resonance?
From the simulation there is no visible change in the gain.
5:31pm - This is still a work in progress, but I'm going to submit so that I save my writing so far. I think I'm done writing now.
First, a transcription of some of the notes that I took last Tuesday night, then a few looks at the data, and finally some thoughts on things to investigate.
MICH and PRCL Transfer Functions while arms brought in to resonance (both arms locked to ALS beatnotes):
This is summarized in elog 9317, which I made as we were finishing up Tuesday night. Here's the full story though. Note that I didn't save the data for these, I just took notes (and screenshots for the 1st TF).
POP22I was ~140 counts, POP110I was ~100 counts.
MICH gain = -2.0, PRCL gain = 0.070.
First TF (used as reference for 2-10), PRMI locked on REFL165, Xarm transmission = 0.03, Yarm transmission = 0.05 (both arms off resonance). MICH UGF~40Hz, PRCL UGF~80Hz.
2: X=off-res (xarm not moved), Y=0.13, no change in TF
3: X=off-res (xarm not moved), Y=0.35, no change in TF
4: X=off-res (xarm not moved), Y=0.60, MICH high freq gain went up a little, otherwise no change (no change in either UGF)
5: X=off-res (xarm not moved), Y=0.95, same as TF#4.
6: X=0.20, Y=1.10 (yarm not moved), same as TF#4
7: X=0.40, Y=1.30 (yarm not moved), same as TF#4
8: X=0.70, Y=1.55 (yarm not moved), same as TF#4
9: X=1.40, Y=2.20 (yarm not moved), same as TF#4
10: X=4.0, Y=4.0 (yarm not moved), PRCL UGF is 10Hz higher than TF#4, MICH UGF is 20Hz lower than TF#4.
11: (No TF taken), Xarm and Yarm transmission both around 20! To get this, MICH FMs that were triggered, are no longer triggered to turn on. Also, MICH gain was lowered to -0.15 and PRCL gain was increased to 0.1
12: (No TF taken), Xarm and Yarm transmissions both around 40! The peaks could be higher, but we don't have the QPD ready yet.
After that, we started moving away from resonance, but we didn't take any more transfer functions.
OpLev spectra for different arm resonance values:
We were concerned that the ETMs and ITMs might be moving more, when the arms are resonating high power, due to some optical spring / radiation pressure effects, so I took spectra of oplevs at various arm transmissions.
I titled the first file "no lock", and unfortunately I don't remember what wasn't locked. I think, however, that nothing at all was locked. No PRMI, no arm ALS, no nothing. Anyhow, here's the spectrum:
I have a measurement when the Yarm's transmission was 1, and the Xarm's transmission was 1.75. This was a PRMI lock, with ALS holding the arms partially on resonance:
Next up, I have a measurement when Yarm was 0.8, Xarm was 2. Again, PRMI with the arms held by ALS:
And finally, a measurement when Xarm was 5, Yarm was 4:
Just so we have a "real" reference, I have just now taken a set of oplev spectra, with the ITMs, ETMs and PRM restored, but I shut the PSL shutter, so there was no light flashing around pushing on things. I noticed, when taking this data, that if the PSL shutter was open, so the PRFPMI is flashing (but LSC is off), the PRM oplev looks much like the original "no Lock" spectra, but when I closed the shutter, the oplev looks like the others. So, perhaps when we're getting to really high powers, the PRM is getting pushed around a bit?
Conclusions from OpLev Spectra: At least up to these resonances (which is, admittedly, not that much), I do not see any difference in the oplev spectra at the different buildup power levels. What I need to do is make sure to take oplev spectra next time we do the PRMI+2arms test when the arms are resonating a lot.
Time series while bringing arms into resonance:
I had wondered if, since the POP 22 and 110 values looked so shakey, we were increasing the PRCL RIN while we brought the arms into resonance. You can see in the above time series that that's not true. The left side of the plot is PRMI locked, arms held out of resonance using ALS. First the Yarm is brought close to resonance, then the Xarm follows. The RIN of the arms is maybe increasing a little bit as we get closer to resonance, but not by that much. But there seems to be no correlation between arm power and RIN of the power recycling cavity.
Alternatively, here is some time series when the arm powers got pretty high:
Possible Saturation of Signals:
One possibility for our locklosses of PRMI is that some signal somewhere is saturating, so here are some plots showing that that's not true for the error and control signals for the PRMI:
Here, for the exact same time, is a set of time series for every optic except the SRM. We can see that none of the signals are saturating, and I don't see any big differences for the ITMs or ETMs in the times that the PRMI is locked with high arm powers (center of the x-axis on the plot) and times that the PRMI is not locked, so we don't have high arm powers (edges of the plot - first half second, and last full second). You can definitely see that the PRM moves much more when the PRMI is locked though, in both pitch and yaw.
DCPD signals at the same time:
NB: These latest 3 plots were created with the getdata script, with arguments "-s 1067163405 -d 7". It may be a good idea to take some spectra starting at, say 1067163406, 1 second in, and going for ~2 seconds. (It turns out that this is kind of a pain, and I can't convince DTT to give me a sensible spectrum of very short duration....we'll just need to do this live next time around).
Things to think about and investigate:
Why are we losing lock?
On paper, is the (will the) optical spring a problem once we get high resonance in the arms?
Spectra of oplevs when we're resonating high arm power.
What is the coupling between 110MHz and 165MHz on the REFL165 PD? Do we need a stronger bandpass?
Why are things so shakey when the arm power builds up?
Why do PRCL and MICH have different UGFs when the arms are controlled by ALS vs. ETMs misaligned?
Does QPD for arm transmissions switching work? Can we then start using TRX and TRY for control?
What is the meaning of the similar features in both transmission signals, and the power recycling cavity? Power fluctuation in the PRC due to PRM motion?
Gabriele and I talked for a while on Wednesday afternoon about ideas for transitioning to IR control, from ALS.
I think one of the baseline ideas was to use the sqrt(transmission) as an error signal. Gabriele pointed out to me that to have a linear signal, really what we need is sqrt( [max transmission] - [current transmission] ), and this requires good knowledge of the maximum transmission that we expect. However, we can't really measure this max transmission, since we aren't yet able to hold the arms that close to resonance. If we get this number wrong, the error signal close to the resonance won't be very good.
Gabriele suggested maybe using just the raw transmission signal. When we're near the half-resonance point, the transmission gives us an approximately linear signal, although it becomes totally non-linear as we get close to resonance. Using this technique, however, requires lowering the finesse of PRCL by putting in a medium-large MICH offset, so that the PRC is lossy. This lowering of the PRC finesse prevents the coupled-cavity linewidth of the arm to get too tiny. Apparently this trick was very handy for Virgo when locking the PRFPMI, but it's not so clear that it will work for the DRFPMI, because the signal recycling cavity complicates things.
I need to look at, and meditate over, some Optickle simulations before I say much else about this stuff.
You have the data. Why don't you just calculate 1/SQRT(TRX)?
...yeah, you can calculate it but of course you don't have no any reference for the true displacement...
I made some small edits to the LSC screen.
* When I added columns for the new AS110 PD, I had forgotten to make the Trigger matrix and Power Normalization matrix icons on the screen bigger, so we weren't seeing the last 2 columns in the overview screen.
* I added "show if not zero" oscillator icons to the Sensing Matrix part of the LSC overview screen, so that it's easier at a glance to see that there is an oscillator on.
The idea of introducing a large MICH offset to reduce the PRC finesse might help us to get rid of the transmitted power signal. We might be able to increase enough the line width of the double cavity to make it larger than the ASL length fluctuations. Then we can switch from ASL to the IR demodulated signal without transitioning through the power signal.
I think Steve is trying to align the end transmission QPDs, since the arms are locked nicely right now. I noticed that the QPDX pitch and yaw signals were digital zeros. A quick look determined that the QPDX matrix to go from 4 quadrants to 3 degrees of freedom had been filled in for the POS row, but not pitch and yaw. So, I copied the QPDY matrix over to QPDX (so the ordering of the rows and columns is assumed to be the same).
Hopefully this will get us close to centered, but I suppose we ought to check really which quadrant is which, by shining a laser pointer at each quad at each end.
If so, or if not but you care about the signal that passes through these amplifiers, I suggest you remove this temporary power supply and wire the power from the rack power supplies through the fuse blocks and possibly use a voltage regulator.
In 24 hours, that power supply will be disconnected and the wires snipped if they are still there.
Full list tomorrow: IP-Ang & Pos, ETMY-T, ETMY-Oplev, ETMX-T, IOO-Ang & Pos
RA: No one in the control room this evening can understand what this ELOG means. Please use more words.
Steve has promised to add another row of fuses to the LSC rack first thing in the morning. Then, during Wednesday Chores, we can move the wires from the power supply to the fused power.
STEVE: NEVER MIND about doing this in the morning. Let's chat at the lunch meeting about what needs to be done to power things down, then back up again, in a nice order, and we can do it after lunch.
So, please do not do anything to the LSC rack tomorrow! Thank you.
We looked at the time series for all the oplevs except the BS, from last Tuesday night, during a time when we were building up the power in the arms. We conclude from a 400 second stretch of data that there is not discernible difference in the amount of motion of any optic, when the cavities are at medium power, and when they're at low power. Note however, that we don't have such a nice stretch of data for the really high powers, so the maximum arm power in these plots is around 5. Both the TRX and TRY signals look fairly stationary up to powers of 1 or 2, but once you get to 4 or 5, the power fluctuations are much more significant. So, since this isn't caused by any optic moving more, perhaps it's just that we're more sensitive to optic motion when we're closer to resonance in the arms.
However, from this plot, it looks like the ETMY is moving much more than any other optic. On the other hand, ETMY has not ever been calibrated (there's an arbitrary 300 in there for the calibration numbers on the ETMY oplev screen). So, perhaps it's not actually moving any more than other optics. We should calibrate the ETM oplevs nicely, so we have some real numbers in there. ETMX also only is roughly calibrated, relative to the OSEMs. We should either do the move-the-QPD calibration, or a Kakeru-style pitch and yaw some mirrors and look at transmitted power.
Traces on this xml file have been filtered with DTT, using zpk(,[0.03],1,"n").
The north side of the LSC rack is full. I installed more DIN connectors with fuses on the south side of the rack 1Y2
The access to this may be a little bit awkward. You just remove the connector, wire it and put it back in.
We have decided that, rather than replacing the power source for the amplifiers that are on the rack, and leaving the Thorlabs PD as POP22/110, we will remove all of the temporary elements, and put in something more permanent.
So, I have taken the broadband PDs from Zach's Gyro experiment in the ATF. We will figure out what needs to be done to modify these to notch out unwanted frequencies, and amplify the signal nicely. We will also create a pair of cables - one for power from the LSC rack, and one for signal back to the LSC rack. Then we'll swap out the currently installed Thorlabs PD and replace it with a broadband PD.
Between the 40m meeting, and chatting with Gabriele, there was lots of talking yesterday about our 40m Lock Acquisition game plan.
From those talks, here is my current understanding of the plan, in a Ward-style cartoon:
(This is a 2 page document - description of steps is on 2nd page)
If you look closely, you will notice that there are several places that I have used "?" rather than numbers, to indicate what RFPD signal we should be using. To fill these in, I need to look at some more simulations, and think more carefully about what signals exist at what ports, and what SNR we have at each of those ports.
Also, while the overall scale of the arm power plot is correct, the power level at each step is totally arbitrary right now, and should just be taken to mean places (in time) where the CARM offset is reduced a little more.
There are several things at this point that we know we need to look into:
* POP 22/110 PD and filtering electronics should be switched to a broadband PD, rather than the Thorlabs PD + Miniciruits filters. (Hardware)
* Whitening for the transmission QPDs needs to be thought about more carefully. (Calculation, then hardware)
* Chose a good SNR REFL DC signal, which may or may not be from the PD we are currently using (I think it's the DC of REFL11, but I'll have to check). (Calculation)
* For DRMI locking, what is the size of the SRCL error signal at AS55, AS165, and the REFL ports? Do we need to lock with AS port, and then switch over to a REFL 3f port, to make acquisition easier? (Simulation)
* Similarly, I want to make the equivalent of Figure 3 of T1000294, with our 40m parameters. (Simulation)
* To set the phase of AS110, simulate the demod phase of AS110 in both DRMI and SRMI cases. If no (significant) change, maybe we can set the phase in the real system by misaligning the PRM, and watching the SRMI flash. (Simulation)
* Simulate an arm sweep, up to many orders of the sidebands, to see how close to the carrier resonance any sideband resonances might be. If something like the 4th order sideband resonates, and then beats with a 1st order sideband, is that signal big enough to disturb our 3f locking of the PRMI / DRMI? We want to be holding the arms off resonance with ALS closer to the carrier than any "important" sideband resonances (where the definition of "important" is still undetermined). (Simulation)
* Check if we can hand DARM from the DC transmission signals to the final RF signal while we still have a large CARM offset. Is there a point where the CARM offset is too large, and we must be still using the DC signals? (Simulation)
* At what arm power level can we transition from ALS to IR DC transmission signals for the individual arms? (Simulation)
* Still need to finish calculating what could be causing our big arm power fluctuations (Test mass angular motion? PRM angular motion? ALS noise?) (Calculation)
Replys, and comments are welcome, particularly to help me understand where I may have (likely did) go wrong in drawing my cartoon.
Here is a photo of the board inside the broadband photodiode (one of them) that I took from the Gyro experiment:
This PD is Serial Number S1200271.
We need to have a look at the schematic, figure out what's in here now, and then modify this to be useful (appropriate resonances / notches, as well as amplification) for POP 22/110.
I have done a sweep of CARM, while looking at the fields inside of one arm (I've chosen the Xarm), to see where any resonances might be, that could be causing us trouble in keeping the PRMI locked as we bring the arms into resonance.
Since Gabriele pointed out to me that we're using the 3x55MHz signal for locking, we should be most concerned about resonances of the higher orders of 55, and not of 11. So, on this plot, I have up to the 6th order 55 MHz sidebands, which are 332 MHz. Although the Matlab default color chart has wrapped around, it's clear that the carrier is the carrier, and the +4f2, which is the same blue, is not the giant central peak. So, it's kind of clear which trace is which, even though the legend colors are degenerate. Also, the main point that I want to show here is that there is nothing going on near the carrier, with any relevant amplitude. The nearest things are the plus and minus 55 MHz sidebands themselves, and they're more than 50 nm away from the carrier.
Recalling from elog 9122, the PRFPMI and DRFPMI linewidths are about 40pm. 50pm away from the resonant point is ~1/10 the power, and 100pm away from the resonant point is ~1/100 the power. So, 50 nm is a looooong ways away.
Just for kicks, here is a plot of all the resonances of the 1f and 2f modulation frequencies, up to 30*f1, which is the same 6*f2:
The resonances which are "close" to the carrier are the 9th order 11 MHz sidebands, and they're 280pm from the carrier, so twice as far as we need to be, to get our arm powers to ~1/100 of the maximum, and, they're a factor of ~1e4 smaller than the carrier.
General Remarks on the BBPD
- To form the LC network: Use fixed SMD inductors from Coilcraft. SMD tunable capacitors are found in the shelf right next to Steve's desk.
If the tuning is too coarse, combine an appropriate fixed ceramic SMC C and the tunable C (in parallel, of course)
- L1/C1a/C1b pads are specifically designed for an additional notch
- Another notch at the diode stage can be formed between the middle PD pin (just left of the marking "C3b") to the large GND pad (between C1a/C1b to C3a).
You have to scratch off the green resin with a small flat screw driver (or anything similar)
- A notch at the amplifier stage can be formed between the output of MAR-6SM ("+" marking) and one of the GND pads (left side of the "U1" marking)
- The original design of the PD is broadband. So additional notches on the diode stage provides notches and resonances.
Check if the resonances do not hit the signal frequencies.
- One would think the PD can have resonant feature to reduce the coupling of the undesired signals.
In some sense it is possible but it will be different from the usual resonant tank circuit in the following two points.
* Just adding a parallel L between the cathode and ground does not work. As this DC current should be directed to the DC path,
L&C combo should be added. In fact this actually give a notch-resonance pair. This C should be big enough so that you can ignore it
at the target resonant frequency. Supply complimentary small C if necessary to keep low impedance of the Cs at the target frequency.
(i.e. Check SRF - self-resonant frequency of the big C)
* Since the input impedance of MAR-6SM is 50Ohm, the top of the resonant curve will be cut at 50Ohm. So the resultant shape looks
like a bandpass rather than a resonance.
- So in total, simulation of the circuit is very important to shape the transimpedance. And, consider the circuit can not be formed as simulated
because of many practical imperfections like stray Ls and Cs.
I have the X end transmission QPD, as well as the whitening board, out on the electronics bench. Since the Thorlabs high-gain TRX PD also goes through this whitening board, we have no transmission signal for the Xarm at this time. The whitening board was in the left-most slot, of the top crate in the Xend rack. The only cables that exist for it (like the Yend), are the ribbon from the QPD, the 4-pin lemo from the Thorlabs PD, and the ribbon going to the ADC.
I have taken photos, and want to make sure that I know what is going on on the circuits, before I put them back in.
The whitening board:
I think that our problem of seeing significant arm power fluctuations while we bring the arms into resonance during PRMI+arms tests is coming from PRM motion. I've done 3 calculations, so I will describe below why I think the first two are not the culprit, and then why I think the PRM motion is our dominant problem.
ALS length fluctuations
Arm length fluctuations seem not to be a huge problem for us right now, in terms of what is causing our arm power fluctuations.
What I have done is to calculate the derivative of the power in the arm cavity, using the power buildup that optickle gives me. The interferometer configuration I'm using is PRFPMI, and I'm doing a CARM sweep. Then, I look at the power in one arm cavity. The derivative gives me Watts buildup per meter CARM motion, at various CARM offsets. Then, I multiply the derivative by 60 nm, which is my memory of the latest good rms motion of the ALS system here at the 40m. I finally divide by the carrier buildup in the arm at each offset, to give me an approximation of the RIN at any CARM offset.
I don't know exactly what the calibration is for our ALS offset counts, but since we are not seeing maximum arm cavity buildup yet, we aren't very close to zero CARM offset.
From this plot, I conclude that we have to be quite close to zero offset for arm length fluctuations to explain the large arm power fluctuations we have been seeing.
AS port contrast defect from ETM motion
For this calculation, I considered how much AS port contrast defect we might expect to see given some ETM motion. From that, I considered what the effect would be on the power recycling buildup.
Rather than doing the integrals out, I ended up doing a numerical analysis. I created 2 Gaussian beams, subtracted the fields, then calculated the total power left. I did this for several separations of the beams to get a plot of contrast defect vs. separation. My simulated Gaussian beams have a FWHM of 1 unit, so the x-axis of the plot below is in units of spot motion normalized by spot size.
Unfortunately, my normalization isn't perfect, so 2 perfectly constructively interfering beams have a total power of 0.3, so my y-axis should all be divided by 0.3.
The actual beam separation that we might expect at the AS port from some ETM motion (of order 1e-6 radians) causing some beam axis shift is of the order 1e-5 meters, while the beam spot size is of the order 1e-3 meters. So, in normalized units, that's about 1e-2. I probably should change the x-axis to log as well, but you can see that the contrast defect for that size beam separation is very small. To make a significant difference in the power recycling cavity gain, the contrast defect, which is the Michelson transmission, should be close to the transmission of the PRM. Since that's not true, I conclude that ETM angular motion leading to PRC losses is not an issue.
I still haven't calculated the effect of ITM motion, nor have I calculated either test mass' angular effect directly on arm cavity power loss, so those are yet to be done, although I suspect that they aren't our problem either.
I think that the PRM moving around, thus causing a loss in recycling gain, is our major problem.
First, how do I conclude that, then some thoughts on why the PRM is moving at all.
theta = 12e-6 radians (ref: oplev plot from elog 9338 last week)
L = 6.781 meters
g = 0.94
a = theta * L /(1-g) = 0.0014 meters axis displacement
w0 = 3e-3 meters = spot size at ITM
a^2/w0^2 = 0.204 ==>> 20% power loss into higher order modes due to PRM motion.
That means 20% less power circulating, hitting the ITMs, so less power going into the arm cavities, so less power buildup. This isn't 50%, but it is fairly substantial, using angular fluctuation numbers that we saw during our PRMI+arms test last week. If you look at the oplev plot from that test, you will notice that when the arm power is high (as is POP), the PRM moves significantly more than when the carrier buildup in the cavities was low. The rms motion is not 12 urad, but the peak-to-peak motion can occasionally be that large.
So, why is that? Rana and I had a look, and it is clear that there is a difference in PRM motion when the IFO is aligned and flashing, versus aligned, but PSL shutter is closed. Written the cavities flash, the PRM gets a kick. Our current theory is that some scattered light in the PRC or the BS chamber is getting into the PRM's OSEMs, causing a spike in their error signal, and this causes the damping loops to push on the optic.
We should think a little more on why the PRM is moving so much more that any other optic while the power is building up, and if there is anything we can do about the situation without venting. If we have to, we should consider putting aluminum foil beam blocks to protect the PRM's OSEMs.
Interesting results. When you compute the effect of ETM motion, you maybe should also consider that moving around the arm cavity axis changes the matching of the input beam with the cavity, and thus the coupling between PRC and arms. But I believe this effect is of the same order of the one you computed, so maybe there is only one or two factors of two to add. This do not change significantly the conclusion.
Instead, the numbers you're giving for PRM motion are interesting. Since I almost never believe computations before I see that an experiment agrees with them, I suggest that you try to prove experimentally your statement. The simplest way is to use a scatter plot as I suggested the past week: you plot the carrier arm power vs PRM optical lever signals in a scatter plot. If there is no correlation between the two motions, you should see a round fuzzy ball in the plot. Otherwise, you will se some non trivial shape. Here is an example: https://tds.ego-gw.it/itf/osl_virgo/index.php?callRep=18918
Nic and Evan put the ISS together (elog 9376), and we used an injection into the error point (?) to modulate the laser power before the PMC (The AOM had a bias offset, but there is no loop). This gives us some RIN, that we can try to correlate with the PRM OSEM sensors.
We injected several lines, around 100, 200, 500 and 800 Hz. For 100, 200 and 800 Hz lines, we see a ratio between POPDC and the OSEM sensors of 1e-4, but at 500 Hz, the ratio was more like 1e-3. We're not sure why this ratio difference exists, but it does. These ratios were true for the 4 face OSEMs. The side OSEM saw a slightly smaller signal.
For these measurements, the PRMI was sideband locked, and we were driving the AOM with an amplitude of 10,000 counts (I don't know what the calibration is between counts and actual drive, which is why we're looking at the POPDC to sensor *ratio*).
To get a more precise number, we may want to consider locking the PRMI on carrier, so we have more power in the cavity, and so more signal in the OSEMs.
These ratios look, by eye, similar to the ratios we see from the time back on 30 Oct when we were doing the PRMI+2arms test, and the arms were resonating about 50 units. So, that is nice to see some consistency.
This time series is from 1067163395 + 27 seconds, from 30 Oct 2013 when we did the PRMI+2arms.
Ideas to go forward:
We should think about chopping the OSEM LEDs, and demodulating the PD sensors.
We should also take a look in the chamber with a camera from the viewport on the north side of the BS chamber, to see if we see any flashes in the chamber that could be going into the OSEMs, to see where we should maybe put aluminum foil shields.
In the process of figuring out what we can do to fix our PRM motion problem, I am looking at the PRM oplev.
Eventually (as in, tomorrow), I'd like to be able to simulate some optic motion as a result of an impulse, and see what the oplev loops do to that motion. (For starters, I'll take the impulse response of the OSEM loop as my time series that the oplev loop sees).
One thing that I have done is look at the oplev model that Rana put together, which is now in the noisebudget svn: /ligo/svncommon/NbSVN/aligonoisebudget/trunk/OpLev/C1
This script plots the open loop gain of the modeled oplev:
This should be compared to the pitch and yaw measured transfer functions:
In the YAW plot, there are 2 transfer functions. The first time around, the UGF was ~2.5Hz, which is too low, so I increased the gain in the C1:SUS-PRM_OLYAW filter bank from -3 to -9.
The shapes of the measured and modeled transfer functions look reasonably similar, but I haven't done a plot overlay. I suspect that the reason I don't see the same height peak as in the model is just that I'm not taking a huge number of points. However, if the other parts of the TF line up, I'll assume that that's okay.
I want to make sure that the modeled transfer function matches the measured ones, so that I know I can trust the model. Then, I'll figure out how to use the time series data with the simulated loop. Ideally, I'd like to see that the oplev loop can fully squish the motion from the OSEM kicks. Once I get something that looks good (by hand-tweaking the filter shape), I'll give it a try in the actual system. We should, as soon as I get the optimal stuff working, redo this in a more optimal way. Both now, and after I get an optimal design, I'll look at the actual step and impulse responses of the loop, to make sure there aren't any hidden instabilities.
Other thoughts for the night:
Rana suggests increasing the gain in some of the oplev QPD heads (including PRM), so that we're getting more than a few hundred counts of power on each quadrant. Since our ADCs go to 32,000 counts, a few hundred is very small, and keeping us close to our noise limits.
Also, just an observation, but when I watch the REFL camera along with POP and AS, it's clear that the PRM is getting kicked, and I don't have the ETMs aligned right now, so this is just PRMI flashes. There is also a lot of glow in the BS chamber during flashes (as seen on the PRM face video camera).
I have created a new filter for the PRM oplev damping loops. The biggest change is an increase in the gain between 0.4 - 7 Hz.
Here is a plot of the old, and my new modelled open loop gain:
When I look at my step and impulse response time series, the notches for the bounce and roll were causing some ringing, so for now they are turned off, both in the model and in the real time system. Also, the "OLG orig" trace has a 4th order elliptic lowpass at 75 Hz, but the real system had a 4th order elliptic low pass at 35 Hz. When we use 35 Hz in the model, we get lots of ringing. So, we have moved both model and real system to 55 Hz 4th order elliptic low passes. Also, also, we haven't been using the 3.3 Hz resonant gain, so I removed that from the modelled loop.
I have put the "boost" for the .4-7 Hz emphasis into FM 7 of the PRM oplev filters. I also removed several old filters that are never used. So, for now, the PRM oplevs should have engaged: FM 1, 7, 9. Pitch gain is +5, yaw gain is -9. We can consider re-implementing the bounce-roll notches, and the stack resgain if it looks like those are getting rung up, and causing trouble.
Here is a set of spectra, showing the improvement. It's unclear why yaw is worse than pitch below 4Hz, and why pitch is so much worse than yaw between 4-15 Hz, however for each of pitch and yaw, the before (reference pink and cyan traces) is higher than the improved (dark red, dark blue traces) between a few tenths of a Hz up to 3ish Hz. And, we're not causing more noise elsewhere. We do want to monitor to make sure we're not ringing up the bounce and roll modes, but for now they seem fine.
I forgot how we could turn on the PRM oplev servo and the PRM ASC servo at the same time without conflict.
It seems that this new oplev servo covers 0.04 to 8Hz. It's pretty broadband. Do we inject the ASC signal to the oplev error?
After I aligned the IR interferometer (no ASS - we still need to figure out what's going on with that), I am trying to find the green beatnotes for each arm.
First, I locked the green lasers to each arm.
I then went out to the PSL table and aligned the Green Yarm path by overlapping the near-field and far-field of the yarm transmission and the PSL green pickoff. I then turned on the power for the Beat PDs, since it was off (I confirmed that the outputs were plugged into the beatbox, so they are seeing 50 ohms). I assume that the beat PDs were off since Manasa pulled the Beatbox last week, but there is no elog reference!! Anyhow, after seeing a real signal, I maximized the DC power on the beat PD for the Yarm. I then maximized the light on the DC transmission PD for the Yarm.
I looked at the Xarm, and the near-field alignment looks okay, but I haven't checked the far-field.
I started looking for the beatnotes from the control room:
I am changing the SLOW_SERVO2_OFFSETs by 30 counts, and then unlocking and relocking the arms, and checking to see if I see a peak on the RF spectrum analyser.
The Y offset started at -10320, and I found a beatnote at -11230 (beatnote is about 26MHz). The X offset started at 4500. Going larger seemed to get me to a less bright TEM00 mode, so I switched and have been searching by going down in offset, but haven't yet found the beatnote. I suspect that I actually need to align the X path on the PSL table. The Y beatnote is very small, about -30dBm, so I also need to tweak the alignment by maximizing the peak value.
EricQ said that he's going to start hanging out at the 40m a bit, and I was thinking about what I can have him help me with. This lead to me writing up a wishlist for things that have to do with the ALS system and green lasers. Some of these are very small tasks, while others are pretty big. They are certainly not all high priority. But, they're on my wishlist.
Automation / script writing
I am able to lock the Yarm ALS, but not at the full gain that I should be. I attribute this to my mediocre alignment of the path on the PSL table. EDIT: Manasa pointed out that I forgot to set the PSL FSS slow adjust to ~zero, so the PSL temperature was off, so there wasn't really any hope for me last night.
However, I decided that I should write down the ALS locking procedure, as shown to me by Masayuki on 29Oct2013, that is written in one of the Control Room notebooks. So, here it is. I will write channel names and DTT template names for the Y arm, but the procedure is the same for both arms.
Can't we somehow hook up this camera to the MUX with the movie mode?
I think both the MUX and the sensoray are compatible with the color video signal.
Only the old CRT is B/W.
Watek ccd with Tamron lens is hooked up to MUX
This set up close to the viewport glass! Please be careful!
Video captures when power recycling cavity is locked (videos 1 & 2) and flashing (video 3). Arms stayed misaligned.
1. CH1 and CH2 are loooking at PRM front and back faces. CH3 and CH4 are looking at POP and REFL
2. CH1 and CH2 are loooking at PRM front and back faces. CH3 and CH4 are looking at the ITMs
3. CH1 and CH2 are loooking at PRM front and back faces. CH3 and CH4 are looking at POP and REFL
I forgot how we could turn on the PRM oplev servo and the PRM ASC servo at the same time without conflict.
It seems that this new oplev servo covers 0.04 to 8Hz. It's pretty broadband. Do we inject the ASC signal to the oplev error?
Right now all 3 servos that control PRM angle (OSEM damping, Oplev, and ASC) run in parallel, and they're all AC coupled.
I found the beatnotes for both the X and Y arm ALS this morning. The beat amplitudes measured -5dBm and -18dBm respectively and occurred at SLOW SERVO2 OFFSET 4550 and -10340. I had to only tweak the Y green PSL alignment to increase the beat amplitude.
I locked both the arms using ALS and they were stably locked until MC unlocked for a moment (nearly 16 minutes).
The only thing missing in the list of things you looked into is the status of the PSL slow actuator adjust. Check if this is near zero.
So far this afternoon, I have redone the IFO alignment, locked both arms with ALS, moved both arms off resonance, locked PRMI, and started bringing one arm back to resonance.
The alignment was really not good, which I knew yesterday, but the ASS wasn't working yesterday. I hand-did the alignment, and tried locking, which was easier with the slightly better alignment.
I locked both arms with ALS, found the resonances, and then moved them off resonance using Masayuki's scripts.
I then restored the PRM alignment, and locked the PRMI.
I started bringing the Yarm back, but I kept losing lock when I got to about 0.1 transmission.
After losing lock several times, I switched over to looking at the ASS. I have figured out the problem, and fixed it. The ASS for the arms now works again.
Looking at the StripTool plots of the lockin outputs for each arm, it was clear that the "L" traces were their usual size, but the "T" traces, which are demodulated versions of the transmission DC PDs, were tiny. I investigated in the model, and the answer is obvious: both the LSC and the ASS get the transmission information directly from the end sus computers. Since we recently moved the normalization gain for the transmission diodes into the SUS models from the LSC model, this means that the ASS was seeing a differently sized signal than it had in the past.
To fix this, I put a gain into the T_DEMOD_SIG filter banks for all 8 lockins that use info from the transmission DC PDs. I used 1/g , where g is the gain that is in the C1:SUS-ETM#_TR#_GAIN channels. For TRX, that number is -0.003, and for TRY that number is 0.002 . So, in the .snap file that is used when turning on the ASS, I have given the Xarm lockins a gain of -333, and the Yarm lockins a gain of 500. I chose this place, because the only thing that has happened to the signal until this point is a bandpass, so the rest of the servo gains can remain the same.
I tested the ASS, and it works just like it used to. I let it run, and align all of the optics, then I misaligned by a small amount each of the ETMs, saw that the lockin output values changed, and then were servoed back to zero. So, it seems all good.
Since we have never tried to lock PRMI on carrier after the folding mirrors were flipped, I tried to lock PRCL on carrier.
I thought this might give us some idea about the PRC stability for resonance or some clue as to what happens to the PRM suspensions and PRMI stability when we have carrier resonating in the cavity.
I changed the sign of the PRCL gain and also tried increasing the gain. But this did not work and I was not able to carrier lock PRMI. May be I am missing to change some parameter that is very trivial?
Since we have never tried to lock PRMI on carrier after the folding mirrors were flipped, I tried to lock PRCL on carrier.
PRMI could not be locked on carrier using 3f. The configuration from the last time when PRMI was carrier locked (elog) were used and PRMI locked on carrier with these settings.
== PRMI carrier ==
MICH: AS55_Q_ERR, AS55_PHASE_R = -12 deg, MICH_GAIN = -0.2, feedback to ITMX(-1),ITMY(+1)
PRCL: REFL55_I_ERR, REFL55_PHASE_R = 70 deg, PRCL_GAIN = 1.0, feedback to PRM
Below is the video capture showing the PRM front and back face when carrier flashes with few second locks.
EDIT by JCD:
The demod phase numbers that Manasa is quoting above were correct back in March, when the elog she's quoting from was written. They are not true now, since we've adjusted things in the last 8 months. Also, I'm using a gain of -1.5 for MICH, and +1.5 for PRCL. MICH has no FMs triggered, PRCL has FM 2,3,6 triggered. Since we won't be using this configuration for full locking, but just for some tests, I'm currently using AS55 Q for MICH, and REFL 55I for PRCL, and using the ITMs to actuate on MICH for today.
I have increased the gain of the MICH loop to -100, and set FMs 2,3,7 to be triggered. I have also increased the PRCL gain to 2. The PRCL ASC pitch and yaw gains used to be -0.004, but I have increased them both to -0.01.
Now, I'm seeing power fluctuations in POPDC of ~200 pk-pk, at an average value of 2650. That's a RIN of 7.5% . If I turn off all OSEM damping for the PRM (after the cavities are already locked), I get POP DC fluctuations of 100 pk-pk at the same average value, so a RIN of 4%.
Back on October 30th (elog 9338), we had an average POPDC of 400, with fluctuations of 200 pk-pk, so a RIN of 50%.
So, I am pleased that, with the carrier locking, I have lower power fluctuations. And, since there is more overall power in the PRC right now than we had 3 weeks ago, I'm hopeful that a PRMI+arms test will have lower power fluctuation.
Also, a note, when my MICH gain was still low, I had lots of power fluctuation at the AS port, which was coherent with my POPDC power fluctuations (which makes sense). At that time, my overall RIN was higher than it is now (although I neglected to write down the numbers), but more significantly, I saw occasional 'kicks', where the ASDC and POPDC powers would ring for 1 or 2 seconds, with power fluctuations of order 40%. I have not seen any of those kicks since increasing the MICH gain.
We locked the PRMI on carrier again today, after lunch. Following a suggestion from the 40m meeting, we wanted to compare the PRMI carrier fluctuations with the new vs. old OpLev servo for the PRM.
To do change between the servo shapes, I put in an elliptic lowpass at 35Hz, since I overwrote that with the 55Hz lowpass the other day. The only other change between shapes is turning on and off my boost / emphasis filter.
So, the scenarios were:
(1) New OpLev servo
(2) Old OpLev servo (no boost, but 3.2Hz res gain and bounce roll notches on), with 55Hz lowpass
(3) Old OpLev servo with 35Hz lowpass
For scenario (1), like last night, there were small power fluctuations. For scenario (2), most of the time there were small power fluctuations, but occasionally there would be a kick somewhere, and the power would dip down by ~50%, and the fluctuations would continue like a ringdown for a few seconds, and then we'd be back to small fluctuations until the next kick. For scenario (3), even with trying different LSC servo gains, we could not get the PRMI to lock on carrier for more than a few tenths of a second. During that time, the power fluctuations were very large.
So, the old oplev servo was kind of okay, but the lowpass at 35 Hz was bad, bad, bad. It seems that the new OpLev servo is doing good things for us.
We have put the Xend QPD back in place, and centered it. The whitening board was replaced by me a few days ago.
We also went down to the Yend and centered the Yend QPD.
I used the offset.py script that Masayuki wrote to zero the offsets of the individual quadrants when the PSL shutter was closed, and then I averaged the output of the SUM filter banks, and made the gains 1/AvgSum, so that both the Thorlabs PD and the QPD are normalized to 1 at single-arm resonance, for each arm.
I don't know what the gain is of the QPD head off the top of my head, relative to the Thorlabs PD, but eventually we want them to be the same, so that 1=1 and 700=700 on each PD.
The Phase tracker outputs (= ALS X/Y error signals) are now conveyed to the LSC model.
Their entry points at the LSC model are C1:LSC-ALSX_IN1 and C1:LSC-ALSY_IN1.
They are connected to the signal matrix (28th and 29th signals) via signal conditioning filters (C1:LSC-ALSX and C1:LSC-ALSY).
The main LSC screen has not been updated. The conventional ALS servos are still remains as they were.
This renovation required the recompilation of c1als, c1rfm, and c1lsc. Two PCIe-RFM bridge paths were added resulting in
increase of the c1rfm timing budget from 38 to 44.
2 weeks ago I took some data, and remembered today at the 40m meeting that I hadn't posted it. Bad grad student.
All I'm trying to show here is that we see flashes in the arms that are larger than the ~50 units that we see saturate the Thorlabs transmission PDs. For arm power values below ~50, the QPD sum and Thorlabs PDs give approximately the same values. So, 1 unit on the Thorlabs PDs is equivalent to 1 unit on the QPD sum, and 50 units on the Thorlabs diode is equivalent to 50 units on the QPD sum.
The situation was arms held on resonance with ALS, and the PRMI was flashing.
Arm powers of ~140 imply a power recycling gain of ~7.
Last week, Koji cleaned up the LSC model to make it much more readable, while he was working on piping the ALS signals to the LSC model. However, somehow the DAQ Channels block got deleted before the model was committed to the svn. Since there were 2 months between svn checkins for c1lsc.mdl, it's possible that someone had the model open just to look at, and the block got deleted, and that's the version that Koji started with.
Anyhow, thankfully we have the svn, so Koji and I found that the DAQ Channels block was (as expected) in the previously checked-in version of the LSC model. I put a copy of the old model onto my desktop, opened it up, copied the DAQ Channels block, and then pasted it into the new cleaned-up version of the model. (Jamie - is there a way to conveniently download a previous version through the web interface?)
I have checked it in, compiled and restarted the lsc model. The _DQ channels are back now.
I worked on the CDS related stuffs for LSC yesterday and today.
1. Slow machines:
I checked the database files for c1iscaux and c1iscaux2 (slow machines). They are mainly
used for the control of LSC whitening filters. The channel names were totally random as we
reconfigured the RF PDs while the channel names had been unchanged.
- Now the database was modified so that the PD name and the channels are related.
- saverestore.req and autoBurt.req were also changed accordingly.
- PD interface channels are completely random. Don't use them.
- I found the whitening of DCPDs are not effective.
- We need to clean up /cvs/cds/caltech/target directory. The autoBurt requests in the old targets
are making unnecessary burt files.
2. LSC screens
- The channel names on the LSC OVERVIEW screen was modified. (Attachment 1)
- A new LSC Whitening screen was made. (Attachment 2)
3. LSC screen generator
To touch the main LSC screen is very tough. The screen was split in to several sub screens
and combined with a command.
This command combines the multiple adl files into a single file with x&y offsets.
This way, you can work with the each section of the screen.
Also, moving the blocks are just easy.
4. LSC Code Bug?
During the screen making, I found that a couple of the whitening switches are not
working properly. e.g. When AS165 (either I or Q) FM1 is activated throught the whitening trigger,
the MSB bit (bit15) of the binary I/O (C1:LSC-BIO_0_0) does not .
SImilarly ASDC FM1 does not toggle bit15 of C1:LSC-BIO_0_1.
The other channels seems OK.
At first, I thought this is a bug of "Bit2Word" block. But an individual test of the block showed that
the block is not guilty. So why is only Bit15 malfunctioning???
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:
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.
Tonight we worked on tweaking up the PRCL new ASC, and then PRMI+1 arm locking. We were unable to get the Xarm to stay locked on a TEM00 mode for very long, and after an hour or two of using the PZTs to try to align the beam to the cavity, we gave up and just used Yarm green.
NB: We haven't done anything to MCL, although it is not in use. Den is still going to get around to elogging what servo shaping he changed on that last night.
I wrote a script that will handle the transitions between the new PRCL ASC and the PRM oplev and local damping. The script is accessible from the PRC ASC screen, and will detect when the PRMI is locked or not. When it is locked, it will turn down the PRM oplev gains and turn on the ASC, and then it will turn off the local shadow sensor damping for PRM pitch and yaw. When the PRMI unlocks, the script will turn off the ASC and restore oplev and local shadow sensor damping.
We saw that the bounce mode of the PRM was getting rung up with our new ASC, so we included a band stop in the ASC, and also turned on the triggering for the PRCL LSC FM6, which has the resonant gain for the bounce mode (as well as roll, and the stack mode). This made the PRMI spot very stable.
We then moved on to green arm locking. The Yarm is behaving perfectly nicely (as nice as it has been lately - it's alignment and mode matching could also use some work), but Xarm was giving us a bit of trouble. As always (since the PZTs were installed?), the mode matching isn't excellent for the green to the arm, so it can be hard to catch a TEM00 mode. Also, even if we did catch a good mode, it would often not stay locked for more than a few tens of seconds. We tried several alignment tweakings, and several different end laser temperatures (within the confines of seeing the beatnote under 100MHz), and didn't have a lot of success. It looks like Eric had the slow servo engaged for the Xend laser, so the temperature offset was something like +300,000, which seemed totally crazy. I turned that off, and found the beatnote somewhere around output of -10,300. So, I haven't gone to the end to look at the temperature, but it's going to be different than when Eric was taking measurements this afternoon. It seems like the main problem with the Xarm is poor mode matching - the maximized input pointing for TEM00, when you unlock and relock the cavity, is just as likely to give you a TEM_9_0 mode, as TEM00.
So, we gave up on the Xarm for the evening, and tried PRMI+1arm, with the new PRCL ASC. This was successful! The Yarm beatnote was around laser slow servo output of +4450. Beatnote at 46.0MHz, -26dBm. We found the IR resonance, moved off, locked the PRMI, transitioned to the new ASC, and brought the Yarm back to IR resonance. What we see is that the power fluctuations in the PRC are much smaller than they were back around Halloween (elog 9338), however the arm power fluctuations still seem very, very large. This is certainly partly due to the fact that we haven't done a thorough Yarm alignment since before messing with the greens, so we will have drifted somewhat. Also, the ALS beatnote sensor isn't perfect, so won't be perfect at holding us near resonance.
Den is thinking about whether we can use the arm transmission QPD signals to feed back to the ETM ASC servos, to try to reduce the RIN in the arms. I feel like we should also see if this amount of power fluctuation can be explained by our ALS noise, because maybe we'll be fine once we transition to IR and turn off the ALS system. Attached is a plot showing that the arm's RIN is coherent with the spot motion seen by the transmission QPD, so we need to check the alignment of the cavity, as well as consider using the trans QPD in an ASC feedback loop.
Here is a plot of the PRC sideband power, as well as the Yarm transmission. The GPS time for this plot is approximately 1070963372.
According to the measurement by Eric, the X-arm green PDH UGF is too low. We still have some room to increase the gain.
The out of loop stability of the ALS for each arm should be measured everyday.
Otherwise we can't tell whether the arm is prepared for advanced locking activities or not.
We expect to see the arm stablity of ~50pm_rms for the Y arm and ~150pm_rms for the X arm.
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.
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.
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.
These seem like pretty terrible loop shapes. Can you give us a plot with the breakdown of several of the TFs and some .m file?
We should be able to estimate the noise coming out of the MC using the single arm and then make a guess for the CM loop gain requirement. There's no reason to keep the old Boost shapes; those were used in the old MC configuration which had a RefCav. In addition to minimizing the EOM range, we should also minimize the AO signal as Koji has pointed out. In practice, I've seen that using ~300 Hz of offset makes no harm with 4 kHz MC pole.
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;
% 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.