My hunch is that the PRC is SHORT by a few cm, not long.
In my Optickle simulation, the sidebands are not perfectly co-resonating in the PRMI when the arms are not locked. See Fig 1, which is the fields in the PRMI using the design PRC length. If I add 5cm to the PRC length, I get Fig 2, where the peaks are about the same separation, but the upper and lower sidebands have swapped sides of the 0 mark. However, if I remove 5cm from the PRC length, I get Fig 3, where the peaks are much farther apart than in Fig 1. This case looks more similar to the data that Gabriele plotted in his elog entry, where the peaks are separated by at least a linewidth. This is not at all conclusive, but it's a guess for which direction we need to move. Obviously doing an actual measurement will be better.
My tummy feelings also agree with this simulation: When we flipped PR3 (the only optic change in the PRC since Gabriele and I measured the 55MHz peak separation in April), since the HR side of the optic is now at the back, we had to push the whole suspension cage forward to get the beam aligned to the Yarm. Conversely, however, transmitting through the glass substrate adds to the optical path length. So, my tummy feelings may be wrong.
Figure 1, PRC at design length, PRMI sweep:
Figure 2, PRC 5cm longer than design length:
Figure 3, PRC 5cm shorter than design length:
Maybe I'm getting confused, but I still believe there is no way to decide the direction from yesterday's measurement.
Let's say for example that the arm sideband detuning from antiresonance is equivalent to a PRC length change of +1cm away from the position of ideal resonance of the sidebands without arms. Then we can get a measured separation of the sidebands, without arms, corresponding to 5cm both if the PRC is off by +4cm or by -6cm...
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
up/down scripts are to be made
(Offset Edit on Dec 20 10:38PM)
POY11QMon -> CM Servo In1 -> CM Servo -->Out1 -> ADC -> CM Slow FM -> LSC MC Servo FM -> ETMY(x1.0) -> DAC -> ETMY
-->Servo Out -> SR560 (DC, 1st order 30kHz LPF) -> MC In2
POY11QMon -> CM Servo In1 -> CM Servo -->Out1 -> ADC -> CM Slow FM -> LSC MC Servo FM -> ETMY(x1.0) -> DAC -> ETMY
-->Servo Out -> SR560 (DC, 1st order 30kHz LPF) -> MC In2
Lock acquisition path 1
CM Slow FM:
CM Servo setting:
MC Servo setting:
Lock acquisition path 2
Transition to ETMY LSC to MCL
This too huge offset difference with/without "BOOST" switch should be checked.
I checked the offset situation in the CM servo boost circuit.
- The offset voltage on the CM servo screen is a raw DAC output. This number is diluted by the voltage divider before the amplifier.
So, the actual offset of the boost circuit was much smaller. (~20mV)
- There is a offset trimmer on the board. This was adjusted so that the boost does not generate an output offset.
- So the default offset is 0V.
- When the arm was locked with (digital) POY11, the CM servo offset is necessary to be -2.7 (now).
This means that analog POY11Q and digital POY11 has different offset for the best resonance transmission.
That is believable if POY11I is contributing to the digital POY11 signal.
The previous LSC whitening filters for the DCPDs were in an unknown state (although the transfer functions were actually measured and fit a while ago)
They had no DC gain control and some of the channels had modifications.
To make the setup clear, the filter module was replaced with the spare module without any modification.
The channels are now respoding to the whitening gain switches. So far there is no screen for the new whitening gains yet.
Also I found that POX11 DC cable has not been connected. Now it is connected.
The PRCL once again doesn't want to lock on sidebands for me. I can lock on the carrier just fine (using the IFO Config settings, along with some hand-alignment of the PRM).
However, I can't convince it to lock on sidebands. Using the configs that I used on Dec 18th (elog 9491), I'm not getting it. I've done the arm ASS alignment, and I've run LSCoffsets, both of which seemed to do their things appropriately.
I'm going to attribute this today to not being in the groove yet, and I'll look at it again in the morning.
I ran a simulation of a double cavity with a PRC length mismatched w.r.t. the modulation frequency. I summarized the results in the attached PDF. I think it would be important to have a cross check of the results.
A mismatch between PRC length and modulation frequency do have an effect on error signals
Multiple zeros appear in REFL_3f/PRCL that can be removed by careful tuning of the demodulation phase (however, the shape of the signal makes difficult to understand which phase is good…)
No visible effect on REFL_1f/CARM
But a large PRCL signal appears in REFL_1f_I, which is used to control CARM. This is not good.
A mismatch of the order of 0.5 cm has a small effect.
So, we want an relatively quick measurement of the PRC length error (with sign!) at the order of .5 centimeter or so. Rana suggested the "demodulation phase method," i.e. lock the simple Michelson, measure what demodulation phase brings the 1F signal entirely within the phase quadrature, then lock the PRMI and measure the demodulation phase again. This tells you something about the length of the PRC.
Gabriele and I worked through a simulation using MIST to determine how to actually do this. We simulated the case of injecting a line at 1kHz in the laser frequency via the laser's PZT and looking at the transfer function of the 1kHz signal to the I and Q at the 1F AS demodulated signal when locked. (Michelson locked on the dark fringe, PRC locked on 11MHz sideband) With the I and Q in hand, we can measure some demodulation phase angle that would bring everything into I.
When the PRC length is in the ideal location, the demodulation phases in the two cases are the just about the same. Sweeping the length of the PRC around the ideal length gives us a monotonic function in the difference in the demodulation phases:
So, with this simulation, we should be able to calibrate a measured difference in demod phase into the length error of the cavity! We will proceed and report...
Actually it is difficult to see any laser frequency line in the dark fringe signal, since the Schnupp asymmetry is small. It is much better to use a differential MICH excitation which gives a better signal at the dark port.
We repeated the simulation explained before. We can use both the AS55 or the AS11 signals, bout the first one has a limited linear range and the expected 4cm value is very close to saturation.
[ericq, Gabriele, Manasa]
We wanted to perform the PRC length measurement today with an AS11 signal, but such a signal didn't exist. So, we have temporarily connected the AS110 PD signal (which is some Thorlabs PD, and not a resonant one) into the REFL11 demod board.
We then proceeded with the goal of locking the PRC with REFL165. A few parameters that were changed along the way as we aligned and locked things:
Sadly, in the end, we couldn't lock the PRC on a sideband in a stable manner. The alignment would drift faster than we could optimize the alignment and gains for the PRC. I.e. we would lock the PRC on the carrier, align PRM (and maybe touch ITMX) to maximize POPDC, switch to sideband locking, try to lock, and things would start looking misaligned. Switching back to carrier locking, the beam spots on REFL (for example) would have moved.
Manasa noted the MC_TRANS_Y has been substantially drifting along with small drift in MC_TRANS_P as well. So we need to fix the source of the mode cleaner beam drifting if we want to make this measurement.
Its very doubtful that the MC yaw drift matters for the IFO. That's just a qualitative correlation; the numbers don't hang together.
Then there must be something else slowly drifting. It was very clear that the good alignment of the IFO was every time lost after few minutes...
We wanted to try the PRC length measurement,but we ended up spending all the afternoon to lock the PRMI on sidebands. Here are some results
Finally, we managed to lock PRMI on sidebands:
We could carry out the measurement of PRC length. The AS110 photodiode was plugged into REFL11. So REFL11 is giving us the AS11 signal. Here is the procedure.
We repeated the same measurement also using AS55, with the same procedure.
Roughly, the phase difference for AS11 was 11 degrees and for AS55 it was 23 degrees. A more detailed analysis and a calibration in terms of PRC length will follow.
I analyzed the data we took yesterday, both using AS11 and AS55. For each value of the phase I estimated the Q/P ratio using a demodulation code. Then I used a linear regression fit to estimate the zero crossing point.
Here are the plots of the data points with the fits:
The measurements a re more noisy in the PRMI configuration, as expected since we had a lot of angular motion. Also, the AS11 data is more noisy. However, the estimated phase differences between PRMI and MICH configurations are:
The simulation already described in slogs 9539 and 9541 provides the calibration in terms of PRC length. Here are the curves
The corresponding length errors are
The two results are not consistent one with the other and they are both not consistent with the previous estimate of 4 cm based on the 55MHz sideband peak splitting.
I don't know the reason for this incongruence. I checked the simulation, repeating it with Optickle and I got the same results. So I'm confident that the simulation is not completely wrong.
I also tried to understand which parameters of the IFO can affect the result. The following ones have no impact
The only parameters that could affect the curves are offsets in MICH and PRCL locking point. We should check if this is happening. A first quick look (with EricQ) seems to indicate that we indeed have an offset in PRCL. However, tonight the PRMI is not locking stably on the sidebands.
If possibile, we will repeat the measurement later on tonight, checking first the PRCL offset.
Since we don't have agreement between the measurements we made the other day and the earlier estimations, I wanted to repeat the demodulation angle measurement. We had to do a few things to keep the PRMI locked, since in the last few days, it hasn't been stable enough.
The mode cleaner had been very fussy lately; the WFS were pushing in a way that caused fast oscillations of the transmission and reflection powers. I turned off the servos, manually aligned the mode cleaner to transmission of about 15k and refl of about .4, centered the beams on the WFS QPDs, and turned the loops back on. Things were much stable after that. Also, Jenne noticed that the PMC loop had walked the laser PZT temperature to a bad place, and fixed it.
After aligning the carrier locked PRMI, the last piece needed to get things stable enough for sideband locking was turning off the angular damping on the PRM suspension screen (this was turned back on when we were done). Waiting until evening noise levels probably helped too. We used a 1000 count MICH excitation in the PRMI case, and recorded data for about a minute in one degree steps around the demodulation phase that looked to put the excitation entirely within the Q of the PD. Also, we notched out the excitation frequency in the MICH servo bank for today's measurement; I think it's outside of the loop bandwidth anyways, but it's good to be sure.
Jenne and I pondered a bit whether changing the AS55 demodulation phase while it (AS55 Q) is being used as the MICH control signal introduces subtleties that we haven't anticipated, but couldn't come up with anything concrete. Changing the angle from the what maximizes the Q just looks like a slight change in MICH gain, and shouldn't affect the phase of the excitation signal on the PD...
In any case, the data have been recorded, and the results will follow soon.
I analyzed the data taken yesterday.
The AS11 data in PRMI configuration is very bad, while the AS55 seems good enough:
The phase differences are
AS11 = 21 +- 18 degrees (almost useless due to the large error)
AS55 = 11.0 +- 0.4 degrees
The AS55 phase difference is not the same measured in the last trial, but about half of it. The new length estimates are:
AS11 = 3.2 +- 2.8 cm
AS55 = 0.47 +- 0.01 cm
We can probably forget about the AS11 measurement, but the AS55 result is different from the previous estimate... Maybe this is due to the fact that Eric adjusted the PRCL offset, but then we're going in the wrong direction....
Yesterday night I plugged back the REFL11 RF cable into the corresponding demodulation board.
Here is how to measure the PRC length with a set of distance measurements in the optical setup.
We need to take distance measurements between reference points on each mirror suspension. For the large ones (SOS) that are used for BS, PRM and ITMs, the reference points are the corners of the second rectangular base: not the one directly in contact with the optical bench (since the chamfers make difficult to define a clear corner), but the rectangular one just above it. For the small suspensions (TT) the points are directly the corners of the base plates.
From the mechanical drawings of the two kind of suspensions I got the distances between the mirror centers and the reference corners. The mirror is not centered in the base, so it is a good idea to cross check if the numbers are correct with some measurements on the dummy suspensions.
I assumed the dimensions of the mirrors, as well as the beam incidence angles are known and we don't need to measure them again. Small errors in the angles should have small impact on the results.
I wrote a MATLAB script that takes as input the measured distances and produce the optical path lengths. The script also produce a drawing of the setup as reconstructed, showing the measurement points, the mirrors, the reference base plates, and the beam path. Here is an example output, that can be used to understand which are the five distances to be measured. I used dummy measured distances to produce it.
In red the beam path in vacuum and in magenta the beam path in the substrate. The mirrors are the blue rectangles inside the reference bases which are in black. The thick lines are the HR faces. The green points are the measurement points and the green lines the distances to be measured. The names on the measurement lines are those used in the MATLAB script.
The MATLAB scripts are attached to this elog. The main file is survey_v2.m, which contains all the parameters and the measured values. Update it with the real numbers and run it to get the results, including the graphic output. The other files are auxiliary functions to create the graphics. I checked many times the code and the computations, but I can't be sure that there are no errors, since there's no way to check if the output is correct... The plot is produced in a way which is somehow independent from the computations, so if it makes sense this gives at least a self consistency test.
global sos_lx sos_ly sos_cx sos_cy tt_lx tt_ly tt_cx tt_cy
%% Survey of the PRC length
%% measured distances
d_MB2_MY = 2000.0;
d_MB3_MX = 2000.0;
d_MB1_M31 = 400.0;
d_M32_M21 = 3000.0;
d_M22_MP = 2000.0;
function d = distance(c1, c2)
d = sqrt(sum((c1-c2).^2));
function draw_beam(c1, c2, color)
plot( [c1(1), c2(1)], [c1(2), c2(2)], color, 'LineWidth', 2)
function draw_measurement(c1, c2, color, name)
plot( [c1(1), c2(1)], [c1(2), c2(2)], color)
text( (c1(1)+c2(1))/2, (c1(2)+c2(2))/2 + 20, name, ...
'FontSize', 5, 'HorizontalAlignment', 'center', ...
plot(c(1), c(2), 'go', 'LineWidth', 2, 'MarkerSize', 3);
function draw_sos(C, angle)
global sos_lx sos_ly sos_cx sos_cy tt_lx tt_ly tt_cx tt_cy
c(:,1) = [-sos_lx/2, -sos_ly/2 + sos_cy-sos_ly/2]';
c(:,2) = [-sos_lx/2, sos_ly/2 + sos_cy-sos_ly/2]';
c(:,3) = [sos_lx/2, sos_ly/2 + sos_cy-sos_ly/2]';
c(:,4) = [sos_lx/2, -sos_ly/2 + sos_cy-sos_ly/2]';
c(:,5) = [-sos_lx/2, -sos_ly/2 + sos_cy-sos_ly/2]';
m_lx = 25.4*2;
function draw_tt(C, angle)
global sos_lx sos_ly sos_cx sos_cy tt_lx tt_ly tt_cx tt_cy
c(:,1) = [-tt_lx/2, -tt_ly/2 + tt_cy-tt_ly/2]';
c(:,2) = [-tt_lx/2, tt_ly/2 + tt_cy-tt_ly/2]';
c(:,3) = [tt_lx/2, tt_ly/2 + tt_cy-tt_ly/2]';
c(:,4) = [tt_lx/2, -tt_ly/2 + tt_cy-tt_ly/2]';
c(:,5) = [-tt_lx/2, -tt_ly/2 + tt_cy-tt_ly/2]';
m_lx = 25.4;
This path does not look correct to me. Maybe it's because this is supposed to represent "optical path lengths" as opposed to actual physical location of optics, but I think locations should be checked. For instance, PRM looks like it's floating in mid-air between the BS and ITMX chambers, and PR2 is not located behind ITMX. Actually, come to think of it, it might just be that ITMX (or the ITMs in general) is in the wrong place?
Here is a similar diagram I produced when building a Finesse model of the 40m, based on the CAD drawing that Manasa is maintaining:
I know the drawing is wrong. I put random distances, not realistic ones, and I did not try to get something close to reality. Once we put the measured distances, the drawing should (hopefully) be correct.
[Manasa, EricQ, Gabriele]
We managed to measure the PRC length using a procedure close to the one described in slog 9573.
We had to modify a bit the reference points, since some of them were not accessible. The distances between points into the BS chamber were measured using a ruler. The distances between points on different chambers were measured using the Leica measurement tool. In total we measured five distances, shown in green in the attached map.
We also measured three additional distances that we used to cross check the results. These are shown in the map in magenta.
The values of the optical lengths we measured are:
LX = 6828.96 mm
LY = 6791.74 mm
LPRC = 6810.35 mm
LX-LY = 37.2196 mm
The three reference distances are computed by the script and they match well the measured one, within half centimeter:
M32_MP1 = 117.929 mm (measured = 119 mm)
MP2_MB3 = 242.221 mm (measured = 249 mm)
M23_MX1p = 220.442 mm (measured = 226 mm)
See the attached map to see what the names correspond to.
The nominal PRC length (the one that makes SB resonant without arms) can be computed from the IMC length and it is 6777 mm. So, the power recycling cavity is 33 mm too long w.r.t. the nominal length. This is in good agreement with the estimate we got with the SB splitting method (4cm).
According to the simulation in the wiki page the length we want to have the SB resonate when the arms are there is 6753 mm. So the cavity is 57 mm too long.
Attached the new version of the script used for the computation.
Today we changed the PRC length translating PR2 by 27 mm in the direction of the corner. After this movement we had to realign the PRC cavity to get the beam centered on PRM, PR2, PR3, BS (with apertures) and ITMY (with aperture). To realign we had to move a bit both PR2 and PR3. We could also see some flashes back from the ETMY . //Edit by Manasa : We could see the ETMY reflection close to the center of the ITMY but the arm is not aligned or flashing as yet//.
After the realignment we measured again the PRC length with the same method of yesterday. We only had to change one of the length to measure, because it was no more accessible today. The new map is attached as well as the new script (the script contains also the SRC length estimation, with random numbers in it).
The new PRC length is 6753 mm, which is exactly our target!
The consistency checks are within 5 mm, which is not bad.
We also measured some distances to estimate the SRC length, but right now I'm a bit confused looking at the notes and it seems there is one missing distance (number 1 in the notes). We'll have to check it again tomorrow.
global sos_lx sos_ly sos_cx sos_cy tt_lx ...
tt_ly tt_cx tt_cy sos_sx sos_sy sos_dy
%% Survey of the PRC+SRC lengths %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% measured distances
d_MB2_MY = 2114 + 27 + 9;
Today we measured the missing distance to reconstruct SRC length.
I also changed the way the mirror positions are reconstructed. In total for PRC and SRC we took 13 measurements between different points. The script runs a global fit to these distances based on eight distances and four incidence angles on PR2, PR2, SR2 and SR3. The optimal values are those that minimize the maximum error of the 13 measurements with respect to the ones reconstructed on the base of the parameters. The new script is attached (sorry, the code is not the cleanest one I ever wrote...)
The reconstructed distances are:
Reconstructed lengths [mm]:
LX = 6771
LY = 6734
LPRC = 6752
LX-LY = 37
LSX = 5493
LSY = 5456
LSRC = 5474
The angles of incidence of the beam on the mirrors are very close to those coming from the CAD drawing (within 0.15 degrees):
Reconstructed angles [deg]:
aoi PR3 = 41.11 (CAD 41)
aoi PR2 = 1.48 (CAD 1.5)
aoi SR3 = 43.90 (CAD 44)
aoi SR2 = 5.64 (CAD 5.5)
The errors in the measured distances w.r.t. the reconstructed one are all smaller than 1.5 mm. This seems a good check of the global consistency of the measurement and of the reconstruction method.
NOTES: in the reconstruction, the BS is assumed to be exactly at 45 degrees; wedges are not considered.
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
Today, I kicked the PRM to see the sideband splitting in POP110.
First, we can qualitatively see we moved in the right direction! (See ELOG 9490)
I fit the middle three peaks to a sum of two Lorentzian profiles ( I couldn't get Airy peaks to work... but maybe this is ok since I'm just going to use the location parameter?), and looked at the sideband splitting as a fraction of the FSR, in the same way as in Gabriele's ELOG linked above.
This gave: c / (4 * f55) * (dPhi / FSR) = 0.014 +- .001
Since the PRC length with simultaneous resonance (to 1mm) is given by c / (4 * f11) = 6.773, this means our length is either 6.759m or 6.787m (+- .001). Given the measurement in ELOG 9588, I assume that we are on the short side of the simultaneous resonance. Thus
The sideband splitting observed from this kick indicates a PRC length of 6.759m +- 1mm
[Rana, Jenne, Manasa]
We looked at the I vs. Q separation in several of the Refl PDs, while driving the PRM, while the PRMI was locked on sidebands.
For REFL 55, we adjusted the demod phase to try to minimize the peak in the Q signal, and were only able to get it to be about 1/10th the size of the I peak. This is not good, since it should be more like 1/100, at least.
For both REFL 11 and REFL 165, we were able to get the Q peaks to less than 1/100 of the I peak height.
We changed the REFL55 phase from 17 to 16, and the REFL165 phase from -160.5 to -162.5.
Since we believed that we had done a good job of setting the demod phase for REFL165, we used it to also check the balance of BS/PRM for MICH locking. I drove the BS with an arbitrary number (0.5), which creates a peak in the I phase of REFL165, and then I put in a drive on the PRM and tweaked it around until that peak was minimized. I came up with the same ratio as Koji had last Friday: BS=0.5, PRM=-0.2625. (The old ratio we were using, up until ~December when we started locking MICH with the ITMs, was BS=0.5, PRM=-0.267).
Also, while we were locked using REFL55 I&Q, we noticed that the other REFL PDs had lots of broadband noise in their I signals, as if some noise in the REFL55 diode is being injected into the PRM, that we are then seeing in the other PDs.
Some checks that we need to do:
* Inject a calibration line, set all the peak heights equal, and look at the noise floors of each PD.
* Use the calibration line to calibrate the PDs (especially REFL165) into meters, so that we know that it's noise is low enough to hold the PRC through the CARM offset reduction.
* Check out the state of the transmission QPDs - what is their noise, and is it good enough to use for holding the arms after we transition from green beatnote locking? Does the whitening switching do anything? What is the state of the whitening?
I calibrated the REFL signals to meters from counts. The I-phase signals all line up very nicely, but the Q-phase signals do not at all. I'm not sure what the deal is.
I locked the PRMI on sidebands, and drove the PRM. I looked at the peak values at the drive frequency in the REFL signals, and used that as my "COUNTS" value for each PD.
I know the PRM actuator calibration is 19.6e-9 (Hz/f)^2 m/ct , so if I plug in my drive frequency (564 Hz, with the notch in the PRC loop enabled), and multiply by my drive amplitude in counts, I know how many meters I am pushing the PRM. Then, to get a meters per count calibration, I divide this calibration number (common for every PD) by the peak value in each PD, to get each signal's calibration.
As a side note, I also drove MICH, and tried to use this technique for the Q-phase calibrations, but neither calibration (using the PRCL drive nor the MICH drive) made the Q-phase signals line up at all.
At least for the I-phase signals, it's clear that REFL33 has more noise than REFL11 or REFL165, and that REFL55 has even more noise than REFL33.
Here are the calibration values that I used:
We usually want to remove PRCL from the Q quadrature for each PD.
Therefore, you are not supposed to see any PRCL in Q assuming the tuning of the demod phases are perfect.
Of curse we are not perfect but close to this regime. Namely, the PRCL in Qs are JUNK.
In the condition where MICH is supressed by the servo, it is difficult to make all of the Qs line up because of the above PRCL junk.
But you shook MICH at a certain freq and the signal in each Q signal was calibrated such that the peak has the same height.
So the calibration should give you a correct sensing matrix.
If you tune the demod phases precisely and use less integrations for MICH, you might be able to see the residual MICH lines up on the Q plot.
Jenne and I noticed high pitch sound from our acoustic interferometer noise diagnostic system.
The frequency of this narrow band noise was 1256Hz, which is enough close to twice of the PRM violin mode freq.
After putting notch filter at 1256+/-25Hz at the violin filters, the noise is gone. Just in case I copied the same filters to all of the test masses.
Later, I found that the 4th violin modes are excited. Additional notch filters were added to "vio3" filter bank to mitigate the oscillation.
I was able to get the PRMI locked on REFL33 I&Q, but it wasn't overly stable, since there is so little separation between the MICH and PRCL signals in that PD.
We have already adjusted the phase to maximize PRCL in the I-phase. Since MICH is ~45 degrees separated from PRCL, there is some projection of MICH in the I-phase, and some in the Q-phase.
To remove this MICH component, I locked the PRMI on REFL55, and drove MICH. I looked at REFL33I at the CARM filter bank input (as just a dummy location to get a signal into DTT). I then added REFL33Q to the CARM row of the input matrix, to try to get the MICH line minimized. I then used these values for PRCL, and used just REFL33Q for MICH, and re-locked the PRMI. The PRMI was much more stable and happy.
The input matrix values that I used were:
MICH: REFL33Q = -0.487, Servo Gain = -20.0
PRCL: REFL33I = 1.556, REFL33Q = 1.8, Servo Gain = -0.020
Some locking notes:
The PRMI is very sensitive to alignment, and the PRM tends to drift away from optimal alignment on a ~1 hour timescale. When the PRM was not well aligned, it looked like MICH had a locking offset (manifested as non-equally sized blobs at AS). The MICH offset seemed to go away when we realigned the PRM.
[Koji, Jenne, EricQ, Manasa]
We had a short discussion this evening about what our game plan should be for transitioning from using the ALS system to IR-generated error signals.
The most fundamental piece is that we want to, instead of having a completely separate ALS locking system, integrate the ALS into the LSC. Some time ago, Koji did most of the structural changes to the LSC model (elog 9430), and exposed those changes on the LSC screen (elog 9449). Tonight, I have thrown together a new ALS screen, which should eventually replace our current ALS screen. My goal is to retain all the functionality of the old screen, but instead use the LSC-version of the error signals, so that it's smoother for our transition to IR. Here is a screenshot of my new screen:
You will notice that there are several white blocks in the center of the screen. From our discussion this evening, it sounds like we may want to add 4 more locking servo paths to the LSC (ALS for each individual arm, and then ALS for CARM and DARM signals). The reason these should be separate is that the ALS and the "regular" PDH signals have different noise characteristics, so we will want different servo shapes. I am proposing to add these 4 new servo blocks to the c1lsc model. If I don't hear an objection, I'll do this on Monday during the day, unless someone else beats me to it. The names for these filter modules should be C1:LSC-ALS_XARM, C1:LSC-ALS_YARM, C1:LSC-ALS_DARM and C1:LSC_ALS_CARM. This will add new rows to the input matrix, and new columns to the output matrix, so the LSC screen will need to be modified to reflect all of these changes. The new ALS screen should automatically work, although the icons for the input and output matrices will need to be updated.
The other major difference between this new paradigm and the old, is the place of the offset in the path. Formerly, we had auxiliary filter banks, and the summation was done by entering multiple values in the ALS input matrix. Now, since there is a filter bank in the c1lsc model for each of the ALS signals precisely where we want to add our offsets, and I don't expect us to need to put any filters into those filter modules, I have used the offset and TRAMP of those filter banks for the offsets. Also, you can access the offset value, and the ramp time, as well as the "clear history" button for the phase tracker, all from the main screen, which should help reduce the number of different screens we need to have open at once when locking with ALS. Anyhow, the actual point where the offset is added has not changed, just the way it happens has.
When we make the move to using the ALS in the LSC, we'll also need to make sure our "watch arm" and "scan arm" scripts are updated appropriately.
As an intermediary locking step, we want to try to use the ALS system to actuate in a CARM and DARM way, not XARM and YARM. We will transition from using each ALS signal to feed back to its own ETM, to having DARM feed back to the ETMs, and CARM feed back to MC2. We may want to break this into smaller steps, first lock the arms to the beatnotes, then find the IR resonance points. Transition to CARM and DARM feedback, but only using the ETMs. After we've done that, then we can switch to actuating on MC2. If we do this, then we'll be using the MC to reduce the CARM offset.
Once we can do this, and are able to reduce the CARM offset, we want to switch CARM over to a combination of the 1/sqrt(transmission) signals. The CARM loop has a tighter noise requirement, so we can do this, but leave DARM locked to the beatnotes for a while.
After continuing to reduce the CARM offset, we will switch CARM over to one of the RF PDs, for its final low-noise state.
We'll then do a quick swap of the DARM error signal to the AS port (maybe around the same time as CARM goes over to a PDH signal, before the CARM offset is zero?).
During all of this, we hope that the vertex has stayed locked. If our 3f sensing matrix elements are totally degenerate when the arms are out of resonance, then we may need to acquire lock using REFL 1f signals, and as we approach the delicate point in the CARM offset reduction, move to 3f signals, and then move back to 1f signals after the arm reflection has done its phase flip. Either way, we'll have to move from 3f to 1f for the final state.
I wanted to try common/differential ALS Friday evening. I tried ALS using the LSC servo but this was not successfull.
The usual ALS servo in the ALS model works without problem. So this might be coming from the shape of the servo filter.
The ALS one has 1:1000 filter but the LSC one has 10:3000. Or is there any problem in the signal transfer between
ALS and LSC???
Slow offset -0.302V
TRX=1.18 / TRY=1.14, XARM Servo gain = 0.25 / YARM Servo gain = 0.10
- Green Xarm:
GTRX without PSL green 0.562 / with PSL green 0.652 -> improved upto 0.78 by ASX and tweaking of PZTs
Beat note found at SLOW OFFSET +15525
Set the beat note as +SLOW OFFSET gives +BEAT FREQ
- Green Yarm:
GTRY without PSL green 0.717 / with PSL green 1.340
Beat note found at SLOW OFFSET -10415
Set the beat note as +SLOW OFFSET gives -BEAT FREQ
- BEAT X -10dBm on the RF email@example.comMHz / Phase tracker Qout = 2300 => Phase tracking loop gain 80 (Theoretical UGF = 2300/180*Pi*80 = 3.2kHz)
- BEAT Y -22dBm on the RF firstname.lastname@example.orgMHz / Phase tracker Qout = 400 => Phase tracking loop gain 300 (Theoretical UGF = 2.1kHz)
Transfer function between ALSX/Y and POX/Y11I @560Hz excitation of ETMX
POX11I/ALSX = 54.7dB (~0deg)
POY11I/ALSY = 64.5dB (~180deg)
ALSX[cnt]*19230[Hz/cnt] = POX11I[cnt]/10^(54.7/20)*19230[Hz/cnt]
= 35.4 [Hz/cnt] POX11I [cnt] (Hz in green frequency)
35.4 [Hz/cnt]/(2.99792458e8/532e-9 [Hz]) * 37.8 [m] = 2.37e-12 [m/cnt] => 4.2e11 [cnt/m] (c.f. Ayaka's number in ELOG #7738 6.7e11 cnt/m)
ALSY[cnt]*19230[Hz/cnt] = POY11I[cnt]/10^(64.5/20)*19230[Hz/cnt]
= 11.5 [Hz/cnt] POX11I [cnt] (Hz in green frequency)
11.5 [Hz/cnt]/(2.99792458e8/532e-9 [Hz]) * 37.8 [m] = 7.71e-13 [m/cnt] => 1.3e12 [cnt/m] (c.f. Ayaka's number in ELOG #7738 9.5e11 cnt/m)
Koji mentioned to me (and elogged) that he was unsuccessful locking the ALS using the LSC servos. He suggested I look into this.
So, rather than just looking at the transfer function between POX or POY and the green beatnotes at a single frequency, I did a whole transfer function. The point was to see if the TF is flat, and if we get any significant phase lag in the transfer from c1als to c1lsc. (c1als is running on the IOO machine, so an RFM connection is involved in getting it over to the LSC machine.)
In the first figure, I have plotted POX vs. Beatnote_PHASE_OUT (ALS error signal, still in the c1als model), and POX vs. ALSX_IN1 (the ALS error signal, after transfer over to the c1lsc model). You can see that we have a little phase lead in the blue transfer function, and fairly significant phase lag in the red (red is after transfer over to the lsc model). In the grand scheme of things, the magnitude is fairly flat, however that is not perfectly true - the peaks seen near 50 Hz and 300Hz are repeatable. The relative phase lag between the "BEATX" version of the signal in the ALS model, and the "ALSX" version of the signal in the LSC model is 15 degrees at 200 Hz, which corresponds to 33 usec.
The second figure is the same as the first, except for the Yarm. The relative phase lag between the ALS version of the error signal and the LSC version is 16 degrees at 200 Hz, which is about 35 usec.
As a side note, before trying any ALS locking, I took a spectrum of the beatnote (in the ALS model) while the arms were locked with IR:
To check things, I made sure that I could lock the Xarm ALS using the old ALS system - I was able to do so. (Has someone put the "watch" script as a constantly-on thing? It's kind of nice not to have to turn it on, although we'll need to change it to turn off the LSC versions of the servos eventually).
Then, I tried locking the Xarm using the LSC system (using only FM5 of the regular LSC-XARM filter bank). Like Koji, I was not able to acquire lock. As a next step, I copied all of the LSC-XARM filters into an empty filter module, LSC-XXXDC (the first one on the list underneath LSC-XARM), and copied over the ALS Xarm filters to the LSC Xarm filter bank. I then tried to acquire lock, but am unable to get it to stay. Using the ALS system, when you put in a small gain, the beatnote starts to settle down, and as you increase the gain, the beatnote stops moving (as seen on the spectrum analyzer) almost completely. However, using the LSC system, the beatnote never really stops moving or settles down. And if I increase the gain, I push the ETM hard enough that I lose green lock. I have put the regular LSC filters back for now.
Here is a plot from Foton comparing the FM5 filter modules from the LSC-XARM (regular IR locking) and the ALS-XARM servo. They are pretty different, and have 10 degrees of phase difference at 200 Hz, because 2 of the 3 poles are complex in the LSC version, while the ALS version is just a single real pole.
Anyhow, I am declaring it to be dinnertime, and I plan to return in a few hours. Since I put the regular LSC filters back (since I'm going to have to realign after dinner anyway), the IFO should be in its nominal state if anyone wants to come in and play with it.
Hmm. Wierd. Can you look at the TFs between ETMX-EXC and the error signals so that we can identify which one has these structures.
It looks like its somehow a discrepancy between the TFs of each error signal, because features are similar, and present, in both error signals.
I'm really excited, so I'm posting this, even though I'm still working:
I currently have ALS locked using the LSC system, and have (by hand, coarsely) found IR resonance! Hooray!
I looked at my error signals, as well as LSC-XARM_IN1 with dataviewer, and noticed that the XARM_IN1 signal was crazy when I was using the ALS signal as the error. I soon realized that this is because there was a non-zero element in the power normalization matrix, and I'm overriding the trigger. So, I was trying to divide by zero, and was getting crazy numbers. After zeroing the power normalization matrix element for the Xarm, the XARM_IN1 signal matched the ALSX_OUT, and I was easily able to acquire lock.
I had already re-transferred over the ALS versions of the filters, so that's what I'm using right now. Next up (on a 5 minute time-scale) is trying to acquire lock using the regular LSC filters.
Oh, also, something I hadn't thought of before dinner: I am setting the offset of the ALSX filter bank such that the output is centered around zero, so that I can lock, since these are not AC coupled servos.
Great. I indeed disabled all of the triggers and the normalization during my trial but in vain.
So I'm curious this is actually because of the filter shape or not.
I am also not able to lock the ALS using the 'regular' LSC filters. To figure out what filters were doing what, I made several comparison plots from Foton.
The first one is the progression of ALS locking, using the filters from ALS-XARM. FM5 is always engaged, then FMs 2, 3, 6, 7, and 8, and finally FM 10 (the low frequency boost) is engaged.
The next plot is a comparison between the ALS version of the filters, and the LSC-XARM equivalents.
Finally, just so I remember which LSC filters do what, I made an equivalent of the first plot, but for the LSC filters.
When I try to lock the Xarm ALS using the regular LSC filters, I'm getting an oscillation somewhere, that grows and eventually knocks me out of lock. It looks from dataviewer to be in the ~few Hz range, but it's hard to see it in DTT, since I don't stay locked all that long once the oscillation starts. (If I catch it, I can back off the gain and turn off the servo without losing lock, but if I don't turn off the servo, I inevitably push the ETM too hard and lose green lock to the arm.) I tried engaging the 3.2 Hz resonant gain filter, and it just makes things oscillate sooner, so that's not a solution with the current filter designs.
Also, I'm not able to lock the IR using the ALS version of the XARM filters. I'll have to meditate more on the situation, but the filters seem to be different enough that there's no crossover at this point.
No more progress tonight. I am still unable to lock the ALS using the regular LSC filters. I went back to putting the ALS filters into the LSC filter banks, and locked both arms with ALS, and found their IR resonances. I then held them off resonance, and tried to lock PRMI with REFL 55 I&Q, with no success. Just before locking the arms, I had redone the whole IFO alignment (lock arms in IR, ASS, lock and align MICH, lock and align PRMI), and the PRMI was flashing very nicely. I'm not sure why I wasn't able to catch lock, except that perhaps 3 or 6 ALS offset counts isn't far enough away from the IR resonance to make the 1f signals happy. The MC lost lock, which I then took as a sign that it's time to go home. (I was hoping to do a quick PRMI + 2arms, and see that we don't lose PRMI lock. I was going to catch lock with REFL55, then transition to REFL33, although if I had thought about it before the MC lost lock, I would have tried just catching lock with REFL33).
I restored the regular LSC filters for the X and Y arms, and locked the arms in IR just to make sure it's all honkey-dory. Which, it's not quite. I don't know why, but right now, neither arm wants its boost (FM9) enabled. It's part of the restore script that FM9 is triggered along with the rest of the filters, but even if I turn on the filters manually, I can turn on all but FM9, and then when I turn on the boost, the arm falls out of lock. Same behavior for both arms. Anyhow, they lock, and they seem okay modulo the boost not being able to engage.
As Koji measured the other day: MICH and PRCL seem very degenerate in the 3f REFL PDs.
I'm using this as a motivation to do some simulation in MIST and try to understand the best way to implement the 3F locking scheme. Hopefully my thinking below isn't nonsense...
First, I modeled the PRC with no arm cavities and the estimated cavity length I got with the PRM kick measurement, and looked at the REFL sensing matrix.
This agrees with the observed degeneracy. I then modeled the case of the PRC length that gives coincident SB resonance, again with no arm cavities.
Now there is good separation in REFL165. (REFL33 still looks pretty degenerate, however). This raised the question, "What does the angle between MICH and PRCL in REFL165 do as a function of macroscopic PRC length?"
To me, this implies that locking the PRC on 3F from scratch won't be simple. However, the whole point of the PRC length choice is to have coincident SB resonance when the arms are resonating.
So: even if we're not spot on, we should be relatively close to the PRC length where having arms resonant gives us simultaneously resonant upper and lower sidebands, where MICH and PRCL should be orthogonal-ish. I.e. building up a little bit of IR power in the arms may start to break the degeneracy, perhaps allowing us to switch from 1F to 3F locking, and then continue reducing the CARM offset.
So, I ultimately want to model the effect of arm power buildup on the angle between MICH and PRCL in the 3f PDs. This is what I'm currently working on.
So far, I have reproduced some of the RC modeling results on the wiki to make sure I model the arms correctly. (I get 37.7949 m as the ideal arm length for a modulation freq of 11.066134 MHz vs. 37.7974m for 11.065399 MHz as stated on the wiki). Next, I will confirm the desired PRC length that accounts for the arms, and then look at the MICH vs PRCL angle in the REFL PDs as a function of arm power or detuning.
We need to change several scripts for use with the new ALS-in-the-LSC paradigm:
* Watch arms (to turn off ALS if we lose the beatnote, before pushing optics too hard)
* Find IR resonance
* Offset from resonance
None of these should be difficult, just changing the filter bank names to match the new ones (ex. LSC-XARM rather than ALS-XARM, and LSC-ALSX rather than ALS-OFFSETTER1).
So far, I have changed the "find resonance" script (ALSfindIRresonance.py). I believe, in principle, to first order, that my modifications should work, however I have not yet tested the script. So. If you use it, watch the output of the script and ensure it's doing what it ought. I'll check it after the lunch meeting and update this log entry. (I changed the name of the "OFSFILT" variable, line 26, and also modified line 114. Both of those lines have comments on how to revert the changes).
I have also changed the "offset from resonance" script (ALSchangeOffset.py). Again, since I'm not locking right now, I have not tested this script either. So, pay attention if you need to use it, before I check it. (I changed the name of the OFSFILT variable, and the check which arm logic around line 37. Again, both of those lines have comments on how to revert the changes.)
Koji noted oddities in the sensing matrix results I had gotten; namely that the plots showed REFL33 not changing at all, when we know for a fact that this should not be the case.
Gabriele lent his eyes to my code, and came up with the idea that the modulation depths I was using were maybe not ideal (.1 for both 11 and 55). This affects REFL33 in that it is not simply Carrier * 33Mhz + 11Mhz * -22Mhz but also 22MHz * 55MHz, etc.
I got more realistic values from Jenne (0.19 for 11MHz and .26 for 55Mhz) and re-ran the code, with more realistic results. The behavior for 165 has remained the same, but the other signals are more well behaved.
Moral of the story: the modulation depths affect the 3f signals in a complicated way.
Locked on the sideband, the MICH / PRCL angle is much less sensitive to the PRC length, and shouldn't in fact be as degenerate as we've seen in reality.
So, my simulations no longer provide any reason for the 3F signals to be so degenerate.
Watch arms script (ALSdown.py) has been modified and now watches the LSC-$ARM filter module instead of the ALS-$ARM filter module. Threshold has been kept the same +/-5000 counts to the ETM suspensions. The script has been tested and works just fine. It exists in the same place scripts/ALS/.
Jenne's modified versions of ALSfindResonance.py and ALSchangeOffset.py were tested and work just fine.
[Jenne, Koji, Manasa, EricQ]
Today we successfully locked the ALS using the LSC system, with filters that are good for both the IR PDH and the ALS locking. We tried PRFPMI, but were unable to hold PRMI lock while the arms were held with ALS. We combined the ALS signals into common and differential signals, and successfully transitioned over to a combined set of 1/sqrt(TRANS) signals for the common mode part of the lock (differential stayed with ALS).
Locking the ALS using filters in the LSC system that are also good for IR PDH
The biggest difference between the ALS and LSC filters were the ones used for lock aquisition. At Koji's suggestion, I made FM5 of the LSC servos (for X and Y arms) the filter needed for ALS locking. Then, I made FM4 into a combination of old LSC FM4 and FM5, as well as an inverse of the new FM5, so that when both FM4 and FM5 are engaged, the servo shape is the same as the old LSC. I left the other LSC filters where they were. I replaced the FM1 +6dB with the combined integrators (really, just gentle DC boosts) for the ALS, since we were never using this +6dB filter module. The LSC resonant gain filter for the bounce mode also included a resgain for 18.5 Hz. I don't know what that was for, and it was eating into phase that I needed, so I removed it.
The other filter that changed significantly was the Boost filter. The ALS system had been using more DC gain than the LSC had. However, the current ALS boost filter (in FM10 of the old ALS servos) was eating too much phase near my UGF. So, I scooted the whole boost filter to lower frequencies, to give myself some extra phase margin. The boost was set to "zero history", "zero crossing", with 0.01 tolerance and an 8 second timeout. Setting it to zero crossing with a low tolerance, rather than just ramping it on, was the key to engaging the boost.
I had to be so careful about phase margin, since I lost ~15 degrees of phase at 200 Hz from the lag of going through the RFM network. This was pretty frustrating, but I don't have a better plan yet, save moving the c1als model and ADC to the SUS machine, which has Dolphin access to the LSC. I may back off my safety margin, and give myself some gain in the boost back at 10Hz, since we are now seeing too much noise at 10Hz in the closed-loop spectra. I also "cheated" and lowered my UGF from the ~150Hz it used to be in the ALS model, to 100Hz, where I was closer to the top of the new phase bubble.
With the new filter situation, I was able to lock the Xarm (the one I was using for design work) with both IR and ALS. To lock IR, the "restore" script still works. For the ALS, we should put in a separate "restore" script into the IFO_CONFIGURE screen.
The ALS locking procedure is as follows:
* Prepare ALS and green locking. Green locked to 00 mode, alignment all nice, etc, etc. Beatnote within 100MHz on spectrum analyzer. If doing both arms, try to get beatnotes on opposite sides of PSL, to keep crossbeatnotes at higher frequencies, and out of the way.
* Turn on Watch script.
* Set LSC parameters (this is where a new restore script will come in handy):
* Zeros in RFPD columns of input matrix (i.e. POX and POY).
* Ones in AUX input matrix elements.
* Zeros in power normalization matrix rows for arms.
* All FM triggers for arms set to "Man" for manual.
* Override main trigger, so that signals are always going through to the servo.
* Only FM5 engaged in arm servo.
* Gain of servo set to zero, output on, then engage main LSC master switch. ETM output on.
* Clear history in phase tracker.
* Check sign of gain using + or - 0.1 in the servo. You'll know if you got it wrong (the ETM will be kicked, and the beatnote will fly around). If you didn't get it wrong, you probably got it right.
* Increase gain to about 12 (with correct sign).
* Engage FM1 (gentle DC boost), FM6,7,8 (resonant gains for stack, bounce, roll)
* Wait a few seconds for filters to settle, then engage FM9 (boost).
* Run find IR resonance script.
* Move off resonance by ~36 counts (12 times the +3 script). This number comes from trying to be completely off the IR resonance, even when the PRMI was locked.
* Do whatever locking (ex. PRMI) you set out to do.
After locking both arms with ALS using the LSC system, we attempted to lock the PRMI. We were able to lock PRMI on REFL55 I&Q, REFL33 I&Q, and REFL55 I&AS55Q before the arms were locked, so we were hoping that we wouldn't have too much trouble.
We found the IR resonance for both arms, then moved off resonance. Then, restored the PRM. For REFL55, Koji coarsely turned the REFL 55 demod phase from 16 degrees to 87, while we were locked on the carrier. After this, I stepped farther and farther from the IR resonance, since at first I found that our transmitted powers were something like 4, rather than almost zero, so the demod phase may not be totally correct.
We were having trouble, so we locked the PRMI on carrier using REFL55 I and AS55 Q, with 1's in both elements in the input matrix. MICH gain was about -10, PRCL +0.010. We used this time to tweak up the alignment of the PRMI. At some point, Koji tweaked the REFL33 demod phase from 124 to 134 degrees. Then we switched back to sideband locking. After some trials with REFL55 I&Q, and REFL55/AS55, we went to REFL33 I&Q. REFL33I->PRCL was 1.556 in the input matrix, and REFL33Q->MICH was -0.487. No other elements in the input matrix. MICH gain was reduced to -6, PRCL gain to -0.020. MICH FMs 3,6,9 triggered, PRCL FMs 2,3,6,8,9 triggered. We were able to keep short locks on the order of ~10 seconds, but not longer. We played with every parameter we could think of (alignment being good is one of the most important!), but were not able to keep better lock. The POP spot is moving around a lot, so the PRCL ASC needs to be examined, hopefully tomorrow.
We started losing the Xarm lock fairly regularly, I'm not sure why, but the Yarm was locked for almost 2 hours straight, held off resonance with ALS!
ALS Common and Differential, transition to IR control
We set PRMI aside for the rest of the night, and looked at using ALS to control the arms in common and differential modes.
Regular ALS locking procedures were used (see above), with the exception of the AUX input matrix:
Since the beatnotes were on opposite sides of the PSL frequency, the common and differential modes look opposite of what you'd expect.
We then used the regular find IR resonance scripts running simultaneously, which worked really well to find both arms' IR resonance points.
I put a 1 count offset in the Xarm servo (which was our proxy for common mode), although in retrospect this should have been +0.5 in ALSX, and -0.5 in ALSY, so that our signals going through the input matrix were at their zero crossings. Anyhow, this offset put us at about half fringe on both arms (transmissions were about 0.6).
Koji set the offsets in the 1/sqrt(trans) filter banks before the input matrix so that they would have zero crossings at this point (avg the IN1, put negative of that value into the offset).
We then stepped the input matrix values until our common mode (Xarm) row was:
We left the differential (YARM) row alone, so that the ALS system would still be controlling the differential degree of freedom. The values and sign for the 1/sqrt(trans) signals came from a transfer function of dividing the spectra of each error signal and noting the relative gain and sign.
After we swapped the error signals, we realized that we had to remove the offset from the XARM servo, which is why we should have put the offsets elsewhere in the first place.
Then, Koji took a spectrum, which is attached to this entry. We note that the ALS signals are strongly correlated, and mostly common.
To Do List
Going forward, we need to figure out what is going on with the PRMI, and why we're having trouble keeping lock.
We need to redo the PRCL ASC servo, with the anti-oplev trick that Rana mentioned a week or two ago.
We need to investigate the degeneracy of REFL165, now that Q's simulation doesn't justify / explain it.
EQ UPDATE: Measured it wrong the first time, fixed now.
I measured the spectra of the SQRTINV channels from dark QPDs, with offsets adjusted to imitate various transmission levels. (While the dark noise stays constant in terms of, say, TRX counts, 1/sqrt(TRX) isn't linear, and so the noise coupling depends on the TRX offset).
I did some calculations to turn this into the equivalent displacement noise when using SQRTINV as an error signal. This depends on where on the fringe you are locking, since the slope of SQRTINV vs. position is not constant, and can only really be treated as linear down to about 1/3 of a line width away from full resonance. In my calculations, I assumed a coupled arm line width of 38pm, and a full transmission of 700 counts in TRX/Y.
The QPD dark noise RMS when two line widths away (TR = 40) is about 5fm, and only goes down from there.