Yes, \eta_A is the (average) round-trip loss for an arm cavity. I'd estimate this is ~100ppm currently. I edited the original elog to fill in this omission.

The RC mirror specs require some guesswork - the available specs for the Laseroptik mirrors (PR3) are for a 48 degree angle of incidence, and could be as high as 0.5 %. According to the poster, the spec is 2.6% loss inside the recycling cavity but I don't know where I got the number for the AR surface of the G&H PR2, and presumably that includes some guess I made for the MM between the PRC and the arm. Previously, assuming ~1-2% loss inside the RC gave good agreement between model and measurement. Certainly, if we assume similar numbers, a recycling gain of ~11 (200 * T_P=5.637%) is reasonable. But I think we need more data to make a stronger statement.

Koji pointed out during the group meeting that I should compensate for local tilt when I move the beam around the mirror for calculating the loss map.

So I did.

Also, I made a mistake earlier by calculating the loss map for a much bigger (X7) area than what I thought.

Both these mistakes made it seem like the loss is very inhomogeneous across the mirror.

Attachment 1 and 2 show the corrected loss maps for ITMX and ETMX respectively.

The loss now seems much more reasonable and homogeneous and the average total arm loss sums up to ~ 22ppm which is consistent with the after-cleaning arm loss measurements.

Summary:

I think the boosts that are currently stuffed on the CM board are too aggressive to be usable for locking the interferometer. I propose some changes.

Details:

[CM board schematic]

[CM board transfer function measurement]

[Measurement of the AO path TF]. Empirically, I have observed that the CARM OLTF has ~90 degrees phase margin available at the UGF when no boosts are engaged, which is consistent with Koji's measurement. Assuming we want at least 30 degrees phase margin in the final configuration, and assuming a UGF to be ~10 kHz, the current boosts eat up way too much phase at 10 kHz. Attachment #1 shows the current TFs (dashed lines), as the boosts are serially engaged. I have subtracted the 180 degrees coming from the inverting input stage. The horizontal dash-dot line on the lower plot is meant to indicate the frequency at which the boost stages eat up 60 degrees of phase, which tells us if we can meet the 30 degree PM requirement.

In solid lines on Attachment #1, I have plotted the analogous TFs, with the following changes:

• R52, R54: 1.21k --> 3.16k (changes 4 kHz zero to 1.5 kHz).
• R61, R62: 82.5 --> 165 (changes 20 kHz zero to 10 kHz).
• R63: 165 --> 300 (changes 10 kHz zero to 5 kHz).

These changes will allow possibly two super boosts to be engaged if we can bump up the CARM UGF to ~15 kHz. We sacrifice some DC gain - I have not yet done the noise analysis of the full CARM loop, but it may be that we don't need 120 dB gain at DC to be sensing noise limited. I suppose the pole frequencies can also be halved if we want to keep the same low frequency gain. In any case, in the current form, we can't access all that gain anyways because we can't enable the boosts without the loop going unstable.

The input referred noise gets worse by a factor of 2 as a result of these changes, but the IN1 gain stage noise is maybe already higher? If this sounds like a reasonable plan, I'll implement it the next time I'm in the lab.

This is to facilitate the summary page config fines to be pulled from nodus in a scripted way, without being asked for authentication. If someone knows of a better/more secure way for this to be done, please let me know. The site summary pages seem to pull the config files from a git repo, maybe that's better?

I finished calculating the X Arm loss using first-order perturbation theory. I will post the details of the calculation later.

I calculated loss maps of ITM and ETM (attachments 1,2 respectively). It's a little different than previous calculation because now both mirrors are considered and total cavity loss is calculated. The map is calculated by fixing one mirror and shifting the other one around.

The losin total is pretty much the same as calculated before using a different method. At the center of the mirror, the loss is 21.8ppm which is very close to the value that was calculated. 

Next thing is to try SIS.

Perturbation theory:

The cavity modes  , where q is the complex beam parameter and m,n is the mode index, are the eigenmodes of the cavity propagator. That is:

,

where is the mirror reflection matrix. At the 40m, ITM is flat, so . ETM is curved, so , where R is the ETM's radius of curvature.

is the Gouy phase.

is the free-space field propagator. When acting on a state it propagates the field a distance L.

The phase maps perturb the reflection matrices slightly so:

,

Where h_12 are the height profiles of the ITM and ETM respectively. The new propagator is

, where is the unperturbed propagator and

To find the perturbed ground state mode we use first-order perturbation theory. The new ground state is then

Where N is the normalization factor. The (0,1) and (1,0) modes are omitted because they can be zeroed by tilting the mirrors. Gouy phase of TEM00 mode is taken to be 0.

Some simplification can be made here:

The last step is possible since the beam parameter q matches the cavity.

The loss of the TEM00 mode is then:

Hang and I have reanalyzed the BHD telescope designs, with the goal of identifying sufficiently non-degenerate locations for ASC actuation. Given the limited room to reposition optics and the requirement to remain insensitive to small positioning errors, we conclude it is not possible put sufficient Gouy phase separation between the AS1/AS2 and LO1/LO2 locations. However, we can make the current layout work if we instead actuate AS1/AS4 and LO1/LO4. This would require actuating one optic on the breadboard for each relay path. If possible, we believe this offers the simplest solution (i.e., least modification to the current layout).

LO Telescope Design (Attachment 1)

Radius of curvatures:

• LO1: +10 m
• LO2: flat
• LO3: +15 m
• LO4: flat

AS Telescope Design (Attachment 2)

Radius of curvatures:

• AS1: +3 m
• AS2: flat
• AS3: -1 m
• AS4: flat

This EQ in Nevada seems to have tripped all watchdogs. ITMX was stuck. It was released, and all the watchdogs were restored. Now the IMC is locked.

[Jon, Tega, Hang]

We proposed a few BHD mode-matching telescope designs and then preformed a few monte-carlo experiments to see how the imperfections would change the story. We assumed a 2 mm (1-sigma) error on the location of the components and 1% (1-sigma) fractional error on the RoC of the curved mirrors. The angle of incidence has not yet been taken into account (no astigmatism at the moment but will be included in the follow-up study.)

For the LO path things are mostly fine. We can use LO1 and LO2 as the actuators (Sec. 2.2 of the note), and when errors are taken into account more than 90% of times we can still achieve 98% mode matching. The gouy phase separation between LO1 and LO2 > 34 deg for 90% of the time, which corresponds to a condition number of the sensing matrix of ~ 3. 

The situation is more tricky for the AS path. While the telescopes are usually robust against 2 or 3 mm of positional error, the 1% RoC does affect the performance quite significantly. In the note we choose two best-performing ones but still only 50% of the time they can maintain a power-overlap of > 99%. In fact, the 1% RoC error assumed should be quite optimistic... Not sure if we could achieve this in reality. 

One potential way out is to ignore the MM for the first round of BHD. Here anyway we only need to test the ISC schemes. Then in the second round when we have the whole BHD board suspended, we can then use AS1 and the BHD board as the actuators. This might be able to make things more forgiving if we don't need to shrink the AS beam very fast so that it could be separated from AS4 in gouy phase.

It would be good to have a corner plot with all the distances/ RoCs. Also perhaps a Jacobian like done in this breathtaking and seminal work.

I have a serious concern about this low angle scattering analysis:

Phase maps perturb the spatial mode of the steady-state of the cavity, but how is this different than mode-mismatch? The loss that I calculated is an overall loss, not roundtrip loss.

The only way I can think this can become serious loss is when the HOMs themselves have very high roundtrip loss. Attached is the modal power fraction that I calculated.

As Rana suggested, we present the scattering plot of the AS path mode matching for various variables. The plot is for the AS path, Plan 2 (whose params we summarize at the end of this entry).

In the corner plot, we color-coded each realization according to the mode matching. We use (purple, olive, grey) for (MM>0.99, 0.98<MM<=0.99, MM<=0.98), respectively. From the plot, we can see that it is most sensitive to the RoC of AS1. The plot also shows that we can compensate for some of the MM errors if we adjust the distance between AS1-AS3 (note that AS2 is a flat mirror). The telescope is quite robust to other errors.

The compensation requirement is further shown in the second plot. To correct for the 1% RoC error of AS1, we typically need to adjust AS1-AS3 distance by ~ 1 cm (if we want to go back to MM=1; the window for >0.99 MM spans also about 1 cm). This should be doable because the nominal distance between AS1-AS3 is 115 cm. 

The story for plan1 is similar and thus not shown here. 

==============================================================

AS path plan2 nominal params:

label     z (m)     type             parameters  
-----     -----     ----             ----------  
SRMAR          0    flat mirror      none:     
AS1       0.7192    curved mirror    ROC: 2.5000 
AS2       1.2597    flat mirror      none:     
AS3       1.8658    curved mirror    ROC: -0.5000
AS4       2.5822    curved mirror    ROC: 0.6000  
OMCBS1    3.3271    flat mirror      none:   

Two ITM spares (ITMU01/ITMU02) and five new PR3 mirrors (E1800089 Rev 7-1~Rev7-5) were transported to Downs for phasemap measurement

We noticed about a week ago that the NDS2 channel lists were not getting updated on megatron. JZ and I investigated; he was able to fix it all up this afternoon by logging in and snooping around Megatron.

Please try it out and tell me about any problems in getting fresh data.

1. The NDS2 server is what we connect to through our python NDS2 client software to download some data.
2. It has been working for years, but it looks like there was a file corruption of the channel lists that it makes back in 2017.
3. Since the NDS2 server code tries to make incremental changes, it was failing to make a new channel list. Was failing to parse the corrupted file.
4. there was a controls crontab entry to restart the server every morning, but the file name in that tab had a typo, so that wasn't working. I commented it out, since it shouldn't be necessary (lets see how it goes...)
5. the nds2mgr account also has a crontab, but that was failing since it didn't have sudo permission. JZ added nds2mgr to the sudoers list so that should work now.
6. I was able to get new channels as of 4 PM today, so it seems to be working.

* we should remember to rebuild the NDS2 server code for Ubuntu. The thing running on there is for CentOS / SL7, but we moved to Ubuntu recently since the SL7 support is going away.

** the nds2 code & conf files are not backed up anywhere since its not on /cvs/cds. It has 52 GB(!!) of txt channel lists & archives which we don't need to backup

The service had failed at 16:09 yesterday. I just restarted it and am now able to fetch data again. 

Unrelated to this work: I restarted the httpd service on nodus a couple of times this afternoon while experimenting with the summary pages.

To test a hypothesis, I have left the PSL shutter closed. I notice significant glitches in the dark electronics offsets on all the 11 MHz photodiode I/Q demodulated input channels, which appear coherent. These are non-negligible in magnitude - for now they are uncalibrated in cts, but for an estimate, the POX11 channel shows a shift of ~20 cts (~200uV at the input to the whitening board), while the PDH fringe is ~200 cts pk2pk. A first look is in Attachment #1. The fact that it's in all the 11 MHz channels makes me suspect something in the RF chain, maybe some amplifier? I'll open the shutter tomorrow.

I was in the lab for Clean and Bake activities and I replaced an empty N2 tank. Left tank is at 2600 psi right tank at ~1300 psi.

was dead again this morning - JZ notified

current restart instructions (after ssh to megatron):

cd /home/nds2mgr/nds2-megatron

sudo su nds2mgr

make -f test_restart

so far it has run through the weekend with no problems (except that there are huge log files as usual).

I have started to set up monit to run on megatron to watch this process. In principle this would send us alerts when things break and also give a web interface to watch monit. I'm not sure how to do web port forwarding between megatron and nodus, so for now its just on the terminal. e.g.:

monit>sudo monit status
Monit 5.25.1 uptime: 4m

System 'megatron'
  status                       OK
  monitoring status            Monitored
  monitoring mode              active
  on reboot                    start
  load average                 [0.15] [0.22] [0.25]
  cpu                          0.6%us 1.0%sy 0.2%wa
  memory usage                 1001.4 MB [25.0%]
  swap usage                   107.2 MB [1.9%]
  uptime                       40d 17h 55m
  boot time                    Tue, 14 Apr 2020 17:47:49
  data collected               Mon, 25 May 2020 11:43:03

Process 'nds2'
  status                       OK
  monitoring status            Monitored
  monitoring mode              active
  on reboot                    start
  pid                          25007
  parent pid                   1
  uid                          4666
  effective uid                4666
  gid                          4666
  uptime                       3d 1h 22m
  threads                      53
  children                     0
  cpu                          0.0%
  cpu total                    0.0%
  memory                       19.4% [776.1 MB]
  memory total                 19.4% [776.1 MB]
  security attribute           unconfined
  disk read                    0 B/s [2.3 GB total]
  disk write                   0 B/s [17.9 MB total]
  data collected               Mon, 25 May 2020 11:43:03

A big factor in how much IFO locking activities can take place is how cooperative the IMC is.

Since the c1psl upgrade, the IMC duty cycle has definitely deteriorated. I took a measurement of the dark noise at the IMC error point with 1 Hz FFT binwidth, with all electrical connections to the IMC servo board except the Acromag and Eurocrate power disconnected. I was horrified at the prominence of 60 Hz harmonics - see Attachment #1. In the past, this kind of feature has been indicative of some error in the measurement technique - but I confirmed that the lines remain even if I unplug the GPIB box, and all combinations of floating/grounded inputs that I tried. We know for sure that there is some excess noise imprinted on the laser light post upgrade. While these lines almost certainly are not responsible for the PCdrive RMS going bonkers, surely this kind of electrical situation isn't good?

Attachment #2 shows the same information translated to frequency noise units, taking into account the complementary sensitivity function, L/(1+L) - the sum contribution of the 60 Hz peaks to the RMS is ~11.5% of the total over the entire band (c.f. 1.7 % that is expected if the noise at multiples of 60 Hz was approximately equal to the surrounding noise levels). Moreover, the measured RMS is 55 times higher than a LISO model. 

How can this be fixed?

Summary:

Provided the IMC is cooperative, the input pointing isn't drifting, and the RF offsets aren't jumping around too much, the locking sequence is now pretty robust.

Details:

• Lock acquisition sequence [ELOG 15349]
• DARM loop measurement and fitting [ELOG 15350]
• CARM loop measurement and fitting [ELOG 15351]
• Sensing matrix measurement [ELOG 15352]
• Preliminary noise budget [ELOG 15353]
• ASC and arm RIN stabilization [ELOG 15355]
• Buildup of DC and SB fields [ELOG 15356]

Most of the analysis uses data between the GPS times 1274418176 and 1274419654 that are recorded to frames.

Here, I provide some details of the sequence. Obviously, I am presenting one of the quickest transitions to the fully locked state, I don't claim that every attempt is so smooth. But it is pretty cool that the whole thing can be done in ~3 minutes.

See Attachment #1 for the labels.

• A --- Arms are locked on POX/POY, and EX/EY lasers are also locked to their respective arms. The phase tracker outputs are averaged in preparation for transitioning control from POX/POY to ALS. 
• B --- Aforementioned transition has been realized. CARM offset of -4 is applied. Based on this calibration, this is ~ 4 nm.
• C --- PRM is aligned in preparation for 3f vertex locking. Between C and D, the long pause is because I also use this time to DC couple the ITM Oplev servos, which requires some averaging. 
• D --- PRMI is locked. CARM offset reduction begins. Between D and E, I scan CARM through a resonance, and look at the necessary offset requried in the CARM_B (=RF) path. It is a mystery to me why this is required.
• E --- Ramp CARM offset completely to 0. Twiddle CARM_A and DARM_A offsets (=ALS path) to maximize the arm transmitted powers. Between E and F, you can see that the arm powers stabilize somewhat before any RF control is engaged (more on this later), which means we are approximately in the linear regime of the CARM PDH signal, and the switchover can be effected. As I write this, I wonder if there is any benefit to normalizing the REFL_11 error signal (=CM_SLOW) by the arm transmission for a broader capture range?
• F --- CARM_B and DARM_B (=RF) paths engaged. I ramp off the ALS servos between F and G using a 10 second ramptime.
• G --- IFO is now under RF control, ALS control has been turned off completely.
• H --- Rudimentary ASC is enabled. The ITMs are already running with DC coupled Oplev servos, and for the ETMs, I use the Transmon QPDs. The loop shapes/gains for this part haven't been finalized yet, but some improvement in the stability is seen.

This particular lock held for ~20 minutes so I could run some loop characterization measurements etc.

I am struggling to explain:

1. Why POP22 goes to 0 when we zero the CARM offset? The arm length is such that the 2f fields don't experience any abrupt changes in reflectivity from the arm cavity for a wide range of offsets. This signal is the trigger signal for the PRMI LSC control - right now, I get around this problem by mixing in some amount of POP DC once the PRMI is locked. But if the lock is lost, this requires some EPICS button gynmastics to try and salvage the lock... I guess the 1f field components experience a different phase on reflection at various offsets, so maybe I should be looking at sqrt(POP22_I^2 + POP22_Q^2) instead of just POP22_I.
2. Why is an error point offset required in the CARM RF path?

Summary:

In order to estimate the free-running DARM displacement noise, I measured the DARM OLTF using the usual IN1/IN2 prescription. The measured data was then used to fit some model paramters for a loop model that can be used over a larger frequency range.

Details:

• Attachment #1 shows an overlay of the measured and modelled TFs.
• Attachment #2 shows the various components that went into building up this model. 
  • The digital AA and AI filter coefficients were taken from the RTCDS code.
  • The analog AA and AI filter zpks were taken from here and here respectively.
  • CDS filters taken from the banks enabled. The 20Hz : 0Hz z:p filter in the CARM_B path is also accounted for, as have the violin-mode notches.
  • Pendulum TF is just 1/f^2, the overall scaling is unimportant because it will be fitted (in combination with the overall scaling uncertainty on the DC optical gain), but I used a value of 10 nm/f^2 which should be in the right ballbark.
  • The optical gain includes the DARM pole at ~4.5 kHz for this config.
• With all these components, to make the measurement and fit line up, I added two free parameters - an overall gain, and a delay. 
  • NLSQ minimizer was used to find the best-fit values for these parameters.
  • I'm not sure what to make of the relatively large disagreement between measurement and model below 100 Hz - I'm pretty sure I got all the CDS filters included...
  • Moreover, I don't have a good explanation for why the best-fit delay is 400 us. One RTCDS clock cycle is onyl 60 us, and even with an extra clock cycle for the RFM transfer, I still can't get up to such a high delay...

In summary, the UGF is ~150 Hz and phase margin is ~30 deg. This loop would probably benefit from some low-pass filter being turned on.

Summary:

I am able to realize ~8 kHz UGF with ~60 degrees of phase margin on the CARM loop OLTF (combination of analog and digital signal paths).

Details:

• Attachment #1 shows the measured OLTF.
• The measurement is made by using the "EXC A" bank on the CM board, with an SR785. With this technique, the measurement will be poor where the loop gain is high, as the excitation will be squished. Nevertheless, we can estimate the behavior in those regimes by using a model, and fitting it to the regions where the measurement is valid (in this case, above ~1 kHz).
• This measurement was made with IN1 Gain = +4 dB, AO gain = 0 dB, and IMC IN2 gain = 0 dB.
• The regular boost has been enabled, but no super-boosts yet, mainly because I think they consume too much phase close to the UGF. 
• The modeling/fitting of this, including a more thorough characterization of the crossover, will follow...

Summary:

The response of the PRFPMI length degrees of freedom as measured in the LSC PDs was characterized. Two visualizations are in Attachment #1 and Attachment #2.

Details:

• The sensing matrix infrastructure in the c1cal model was used.
• The oscillator frequencies are set between 300 - 315 Hz.
• Notch filters at these frequencies were enabled in the CDS filter banks, to prevent actuation at these frequencies (except for CARM, in which case the loop gain is still non-negligible at ~300 Hz, this correction has not yet been applied).
• Mainly, I wanted to know what the DARM sensing response in AS55_Q is. 
  • The measurement yields 2.3e13 cts/m. This is a number that will be used in the noise budget to convert the measured DARM spectrum to units of m/rtHz.
  • We have to multiply this by 10/2^15 V/ct, undo the 6dB whitening gain on the AS55_Q channel, and undo the ~5x gain from V_RF to V_IF (see Attachment #4 of this), to get ~0.69 GV/m from the RFPD.
  • The RF transimpedance of AS55_Q is ~550 ohms, and accounting for the InGaAs responsivity, I get an optical gain of 1.8 MW/m. Need to check how this lines up with expectations from the light levels, but seems reasonable.
  • Note that T_SRM is 10%, we dump 70% of the output field into the unused OMC, and there is a 50/50 BS splitting the light between AS55 and AS110 PDs. Assuming 90% throughput from the rest of the chain, we are only sensing ~1.3 % of the output DARM field.
• Apart from this, I can also infer what the matrix elements / gains need to be for transitioning the PRMI control from 3f to 1f signals. To be done...
• I found these histograms in Attachment #2 to be a cute way of (i) visualizing the variance in the magnitude of the sensing element and (ii) visualizing the separation between the quadratures, which tells us if the (digital) demod phase needs to be modified.
  • The sensing lines were on for 5 minutes (=300 seconds) and the FFT segment length is 5 seconds, so these histograms are binning the 60 different values obtained for the value of the sensing element.
  • The black dashed lines are "kernel density estimates" of the underlying PDFs
  • I haven't done any rigorous statistical analysis on the appropriateness of using this technique for error estimation, so for now, they are just lines...

Summary:

This isn't meant to be a serious budget, mainly it was to force myself to write the code for generating this more easily in the future.

Details:

• DARM OLTF model from here was used to undo the loop to convert the in-loop measurement to a free-running estimate.
• The AS55 PD channels were whitened to reduce the effect of ADC noise.
• To measured channel was 'C1:LSC-DARM_IN1_DQ'.
  • Some care needs to be taken when applying the conversion from counts to meters using the sensing element measured here.
  • This is because the sensing matrix measurement was made using the response in the channel 'C1:LSC-AS55_Q_ERR_DQ'.
  • Between 'C1:LSC-DARM_IN1_DQ' and 'C1:LSC-AS55_Q_ERR_DQ' there is a scalar gain of 1e-4, and a z:p = 20:0 filter.
  • These have to be corrected for when undoing the loop, since the measurement point is 'C1:LSC-DARM_IN1_DQ'. 
• The "Dark noise" trace was measured with the PSL shutter closed, but all CDS filters up to 'C1:LSC-DARM_IN1_DQ' enabled as they were when the DARM measurement was taken.
• It would be interesting to see what the budget looks like once the DARM loop gain has been turned down a bit, some low-pass filtering is enabled, and the vertex DoFs are transitioned to 1f control which is hopefully lower noise.

Replaced empty N2 tank, left tank at ~2000 psi, right tank ~2600 psi.

Summary:

The measured RIN of the arm cavity transmission when the PRFPMI is locked is ~10x in RMS relative to the single arm POX/POY lock. It is not yet clear to me where the excess is coming from.

Details:

Attachment #1 shows the comparison.

• For the PRFPMI lock, the ITM Oplev Servos are DC coupled, and the ETM QPD ASC servos are also enabled.
• Admittedly, the PD used in the POX/POY lock case is the Thorlabs PD while when the PRFPMI is locked, it is the QPD.
• I found that there isn't really a big difference in the RIN if we normalize by the IMC transmission or not (this is what the "un-normalized" in the plot legend is referring to).  A scatter plot of TRX vs TRY and TRX/MCtrans vs TRY/MCtrans have nearly identical principal components. 
• To convert to RIN, I divided the ocmputed spectra by the mean value of the data stream. For the POX/POY lock, the arm transmission is normalized to 1, so no further manipulation is required.
• The spectra are truncated to 512 Hz because the IMC sum channel is DQ-ed at 1 kHz, but because of the above bullet point, in principle, I could calculate this out to higher frequencies.

Summary:

I looked at some DC signals for the buildup of the carrier and sideband fields in various places. The results are shown in Attachments #1 and #2.

Details:

• A previous study may be found here.
• For the carrier field, REFL, POP and TRX/TRY all show the expected behavior. In particular, the REFL/TRX variation is consistent with the study linked in the previous bullet.
• There seems to be some offset between TRX and TRY - I don't yet know if this is real or just some PD gain imbalance issue.
• The 1-sigma variation in TRX/TRY seen here is consistent with the RMS RIN of 0.1 evaluated here.
• For the sideband powers, I guess the phasing of the POP22 and AS110 photodiodes should be adjusted? These are proxies for the buildup of the 11 MHz and 55 MHz sidebands in the vertex region, and so shouldn't depend on the arm offset, and so adjusting the digital demod phases shouldn't affect the LSC triggering for the PRMI locking, I think.
• Based on this data, the recycling gain for the carrier is ~12 +/- 2, so still undercoupled. In fact, at some points, I saw the transmitted power exceed 300, which would be a recycling gain of ~17, which is then nearly the point of critical coupling. REFLDC doesn't hit 0 because of the mode mismatch I guess.

Please see the attached doc. 

I think the conclusion is that if the AS1 RoC error is not significantly more than 1%, then with some adjustment of the AS1-AS3 distance (~ 1 cm), we could find a solution that simultaneously makes the AS path mode-matching better than 99% for the t- and s-planes. 

The requirement of the LO path is less strict and the current plan using LO1-LO2 actuation should work. 

This is very interesting. Do you have the ASDC vs PRG (~ TRXor TRY) plot? That gives you insight on what is the cause of the low recycling gain.

My speculation for the worse RIN is:

- Unoptimized alignment -> Larger linear coupling of the RIN with the misalignment
- PRC TT misalignment (~3Hz)

Don't can you check the correlation between the POP QPD and the arm RIN?

I see. At the 40m, we have the direct transition from ALS to RF. But it's hard to compare them as the storage time is very different.

I agree, I think the PRC excess angular motion, PIT in particular, is a dominant contributor to the RIN. Attachments #1-#3 support this hypothesis. In these plots, "XARM" should really read "COMM" and "YARM" should really read "DIFF", because the error signals from the two end QPDs are mixed to generate the PIT and YAW error signals for these ASC servos - this is some channel renaming that will have to be done on the ASC model. The fact that the scatter plot between these DoFs has some ellipticity probably means the basis transformation isn't exactly right, because if they were truly orthogonal, we would expect them to be uncorrelated?

• In the corner plots, I am plotting the error signals of the ASC servos and the arm transmission. POP feedback is not engaged, but some feedback control to the ETMs based on the QPD signals is engaged.
• In the coherence plot, I show the coherence of the ASC error signals with the POP and TR QPD based error signals, under the same conditions. The coherence is high out to ~20 Hz.

I guess what this means is that the stability of the lock could be improved by turning on some POP QPD based feedback control, I'll give it a shot.

how bout corner plot with power signals and oplevs? I think that would show not just linear couplings (like your coherence), but also quadratic couplings (chesire cat grin)

We computed the required actuation range for the telescope design in elog:15357. The result is summarized in the table below. Here we assume we misalign an IFO mirror by 1 urad, and then compute how many urad do we need to move the (AS1, AS4) or (LO1, LO2) mirrors to simultaneously correct for the two gouy phases. 

The most demanding ifo mirrors are the ETMs and the BS, for every 1 urad misalignment the telescope needs to move 10-15 urad to correct for that. However, it is unlikely for those mirrors to move more 100 nrad for a locked ifo with ASC engaged. Thus a few urad actuation should be sufficient. For the recycling mirrors, every 1 urad misalignment also requires ~ 1 urad actuation. 

As a result, if we could afford 10 urad actuation range for each telescope suspension, then the gouy phase separations we have should be fine. 

================================================================

Edits:

We looked at the oplev spectra from gps 1274418500 for 512 sec. This should be a period when the ifo was locked in the PRFPMI state according to elog:15348. We just focused on the yaw data for now. Please see the attached plots. The solid traces are for the ASD, and the dotted ones are the cumulative rms. The total rms for each mirror is also shown in the legend. 

I am now confused... The ITMs looked somewhat reasonable in that at least the < 1 Hz motion was suppressed. The total rms is ~ 0.1 urad, which was what I would expect naively (~ x100 times worse than aLIGO). 

There seems to be no low-freq suppression on the ETMs though... Is there no arm ASC at the moment???

Highlights:

• With better ASC servos implemented, I think the lock stability has been improved. 
• Arm transmission of ~350 was stably maintained (PRG~20, overcoupled). It went as high as 410, so this is now very close to the highest (~425) I've ever managed to get.
• I was trying to get the vertex transitioned to 1f control but it remains out of reach for now.  The noise at ~100 Hz is dominated by MICH-->DARM coupling (as judged by coherence, I haven't yet done the broadband noise injection characterization). I figured I'd try the 1f transition before thinking about feedforward.
• The biggest problems remain flaky electronics (poor IMC duty cycle, jumping RF offsets, newly glitchy seismometer, ...)

Details:

• Faulty seismometer affecting the PRC angular feedforward [ELOG 15365].
• CARM loop modeling [ELOG 15366].
• PRC ASC performance [ELOG 15367].
• Field buildup update [ELOG 15368].

There were many locklosses from the point where the arm powers were somewhat stabilized. Attachments #1 and #2 show two individual locklosses. I think what is happening here is that the BS seismometer X channel is glitching, and creating a transient in the angular feedforward filter that blows the lock. The POP QPD based feedback loop cannot suppress this transient, apparently. For now, I get around this problem by boosting the POP QPD feedback loop a bit, and then turning the feedforward filters off. The fact that the other seismometer channels don't report any transient makes me think the problem is either with the seismometer itself, or the readout electronics. The seismometer masses were recently recentered, so I'm leaning towards the latter.

I didn't explicitly check the data, but I am reasonably certain the same effect is responsible for many PRMI locklosses even with the arms held off resonance (though the tolerance to excursions there is higher). Pity really, the feedforward filters were a big help in the lock acquisition...

Summary:

The CARM loop now has a UGF of ~12 kHz with a phase margin of ~60 degrees. These values of conventional stability indicators are good. The CARM optical gain that best fits the measurements is 9 MW/m.

I've been working on understanding the loop better, here are the notes.

Details:

Attachment #1 shows a block diagram of the loop topology.

• The "crossover" measurement made at the digital CARM error point, and the OLG measurement at the CM board error point are shown.
• I've tried to include all the pieces in the loop, and yet, I had to introduce a fudge gain in the digital path to get the model to line up with the measurement (see below).

Attachment #2 shows the OLGs of the two actuation paths.

• Aforementioned fudge factor for the digital path is included.
• For the AO path, I assumed a value of the PDH discriminant at the IMC error point to be 13 kHz/V, per my earlier measurement. 
• I trawled the elog for the most up-to-date info about the IMC servo (elog9457, elog13696, elog15044) and CM board, to build up the model. 

Attachment #3 and #4 show the model, overlaid with measurements of the loop OLG and crossover TF respectively.

• No fitting is done yet - the next step would be to add the delay of the CDS system for the digital path, and the analog electronics for the AO path. Though these are likely only small corrections.
• For the crossover TF - I've divided out the digital filters in the CARM_B filter bank, because the injection is made downstream of it (see Attachment #1).
• There is reasonably good agreement between model and measurement.
• I think the biggest source of error is the assumed model for the IMC OLTF.

Attachment #5 shows the evolution of the CARM OLG at a few points in the lock acquisition sequence.

• "Before handoff" corresponds to the state where the primary control is still done by the ALS leg, but the REFL11 signal has begun to enter the picture via the CARM_B path.
• "IN2 ramped" corresponds to the state where the AO path gain (=IN2 gain on the IMC servo board) has been ramped up to its final value (+0 dB), but the overall loop gain (=IN1 gain on the CM board) is still low. So this is preparation for high bandwidth control. Typically, the arm powers will have stabilized in this state, but ALS control is still on.
• "Pre-boost" corresponds to an intermediate state - ALS control is off, but the low frequency boosts have not yet been enabled. I typically first engage some ASC to stabilize things somewhat, and then turn on the boosts.
• "Final" - self explanatory.

Next steps:

Now the I have a model I believe, I need to think about whether there is any benefit to changing some of these loop shapes. I've already raised the possibility of changing the shape of the boosts on the CM board, with which we could get a bit more suppression in the 100 Hz - 1kHz region (noise budget of laser frequency noise --> DARM required to see if this is necessary). 

Attachments #1 and Attachments #2 are in the style of elog15356, but with data from a more recent lock. It'd be nice to calibrate the ASDC channel (and in general all channels) into power units, so we have an estimate of how much sideband power we expect, and the rest can be attributed to carrier leakage to ASDC.

On the basis of Attachments #1, the PRG is ~19, and at times, the arm transmission goes even higher. I'd say we are now in the regime where the uncertainty of the losses in the recycling cavity - maybe beamsplitter clipping? is important in using this info to try and constrain the arm cavity losses. I'm also not sure what to make of the asymmetry between TRX and TRY. Allegedly, the Y arm is supposed to be lossier.

Summary:

I implemented an ASC servo for the PRC, with the POP QPD as a sensor, and the PRM as the actuator. This has improved the stability of the lock (longer locks are possible), and also reduced the RIN of the arm transmission.

Details:

Attachment #1 shows the in-loop error signal suppression, and some out-of-loop monitors (POP22 and POPDC).

• To practise and get some workable servo settings, I locked the PRMI with carrier resonant (no ETMs).
• Then, I compare the beam motion witnessed by the POP QPD with and without the feedback loop enabled.
• I also look at the spectra of the POPDC and POP22 signals, as out-of-loop proxies, to get an estimate of how much noise is being injected out of band.
• In this toy study, both the in-loop and out of loop monitors show good performance.
• However, when repeating the same diagnostics with the PRFPMI locked, I note that while the in-loop suppression looks good, POPDC and POP22 report elevated noise, relative to the PRMI carrier case.
• I don't have a comparison to the PRFPMI locked with the feedback disabled, because of stability reasons. Plus, for the PRMI, the angular feedforward loops were engaged, but for the PRFPMI traces, they were disabled.
• Nevertheless, the arm RIN goes down by ~2.5 in RMS, so this is doing something good.

Attachment #2 compares the arm transmission RIN with the PRFPMI locked, with and without PRC ASC. The 3 Hz bump is definitely squished, but I think we can do better yet. 

Attachments #3-5 are in the style of elog15361. No Oplev signals yet, I'll add them soon.

Woo hoo!

Which 1f signals are you going to use? PRCL has sign flipping at the carrier critical coupling. So if the IFO is close to that condition, 1f PRCL suffers from the sign flipping or large gain variation.

Summary:

The 40m summary pages have been revived. I've not had to make any manual interventions in the last 5 days, so things seem somewhat stable, but I'm sure there will need to be multiple tweaks made. The primary use of the pages right now are for vacuum, seismic and PSL diagnostics.

Resources:

• Git repo
• Documentation
• Workflow

Caveats:

• Intermittent failures of cron jobs
  • ​The status page relies on the condor_q command executing successfully on the cluster end. I have seen this fail a few times, so the status page may say the pages are dead whereas they're actually still running.
  • Similarly, the rsync of the pages to nodus where they're hosted can sometimes fail.
  • Usually, these problems are fixed on the next iteration of the respective cron jobs, so check back in ~half hour.
• I haven't really looked into it in detail, but I think our existing C1:IFO-STATE word format is not compatible with what gwsumm wants - I think it expects single bits that are either 0 or 1 to indicate a particular state (e.g. MC locked, POX and POY locked etc). So if we want to take advantage of that infrastructure, we may need to add a few soft EPICS channels that take care of some logic checking (several such bits could also be and-ed together) and then assume either 0 or 1 value. Then we can have the nice duty cycle plots for the IMC (for example).
• I commented out the obsolete channels (e.g. PEM MIC channels). We can add them back later if we so desire.
• For some reason, the jobs that download the data are pretty memory-heavy: I have to request for machines on the cluster with >100 GB (yes 💯GB) ! of memory for the jobs to execute to completion. The frame-data certainly isn't so large, so I wonder what's going on here - is GWPy/GWsumm so heavy? The site summary pages run on a dedicated cluster, so probably the code isn't built for efficiency...
• Weather tab in PEM is still in there but none of those channels mean anything right now.
• The MEDM screenshot stuff is commented out for now too. This should be redone in a better way with some modern screen grab utilities, I'm sure there are plenty of python based ones.
• There seems to be a problem with the condor .dag lockfile / rescue file not being cleared correctly sometimes - I am looking into this.

For these initial attempts, I was just trying to transition MICH to REFL55Q. I agree, the PRCL situation may be more complicated.

Summary:

I am inclined to believe that the arm cavity losses are such that the IFO is overcoupled. Some calculations, validated with Finesse modeling also suggest that there isn't a sign change for the CARM error signal when the IFO goes from being undercoupled to overcoupled, but I may have made a mistake here?

Details:

• We’d like to gain some insight into whether the interferometer is undercoupled, critically coupled, or overcoupled. Factors that determine which of these is true include:
  • Arm cavity losses
  • Recycling cavity losses
• The proxy by which we determine the recycling gain is usually the arm cavity transmission. Assuming T_PRM = 5.637 % according to the wiki, and assuming the arm cavity transmission is normalized to 1 when locked in the POX/POY state, we can say that the PRG is given by G_PRC = TRX × T_PRM, assuming that the (i) the RF sideband fields are perfectly rejected by the arm cavities and (ii) mode-matching efficiency between the input beam and the arm mode is the same as that between the input beam and the CARM mode.
• Apart from this, the other measurement we have available to us is the buildup of the sideband fields, namely POP22 and POP110. We can compare the values in the PRMI lock vs the PRFPMI to make some inference.
• I started off with an analytic calculation of the reflectivity of the compound arm cavity mirror.
  • Attachment #1 suggests we will have an over-coupled IFO for arm cavity losses below ~200 ppm, which is a regime we are almost certainly in now.
• Then, I repeat the analysis for the coupled CARM cavity, with the end mirror as the compound arm mirror and the input mirror as the PRM.
  • I assume 2 % loss in the PRC.
  • Attachment #2 shows that while the carrier field goes through a sign change in amplitude reflectivity (as expected), the sideband fields dont.
  • Per equation 4.2 of Koji's thesis, the error signal for CARM depends on the (signed) IFO reflectivity, and the absolute value of the derivative of the arm cavity reflectivity for the carrier w.r.t. CARM phase.
  • So, we don't expect the REFL11 signal to show a sign change.
  • The situation is more complicated for PRCL in REFL11, because as explicitly evaluated in Eq 4.3 of Koji's thesis, there are two terms that contribute, and their relative magnitudes will dictate the overall sign. 
• For a Finesse validation, I use a simplified 3 mirror coupled cavity to approximate the PRFPMI. I also retained the RF sidebands for diagnostic purposes. The idea was to study these PRG proxies and what their expected behavior is.
  • Attachment #3 shows the PDH error signal in the (arbitrarily defined) REFL11 I quadrature. While the optical gain changes as a function of the arm cavity loss, the actual slope does not change sign. The fact that the zero crossing doesn't happen at exactly 0 CARM offset is because of higher order mode light at the REFL port (in my model, I tried to preserve the flipped folding mirror situation so the mode matching between the arm cavity and PRC in my model is ~96%).
  • In fact, this may explain why a CARM_B offset is required to do the ALS-->IR handoff - the ALS servo wants to keep the arm offset to zero, but at that point, the PDH error signal isn't zero, and so the two loops end up fighting each other?
  • Attachment #4 is a more detailed study of the recycling gain as a function of arm cavity loss, but now including losses in the recycling cavity.

Conclusions:

1. I think the arm cavity losses are in the 60-80 ppm round-trip region. I don't see how we can explain the arm cavity transmission of ~350 otherwise.
2. The fact that REFLDC decreases as the arm transmission increases is because the input beam is getting better matched to the CARM mode, and there is less junk carrier light. 

Thoughts from others?

This EQ seems to have knocked all suspensions out. ITMX was stuck. It is now released, and the IMC is locked again. It looks like there are some serious aftershocks going on so let's keep an eye on things.

GariLynn worked on the measurement of E1800089 mirrros.

The result of the data analysis, as well as the data and the codes, have been summarized here:
https://nodus.ligo.caltech.edu:30889/40m_phasemap/#E1800089
 

I will be at the 40m, in the Clean and bake lab today from ~9am to ~3pm.

Summary:

I found that there is an issue with the MC1 slow bias voltages. 

Details:

I usually offload the DC part of the output voltage from the WFS servos to the slow bias voltage sliders, so as to preserve maximum actuation range from the fast system. However, today, I found that this servo wasn't working well at all. So I dug a little deeper. Looking at the EPICS database records:

• The user-facing channels are "PIT" and "YAW" bias voltages.
• These are converted to voltages to be sent to individual coils by some calc channels in the EPICS database record. So, for example, the voltage to be sent to the "UL" coil (Upper Left, as viewed from the AR side of the optic), is A+B, where A is the "PIT" voltage and B is the "YAW" voltage. Similar combinations of A and B are used for the other 3 face coils.
• The problem is obvious - if either A or B > 5V, then the requested voltage to be sent to the UL coil is > 10 V, while the Acromag DACs can put out a maximum of 10 V. 
• As it happens, with the IFO currently aligned, MC1 is the only optic which faces this problem. 
• Why has this not been an issue before? In fact, looking at some old data, the "PIT" and "YAW" bias voltages to MC1 were both ~1-2 V in 2018. But I confirmed that something in the region of ~5 V is required from each of the "PIT" and "YAW" channels to bring the MCREFL spot back to the center of the camera, so something has changed the DC alignment of MC1, maybe an earthquake or something? Anyway, with these settings, 2/4 coils are basically saturated, and so we can only move the optic diagonally. 😢 
• Other coils that have  requested output voltages > 5V (so more than half the range of the DAC) include MC2 LL (5.2V), and ETMX LL and LR (5.5 and 5.8 V respectively).
• Either a factor of 0.5 should be included in all the EPICS database records, or else, we should make the "PIT" and "YAW" sliders range only from -5 to +5 V, so that this kind of misleading info isn't wasting time.

We can limit the EPICS values giving some parameters to the channels. cf https://epics.anl.gov/tech-talk/2012/msg00147.php

But this does not solve the MC1 issue. Only we can do right now is to make the output resister half, for example.