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  10947   Wed Jan 28 03:01:24 2015 JenneUpdateLSCTransitioned DARM to AS55Q

[Jenne, Diego]

Tonight we were able to transition DARM from DC transmission signals to AS55Q/(TRX+TRY).  That's about as far as we've gotten though.

Here are the details:

  • Set the ASDC->MICH matrix element such that the MICH fringes were 0-1.  For some reason this number seems to change by ~10% or so each night.
  • Followed main carm_cm_up script, although stopped at MICH offset of 25% (mostly because I forgot to let it go to 50% - no fundamental reason)
  • So, MICH was at 25% (with a + for the gain accidentally, even though we decided yesterday that - was better), arm powers were about 1.1 or so.
  • Took transfer functions driving DARM and looking at normalized AS55Q, and driving CARM looking at normalized REFL11I.
    • There is still not a lot of coherence in the CARM->REFL11I case, so we decided to stick with DARM for starters.
    • The TF between DARM and AS55Q looked really nice!
  • Prepared the unused DARM error signal row, including an offset before the blend matrix.
  • Transitioned over to normalized AS55Q.
    • This left the DARM servo filterbank with a zero digital offset.
    • But, the error signal had an offset before it got to the DARM filter bank.
      • This offset does not have any ramping (I don't know how to do that when building a model), so it's not as nice for reducing an offset.
      • Maybe we can, after transitioning to the new signal, move the offset to the DARM servo filterbank?
  • Was reducing the DARM offset so that we were at the true AS55Q zero crossing.
  • Saw that the UGF servo lines were starting to get a bit lost in the noise, so I increased the DARM's amplitude.
    • I don't know if the UGF servo was already too far gone and increasing the SNR couldn't recover it, or if I was driving too hard and directly kicked myself out of lock.  Either way, we lost lock.

The carm_cm_up script now should get all the way to this point by itself, although occasionally the PRMI part will lose lock (but not the arms), so you have to go back to the 3nm CARM offset and relock the central part.  I have written a little "relockPRMI.sh" script that lives in ..../scripts/PRFPMI/ that will take care of this for you.  

We were able to transition DARM to AS55Q a total of 3 or so times tonight.  The first time was with the + MICH gain, and the rest of the times were with - MICH gain.  The carm_up script now asks for a sign for the MICH gain just after asking for a CARM offset sign. 

I think that we understand all of our locklosses from these states.  Twice (including the time described above) the UGF lines got lost in the noise, and the UGF servos went crazy.  Once the PRCL loop rang up, because a filter that wasn't supposed to be on was on.  This was a terrible filter that I had made a long time ago, and was never supposed to be part of the locking sequence, but it was getting turned on by a restore script, and kept eating our phase.  Anyhow, I have deleted this terrible boost filter so it won't happen again (it was called "boost test", which may give you an idea of how non-confident I was in its readiness for prime-time).  The last time of the night I must not have been quite close enough in CARM offset, so we should probably check with a TF before making this last jump.

Diego wrote a nifty burt restoring script that will clear out all the elements of the input matrix and the normalization matrix for a row that you tell it (i.e. DARM_A will clear out all the elements in the first row of those 2 matrices).  This is useful for the switches back and forth between the _A and _B signals, to make sure that everything is in order.  So, I now run those clear scripts, then put in the elements that I want for the next step.  For example, DARM initially locks with ALS using the A row.  Then, DARM transitions to the B row for DC transmission.  Then, I prepare the A row for AS55Q locking, and I don't want any elements accidentally left from the ALS signal.  It lives in ..../scripts/LSC/InputMatrix/


Thoughts for tomorrow:

Daytime re-commission the Xarm ASS.

Nighttime try to get back to DARM on AS55Q and push farther forward. 


  10949   Wed Jan 28 14:19:02 2015 ranaUpdateLSCTransitioned DARM to AS55Q

Why AS55/(TRX + TRY) instead of just TRX? Isn't (TRX+TRY) controlled by CARM?cool

(question is secretly from Kiwamu)

  10953   Thu Jan 29 04:27:35 2015 ericqUpdateLSCCARM on REFL11

[ericq, Diego]

Tonight, we transitioned CARM from ALS directly to REFL11 I at 25% Mich Offset. yes

We attempted the transition twice, the first time worked, but we lost lock ~5 seconds after full transition due to a sudden ~400Hz ringup (see attached lockloss plot). The second barfed halfway, I think because I forgot to remove the CARM B offset from the first time frown

The key to getting to zero CARM offset with CARM and DARM on ALS is ekeing out every bit of PRMI phase margin that you can. Neither MICH nor PRCL had their RG filters on and I tweaked the MICH LP to attenuate less and give back more phase (the HF still isn't the dominant RMS source.) PRCL had ~60 degrees phase margin at 100Hz UGF, MICH had ~50 deg at 47Hz UGF. The error signals were comparitively very noisy, but we only cared that they held on. Also important was approaching zero slooooooooowly, and having the CARM and DARM UGF servo excitations off, because they made everything go nuts. Diego stewarded the MICH and PRCL excitation amplitudes admirably. 

Oddly, and worringly, the arm powers at zero CARM offset were only around 10-12. Our previous estimations already include the high Xarm loss, so I'm not sure what's going on with this. Maybe we need to measure our recycling gain?

I hooked up the SR785 by the LSC rack to the CM board after the first success. For the second trial, I also took TFs with respect to CM slow, but they looked nowhere near as clean as the normal REFL11 I channel; I didn't really check all the connections. I will be revisiting the whole AO situation soon. 

In any case, I think we're getting close...

Attachment 1: Jan29_REFL11_lockloss.png
  10960   Fri Jan 30 03:12:15 2015 diegoUpdateLSCCARM on REFL11I

[Jenne, Diego]

Tonight we continued following the plan of last night: perform the transition of CARM to REFL11_I while on MICH offset at -25%:

  • we managed to do the transition several times, keeping the UGF servos on for MICH and PRCL but turning off the DARM and CARM ones, because their contribution was rather unimportant and we feared that their excitations could affect negatively the other loops (as loops tend to see each other's excitation lines);
  • we had to tweak the MICH and PRCL UGF servos:
    • the excitation frequency for MICH was lowered to ~41 Hz, while PRCL's one was lowered to ~50 Hz;
    • PRCL's amplitude was lowered to 75 because it was probably too high and it affected the CARM loop, while MICH's one was increased to 300 because during the reduction of the CARM offset it was sinking into the noise; after a few tries we can say they don't need to be tweaked on the fly during the procedure but can be kept fixed from the beginning;
    • after the transition to REFL11_I for CARM, we engaged also its UGF servo, still at the highest frequency of the lot (~115 Hz) and with relatively low amplitude (2), to help keeping the loop stable;
    • as DARM was still on ALS, we didn't engage its UGF servo during or after the transition, but we just hold its output from the initial part of the locking sequence (after we lowered its frequency to 100 Hz;
  • however, at CARM offset 0 our arm power was less that what we had yesterday: we managed to get higher than ~8, but after Koji tweaked the MC alignment we reached ~10; we still don't understand the reason of the big difference with respect to what the simulations show for MICH offset at 25% (arm power ~50);
  • after the CARM transition to REFL11_I we felt things were pretty stable, so we tried to reduce the MICH offset to get us in the ~ -10% range, however we never managed to get past ~ -15% before losing lock, at arm power around 20;
  • we lost lock several times, but for several different reasons (IMC lost lock a couple of times, PRCL noise increased/showed some ringing, MICH railed) but our main concern is with the PRCL loop:
    • we took several measurements of the PRCL loop: the first one seemed pretty good, and it had a bigger phase bubble than usual; however, the subsequent measurements showed some weird shapes we struggle to find a reason for; these measurements were taken at different UGF frequencies, so maybe it is worth looking for some kind of correlation; morever, in the two weird measurements the UGFs are not where they are supposed to be, even if the servo was correctly following the input (or so it seemed); the last measurement was interrupted just before we lost lock because of PRCL itself;
    • we noticed a few times during the night that the PRCL loop noise in the 300-500 Hz range increased suddenly and we saw some ringing; at least a couple of times it was PRCL who threw us out of lock; this frequency range is similar to the 'weird' range we found in our measurements, so we definitely need to keep an eye on PRCL on those frequencies;
  • in conclusion, the farthest we got tonight was CARM on REFL11_I at 0 offset, DARM at 0 offset still on ALS and MICH at ~ 15% offset, arm power ~20.


Attachment 1: PRCL_29Jan2015_Weird_Shape.pdf
Attachment 2: ArmPowers20_MICHoffsetBeingReduced_0CARMoffset_29Jan2015.pdf
  10962   Sat Jan 31 01:34:12 2015 JenneUpdateLSCNot able to engage AO path

Nothing earth-shattering today.

A few things of note:

  • I checked the coherence (no lock present, just noise) between REFL11_I_IN1 and CM_SLOW_OUT, which are meant to be the same thing when only the REFL1 path is allowed through the CM board.
    • However, at first, there was very little coherence - small band, and only about 0.7 or so.
    • I went inside and jiggled the cables, and also toggled the whitening switches for REFL11 and the CM_SLOW, and after that I had excellent coherence. 
      • I didn't take a coherence spectrum in between those activities, but since the cable connections were all solid, I believe that it may have been a sticky slider -esque problem, and the CM whitening wasn't matched between the analog and digital.
    • I tried two or three times to engage the AO path, but I always lost lock before I was getting any meaningful gain through.
      • I took some TFs remotely with the SR785, but they're totally noise.  I don't even know which sign of the CM board is correct, so no real knkowledge added there, from today.
  • The ~400Hz ringing that we have been seeing, we have been blaming on the PRCL loop.  However, just before my last lockloss I saw gain peaking around 400Hz in the CARM input spectrum. I didn't see if it was also there in the PRCL spectrum.  So, either it is coupling from PRCL to CARM, or CARM itself.  But I think we need to see if we can eek out a little more phase at higher frequencies for both of those loops.  I  just looked, and about 16 seconds before the last lockloss, I see the PRCL loop coupling into the CARM loop.
    • Since yesterday, we have been lowering the PRCL UGF using the servos to be about 70Hz, to give us more gain margin at the high end of the phase bubble, but we still see this ringing. 
  • Two or three times my arm power buildup at 0 CARM offset, 25% MICH offset was at 20 or 21.  Then, a few other times I was only getting about 10 (which is what we have been seeing the last few days.)
    • I'm running the ASS between each lock, although I'm not running it for a full ~2 minutes or so usually. 
    • I think that the reason I was able to get to such high arm powers was excellent alignment, so maybe it's worth sitting and waiting for the ASS to have a full 2 or 3 minutes between locks, even if the ASS error signals look zero-ed out.
    • This is still a factor of 2 lower than we expect for 25% MICH offset, but the whole factor of 5 isn't explained by some mysterious loss.  At least half of it is alignment.
  • The PRCL ASC feedforward still isn't working, but I'd like to try Q's trans qpd ASC soon, with the full lock.  I think the system is ready, but scripts are not, so Q has to be here to run it.

See first plot below for the PRCL->CARM coupling just before lockloss.  The second plot is the corresponding lockloss, where the PRCL loop is starting to see that oscillation again, and it's just barely starting to get into CARM. 

  10965   Mon Feb 2 22:59:49 2015 diegoUpdateLSCCM board input switched to AS55

[Diego, Jenne]

We just changed the input to the CM board from REFL11 to AS55.


  10966   Tue Feb 3 04:01:55 2015 diegoUpdateLSCCM servo & AO path status

[Diego, Jenne]

Tonight we worked on the CM board and AO path:

  • at first we changed the REFL1 input to the CM board from REFL11 to AS55, as written in my previous elog; we tried following Koji's procedures from http://nodus.ligo.caltech.edu:8080/40m/9500 but we didn't get any result: we could lock using the regular digital path but no luck at all for the analog path;
  • then we decided to follow the procedure to the letter, using POY11Q as input to the CM board;
    • we still couldn't lock following the Path #2, even after adjusting the gains to match the current configuration for the Yarm filter bank;
    • we had some more success using Path #1, but we had to lower the REFL1 Gain to ~3-4 (from the original 31) because of the different configuration of the Yarm filter bank, in order to have the same sensing in both of them; we managed to acquire lock a few times, it's not super stable but it can keep lock for a while;
    • when we tried to increase the gain of the MC filter bank and the AO Gain, however, we immediately had some gain peaking, and we couldn't go further then 0.15 and 9db respectively. We currently don't have an answer for that.
    • anyhow, we took a few measurements with the SR785:


The BLUE plot is at MC Gain = 0.10 and REFL1 Gain = 4dB; the GREEN plot is for MC Gain = 0.10 and REFL1 Gain = 3dB, which seemed a more stable configuration; after this last configuration, we increased the MC Gain to 0.15 and the AO Gain from 8dB to 9dB and took another measurement, the RED plot; this is as far as we got as of now. We also couldn't increase the REFL11 Gain because it made things unstable and more prone to unlock.

So, some little progress on the AO path procedure, but we are very low on our UGF and we have to find a way to increase our gains without breaking the lock and avoiding the gain peaking we have witnessed tonight.



  • is the REFL1 Gain dB slider supposed to go to negative dBs? During the night we also tried to use negative dBs, but it seemed it wasn't doing anything instead;
  • when we plugged POY11Q to the CM board, we noticed that it wasn't connected to anything at the moment; since we phase rotate POY11, we were assuming that we were using that signal somewhere. We are confused by this...
  • we remind that REFL11 is no more connected to the CM board input, as POY11 is.
Attachment 1: CARM_03-02-2015_031754.pdf
  10969   Tue Feb 3 16:36:33 2015 ericqUpdateLSCCM servo & AO path status

I have removed REFLDC and the SR560 offsetter from the CM board IN2. Now, analog AS55 I lives there, for our single arm testing. (Analog I has more of the single arm Y PDH signal in it). REFL11 has been reconnected to IN1. 

With ITMX super misaligned, Diego and I locked the Y-arm with the AO path on AS55, ultimately at 4kHz bandwidth, but with plenty of gain margin. We didn't allocate the gains too intelligently, and had the CM board input gain slider maxed out, but plenty of headroom in the digital and AO sliders, making it inconvenient to up the UGF even more, to engage the super boosts. However, since this is just a test case to make sure we still can AO lock, I'm not too worried about this. 

Since LSC FMs and such had changed around, old recipies didn't neccesarily work 1:1. Diego is writing a script for the current recipe, and will post an elog with the steps. 

Gains and signs are able to be tracked by loop TFs, the real sticking point is a stable crossover. We used the 1.6k:80 hardware filter in the CM board to give the AO Path a 1/f shape in the crossover region, and undid it digitally in the CM_SLOW input FM. However, we do use a 300:80 in the MC2 sus FM to make the digital loop like 1/f^2 around the crossover, once a little bit of AO has come in to pull up the digital loop's phase. We used the CARM filter bank to do this, so I think we should be able to use a similar technique to do it in the PRFPMI case, as long as the coupled cavity pole is around ~100Hz. 

Attached are a few OLTFs from the progression.

Attachment 1: yarmAO.pdf
  10971   Wed Feb 4 04:51:14 2015 diegoUpdateLSCCARM Transition to REFL11 using CM_SLOW Path

[Diego, Jenne, Eric]

Tonight we kept on following our current strategy for locking the PRFPMI:

  • the first few tries were pretty unsuccessful: the PRMI lock wasn't much stable, and we never managed to reduce CARM offset to zero before losing lock;
  • then we did some usual manteinance: we fixed the X arm green beatnote, fixed the phase tracker and given much attention to ASS alignment, since the X arm wasn't doing great;
  • the last few locks were consintently better: we managed to get to CARM offset zero "easily", but the arm power was not very high (~8);
  • then we tried to transition CARM to REFL11, both with the usual configuration and using CM_SLOW, using REFL11 as input for the Common Mode Board;
    • with the usual configuration, we lost lock right after the transition, because of MICH hitting the rail;
    • we did a very smooth CARM transition directly to REFL11 on the CM_SLOW path; we managed to take a spectrum with the SR785, but we couldn't take any more measurements before losing lock because of some weird glitch, as we can see from the lockloss plot;
  • another thing that helped tonight was changing the ELP of the MICH filter bank: it went from 4th order to 6th order, and from 40 dB suppression to 60 dB suppression;

both of the last two locks, the most stable ones (one transition to usual REFL11 and one transition to "CM_SLOW" REFL11) were acquired actuating on MC2;


EDITs by JCD:  At least one of the times that we lost PRMI lock (although kept CARM and DARM lock on ALS), was due to MICH hitting the rail, even after we increased the limiter to 15,000 counts.

 Here is the transfer function between CARM ALS (CARM_IN1) and REFL11 coming through the CM board (CARM_B), just before we transitioned over.  Coherence was taken simultaneously as usual, I just printed it to another sheet.



Here is the lockloss plot for the very last lockloss.  This is the time that we were sitting on REFL11 coming through the CM_SLOW path.  A DTT transfer function measurement was in progress (you can see the sine wave in the CARM input and output data), but I think we actually lost lock due to whatever this glitch was near the right side of the plots.  This isn't something that I've seen in our lockloss plots before.  I'm not sure if it's coming from REFL11, or the CM board, or something else.  We know that the CM board gives glitches when we are changing gain settings, but that was not happening at this time.

Q: Here's the SR785 TF of CARM locked through CM board, but still only digital control; nothing exciting. Excitation amplitude was only 1mV, which explains the noisy profile. 

Attachment 1: CARM_3Feb2015_CarmBwasCMslow_CarmAwasLiveALS.pdf
Attachment 2: CARM_3Feb2015_CarmBwasCMslow_CarmAwasLiveALS_Coh.pdf
Attachment 3: Glitch_in_CARM_and_PRCL_3Feb2015.png
Attachment 4: slowCM_04-02-2015_042805.png
  10972   Wed Feb 4 14:30:05 2015 ericqUpdateLSCASDC Whitening Gain

At the lunch meeting, we were thinking about the exess high frequency content of the MICH control signal, which leads to railing against the FM output limiter and lock loss. I propsed that POPDC sensor/ADC noise was the culprit. 

In short, I was wrong. Just now, I locked the PRMI with a MICH offset as we normally do, and then froze the POPDC output. The MICH spectrum did not change in any noticible way. 

However, increasing the analog ASDC whitening gain showed a direct improvement of the error signal noise floor, and thus a reduction in the control signal spectrum. I.e. we have been suffereing from ASDC ADC noise.

We had previously set the ASDC whitening gain so that half fringe of the PRMI would be well within the ADC range, but since we're actually only ever going to 25%, I feel fine upping this gain. Interestingly, when increasing the whitening gain by 12dB,  the control signal spectrum has fallen by more like 20 dB in the 400Hz-1kHz region, which is great. 

The only potential hurdle I can think of is that when we start reducing the MICH offset at zero CARM offset, we may approach ADC saturation in ASDC before we can hand off to RF signals, in which case we would have to dynamically lower the whitening gain, which introduces offsets, which could get hairy. But, since MICH railing has been directly seen to lead to lock-loss, I'd rather solve that problem first. 

  10973   Wed Feb 4 18:16:44 2015 KojiUpdateLSCData transfer rate of c1lsc reduced from ~4MB/s to ~3MB/s

c1lsc had 60 full-rate (16kS/s) channels to record. This yielded the LSC to FB connection to handle 4MB/s (mega-byte) data rate.
This was almost at the data rate limit of the CDS and we had frequent halt of the diagnostic systems (i.e. DTT and/or dataviewer)

Jenne and I reviewed DAQ channel list and decided to remove some channels.  We also reviewed the recording rate of them
and reduced the rate of some channels. c1lsc model was rebuilt, re-installed, and restarted. FB was also restarted. These are running as they were.
The data rate is now reduyced to ~3MB nominal.

The following is the list of the channels removed from the DQ channels:


The following is the list of the channels with the new recording rate:


  10979   Thu Feb 5 04:35:14 2015 diegoUpdateLSCCARM Transition to REFL11 using CM_SLOW Path

[Diego, Eric]

Tonight was a sad night... We continued to pursue our strategy, but with very poor results:

  • before doing anything, we made sure we had a good initial configuration: we renormalized the arm powers, retuned the X arm green beatnote, did extensive ASS alignment;
  • since the beginning of the night we faced a very uncooperative PRMI, which caused a huge number of locklosses, often just by itself, without even managing to reduce the MICH offset before reducing the CARM one;
  • we had to reduce the PRCL gain to -0.002 in order to acquire PRMI lock, but keeping it such or restoring it to -0.004 once lock was acquired either didn't improve the PRMI stability at all;
  • we also tweaked a bit the PRCL and MICH UGF servos (namely, their frequencies to ~80 Hz and ~40 Hz respectively) and that seemed to help earlier during the night, but not much longer;
  • we only managed to transition CARM to REFL11 via CM SLOW twice;
    • the first time we lost lock almost immediately, probably because of a non-optimal offset between CARM A and B;
    • the second time we managed to stay there a little longer, but then some spike in the PRCL loop and/or the MICH loop hitting the rails threw us out of lock (see the lockloss plot);
    • both times we transitioned at arm power ~18;
  • during the night we used an increased analog ASDC whitening gain, as from Eric's elog here http://nodus.ligo.caltech.edu:8080/40m/10972 ; even with this fix, though, MICH is still often hitting the rails and causing the lock losses;
  • the conclusion for tonight is that we need to figure what is going on with the PRMI...


Attachment 1: 4Feb2015_Transition_CARM_REFL11_CM_SLOW_AP_18.png
  10982   Fri Feb 6 03:21:17 2015 diegoUpdateLSCCARM Transition to REFL11 using CM_SLOW Path

[Diego, Jenne]

We kept struggling with the PRMI, although it was a little better than yesterday:

  • we retuned the X Green beatnote;
  • we managed to reach lower CARM offsets than yesterday night, but we still can't keep lock long enough to perform a smooth transition to CM SLOW/REFL11;
  • we tweaked MICH a bit:
    • the ELP in FM8 now is always on, because it seems to help;
    • we tried using a new FM1 1,1:0,0 instead of FM2 1:0 because we felt we needed a little more gain at low frequencies, but unfortunately this didn't change much MICH's behaviour;
    • now, after catching PRMI lock, the MICH limiter is raised to 30k (in the script), as a possible solution for the railing problem; the down/relock scripts take care of resetting it to 10k while not locked/locking;

So, still no exciting news, but PRMI lock seems to be improving a little.

  10987   Sat Feb 7 21:30:45 2015 JenneUpdateLSCPRC aligned

I'm leaving the PRC aligned and locked.  Feel free to unlock it, or do whatever with the IFO.

  10991   Mon Feb 9 17:47:17 2015 diegoUpdateLSCCM servo & AO path status

I wrote the script with the recipe we used, using the Yarm and AS55 on the IN2 of the CM board; however, the steps where the offset should be reduced are not completely deterministic, as we saw that the initial offset (and, therefore, the following ones) could change because of different states we were in. In the script I tried to "servo" the offset using C1:LSC-POY11_I_MON as the reference, but in the comments I wrote the actual values we used during our best test; the main points of the recipe are:

  • misalign the Xarm and the recycling mirrors;
  • setting up CARM_B for POY11 locking and enabling it;
  • setting up CARM_A for CM_SLOW;
  • setting up the CM_SLOW filter bank, with only FM1 and FM4 enabled;
  • setting up the CARM filter bank: FM1 FM2 FM6 triggered, only FM3 and FM5 on; usual CARM gain = 0.006;
  • setting up CARM actuating on MC2;
  • turn off the violin filter FM6 for MC2;
  • setting up the default configuration for the Common Mode Servo and the Mode Cleaner Servo; along with all the initial parameters, here is where the initial offset is set;
  • turn on the CARM output and, then, enable LSC mode;
  • wait until usual POY11 lock is acquired and, a bit later, transition from CARM_B to CARM_A;
  • then, the actual CM_SLOW recipe:
    • CM_AO_GAIN = 6 dB;
    • SUS-MC2_LSC FM6 on (the 300:80 filter);
    • CM_REFL2_GAIN = 18 dB;
    • servo CM_REFL_OFFSET;
    • CM_AO_GAIN = 9 dB;
    • CM_REFL2_GAIN = 21 dB;
    • servo CM_REFL_OFFSET;
    • CM_REFL2_GAIN = 24 dB;
    • servo CM_REFL_OFFSET;
    • CM_REFL2_GAIN = 27 dB;
    • servo CM_REFL_OFFSET;
    • CM_REFL2_GAIN = 31 dB;
    • servo CM_REFL_OFFSET;
    • CM_AO_GAIN = 6 dB;
    • SUS-MC2_LSC FM7 on (the :300 compensating filter);

I tried the procedure and it seems fine, as it did during the tries Q and I made; however, since it touches many things in many places, one should be careful about which state the IFO is into, before trying it.

The script is in scripts/CM/CM_Servo_OneArm_CARM_ON.py and in the SVN.


  10992   Tue Feb 10 02:40:54 2015 JenneUpdateLSCSome locking thoughts on PRMI

[EricQ, Jenne]

We wanted to make the PRMI lock more stable tonight, which would hopefully allow us to hold lock much longer.  Some success, but nothing out-of-this-world.

We realized late last week that we haven't been using the whitening for the ASDC and POPDC signals, which are combined to make the MICH error signal.  ASDC whitening is on, and seems great.  POPDC whitening (even if turned on after lock is acquired) seems to make the PRMI lock more fussy.  I need to look at this tomorrow, to see if we're saturating anything when the whitening is engaged for POPDC.

One of the annoying things about losing the PRMI lock (when CARM and DARM have kept ALS lock) is that the UGF servos wander off, so you can't just reacquire the lock.  I have added triggering to the UGF servo input, so that if the cavity is unlocked (really, untriggered), the UGF servo input gets a zero, and so isn't integrating up to infinity.  It might need a brief "wait" in there, since any flashes allow signal through, and those can add up over time if it takes a while for the PRMI to relock.  UGF screens reflect this new change.

  10994   Tue Feb 10 03:09:02 2015 ericqUpdateLSCSome locking thoughts on PRMI

Unfortunately, we only had one good CARM offset reduction to powers of about 25, but then my QPD loop blew it. We spent the vast majority of the night dealing with headaches and annoyances. 

Things that were a pain:

  • If TRX is showing large excursions after finding resonance, there is no hope. These translate into large impulses while reducing the CARM offset, which the PRMI has no chance of handling. The first time aligning the green beat did not help this. For some reason, the second time did, though the beatnote amplitude wasn't increased noticibly. 
    • NOTICE: We should re-align the X green beatnote every night, after a solid ASS run, before any serious locking work. 
    • Afterwards, phase tracker UGFs (which depend on beatnote amplitude, and thereby frequency) should be frequently checked. 
  • We suffered some amount from ETMX wandering. Not only for realigning between lock attempts, but on one occasion, with CARM held off, GTRX wandered to half its nominal value, leading to a huge effective DARM offset, which made it impossible to lock MICH with any reasonble power in the arms. Other times, simply turning off POX/POY locking, after setting up the beatnotes, was enough to significantly change the alignment. 
  • IMC was mildly tempermental, at its worst refusing to lock for ~20min. One suspicion I have is that when the PMC PZT is nearing its rail, things go bad. The PZT voltage was above 200 when this was happening, after relocking the PMC to ~150, it seems ok. I thing I've also had this problem at PZT voltages of ~50. Something to look out for. 

Other stuff:

  • We are excited for the prospect of the FOL system, as chasing the FSS temperature around is no fun. 
  • UGF servo triggering greatly helps the PRMI reacquire if it briefly flashes out, since the multipliers don't run away. This exacerbated the ALS excursion problem. 
  • Using POPDC whitening made it very tough to hold the PRMI. Maybe because we didn't reset the dark offset...?
  10995   Tue Feb 10 13:48:58 2015 manasaUpdateLSCProbable cause for headaches last night

I found the PSL enclosure open (about a feet wide) on the north side this morning. I am assuming that whoever did the X beatnote alignment last night forgot to close the door to the enclosure before locking attempts frown


Unfortunately, we only had one good CARM offset reduction to powers of about 25, but then my QPD loop blew it. We spent the vast majority of the night dealing with headaches and annoyances. 

Things that were a pain:

  • If TRX is showing large excursions after finding resonance, there is no hope. These translate into large impulses while reducing the CARM offset, which the PRMI has no chance of handling. The first time aligning the green beat did not help this. For some reason, the second time did, though the beatnote amplitude wasn't increased noticibly. 
    • NOTICE: We should re-align the X green beatnote every night, after a solid ASS run, before any serious locking work. 
    • Afterwards, phase tracker UGFs (which depend on beatnote amplitude, and thereby frequency) should be frequently checked. 
  • We suffered some amount from ETMX wandering. Not only for realigning between lock attempts, but on one occasion, with CARM held off, GTRX wandered to half its nominal value, leading to a huge effective DARM offset, which made it impossible to lock MICH with any reasonble power in the arms. Other times, simply turning off POX/POY locking, after setting up the beatnotes, was enough to significantly change the alignment. 
  • IMC was mildly tempermental, at its worst refusing to lock for ~20min. One suspicion I have is that when the PMC PZT is nearing its rail, things go bad. The PZT voltage was above 200 when this was happening, after relocking the PMC to ~150, it seems ok. I thing I've also had this problem at PZT voltages of ~50. Something to look out for. 

Other stuff:

  • We are excited for the prospect of the FOL system, as chasing the FSS temperature around is no fun. 
  • UGF servo triggering greatly helps the PRMI reacquire if it briefly flashes out, since the multipliers don't run away. This exacerbated the ALS excursion problem. 
  • Using POPDC whitening made it very tough to hold the PRMI. Maybe because we didn't reset the dark offset...?


  10998   Wed Feb 11 00:07:54 2015 ranaUpdateLSCLock Loss plot

Here is a lock loss from around 11 PM tonight. Might be due to poor PRC signals.  \oint {\frac{\partial PRCL}{\partial x}}

This is with arm powers of ~6-10. You can see that with such a large MICH offset, POP22 signal has gone done to zero. Perhaps this is why the optical gain for PRCL has also dropped by a factor of 30 crying.

This seems untenable no. We must try this whole thing with less MICH offset so that we can have a reasonable PRCL signal.cool

Attachment 1: 1107673198.png
  10999   Wed Feb 11 02:42:05 2015 JenneUpdateLSCPRC error signal RF spectra

Since we're having trouble keeping the PRC locked as we reduce the CARM offset, and we saw that the POP22 power is significantly lower in the 25% MICH offset case than without a MICH offset, Rana suggested having a look at the RF spectra of the REFL33 photodiode, to see what's going on. 

The Agilent is hooked up to the RF monitor on the REFL33 demod board.  The REFL33 PD has a notch at 11MHz and another at 55MHz, and a peak at 33MHz. 

We took a set of spectra with MICH at 25% offset, and another set with MICH at 15% offset.  Each of these sets has 4 traces, each at a different CARM offset.  Out at high CARM offset, the arm power vs. CARM offset is pretty much independent of MICH offset, so the CARM offsets are roughly the same between the 2 MICH offset plots. 

What we see is that for MICH offset of 25%, the REFL33 signal is getting smaller with smaller CARM offset!!  This means, as Rana mentioned earlier this evening, that there's no way we can hold the PRC locked if we reduce the CARM offset any more. 

However, for the MICH offset 15% case, the REFL 33 signal is getting bigger, which indicates that we should be able to hold the PRC.  We are still losing PRC lock, but perhaps it's back to mundane things like actuator saturation, etc. 

The moral of the story is that the 3f locking seems to not be as good with large MICH offsets.  We need a quick Mist simulation to reproduce the plots below, to make sure this all jives with what we expect from simulation.

For the plots, the blue trace has the true frequency, and each successive trace is offset in frequency by a factor of 1MHz from the last, just so that it's easier to see the individual peak heights.

Here is the plot with MICH at 25% offset:

And here is the plot with MICH at 15% offset:

Note that the analyzer was in "spectrum" mode, so the peak heights are the true rms values.  These spectra are from the monitor point, which is 1/10th the value that is actually used.  So, these peak heights (mVrms level) times 10 is what we're sending into the mixer.  These are pretty reasonable levels, and it's likely that we aren't saturating things in the PD head with these levels. 

The peaks at 100MHz, 130MHz and 170MHz that do not change height with CARM offset or MICH offset, we assume are some electronics noise, and not a true optical signal.

Also, a note to Q, the new netgpib scripts didn't write data in a format that was back-compatible with the old netgpib stuff, so Rana reverted a bunch of things in that directory back to the most recent version that was working with his plotting scripts.  sorry.


Attachment 1: REFL33_25.pdf
Attachment 2: REFL33_15.pdf
  11000   Wed Feb 11 03:41:12 2015 KojiUpdateLSCPRC error signal RF spectra

As the measurements have been done under feedback control, the lower RF peak height does not necessary mean
the lower optical gain although it may be the case this time.

These non-33MHz signals are embarassingly high!
We also need to check how these non-primary RF signals may cause spourious contributions in the error signals,
including the other PDs.

  11001   Wed Feb 11 04:08:53 2015 JenneUpdateLSCNew Locking Paradigm?

[Rana, Jenne]

While meditating over what to do about the fact that we can't seem to hold PRMI lock while reducing the CARM offset, we have started to nucleate a different idea for locking

We aren't sure if perhaps there is some obvious flaw (other than it may be tricky to implement) that we're not thinking about, so we invite comments.  I'll make a cartoon and post it tomorrow, but the idea goes like this.....

Can we use ALS to hold both CARM and DARM by actuating on the ETMs, and sit at (nominally) zero offset for all degrees of freedom?  PRMI would need to be stably held with 3f signals throughout this process. 

1) Once we're close to zero offset, we should see some PDH signal in REFL11.  With appropriate triggering (REFLDC goes low, and REFL11I crosses zero), catch the zero crossing of REFL11I, and feed it back to MC2. We may want to use REFL11 normalized by the sum of the arm transmissions to some power (1, 0.5, or somewhere in between may maximize the linear range even more, according to Kiwamu).  The idea (very similar to the philosophy of CESAR) is that we're using ALS to start the stabilization, so that we can catch the REFL11 zero crossing. 

2) Now, the problem with doing the above is that actuating on the mode cleaner length will change the laser frequency.  But, we know how much we are actuating, so we can feed forward the control signal from the REFL11 carm loop to the ALS carm loop.  The goal is to change the laser frequency to lock it to the arms, without affecting the ALS lock.  This is the part where we assume we might be sleepy, and missing out on some obvious reason why this won't work.

3) Once we have CARM doubly locked (ALS pushing on ETMs, REFL11 pushing on MC/laser frequency), we can turn off the ALS system. Once we have the linear REFL11 error signal, we know that we have enough digital gain and bandwidth to hold CARM locked, and we should be able to eek out a slightly higher UGF since there won't be as many digital hops for the error signal to transverse. 

4) The next step is to turn on the high bandwidth common mode servo.  If ALS is still on at this point, it will get drowned out by the high gain CM servo, so it will be effectively off. 

5) Somewhere in here we need to transition DARM to AS55Q.  Probably that can happen after we've turned on the digital REFL11 path, but it can also probably wait until after the CM board is on.

The potential show-stoppers:

Are we double counting frequency cancellation or something somewhere?  Is it actually possible to change the laser frequency without affecting the ALS system?

Can we hold PRMI lock on 3f even at zero CARM offset?  Anecdotally from a few trials in the last hour or so, it seems like coming in from negative carm offset is more successful - we get to slightly higher arm powers before the PRMI loses lock.  We should check if we think this will work in principle and we're just saturating something somewhere, or if 3f can't hold us to zero carm offset no matter what.

A note on technique:  We should be able to get the transfer function between MC2 actuation and ALS frequency by either a direct measurement, or Wiener filtering.  We need this in order to get the frequency subtraction to work in the correct units.

  11003   Wed Feb 11 17:31:11 2015 ericqUpdateLSCRFPD spectra

For future reference, I've taken spectra of our various RFPDs while the PRMI was sideband locked on REFL33, using a 20dB RF coupler at the RF input of the demodulator boards. The 20dB coupling loss has been added back in on the plots. Data files are attached in a zip.


  • The REFL165 trace was taken at the input of the amplifier that immediately preceeds the demod board. 
  • The 'POPBB' trace was taken with the coupler at the input of the bias tee, that leads to an amplifier, then splitter, then the 110 and 22 demod boards. 

I also completely removed the cabling for REFLDC -> CM board, since it doesn't look like we plan on using it anytime in the immediate future. 

Attachment 1: REFL.png
Attachment 2: AS.png
Attachment 3: POP.png
Attachment 4: 2015-02-PDSpectra.zip
  11004   Wed Feb 11 18:07:42 2015 ericqUpdateLSCRFPD spectra

After some discussion with Koji, I've asked Steve to order some SBP-30+ bandpass filters as a quick and cheap way to help out REFL33. (Also some SBP-60+ for 55MHz, since we only have 1*fmod and 2*fmod bandpasses here in the lab). 

  11005   Wed Feb 11 18:11:46 2015 KojiSummaryLSC3f modulation cancellation

33MHz sidebands can be elliminated by careful choice of the modulation depths and the relative phase between the modulation signals.
If this condition is realized, the REFL33 signals will have even more immunity to the arm cavity signals because the carrier signal will lose
its counterpart to produce the signal at 33MHz.

Formulation of double phase modulation

m1: modulation depth of the f1 modulation
m2: modulation depth of the f2 (=5xf1) modulation

The electric field of the beam after the EOM

E=E_0 \exp \left[ {\rm i} \Omega t + m_1 \cos \omega t +m_2 \cos 5 \omega t \right ]
\flushleft = {\it E}_0 e^{{\rm i} \Omega t} \\ \times \left[ J_0(m_1) + J_1(m_1) e^{{\rm i} \omega t}- J_1(m_1) e^{-{\rm i} \omega t} + J_2(m_1) e^{{\rm i} 2\omega t}+ J_2(m_1) e^{-{\rm i} 2\omega t} + J_3(m_1) e^{{\rm i} 3\omega t}- J_3(m_1) e^{-{\rm i} 3\omega t} + \cdots \right] \\ \times \left[ J_0(m_2) + J_1(m_2) e^{{\rm i} 5 \omega t}- J_1(m_2) e^{-{\rm i} 5 \omega t} + \cdots \right]
\flushleft = {\it E}_0 e^{{\rm i} \Omega t} \\ \times \left\{ \cdots + \left[ J_3(m_1) J_0(m_2) + J_2(m_1) J_1(m_2) \right] e^{{\rm i} 3 \omega t} - \left[ J_3(m_1) J_0(m_2) + J_2 (m_1) J_1(m_2) \right] e^{-{\rm i} 3 \omega t} + \cdots \right\}

Therefore what we want to realize is the following "extinction" condition
J_3(m_1) J_0(m_2) + J_2(m_1) J_1(m_2) = 0

We are in the small modulation regime. i.e. J0(m) = 1, J1(m) = m/2, J2(m) = m2/8, J3(m) = m3/48
Therefore we can simplify the above exitinction condition as

m_1 + 3 m_2 = 0

m2 < 0 means the start phase of the m2 modulation needs to be 180deg off from the phase of the m1 modulation.

E = E_0 \exp\left\{ {\rm i} [\Omega t + m_1 \cos \omega t + \frac{m_1}{3} \cos (5 \omega t + \pi)] \right \}

Field amplitude m1=0.3, m2=-0.1 m1=0.2, m2=0.2
Carrier 0.975 0.980
1st order sidebands 0.148 9.9e-2
2nd 1.1e-3 4.9e-3
3rd 3.5e-7 6.6e-4
4th 7.4e-3 9.9e-3
5th 4.9e-2 9.9e-2
6th 7.4e-3 9.9e-3
7th 5.6e-4 4.9e-4
8th 1.4e-5 4.1e-5
9th 1.9e-4 5.0e-4
10th 1.2e-3 4.9e-3
11th 1.9e-4 5.0e-4
12th 1.4e-5 2.5e-5
13th 4.7e-7 1.7e-6
14th 3.1e-6 1.7e-5
15th 2.0e-5 1.6e-4


  11007   Wed Feb 11 22:13:44 2015 JenneUpdateLSCNew Locking Paradigm - LSC model changes

In order to try out the new locking scheme tonight, I have modified the LSC model.  Screens have not yet been made.

It's a bit of a special case, so you must use the appropriate filter banks:

CARM filter bank should be used for ALS lock.  MC filter bank should be used for the REFL1f signal. 

The output of the MC filter bank is fed to a new filter bank (C1:LSC-MC_CTRL_FF).  The output of this new filter bank is summed with the error point of the CARM filter bank (after the CARM triggered switch).

The MC triggering situation is now a little more sophisticated than it was.  The old trigger is still there (which will be used for something like indicating when the REFL DC has dipped).  That trigger is now AND-ed with a new zero crossing trigger, to make the final trigger decision.  For the zero crossing triggering, there is a small matrix (C1:LSC-ZERO_CROSS_MTRX) to choose what REFL 1f signal you'd like to use (in order, REFL11I, REFL11Q, REFL55I, REFL55Q).  The absolute value of this is compared to a threshold, which is set with the epics value C1:LSC-ZERO_CROSS_THRESH.  So, if the absolute value of your chosen RF signal is lower than the threshold, this outputs a 1, which is AND-ed by the usual schmidt trigger. 

At this moment, the input and output switches of the new filter bank are off, and the gain is set to zero.  Also, the zero crossing selection matrix is all zeros, and the threshold is set to 1e9, so it is always triggered, which means that effectively MC filter bank just has it's usual, old triggering situation.

  11008   Thu Feb 12 01:00:18 2015 ranaUpdateLSCRFPD spectra

The nonlinearity in the LSC detection chain (cf T050268) comes from the photodetector and not the demod board. The demod board has low pass or band pass filters which Suresh installed a long time ago (we should check out what's in REFL33 demod board). 

Inside the photodetector the nonlinearity comes about because of photodiode bias modulation (aka the Grote effect) and slew rate limited distortion in the MAX4107 preamp.

  11009   Thu Feb 12 01:43:09 2015 ranaUpdateLSCNew Locking Paradigm - LSC model changes

With the Y Arm locked, we checked that we indeed can get loop decoupling using this technique.

The guess filter that we plugged in is a complex pole pair at 1 Hz. We guessed that the DC gain should be ~4.5 nm count. We then converted this number into Hz and then into deg(?) using some of Jenne's secret numbers. Then after measuring, we had to increase this number by 14.3 dB to an overall filter module gain of +9.3.

The RED trace is the usual 'open loop gain' measurement we make, but this time just on the LSC-MC path (which is the POY11_I -> ETMY path).

The BLUE trace is the TF between the ALS-Y phase tracker output and the FF cancellation signal. We want this to be equal ideally.

The GREEN trace is after the summing point of the ALS and the FF. So this would go to zero when the cancellation is perfect.

So, not bad for a first try. Looks like its good at DC and worse near the red loop UGF. It doesn't change much if I turn off the ALS loop (which I was running with ~10-15x lower than nominal gain just to keep it out of the picture). We need Jenne to think about the loop algebra a little more and give us our next filter shape iteration and then we should be good.

Attachment 1: TF.gif
TF.gif TF.gif TF.gif TF.gif TF.gif TF.gif TF.gif TF.gif TF.gif TF.gif TF.gif TF.gif TF.gif TF.gif TF.gif TF.gif TF.gif TF.gif TF.gif TF.gif TF.gif TF.gif TF.gif TF.gif TF.gif TF.gif
  11010   Thu Feb 12 03:43:54 2015 ericqUpdateLSC3F PRMI at zero ALS CARM

I have been able to recover the ability to sit at zero CARM offset while the PRMI is locked on RELF33 and CARM/DARM are on ALS, effectively indefinitely. However, I feel like the transmon QPDs are not behaving ideally, because the reported arm powers freqently go negative as the interferometer is "buzzing" through resonance, so I'm not sure how useful they'll be as normalizing signals for REFL11. I tried tweaking the DARM offset to help the buildup, since ALS is only roughly centered on zero for both CARM and DARM, but didn't have much luck.


Turning off the whitening on the QPD segments seems to make everything saturate, so some thinking with daytime brain is in order.

How I got there:

It turns out triggering is more important than the phase margin story I had been telling myself. Also, I lost a lot of time to needing demod angle change in REFL33. Maybe I somehow caused this when I was all up on the LSC rack today?

We have previously put TRX and TRY triggering elements into the PRCL and MICH rows, to guard against temporary POP22 dips, because if arm powers are greater than 1, power recylcing is happening, so we should keep the loops engaged. However, since TRX and TRY are going negative when we buzz back and forth through the resonsnace, the trigger row sums to a negative value, and the PRMI loops give up. 

Instead, we can used the fortuitously unwhitened POPDC, which can serve the same function, and does not have the tendancy to go negative. Once I enabled this, I was able to just sit there as the IFO angrily buzzed at me. 

Here are my PRMI settings

REFL33 - Rotation 140.2 Degrees, -89.794 measured diff

PRCL = 1 x REFL33 I; G = -0.03; Acquire FMs 4,5; Trigger FMs 2, 9; Limit: 15k ; Acutate 1 x PRM

MICH = 1 x REFL33 Q, G= 3.0, Acquire FMs 4,5,8; Trigger FM 2, 3; Limit: 30k; Actuate -0.2625 x PRM + 0.5 x BS

Triggers = 1 x POP22 I + 0.1 * POPDC, 50 up 5 down

Just for kicks, here's a video of the buzzing as experienced in the control room

Attachment 1: Feb12_negativeTR.png
  11011   Thu Feb 12 11:14:29 2015 JenneUpdateLSCNew Locking Paradigm - Loop-gebra

I have calculated the response of this new 2.5 loop system.

The first attachment is my block diagram of the system.  In the bottom left corner are the one-hop responses from each green-colored point to the next.  I use the same matrix formalism that we use for Optickle, which Rana described in the loop-ology context in http://nodus.ligo.caltech.edu:8080/40m/10899

In the bottom right corner is the closed loop response of the whole system.


Also attached is a zipped version of the mathematica notebook used to do the calculation.

EDIT, JCD, 17Feb2015:  Updated loop diagram and calculation:

Attachment 1: ALS_REFL_comboLockingCartoon_11Feb2015.PDF
Attachment 2: ALS_REFL_comboLocking_11Feb2015.zip
  11012   Thu Feb 12 11:59:58 2015 KojiUpdateLSCNew Locking Paradigm - Loop-gebra

The goals are:

- When the REFL path is dead (e.g. S_REFL = 0), the system goes back to the ordinary ALS loop. => True (Good)

- When the REFL path is working, the system becomes insensityve to the ALS loop
(i.e. The ALS loop is inactivated without turning off the loop.) => True when (...) = 0

Are they correct?


Then I just repeat the same question as yesterday:

S is a constant, and Ps are cavity poles. So,  approximately to say, (...) = 0 is realized by making D = 1/G_REFL.
In fact, if we tap the D-path before the G_REFL, we remove this G_REFL from (...). (=simpler)
But then, this means that the method is rather cancellation between the error signals than
cancellation between the actuation. Is this intuitively reasonable? Or my goal above is wrong?

  11016   Thu Feb 12 19:18:49 2015 JenneUpdateLSCNew Locking Paradigm - Loop-gebra

EDIT, JCD, 17Feb2015:  Updated loop diagram and calculation:

Okay, Koji and I talked (after he talked to Rana), and I re-looked at the original cartoon from when Rana and I were thinking about this the other day.

The original idea was to be able to actuate on the MC frequency (using REFL as the sensor), without affecting the ALS loop.  Since actuating on the MC will move the PSL frequency around, we need to tell the ALS error signal how much the PSL moved in order to subtract away this effect. (In reality, it doesn't matter if we're actuating on the MC or the ETMs, but it's easier for me to think about this way around).  This means that we want to be able to actuate from point 10 in the diagram, and not feel anything at point 4 in the diagram (diagram from

This is the same as saying that we wanted the green trace in to be zero.

So.  What is the total TF from 10 to 4? 

{\rm TF}_{\rm (10 \ to \ 4)} = \frac{D_{\rm cpl} + {\color{DarkRed} A_{\rm refl}} {\color{DarkGreen} P_{\rm als}}}{1-{\color{DarkRed} A_{\rm refl} G_{\rm refl} S_{\rm refl} P_{\rm refl}} - {\color{DarkGreen} A_{\rm als} G_{\rm als} S_{\rm als}} ({\color{DarkGreen} P_{\rm als}} + D_{\rm cpl} {\color{DarkRed} G_{\rm refl} P_{\rm refl} S_{\rm refl}})}

So, to set this equal to zero (ALS is immune to any REFL loop actuation), we need D_{\rm cpl} = - {\color{DarkRed} A_{\rm refl}} {\color{DarkGreen} P_{\rm als}}.

Next up, we want to see what this means for the closed loop gain of the whole system.  For simplicity, let's let H_* = A_* G_* S_* P_*, where * can be either REFL or ALS. 

Recall that the closed loop gain of the system (from point 1 to point 2)  is

{\rm TF}_{\rm (1 \ to \ 2)} = \frac{1}{1-{\color{DarkRed} A_{\rm refl} G_{\rm refl} S_{\rm refl} P_{\rm refl}} - {\color{DarkGreen} A_{\rm als} G_{\rm als} S_{\rm als}} ({\color{DarkGreen} P_{\rm als}} + D_{\rm cpl} {\color{DarkRed} G_{\rm refl} P_{\rm refl} S_{\rm refl}})} , so if we let  D_{\rm cpl} = - {\color{DarkRed} A_{\rm refl}} {\color{DarkGreen} P_{\rm als}} and simplify, we get

{\rm TF}_{\rm (1 \ to \ 2)} = \frac{1}{1-{\color{DarkRed} H_{\rm refl}} - {\color{DarkGreen} H_{\rm als}} + {\color{DarkRed} H_{\rm refl}}{\color{DarkGreen} H_{\rm als}}}

This seems a little scary, in that maybe we have to be careful about keeping the system stable.  Hmmmm.  Note to self:  more brain energy here.

Also, this means that I cannot explain why the filter wasn't working last night, with the guess of a complex pole pair at 1Hz for the MC actuator.  The  ALS plant has a cavity pole at ~80kHz, so for our purposes is totally flat.  The only other thing that comes to mind is the delays that exist because the ALS signals have to hop from computer to computer.  But, as Rana points out, this isn't really all that much phase delay below 100Hz where we want the cancellation to be awesome. 

I propose that we just measure and vectfit the transfer function that we need, since that seems less time consuming than iteratively tweaking and checking. 

Also, I just now looked at the wiki, and the MC2 suspension resonance for pos is at 0.97Hz, although I don't suspect that that will have changed anything significantly above a few Hz.  Maybe it makes the cancellation right near 1Hz a little worse, but not well above the resonance.


  11017   Thu Feb 12 22:28:16 2015 JenneUpdateLSCNew Locking Paradigm - LSC model changes, screens modified

I have modified the LSC trigger matrix screen, as well as the LSC overview screen, to reflect the modifications to the model from yesterday. 

Also, I decided that we probably won't ever want to trigger the zero crossing on the Q phase signals of REFL.  Instead, we may want to try it out with the single arms, so the zero crossing selection matrix is now REFL11I, REFL55I, POX11I, POY11I, in that order. 


  11019   Thu Feb 12 23:47:45 2015 KojiUpdateLSC3f modulation cancellation

- I built another beat setup on the PSL table at the South East side of the table.
- The main beam is not touched, no RF signal is touched, but recognize that I was present at the PSL table.
- The beat note is found. The 3rd order sideband was not seen so far.
- A PLL will be built tomorrow. The amplifier box Manasa made will be inspected tomorrow.

- One of the two beams from the picked-off beam from the main beam line was introduced to the beat setup.
(The other beam is used of for the beam pointing monitors)
There is another laser at that corner and the output from this beam is introduced into the beat setup.
The combined beam is introduced to PDA10CF (~150MHz BW).

- The matching of the beam there is poor. But without much effort I found the beat note.
  The PSL laser had 31.33 deg Xtal temp. When the beat was found, the aux laser had the Xtal temp of 40.88.

- I could observe the sidebands easily, with a narrower BW of the RF analizer I could see the sidebands up to the 2nd order.
  The 3rd order was not seen at all.

- The beat note had the amplitude of about -30dBm. One possibility is to amplify the signal. I wanted to use a spare channel
of the ALS/FOLL amplifier box. But it gave me rather attenuation than any amplification.
I'll look at the box tomorrow.

- Also the matching of two beams are not great. The PD also has clipping I guess. These will also be improved tomorrow

- Then the beat note will be locked at a certain frequency using PLL so that we can reduce the measurement BW more.


  11020   Fri Feb 13 03:28:34 2015 ranaUpdateLSCNew Locking Paradigm - Loop-gebra

Not so fast!

In the drawing, the FF path should actually be summed in after the Phase Tracker (i.e. after S_ALS). This means that the slow response of the phase tracker needs to be taken into account in the FF cancellation filter. i.e. D = -A_REFL * P_ALS * S_ALS. Since the Phase Tracker is a 1/f loop with a 1 kHz UGF, at 100 Hz, we can only get a cancellation factor of ~10.

So, tonight we added a 666:55 boost filter into the phase tracker filter bank. I think this might even make the ALS locking loops less laggy. The boost is made to give us better tracking below ~200 Hz where we want better phase performance in the ALS and more cancellation of the ALS-Fool. If it seems to work out well we can keep it. If it makes ALS more buggy, we can just shut it off.

Its time to take this loop cartoon into OmniGraffle.

  11021   Fri Feb 13 03:44:56 2015 JenneUpdateLSCHeld using ALS for a while at "0" CARM offset with PRMI

[Jenne, Rana]

We wanted to jump right in and see if we were ready to try the new "ALS fool" loop decoupling scheme, so we spent some time with CARM and DARM at "0" offset, held on ALS, with PRMI locked on REFL33I&Q (no offsets).  Spoiler alert:  we weren't ready for the jump.

The REFL11 and AS55 PDs had 0dB analog whitening, which means that we weren't well-matching our noise levels between the PD noise and the ADC noise.  The photodiodes have something of the order nanovolt level noise, while the ADC has something of the order microvolt level noise.  So, we expect to need an analog gain of 1000 somewhere, to make these match up.  Anyhow, we have set both REFL11 and AS55 to 18dB gain. 

On a related note, it seems not so great for the POX and POY ADC channels to be constantly saturated when we have some recycling gain, so we turned their analog gains down from 45dB to 0dB.  After we finished with full IFO locking, they were returned to their nominal 45dB levels. 

We also checked the REFL33 demod phase at a variety of CARM offsets, and we see that perhaps it changes by one or two degrees for optimal rotation, but it's not changing drastically.  So, we can set the REFL33 demod phase at large CARM offset, and trust it at small CARM offset.

We then had a look at the transmon QPD inputs (before the dewhitening) for each quadrant.  They are super-duper saturating, which is not so excellent. 

We think that we want to undo the permanently-on whitening situation.  We want to make the second stage of whitening back to being switchable.  This means taking out the little u-shaped wires that are pulling the logic input of the switches to ground.  We think that we should be okay with one always on, and one switchable.  After the modification, we must check to make sure that the switching behaves as expected.  Also, I need to figure out what the current situation is for the end QPDs, and make sure that the DCC document tree matches reality.  In particular, the Yend DCC leaf doesn't include the gain changes, and the Xend leaf which does show those changes has the wrong value for the gain resistor.

After this, we started re-looking at the single arm cancellation, as Rana elogged about separately.


Attachment 1: QPDsaturation_12Feb2015.pdf
Attachment 2: ALSfool_12Feb2015.pdf
  11028   Sat Feb 14 00:48:13 2015 KojiUpdateLSC3f modulation cancellation

[SUCCESS] The 3f sideband cancellation seemed worked nicely.

- Beat effeciency improved: ~30% contrast (no need for amplification)

- PLL locked

- 3f modulation sideband was seen

- The attenuation of the 55MHz modulation and the delay time between the modulation source was adjusted to
have maximum reduction of the 3f sidebands as much as allowed in the setup. This adjustment has been done
at the frequency generation box at 1X2 rack.

- The measurement and receipe for the sideband cancellation come later.

- This means that I jiggled the modulation setup at 1X2 rack. Now the modulation setup was reverted to the original,
but just be careful to any change of the sensing behavior.

- The RF analyzer was returned to the control room.

- The HEPA speed was reduced from 100% (during the action on the table) to 40%.

  11029   Sat Feb 14 19:54:04 2015 KojiSummaryLSC3f modulation cancellation

Optical Setup

[Attachment 1]

Right before the PSL beam goes into the vacuum chamber, it goes through an AR-wedged plate.
This AR plate produces two beams. One of them is for the IO beam angle/position monitor.
And the other was usually dumped. I decided to use this beam.

A G&H mirror reflects the beam towards the edge of the table.
A 45deg HR mirror brings this beam to the beat set up at the south side of the table.
This beam is S-polarlized as it directly comes from the EOM.

[Attachment 2]

The beam from the PSL goes through a HWP and some matching lenses before the combining beam splitter (50% 45deg P).
The AUX laser beam is attenuated by a HWP and a PBS. The transmitted beam from the PBS is supposed
to have P-polarization. The beam alignment is usually done at the PSL beam side.

The combined beam is steered by a HR mirror and introduced to Thorlabs PDA10CF. As the PD has small diameter
of 0.5mm, the beam needed to be focused by a strong lens.

After careful adjustment of the beam mode matching, polarization, and alignment, the beatnote was ~1Vpp for 2.5Vdc.
In the end, I reduced the AUX laser power such that the beat amplitude went down to ~0.18Vpp (-11dBm at the PD,
-18dBm at the mixer, -27dBm at the spectrum analyzer) in order to minimize nonlinearity of the RF system and
in order that the spectrum analyzer didn't need input attenuation.

Electrical Setup

[Attachment 3]

The PD signal is mixed with a local oscillator signal at 95MHz, and then used to lock the PLL loop.
The PLL loop allows us to observe the peaks with more integration time, and thus with a better signal-to-noise ratio.

The signal from the PD output goes through a DC block, then 6dB attenuator. This attenuator is added to damp reflection
and distortion between the PD and the mixer. When the PLL is locked, the dominant signal is the one at 95MHz. Without this attenuator,
this strong 95MHz signal cause harmonic distortions like 190MHz. As a result, it causes series of spurious peaks at 190MHz +/- n* 11MHz.

10dB coupler is used to peep the PD signal without much disturbing the main line. Considering we have 6dB attanuator,
we can use this coupler output for the PLL and can use the main line for the RF monitor, next time.

The mixer takes the PD signal and the LO signal from Marconi. Marconi is set to have +7dBm output at 95MHz.
FOr the image rejection, SLP1.9 was used. The minicirsuit filters have high-Z at the stop band, we need a 50Ohm temrinator
between the mixer and the LPF.

The error signal from the LPF is fed to SR560 (G=+500, 1Hz 1st-order LPF). I still don't understand why I had to use a LPF
for the locking.
As the NPRO PZT is a frequency actuator, and the PLL is sensitive to the phase, we are supposed to use
a flat response for PLL locking. But it didn't work. Once we check the open loop TF of the system, it will become obvious (but I didn't).

The actuation signal is fed to the fast PZT input of the AUX NPRO laser.

Attachment 1: beat_setup1.JPG
Attachment 2: beat_setup2.JPG
Attachment 3: electrical_setup.pdf
  11030   Sat Feb 14 20:20:24 2015 JenneUpdateLSCALS fool cartoon

The ALS fool scheme is now diagrammed up in OmniGraffle, including its new official icon.  The mathematica notebook has not yet been updated.

EDIT, JCD, 17Feb2015:  Updated cartoon and calculation:


Attachment 1: ALSfool_LoopDiagram.png
Attachment 2: ALSfool_LoopDiagram.graffle.zip
  11031   Sat Feb 14 20:37:51 2015 KojiSummaryLSC3f modulation cancellation

Experimental results

- PD response [Attachment 1]

The AUX laser temperature was swept along with the note by Annalisa [http://nodus.ligo.caltech.edu:8080/40m/8369]
It is easier to observe the beat note by closing the PSL shutter as the MC locking yields more fluctuation of the PSL
laser freuqency at low frequency. Once I got the beat note and maximized it, I immediately noticed that the PD response
is not flat. For the next trial, we should use Newfocus 1611. For the measurement today, I decided to characterize the
response by sweeping the beat frequency and use the MAXHOLD function of the spectrum analyzer.

The measured and modelled response of the PD are shown in the attachment 1. It has non-intuitive shape.
Therefore the response is first modelled by two complex pole pair at 127.5MHz with Q of 1, and then the residual was
empirically fitted with 29th polynomial of f.

- Modulation profile of the nominal setting [Attachment 2]

Now the spectrum of the PD output was measured. This is a stiched data of the spectrum between 1~101MHz and 99~199MHz
that was almost simultaneously measured (i.e. Display 1 and Display 2). The IF bandwidth was 1kHz. The PD response correction
described above was applied.

It obviously had the peaks associated with our main modulations. In addition, there are more peaks seen.
The attachment 2 breaks down what is causing the peaks.

  • Carrier: The PLL LO frequency is 95MHz. Therefore the carrier is locked at 95MHz.
  • Modulation sidebands (11/55MHz series):
    Series of sidebands are seen at the both side of the carrier. Their frequency is 95MHz +/- n * fmod  (fmod = 11.066128MHz).
    Note that the sidebands for n>10 were above 200MHz, and n<-9 (indicated in gray) were folded at 0Hz.
    With this measurement BW, the following sidebands were buried in the noise floor.
    n = -8, -12, -13, and -14, n<= -16, and n>=+7
  • Modulation sidebands for IMC and PMC (29.5MHz and 35.5MHz):
    First order sidebands for the IMC and PMC modulations of sidebands are seen at the both side of the carrier.
    Their frequency is 95MHz +/- 29.5MHz or 33.5MHz. The PMC modulation sidebands are supposed to be blocked
    by the PMC. However, due to finite finesse of the PMC, small fraction of the PMC sidebands are transmitted.
    In deed, it is comparable to the modulation depth of the IMC one.
  • RF AM or RF EMI for the main modulation and the IMC modulationand:
    If there is residual RF AM in the PSL beam associated with the IMC and main modulations, it appears as the
    peaks at the modulation frequency and its harmonics. Also EM radiation couples into this measument RF system
    also appears at these frequencies. They are seen at n * fmod  (n=1,2,4,5) and 29.5MHz.
  • Reflection/distortion or leakage from mixer IF to RF:
    The IF port of the mixer naturally has 190MHz signal when the PLL is locked. If the isolation from the IF port to the RF port
    is not enough, this signal can appear in the RF monitor signal via an imperfection of the coupler or a reflection from the PD.
    Also, if the reflecrtion/distortion exist between the PD and the mixer RF input, it also cause the signal around 190MHz.
    It is seen at 190MHz +/- n* fmod. In the plot, the peak at n=0, -1 are visible. In fact these peak were secondarily dominant
    in the spectrum when there was no 6dB attenuation in the PD line. WIth the attenuator, they are well damped and don't disturb
    the main measurment.

From the measured peak height, we are able to estimate the modulation depths for 11MHz, 55MHz, IMC modulations, as well as
the relative phase of the 11MHz and 55MHz modulation. (It is not yet done).

- 3f modulation reduction [Attachment 3]

Now, the redcution of the 3f modulation was tried. The measured modulation levels for the 11MHz and 55MHz were almost the same.
The calculation predicts that the modulation for the 55MHz needs to be 1/3 of the 11MHz one. Therefore the attenuation of 9dB and 10dB
of the modulation attenuation knob at the frequency generation box were tried.

To give the variable delay time in the 55MHz line, EG&G ORTEC delay line unit was used. This allows us to change the delay time from
0ns to 63.5ns with the resolution of 0.5ns. The frequency of 55MHz yields a phase sensitivity of ~20deg/ns (360deg/18ns).
Therefore we can adjust the phase with the precision of 10deg over 1275deg.

The 3rd-order peak at 61.8MHz was observed with measurement span of 1kHz with very narrow BW like 30Hz(? not so sure). The delay
time was swept while measuring the peak height each time. For both the atteuation, the peak height clearly showed the repeatitive dependence
with the period of 18ns, and the 10dB case gave the better result. The difference between the best (1.24e-7 Vpk) and the worst (2.63e-6 Vpk)
was more than a factor of 20.
The 3rd-order peak in the above broadband spectrum measurement was 6.38e-6 Vpk. Considering the attenuation
of the 55MHz modulation by 10dB, we were at the exact unluck phase difference.
The improvement expected from the 3f reduction (in the 33MHz signal)
will be about 50, assuming there is no other coupling mechanism from CARM to REFL33.

I decided to declare the best setting is "10dB attenuation & 28ns delay".

- Resulting modulation profile [Attachment 4]

As a confirmation, the modulation profie was measured as done before the adjustment.
It is clear that the 3rd-order modulation was buried in the floor noise. 10dB attenuation of the 55MHz modulation yields corresponding reduction of the sidebands.
This will impact the signal quality for the 55MHz series error signals, particularly 165MHz ones. We should consider to install the Teledyne Cougar amplifier
next to the EOM so that we can increase the over all modulation depth.

Attachment 1: beat_pd_response.pdf
Attachment 2: beat_nominal.pdf
Attachment 3: 3f_reduction.pdf
Attachment 4: beat_3f_reduced.pdf
  11032   Sat Feb 14 22:14:02 2015 KojiSummaryLSC[HOW TO] 3f modulation cancellation

When I finished my measurements, the modulation setup was reverted to the conventional one.
If someone wants to use the 3f cancellation setting, it can be done along with this HOW-TO.

The 3f cancellation can be realized by adding a carefully adjusted delay line and attenuation for the 55MHz modulation
on the frequency generation box at the 1X2 rack.  Here is the procedure:

1) Turn off the frequency generation box

There is a toggle switch at the rear of the unit. It's better to turn it off before any cable action.
The outputs of the frequency generation box are high in general. We don't want to operate
the amplifiers without proper impedance matching in any occasion.

2) Remove the small SMA cable between 55MHz out and 55MHz in (Left arrow in the attachment 1).

According to the photo by Alberto (svn: /docs/upgrade08/RFsystem/frequencyGenerationBox/photos/DSC_2410.JPG),
this 55MHz out is the output of the frequency multiplier. The 55MHz in is the input for the amplifier stages.
Therefore, the cable length between these two connectors changes the relative phase between the modulations at 11MHz and 55MHz.

3) Add a delay line box with cables (Attachment 2).

Connect the cables from the delay line box to the 55MHz in/out connectors. I used 1.5m BNC cables.
The delay line box was set to have 28ns delay.

4) Set the attenuation of the 55MHz EOM drive (Right arrow in the attachment 1) to be 10dB.

Rotate the attenuation for 55MHz EOM from 0dB nominal to 10dB.

5) Turn on the frequency modulation box

For reference, the 3rd attachment shows the characteristics of the delay line cable/box combo when the 3f modualtion reduction
was realized. It had 1.37dB attenuation and +124deg phase shift. This phase change corresponds to the time delay of 48ns.
Note that the response of a short cable used for the measurement has been calibrated out using the CAL function of the network analyzer.

Attachment 1: freq_gen_box.JPG
Attachment 2: delay_line.JPG
Attachment 3: cable_spec.pdf
  11033   Sun Feb 15 16:20:44 2015 KojiSummaryLSC[ELOG LIST] 3f modulation cancellation

Summary of the ELOGS

3f modulation cancellation theory http://nodus.ligo.caltech.edu:8080/40m/11005

3f modulation cancellation adjustment setup http://nodus.ligo.caltech.edu:8080/40m/11029

Experiment http://nodus.ligo.caltech.edu:8080/40m/11031

Receipe for the 3f modulation cancellation http://nodus.ligo.caltech.edu:8080/40m/11032

Modulation depth analysis http://nodus.ligo.caltech.edu:8080/40m/11036

  11034   Sun Feb 15 20:55:48 2015 ranaSummaryLSC[ELOG LIST] 3f modulation cancellation

I wonder if DRMI can be locked on 3f using this lower 55 MHz modulation depth. It seems that PRMI should be unaffected, but that the 3*f2 signals for SRCL will be too puny. Is it really possible to scale up the overall modulation depths by 3x to compensate for this?

  11035   Mon Feb 16 00:08:44 2015 KojiSummaryLSC[ELOG LIST] 3f modulation cancellation

This KTP crystal has the maximum allowed RF power of 10W (=32Vpk) and V_pi = 230V. This corresponds to the maximum allowed
modulation depth of 32*Pi/230 = 0.44. So we probably can achieve gamma_1 of ~0.4 and gamma_2 of ~0.13. That's not x3 but x2,
so sounds not too bad.

Then Kiwamu's triple resonant circuit LIGO-G1000297-v1 actually shows the modulation up to ~0.7. Therefore it is purely an issue
how to deliver sufficient modulation power. (In fact his measurement shows some nonlinearity above the modulation depth of ~0.4
so we should keep the maximum power consumption of 10W at the crystal)

This means that we need to review our RF system (again!)

- Review infamous crazy attn/amp combinations in the frequency generation box.
- Use Teledyne Cougar ampilfier (A2CP2596) right before the triple resonant box. This should be installed closely to the triple resonant box in order to
minimize the effects of the reflection due to imperferct impedance matching.
- Review and refine the triple resonant circuit - it's not built on a PCB but on a universal board. I think that we don't need triple
resonance, but double is OK as the 29.5MHz signal is small.

We want +28V supply at 1X1 for the Teledyne amp and the AOM driver. Do we have any unused Sorensen?

  11036   Mon Feb 16 01:45:12 2015 KojiSummaryLSCmodulation depth analysis

Based on the measured modulation profiles, the depth of each modulation was estimated.
Least square sum minimization of the relative error was used for the cost function.
-8th, -12th~-14th, n=>7th are not included in the estimation for the nominal case.
-7th~-9th, -11th~-15th, n=>7th are not included in the estimation for the 3f reduced case.

Nominal modulation

m_f1 = 0.194
m_f2 = 0.234
theta_f1f2 = 41.35deg
m_IMC = 0.00153

3f reduced modulation

m_f1 = 0.191
m_f2 = 0.0579
theta_f1f2 = 180deg
m_IMC = 0.00149

(Sorry! There is no error bars. The data have too few statistics...)

Attachment 1: modulation_nominal.pdf
Attachment 2: modulation_3f_reduced.pdf
  11037   Mon Feb 16 02:49:57 2015 JenneUpdateLSCALS fool measured decoupling TF

I have measured very, very carefully the transfer function from pushing on MC2 to the Yarm ALS beatnote.  In the newest loop diagram in http://nodus.ligo.caltech.edu:8080/40m/11030, this is pushing at point 10 and sensing at point 4. 

Since it's a bunch of different transfer functions (to get the high coherence that we need for good cancellation to be possible), I attach my Matlab figure that includes only the useful data points.  I put a coherence cutoff of 0.99, so that (assuming the fit were perfect, which it won't be), we would be able to get a maximum cancellation of a factor of 100. 

This plot also includes the vectfit to the data, which you can see is pretty good, although I need to separately plot the residuals (since the magnitude data is so small, the residuals for the mag don't show up in the auto plot that vectfit gives). 

If you recall from http://nodus.ligo.caltech.edu:8080/40m/11020, we are expecting this transfer function to consist of the suspension actuator (pendulum with complex pole pair around 1Hz), the ALS plant (single pole at 80kHz) and the ALS sensor shape (the phase tracker is an integrator, with a boost consisting of a zero at 666Hz and a pole at 55Hz).  That expected transfer function does not multiply up to give me this wonky shape.  Brain power is needed here.

Just in case you were wondering if this depends on the actuator used (ETM vs MC2), or IFO configuration (single arm vs. PRFPMI), it doesn't.  The only discrepancy between these transfer functions is the expected sign flip between the MC2 and ETMY actuators.  So, they're all pretty consistent. 

Before locking the PRFPMI, I copied the boost filter (666:55) from the YARM ALS over to Xarm ALS, so now both arms have the same boost.


Things to do for ALSfool:

  • Put fitted TF into the MC_CTRL_FF filter bank, and try to measure the expected cancellation, a la http://nodus.ligo.caltech.edu:8080/40m/11009
  • Quick test with single arm, ALS locked using full loop (high gain, all boosts), since the previous versions were with ALS very loosely locked.
    • Does this measured transfer function actually give us good cancellation? 
  • Think.  Why should the transfer function look like this??
  • Try it on the full PRFPMI
Attachment 1: ALSfool_measuredActuatorTF_YarmOnly_15Feb2015.png
Attachment 2: YARM_actTF_compareActuators.pdf
  11038   Mon Feb 16 03:10:42 2015 KojiUpdateLSCALS fool measured decoupling TF

Wonkey shape: Looks like a loop supression. Your http://nodus.ligo.caltech.edu:8080/40m/11016 also suggests it too, doesn't it?

  11039   Mon Feb 16 15:08:26 2015 JenneUpdateLSCALS fool measured decoupling TF

Dang it, yes. You're right.  I should have caught that. 

Since Dcpl and Srefl are both zero during the measurement (since it was an ALS lock), this is actually

\frac{{\color{DarkRed} A_{\rm refl}} {\color{DarkGreen} P_{\rm als} S_{\rm als}}}{1 - {\color{DarkGreen} A_{\rm als} G_{\rm als} S_{\rm als} P_{\rm als}}}

So, I need to remove the effect of the ALS closed loop, to get the actual quantity I was looking for.

  11041   Tue Feb 17 00:24:47 2015 rana, jenneUpdateLSCALS Fool filter updated for more cancellation

Today we measured the TFs again and then updated the filter in the POY -> ALS FF path so as to get 10x better cancellation.

The cancellation went from ~10 dB to ~30 dB. This seems good enough. The new filter 'Comp1' is just constructed by eye. We then had to tune the filter module gain to a few %. Seems good enough for now, but we should really try to understand what it is and why it is the way that it is. In the above plot, the ORANGE trace is the old cancellation and the GREEN one is the new one. The filter TF is attached below - its not special, we made it by presing buttons in FOTON until the TF matched the measured TF of ALSY/LSC-MC_CTRL_FF_OUT.

Attachment 1: ALSfoo_150216.png
Attachment 2: 15.png
  11042   Tue Feb 17 04:04:32 2015 JenneUpdateLSCALS fool math

I re-did the Mathematica notebook according to the most current diagram (note to daytime self: attach .nb file!!!), and found that the denominator has changed, such that plugging in the new D=-A_refl*P_als*S_als gives the same

full-system closed loop gain of    \frac{1}{1-H_{\rm als} - H_{\rm refl} + H_{\rm als}H_{\rm refl}}

where H_{*} = A_* G_* S_* P_*  is the open loop gain, and the * indicates either the REFL or ALS portions of the system. 

I have also plotted some things with Matlab, although I'm a little confused, and my daytime self needs to spend some more time thinking about this.

In the actuators (both for REFL and ALS), I include a pendulum, the digital anti-imaging filters that let us go from the 16kHz model to the 64kHz IOP and the analog anti-imaging filters after the DAC.  Note to self:  still need to include violin filters here.

For the servo gains, I copy the filters that we are using from Foton, and give them the same overall gain multiplier that is in the filter bank.  For the ALS going through the CARM filter bank, this is FMs 1, 2, 3, 5, 6 with a gain of 15.  For the RF (actually, POY here) going through the MC filter bank, this is FMs 4, 5, 7 with a gain of 0.08. 

For the plants of each system, since this is still single arm lock, I just include a cavity pole (80kHz for ALS, 18kHz for REFL). 

In the sensors (both for REFL and ALS), I include the analog anti-aliasing as well as the digital anti-aliasing to allow us to go from the 64kHz IOP to the 16kHz front end system.  For the ALS I also include in the sensor the closed loop response of the phase tracker loop (H/(1-H), where H is the open loop gain of the phase tracker).  For both sensors, I also include a semi-arbitrary number to make the full single-loop open loop gain have a UGF of 200Hz.  In the ALS sensor, I also include a minus sign to make the full open loop gain have the correct phase.

Here I plot the open loop gains of the individual single loops, as well as the open loop gain of the full system (Hals + Hrefl - Hals*Hrefl).  I feel like I must be missing a minus sign in my ALS loop, but I don't know where, and my nighttime brain doesn't want to just throw in minus signs without knowing why.  That will affect how the final ALSfool (blue trace) looks, so maybe it's not really as crazy as it looks right now.

Also, I was trying to explain to myself why we are getting the shape that we are in our measurements of the cancellation (http://nodus.ligo.caltech.edu:8080/40m/11041).  But, I can't.  Below are the plots of the transfer functions from either point 9 or 10 (before or after the G_refl) to point 5, which is the ALS error point.  The measurement in elog 11041 should correspond to the blue trace here.  For these traces, the decoupling is set to just (-A_refl), although there aren't any noticeable changes in the shape if I just set D=0.  If we start with the assumption that D=0, the shape and magnitude are basically identical to this plot, and then as we make D=-A_refl P_als S_als, the transfer functions both go to zero. 

So.  Why is it that with no decoupling, the transfer function from 10 to 5 is tiny?  Why do the shapes plotted below look nothing at all like the measured cancellation shape?  Daytime brain needs to think some more.

Attachment 1: OpenLoopGainComparison_16Feb2015.png
Attachment 2: CancellationTFs_DecouplingIsArefl.png
ELOG V3.1.3-