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  16587   Fri Jan 14 13:46:25 2022 AnchalUpdateBHDPR2 transmission calculation updated

I updated the arm cavity roundtrip losses due to scattering. Yehonathan told me that arm cavity looses 50ppm every roundtrip other than the transmission losses. With the updated arm cavity loss:

  PRFPMI LO Power (mW) Unlocked PRC LO Power (uW) PRC Gain
pre-2010 ITM 8 28 15.2
V6:704 24 113 12


Attachment 1: LO_power_vs_PR2_transmission.pdf
Attachment 2: PRC_Gain_vs_PR2_transmission.pdf
Attachment 3: PR2_Trans_Calc.ipynb.zip
  16598   Wed Jan 19 16:22:48 2022 AnchalUpdateBHDPR2 transmission calculation updated

I have further updated my calculation. Please find the results in the attached pdf.

Following is the description of calculations done:

Arm cavity reflection:

Reflection fro arm cavity is calculated as simple FP cavity reflection formula while absorbing all round trip cavity scattering losses (between 50 ppm to 200 ppm) into the ETM transmission loss.

So effective reflection of ETM is calculated as

r_{\rm ETMeff} = \sqrt{1 - T_{\rm ETM} - L_{\rm RT}}

r_{\rm arm} = \frac{-r_{\rm ITM} + r_{\rm ETMeff}e^{2i \omega L/c}}{1 - r_{\rm ITM} r_{\rm ETMeff}e^{2 i \omega L/c}}

The magnitude and phase of this reflection is plotted in page 1 with respect to different round trip loss and deviation of cavity length from resonance. Note that the arm round trip loss does not affect the sign of the reflection from cavity, at least in the range of values taken here.

PRC Gain

The Michelson in PRFPMI is assumed to be perfectly aligned so that one end of PRC cavity is taken as the arm cavity reflection calculated above at resonance. The other end of the cavity is calculated as a single mirror of effective transmission that of PRM, 2 times PR2 and 2 times PR3. Then effective reflectivity of PRM is calculated as:

r_{\rm PRMeff} = \sqrt{1 - T_{\rm PRM} - 2T_{\rm PR2} - 2T_{\rm PR3}}

t_{\rm PRM} = \sqrt{T_{\rm PRM}}

Note, that field transmission of PRM is calculated with original PRM power transmission value, so that the PR2, PR3 transmission losses do not increase field transmission of PRM in our calculations. Then the field gain is calculated inside the PRC using the following:

g = \frac{t_{\rm PRM}}{1 - r_{\rm PRMeff} r_{\rm arm}e^{2 i \omega L/c}}

From this, the power recycling cavity gain is calculated as:
G_{\rm PRC} = |g|^2

The variation of PRC Gain is showed on page 2 wrt arm cavity round trip losses and PR2 transmission. Note that gain value of 40 is calculated for any PR2 transmission below 1000 ppm. The black verticle lines show the optics whose transmission was measured. If V6-704 is used, PRC Gain would vary between 15 and 10 depending on the arm cavity losses. With pre-2010 ITM, PRC Gain would vary between 30 and 15.

LO Power

LO power when PRFPMI is locked is calculated by assuming 1 W of input power to IMC. IMC is assumed to let pass 10% of the power (L_{\rm IMC}=0.1). This power is then multiplied by PRC Gain and transmitted through the PR2 to calculate the LO power.

P_{\rm LO, PRFPMI} = P_{\rm in} L_{\rm IMC}G_{\rm PRC}T_{\rm PR2}

Page 3 shows the result of this calculation. Note for V6-704, LO power would be between 35mW and 15 mW, for pre-2010 ITM, it would be between 15 mW and 5 mW depending on the arm cavity losses.

The power available during alignment is simply given by:
P_{\rm LO, align, PRM} = P_{\rm in} L_{\rm IMC} T_{\rm PRM} T_{\rm PR2}

P_{\rm LO, align, no PRM} = P_{\rm in} L_{\rm IMC} T_{\rm PR2}

If we remove PRM from the input path, we would have sufficient light to work with for both relevant optics.

I have attached the notebook used to do these calculations. Please let me know if you find any mistake in this calculation.

Attachment 1: PR2transmissionSelectionAnalysis.pdf
PR2transmissionSelectionAnalysis.pdf PR2transmissionSelectionAnalysis.pdf PR2transmissionSelectionAnalysis.pdf PR2transmissionSelectionAnalysis.pdf
Attachment 2: PR2_Trans_Calc.ipynb.zip
  16602   Thu Jan 20 01:48:02 2022 KojiUpdateBHDPR2 transmission calculation updated

IMC is not such lossy. IMC output is supposed to be ~1W.

The critical coupling condition is G_PRC = 1/T_PRM = 17.7. If we really have L_arm = 50ppm, we will be very close to the critical coupling. Maybe we are OK if we have such condition as our testing time would be much longer in PRMI than PRFPMI at the first phase. If the arm loss turned out to be higher, we'll be saved by falling to undercoupling.
When the PRC is close to the critical coupling (like 50ppm case), we roughly have Tprc x 2 and Tarm to be almost equal. So each beam will have 1/3 of the input power i.e. ~300mW. That's probably too much even for the two OMCs (i.e. 4 DCPDs). That's OK. We can reduce the input power by 3~5.


LO Power

LO power when PRFPMI is locked is calculated by assuming 1 W of input power to IMC. IMC is assumed to let pass 10% of the power (L_{\rm IMC}=0.1).


  8049   Fri Feb 8 23:59:42 2013 yutaUpdateLockingPR2-flipped half-PRC mode scan

I did mode scan of PR2-flipped half-PRC to see if it behaves as we expect.
Measured finesse was 107 +/- 5 and g-factor is 0.98997 +/- 0.00006.
g-factor is 0.9800 +/- 0.0001.  (Edited by YM; see elog #8056)

Finesse tells you that we didn't get large loss from flipped PR2.
Since we have convex TM in front of BS, PRC will be more stable than this half-PRC.

 1. Aligned half-PRC using input TT1 and TT2 by maximizing POP DC during lock. It was not so easy because POP DC fluctuates much at ~ 3 Hz with amplitude of ~ 30 % of the maximum value because of the beam motion (movie on  elog #8039).

 2. Unlocked half-PRC and took POP DC and PRC error signal data;

> /opt/rtcds/caltech/c1/scripts/general/getdata -d 1 -o /users/yuta/scripts/PRCmodescan C1:LSC-POPDC_OUT C1:LSC-REFL11_I_ERR

  Ran again and again until I get sufficiently linear swing through upper/lower sidebands.

 3. Ran modescan analyzing scripts (elog #8012).

 Below is the plot of POP DC and PRCL error signal (REFL11_I).

 By averaging 5 sets of peaks around TEM00;

Time between TEM00 and sideband  0.0347989  pm  0.00292257322372  sec
Calibration factor is  317.995971137  pm  26.7067783894  MHz/sec
FSR is  34.5383016129  MHz
FWHM is  0.323979022488  pm  0.0145486106353  MHz
TMS is  1.55827297374  pm  0.00439737672808  MHz
Finesse is  106.606598624  pm  4.78727876459
Cavity g-factor is  0.989971692098  pm  5.65040851566e-05
Cavity g-factor is  0.980043951156  pm  0.000111874889586

 Measured finesse is similar to measured PRM-PR2 cavity finesse(108 +/- 3, see elog #8012). This means loss from flipped PR2 and beam path from PR2 to TM is small.

 I'm a little suspicious about measured g-factor because it is hard to tell which peak is which from the mode scan data. Since half-PRC was not aligned well, high HOMs may contribute to POP DC. Astigmatism also splits HOM peaks.

 PRC 3 Hz beam motion was there for long time (see, for example, elog #6954). BS is unlikely to be the cause because we see this motion in half-PRC, too.
 Also, beam spot motion was not obvious in the PRM-PR2 cavity. My hypothesis is; stack resonance at 3 Hz makes PR2/PR3 angular motion and folding by PR2/PR3 makes the beam spot motion.

Next things to do:
 * PRC g-factor
   - Calculate expected half-PRC g-factor with real measured curvatures, with error bar obtained from RoC error and length error (JAMIE)
   - Calculate expected PRC g-factor using measured half-PRC g-factor (JAMIE)
 * PRC 3 Hz beam motion
   - Do we have space to put oplevs for PR2/PR3?
   - Can we fix PR2/PR3 temporarily?
   - Align incident beam, BS, REFL, AS, and MI using arms as reference
   - lock PRMI
   - PRC mode scan

  8050   Sat Feb 9 11:25:35 2013 KojiUpdateLockingPR2-flipped half-PRC mode scan

Don't  Shouldn't you apply a small misalignment to the input beam? Isn't that why the peak for the 1st-order is such small?


 1. Aligned half-PRC using input TT1 and TT2 by maximizing POP DC during lock. It was not so easy because POP DC fluctuates much at ~ 3 Hz with amplitude of ~ 30 % of the maximum value because of the beam motion (movie on  elog #8039).

 2. Unlocked half-PRC and took POP DC and PRC error signal data;

> /opt/rtcds/caltech/c1/scripts/general/getdata -d 1 -o /users/yuta/scripts/PRCmodescan C1:LSC-POPDC_OUT C1:LSC-REFL11_I_ERR

  Ran again and again until I get sufficiently linear swing through upper/lower sidebands.


  8052   Sun Feb 10 17:30:39 2013 yutaUpdateLockingPR2-flipped half-PRC mode scan

I redid half-PRC mode scan by applying mislignment to PRM.
Half-PRC's sagittal g-factor is 0.9837 +/- 0.0006 and tangential g-factor is 0.9929 +/- 0.0005.
sagittal g-factor is 0.968 +/- 0.001 and tangential g-factor is 0.986 +/- 0.001. (Edited by YM; see elog #8056)

 1. Same as elog #8049, but with small misalignment to PRM.

 2. Algined half-PRC, and misaligned PRM in pitch to get sagittal g-factor.

 3. Restored pitch alignment and misaligned PRM in yaw to get tangential g-factor.

 Below left is the plot of POP DC and PRCL error signal (REFL11_I) when PRM is misaligned in pitch. Below left is the same plot when misaliged in yaw.
left:modescan_pitmisalign.png    right:modescan_yawmisalign.png

 By averaging 5 sets of peaks around TEM00, I get sagittal/tangential g-factors written above.

  The fact that tangential g-factor is larger than sagittal g-factor comes from astigmatism mainly from PR3. Effective PR3 curvature is

sagittal Re = R/cos(theta) = -930 m
tangential Re = R*cos(theta) = -530 m   (where R = -700 m , theta = 41 deg)

so, PR3 is more convex in tangential plane and this makes half-PRC close to unstable. This is opposite of Jamie's calculation(elog #8022). I'm confused.

  I first thought I don't need to misalign PRM because alignment was not so good - it was hard to align when beam motion is large. Also, this motion makes angular misalignment, so I thought free swinging is enough to make higher order modes. However, misaligning PRM intentionally made it easier to resolve higher order modes. I could even distinguish (10,01) and (20,11,02), as you can see from the plot.

  We have to compare with expected g-factor before moving on to PRMI.

  8056   Mon Feb 11 13:15:16 2013 yutaUpdateLockingPR2-flipped half-PRC mode scan

I found a mistake in my code (thanks Jamie!).
I forgot to square the g-factor.
I corrected the following elogs;

PRM-PR2 cavity
  elog #7994 : g-factor will be 0.9889 +/- 0.0004
  elog #8012 : g-factor is 0.988812630228 pm 0.000453751681357

half-PRC g-factor
  elog #8040 : g-factor is 0.9800 +/- 0.0001
  elog #8052 : sagittal g-factor is 0.968 +/- 0.001 and tangential g-factor is 0.986 +/- 0.001

I checked that I was correct in July 2012 (elog #6922)

Cavity g-factor formula:
  gm = ( cos(pi*nu_TMS/nu_FSR) )**2

  8064   Mon Feb 11 21:03:15 2013 yutaUpdateLockingPR2-flipped half-PRC mode scan

To estimate the systematic effects to the g-factor measurement, I changed how to analyze the data in multiple ways.
From the estimation, I get the following g-factors for half-PRC;
  tangential: 0.986 +/- 0.001(stat.) +/- 0.008(sys.)
    sagittal: 0.968 +/- 0.001(stat.) +/- 0.003(sys.)

The a la mode/arbcav calculation is not so far from the measurement(elog #8059). So, mirror curvatures and lengths are not far from what we expect.

  Method I used to analyze the mode scan data is as follows;

  1. Use the spacing between upper sideband and lower sideband to calibrate the data.
  2. Measure the position of 00, 1st, 2nd and 3rd mode.
  3. Used the following formula to get TMS

  nu_TMS = sum((n_i-n)*(nu_i-nu)) / sum((n_i-n)^2)

  where n_i is the order of transverse mode, n is average of n_i's, nu_i is the frequency if i-th order mode and nu is average of nu_i's. This is just a linear fitting.

  But since it is hard to resolve where the higher order mode is, it is maybe better to use only 00, 1st, and 2nd mode. Also, since cavity sweep is not linear enough, it is maybe better to use spacing between 00 and lower sideband (sideband closer to HOMs) to calibrate the data. Changing the analysis will give us information about the effect of peak choosing and linearity.

How the result differ:
  Below are the plots of order of tranverse mode vs measured relative frequency difference from 00 mode. 5 plots on left are when PRM is misaligned in pitch and right are same in yaw. From the plot, you can see using 3rd order mode tend to give larger TMS. Did I picked the wrong one??
left:modespacing_pit.png    right:modespacing_yaw.png

  Below table is the result when I changed the analyzing method;

PRM misaligned in pitch
  calibration    how many HOMs    measured g-factor
  upper-lower    up to 3rd    0.968
  upper-lower    up to 2nd    0.974
  upper-lower    up to 1st    0.975
  00-lower       up to 3rd    0.952
  00-lower       up to 2nd    0.962
  00-lower       up to 1st    0.963

PRM misaligned in yaw
  calibration    how many HOMs    measured g-factor
  upper-lower    up to 3rd    0.986
  upper-lower    up to 2nd    0.989
  upper-lower    up to 1st    0.991
  00-lower       up to 3rd    0.964
  00-lower       up to 2nd    0.988
  00-lower       up to 1st    0.991

  Using 00-lower calibration tend to give us smaller g-factor. Using less higer order-mode tend to give us higher g-factor.
  By taking standard deviation of these, I roughly estimated the systematic error as above.

  I think it is OK to move on to PRMI now.
  But I wonder how much astigmatism is needed to get this measurement data. If astigmatism is not so crazy, it's OK. But if it's not, I think it is better to do more measurement like PRM-PR2-TM cavity.

  8053   Sun Feb 10 18:00:13 2013 yutaSummaryLSCPR2-flipped half-PRC spectra/OLTF

To compare with future PRMI locking, I measured spectra of POPDC and feedback signal. I also measured openloop transfer function of half-PRC locking.
Beam spot motion was at ~ 2.4 Hz, not 3.3 Hz.

  Below is uncalibrated spectra of POPDC and LSC feedback signal (C1:LSC-PRM_OUT).

  Below is openloop transfer function of the half-PRC locking loop. UGF is ~ 120 Hz and phase margin is ~ 45 deg. This agrees with the expected curve.

  Data was taken when half-PRC was locked using REFL11_I as error signal and actuating on PRM.


  For comparison, POPDC when PRMI was locked in July 2012: elog #6954 and PRCL openloop transfer function: elog #6950.

  Peak in the spectra of POPDC and feedback signal was at ~ 3.3 Hz in July 2012 PRMI, but it is now at ~ 2.4 Hz in half-PRC. The peak also got broader.
  Is it because of the change in the resonant frequency of the BS-PRM stack? How much the load on BS-PRM changed?
  Or is it because of the change in the resonant frequency of PR2/PR3?

  Phase margin is less now because of gain boost ~ 5 Hz and resonant gain at 24 Hz.

  8006   Tue Feb 5 19:32:47 2013 yutaSummaryGeneralPR2/PR3 flipping and PRC stability

We are considering of flipping PR2 and/or PR3 to make PRMI stable because PR2/PR3 seems to be convex.
I calculated dependency of the PRC stability on the PR2/PR3 curvature when PR2/PR3 flipped and not flipped.
Flipping looks OK, from the stability point of view.

 PRM-PR2 distance = 1.91 m
 PR2-PR3 distance = 2.33 m
 PR3-ITM distance = 2.54 m
 PRM RoC = +122.1 m
 ITM RoC = Inf

 theta_inc PRM = 0 deg
 theta_inc PR2 = 1.5 deg
 theta_inc PR3 = 41 deg 
          (all numbers from elog #7989)

 Here, RoC means RoC measured from HR side. RoC measured from AR side will be -n_sub*RoC, assuming flat AR surface.
 I also assumed mirror thickness to be negligible.

  1. I used Zach's arbcav and modified it so that it only tells you your cavity is stable or not.
   (It lives in /users/yuta/scripts/mode_density_PRC/stableornot.m)

  2. Swept PR2/PR3 RoC (1/RoC from -0.005 to 0.005 1/m) to see the stability condition.

  1. Stability condition of the PRMI when PR2 and PR3 is not flipped is depicted in the graph below. Black region is the unstable region. We all know that current PRMI is unstable, so we are in the black region.

  2. Stability conditions of PRMI with one of the PR2/PR3 flipped are depicted in the graphs below. If we flip one of them, PRMI will likely to be stable, but if the flipped one is close to flat and the RoC of the other one is  >~ -250 m (more convex than -250 m), PRMI will remain unstable.

  3. Stability condition of PRMI with both PR2 and PR3 flipped is depicted in the graph below. If we flip both, PRMI will be stable.

  1. Flipping one of PR2/PR3 seems OK, but I cannot guarantee. TMS measurement insists RoC of PR2 to be ~ -190 m, if we believe PRM RoC = +122.1 m (elog #7997). We need more precise measurement if we need to be sure before flipping. I prefer PR2 flipping because PR3 flipping gives us longer path in the substrate and larger astigmatism. Also, PR3 RoC is phase-map-measured to be ~ -600 m and PR2 RoC seems to be more convex than -600 m from the TMS measurement.

  2. Flipping both is good from stability point of view. We need calculation of the loss in the PRC (and mode-mismatch to the arms). Are there any requirements?

  3. If we are going to flip PR3, are there any possibilities of clipping the beam at PR3? We need to check.

  4. I need to calculate whether mirror thickness and AR surface curvature are negligible or not.

  I want to flip only PR2 and lock PRMI.

By the way:
 I don't like matlab plots.

  7816   Wed Dec 12 16:52:12 2012 JenneUpdateAlignmentPR2_face, PR3_back cameras in place

I have setup cameras looking at the back of PR3 (through the north viewport on the MC chamber) and the face of PR2 (through the north viewport on the ITMX chamber). We would like a view of the face of PR3, but that isn't possible without placing another in-vac mirror.  The best we can do is the current PRM_BS camera setup, which sees a small portion of the PR3 face.  Most of the face is obscured by the PRM itself. 

I have taken images with the PRM misaligned.  The spot near the top of PR2 is the first reflection from the pitch-misaligned PRM, so it should be ignored for the purposes of trying to see the straight-shot, no PRM beam.

Images are taken with my videocapture50 script, in ..../scripts/general/videoscripts.  This takes 10 sets of 50 images and saves them.  Then ImageBkgndSubtractor.m located in the same folder takes the images (you must edit the beginning of the script to tell it where the images are), averages the noBeam images (PSL shutter closed), and averages the withBeam images, and subtracts them.  Results below:



  8923   Thu Jul 25 13:54:35 2013 manasaUpdateGeneralPR3 clamped and Y arm is back flashing

[Jenne, Annalisa, Manasa]

After yesterday's flipping of PR3, we lost our input pointing. Koji spent a few hours last night but couldn't restore the Y arm. I did my set of trials this morning which also didn't help.

So Jenne and I went ahead and requested Steve to get the ETMY door off.

We set the tiptilts TT1 and TT2 to the slider values from yesterday and started aligning the PR3 to hit the center of ITMY.
When we were hitting close to the center of ITMY, we decide to use the tip-tilts because the movement of PR3 was coarse at this point.
We used TT1 to get the beam to the center of ITMY and TT2 to get the beam at the center of ETMY. We did this iteratively until we were at the center of both the ITMY and ETMY.
We then went to fix IPANG.
The IPANG steering mirror on the BS table was steered to hit the center of the steering mirrors at the ETMY table. We aligned the beam to the IPANG QPD on the green endtable. The steering mirror on the BS table was then steered to misalign the beam in pitch by an inch at the last IPANG steering mirror. This should fix the IPANG clipping we have everytime we pump down.
We closed the chambers with light doors and saw IR flashing in the arm cavity. Koji is now trying to lock the cavity with IR.

  8960   Fri Aug 2 17:50:10 2013 JenneUpdateGeneralPR3 wedge angle adjusted

[Jenne, Manasa, Koji]

Earlier today, we locked and aligned both the X and Y arms. 

I then went into the BS chamber, put on the BS' aperture, and put an aperture along the AS path.  (We had Michelson fringes, so I centered the aperture around the fringes.  I used one of the brass ruler things that we use to center the beam on ITMs and ETMs, on a riser.  I put this aperture at the edge of the BS table, after the AS beam is launched toward the OMC chamber.  The idea was to replace PR3 such that I could get the beam back through the BS aperture, and the brass ruler aperture, in hopes that we would see arm flashes, and not have to open the ITMY and ETMY heavy doors.)

I set references on the table so that I could put PR3 back in its original position, then removed PR3 from the chamber.

Steve set up a HeNe for me, that we pointed through the optic.  The ghost beam was very high, indicating (as expected) that the wedge was not perfectly horizontal.

I took the suspension off of the cage and laid it down, as I have in the past. 

I removed the optic from the suspension, to try to figure out which was the fat vs. skinny side.  I noticed that there are very faint marks on the actual fat and skinny sides of the optic.  (Mpral - for the LaserOptik mirrors, look for the faint lines that are the full width of the barrel, not the placement of the arrow which marks the HR side).  I put the optic back in (HR side toward the back, fat side on the left (as you look at the face of the optic), which is consistent with the picture in the Optical Layout page of the Wiki, near the bottom.) the optic holder ring.

I put the suspension back on the cage, and saw that the HeNe's ghost beam was now nearly horizontal relative to the straight-through beam.  Excellent.  Also, the pitch balancing didn't seem to change noticably, which I determined was within "poking" distance of where we need it to be.

I put PR3 back onto the BS table, and adjusted it around until I got the beam through both the BS aperture, and the one on the AS path.  As usual, this took quite a while, but as soon as I got through both of those apertures (really at the same place, not close to being through them, but as close as I could tell by eye - this is what took forever), Koji and Manasa saw flashes in the Yarm!  Yay! 

Since I had to move PR3 in angle a tiny bit, I reset the references, then dogged down PR3.  We still had flashes, this time in both arms, so we closed up the light doors.

We have now locked and aligned both arms in IR after the adjustment of PR3, and see both arms' green at 01 or 02. We are about to start checking the green positioning on the periscopes.  We will also need to check the AS path, as well as IPPOS and IPANG before we close up.  We see REFL on the camera.

Separately - Manasa remembered that 2 clean things were dropped yesterday - a screw, and an allen key.  Since they're both Clean, we're not too worried, although she thinks a long-armed person may be able to reach the allen key.

  15368   Wed Jun 3 02:14:32 2020 gautamUpdateASCPRC ASC improves arm transmission RIN


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.


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.

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

Attachment 1: PRC_ASCsignals.pdf
Attachment 2: armRIN_PRC_ASC.pdf
Attachment 3: PRFPMIcorner_ASC_PIT_1275190251_1275190551.pdf
Attachment 4: PRFPMIcorner_ASC_YAW_1275190251_1275190551.pdf
Attachment 5: PRFPMIcorner_ASC_coherence_1275190251_1275190551.pdf
  11489   Tue Aug 11 02:26:46 2015 ericqUpdateASCPRC Angular FF Lives!

PRC Angular FF is back in action!

Short and sweet of it:

  • Took witness (T240 channels) and target (POP QPD) with DC coupled oplevs on. About 25 minutes of nice stationary data.
  • Downsampled everything to 32Hz, since coherence suggests subtraction only really possible from 1-5Hz. 
  • Prefiltering done by detrending and ellip(3,3,40,5Hz)
  • 4 second FIR impulse time was enough
  • Filtered target by inverse actuator TF before sending to wiener code. The only difference between this and filtering the witnesses with the actuator TF directly is an effective RMS cost function, i.e. prefiltering. 
  • Spending time tweaking IIR fitting pays off. Divided out zpk(0, [p3, p3*],1), where p3 is some well fit stack/suspension resonance, so that vectfit fits remaining portion with equal numbers of poles and zeros, guaranteeing AC coupling and 1/f rolloff to prevent noise injection
  • Quack->foton->OAF all worked fine
  • All in all, seems to work well. POPDC RMS goes down by a factor of 2 yes

  • Code used lives in /users/ericq/2015-08-PRCFF and the NoiseCancellation github repo

Fit example:

Subtraction spectra

Subtraction prediction vs. reality (positive dB is good)

Attachment 1: fitExample.png
Attachment 2: FFspectra.png
Attachment 3: PITsub.png
Attachment 4: YAWsub.png
  2550   Wed Jan 27 11:02:30 2010 AlbertoUpdateABSLPRC Cavity Length
 I fitted the data from scanning the PRC by changing the beat frequency of the auxiliary laser beam with the PSL beam.
The data points that I've taken so far over the entire frequency range (0-300 MHz) are not continuous. For several reasons the PLL was unable to maintain lock for such a large range and I had to break it into smaller segments. The measurements to acquire them stretched over a too long period of time during which the status of the PRC changed.
Because of that, before I get a continuous set of data points (perhaps normalized by the circulating power inside of the cavity), I restricted the fit to a 55MHz range around 100MHz. I obtained the following numbers for the fit parameters:
Length PRC = 2.169 +/- 0.007 m
Schnupp Asymmetry: 0.471+/- 0.006 m
The fit is shown in the attached plot:
When I fit over the entire set of data I get this:
Length PRC = 2.224 +/- 0.005 m
Schnupp Asymmetry: 0.457+/- 0.005 m
The results are different. Evidently I have to improve the measurement. I'm working on it.
For posterity:
The function I used to fit the transmitted beat power vs. frequency is the following:
E_trans = - t_prm * r_itm * exp(1i*2*wb*l_prc/c) .* sin(wb*l_/c) ./ ( 1 + r_prm * r_itm * exp(1i*2*wb*l_prc/c) .* cos(wb*l_/c)
Where wb is the angular frequency of the beat, l_prc and l_ are the length of the PRC and the Schnupp asymmetry, respectively; r_itm, t_itm, r_prm, t_prm are reflectances and transmittances of PRM and ITM; c is the speed of light.
  6421   Thu Mar 15 04:04:23 2012 KojiConfigurationLockingPRC Matching issues

Kiwamu and Koji

We found that the intra-cavity mode of the PRC is not round although it was obvious even with the DARK and REFL port images.
We need to review the mode matching situation.

In order to look at the PRC intra-cavity mode, we reconfigured the POP CCD.

If we look at the beam reflected from the Michelson, the beam is round. However, the PRC intra-cavity mode can never be round
in any resonant conditions. (Pict 1, 2, and 3, for the sideband resonant, carrier resonant conditions and another carrier resonant
one, respactively). Particularly the mode of the carrier resonant case is very unstable and always changing.



By misaligning the PRM, we can compare between the spot directly reflected from the Michelson and the one after additional round trip in the PRC (Pic 4).

They looks round, but it was obvious the secondary reflection is dimmer and larger (Pic 5). The intensity difference corresponds to the factor RPRM RMI
(i.e. product of the reflectivities for the PRM and MI). It can be understand if the dimmer spot looks smaller due to the artifact of the CCD. But it is opposite.

This may mean the mode matching is not correct. We are not sure what is not right. This could be just an incorrect incident beam, the curvature error of the PRM,
beam is distortec by the TT mirrors, or some other unknown reasons.

More precise analysis can be done with quantitative analysis of those two spots with Beamscan. This could happen tomorrow.


  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.

  7641   Mon Oct 29 18:50:02 2012 JenneUpdateAlignmentPRC aligned, Yarm almost aligned

[Jamie, Jenne, Raji, with consultation from Nic, Ayaka and Manasa]

We went back and re-looked at the input alignment, and now we're "satisfied for the moment" (quote from Jamie) with the PRC alignment.  Also, by adjusting the PR folding mirrors, we are almost perfectly aligned to the Yarm.

What we did:

Set PRM DC biases to 0 for both pitch and yaw.

Aperture was attached to PRM cage, double aperture was attached to BS cage, free-standing aperture was placed in front of PR2. 

Adjusted PZT1, PZT2 such that we were centered on PZT2, and through apertures at PRM and PR2.   This was mainly for setting beam height in PRC.

Checked centering on PZT1, MMT1, MMT2, PZT2.

Adjusted PRM pitch bias and PZT2 yaw such that REFL beam was retro-reflected from PRM.

Checked that REFL beam came nicely out of Faraday.

Checked that beam was still going through center of PRM aperture, and pitch height at PR2 was good.

Moved PR2 sideways until beam hit center in yaw of PR2.

Twisted PR2 such that beam was hitting center of PR3.

Moved and twisted PR3 (many times) so that beam went through BS input and output apertures, and through center of ITMY aperture.

Found that beam was just getting through black glass aperture at ETMY, top left corner, if looking at the face of ETM from ITM.

Locked down dog clamps on PR2.

This required some re-adjustment of PR3.  Re-did making sure going through BS apertures and ITMY aperture, locked down PR3 dog clamps.

Found that we are centered in yaw at ETMY, a little high in pitch on ETMY.

Replaced all of the light doors, to take a break.  4 hours in bunny suits seemed like enough that we earned a break.

This all sounds more straighforward than it was.  There was a lot of iteration, but we finally got to a state that we were relatively happy with.


What we will do:

Tweak PZT2 a *tiny* bit in pitch, ~0.5 mrad, so that the beam goes through the ETMY aperture.

See if we can align EMTY and ITMY to get multiple bounces through the Yarm.

Remove ETMX heavy door, steer BS such that we're getting through the center of an aperture at ETMX.

Align ETMX and ITMX such that we get multiple bounces through the Xarm.

Check SRM, AS path alignment.

Check REFL out of vac alignment.

Check other pickoffs.

Check all oplevs.



We have a open-sided 2" mirror mount that we are considering using for the POY pick-off mirror.  This might help us get a little more clearance in the Y-arm of the Michelson.  Problem is the mount is not steerable, so we need to determine if that's doable or not.


  7642   Tue Oct 30 11:51:45 2012 JenneUpdateAlignmentPRC aligned, Yarm almost aligned

[Raji, Jenne]

We tweaked PZT2, PZT1 (yaw only), and PR3 (pitch only) to get the beam ~centered on the BS aperture, the ITMY aperture, and the ETMY aperture.

After lunch I'll tweak up the MC alignment, since, although the spots are in the right places, the transmitted beam could be higher power.  This will make it easier to check our pointing, especially since the ETMY spot is larger than our aperture, but the beam is dim.

We're getting there!

  3227   Thu Jul 15 12:21:08 2010 AlbertoConfigurationLSCPRC and SRC length adjustements

Lately I've been trying to calculate the corrections to the recycling cavity lengths that would compensate for the phase that the sidebands will pick up from the arms in the upgraded interferometer.

To do that calculation , I tried two quite different ways, although equivalent in principle. They both use the optickle model of the 40m, but the calculation is made differently.

In the first way, I looked directly at the phases of the field: phase of [input field] / [reflected field], phase of [input field at PRM] / [transmitted field at SRM].

In the second way I looked at the demodulation phases of the LSC signals.

The first way is much simpler, especially from a computational point of view. It is the first I tried several weeks ago, but then I had abandoned because back then I thought it wasn't the correct way.

Anyway, both ways gave me the same results for the PRC length.
For the SRC length, the first way has given me a clear outcome. On the other hand, the second way has produced a less clear result.

According to these results, these would be the proposed adjustements to the cavity lengths:
dl(PRC) = -0.0266 m; dl(SRC) = 0.0612 m

I) 1st Way
a) case of arms ideal length (33.86 m)

sidebandPhaseRotation_73433447384.png sidebandPhaseRotation_73433447590.png

b) case arm length = 38.40 m


 sidebandPhaseRotation_73433447960.png zoom -> sidebandPhaseRotation_73433448864.png


sidebandPhaseRotation_73433445372.png zoom -> sidebandPhaseRotation_73433449354.png

II) 2nd Way
a) case of arms ideal length (33.86 m)


b) case arm length = 38.40 m


  3228   Thu Jul 15 15:57:10 2010 KojiConfigurationLSCPRC and SRC length adjustements

Tell me whether it is correct or not. Otherwise I won't be able to sleep tonight.


According to these results, these would be the proposed adjustements to the cavity lengths:
dl(PRC) = -0.0266 m; dl(SRC) = 0.612 m

  3229   Thu Jul 15 16:16:51 2010 AlbertoConfigurationLSCPRC and SRC length adjustements


Tell me whether it is correct or not. Otherwise I won't be able to sleep tonight.


According to these results, these would be the proposed adjustements to the cavity lengths:
dl(PRC) = -0.0266 m; dl(SRC) = 0.612 m

 Sorry. I was in a rush to go to the LIGO "all hands" meetings when I posted that elog entry, that I forgot a zero in the SRC length value. The correct values are:

dl(PRC) = -0.0266 m; dl(SRC) = 0.0612 m

The cavity absolute lengths are then:

L(PRC) = 0.5/2/f1*c - 0.0266 = 6.7466 m

L(SRC) = c/f2 + 0.0612 = 5.4798 m

where c is the speed of light; f1 = 11065399 Hz; f2 = 55326995 Hz

  9590   Fri Jan 31 19:29:36 2014 GabrieleSummaryLSCPRC and SRC lengths

 Today we measured the missing distance to reconstruct SRC length.

I also changed the way the mirror positions are reconstructed. In total for PRC and SRC we took 13 measurements between different points. The script runs a global fit to these distances based on eight distances and four incidence angles on PR2, PR2, SR2 and SR3. The optimal values are those that minimize the maximum error of the 13 measurements with respect to the ones reconstructed on the base of the parameters. The new script is attached (sorry, the code is not the cleanest one I ever wrote...)

The reconstructed distances are:

Reconstructed lengths [mm]:
LX    = 6771
LY    = 6734
LPRC  = 6752
LX-LY = 37
LSX   = 5493
LSY   = 5456
LSRC  = 5474

The angles of incidence of the beam on the mirrors are very close to those coming from the CAD drawing (within 0.15 degrees):

Reconstructed angles [deg]:
aoi PR3 = 41.11 (CAD 41)
aoi PR2 = 1.48  (CAD 1.5)
aoi SR3 = 43.90 (CAD 44)
aoi SR2 = 5.64  (CAD 5.5)

The errors in the measured distances w.r.t. the reconstructed one are all smaller than 1.5 mm. This seems a good check of the global consistency of the measurement and of the reconstruction method.

NOTES: in the reconstruction, the BS is assumed to be exactly at 45 degrees; wedges are not considered.



Attachment 1: map_jan31st.pdf
Attachment 2: survey_v3.zip
  13393   Wed Oct 18 19:17:42 2017 gautamUpdateGeneralPRC angular feedforward

Last night, I collected ~30mins of data for the vertex seismometer channels and the POP QPD PIT/YAW signals with the PRMI locked on carrier (angular FF OFF). The ITM Oplev loops weren't DC coupled, as they are in the full IFO locking sequence, but I feel like the angular FF filters can be improved - there are frequent sharp dives in the AS110 signal level which are correlated with large amplitude motion of the POP spot on the control room CCD monitor.

Repeating the frequency domain multicoherence analysis using BS_X and BS_Y seismometer channels as witnesses suggest that we can win significantly (see Attachment #1).

I've never really implemented feedforward filters - I was planning on using ericq's latest entry on this subject as a guide. From what I gather, the procedure is as follows:

  1. Pre-filter the target (POP QPD PIT or YAW) and witness (BS_X, BS_Y) channels
    • Downsample the 2k target data and 256Hz witness data to 32 Hz (how to choose this?)
    • Detrend (linear?)
    • Apply elliptic low pass filter (previously, a 3rd order Elliptic Low pass with 3dB ripple, 40dB stopband attenuation, corner at 5Hz was used).
  2. Filter the target signal (i.e. POP QPD PIT/YAW) by the inverse actuator TF.
    • This "actuator TF" is a measurement of how actuating on the angular DoFs of the PRM affects the POP QPD spot.
    • So by pre-filtering the target signal through the inverse actuator TF, we get a measure of how much the PRM angular motion is.
    • The reason we want to do this is to give the FIR filter that produces optic motion (output) given ground motion sensed by the seismometer (input) fewer poles/zeros to fit (?).
    • The actual actuator TF has to be measured using DTT, and fit - is there anything critical about this fitting? Seems like this should be just a simple pendulum transfer function so a pair of complex poles should be sufficient?
  3. The actual Wiener filter is calculated by the function miso_firlev.m. There are many versions of this floating around from what I can gather.
    • This function requires 3 input parameters.
      • Order of filter to be fit
      • Witness channels (can be multiple)
      • Target channel (has to be single, hence the "miso" in the function name).
    • Today, at the meeting, we talked about weighting the cost function that the optimal Wiener filter calculator minimizes.
    • The canonical wiener filter minimizes the mean squared error between the output of the filter and the desired signal profile (which for this particular problem is the angular motion of the PRM, calculated by dividing the target signal by the actuator TF, knowing which we can cancel it out).
    • But as seen in Attachment #1, the main reduction in RMS comes below f=5Hz.
    • So can we weight the cost function more heavily at lower frequencies? From what I can find in previous calculations, it looks like this weighting happens in the pre-filtering stage, which is not the same thing as including the frequency dependent weighting in the calculation of the Weiner filter? The PSD and acf are F.T. pairs per the Wiener-Khinchin theorem so intuitively I would think that weighting in the frequency domain corresponds to weighting on the lags at which the acf is calculated, but I need to think about this.
    • What kind of low-pass filter do we use to prevent noise injection at higher frequencies? Does the optimal filter calculation automatically roll-off the filter response at high frequencies?
  4. As I write this, seems like there is another level of optimization of "meta-parameters" possible in this whole process - e.g. what is the optimal order of filter to fit? what is the optimal pre-filtering of training data? Not sure how much we can gain from this though.

Some notes from Rana from some years ago: https://nodus.ligo.caltech.edu:8081/40m/11519

If anyone has pointers / other considerations I should take into account, please post here.

Attachment 1: pop_feedforward_potential.pdf
  14991   Thu Oct 24 11:58:16 2019 gautamUpdateASCPRC angular feedforward


I'd like to revive the PRC angular feedforward system. However, it looks like the coherence between the vertex seismometer channels and the PRC angular motion witness sensor (= POP QPD) is much lower than was found in the past, and hence, the stabilization potential by implementing feedforward seems limited, especially for the Pitch DoF.


I found that the old filters don't work at all - turning on the FF just increases the angular motion, I can see both the POP and REFL spots moving around a lot more on the CRT monitors.

I first thought I'd look at the frequency-domain weiner filter subtraction to get a lower bound on how much subtraction is possible. I collected ~25 minutes of data with the PRC locked with the carrier resonant (but no arm cavities). Attachment #1 shows the result of the frequency domain subtraction (the dashed lines in the top subplot are RMS). Signal processing details:

  • Data was downloaded and downsampled to 64 Hz (from 2kHz for the POP QPD signals and from 128 Hz for the seismometer signals). The 'FIR' option of scipy decimate was used.
  • FFT time used was 16 seconds for the multi-coherence calculations

The coherence between target signal (=POP QPD) and the witness channels (=seismometer channels) are much lower now than was found in the past. What could be going on here?

Attachment 1: ffPotential.pdf
  8007   Wed Feb 6 11:59:12 2013 JenneUpdateLockingPRC cavity gains

EDIT:  These numbers are for a perfect, non-lossy arm cavity.  So, a half real, half imaginary world.

Carrier uses arm cavity reflectivity for perfectly resonant case.

PRC carrier gain, flipped PR2, PR3 = 61

PRC carrier gain, regular PR2, PR3 = 68  (same value, within errors, for no folding at all).

Carrier gain loss = (68-61)/68 = 10%


SB uses arm cavity reflectivity for perfectly anti-resonant case.

PRC SB gain, flipped PR2, PR3 = 21

PRC SB gain, regular PR2, PR3 = 22 (same value, within errors, for no folding at all). <--- yes, this this "regular PR2, PR3 = 22..."

SB % gain loss = (22-21)/22 = 4.5%


I claim that we will be fine, recycling gain-wise, if we flip the folding mirrors.  If we do as Yuta suggests and flip only one folding mirror, we'll fall somewhere in the middle.

  8014   Wed Feb 6 18:39:08 2013 JenneUpdateLockingPRC cavity gains

[Yuta, Jenne]

We have both calculated, and agree on the numbers for, the PRC gain for carrier and sideband.

We are using the measured arm cavity (power) loss of 150ppm....see elog 5359.

We get a PRC gain for the CARRIER (non-flipped folding) of 21, and PRC gain (flipped folding) of 20This is a 4.7% loss of carrier buildup.

We get a PRC gain for the SIDEBANDS (non-flipped folding) of 69, and PRC gain (flipped folding) of 62This is an 8.8% loss of sideband buildup.

The only difference between the "flipped" and "non-flipped" cases are the L_PR# values - for "non-flipped", I assume no loss of PR2 or PR3, but for the "flipped" case, I assume 1500ppm, as in Rana's email.  Also, all of these cases assume perfect mode matching.  We should see what the effect of poor mode matching is, once Jamie finishes up his calculation.

Why, one might ask, are we getting cavity buildup of ~20, when Kiwamu always quoted ~40?  Good question!  The answer seems, as far as Yuta and I can tell, to be that Kiwamu was always using the reflectivity of the ITM, not the reflectivity of the arm cavity.  The other alternative that makes the math work out is that he's assuming a loss of 25ppm, which we have never measured our arms to be so good.


For those interested in making sure we haven't done anything dumb:

ppm = 1e-6;

% ||      |      |        ||            ||
% PRM    PR2    PR3      ITM           ETM

T_PRM = 0.05637;
t_PRM = sqrt(T_PRM);
L_PRM = 0 *ppm;
R_PRM = 1 - T_PRM - L_PRM;
r_PRM = sqrt(R_PRM);

T_PR2 = 20 *ppm;
t_PR2 = sqrt(T_PR2);
L_PR2 = 1500 *ppm;
R_PR2 = 1 - T_PR2 - L_PR2;
r_PR2 = sqrt(R_PR2);

T_PR3 = 47 *ppm;
t_PR3 = sqrt(T_PR3);
L_PR3 = 1500 *ppm;
R_PR3 = 1 - T_PR3 - L_PR3;
r_PR3 = sqrt(R_PR3);

T_ITM = 0.01384;
t_ITM = sqrt(T_ITM);
L_ITM = 0;%100 *ppm;
R_ITM = 1 - T_ITM - L_ITM;
r_ITM = sqrt(R_ITM);

T_ETM = 15 *ppm;
t_ETM = sqrt(T_ETM);
L_ETM = 0 *ppm;
R_ETM = 1 - T_ETM - L_ETM;
r_ETM = sqrt(R_ETM);

rtl = 150*ppm;  % measured POWER round trip loss of arm cavities.
rtl = rtl/2;     %    because we need the sqrt of the exp() for ampl loss....see Siegman pg414.

eIkx_r = exp(-1i*2*pi);
r_cav_res = -r_ITM + (t_ITM^2 * r_ETM * eIkx_r * exp(-rtl)) / (1 - r_ITM*r_ETM * eIkx_r * exp(-rtl) );

eIkx_ar = exp(-1i*pi);
r_cav_antires = -r_ITM + (t_ITM^2 * r_ETM * eIkx_ar * exp(-rtl)) / (1 - r_ITM*r_ETM * eIkx_ar * exp(-rtl) );

%% PRC buildup gain

g_antires = t_PRM*eIkx_ar / (1-r_PRM*r_PR2*r_PR3*r_cav_antires*eIkx_ar);
G_ar = g_antires^2;
G_ar = abs(G_ar)  % Just to get rid of the imag part that matlab is keeping around.

g_res = t_PRM*eIkx_r / (1-r_PRM*r_PR2*r_PR3*r_cav_res*eIkx_r);
G_r = g_res^2;
G_r = abs(G_r)

  8015   Wed Feb 6 19:59:35 2013 ranaUpdateLockingPRC cavity gains

  Getting closer, but need to use the real measured AR reflectivity values, not the 1500 ppm guess. These should be measured at the correct angles and pol, using an NPRO.

  8017   Wed Feb 6 20:03:50 2013 ManasaUpdateLockingPRC cavity gains


  Getting closer, but need to use the real measured AR reflectivity values, not the 1500 ppm guess. These should be measured at the correct angles and pol, using an NPRO.

 I'm still on that!

  8076   Wed Feb 13 14:21:19 2013 JenneUpdateLockingPRC cavity gains


With 1500ppm loss on both PR2 and PR3, 150ppm arm cavity loss:

We get a PRC gain for the CARRIER (non-flipped folding) of 21, and PRC gain (flipped folding) of 20.  This is a 4.7% loss of carrier buildup.

We get a PRC gain for the SIDEBANDS (non-flipped folding) of 69, and PRC gain (flipped folding) of 62.  This is an 8.8% loss of sideband buildup.

 With a PR2 loss of 896ppm (from the plot on the wiki), but no loss from PR3 because we didn't flip it, and the same 150ppm round trip arm cavity loss, I get:

Carrier gain = 21.0

Sideband gain = 66.7

(No loss case, with an extra sig-fig, so you can see that the numbers are different:  Carrier = 21.4, Sideband = 68.8 .)

So, this is 1.6% loss of carrier buildup and 3.1% loss of sideband buildup.  Moral of the story - G&H's measured AR reflectivity is less than Rana's guess, and we didn't flip PR3, so we should have even less of a power recycling gain effect than previously calculated.

  6913   Wed Jul 4 20:13:46 2012 yutaBureaucracyLockingPRC commissioning plan

Issues in PRC:
  1. Power recycling gain is too low (~ 15 instead of 40, according to Kiwamu).
  2. Mode matching to both arms are ~90%(see #6859), but PRC has terrible mode.
       Clipping/flipping in PRC?
  3. From cameras, beam spot moves so much when PRMI is locked.
       Alignment? Mirrors(especially PR2/3) moves too much?
  4. Error signals are glitchy when PRMI is locked.
       Servo design? Mirrors moves too much?

What we have learned from the vent:

  1. PRM, PR2, PR3 was not flipped.
  2. Their suspensions looked OK, too.
  3. We noticed clipping at BS and Faraday. They must be avoided when tip-tilts are installed on next vent.

  4. Took useful photos for next vent. Positions of green optics on optical layout CAD must be updated.
  5. It is not so difficult to recover the IFO state after cycling the vacuum if we use attenuator setup using PBS (see elog #6892).  But, of course, we need plans before cycling.

Commissioning Plan:
  - measure PRMI power recycling gain from POP
  - FPMI using ALS
  - measure PRFPMI power recycling gain from TRY/X
  - correlation between beam spot motion at POP camera and glitch
  - correlation between PR2/PR3 motion and glitch (how can we measure PR2/3 motion? set up oplevs?)
  - mode scan for PRC, using AS AUX laser
  - beam profile measurement at REFL,POP
  - refine servo design of MICH and PRCL

  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.

  14722   Wed Jul 3 11:47:36 2019 gautamUpdateBHDPRC filtering

A question was raised as to how much passive filtering we benefit from if we pick off the local oscillator beam for BHD from the PRC. I did some simplified modeling of this. For the expected range of arm cavity round trip losses (20-50 ppm), I think that the 40m CARM pole will be between 75-85 Hz. The corresponding recycling gain will be 40-50, with the current PRM. I assumed 1000 ppm loss inside the PRC. The net result is that, assuming the single pole coupled cavity response, we will get ~8-9 dB of filtering at ~200 Hz of the intensity noise of the input laser field to the interferometer if we pick the LO beam off from the PRC (e.g. PR2 transmission), instead of picking it off before.

The next questions are: (i) can we do a sufficiently good job of achieving the required RIN stability on the LO field for BHD without relying on the passive filtering action of the PRC? and (ii) is the benefit of the PRC filtering ruined in the process of routing the LO field from wherever the pickoff happens to the BHD setup?

Attachment 1: PRCfiltering.pdf
  8115   Wed Feb 20 10:13:41 2013 yutaUpdateAlignmentPRC flashing brighter than last week

After in-vac alignment work last night, PRC is flashing brighter than PRMI alignment last week.
My hypothesis is that "we aligned PRM to junk MI fringe last week". Possibly, we used MI fringe caused by AR reflection of ITMs, or MI fringe reflected from SRM.

  PRC flashing last week (youtube, elog #8085, elog #8091)

  PRC flashing this time (Lens in-front of AS camera was taken out)

My hypothesis can explain:
 - why we had dimmer POP last week (flash in half-PRC was way brighter even when we had more attenuators (youtube))
 - why I thought AS55 is broken (AS was too dim)

  Be careful of junk beams.

  9588   Thu Jan 30 19:00:25 2014 GabrieleSummaryLSCPRC length changed

 [Manasa, EricQ, Gabriele]

Today we changed the PRC length translating PR2 by 27 mm in the direction of the corner. After this movement we had to realign the PRC cavity to get the beam centered on PRM, PR2, PR3, BS (with apertures) and ITMY (with aperture). To realign we had to move a bit both PR2 and PR3. We could also see some flashes back from the ETMY . //Edit by Manasa : We could see the ETMY reflection close to the center of the ITMY but the arm is not aligned or flashing as yet//. 

After the realignment we measured again the PRC length with the same method of yesterday. We only had to change one of the length to measure, because it was no more accessible today. The new map is attached as well as the new script (the script contains also the SRC length estimation, with random numbers in it).

The new PRC length is 6753 mm, which is exactly our target!


The consistency checks are within 5 mm, which is not bad.

We also measured some distances to estimate the SRC length, but right now I'm a bit confused looking at the notes and it seems there is one missing distance (number 1 in the notes). We'll have to check it again tomorrow.




Attachment 1: map_jan30.pdf
Attachment 2: survey_v3_jan30.m
clear all

global sos_lx sos_ly sos_cx sos_cy tt_lx ...
       tt_ly tt_cx tt_cy sos_sx sos_sy sos_dy

%% Survey of the PRC+SRC lengths %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% measured distances
d_MB2_MY  = 2114 + 27 + 9;
... 446 more lines ...
  9555   Tue Jan 14 19:10:51 2014 GabrieleSummaryLSCPRC length measurement

 [EricQ, Gabriele]

We could carry out the measurement of PRC length. The AS110 photodiode was plugged into REFL11. So REFL11 is giving us the AS11 signal. Here is the procedure.

  1. Lock MICH.
  2. Add a line in MICH (amplitude 20000 counts)
  3. Tune AS11 demod phase to have the line in I.
  4. Change the demod phase by steps of 1 degree around the rough optimum, taking one minute of data at each point
  5. Lock PRMI on sidebands
  6. Add a line in MICH (amplitude 500 counts)
  7. Tune AS11 demod phase to have the line in I.
  8. Change the demod phase by steps of 1 degree around the rough optimum, taking one minute of data at each point

We repeated the same measurement also using AS55, with the same procedure.

Roughly, the phase difference for AS11 was 11 degrees and for AS55 it was 23 degrees. A more detailed analysis and a calibration in terms of PRC length will follow.

  9557   Wed Jan 15 18:18:15 2014 GabrieleSummaryLSCPRC length measurement analysis

 I analyzed the data we took yesterday, both using AS11 and AS55. For each value of the phase I estimated the Q/P ratio using a demodulation code. Then I used a linear regression fit to estimate the zero crossing point.

Here are the plots of the data points with the fits:


The measurements a re more noisy in the PRMI configuration, as expected since we had a lot of angular motion. Also, the AS11 data is more noisy. However, the estimated phase differences between PRMI and MICH configurations are:

  • AS11 = -10.9 +- 1.0 degrees
  • AS55 = -21.1 +- 0.4 degrees

The simulation already described in slogs 9539 and 9541 provides the calibration in terms of PRC length. Here are the curves


The corresponding length errors are

  • AS11 = 1.44 +- 0.13 cm
  • AS55 = 0.59 +- 0.01 cm

The two results are not consistent one with the other and they are both not consistent with the previous estimate of 4 cm based on the 55MHz sideband peak splitting.

I don't know the reason for this incongruence. I checked the simulation, repeating it with Optickle and I got the same results. So I'm confident that the simulation is not completely wrong.

I also tried to understand which parameters of the IFO can affect the result. The following ones have no impact

  • Beam matching
  • ITM curvatures
  • Schnupp asymmetry
  • Distance PR-BS
  • ITM and PRM misalignments

The only parameters that could affect the curves are offsets in MICH and PRCL locking point. We should check if this is happening. A first quick look (with EricQ) seems to indicate that we indeed have an offset in PRCL. However, tonight the PRMI is not locking stably on the sidebands. 

If possibile, we will repeat the measurement later on tonight, checking first the PRCL offset.


  9586   Wed Jan 29 21:01:03 2014 GabrieleSummaryLSCPRC length measurement analysis

 [Manasa, EricQ, Gabriele]

We managed to measure the PRC length using a procedure close to the one described in slog 9573.

We had to modify a bit the reference points, since some of them were not accessible. The distances between points into the BS chamber were measured using a ruler. The distances between points on different chambers were measured using the Leica measurement tool. In total we measured five distances, shown in green in the attached map.

We also measured three additional distances that we used to cross check the results. These are shown in the map in magenta.

The values of the optical lengths we measured are:

LX    = 6828.96 mm
LY    = 6791.74 mm
LPRC  = 6810.35 mm
LX-LY = 37.2196 mm  

The three reference distances are computed by the script and they match well the measured one, within half centimeter:

M32_MP1  = 117.929 mm   (measured = 119 mm)
MP2_MB3  = 242.221 mm   (measured = 249 mm)
M23_MX1p = 220.442 mm   (measured = 226 mm)

See the attached map to see what the names correspond to.

The nominal PRC length (the one that makes SB resonant without arms) can be computed from the IMC length and it is 6777 mm. So, the power recycling cavity is 33 mm too long w.r.t. the nominal length. This is in good agreement with the estimate we got with the SB splitting method (4cm).

According to the simulation in the wiki page the length we want to have the SB resonate when the arms are there is 6753 mm. So the cavity is 57 mm too long.

Attached the new version of the script used for the computation.

Attachment 1: map.pdf
Attachment 2: script.zip
  8562   Sat May 11 01:11:52 2013 KojiUpdateASCPRC mode stabilization with a shadow sensor at POP

Ah, AWESOME. Indefinite PRMI lock was finally achieved.

POP setup

- Looked at the POP setup. Checked the spot on POP110 PD. Found some misalignment of the beam.
  The beam spot was aligned to the PD with PRMI locked. The value of POP110I almost doubled by the alignment
  and recovered previous value of 400. Therefore previous normalization values of MICH 0.01 / PRCL 100 were restored.

- Placed PDA36A (Si 3.6mmx3.6mm) on the POP path that Jenne prepared. The gain knob was set to 40dB.
  Since the original spot had been too small, a lens with f=50mm was inserted in order to expand the beam.
  Connected the PD output to the SMA feedthrough on the ITMX table enclosure.
  I found the BNC cable labeled "PO DC" hanging. Connected this cable to the enclosure SMA.

- Went to the LSC rack. Found the corresponding PO DC cable. Stole the POPDC channel from POP110I Bias T to this PO DC cable.

- Razor blade setup: Machined a junk Al bracket in order to fix a razor blade on it. Attached the Al bracket to a sliding stage.


- Locked the PRMI with REFL33I&AS55Q. Cut the beam into half by the razor blade.

- Made a temporary PRM_ASC_YAW filter.
  Zero: 0Hz Pole: 2kHz
  Resonant Gain 3.2Hz Q:2 Height 30dB
  Butterworth 2nd-order 60Hz

  => Expected UGF 0.1Hz&10Hz

- CDS: By the work described in this entry, the POPDC signal was connected to the "MC" bank of the LSC.
            BTW, the 11th row of the LSC output matrix is connected to the PRM_ASC_YAW.

- The "MC" servo input (i.e. the POPDC signal) was normalized by POP110I (without SQRTing).

- Engaged the PRM ASC path. Gradually increased the gain of PRM_ASC_YAW. G=+100 seemed to be the best so far.
  It was visible that the spot on the POP CCD was stablized in yaw.

- The lock lasted for ~40min. Took several measurements, alignment adjustment, etc.

- Tweaking the PRM ASC unlocked the PRMI.

- Locked again. Switched from REFL33I/AS55Q (x1/x1) combination to REFL55I/REFL55Q (x1/x0.3) combination.
  This also kept the lock more than 20min.

Attachment 1: Screenshot.png
Attachment 2: 130510_PRMI.pdf
  13974   Sat Jun 16 00:26:48 2018 gautamUpdateGeneralPRC modescan attempt

[Jon, Gautam, Johannes]

We did the following today:

  1. Dither align arms such that ITMs were reliable arm references.
  2. Configure the IFO such that ITMX single bounce was the only visible beam reaching the AS port from the symmetric side - ITMY, both ETMs, PRM and SRM were misaligned.
  3. Do coarse alignment on the AS table using the usual near field / far field overlap technique, with "near" and "far" dictated by arm reach on the AS table. In this way, the ingoing AUX beam and the PSL single bounce from ITMX were collimated on the AS table.
  4. Lock the AUX / PSL PLL. We expected a beatnote on AS110 at eithe (80-50)=30 MHz or (80+50)=130 MHz. 80 MHz is the AOM driver frequency, while 50 MHz is the PLL offset. (Marconi was actually set to 60 MHz, prolly Keerthana forgot to reset it after some remote experimentation).
  5. Beat was found at 30 MHz. 
  6. Input steering of AUX beam into the IFO was tweaked to maximize the beat. Johannes claims he saw -35 dBm on AS110 last week. But Jon reported a best effort of ~-60 dBm today. Not sure how to square that circle.
  7. Once we were confident that the input of the AUX and PSL beams were well aligned, we decided to do a scan. PRC was chosen as PRMI can be locked but I don't yet know the correct settings for SRMI locking, and DRMI seemed too ambitious for daytime.
    • PRMI was locked on carrier.
    • Jon can comment more here, but the measurement with AM sidebands does not rely on any beatnote on the AS110 PD, it is just looking for coupling of the AM sideband into the IFO from the AS port at resonant frequencies of the PRC.
    • For a coarse sweep, we swept from 1-60 MHz, 801 points, and the IF bandwidth was set at 30 kHz on the AG4395.
    • Transfer function being measured was the ratio of AM signal detected at AS110 PD, to RF drive applied to the AOM driver.
    • We were expecting to see dips separated by the PRC FSR (~25 MHz, since the PRC RT length is ~12.5m), when the AM sideband becomes resonant in the PRC.
    • But we saw nothing. Need to think about if this is an SNR problem, or if we are overlooking something more fundamental in the measurement setup.

This measurement seems like a fine candidate to trial the idea of looking for the FSRs (and in general, cavity resonances) of the PRC in the phase of the measured TFs, rather than the amplitude.

  13975   Sat Jun 16 01:25:29 2018 KojiUpdateGeneralPRC modescan attempt

The PRC FSR is, of course, very close to twice of our f1 moudlation frequency (11MHz x 2 = 22MHz) .

I still don't understand what response the measurement is looking for. I understood the idea of using the subcarrier as a stablized carrier to the PRC with a certain freq offset from the main carrier. I suppose what was swept was the AOM modulation frequency (i.e. modulation frequency of the AM applied to the subcarrier). If that is the case, the subcarrier seemed fixed at an arbitorary frequency (i.e. 50MHz) away from the carrier. If one of the AM sidebands hits the PRC resonance (i.e. 22, 44, 66MHz away from the main carrier), you still have the other sideband reflected back to the AS. Then the RF signal at the AS is still dominated by this reflected sideband. I feel that the phase modulation is rather suitable for this purpose.

If you are talking about ~MHz AM modulation by the AOM and scanning the PLL frequency from 1MHz to 60MHz, the story is different. And this should involve demodulation of the AS signal at the AM modulation frequency. But I still don't understand why we don't use phase modulation, which gives us the PDH type signal at the reflection (i.e. AS) port...


  13976   Sat Jun 16 20:57:59 2018 JonUpdateGeneralPRC modescan attempt

Here's a Finesse modeling of what we're expecting to observe with this test. It uses Gautam's base model of the 40m IFO with appropriate modifications for the needed configuration.

The idea is to lock the IFO in the SRMI configuration, with the phase-locked AUX beam injected from the AS port. The AUX beam is imprinted with AM sidebands and slightly misaligned relative to the SRC so as to transfer power into HOM1. The RF network analyzer provides the drive signal for the AOM, and its frequency is swept to coherently measure the transfer function [reflected AUX beam / drive]. The reflected AUX beam is sensed by the AS110 PDA10CF.

It is also possible to drive PM sidebands as Koji suggests, but the squeezer group has encouraged using AM for practical advantages. The SNR with AM is a bit higher (less power lost into harmonics at large modulation index), there is a broadband AOM already available aligned to the SQZ beam at LLO, and there is also concern that driving strong PM could interfere with the SQZ control loops.

Expected SRMI Response

Attachment #1 shows the expected response to swept-AM in SRMI. Resolving just the FSR and the first-order mode splitting is sufficient to extract the SRC Gouy phase.

Expected response in the SRMI configuration.

Expected DRMI Response

Since the 40m has not been opearted in SRMI since ~2016 (last done by Eric Q.), Gautam believes it may take some time to relock this configuration. However, the modeling indicates that we can likely obtain sufficient sensitivity in DRMI, which would allow us to proceed faster. Attachment #2 shows the expected response to swept-AM in DRMI. The PRC leakage signal turns out to be significantly smaller than the SRC reflection (a factor of ~30 in amplitude), so that the signal still retains its characteristic shape to a very good approximation. The tradeoff is a 10x reduction in SNR due to increased PSL shot noise reaching AS110.

Expected DRMI response. The main difference is a 10x increase in shot noise on AS110.

Based on this, we should proceed with DRMI scans instead of PRMI next week.


The PRC FSR is, of course, very close to twice of our f1 moudlation frequency (11MHz x 2 = 22MHz) .

I still don't understand what response the measurement is looking for. I understood the idea of using the subcarrier as a stablized carrier to the PRC with a certain freq offset from the main carrier. I suppose what was swept was the AOM modulation frequency (i.e. modulation frequency of the AM applied to the subcarrier). If that is the case, the subcarrier seemed fixed at an arbitorary frequency (i.e. 50MHz) away from the carrier. If one of the AM sidebands hits the PRC resonance (i.e. 22, 44, 66MHz away from the main carrier), you still have the other sideband reflected back to the AS. Then the RF signal at the AS is still dominated by this reflected sideband. I feel that the phase modulation is rather suitable for this purpose.

If you are talking about ~MHz AM modulation by the AOM and scanning the PLL frequency from 1MHz to 60MHz, the story is different. And this should involve demodulation of the AS signal at the AM modulation frequency. But I still don't understand why we don't use phase modulation, which gives us the PDH type signal at the reflection (i.e. AS) port...



Attachment 1: 40M_SRMI_AM_annotated.pdf
Attachment 2: 40M_DRMI_AM.pdf
  7533   Thu Oct 11 21:26:40 2012 janoschUpdateGeneralPRC phase maps

Just some plots. There is nothing new here except for the fact that I learned how to analyze phase maps myself and how to prepare them for Finesse. In other words, everything is ready for a Finesse simulation.

These phase maps show the raw measurement of ITMY, ITMX and PRC:


Subtracting out the tilt from all phase maps, and the curvature from the PRC (I found the fit 121m consistent with previous fits), the one obtains the following residuals that can be used in Finesse (order is again ITMY, ITMX and PRC):


Attachment 3: PRC_40m.png
  2493   Sat Jan 9 15:02:01 2010 AlbertoUpdateABSLPRC scanning
I scanned the PRC in the frequency range of 30-60 MHz, untill the PLL lost lock. But everything is working fine.
The PRC remained lock for all time, with SPOB at ~1000.
I'm leaving the lab now, planning to come back tomorrow.
I turned the flipping mirrors down and closed the mechanical shutter of the auxiliary NPRO.
  7357   Fri Sep 7 01:25:53 2012 JenneUpdateGeneralPRC, SRC flashing

[Koji, Jenne]

* Found that IPANG was no longer centered, so we used PZT2's sliders to get the spot back on the center of the QPD.  Koji points out that I should have moved the lens even farther away, to have a larger beam (many mm, not just ~1) on the QPD.

* Found that MICH alignment had drifted, so used ITMX to realign MICH.

* Aligned PRM, got REFL beam through viewport.  Just made sure reflected beam was colinear with incident beam.

* PRC flashes were visible on AS camera. 

* PRM was more precisely aligned to have good interference with ITM reflections, by looking at AS camera.

* Decided to align SRM.  Spot was ~5mm too far to the north on the SRM....so we were off from center by ~5mm.

* Moved SR2 yaw a little bit to get spot centered on SRM.

*  Couldn't align SRM within bias slider range, so moved SRM in yaw to get reflected beam colinear with incident beam.

* Centered the spot on the steering mirrors.  The 2nd steering mirror after the SRM was moved by ~1 inch.  All mirrors after that were aligned to match this new beam.

* Found spot on AS table, aligned AS table mirrors so that beam hits AS55 PD window.  Haven't actually centered beam on PD.

* Transmission of 99% reflector was too weak to use with a card to get the beam back on the AS camera, so we moved the camera over to the AS110 path.

* Precisely aligned PRM and SRM by watching AS camera.

* Both the PRC and SRC look kind of funny.  Koji agrees.  Seriously.  They're a little weird. We can't align either recycling cavity, one ITM at a time (so PRM with ITMX, PRM with ITMY, SRM with either single ITM) to get rid of all the fringes.  Something is definitely funny.  It's got to be in the recycling cavities, since the weirdness is common between both ITMs for a given recycling mirror.  We need to take Sensoray views of these tomorrow.=

* There is some clipping on the right side of the AS camera view.  We have determined that it is not clipping at the viewport exiting the vacuum, but we aren't sure where it is.  It is at least before PZT4 (the 2nd PZT in the output AS path). 

  8022   Thu Feb 7 12:56:18 2013 JamieSummaryGeneralPRC/arm mode matching calculations

NOTE: There was a small bug in my initial calculation.  The plots and numbers have been updated with the fixed values.  The conclusion remains the same.

Using Nic's a la mode mode matching program, I've calculated the PRC mode and g-parameter for various PR2/3 scenarios.  I then looked at the overlap of the resultant PRC eigenmodes with the ARM eigenmode.  Here are the results:

NOTE: each optical element below (PR2, ITM, etc.) is represented by a compound M matrix.  The z axis in these plots is actually just the free space propagation between the elements, not the overall optical path length.


This is the ARM mode I used for all comparisons:


  tangential sagittal
gouy shift, one-way 55.63 55.63
g (from gouy) 0.303 0.303
g (product of individual mirror g) 0.303 0.303

PRC, nominal design (flat PR2/3)

This is the nominal "as designed" PRC, with flat PR2/3 folding mirrors.


  tangential sagittal
gouy shift, one-way 14.05 14.05
g (from gouy) 0.941 0.941
g (product of individual mirror g) 0.942 0.942

 ARM mode matching: 0.9998

PRC, both PR2/3 flipped

This assumes both PR2 and PR3 have a RoC of -600 when not flipped, and includes the affect of propagation through the substrates.


  tangential sagittal
gouy shift, one-way 19.76 18.45
g (from gouy) 0.886 0.900
g (product of individual mirror g) 0.888 0.902

ARM mode matching: 0.9806

PRC, only PR2 flipped

In this case we only flip PR2 and leave PR3 with it's bad -600 RoC:


  tangential sagittal
gouy shift, one-way 18.37 18.31
g (from gouy) 0.901 0.901
g (product of individual mirror g) 0.903 0.903

ARM mode matching: 0.9859


I left out the current situation (PR2/3 with -600 RoC) and the case where only PR3 is flipped, since those are both unstable according to a la mode.

I guess the main take away is that we get slightly better PRC stability and mode matching to the arms by only flipping PR2.

  8025   Thu Feb 7 17:10:11 2013 KojiSummaryGeneralPRC/arm mode matching calculations


I left out the current situation (PR2/3 with -600 RoC) and the case where only PR3 is flipped, since those are both unstable according to a la mode.

This surprises me. I am curious to know the reason why we can't make the cavity stable by flipping the PR3 as PR3 was supposed to have more lensing effect than PR2 according to my statement.

  8029   Fri Feb 8 00:23:33 2013 ranaSummaryGeneralPRC/arm mode matching calculations


 I would guess that either flipping PR2 or PR3 would give nearly the same effect (g = 0.9) and that flipping both makes it even more stable (smaller g). But what we really need is to see the cavity scan / HOM resonance plot to compare the cases.

The difference of 0.5% in mode-matching is not a strong motivation to make a choice, but sensitivity to accidental HOM resonance of either the carrier or f1 or f2 sidebands would be. Should also check for 2*f2 and 2*f1 resonances since our modulation depth may be as high as 0.3. Accidental 2f resonance may disturb the 3f error signals.

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