Two quadratures working in harmony.

The PR-flat cavity is flashing, although not locked.  I am too hungry to continue right now.

I put the FI_Back camera on a tripod, looking at the back of the Faraday.  The beam that Jamie and I were working with on Friday was clipped going back through the Faraday.  I twiddled the TT2 and PRM pointing such that the beam is retroreflecting, and getting back through the Faraday, and the cavity is still flashing.  I then redid the REFL path on the AS table a little bit.  The beam is currently going to the REFL camera, as well as REFL11 and REFL55. 

Some notes about the AS table:  The Y1 separating the main REFL beam from the REFL camera beam was mounted 90 degrees (rotated about the beam's axis) from what it should be.  I fixed it, so that the straight-through beam that goes to the camera is not clipped by the edge of the mount.  The reason (I think) this mirror was mounted backwards is that when mounted correctly, the back of the mount and the knobs interfere with the AS beam path.  I solved this by rotating the first out-of-vac REFL mirror a small amount so that the REFL and AS beams are slightly more separated. 

I am not seeing any nice PDH signal on dataviewer, so I went to check the signal path for the PDs.  The 11MHz marconi is on and providing RF, the EOM is plugged in to 11, 55 and 29.5 signals (no aux cavity scan cables are plugged in).  Both of the RF Alberto boxes are on.  I measured the RF output of both REFL11 and REFL55, although after the fact I realized that I was BAD, and had not found a 'scope that lets me change the input impedance to 50 ohms.  BAD grad student.  However, since I have numbers, I will post them, despite their being not quite correct:

284mVpp at 11MHz out of REFL11.  This is -6.9dBm

2mVpp at 55MHz out of REFL55, measured by 'scope

So, I can clearly see the 11MHz on the 'scope, and can see a very noisy, small 55MHz signal on the 'scope.  I need to think over dinner about what level of signal we should be sending to the demod boards, and whether or not I need more power coming out of the RFPDs.  There is a wave plate and PBS before beam goes to any of the REFL PDs, presumably to ensure that none of them get fried when we're at high power.  If I need more signal, I suspect I can rotate the wave plate and let more light go to the diodes.

[Anchal, Paco]

Yesterday we noticed that one of the ADC channels was overflowing. I checked the signal chain and found that CH3 on PR2 Sat Amp was railing. After a lot of debugging, our conclusion is that possible the PD current input trace is shorted to the positive supply through a finite resistance on the PCB. This would mean this PCB has a manufacturing defect. The reason we come to this conclusion is that even after removing the opamp U3 (AD822ARZ), we still measure 12.5 V at the pins of R25 (100 Ohm input resistance)

Please see the schematic for reference. We also checked the resistance between input of R25 (marked PDA above) and positive voltage rail and it came out as 3 kOhms. While I all other channels, this value was 150 kOhms.

I would like it if someone else also takes a look at this. We probably would need to change the PCB in this chassis or use a spare chassis.

Leave the unit to me. I can look it at on Mon. For a while, you can take a replacement unit from the electronics stack.

Also: Was this unit tested before? If so, what was the testing result at the time?

The unit was tested before by Tege. The test included testing the testpoint voltages only. He summarized his work in this doc. The board number is S2100737. Here are the two comments about it:
"This unit presented with an issue on the PD1 circuit of channel 1-4 PCB where the voltage reading on TP6, TP7 and TP8 are -15.1V,  -14.2V, and +14.7V respectively, instead of ~0V.  The unit also has an issue on the PD2 circuit of channel 1-4 PCB because the voltage reading on TP7 and TP8 are  -14.2V, and +14.25V respectively, instead of ~0V."

"Debugging showed that the opamp, AD822ARZ, for PD2 circuit was not working as expected so we replaced with a spare and this fixed the problem. Somehow, the PD1 circuit no longer presents any issues, so everything is now fine with the unit."

Note:  No issues were reported on PD3 circuit is is malfunctioning now.

The issue was present in the cable between the small adapter board and the rear panel. The cable and the Dsub 25 connectors were replaced. The removed parts were resoldered. Did the basic test of the channel.

Attachment 1: I cleaned up the area of the PD3 circuit of S2100556 and checked the voltage when the circuit was energized. The PD photocurrent line from the rear panel had S2100556 even with R25 removed. So the problem was between the rear panel to the outer side of R25. I've started to remove the cables to localize the issue and found that the issue disappeared when the ribbon cable was removed.

Attachment 2: I didn't investigate how the ribbon cable was bad. It was just trashed. The cable and the 25pin Dsub connectors were replaced and the line in question looked normal.

Attachment 3: All the components removed were stuffed again. The I/V-output of the circuit showed a 0.7mV offset but it seemed within the normal range. By touching R25 with a finger made it up to ~10mV as the other channels do. BTW: For 1000pF cap (C10) I used a stock 1000pF cap (KEMET, C330C102JDG5TA, 5%, 1kV, C0G) instead of nominal one (KEMET, C317C102G1G5TA,  2%, 100V, C0G).

Attachment 4: Noticed that the jumpers for shield grounding were missing. So they were installed (Attachment 5). This jumper is connected to Pin13. This line becomes Pin1 of the Dsub25 sat-amp cable because of the adapter board D2100148. The sat amp cable is D2100675. Hmm. In fact, this line does not touch the shield anywhere (unlike the aLIGO case). So only the chassis provides the cable shielding, no matter how the jumpers are connected or not connected.

Attachment 6: Final state of the circuit

I picked up the PR2 mirrors (labeled M1, M2) from Anchel's table and took them to the cleanroom. By inspection, I spotted some dust particles on M1. I wasn't able to remove them with clean air so I decided to use M2 which looked much cleaner. I wasn't able to discern any wedge angle on the optic. I inserted the optic into a thin optic adapter. The optic is thicker than I expected so I use long screws for the mirror clamping. I expect that the pitch balance will shift towards the front of the mirror so I assembled only 1 counterweight for now. The side blocks with wires in them were installed.

I engraved the SOS and installed the winches on it. Paco came in and helped me to hang the optic. Looking at the wire hanging angle I realize that 1 counterweight at the front is not enough. I install a second counterweight at the back and observe that I can cross the balancing point.

I locked the EQ stops. Suspension work continues tomorrow...

PR2's side magnet height was adjusted and its roll was balanced (attachment 1,2). I verified that the OpLev beam is still aligned. The pitch was balanced: First, using an iris for rough adjustment. Then, with the QPD. I locked the counterweight setscrew.

I turned off the HEPAs, damped PR2, and measured the QPD spectra (attachment 3). Major peaks are at 690mHz, 953mHz, and 1.05Hz. I screwed back the lower OSEM plate. The wires were clamped to the suspension block and were cut. Winch adapter plate removed. I wanted to push OSEMs into the OSEM plates but the wiki is down so I can't tell what was the plan. This will have to wait for tomorrow. Also here like with AS1 we need to apply glue to the counterweights.

[Raji, Jenne]

After lunch we began where Raji and Jamie had left things.  PR2 was unfortunately pitched down so far that it was almost hitting the table just in front of PR3.  I loosened the 4 clamp screws that hold the wire clamp assembly to the mirror holder, and tapped it back and forth until I was within hysteresis range, re-tightened, then tapped the top and bottom until we were at the correct beam height just in front of PR3.  I also had to unclamp it from the table and twist the base a tiny bit, since the beam was closer to hitting the beam tube than the optic.  Finally, however, PR2 is adjusted such that the beam hits the center of PR3.

Moving on to PR3, the pitch looked good while we were looking at the aperture placed near the face of ITMY, so we left that alone.  The beam is off in yaw though.  Several times I unclamped the tip tilt from the table, and twisted it one way or another, but every time when I tighten the dog clamps, I'm too far off in yaw.  The beam points a little too far south of the center of ITMY, so we were putting the beam a little north of the center before I clamped it, but even tightening the screws in the same order, by the same amount each time, causes a different amount of slipping/twisting/something of the TT mount, so we never end up directly in the center of the ITM.  It seems a little like a stochastic process, and we just need to do it a few more times until we get it right. 

We left it clamped to the table, but not in it's final place, and left for JClub.  On Monday morning we need to go back to it.  As long as we're pretty close to centered, we should probably also have someone at ETMY checking the centering, because we need to be centered in both ITMY and ETMY.

We have not touched the SR tip tilts, so those will obviously need some attention when we get to that point.

git repo: git@git.ligo.org:tega-edo/charmirrormap.git

The analysis code takes in a set of raw images, 10 in our case,  for each mirror and calculates the zernike aberration coefficients for each image, then takes their average. This average value is used to reconstruct the mirror height map.  Finally, the residual error between the reconstructed image and the raw data is calculated.

We repeat the analysis for different field of views (FoV) namely 10mm, 20mm, 30mm, 40mm and 46.5mm and save the results in the output folder of the repo.

The analysis output for a 10mm FoV aperture at the mirror center is shown in the attachement. These three images show the input data, the reconstructed mirror surface map and the residual error.

More correctly, a different G&H mirror (which we have a phase map for) was put into the PR2 TT, backwards.

Order of operations:

* Retrieve flat test G&H from BS chamber.  Put 4th dog clamp back on BS optic's base.

* Remove flat G&H from the DLC mount, put the original BS that was in that mount back.  Notes:  That BS had been stored in the G&H's clean optic box.  The DLC mount is engraved with the info for that BS, so it makes sense to put it back.  The DLC mount with BS is now back in a clean storage box.

* Remove PR2 TT from ITMX chamber.

* Remove suspension mounting block from TT frame, lay out flat, magnets up, on lint-free cloth on top of foil.

* Remove former PR2 G&H optic.

* Put what was the flat G&H test optic into the PR2 optic holder, with AR surface at the front.

* Put PR2 suspension block back onto TT frame.

* Put PR2 assembly back in the chamber, solidly against the placement reference blocks that Evan put in last Thursday.

* Close up, clean up, put labels on all the boxes so we know what optic is where.

Why the switcho-changeo?  We have a phase map for the G&H that is the new PR2, and a measured RoC of -706m, surface rms of 8.7nm.  Now, we can measure the former PR2 and see how it compares to our estimate of the RoC from the cavity measurements we've taken recently.

It is my pleasure to announce that the first lock of PR2 flipped PRMI was succeeded.



POP looks very nice. TEM00 and not wobbling.
We need more I/Q phase and gain/filter adjustment and characterization soon.

Some more details:
  MICH error signal: AS55_Q_ERR (using POP55 PD; phase rotation angle 70 deg)
  PRCL error signal: REFL11_I_ERR (phase rotation angle 80 deg)
  MICH feedback: BS (MICH_GAIN = -60)
  PRCL feedback: PRM (PRCL_GAIN = -0.5)

I wanted to see if PR2 motion makes PRC beam motion or not, using temporary oplev to PR2.
I could not measure the coherence between beam motion and PR2 motion, because I couldn't lock half-PRC today.
But I took spectra of PR2 oplev anyway.

Result:
  Below are the spectra of PR2 oplev outputs (taken using C1:SUS-ITMX_OL(PIT|YAW)_IN1). Bottom plot is POP DC during half-PRC locked yesterday.


Discussion:
  We see bump in PR2 oplev output at ~ 2-3 Hz. But we cannot say this is a evidence for PR2 motion making PRC beam motion because no coherence measurement was done. Also, oplev might be just seeing the ITMX stack motion.

  Resonant frequency of TTs measured were at ~ 1.8-1.9 Hz (elog #8054), but we cannot clearly see these peaks in oplev outputs. Did resonant frequency shifted because of different damping condition?

I did this simple calculation where I assumed 1W power from laser and 10% transmission past IMC. We would go ahead with V6-704/V6-705 ATFilms 3/8" optic. It would bring down the PRC gain to ~30 but will provide plenty of light for LO beam and alignment.

I corrected the calculation by adding losses by the arm cavity ends times the arm cavity finesse and also taking into account the folding of the cavity mirror. I used exact formula for finesse calculation and divided it by pi to get the PRC gain from there. Attachment 3 is the notebook for referring to the calculations I made.

Note that using V6-704 would provide 35 mW of LO power when PRFPMI is locked and 113 uW for alignment, but will bring down the PRC Gain to 17.5.

pre-2010 ITM (if it is still an option) would provide 12 mW of LO power when PRFPMI is locked and 28 uW for alignment, but will keep the PRC Gain to 24.6.

I still have to do a curvature check on the V6-704 optic.

I opened the notebook but I was not sure where you have the loss per bounce for the arm cavity.

    PRC_RT_Loss = 2 * PR3_T + 2 * PR2_T + 2 * Arm_Cavity_Finesse * ETM_T + PRM_T

Do you count the arm reflection loss to be only 2 * 13ppm * 450 = 1.17%?

Yeah, I counted the loss from arm cavities as the transmission from ETMs on each bounce. I assumed Michelson to be perfectly aligned to get no light at the dark port.  Should I use some other number for the round-trip loss in the arm cavity?

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:

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

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:

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:

From this, the power recycling cavity gain is calculated as:

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 (). This power is then multiplied by PRC Gain and transmitted through the PR2 to calculate the LO power.

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:

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.

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.

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.

Method:
 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).

Result:
 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

Discussion:
 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?
 * PRMI
   - Align incident beam, BS, REFL, AS, and MI using arms as reference
   - lock PRMI
   - 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?

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)

Method:
 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.

Result:
 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:    right:

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

Discussion:
  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.

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

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

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:
  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:    right:

Results:
  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.

Discussion:
  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.

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.

Results:
  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.


Discussion:
  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.
 

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.

Assumption:
 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.

Method:
  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.

Results:
  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.



Discussion:
  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.

Conclusion:
  I want to flip only PR2 and lock PRMI.

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

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:

[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.

[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.

Summary:

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

Details:

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

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

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

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

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 

• 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)

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 R_PRM R_MI
(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.

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

[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.

Check IPPOS/IPANG

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.

[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!

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)

b) case arm length = 38.40 m

PRC

  zoom ->

SRC

zoom ->

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

b) case arm length = 38.40 m

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

 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

 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.

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.

Summary:

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.

Details:

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?

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.

[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 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.

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)


  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!

 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.

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

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.