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ID Date Author Type Categorydown Subject
  7134   Thu Aug 9 10:09:32 2012 EricSummaryLockingYARM Locking and Calibration

Quote:

Quote:

 Once you've got C1:LSC-TRY_OUT as large as possible, you've locked the cavity.


 Both the transfer function and the coherence look good above roughly 30 Hz, but do not look correct at low frequencies. There's also a roll-off in the measured transfer function around 200 Hz, while in the model the magnitude of the transfer function drops only after the corner frequency of the cavity, around several kHz. I have attached a plot of the roughly analogous transfer function from the DARM control loop model (the gains are very large due to the large arm cavity gain and the ADC conversion factor of 2^16/(20 V) ). The measured and the modeled transfer functions are slightly different in that the model does not include the individual mirrors, while the excitation was imposed on ITMY for the measurement.

 

The next steps are to figure out what's happening in DTT with the transfer function and coherence at low frequencies, and to understand the differences between the model and the measurement.

 The cavity is actually "locked" as soon as the feedback loop is successfully closed.  One easy-to-spot symptom of this is that, as you mentioned elsewhere in your post, TRY is a ~constant non-zero, rather than spikey (or just zero).  Once you've maximized TRY, you've got the cavity locked, and the alignment optimized.

We didn't get to this part of "The Talk" about the birds, the bees, and the DTTs, but we'll probably need to look into increasing the amplitude of the excitation by a little bit at low frequency.  DTT has this capability, if you know where to look for it.

It would be great to see the model and your measurement overlayed on the same plot - they're easier to compare that way.  You can export the data from DTT to a text file pretty easily, then import it into Matlab and plot away.  Can you check and maybe repost your measured plots?  I think they might have gotten attached as text files rather than images.  At least I can't open them. 

 Here's the same plots in pdf format now. I originally posted them as jpg because I couldn't open the resulting pdf from DTT on rosalba, but I could open the jpg. I'll look into overlaying the measured and modeled curves as well.

Attachment 1: cal_swept_sine3_magnitude.pdf
cal_swept_sine3_magnitude.pdf
Attachment 2: cal_swept_sine3_phase.pdf
cal_swept_sine3_phase.pdf
Attachment 3: cal_swept_sine3_coherence.pdf
cal_swept_sine3_coherence.pdf
  7139   Fri Aug 10 09:51:51 2012 EricSummaryLockingYARM Locking and Measurements

I forgot to post this last night, but I locked the YARM again yesterday and misaligned the other optics. I took measurements on ITMY and ETMY with DTT again as well. At the end of the day I aligned the rest of the optics before I left.

  7145   Fri Aug 10 16:39:44 2012 EricSummaryLockingMichelson Locking

I'm working on locking the Michelson now in order to put an excitation on one of the input test masses and measure the resulting error signal at the anti-symmetric port. I aligned the beams from ITMX and ITMY by looking at the AS camera with the video screens, but the fringes were not destructively interfering. Jenne advised that I look at the gain on the MICH servo filter modules in the LSC screen. We flipped the sign on the gain (it was 0.120 and it is now -0.120) and the fringes destructively interfered as desired after this change.

For purposes of documentation, I locked the YARM earlier in the morning before moving on to the Michelson. The purpose of this was to put another excitation on C1:SUS-ETMY_LSC_EXC and then measure the error signal on C1:LSC-POY11_I_ERR.

  7149   Fri Aug 10 19:49:11 2012 EricSummaryLockingMichelson Locking Procedure and Measurements

Today I worked on locking the Michelson. Here's what I did:

 

  1. Open Data Viewer and Restore Settings /users/Templates/JenneLockingDataviewer/MICH.xml. This opens the C1:LSC-ASDC_OUT and C1:LSC-AS55_Q_ERR plots.

  2. Check the LSC screen to verify that the path between the Servo Filter Modules and the SUS Ctrls are outlined in green. If not turn on the OUT button within the Filter Servo Modules, enable LSC mode, and turn on the SUS Ctrls for the BS.

  3. Misalign all optics other than BS and one of ITMX and ITMY. The ITMY was already well-aligned from my work on locking the YARM, so I actually chose to misalign ITMY at first.

  4. Restore BS and ITMX. Use the AS camera on the video screen as your guide when aligning ITMX.

  5. Adjust pitch and yaw of ITMX until a bright, circular spot appears near the middle of the AS camera.

  6. Now restore ITMY and adjust pitch and yaw until a second circular spot appears on the AS camera.

  7. Adjust both ITMX and ITMY until both bright spots occupy the same location. If the spots remain bright when they are in the same location you are locking onto a bright fringe actually, and need to flip the sign of the gain on the MICH servo filter modules. I had to do this today in fact, as discussed in ELOG 7145.

  8. If the sign is correct, the two beams should interfere destructively and the formerly bright spots will form a comparatively dark spot. The shape of the spot will likely be two bright lobes separated by a dark middle.

  9. C1:LSC-ASDC_OUT should be a roughly flat signal, and the goal now is to minimize the magnitude of this signal. The smaller this signal, the darker the AS camera should look. Decent target values for C1:LSC-ASDC_OUT are around 0.10 to 0.05.

 

Once I did this, I made measurements by exciting C1:SUS-ITMY_LSC_EXC and measuring with C1:LSC-AS55_Q_ERR. I ran a logarithmic swept sine response from 1 to 1000 Hz again, with an envelope amplitude dependence. Again I looked at the measured transfer function and coherence. I was able to get good coherence, but it was somewhat erratic in that it dipped low at high frequency multiple times.

  7168   Tue Aug 14 00:42:40 2012 JenneUpdateLockingPOX signal sometimes looks very funny

I'm trying to lock / align the Xarm, and POX 11 I looks funny sometimes.

I attach 2 screenshots so you can see what I mean.  I'm leaving them uncropped so that you can see the only thing that has changed is the LSC enable / disable button. 

The situation:

PRM, SRM, ITMY, ETMY all misaligned.  BS, ITMX, ETMX aligned so that most of the time I can't lock better than 04, bad in yaw, but very occasionally I'll get lucky and catch a 00.  When the LSC enable switch is ON (2nd attachment), the POX signal (green trace in dataviewer in both attachments) looks almost square-ish, and definitely funny.  It doesn't seem to correspond directly to flashing in the cavity (red trace in dataviewer in both attachments).  However when I disable the LSC, POX goes back to looking normal - 1st attachment.  Right around -5 seconds in the 1st attachment, I disabled the LSC.

I don't really know what this means.

Attachment 1: POX_13Aug2012_LSCdisabled_pox_is_normalish.png
POX_13Aug2012_LSCdisabled_pox_is_normalish.png
Attachment 2: POX_13Aug2012_LSCenabled_pox_is_squareish_funny.png
POX_13Aug2012_LSCenabled_pox_is_squareish_funny.png
  7169   Tue Aug 14 04:32:49 2012 rana, yoichiUpdateLockingPOX signal sometimes looks very funny

 The alignment was way off. We moved the PZT, the BS, and the x arm to get it to lock. Along the way we noticed that giving the ETM and POS offsets makes it tilt a lot. The DC coil balancing is no good at all.

After locking, we tuned up the X arm filters in the LSC and activated the filter module triggers.  I would attach a screenshot of the trigger screen, but sadly it has no snapshot button on it.

WE changed the integrator into a double integrator with a complex zero pair. We also replaced the 1:50 boost with a 2nd order complex pole:zero pair. And added a 18 Hz RG. These were all set by looking at the error point spectra and minimizing the RMS. Hopefully, this kind of work will all be obsolete once we get the optimal feedback code. For now, the arm is very stable - we're leaving it locked overnight since the filter triggering seems to work well.

The loop kept oscillating, so we turned the xarm gain down from the 0.3 that we found it at down to 0.045. We measured the loop gain using our old xarm loopgain DTT template (which is in the Templates directory, not in /users/IAmAnAmateur/secret/secret/bozo/). It shows that we are missing ~20 deg of phase at the peak of the phase bubble compared to the old days. We guess that its because of the downsample/upsample digital AA filters which we now have in addition to the 7kHz hardware AA/AI which we still have from the pre-upgrade times). We (Jamie) have to think about how to rationalize this: we cannot survive with double AA/AI.

Another big hindrance in the lock acquisition is that the whitening filters were on. Because the WG is set to 45 dB, the ADCs are getting saturated when the flashes are large. We should have the whitening filters switch after acquiring lock.

Also, why are all the camera views of the ITMs and ETMs different? Steve, please go back and make them all the same (angles, aperture, lenses, etc.). Without them being the same, we cannot compare them.

ETMXF_1028975007.bmp

ETMXT_1028975105.bmpAS_1028975166.bmp

 I have found the video capture scripts in Yuta's personal directory. This is illegal, of course. All useful scripts (even when in development) go into the shared scripts directory. As a punishment, I have added some nasty typos to a couple of his other scripts and then backdated the timestamps so that he cannot find it easily.

 Also, I fixed the "mcup" script. After the ringdown people inserted the pickoff for MC2 trans, no one adjusted the thresholds in the MC autolocker. I've fixed mcup to trigger at 7000 cts. This should be changed back if the pickoff is removed someday. MC WFS now coming on.

Attachment 1: ITMX_1028974969.bmp
  7208   Thu Aug 16 19:12:30 2012 JenneUpdateLockingLong arm lock stretches

YARM_awesome_lock_stretch.png

After Rana and Yoichi tweaked the arm locking filters, we have had some pretty awesome lock stretches. 5-day minute trend.

  7240   Tue Aug 21 01:54:09 2012 JenneUpdateLockingFPMI locked - arms locked with IR

I (for the first time personally) locked the FPMI.  I have data for the POX11I, POY11I, AS55Q error signals for each arm and the Michelson (JenneLockingDTT/FPMI_error_signals.xml), but I haven't calibrated the data yet - Self: do this!  FPMI with arms locked using IR has been happily locked for a long time now - this is good.

From elogs / my old MICH calibration script, I have the plant calibrations of:

POY:  1.4e12 cts/m

POX: 3.8e12 cts/m

AS55: 9.4e9 cts/m

MICH has FM 5 on, Xarm has FM4-10 all on, Yarm has FM3-10 all on. 

Post note: FM 3 - the integrator - for Xarm wasn't triggered.  It turns on just fine, so I've got it triggered just like Yarm.

Also, just remembered - I turned off the XARM TRX power normalization, since it was causing crazy numbers in the xarm servo.  The XARM locked pretty easily after that.

  7246   Tue Aug 21 22:54:47 2012 JenneUpdateLockingRemoved beam dump from POY path

POY was looking funny, and the YARM wasn't locking.  It looked like POY wasn't seeing any light at all.  I went to check, and it looks like a beam dump got accidentally placed in the POY path during oplev adjustments this morning.  POY is back, locking continues.

  7250   Wed Aug 22 16:50:09 2012 JenneUpdateLockingDouble integrator in ARM LSC servos

Last week, Rana changed the integrators in the arm LSC servo filters to be double integrators with complex poles. 

Yesterday, I found that using the "timeout" feature of Foton (at filter ON/OFF request, waits for zero crossing, or T seconds, whichever comes first) is useful for turning on the integrators, but bad for turning them off.  When we're locked, the error signal is oscillating around zero, so there is often a zero crossing.  When we lose lock, we want to turn off the filter immediately.  But, as soon as lock is lost, the input signal gets large, and doesn't often cross zero, so the filter waits 8 seconds until actually turning off.  If the arm flashes any time during that 8 sec, we send a big kick to the optics.

An alternative option could be ramping the filter on.  However, since the double integrator has -180deg phase at low frequencies (until the poles at ~5Hz), the transition between no filter (0deg phase) and integrator on could be problematic.  I simulated this, and find that for the very beginning of the ramping process, we would have a problem. 

The filter is defined as:  NoFilter * (1 - R) + Integrator * (R), so for R=0, the integrator is off, and for R=1, the integrator is fully on.  R can be any value [0,1]. 

The first figure is the time series (1 second, 16kHz), ramp goes from 0->1 or 1->0 in 1 second:

 DoubleIntegrator_timeSeries_LowRes.png

 

The second figure is bode plots for selected values of R:

DoubleIntegrator_Bode_vs_Ramp_LowRes.png

As R gets smaller and smaller, the notch goes to lower frequency, and becomes higher Q.  So perhaps ramping is not a good answer here. 

What if we go for single or triple integrator, to get rid of the (+1) + (-1) problem?

  7334   Tue Sep 4 11:32:58 2012 JenneUpdateLockingFriday in-vac work

Elog re: Friday's work

Adjusted PZT2 so we're hitting the center of PR2. 

Noticed that the beam centering target is too low by a few mm, since the OSEM set screw holes that it mounts to are lower than the center line of the optic.  This meant that while we were hitting the center of PR2, the beam was half clipped by PRM's centering target.  We removed the target to confirm that the beam is really centered on PR2.

Checked the beam on PR3 - it looked fine.  There had been concern last week that PR2 was severely pitched forward, but this turns out to be an effect of the PRM centering target being too low - shoot the beam downward to go through the hole, beam continues downward to hit the bottom of PR2, so beam is falling of the bottom of PR3.  But when we actually centered the beam on PR2, things looked fine on PR3. 

Checked that the beam approximately goes through the beam splitter.  Again, the targets are too low, and these 45 deg targets' holes are smaller than the 0 deg targets, so we don't see any beam going through the target, since the beam is hitting the target higher than the hole.  The beam looked left/right like it was pretty close to the hole, but it was hard to tell since the angle is bad, and I'm not infinitely tall.  We should check again to make sure that the beam is going through properly, and we're not clipping anywhere.  I'll need help from a height-advantaged person for this.

Checked that the beam is hitting the center of the ITMY, as best we can see by using an IR card at the back of the optic.  We didn't try reaching around to put a target on the front side. 

We were debating whether it would be worth it to open ETMY this week, to check that the beam transmitted through the BS hits the center of ETMY.

We also took a quick look around the AS optics, but since that depends on BS/ITMX alignment, we weren't sure how to proceed.  We need a plan for this part.  All suspended optics were restored to their last good alignment, but we haven't tried locking MICH or anything to confirm that the alignment. 

To do list:  Check no clipping on ITMY table of beam between BS and ITMY, clipping on POY optics.  Also, oplev is clipping on cable holder thing on the table - this needs to be moved.  .....other?

  7339   Tue Sep 4 20:06:04 2012 JenneUpdateLockingMC scan input switched to the 11MHz port of EOM

Since the EOM's signal combiner (splitter backwards) is frequency-independent, Koji and Jamie (in the proper turn off, turn on order) put the 55MHz signal back to the EOM, and put the MC mode scan input to the 11MHz port.  This way we can lock the Michelson tomorrow, and we don't have to keep switching cables around when Riju wants to take some scans.

  7514   Wed Oct 10 00:18:58 2012 JenneUpdateLockingREFL camera aligned

I moved some of the REFL optics on the AS table by a teeny bit to accomodate the new place that the REFL beam exits the chamber (none of this was done while we were at air....we were only dealing with the AS beam at the time, and were happy that REFL came out of the vacuum).

The REFL beam is now on the REFL camera (with PRMI aligned), and the beam is going toward the 4 REFL RF PDs, but it's not aligned to any of them.

I have some questions as to mystery optics on in the REFL path.  There is a 90% BS, and I don't know where the 10% reflection goes....is it going to beat against the AUX Stochino laser?

I have to go, and I didn't fix the videocapture script today, so pix tomorrow, I promise.

  7573   Thu Oct 18 03:57:20 2012 JenneUpdateLockingAlignment is really bad??

The goal of the night was to lock the Y arm.  (Since that didn't happen, I moved on to fixing the WFS since they were hurting the MC)

I used the power supplies at 1Y4 to steer PZT2, and watched the face of the black glass baffle at ETMY.  (elog 7569 has notes re: camera work earlier)  When I am nearly at the end of the PZT range (+140V on the analog power supply, which I think is yaw), I can see the beam spot near the edge of the baffle's aperture.  Unfortunately, lower voltages move the spot away from the aperture, so I can't find the spot on the other side of the aperture and center it.  Since the max voltage for the PZTs is +150, I don't want to go too much farther.  I can't take a capture since the only working CCD I found is the one which won't talk to the Sensoray.  We need some more cameras....they're already on Steve's list.

When the spot is a little closer to the center of the aperture than the edge of the aperture (so the full +150V!!), I don't see any beam coming out of AS....no beam out of the chamber at all, not just no beam on the camera.  Crapstick.  This is not good.  I'm not really sure how we (I?) screwed up this thoroughly.  Sigh.  Whatever ghost REFL beam that Kiwamu and Koji found last week is still coming out of REFL.

Previous PZT voltages, before tonight's steering:  +32V on analog power supply, +14.7 on digital.  This is the place that the PRMI has been aligned to the past week or so.

Next, just to see what happens, I think I might install a camera looking at the back (output) side of the Faraday so that I can steer PRM until the reflected beam is going back through the Faraday.  Team K&K did this with viewers and mirrors, so it'll be more convenient to just have a camera.

Advice welcome.

  7579   Fri Oct 19 01:21:42 2012 EvanUpdateLockingAligning PZTs, PRM

[Evan, Jenne]

Tonight we made an attempt at getting the PRM + ITMY aligned with correct input pointing. We steered the good PZT so that the input beam makes it through the aperture in front of ETMY. We then aligned the PRM so that the retroreflection of the input beam makes it back into the Faraday. After that we tried dithering the alignment of ITMY and the beamsplitter to see if we could see a spot flash across the AS port, but we saw nothing.

For the PRM alignment we set up a camera looking into the window at the Faraday in the IOO chamber; it's called FI_BACK. We stole a 50mm lens from the ETMY face camera.

We also tried looking for beam on IP_POS and IP_ANG. When the input beam is aligned to pass through the ETMY aperture, we can see beam on the steering mirrors preceding IP_POS, but it hits a mirror mount. When the input beam is aligned as it was on Monday, it clips on the ETMY aperture but makes it further along the IP_POS optical path.   In both cases, we weren't able to see any beam coming out for IP ANG. 

  7581   Fri Oct 19 16:24:39 2012 ranaUpdateLockingAlignment is really bad??

 

 VENT NOW and FIX ALIGNMENT!

  7730   Tue Nov 20 02:57:24 2012 Ayaka, Den, KojiUpdateLockingred in arms

We aligned and locked x and y arms.

MCL loop makes arms lock unstable, adds a lot of noise at frequencies 60-100 Hz. We'll fix it.

At some point we were not able to lock because of ADC overflows of PO signals. They happened if whitening filters were enabled. So we reduced the gain of POX whitening filters down to 36 dB and POY - to 39 dB. Now cavities can be locked with whitening filters.

Also we changed the pedestal of the lens in the beam path to the POX because the beam was too high.

 

arms.png    arms_psd.png

etmxf.png  etmyf.png

itmxf.png     itmyf.png

etmxt.png    etmyt.png

  7736   Wed Nov 21 01:31:37 2012 Koji, AyakaUpdateLockingalignment on ETMX table

Since the transmission beam on ETMXT camera seemed to be clipped, we checked the optics on ETMX table.

We aligned the lens so that it is orthogonal to the beam, then the beam shape looks fine.

output.nv12.bmp

Also we removed some an-used optics which were used for fiber input.

  7872   Wed Jan 2 15:33:23 2013 JenneHowToLockingWe should retry in-air locking

Immediate things to do include finishing installation of new TTs and re-routing of oplev paths in the BS chamber, but after all that, we should retry in-air locking.

The last time we (I) tried in-air locking, MICH wouldn't lock since there was only ~ 6uW of light on AS55 (see elog 7355).  That was before we increased the power into the MC by a factor of 10 (see elog 7410), so we should have tens of microwatts on the PD now.  At that time, we could barely see some PDH signal hidden in the noise of the PD, so with a factor of 10 optical gain, we should be able to lock MICH.

REFL should also have plenty of power - about 1.5 times the power incident on the PRM, so we should be able to lock PRCL. 

Even if we put a flat G&H mirror after the PRM to make a mini-cavity, and we lose power due to poor mode matching, we'll still have plenty of power at the REFL port to lock the mini-cavity.

For reference, I calculate that at full power, POX and POY see ~13uW when the arms are locked.

 

POX/POY power =  [  (P_inc on ITM) + (P_circ in arm)*(T_itm)  ] * (pickoff fraction of ITM ~ 100ppm)

REFL power = (P_inc on PRM) + (P_circ in PRCL)*(T_prm)     =~ 1.5*(P_inc on PRM)

  7905   Wed Jan 16 18:08:06 2013 JenneUpdateLockingExpected PRC gains

I was calculating the power recycling gains we expect for different versions of the PRC, and I am a little concerned that we aren't going to have much gain with the new LaserOptik mirrors.

I'm using

                       t_PRM^2

G =  -------------------------------------------

       (1 - r_PRM * r_PR2 * r_PR3 * r_end)^2

 

from eqn 11.20 in Siegman.

r_end is either the ITM (for a symmetric Michelson) or the flat mirror that we'll put in (for the PR-flat test case).

r = sqrt( R ) = sqrt( 1 - T ) for mirrors whose power transmission is the quoted value.

 

Some values: 

t_PRM^2 = T_PRM = 0.055   --------->   r_PRM = sqrt( 1 - 0.055 )

T_G&H = 20e-6   ---->   r_G&H = sqrt( 1 - 20e-6 )

T_LaserOptic = 0.015 (see elog 7624 where Raji measured this...1.5% was the best that she measured for P polarization.  Elog 7644 has more data, with 3.1% for 40deg AoI) -------> r_LasOpt = sqrt( 1 - 0.015 ) or sqrt( 1 - 0.031)

T_ITM = 0.014 -----------> r_ITM = sqrt( 1 - 0.014 )

 

Some calculations with 1.5% LaserOptik transmission:

G_PRC_2G&H = 45

G_PRC_G&H_LasOpt = 31

G_PRM_flatG&H = 51

With the 3% LaserOptik transmission:

G_PRC_G&H_LasOpt = 22

G_PRM_flatG&H = 30

More ideal case of just PRM, flat mirror (either ITM or G&H), ignoring the folding mirrors:

G_PRM_ITM = 45

G_PRM_flatG&H = 70

 

Punchline:

If the LaserOptik mirror has 1.5% transmission at ~45 degrees, the regular PRC expected gain goes down to 31, from 45 with both folding mirrors as G&Hs.

  7906   Wed Jan 16 18:52:49 2013 JenneUpdateLockingPRM - Flat mirror cavity plan

Game plan:

* Put 2" G&H mirror into BS chamber, in front of BS.

* Align it, lock cavity using an existing REFL PD.

* Align POP setup so I can use POP camera to take image of transmitted cavity mode, and actually take that image.

* Take image of face of PR2.

* Measure finesse of cavity using POP, or a Thorlabs PD at POP (looking at transmission through PR2) by scanning PRM, and infer cavity gain....compare with values in elog 7905.

* If time / inclination allow, take beam scan measurements of the REFL port.

I will not be able to do as was done in elog 6421 to look at the beam size at POP for non-resonating beams.  I expect ~0.1uW of light at POP in the non-resonant case:  100mW * 5.5% * 20ppm = 0.11microwatts.

 

  7909   Wed Jan 16 20:27:16 2013 ranaUpdateLockingExpected PRC gains

Why would we use such a bad optic in our recycling cavity? Is 1.5% the spec for these mirrors? Is this the requirement that Kiwamu calculated somehow? Did anyone confirm this measurement?

I can't believe that we'll have low noise performance in a RC where we dump so much power.

  7910   Thu Jan 17 00:17:31 2013 JenneUpdateLockingExpected PRC gains

Quote:

Why would we use such a bad optic in our recycling cavity? Is 1.5% the spec for these mirrors? Is this the requirement that Kiwamu calculated somehow? Did anyone confirm this measurement?

I can't believe that we'll have low noise performance in a RC where we dump so much power.

 Yeah, Koji mentioned in response to Raji's measurements several months ago that the LaserOptic mirros were pretty far out of spec. We should probably redo the measurement to confirm.

  7913   Thu Jan 17 15:48:21 2013 JenneUpdateLockingPRM - Flat mirror cavity

 

 2" G&H mirror is installed on a DLC mount just in front of the BS.  I had to remove one of the 4 BS dog clamps, so we must put it back when we are finished with this test.

I aligned the G&H mirror such that the reflected beam is overlapped with the incident beam, and I aligned the PRM such that the regular REFL beam is retro-reflected.  This is the same as getting the beam bouncing off the PRM back to the G&H to be overlapped.

I then saw flashes of the cavity, when I held a card with a hole in the cavity, so the beam was going through a small aperture in the card, but I still saw flashes.  I was not able to see flashes on the IR card transmitted through the G&H mirror.

I also cannot see any flashes or scattered light on the face of PR2 camera.

I do, however, see flashes on the face of the PRM.  Movie saved, will post soonly.

Light is coming out of REFL on the AS table, but it's clipped somewhere....needs investigation/work before we can lock.

I also didn't see anything at the POP port with a card, but I'm hopeful that perhaps with a camera I'll see something.

  7916   Fri Jan 18 00:41:34 2013 JenneUpdateLockingDust?

I was thinking tonight about more possible reasons that our PRC sucks, and I wonder if dust on the BS could create the problem.

Historically, Kiwamu and I found a few dust particle scattering centers every time we inspected the test masses before drag wiping. Sometimes, there would be one frustratingly close to the center of the optic. I'm not sure if we ever made note of how many we saw and where they were, except out loud to the assembled crowd.

Anyhow, the BS is the only IFO optic that was not replaced, so I'm not sure how long it has been since it was cleaned. If the PR-flat cavity looks okay and we take out the BS to do a PRM-ITMY cavity, we should inspect the beam splitter.

Also, the PRM could need cleaning, but at least it has been drag wiped within recent memory.

My question is, could a few scattering centers cause the behavior that we are seeing?

 

EDIT:  List o' elogs....

 

Elog 5301 - Some details on dust seen on ITMs and ETMs, Aug 2011.

Elog 4084 - Kiwamu's in-situ drag wiping how-to, with details on some of the dust we saw. Dec 2010.

Elog 3736 - PRM drag wiped before suspension (Oct 2010)

Elog 3111 - June 2010, BS drag wiped.

  7917   Fri Jan 18 09:54:18 2013 JenneUpdateLockingPRM - Flat mirror cavity

Quote:

I do, however, see flashes on the face of the PRM.  Movie saved, will post soonly.

 Dang it.  I didn't confirm that the movie was good, just that it was there.  It's corrupted or something, and won't play.  I'll just have to make a new movie today after I realign the cavity.

  7918   Fri Jan 18 12:08:08 2013 KojiUpdateLockingDust?

No

Quote:

My question is, could a few scattering centers cause the behavior that we are seeing?

 

  7928   Tue Jan 22 19:53:01 2013 JenneUpdateLockingPR-flat cavity status - not locked

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.

  7931   Wed Jan 23 19:05:16 2013 JenneUpdateLockingPR-flat cavity status - locks!

Status update

I (with help from Q) have redone the POP path on the ITMX table.  1" iris is a little too small, so I took it out.  2" lens moved to be centered on POP beam.  2" Y1 didn't need moving.  Straight refl from the 2" Y1 was aligned on to a PDA10CS (set to 70dB). This PD is blocking the usual POP55 diode.  BS which sends beam to camera was moved to allow room for the new temp DC PD.  Refl from this BS goes to the POP camera, which was moved so that the POP beam takes up most of the camera.  BS that would normally take half of the camera's beam and send it to POP22 (Thorlabs PD) is removed, so no beam to POP22.

Also, I have taken the output of the PDA10CS and hijacked the "POP110" heliax cable.  This was connected to this Thorlabs PD which is used as POP22.  (Kiwamu and I had long-term borrowed the 110 demod board for an AS 110 diode, so the "POP110" heliax was really only serving POP22.) There are yellow labels on the new temp and old regular cables, so we can undo my hack.  Similarly, on the other end of the heliax at the LSC rack, I have taken the heliax's output and sent it to the POPDC input on the whitening board.  Thus, the regular POPDC SMA cable is unplugged, but labeled again with big yellow labels.

In other news - the PR-flat cavity locks!!! 

Koji and I coarsely rotated the REFL11 phase such that the signal is predominantly in the I phase.  We set the LSC input matrix to use REFL11I for PRCL, and the output matrix is set to actuate on PRM.  Then we set the gain to -0.005, and it locked!!!!

 

EDIT:  I turned back on the PRM oplev (after Manasa aligned it and redid the out-of-vac oplev layout a bit), and the motion of the cavity is slightly reduced, although there's still a lot going on.  The cavity is vaguely well aligned, although it's time to go make sure that the beams are still on the REFL and TRANS PDs.  However, it's dinner time.

  7934   Wed Jan 23 20:46:46 2013 Zen MasterUpdateLockingPR-flat cavity status - locks!

Quote:

I (with help from Q)

 Two quadratures working in harmony.

yinYang.png

  7945   Mon Jan 28 17:01:19 2013 DenUpdateLockingVideo of PRM-flat test cavity

What mode will you get if lock the cavity PRM - ITMY/ITMX/TEST MIRROR without PR2, PR3 and BS?

Is it possible to skip MC1, MC3 and lock the laser to this test cavity to make sure that this is not actuator/electronics noise?

  7951   Tue Jan 29 10:50:02 2013 JenneUpdateLockingVideo of PRM-flat test cavity

 

I think Den accidentally edited and overwrote my entry, rather than replying, so I'm going to recreate it from memory:

I aligned the PRM-flat test cavity (although not as well as Jamie and Koji did later in the evening) and took some videos. Note that these may not be as relevant any more, since Jamie and Koji improved things after I left.

 

Also, before doing anything with the cavity, I tuned up the PMC since the pitch input alignment wasn't perfect (we were getting ~0.7 transmission), and also tuned up the MC alignment and remeasured the MC spot positions, to maintain a record.

  7957   Tue Jan 29 19:50:49 2013 JenneUpdateLockingBetter POP layout, no extra PRM motion with locked cavity

[Jenne, Jamie, Manasa]

Today's activities focused on getting the POP layout improved, so that we could get clean data for the mode scan measurement. 

As Jamie and Koji pointed out yesterday, the beam was still a little too big on the POP DC PD, and was falling off the diode when the beam moved a small amount.  We have fixed things so that the PD is now at the focus of the lens, and the camera is at a place where the beam takes up most of the area on the TVs.  The beam no longer falls off the PD with cavity fluctuations.  A key point of this work was also to use an extra 2" optic to steer the beam down the length of the POP table, and then do the 50/50 beam splitting later with a 1" optic.  The 1" BS that we had been using (including with the "real" POP beam) is too small.  We could not find a 2" 50/50 BS, so we opted to do the splitting closer to the focal point.  Also, the BS that was splitting the beam between the PD and the camera was a 33% reflector, but now is a 50/50 BS. When we put back the 'real' POP path, we need to consider using larger optics, or a faster lens. The POP path is now good, hopefully for the duration of the half cavity test.

After getting the POP path taken care of, and tweaking up the cavity alignment a little bit, the transmitted power on POP DC is ~22,000 counts, with occasional fluctuations as high as 25,000 counts. 

Jamie looked at the REFL path, and things look sensible there.  The unlocked REFL power is ~36 counts, and the locked power is ~20 counts.  I'm not sure what the 160 counts that Koji mentioned in his edits to elog 7949 is about.

I looked at the PRM oplev with the cavity locked and unlocked, and with today's alignment, there seems to be no difference in the amount of PRM motion when the cavity is locked vs unlocked. 

HalfPRCL_PRM-flatMirror_RefsAreLocked_OthersUnlocked.png

 It still looks like we might be seeing some clipping in the in-vac POP steering mirrors - we haven't gotten to them yet.

Jamie is currently modifying Yuta's mode scan analysis script to look at the data that we have of the cavity.

 


We need more 2" optics.  There are no mounted 2" spares in the various optic "graveyards" (which, PS, we should consolidate all into the cabinet with doors near the optics bench), and the options for boxes in the drawers is slim pickin's.  We have some S-pol stuff, but no Y1s or BS-50s for P-pol.  Since POP, POX, POY, IPANG, TRX and TRY all come out of the vacuum with large beams, we should have some options for these laying around for this kind occasional temporary thing.  We also need to choose, then purchase better 2" lenses for the pickoffs.

Attachment 1: HalfPRCL_PRM-flatMirror_RefsAreLocked_OthersUnlocked.pdf
HalfPRCL_PRM-flatMirror_RefsAreLocked_OthersUnlocked.pdf
  7959   Tue Jan 29 21:07:48 2013 JenneUpdateLockingPRM coils need diagonalizing

 

 [Jenne, Jamie]

We tried actuating on PRM so that we go through fringes in a known, linear way.  We used C1:SUS-PRM_LSC_EXC and awggui.  It seems that we get a lot of angular motion when we actuate....we need to look into this tomorrow.

EDIT/UPDATE:  Last night we tried several combinations of frequency and amplitude, but just for an idea,  we were using 2Hz, 1000cts.  Using Kiwamu's calibration in elog 5583 for the PRM actuator of 2e-8/f^2 m/cts, this means that we were pushing ~5nm.  But when we pushed much harder (larger amplitude) than that, we saw angular fringing. 

  7961   Wed Jan 30 11:16:32 2013 JenneUpdateLockingMode spacing calc

[Jenne, Jamie]

We did a few pen and paper calculations yesterday to confirm for ourselves that the half PRC should have nicely separated modes.  The half cavity is L=4.34m long, assuming flat mirror is 3.5 inches in front of BS.  That 3.5" is a guess, not a measurement.

Finesse

F = ( pi * sqrt(r1 * r2) ) / (1 - r1*r2) = 111.

Full width at half max

FWHM = c / (2 * L * F) = 311 kHz

FWHM in meters = FWHM * L/f = L*1064nm/c = 4.8 nm

Free spectral range

nu_fsr = F * FWHM = 34.5 MHz

Mode Spacing (eq 19.23 from Siegman)

omega = (n + m) * arccos(\pm sqrt(g1*g2)) / pi     *   (2*pi*c)/(2L)

For our half cavity, g1*g2 = 0.96

For the 01 or 10 modes, n+m = 1

omega = 13.7e6 rad/sec

mode spacing between 00 and 01 = 2.2 MHz

Thus, the modes should be well separated

=>  spacing is 2.2 MHz while FWHM is 0.311 MHz  (cavity fsr = 34.5 MHz)

 

EDIT JCD 31Jan2013:  Fixed mode spacing eqn to be diff between TEM00 mode and HOM, not plane wave and HOM.  Then fixed the factor of 2 error in the mode spacing numbers.

  7966   Wed Jan 30 15:45:09 2013 ZachUpdateLockingMode spacing calc

Quote:

Thus, the modes should be well separated

=>  spacing is 4.3 MHz while FWHM is 0.311 MHz  (cavity fsr = 34.5 MHz)

Something looks fishy. I calculate a transverse mode spacing of 2.21 MHz---is there a factor of two missing somewhere in your analytical calculation?

delta_f = (1/2/pi) * w01 - w00 = (1/2/pi) * acos(±sqrt(0.96)) /pi *2 * pi * c /2 /L = 2.21 MHz

I guess that's still OK, but if you are using 11-MHz sidebands, there is a n+m=5 mode within one linewidth of resonance. Can you use 55?

-------------

May I suggest my arbcav() tool for things like this? I think it's pretty handy for just this sort of calculations. I'm actually hoping to revamp the I/O to make it much cleaner and more intuitive.

>> T = [0.055 20e-6];

>> L = [4.34 4.34];

>> RoC = [115.5 1e10];

>> theta = [0 0];

>> fmod = 11e6;

>> lambda = 1064e-9;

>> num_pts = 1000;

>> loss = 50e-6;

>> [fin,coefs,df] = arbcav(T,L,RoC,theta,fmod,loss,lambda,num_pts);

>> fmod = 55e6;

>> [fin,coefs,df] = arbcav(T,L,RoC,theta,fmod,loss,lambda,num_pts);

 

HOM11.png HOM55.png

  7968   Wed Jan 30 19:30:21 2013 JenneUpdateLockingPOP in-vac improved

Quote:

It still looks like we might be seeing some clipping in the in-vac POP steering mirrors - we haven't gotten to them yet.

 [Jenne, Jamie]

We fixed up, as best we can, the in-vac POP alignment.  We are entirely limited in yaw by the aperture size of the 2" 45deg mirror launching the beam out of the vacuum.  The main centroid of the beam is well centered, but the inflated weird part of the beam is totally clipped.  There's nothing we can do about it except use a much larger mirror, install a fast lens inside the chamber, or just fix the damn PRC.  I vote for the third option there.

How did we work our magic? 

We put a green laser pointer where the POP DC PD was, and injected it into the vacuum, just like we normally do.  However, this time, we made sure the green laser was centered on all of the out of vacuum mirrors, so that there was no real work to do once we turned off the laser pointer. We locked the cavity, and confirmed that we are well centered on all of the in and out of vacuum mirrors, and discovered our aperture problem with the last in-vac mirror.

Here is a snapshot of the POP camera:

HalfPRCL_PRM-flatMirror_POPtrans_30Jan2013.jpg

  7969   Wed Jan 30 19:34:17 2013 JenneUpdateLockingPRM coils need diagonalizing

[Koji, Jamie, Jenne]

Koji did this, while we actuated on PRM in pos, and watched the oplev.  Empirically, he found the following values for the POS column of the output matrix:

UL = 1.020

UR = 0.990

LL = 1.000

LR = 0.970

SD = 0.000

(The nominal values are all +1, except for Side, which is 0). 

Actuation of PRM was through C1:SUS-PRM_LSC_EXC, f=0.1Hz, A=100 counts.

 

Ed by KA:
This means UL and UR are increased by 2% and UR and LR are decreased by 3%. More precisely UR should be 1.02*0.97.
This is just a quick hack which works only for the DC.

  7973   Thu Jan 31 14:30:50 2013 JenneUpdateLockingMode spacing calc

I have calculated (using Zach's sweet software) the expected mode content for the various possible PRCs that we can make. 

Also, Zach was right about the factor of 2.  I see now that I was calculating the mode spacing between a plane wave and a HOM, so the guoy phase had a factor of (n+m+1).  The right thing to do is to get the spacing between the 00 mode and HOMs, so the guoy phase just has (n+m).  Switching from n+m+1=2 to n+m=1, that fixes the factor of 2 problem.

 I attach my results as a pdf, since I'm listing out 5 configurations.  Each config has a cartoon, with a small (hard to read) HOM plot, and then at the end, each HOM plot is shown again, but larger.  Also, "TM" is the "test mirror", the flat G&H that we're using as the cavity end mirror.

Attachment 1: Half_PRC_Configs.pdf
Half_PRC_Configs.pdf Half_PRC_Configs.pdf Half_PRC_Configs.pdf Half_PRC_Configs.pdf Half_PRC_Configs.pdf Half_PRC_Configs.pdf Half_PRC_Configs.pdf Half_PRC_Configs.pdf
  7975   Thu Jan 31 15:20:46 2013 ZachUpdateLockingMode spacing calc

I should mention that I just found a bug in how it treats odd-mirror-number cavities. For such cavities, HG modes with odd horizontal indices should receive an extra roundtrip phase of pi/2 (due to the rotation by the cavity). Because of a numbering convention issue, arbcav actually used to apply this phase shift to even-order modes. Essentially, the only difference is that the fundamental mode was shifted to anti-resonance. Everywhere else, there are modes at both corresponding locations in frequency space, and so it does not back a big difference in terms of cavity design.

Thanks to this IMC modeling we are doing at the workshop, I caught it! It has been fixed in the SVN.

Quote:

I have calculated (using Zach's sweet software) the expected mode content for the various possible PRCs that we can make. 

Also, Zach was right about the factor of 2.  I see now that I was calculating the mode spacing between a plane wave and a HOM, so the guoy phase had a factor of (n+m+1).  The right thing to do is to get the spacing between the 00 mode and HOMs, so the guoy phase just has (n+m).  Switching from n+m+1=2 to n+m=1, that fixes the factor of 2 problem.

 I attach my results as a pdf, since I'm listing out 5 configurations.  Each config has a cartoon, with a small (hard to read) HOM plot, and then at the end, each HOM plot is shown again, but larger.  Also, "TM" is the "test mirror", the flat G&H that we're using as the cavity end mirror.

 

  7978   Thu Jan 31 20:06:22 2013 EvanUpdateLockingPRM/PR2 cavity

[Jenne, Evan]

Tonight we made a non-folded cavity between the PRM and PR2 as follows. I put down two dog clamps to constrain the original position of the PR2 mount. I then loosened the dog clamps holding the mount to the table and nudged the mount until we saw a few reasonably well-aligned bounces in the cavity. I then dogged down the mount.

We played with the PRM and TT2 steering until we saw flashes of TEM00. However, the resonance is not clean so we couldn't lock.

Since we changed the PRM alignment, we had to redo the last bit of steering for the PRM oplev into the photodiode. We also put a few ND filters on the POP camera.

  7980   Thu Jan 31 23:48:45 2013 KojiUpdateLockingPRM/PR2 cavity

Wow! What's happened?

As the video showed good quality of resonances, I stopped by at the 40m on the way back home.

I looked at the error signals and found that they indicate high finesse and clear resonance of the sidebands.
The lock was immediate once the gain is set to be -0.004 (previous 0.05ish). This implies the optical gain is ~10 times larger than the previous configration.
The alignment was not easy as POPDC was saturated at ~27000I leave this as a daytime job.

As I misaligned the PRM, I could see that the lock hopped into the next higher order. i.e .from TEM00 to TEM01, from TEM01 to TEM02, etc
This means that the modes are closely located each other, but sufficiently separated to sustain each mode.

I definitely certify that cavity scans will give us meaningful information about the cavity.

  7981   Fri Feb 1 09:33:11 2013 JamieUpdateLockingPRM/PR2 cavity

I replaced the BS1 between the POPDC PD and the camera with a 98 reflector, and moved the 50 up before the BS to dump half the light.  Still saturating POPDC, but hopefully the ratio between POPDC and the camera should be better.  We just need to dump more of the power before we get there.  I'll come back to this after C&D if no one else has already gotten to it.

I don't know why I didn't pay more attention last night, but things look way WAY better.  The beams are much cleaner and the power level is much much higher.

  7985   Fri Feb 1 15:12:53 2013 JenneUpdateLockingPRM/PR2 cavity

 After Jamie did all the work this morning on the POP table, I was able to get the cavity to lock.  It's not very stable until I engage the boost filters in the PRCL loop.  After locking, I tuned up the alignment a bit more.  Now we're taking mode scan data.  Look for results hopefully shortly after Journal Club!

  7986   Fri Feb 1 19:55:33 2013 JenneUpdateLockingPRM/PR2 cavity

[Jamie, Koji, Jenne]

We are looking at the mode scan data, and have some preliminary results!  We have data from when the cavity was aligned, when it was slightly misaligned in pitch, and slightly misaligned in yaw.

Inverting the equation for transverse mode spacing, we infer (for pitch misalignment) a cavity g-factor of 0.99, and from there (assuming the G&H mirror is flat and so has a g-factor of 1), we infer a PRM radius of curvature of 168 meters which is ~50% longer than we expected.

 

More results to come over the weekend from Jamie.

  7987   Fri Feb 1 23:12:42 2013 KojiUpdateLockingPRM/PR2 cavity

During the scanning we were riddled by the fact the PDH error and the transmission peaks do not happen simultaneously.

After a little investigation, it was found that "LP100^2" filter is left on in the POPDC filter.

Moreover, it was also found that the whitening filter switches for the POPDC does not switch the analog counterpart.

These were the culprit why we never saw accidental hitting of the max transmission by the peaks when the cavity was not locked.

 

I know that the most of the whitening filter in the RF paths were checked before (by Keiko?), but the similar failure still exists in the POX path.
We should check for the whitening filters in the DC path as well and fix everything at once. I can offer assistance on the fixing part.

  7988   Fri Feb 1 23:52:59 2013 ranaUpdateLockingPRM/PR2 cavity

 Very exciting result, if true. I suppose we should try to reconfirm this result by doing another phase map of PRM03.

Is it possible that PR2 is not flat? How would we test to see if the tip-tilt frame screw gives it a curvature? Perhaps we can check with COMSOL.

  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.

ELOG V3.1.3-