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.
 

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.

 Use the trick I suggested:

Focus the beam so that the beam size at the detector is smaller than the beam separation. Use math to calculate the beam size and choose the lens size and position. You should be able to achieve a waist size of < 0.1 mm for the reflected beam.

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 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

 I wrote a small document on the application of LQG method to a Fabry-Perot cavity control.

n₁Sin(\theta₁) = n₂ Sin(\theta₂)

So it should be

\phi = ArcSin(Sin(\theta) / n 

I did check the reflected images for larger angles of incidence, about 20 deg and visibly (on the IR card) I did not see much change in the separation. But I will check it with the camera again to confirm on that.

How about to measure the AR reflectivity at larger (but small) angles the extrapolate the function to smaller angle,
or estimate an upper limit?

The spot separation is

D = 2 d Tan(\phi) Cos(\theta), where \phi = ArcSin(Sin(\theta) * n)

D = 2 d Tan(\phi) Cos(\theta), where \phi = ArcSin(Sin(\theta) / n)         (<== correction by Manasa's entry)

\theta is the angle of incidence. For a small \theta, D is propotional to \theta.

So If you double the incident angle, the beam separation will be doubled,
while the reflectivity is an even function of the incident angle (i.e. the lowest order is quadratic).

I am not sure until how much larger angle you can use the quadratic function rather than a quartic function.
But thinking about the difficulty you have, it might be worth to try.

 Hours of struggle and still no data 

I tried to measure the AR reflectivity and the loss due to flipping of G&H mirrors

 With almost no wedge angle, separating the AR reflected beam from the HR reflected beam seems to need more tricks.

The separation between the 2 reflected rays is expected 0.8mm. After using a lens along the incident beam, this distance was still not enough to be separable by an iris.

The first trick: I could find a prism and tried to refract the beams at the edge of the prism...but the edges weren't that sharp to separate the beams (Infact I thought an axicon would do the job better..but I think we don't have any of those).

Next from the bag of tricks: I installed a camera to see if the spots can actually be resolved.

The camera image shows the 2 sets of focal spots; bright set to the left corresponding to HR reflected beam and the other from the AR surface. I expect the ghost images to arise from the 15 arcsec wedge of the mirror. I tried to mask one of the sets using a razor blade to see if I can separate them and get some data using a PD. But, it so turns out that even the blade edge is not sharp enough to separate them.

If there are any more intelligent ideas...go ahead and suggest! 

The comment itself was added by me.
The difference between the previous and new measurements should be described by Riju.

In the entry 7984, the description has several PDs mixed up. The measurement was done with the MCREFL PD.
But the DC transimpedance of the thorlabs PD (5e3) was used, according to the text.
I first wonder if this is only a mistake not in the calculation but only in the elog due to a sloppy copy-and-paste.
But the resulting shot-noise-intercept current was 50uA, which is way too small
compared with a realistic value of 0.1~1mA. I have never seen such a good value with
C30642 at the resonant freq ~30MHz. That's why I said "hard to believe". I guessed this wrong
DC transimpedance was actually used for the calculation. 

You may wonder why this 50uA is unreasonable number.
Basically this is just my feeling and probably is same as Rana's feeling.
But "my feeling" can't be a scientific explanation. Here is some estimation.

Looking at my note in 2010:
https://wiki-40m.ligo.caltech.edu/40m_Library (Comparisons of the PD circuits by KA)

The expected shot noise intercept current (idc) is

idc = 2 kB T / (e Rres),

where Rres is the impedance of the resonant circuit at the resonant freq.

This Rres is expressed as

Rres = 1/(4 pi^2 fres^2 Cd^2 Rs),

where Cd and Rs are the capacitance and series resistance of the diode.

If we input realistic numbers,

Cd = 100pF
Rs = 10 Ohm
fres = 30MHz

We obtain, Rres ~ 300Ohm, and idc = 0.2mA

In other words, Rs needs to be 2~3Ohm in order to have idc = 50uA.
This is too small from the previous measurements.
Test Results for C30642 LSC Diode Elements by Rich Abbott

I fixed up the POP path so that there is no clipping, so that Yuta can take a cavity mode scan.

It seems that the cavity trans looks much better than before. Cool.

At least the optical gain is ~x5 of the previous value. This means what we did was something good.

Looking forward to seeing the further analysis of the caivty...

We need expected finesse and g-factor to compare with mode-scan measurement. Can you give us the g-factor of the half-PRC and what losses did you assumed to calculate the finesse?

Also, flipped PR2 should have RoC of - R_HR * n_sub (minus measured RoC of HR surface multiplied by the substrate refractive index) because of the flipping.
According to Jenne dictionary, HR curvature measured from HR side is;

PRM: -122.1 m
PR2: -706 m
PR3: - 700 m
TM in front of BS: -581 m

Please use these values to calculate expected g-factor so that we don't get confused.

Arbcav with half PRC (flat temporary mirror in front of BS), PR2 RoC = 600m, PR3 RoC = -600m:

NOTE: this does NOT include the affect of the PR2 substrate in the cavity.  Arbcav does not handle that.  It would have to be modified to accept arbitrary ABCD matrices.

NOTE: I added to the mode plot the frequency separation of the first HOMs from the carrier (\omega_{10/01}), in units of carrier FSR.

 [Yuta, Jenne]

After much tweaking of the alignment using TT1, TT2 and PRM sliders, we were able to get a TEM00 mode locked with the half PRC!

PRCL gain is -0.010

FM4, 5 are always on.  FM2,3,6 (boosts and stack res-gains) are triggered to come on after the cavity is locked.

We see a little clipping of POPDC, even though there are 2 BSs in the beam path, to dump 50% and then 67% of the beam.  But it's not so much that we can't align. 

REFLDC goes from 28.5 to 24.5, so we don't have great visibility.

Please watch our awesome video of the cavity, where we demonstrate that the half cavity is stable:

The cavity is flashing for the 1st 15 sec, then locks.  Upper right is REFL, Lower right is POP, Upper left is back of the Faraday, Lower left is MC2F.   Note that we definitely see some not so beautiful modes flashing, but most of that is due to the half cavity length and thus greater degeneracy of modes.  Jamie is posting a HOM plot presently.

BEAM MOTION:

The beam is moving way more than it should be.  Right now the PRM oplev is not coming out of the vacuum, since the flat test mirror mount is obstructing it.  However, as we saw with other half-cavity tests, turning on the PRM oplev helps, but does not completely eliminate the beam motion.  We should consider putting oplevs on one of the passive TTs, at least temporarily, so we know what kind of motion is coming from where.

This measurement was done already about a week ago, in elog 7984.  Can you please describe why the numbers for the last measurement were not believable, and what was done differently this time?

 I reminded Jamie this morning that we were not, in fact, set up yesterday for a half PRC.  I had extracted what was the flat test mirror, to put in as PR2.  The test mirror was the better of the 2 G&Hs that we had measurements for, so I had used it as the flat test mirror, but then also wanted it to be the more permanent PR2.  After doing the PR2 flip, the IFO was naturally all aligned for PRMI, which is part of why we just did that.

Anyhow, Jamie used his tallness to put the other measured G&H mirror into the mount, and put that in front of the BS.  He aligned things such that he saw fringes in the half PRC. 

I then aligned POP onto the camera, and onto the PD.  Yuta is confirming that we're maximally on the REFL PDs.

We're starting locking in 5 min.

I updated /opt/rtcds/caltech/c1/scripts/general/videoscripts.py so that it supports movie capturing. It saves captured images (bmp) and movies (mp4) in /users/sensoray/SensorayCaptures/ directory.
I also updated /opt/rtcds/caltech/c1/scripts/pylibs/pyndslib.py because /usr/bin/lalapps_tconvert is not working and now /usr/bin/tconvert works.
However, tconvert doesn't run on ottavia, so I need Jamie to fix it.

videocapture.py -h:
Usage:
    videocapture.py [cameraname] [options]

Example usage:
    videocapture.py MC2F -s 320x240 -t off
       (Camptures image of MC2F with the size of 320x240, without timestamp on the image. MUST RUN ON PIANOSA!)
    videocapture.py AS -m 10
       (Camptures 10 sec movie of AS with the size of 720x480. MUST RUN ON PIANOSA!)


Options:
  -h, --help          show this help message and exit
  -s SIZE             specify image size [default: 720x480]
  -t TIMESTAMP_ONOFF  timestamp on or off [default: on]
  -m MOVLENGTH        specity movie length (in sec; takes movie if specified) [default: 0]

Yes, at 45degrees PR3 will only have a curvature of about 850m for the vertical mode of the beam, apparently not enough to stabilize the cavity.

Half-PRC at this time already have two changes from the previous half-PRC; PR2 replaced/flipped and different TM before BS.
PRMI has only one change from the previous PRMI; PR2 replaced/flipped.
This is why I wanted to try PRMI first. But we now recognized that MI alignment (including REFL and AS alignment) is tough without using the arms, I agree that we should try half-PRC first.

I don't exactly know what the situation in the Jamie's calculation, but to make the optical path length the same before and after flipping, PR2 holder have to move about n*t, where n is the substrate refractive index and t is the thickness of the mirror, towards PRM/PR3.

You would guess, and I would have guessed too, but the calculations tell the story.   Flipping both does not increase the stability.  The main issue is that flipping PR3 induces considerable astigmatism.  This is why flipping PR3 alone does not make the cavity stable.  I will do some simple calculations today that will demonstrate this effect.

But again, we should only change one thing at a time and understand that before moving on.  Given that the calculations show that flipping only PR2 should alone have a positive affect, we should do just that first, and verify that we understand what's going on, before we move on to making more changes.

I will try to make some more arbcav runs as well, for just the flipped PR2.

I completely agree with Koji.  We definitely should have locked the half PRC first.  We were all set up for that.  Why go through all this work to align MICH when we haven't confirmed with the half PRC that the flipping is helping us?  The first rule of debugging is to only make one change at a time.  We have measurements from the half PRC, so we could have made a direct comparison with those to see how things have changed.  If we jump the gun we're going to end up wasting more time when we have to back-track.

Also, we never talked about moving PR2 to adjust optical path length, although I can understand why we would think that should be done.  My calculations were all done assuming the free-space separation between PRM/PR2 and PR2/PR3 were unchanged.  It's possible changing the position is better, but again, it's more work and it changes multiple things at one.  I can redo my calculations for this new scenario, but we need to update our drawings with this new configuration.  Please note precisely where PR2 has moved to.

We should have just flipped PR2 and that's it.  Then we could have run the exact same measurements we had previously.  Only then, once we understood this new simple cavity, should we have done further adjustments.

I feel it's too hasty to use the PRMI.
I support the idea of the half-PRC test, to make an apple-to-apple comparison.

Make haste slowly.

[Jenne, Yuta]

Lots of work, no solid conclusions yet.  In-vac, we aligned MICH and the PRM.  Out of vac, we got beam on AS and REFL paths.  We can lock MICH, but we're not as happy with PRCL.

In-vac alignment: 

To get the beam centered on TT2 in yaw, Koji helped us out and moved TT1 with the sliders a little bit. Then to get the beam centered on PRM and PR2, Koji moved the TT2 sliders a little bit.

Yuta and I then moved PR2 forward a few mm, to keep the optical path length of the PRC approximately (within ~1mm, hopefully) the same as always.  After my PR2 optic swapping earlier, the pitch alignment was no longer good.  I loosened the screws holding the wire clamp to the optic holder, and tapped it back and forth until the alignment was good.  Of course, the screw-tightening / pitch-checking is a stochastic process, but eventually we got it.  A small amount of yaw adjustment by twisting the PR2 TT was also done, but not much was needed.

Beam was a little off in pitch at ITMY, so Yuta poked the top of PR3, and that one single poke was perfect, and the beam was very nicely centered on the ITMY target.  Beam was getting through BS target just fine.  We checked at ITMX, and the beam looked pretty centered, although we didn't put in a target.  We didn't do anything to BS while we were in-vac, since it was already good.

We aligned the ITMs so that their beams were retroreflecting back to the BS.  After this, we saw nice MICH fringes.

We aligned the PRM so that its beam was retroreflecting.

We checked that we were getting REFL and AS beams out of the vacuum, which we were (a small amount of adjustment was done to AS path steering mirrors).

AS table alignment:

We did a bit of tweaking of the REFL path, and lots of small stuff to the AS path. 

The AS beam was coming out of vac at a slightly different place in yaw, so we moved the first out of vac AS steering mirror so the beam hit the center, rather than ~1/3 of the way to the edge.  We then aligned the beam through the lens, to the camera, and to AS55.  Most significantly, we removed the BS that was just before AS55.  This was sending beam to a dump, but it is in place to send beam over to AS110, once we get back to real locking.  We measured ~30 microwatts of power going to the AS55 PD, while MICH fringes were fringing.

The REFL path didn't need much, although we had never been going through the center of the HWP and PBS that are used to reduce the power before going to the PDs, so we translated them a millimeter or two.

We see signal on dataviewer for all of the channels that we're interested in....AS55 I&Q, ASDC, REFL11 I&Q, REFLDC (which comes from REFL55). 

Locking:

Locking MICH was very easy, after we rotated the phase of AS55 to get all the good MICH signal in the Q phase.  Part of the criteria for this was that the AS55_Q_ERR signal should cross zero when ASDC went to 0.  This was done very coarsely, so we need to do it properly, but it was enough to get us locked.  We changed the phase from 24.5 to 90 deg.

PRCL has been more of a challenge, although we're still working on it.

On the back face of the Faraday, we see the michelson fringes, but they are not getting through the Faraday's aperture.  This implies that we have a poorly aligned michelson, in that the interference between the returning beams from the ITMs is happening at a different place than the original beam splitting.  Yuta is working on getting a better MICH right now.  EDIT, 10 minutes later....   This seems to be fixed, and the MICH fringes enter the back aperture of the FI, but there is still the PRM refl problem (next paragraph).

Also, when we get the most bright REFL beam, we see that there is some very obvious clipping in the back of the Faraday aperture, and this is matched by a clipped-looking REFL beam on the AS table.  We must understand what we have done wrong, such that when the beam is actually going through the Faraday, we see a much dimmer beam.  It's possible that there is some clipping happening at that time with the in-vac REFL path....we need to check this.  It's not a clipping problem on the AS table - I checked, and the beams are still reasonably  well centered on all of the mirrors.

We think that the MICH / REFL beam problems may be that the input pointing is close, but not perfect.  We have not confirmed today that the beam is centered on ETMY.  We should do this as part of our final alignment procedure before putting on doors.

Plans for tomorrow:

Get POP aligned, especially the camera, so we can see what our intracavity mode really looks like in the PRC.  This is probably (in part, at least) due to our having moved PR2 around, so the transmitted beams aren't in exactly the same place.

We think that it's more useful in the short term to check out the PRC, and since the clipping problem with the REFL beam is likely an imperfect input pointing, we want to use the other measured G&H mirror, and do another half-PRC test, with the test mirror in front of the BS.  This requires much less perfection in the input pointing, so it should be very quick to set up.

Confirm that PRM oplev is still aligned (turn laser back on first).

Plans for next week:

Perfect the input pointing, by checking the beam position at ETMY.  Recheck all corner alignment.

Try again locking PRMI in air.  First, confirm ITM and BS oplevs are all aligned.

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

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

Filters for C1ALS were all gone. So, I copied /opt/rtcds/caltech/c1/chans/C1GCV.txt and renamed it as C1ALS.txt.

I also fixed links in the medm screens; C1ALS.adl and C1ALS_COMPACT.adl.
I'm not sure what happened to C1SC{X,Y} screens.

 Summary: Measurement and plot of shot-noise-intercept-current for MC REFL PD. 

Motivation:It is to measure the shot noise intercept current for MC REFL PD.

Result: The final plot is attached here. The plot suggests that the value of shot-noise-intercept current is 1.9mA

Discussion:

The plot is for the measured data of Noise voltage (V/sqrt(Hz)) vs DCcurrent(A). The fitted plot to this measured data follows the noise equation

Vnoise = gdet* sqrt[ 2e (iDC+idet)] ,  where gdet= transimpedance of the PD in RF region ~600

To get an approximate idea of the shot noise intercept current, we may follow the same procedure described in 7946 

In the present case minimum noise value is 1.46e-08 V/sqrt(Hz)

Therefore dark current(in2) ~dark noise voltage/RF transimpedance ~25pA/sqrt(Hz)

Therefore the approximate shot noise intercept current value is (25/18)^2 ~ 1.92mA, which matches well to the fitted value.

The fire department weighted and pressure checked our units today. Surprisingly they found one powder filled can. We can only use HALON  gas in the lab.

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

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.

Reflectivity of AR surface of LaserOptik (SN6)

The first step measurements of R for AR surface. I am not convinced with the data....because the power meter is a lame detector for this measurement.

I'm repeating the measurements again with PDs. But below is the log R plot for AR surface.

R percentage

6000ppm @ 42 deg
3560ppm @ 44 deg
7880ppm @ 46 deg
4690ppm @ 48 deg

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

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

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

ARM

This is the ARM mode I used for all comparisons:

PRC, nominal design (flat PR2/3)

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

 ARM mode matching: 0.9998

PRC, both PR2/3 flipped

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

ARM mode matching: 0.9806

PRC, only PR2 flipped

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

ARM mode matching: 0.9859

Discussion

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

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

I'm not the one who opened the ITMX table yesterday, but thanks for reminding me.
I put POP DC oscilloscope and its cables back.

Also, I relocked PMC and MC. It was unlocked since last night.

@Yuta

The ITMX table has been left open since yesterday. I am disconnecting your oscilloscope and closing the table.

To whomsoever it may concern...

I found about half a dozen new cvi optics (beam splitters, waveplates and lenses) lying around on the SP table.

Please store optics back in their respective cabinets if you are not using them immediately. Somebody might be looking around to use them. 

I intended to post a long analysis of the PRC/arm mode matching for the various TT situations using Nic's a la mode mode matching program, but I seem to have encountered what I think might be a bug.  I'll talk to Nic about it first thing in the AM.  Once the issue is resolved I should be able to post the full analysis fairly quickly.  Sorry about the delay.

[Koji, Manasa]

We measured the wedge angle of the G&H and LaserOptik mirrors at the OMC lab using an autocollimator and rotation stage.

The wedge angles:

G&H : 18 arc seconds (rough measurement)

LaserOptik : 1.887 deg

 I'm still on that!

 [Yuta, Steve, Manasa]

There are cables piled up around the access connector area which have been victims of stampedes all the time. I have heard these cables were somehow Den's responsibility. 

Now that he is not around here:

I found piled up bnc's open at one end and with no labels lying on the floor near the access connector and PSL area. Yuta, Steve and I tried to trace them and found them connected to data channels. We could not totally get rid of the pile even after almost an hour of struggle, but we tied them together and put them away on the other side of the arm where we rarely walk.

There are more piles around the access connector...we should have a next cleanup session and get rid of these orphaned cables or atleast move them to where they will not be walked on.

  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.

[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)


 East arm cabinet E9 and E10

I have to blame Jamie for putting extra 2 randomly.
Measured PRM-PR2 cavity finesse was actually 108 +/- 3 (even if you use digital system to get data).

Lorentzian fit:
  Lorentzian function is;

f(x;x0,gamma,A) = A * gamma**2/((x-x0)**2+gamma**2)

  where x0 is the location of the peak, gamma is HWHM, and A is the peak height.
  Lorentzian fitting function in my original code (/users/yuta/scripts/modescanresults/analyzemodescan.py) was

fitFunc = lambda p,x,m: (m-p[2])*p[0]**4/(4*(x-p[1])**2+p[0]**4)+p[2]

  In this function, p[0] is sqrt(FWHM), not sqrt(HWHM). I doubled gamma to make it FWHM and squared it because they should be positive.
  During Jamie's modification of my code, he doubled p[0]**2 to get FWHM, which is wrong (/users/jrollins/modescan/modescan.py).

  I should have commented that p[0] is sqrt(FWHM).

Redoing the analysis:
  1. I pulled 2 out, and modified Jamie's modescan.py so that you can name each peak with peakdistinguish=True option. I also modified fitpeak function so that it throws away "peaks" which don't look like a peak.

  2. If you run /users/yuta/PRCmodescan/run.py and name each peak, you will get peaks.csv which includes peak position, FWHM, and the type of the peak;

0.065017,0.001458,l
0.070446,0.001463,3
0.075940,0.001509,2
0.081552,0.001526,1
0.087273,0.001565,0
0.112027,0.001911,u
0.278660,0.002211,u
0.306486,0.001658,0
0.312480,0.001576,1
0.313626,2.507910,
0.318486,0.001626,2
0.319730,2.633097,
0.324801,0.001739,3
0.331848,0.001922,l
0.527509,0.001603,l
0.533231,0.001445,3
0.538648,0.001488,2
0.544081,0.001455,1
0.549517,0.001498,0
0.551725,2.422759,
0.570972,0.001346,u

  3. /users/yuta/PRCmodescan/calcmodescanresults.py reads peaks.csv and tells you the results;

Time between TEM00 and sideband  0.0239435  pm  0.00115999887452  sec
Calibration factor is  462.167602898  pm  22.3907907867  MHz/sec
FSR is  78.4797010471  MHz
FWHM is  0.729828720682  pm  0.0174145743828  MHz
TMS is  2.64718671684  pm  0.0538858477824  MHz
Finesse is  107.53166986  pm  2.5658325169
Cavity g-factor is  0.994390582331  pm  0.000228155661075
Cavity g-factor is  0.988812630228  pm  0.000453751681357   (Edited by YM; see elog #8056)
RoC of PR2 is  -187.384503001  pm  4.26100999578  m (assuming PRM RoC= 122.1  m)
RoC of PRM is  217.915890722  pm  5.65451518991  m (assuming PR2 RoC= -600  m)

[Jenne, Yuta, Rana, Steve, Manasa]

We have taken stock of the lab "temporary" power supply situation, and things look much better.

This morning, I removed 2 unused power supplies and a function generator from the PSL table - these had been used for MC ringdown things.

I also removed the non-connected cables that had been used for the RAMMON setup, and the EOM temperature controller circuit.

This afternoon, Yuta removed the 2 HV power supplies that were used to keep PZT2 working near the end of its life.  Since we now have the active TTs, these have been turned off for a while, and just needed to be removed.

Manasa removed the power supply under the POP/POX table that was powering the amplifier for POP22.  If we are going to continue using a Thorlabs PD for POP22, then we need to make a twisted pair of wires (~20 feet) to get power from 1X1.  If we are going to (finally) install a gold RF PD, then that will not be necessary.

I removed the power supply sitting near the bottom of the LSC rack, for another amplifier for POP22 (with minicircuits filters attached).  Again, if we get a gold RF PD, we can remove the filters and amplifier.  If not, we can use the existing twisted pair of wires, and plug them into the rack rather than a power supply. 

The power supply under the NE corner of the PSL table was no longer in use.  It was most recently used for amplifiers for the green beat PDs, as Yuta mentioned in elog 6862, those were moved over to 1X2.  In elog 8008 I mentioned that Yuta and I moved those amplifiers over to rack power.

The HV supply, the function generator and the OSA controllers that were on top of the short OMC rack next to the AS table have all been removed.  We need to come up with a better place for the OSAs, since we need to re-install them.  The power supply and the function generator (which was used just for a voltage offset) were formerly used for the output steering PZTs, but lately we have just been using those mirrors as fixed mirrors, since we don't need to steer into the OMC.  Some day, we will replace those mirrors with the output steering active tip tilts, and re-commission the OMC....someday.

The power supply for the amplifier set (that goes with the set of minicircuits filters) for the RAMMON PD (which took light from the IPPOS path) has been removed.  If we determine that we need RAMMON back, we will have to make a twisted pair to power those amplifiers.

SUMMARY:

* If we don't install a gold RF PD for POP22, we need a 20ft twisted pair for +15/GND.

* Also, if we don't install a gold RF PD for POP22, we need to plug the amplifier at the LSC rack into the rack power (twisted pair already exists).

* If we need RAMMON back, we will need a twisted pair to power those amplifiers.

* All other power supplies have been removed, and put away.  We currently have 0 "temporary" power supplies in use in the lab!

 The east and south end of the 40m emergency exit doors received new safety signs.

Cameras must be immediately anchord to avoid a possible collusion with the view port !

 Yuta, Jenne

We fixed things so that we are now using regular fused rack power for these amplifiers.  The fuse no longer had a red LED, but it measured open when we checked the resistance.  Although, somehow (magic?) 13.73V were getting to the other side of the fuse. 

Anyhow, replacing the fuse with a new one fixed the problem right up.

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.

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.

This is just a simple rerun of arbcav from #7995 but with the PR2/3 RoCs set to 600, instead of -600.  Overall g-factor = 0.922, and the modes are well separated:

This doesn't take into account the effect of traveling through the substrates (still working on it).  It assumes the PR2/3 have been moved such that the cavity fold lengths remain the same.

This is something that we need to keep in mind: we will need to adjust the position of the PR2/3 to keep the fold lengths the same.

Manasa, Jamie and Steve,

Tip-Tilts and parts moved into the most north " 40m "  cabinet  in the assembly room.

Green-black glass and related components were moved to the 40m E0 cabinet in plastic boxes.

The north flow bench has a few items that belong to us: HE/Ne laser, qpd on translation stages, an iris and one red mirror.  These were moved to the north edge of this bench.

However this leveled table is still full with other people's stuff