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

Getting started:  Worked on understanding the functionality of summary_page.py.  The problem with the code is that it was written in one 8000 line python script, with sparse documentation.  This makes it difficult to understand and tedious to edit, because it's hard to tell what the precise order of execution is without tracing through the code line by line.  In other words, it's difficult to get an overview of what the code generally does, without literally reading all of it.  I commented several functions / added docstrings to improve clarity and start fixing this problem.

Crontab:  I believe I may have discovered the cause of the 6PM stop on data processing.  I am told that the script that runs the summary_pages.py is called every 6 hours.  I believe that at midnight, the script is processing the next day's data (which is essentially empty) and thus not updating the data from 6PM to midnight for any of the days.

Git:  Finally, created git repository called public_html/__max_40m-summary_testing to use for testing the functionality of my changes to the code (without risking crashing the summary_pages).

Makes sense. I mixed up n and n-1

Probability function: X = (x1 + x2 + ... + xn)/n, where xi = xavg +/- dx

Xavg = xavg*n/n = xavg

dXavg^2 = n*dx^2/n^2
=> dXavg = dx/sqrt(n)

Xavg +/- dXavg = xavg +/- dx/sqrt(n)

 The bad outside air quality is pushing up the inside counts.

The outside air is 5 million counts / cf min for 0.3 micron and 2 million counts / cf min for 0.5 micron particles

Do not open chamber over 10,000 counts / cf min of 0.5 micron

stdev of [0.764, 0.751] is 0.007, but what we need is the error of the averaged number. Statistical error of the averaged number is stdev/sqrt(n).

 The east and south end of the 40m emergency exit doors are sealed- tapped off temporarily.  They will be painted on the out side only.  This job will be done by tomorrow noon

 Do not open chamber if you smell the paint !

0.764 and 0.751 do not give us the stdev of 0.005.

I have never seen any Yokogawa in vicinity.

I redid PRM-PR2 cavity scan using oscilloscope to avoid anti-aliasing effect.
Measured Finesse was 104 +/- 1.

Method:
 1. Splitted POP DC output into three and plugged two into oscilloscope TDS 3034B. Ch1 and Ch2 was set to 1 V/div and 20 mV/div respectively to take the whole signal and higer resolution one at the same time (Koji's suggestion). Sampling frequency was 50 kHz. Sweeping time through FWHM was about 0.001 sec, which is slow enough.
 2. Took mode scan data from the oscilloscope via network.

Preliminary results:
 Below is the plot of the data for one TEM00 peak.


 The data was taken twice.
 Measured FWHM was 0.764 MHz and 0.751 MHz. By taking the average, FWHM = 0.757 +/- 0.005 MHz.
 This gives you Finesse = 104 +/- 1, which is OK compared with the expectation.

What I need:
 I need better oscilloscope so that we can take longer data (~1 sec) with higher resolution (~0.004 V/count, ~50kHz).
 TDS 3034B can take data only for 10 ksamples, one channel by one!  I prefer Yokogawa DL750 or later.

I ran Zach's arbcav on our SRC with curved TTs and the situation looks much worse than the PRC.

I used the following parameters

SRM: RoC = 142 m, T = 10%
ITM: RoC = 83.1e3 m, T = 1.4%
SRC length: 5.37 m

In this case, with TT RoC of -600, the combined cavity g-factor = 0.9986, and astigmatism from SR3 makes the cavity patently not stable.  You have to go up to an RoC of -710 before the cavity is just over the edge.

I noticed that Koji used a high reflector for the ITMs for his full PRC arbcav calculation. I just redo it here with the correct ITM transmission and RoC for completeness.

In this case the finesse is 95, instead of 121.

[Jenne, Yuta]

We redid PRM-PR2 cavity scan because last one (elog #7990) was taken with the sampling frequency of 2 KHz. We have also done TMS measurement.

Method:
 1. Align input TTs and PRM to align PRM-PR2 cavity.
 2. Sweep cavity length using C1:SUS-PRM_LSC_EXC.
 3. Get data using Jamie's getdata and fitted peaks using /users/jrollins/modescan/prc-pr2_aligned/run.py
 4. Calculated cavity parameters

Results:
 Below is the figure containing peaks used to do the calculation.



 From 11 MHz sidebands, calibration factor is 462 +/- 22 MHz/sec (supposing linear scan around peaks)
 FWHM is 1.45 +/- 0.03 MHz.
 TMS is 2.64 +/- 0.05 MHz.
 Error bars are statistical errors of the average over 3 TEM00 peaks.

 If we believe cavity length L to be 1.91 m, FSR is 78.5 MHz.
 So, Finesse will be 54 +/- 1 and cavity g-factor will be 0.9944 +/- 0.0002. 0.9889 +/- 0.0004   (Edited by YM; see elog #8056)
 If we believe RoC of PRM is exactly +122.1 m, measured g-factor insists RoC of PR2 to be -187 +/- 4.
 If we believe RoC of PR2 is exactly -600 m, measured g-factor insists RoC of PRM to be 218 +/- 6.

Discussion:
 1. Finesse is too small (expected to be ~100). This time, data was taken 16 KHz. Cut-off frequency of the digital antialiasing filter is ~ 5 kHz (see /opt/rtcds/rtscore/release/src/fe/controller.c). FWHM is about 0.003 sec, so it should not effect much according to my simulation.

 2. I don't know why FWHM measurement from the last one is similar to this one. The last one was taken 2 KHz, this means anti-aliasing filter of 600 Hz. This should double FWHM.

 3. Oscilloscope measurement may clear anti-aliasing suspicion.

I've added a new program called getdata (to scripts/general/getdata) that will conveniently pull arbitrary data from an NDS server, either DQ or online (ie. testpoints).

Start times and durations may be specified.  If past data is requested, you must of course be requesting DQ channels.  If no start time is specified, data will be pulled "online", in which case you can specify testpoints.

If an output directory is specified, the retrieved data will be stored in that directory in files named after the channels.  If an output directory is not specified, no output will be

Help usage:

controls@pianosa:~ 0$ /opt/rtcds/caltech/c1/scripts/general/getdata --help
usage: getdata [-h] [-s START] [-d DURATION] [-o OUTDIR] channel [channel ...]

Pull online or DQ data from an NDS server. Use NDSSERVER environment variable
to specify host:port.

positional arguments:
  channel               Acquisition channel. Multiple channels may be
                        specified acquired at once.

optional arguments:
  -h, --help            show this help message and exit
  -s START, --start START
                        GPS start time. If omitted, online data will be
                        fetched. When specified must also specify duration.
  -d DURATION, --duration DURATION
                        Length of data to acquire.
  -o OUTDIR, --outdir OUTDIR
                        Output directory. Data from each channel stored as
                        '.txt'. Any existing data files will be
                        automatically overwritten.
controls@pianosa:~ 0$ 

 Another possibility is to use a ring heater to correct the curvature. I talked a bit with Aidan about this.

The expected finesse is 100ish. How much can we beleive the measured number of 50?
From the number we need to assume PR2 has ~93% reflectivity.
This does not agree with my feeling that the cavity is overcoupled.
Another way is to reduce the reflectivity of the PRM but that is also unlikely from the data sheet.

The scan passed the peak in 4ms according to the fitting.
How do the analog and digital antialiasing filters affect this number?

Here's a sort of rough analysis of the aligned PRM-PR2 cavity mode scan.

On Friday we took some mode scan measurements of the PRM-PR2 cavity by pushing PRM (C1:SUS-PRM_LSC_EXT) with a 0.01 Hz, 300 count sine wave.  We looked at the transmitted power on the POP DC PD and the error signal on REFL11_I.

Below is a detail of the scan, chosen because the actuation was in its linear region and there were three relatively ok looking transmission peaks with nice PDH response curves:

The vertical green lines on the bottom plot indicate the rough averaged separation of the 11 MHz side-band resonances from the carrier, at +- 0.0275 s.  If we take this for our calibration, we get roughly 400 MHz / second.

The three peaks in top plot have an average FWHM of 0.00381 s.  Given the calibration above, the average FWHM = ~1.52 MHz.

If we assume a cavity length of 1.91 m, FSR = 78.5 MHz.

Putting this together we get a finesse = ~51.6.

Analysis of misaligned mode scans to follow.

Rana mentioned the possibility that the PR2 curvature makes the impact on the mode stability. Entry 7988
Here is the extended discussion.

Hypothesis:

The small but non-negligible curvatures of the TT mirrors made the recycling cavity unstable or nearly unstable.

Conclusion:

If the RoC of the TT mirrors are -600 m (convex), the cavity would be barely stable.
If the RoC of the TT mirrors are less than -550m, the horizontal modes start to be unstable.
Assumption that all of the TT mirrors are concave should be confirmed.

Fact (I): Cavity stability

- The folded PRMI showed the mode stability issue. (L=6.78m from Jenne's entry 7973)
- The folded PRM-PR2-PR3-flat mirror cavity also showed the similar mode issue. (L=4.34m)
- The unfolded PRM-PR2 cavity demonstrated stable cavity modes. (L=1.91m)

Fact (II): Incident angle

- PRM 0deg
- PR2 1.5deg
- PR3 41deg

Fact (III): Mirror curvature

- RoC of PRM (PRMU02): +122.1m (measured, concave), or +115.6m (measured by the vendor)
- RoC of G&H mirrors: -600m ~ -700m (measured, I suppose the negative number means convex) (Jenne's entry 7851)
  [Note that there is no measurement of the phase map for the PR2 mirror itself.]
- RoC of LaserOptik mirrors: -625m ~ -750m (measured, I suppose that the measurement shows the mirrors are convex.) (Jan's entry 7627 and 7638)

Let's assume that the TT mirrors are always convex and have a single number for the curvature radius, say RTT

Cavity mode calculation with Zach's arbcav

1) The unfolded PRM-PR2 cavity:

The cavity becomes unstable when 0 > RTT > -122m  (This is obvious from the g-factor calculation)
==> The measured RoC of the TT mirrors predicts the cavity is stable. (g=0.98, Transverse Mode Spacing 3.54MHz)

2) The folded PRM-PR2-PR3-flat mirror cavity:

The cavity becomes unstable when RTT < -550 m
==> The measured RoC of the TT mirrors (RTT ~ -600m) predicts the cavity is barely stable (g=0.997, TMS ~600kHz).

- The instability occurs much faster than the unfolded case.
- The horizontal mode hits unstable condition faster than the vertical mode.
- The astigmatism mainly comes from PR3.

3) The folded PRMI:

The cavity becomes unstable when RTT < -550 m
==> The measured RoC of the TT mirrors (RTT ~ -600m) predicts the cavity is barely stable. (g=0.995, TMS ~500kHz)

- The instability occurs with almost same condition as the case 2)

The calculation result for the PRMI with RTT of -600 m. The code was also attached.

Q&A:

Q. What is the difference between unfolded and folded?
A. For the unfolded case, the PR2 reflect the beam only once in a round-trip.
For the folded case, each TT mirror reflects the beam twice. Therefore the lens power by the mirror is doubled.

Q. Why the astigmatism mainly comes from PR3?
A. As the angle of incidence is much bigger than the others (41deg).

Q. Why the horizontal mode is more unstable than the vertical mode?
A. Off-axis reflection of a spherical mirror induces astigmatism. The effective curvature of the mirror in the horizontal direction
is R / Cos(theta) (i.e. longer), while it is R Cos(theta) (i.e. shorter). Indeed, the vertical and horizontal ROCs are factor of 2 different
for the 45deg incidence.

Q. Why the stability criteria for the case 2) and 3) similar?
A. Probably, once the effective curvature of the PRM-PR2-PR3 becomes negative when RTT < -550 m.

Q. You said the case 2 and 3 are barely stable. If the TMS is enough distant form the carrier, do we expect no problem?
A. Not really. As the cavity get close to the instability, the mode starts to be inflated and get highly astigmatic.
For the case 2), the waist radii are 5.0mm and 3.7mm for the horzontal and vertical, respectively.
For the case 3), they are 5.6mm and 4.1mm for the horzontal and vertical, respectively.
(Note: Nominally the waist radius is 3.1mm)

Q. What do you predict for the stability of the PRM-PR2-Flat_Mirror cavity?
A. It will be stable. The cavity is stable until RTT becomes smaller than -240 m.

Q. If the TT mirrors are concave, will the cavity stable?
A. Yes. Particularly if PR3 is concave.

Q. Rana mentioned the possibility that the mirrors are deformed by too tight mounting of the mirror in a ring.
Does it impact the stability of the cavity?
A. Possible. If the curvature is marginal and the mounting emphasizes the curvature, it may meet the unstable condition.

Q. How can we avoid this instability issue?
A.
1. Use flatter mirrors or at least concave mirrors.
2. Smaller incident angle to avoid emphasis of the RoC in the horizontal direction
3. Use weaker squishing force for mounting of the mirrors
4. Flip the PR3 mirror in the mounting ring by accepting the compromise that the AR surface is in the 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.

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.

[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.

 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!

 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 0.041mA

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 as described in manual of PDA255 (i.e. 5e3 when it is not in High-impedance region).

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 2.03e-08 V/sqrt(Hz)

Therefore dark current(in2) ~dark noise voltage/RF transimpedance = 4.06pA/sqrt(Hz)

Therefore the approximate shot noise intercept current value is (4/18)^2 ~ 0.049mA, which is close to the fitted value.

 ... hard to believe these numbers. Wrong DC transimpedance? (KA)

I noticed (while relocking the MC after Jamie and I zeroed the LSC offsets) that the MC refl power was 4.8 V.  Usually we should be ~4.2, so I closed the PSL shutter and went in to measure the power.  We were injecting ~125mW or a little more.  I had adjusted the power the other day, and through yesterday, it looked fine, but overnight it looks like it drifted up.

It's OK; even Siegman got it wrong---48 times.

RA: NO, stil not OK.

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.

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 ~27000.  I 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.

 Gouy not Guoy:

http://www.rp-photonics.com/gouy_phase_shift.html

pronounced Goo-eee, with the emphasis on the second syllable.

[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.

Summary: Measurement and plot of shot-noise-intercept-current for PDA10CF. 

Motivation:It is to measure the shot noise intercept current for PDA10CF.

Result: The final plot is attached here. The plot suggests that the value of shot-noise-intercept current is 0.21mA

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 as described in manual of PDA255 (i.e. 5e3 when it is not in High-impedance region).

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

In the present case dark-noise is 4.3e-08 V/sqrt(Hz)

Therefore dark current(in2) ~dark noise voltage/RF transimpedance = 8.6pA/sqrt(Hz)

Therefore the approximate shot noise intercept current ~ (8.6/18)^2=0.22mA

This value matches well with the fitted data.

From PDA10CF manual, NEP=1.2e-11W/sqrt(Hz) and responsivity~0.9A/W. Therefore the noise current level will be ~10pA.

 Thanks Jenne.

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.

 This work was done in-situ, so no optics on the AS table were moved.  The PSL shutter was blocked since the IR beam was not necessary, and would scatter off the bulb Riju put in front of the PD. 

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.

Today I collected the data for shot noise intercept current for MC REFL PD. I didn't get many data points at higher DC voltage of the photodiode, cause the incandescent bulbs get burnt at that level; two bulbs I have burnt today. I will process the data and report.

 [Jan,Manasa]

We executed plan B. We installed the green laser pointer on POY table and steered the beam  through ITMY to hit the pick off mirror at the ETM end by installing *temporary mirrors. The pick off mirror was adjusted in pitch and yaw to center the reflected beam on the viewport window. We have installed irides on the ring attached to the viewport window to direct the beam to the camera.

*Temporary mirrors were removed from the ITMY chamber after this alignment.

There's definitely a timing issue with this machine.  I looked at it a bit yesterday.  I'll try to get to it by the end of the week.