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.

[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.

 [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:

 The Cleanboot is washable and reusable!

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);

Typically, you can still find a way to model the important parts of the stages that are not as simply added. In the case of the differential input stage, in particular, it is important to include it because it will usually set the input noise level of the circuit. In this case, the noise is the same as the second stage (U5) and it has a gain of 1, so there is essentially no difference (up to factors of sqrt(2) or 2).

You can edit the opamp.lib file and add in custom components. For the input stage, you can just pretend it is a simple non-inverting amplifier with the specified noise characteristics from the datasheet: un = 1.3n, uc = 50 Hz (see below).

For dual op amps, you can usually just model each part separately. For example, the OPA2604 is a dual op amp that is included in the opamp.lib and can be treated as a single one in a model.

Attached are both the circuit diagram and the liso formatted *.fil for the main branch of the ISS, as well as the resulting transfer function when analyzed. Unfortunately, as noted in the file, not all of the elements are possible to analyze in liso, such as any type of op-amp with more than two inputs and one output (AD602 used in this design has 16 pins with two distinct amplifiers contained within).

I have begun prototyping this circuit on a breadboard.

[Koji, Jenne]

We noticed that the iscex computer is still down, but the IOP is (was) running.  When we sat down to look at it, c1x01 was 'breathing', had a non-zero CPU_METER time, and the error was 0x4000, which I've never seen before.  The fb connection was still red though.  Also, it is claiming that its sync source is 1pps, not TDS like it usually is. 

Since things were different, Koji restarted the 2 other models running on iscex, with no resulting change.  We then did a 'rtcds restart all', and the IOP is no longer breathing, and the error message has changed to 0xbad.  The sync source is still 1pps.

Moral of the story:  c1iscex is still down, but temporarily showed signs of life that we wanted to record.

[Jan, Manasa]

To align the camera to see small angle scattering from the ITMY, we tried shooting a green laser pointer at the pickoff mirror that was installed in the ETMY chamber such that we hit the face of ITMY. But we concluded that to be a very bad way to align the camera because we have no means to reconfirm that the camera was exactly looking at the scattering from ITMY.

Since we are in air, we came up with a plan B. The plan is to temporarily install a mirror in the ITMY chamber to steer the beam from the laser pointer (installed on the POY table) through ITMY to the pickoff mirror at the ETMY end. This way, we can install the camera at the ETMY window and be sure we are looking at ITMY scattered light. 

[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.

I can't believe that SR785 can have such a low input noise level (<1nV/rtHz). Review your calibration again.

It is also described in the manual that SR560 typically has the input noise level of 4nV/rtHz, although this number depends on which gain you use.

 [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. 

 [Q, Chloe]

Chloe has been to the lab twice to start up her investigations in acoustic noise coupling to mirrors. The general idea for the setup is a HeNe laser bouncing off a mirror and onto a QPD, whose signal provides a measure of beam displacement noise. The mirror will be mounted and excited in various ways to make quantitative conclusions about the quality of different mounting schemes.

We have set up the laser+mirror+QPD on the SP table, and collected data via SR560s->SR785, with the main aim of evaluating the suitability of this setup. The data we collected is not calibrated to any meaningful units (yet). For now, we are just using QPD volts.

Chloe collected data of vertical displacement noise for the following schemes: Terminated SR785 input, Terminated SR560 inputs, Laser centered directly onto the QPD, Laser shining on mirror centered on QPD, laser/mirror/qpd with some small desktop speakers producing white noise from http://www.simplynoise.com. Data shown below. 

[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. 

 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.