I missed the point.
Do you mean that we can measure the coating thermal noise of the ref cav at the 40m as the IMC is quiet enough?

Yes, it should be. However, what I did was calculating thermal noise of MC. I'm not sure about the 40m IMC's actual noise level. The plot in the entry was taken from LLO's MC in 2003.

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.

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.

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?

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.

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

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 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.

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 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.

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

I have never seen any Yokogawa in vicinity.

Quote:

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.

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.

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, butif 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.

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

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;

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)

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:

tangential

sagittal

gouy shift, one-way

55.63

55.63

g (from gouy)

0.303

0.303

g (product of individual mirror g)

0.303

0.303

PRC, nominal design (flat PR2/3)

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

tangential

sagittal

gouy shift, one-way

14.05

14.05

g (from gouy)

0.941

0.941

g (product of individual mirror g)

0.942

0.942

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.

tangential

sagittal

gouy shift, one-way

19.76

18.45

g (from gouy)

0.886

0.900

g (product of individual mirror g)

0.888

0.902

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:

tangential

sagittal

gouy shift, one-way

18.37

18.31

g (from gouy)

0.901

0.901

g (product of individual mirror g)

0.903

0.903

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 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.

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.

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.

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.

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.

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.

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.

Quote:

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

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.

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

I claim that neither of those things is plausible. We took out 1 PZT, and put in 1 active TT onto the BS table. There is no way the resonant frequency changed by an appreciable amount due to that switch.

I don't think that it is the resonant frequency of the TTs either. Here, I collate the data that we have on the resonant frequencies of our tip tilts. It appears that in elog 3425 I recorded results for TTs 2 and 3, but in elog 3447 I just noted that the measurements had been done, and never put them into the elog. Ooops.

Resonant frequency and Q of modes of passive tip tilts.

Vertical

Yaw

Pos

Side

TT1

f0=20, Q=18

f0=1.89, Q=3.8

f0=1.85, Q=2

f0=1.75, Q=3.2

TT2

f0=24, Q=7.8

f0=1.89, Q=2.2

f0=1.75, no Q meas

f0=1.8, Q=4.5

TT3

f0=20, Q=34

f0=1.96, Q="low"

f0=1.72, Q=3.3

f0=1.85, Q=6

TT4

f0=21, Q=14

f0=1.88, Q=2.3

f0=1.72, Q=1.4

f0=1.85, Q=1.9

TT5

f0=20, Q=22.7

no measurement

f0=1.79, Q=1.8

f0=1.78, Q=3.5

Notes: "Serial Number" of TTs here is based on the SN of the top suspension point block. This does not give info about which TT is where. Pitch modes were all too low of Q to be measured, although we tried.

Tip tilt mode measurements were taken with a HeNe and PD shadow sensor setup - the TT's optic holder ring was partially obscuring the beam.

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?

This is exactly why I added the higher order mode spacing, so you could calculate the g parameter. For TEM order N = n + m with spacing f_N, the overall cavity g parameter should be:

g = (cos( (f_N/f_FSR) * (\pi/N) ))^2

The label on the previous plat should really be f_N/FSR, not \omega_{10,01}

BUT, arbcav does not currently handle arbitrary ABCD matrices for the mirrors, so it's going to be slightly less accurate for our more complex flipped mirrors. The affect would be bigger for a flipped PR3 than for a flipped PR2, because of the larger incidence angle, so arbcav will be a little more correct for our flipped PR2 only case (see below).

Quote:

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.

This is not correct. Multiplying the RoC by -N would be a very large change. For an arbitrary ABCD matrix:

The affect of the substrate is negligible for flipped PR2 but significant for flipped PR3.

The current half-PRC setup

OK, I have now completely reconciled my alamode and arbcav calculations. I found a small bug in how I was calculating the ABCD matrix for non-flipped TTs that made a small difference. I now get the exact same g parameter values with both with identical input parameters.

Quote:

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

Sooooo, I have redone my alamode and arbcav calculations with these updated values. Here are the resulting g parameters

So the sagittal values all agree pretty well, but the tangential measurement does not. Maybe there is an actual astigmatism in one of the optics, not due to angle of incidence?

asc/ (ascii files) --> .asc files are saved in Wyko ascii format.
bmp/ (screen shots of Vision32)
mat/ (Matlab scripts and results)
opd/ (Raw binary files)

Estimated radius of curvature

Mirror / RoC from Vision32 / RoC from KA's matlab code
G&H "A" 0864 / -527.5 m / -505.2 m
G&H "B" 0884 / -710.2 m / -683.6 m
LaserOptik SN1 / -688.0 m / -652.7 m
LaserOptik SN2 / -605.2 m / -572.6 m
LaserOptik SN3 / -656.7 m / -635.0 m
LaserOptik SN4 / -607.5 m / -574.6 m
LaserOptik SN5 / -624.8 m / -594.3 m
LaserOptik SN6 / -658.5 m / -630.2 m

The aperture for the RoC in Vision32 seems a bit larger than the one I have used in the code (10mm in dia.)
This could be the cause of the systematic difference of the RoCs between these, as most of our mirrors
has weaker convex curvature for larger aperture, as seen in the figure. (i.e. outer area is more concave
after the subtration of the curvature)

I did not see any structure like Newton's ring which was observed from the data converted with SXMimage. Why???

Given that we're measuring different g parameters in the tangential and sagittal planes, I went back to alamode to see what astigmatism I could put into PR2 and/or PR3 to match what we're measuring. I looked at three cases: only PR2 is astigmatic, only PR3 is, or where we split the difference. Since the sagittal measurement matches, I left all the sagittal curvatures the same in

I, by chance, found that my windows partition has Vision32 installed.
So I run my usual curvature characterization for the TT phasemaps.

Is it possible to calculate astigmatism with your tools? Can we get curvature in X/Y direction, preferably aligned with some axis that we might align to in the vacuum?

When you estimate the variance of the population, you have to use unbiased variance (not sample variance). So, the estimate to dx in the equations Koji wrote is

It is interesting because when n=2, statistical error of the averaged value will be the same as the standard deviation.

dXavg = dx/sqrt(n) = stdev/sqrt(n-1)

In most cases, I think you don't need 10 % precision for statistical error estimation (you should better do correlation analysis if you want to go further). You can simply use dx = stdev if n is sufficiently large (n > 6 from plot below).

Quote:

Makes sense. I mixed up n and n-1

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

The shape of the REFL beam reflected from PRM is oval after the Faraday.
We tried to fix it by MC spot position centering and by tweaking input TT1/TT2/PRM. But REFL still looks bad (below).

What has changed since:
REFL looks OK in mid-Dec 2012. Possibly related things changed are;

1. New active input TTs with new mirrors installed
2. Leveling of IMC stack changed a little (although leveling was done after installing TTs)

Possible explanations to oval REFL:
A. Angled input beam:
Input beam is angled compared with the Faraday apertures. So, beam coming back from PRM is angled, and clipped by the Faraday aperture at the rejection port.

B. Mode mis-match to PRM:
New input TTs have different curvatures compared with before. Input mode matching to PRM is not good and beam reflected from PRM is expanding. So, there's clipping at the Faraday.

C. Not clipping, but astigmatism:
New input TTs are not flat. Incident angle to TT2 is ~ 45 deg. So, it is natural to have different tangential/sagittal waist sizes at REFL.

How to check:
A. Angled input beam:
Look beam position at the Faraday apertures. If it doesn't look centered, the incident beam may be angled.
(But MC centering didn't help much......)

B. Mode mis-match to PRM:
Calculate how much the beam size will be at the Faraday when the beam is reflected back from PRM. Put some real numbers to curvatures of input TTs for calculation.

C. Not clipping, but astigmatism:
Same calculation as B. Let's see if REFL is with in our expectation or not by calculating the ratio of tangential/sagittal waist sizes at REFL.

Recently the REFL path has been rearranged after I touched it just before Thanksgiving.
(This entry)

If the lenses on the optical table is way too much tilted, this astigmatism happens.
This is frequently observed as you can find it on the POP path right now.

Also the beam could be off-centered on the lens.

I am not sure the astigmatism is added on the in-air table, but just in case
you should check the table before you put much effort to the in-vacuum work.

We checked that REFL beam is already oval in the vacuum. We also centered in-air optics, including lens, in the REFL path, but REFL still looks bad.

By using IR card in vacuum, PRM reflected beam looks OK at MMTs and at the back face of the Faraday. But the beam looks bad after the output aperture of the Faraday.

Let's wait for astigmatism calculation.
In either case(clipping or astigmatism), it takes time to fix it. And we don't need to fix it because we can still get LSC signal from REFL.
So why don't we start aligning input TTs and PRMI tomorrow morning.

Take the same alignment procedure we did yesterday, but we should better check REFL more carefully during the alingment. Also, use X arm (ETMX camera) to align BS. We also have to fix AS steering mirrors in vacuum. I don't think it is a good idea to touch PR2 this time, because we don't want to destroy sensitive PR2 posture.

Calculations need to be done in in-air PRMI work:
1. Explanation for REFL astigmatism by input TTs (Do we have TT RoCs?).
2. Expected g-factor of PRC (DONE - elog #8068)
3. What's the g-factor requirement(upper limit)?
Can we make intra-cavity power fluctuation requirement and then use PRM/2/3 angular motion to break down it into g-factor requirement?
But I think if we can lock PRMI for 2 hours, it's ok, maybe.
4. How to measure the g-factor?
To use tilt-and-measure-power-reduction method, we need to know RoC of the mirror you tilted. If we can prove that measured g-factor is smaller than the requirement, it's nice. We can calculate required error for the g-factor measurement.

After using alamode to calculate the round-trip mode of the beam at the Faraday exit after retro-reflection form the PRM, I'm not able to blame the MMT and TT curvature for the beam ellipticity.

I assume an input waist at the mode cleaner of [0.00159, 0.00151] (in [T, S]). Propagating this through the MMT to PRM, then retro-reflecting back with flat TTs I get

w_t/w_s = 0.9955, e = 0.0045

If I give the TTs a -600 m curvature, I get:

w_t/w_s = 1.0419, e = 0.0402

That's just a 4% ellipticity, which is certainly less than we see. I would have to crank up the TT curvature to -100m or so to see an ellipticity of 20%. We're seeing something that looks bigger than 50% to me.

Below are beam size through MMT + PRM retro-reflection, TT RoC = -600m:

0. Measured MC centering (off by 5mrad) before getting the doors off.

1. Got the TTs to 0.0 in pitch and yaw.

2. Using the MMTs, the beam was centered on the TTs.

3. TT1 was adjusted such that the incident beam was centered at PRM (with target).

4. TT2 was adjusted such that the beam passed through the center of BS (with target).

5. Centered the beam on PR2 by sliding it on the table.

6. Moved PR2 and tweaked TT2 to center the beam on ITMY and BS respectively.

7. Using TTs, we got the beam centered on ETMY while still checking the centering on ITMY.

8. ITMY was adjusted such that it retro-reflected at the BS.

9. ETMY was aligned to get a few bounces in the arm cavity.

10. Centered on ITMX by adjusting BS and then tweaked ITMX such that we retro-reflected at BS.

11. At this point we were able to see the MI fringes at the AS port.

12. Tweaked ITMX to obtain reflected MI fringes in front of MMT2.

13. By fine adjustments of the ITMs, we were able to get the reflected MI to go through the faraday while still checking that we were retro-reflecting at the BS.

14. Tweaked the PRM, such that the PRM reflected beam which was already visible on the 'front faceback face of faraday' camera went through the faraday and made fine adjustments to see it fringing with the reflected MI that was already aligned.

15. At this point we saw the REFL (flashing PRMI) coming out of vacuum unclipped and on the camera.

16. Started with alignment to get the AS beam out of vacuum. We tweaked OM1 and OM2 (steering mirrors in the ITMY chamber) to center the beams on OM4 and OM3 (steering mirrors in the BSC) respectively.

17. We then adjusted steering mirrors OM5 and OM6 (in the OMC chamber) such that the beam went unclipped out of vacuum.

18. Note that we took out the last steering mirror (on the AS table) in front of the AS camera, so that we can find the AS beam easily. This can be fixed after we pump down.

Small, inconsequential point: The camera image in the upper right of your video is the *back* of the Faraday in our usual nomenclature. The camera is listed in the videoswitch script as "FI_BACK". The camera looking at the "front" of the Faraday is just called "FI".

I measured openloop transfer function of the phase tracking loop for the first characterization of phase tracker.
What is phase tracker:
See elog #6832.
For ALS, we use delay-line frequency discriminator, but it has trade-off between sensitivity and linear range. We solved this trade-off by tacking the phase of I/Q signals.
Figure below is the current diagram of the frequency discriminator using phase tracker.

OLTF of phase tracking loop:
Below. UGF at 1.2 kHz, phase margin 63 deg for both BEATX and BEATY. Phase delay can be clearly explained by 61 usec delay. This delay is 1 step in 16 KHz system. Note that UGF depends on the amplitude of the RF input. I think this should be fixed by calculating the amplitude from I/Q signals.
BEAT(X|Y)_PHASE_GAIN were set to 300, and I put -3dBm 100 MHz RF signal to the beatbox during the measurement.
BEATX: BEATY:
Other measurements needed:
- Linear range: By sweeping the RF input frequency and see sensitivity dependence.
- Bandwidth: By measuring transfer function from the modulation frequency of the RF input to phase tracker output.
- Maximum sensitivity: Sensitivity dependence on delay-line length (see PSL_Lab #825).
- Noise: Lock oscillator frequency with phase tracker and measure out-of-loop frequency noise with phase tracker.
- Sensitivity to amplitude fluctuation: Modulate RF input amplitude and measure the sensitivity.

I have found two great FET input chips that rival the storied, discontinued AD743. In some ways, they are even better. These parts are the OPA140 and the OPA827.

Below is a plot of the input-referred voltage noise of the two op amps with R_{source} = 0, along with several others for comparison. The smooth traces are LISO models. The LT1128 and AD797 are BJT-input parts, so their voltage noise is naturally better. However, the performance you see here for the FET parts is the same you would expect for very large source impedances, due to their extremely low current noise by comparison. I have included the BJTs so that you can see what their performance is like in an absolute sense. I have also included a "measured" trace of the LT1128, since in practice their low-frequency noise can be quite higher than the spec (see, for example, Rana's evaluation of the Busby Box). The ADA4627 is another part I was looking into before, the LT1012 is a less-than-great FET chip, and the AD797 a less-than-great BJT.

As you can see, the OPA140 actually outperforms the AD743 at low frequencies, though it is ~2x worse at high frequencies. The OPA827 comes close to the AD743 at high frequencies, but is a bit worse at low ones. Both the OPA140 and OPA827 have the same low-frequency RMS spec, so I was hoping it would be a better all-around part, but, unfortunately, it seems not to be.

The TI chips also have a few more things on the AD743:

Input current noise @ 1kHz

AD743: 6.9 fA/rtHz

OPA827: 2.2 fA/rtHz

OPA140: 0.8 fA/rtHz (!)

Input bias (offset) current, typ

AD743: 30 pA (40 pA) --- only for V_{supply} = ±5 V

OPA827: ±3 pA (±3 pA) --- up to ±18V

OPA140: ±0.5 pA (±0.5 pA) (!) --- up to ±18V

Supply

Both OPA140 and OPA827 can be fed single supplies up to 36V absolute maximum

The OPA140 is a rail-to-rail op amp

These characteristics make both parts exceptionally well suited for very-high source impedance applications, such as very-low-frequency AC-coupling preamplifiers or ultra-low-noise current sources.

(Apologies---the SR785 I was using had some annoying non-stationary peaks coming in. I verified that they did not affect the broadband floor).

With MC REFL PD fixed, we aligned MC in high power enabling a fully functional MC autolocker.
We then unlocked MC and aligned the PD and WFS QPDs. Also we checked the MC demodulator and found a ~20% leakage between the Q-phase and I-phase. This must be fixed later by changing the cable length.

We adjusted MC offsets using /opt/rtcds/caltech/c1/scripts/MC/WFS/WFS_FilterBank_offsets.
We then measured the MC spot positions using /opt/rtcds/caltech/c1/scripts/ASS/MC/mcassMCdecenter
Spot positions seem to have shifted by 2mm in yaw.

Rana suggested that I measure the OPA827 and OPA140 noise with high source impedance so as to see if we could find the low-frequency current noise corner. Below is a plot of both parts with R_{s} = 0, 10k, and 100k.

As you can see, both parts are thermal noise limited down to 0.1 Hz for up to R_{s} = 100k or greater. Given that the broadband current noise level for each part is ~0.5-1 fA/rtHz, this puts an upper limit to the 1/f corner of <100 Hz. This is where the AD743 corner is, so that sounds reasonable. Perhaps I will check with even higher impedance to see if I can find it. I am not sure yet what to make of the ~10-20 kHz instability with high source impedance.

EDIT: The datasheets claim that they are Johnson noise limited up to 1 Mohm, but this is only for the broadband floor, I'd guess, so it doesn't really say anything about the low frequency corner.

Quote:

I have found two great FET input chips that rival the storied, discontinued AD743. In some ways, they are even better. These parts are the OPA140 and the OPA827.

This looks pretty good already. Not sure if we can even measure anything reasonable below 0.1 Hz without a lot of thermal shielding.

The 10-20 kHz oscillation may just be the loop shape of the opamp. I think you saw similar effects when using the AD743 with high impedance for the OSEM testing.

Both arms are aligned starting from Y green.
We have all beams unclipped except for IPANG. I think we should ignore IPANG and go on to PRMI locking and FPMI locking using ALS. IPANG/IPPOS and oplev steering mirrors are kept un-touched after pumping until now.

Current alignment situation:
- Yarm aligned to green (Y green transmission ~240 uW)
- TT1/TT2 aligned to Yarm (TRY ~0.86)
- BS and Xarm alined to each other (TRX ~ with MI fringe in AS)
- X green is not aligned yet
- PRMI aligned

Current output beam situation: IPPOS - Coming out clear but off in yaw. Not on QPD.
IPANG - Coming out but too high in pitch and clipped half of the beam. Not on QPD.
TRY - On PD/camera.
POY - On PD.
TRX - On PD/camera.
POX - On PD.
REFL - Coming out clear, on camera (centered without touching steering mirrors).
AS - Coming out clear, on camera (centered without touching steering mirrors).
POP - Coming out clear, on camera (upper left on camera).
Oplev values: Optic Pre-pump(pit/yaw) PRFPMI aligned(pit/yaw)
ITMX -0.26 / 0.60 0.25 / 0.95
ITMY -0.12 / 0.08 0.50 / 0.39
ETMX -0.03 / -0.02 -0.47 / 0.19
ETMY 0.37 / -0.62 -0.08 / 0.80
BS -0.01 / -0.18 -1 / 1 (almost off)
PRM -0.34 / 0.03 -1 / 1 (almost off)

All values +/- ~0.01. So, oplevs are not useful for alignment reference.

All values +/- ~10.
We checked that if there's ~1200 difference, we still see flash in Watec TR camera. So, OSEM values are quite good reference for optic alignment.

IPANG drift:
On Saturday, when Rana, Manasa, and I are trying to get Y arm flash, we noticed IPANG was drifting quite a lot in pitch. No calibration is done yet, but it went off the IPANG QPD within ~1 hour (attached).
When I was aligning Yarm and Xarm at the same time, TRY drifted within ~1 hour. I had to tweak TT1/TT2 mainly in yaw to keep TRY. I also had to keep Yarm alignment to Y green. I'm not sure what is drifting so much. Suspects are TT2, PR2/PR3, Y arm and Y green.

I made a simple script(/opt/rtcds/caltech/c1/scripts/Alignment/ipkeeper) for keeping input pointing by centering the beam on IPPOS/IPANG using TT1/TT2. I used this for keeping input pointing while scanning Y arm alignment to search for Y arm flash this weekend (/opt/rtcds/caltech/c1/scripts/Alignment/scanArmAlignment.py). But now we have clipped IPANG.

So, what's useful for alignment after pumping?: Optic alignment can be close by restoring OSEM values. For input pointing, IPPOS/IPANG are not so useful. Centering the beam on REFL/AS (POP) camera is a good start. But green works better.

I took the two 'flat' 2" mirrors over to Downs and Garilynn showed me how to measure them with the old Wyko machine.

The files are now loaded onto our Dropbox folder - analysis in process. From eyeball, it seems as if the RoCs are in the neighborhood of ~5 km, with the local perturbations giving ~10-15 km of curvature depending upon position (few nm of sage over ~1 cm scales)

Koji's matlab code should be able to give somewhat more quantitative answers...

Ed: Here you are. "0966" looks good. It has RoC of ~4km. "0997" has a big structure at the middle. The bump is 10nmPV (KA)

Measured actuator response between 50Hz and 200 Hz in (m/counts).

BS = (20.7 +/- 0.1) x 10^{ -9} / f^{2}

ITMX = (4.70 +/- 0.02) x 10 ^{-9}/ f^{2}

ITMY = (4.66 +/- 0.02) x 10 ^{-9}/ f^{2}

Actuator response differs by 30% for all the 3 mirrors from the previous measurements made by Kiwamu in 2011.

Calibration of BS, ITMX and ITMY actuators

We calibrated the actuators using the same technique as in Kiwamu's elog.

A) Measure MICH error

1. Locked Y-arm and X-arm looking at TRY and TRX.
2. Misaligned ETMs
3. Measured MICH error using ASDC and AS55_Q err (MICH_OFFSET = 20 - to compensate for offset in AS_Qerr which exists even after resetting LSC offsets)

B) Open loop transfer function for MICH control

1. Measured the transfer function between C1:LSC-MICH_IN1 and C1:LSC-MICH_IN2 by exciting on C1:LSC-MICH_EXC.
MICH filter modules used for measurements(0:1 , 2000:1, ELP50). ELP50 used so that actuation signals above 50 Hz are not suppressed.

C) Calibration of BS/ ITMX/ ITMY actuators

1. Measured transfer function between actuation channels on BS/ ITMX/ ITMY and C1:LSC-AS55_Q_ERR.

Attempted Battery Replacement on Backup Power Supply in the Control Room:

I tried to replace the batteries in the Smart UPS 2200 with new batteries purchased by Steve. However, the power port wasn't compatible with the batteries. The battery cable's plug was too tall to fit properly into the Smart UPS port. New batteries must be acquired. Steve has pictures of the original battery (gray) and the new battery (blue) plugs, which look quite different (even though the company said the battery would fit).