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ID Date Author Type Category Subject
8108   Tue Feb 19 12:02:00 2013 JamieUpdateIOOIMC table levelling.

In order to address the issue of low MC1 OSEM voltages, Yuta and I looked at the IMC table levelling.  Looking with the bubble level, Yuta confirmed that the table was indeed out of level in the direction that would cause MC1 to move closer to it's cage, and therefore lower it's OSEM voltages.  Looking at the trends, it looks like the table was not well levelled after TT1 installation.  We should have been more careful, and we should have looked at the MC1/3 voltages after levelling.

Yuta moved weights around on the table to recover level with the bubble level.  Unfortunately this did not bring us back to good MC1 voltages.  We speculate that the table was maybe not perfectly level to begin with.  We decided to try to recover the MC1 OSEM voltages, rather than go solely with the bubble level, since we believe that the MC suspensions should be a good reference.  Yuta then moved weights around until we got the MC1/3 voltages back into an acceptable range.  The voltages are still not perfect, but I believe that they're acceptable.

The result is that, according to the bubble level, the IMC table is low towards MC2.  We are measuring spot positions now.  If the spot positions look ok, then I think we can live with this amount of skew.  Otherwise, we'll have to physically adjust the MC1 OSEMS.

8107   Tue Feb 19 09:37:23 2013 SteveUpdateIOOlow MC1 OSEM voltage

See TT DB25 pin swapping   elog#7869

Attachment 1: MC1_MC3.png
Attachment 2: MC1_MC3_.png
8106   Tue Feb 19 08:42:31 2013 KojiUpdateVACETMX door open

[Steve, Yuta, Koji]

The ETMX heavy door was removed.

8105   Tue Feb 19 08:06:02 2013 yutaUpdateElectronicsPOP path set up but AS55 is broken

I didn't use LED flash light. We learned from the past (elog #7355). I checked that POP55 and REFL55/165/33/11 are clearly responding to flash flight, but I didn't expect that much difference in DC gain.
I wonder why we could align AS beam to AS55 in Feb 8 (elog #8030), but not in Feb 15 (elog #8091). I will check during the pump down.

 Quote: 10010 Ohm for POP55 vs 50 Ohm for AS55 (cf. http://nodus.ligo.caltech.edu:8080/40m/4763) I wonder if you used an LED flash light, which emits no IR.

8104   Tue Feb 19 05:42:28 2013 KojiUpdateElectronicsPOP path set up but AS55 is broken

10010 Ohm for POP55 vs 50 Ohm for AS55 (cf. http://nodus.ligo.caltech.edu:8080/40m/4763)

I wonder if you used an LED flash light, which emits no IR.

8103   Tue Feb 19 02:23:40 2013 yutaBureaucracyGeneralaction items for PRFPMI

These are things need to be done for demonstrating PRFPMI using ALS.
All of these should be done before March 8!

CDS:
- Fix c1iscex -JAMIE (done Feb 19: elog #8109)
- Is ASS and A2L working? -JENNE
- Are all whitening filters for PDs toggling correctly? -JENNE, JAMIE

PRMI locking:
- Adjust I/Q rotation angles for error signals -JENNE, YUTA
- Coil balancing for BS (and ITMs/ETMs) -YUTA

PRC characterization in PRMI:

- Measure PR2 loss from flipping -MANASA
- Measure mode matching ratio -JENNE, YUTA
- Measure finesse, PR gain -JENNE, YUTA
- Calibrate PRM and/or ITM oplevs -MANASA, YUTA
- Measure g-factor by tilting PRM or ITMs -JAMIE, YUTA
- Calculate expected mode matching ratio and g-factor -JAMIE
- Calculate expected finesse, PR gain -JENNE
- Align aux laser into AS port? -ANNALISA?

ALS:
- What's the end green situation? Optical layout changed? Laser temperature in CDS? -MANASA
- What's the PSL green situation? Green trans cameras/PD? -JENNE, MANASA
- Make ALS handing off to DARM/CARM LSC script -JENNE, YUTA
- Demonstrate FPMI using ALS -JENNE, YUTA
- Phase tracker characterization -YUTA, KOJI

PRFPMI:
- Measure mode matching between PRC and arms -JENNE, YUTA
- Measure PR gain -JENNE, YUTA
- Calculate expected finesse, PR gain -JENNE

Others:
- Update optical layout CAD after PR2 flipping -JAMIE, MANASA
- AS55 situation? -YUTA
- Look into PMC drift -JENNE, MANASA
- Measure RFAM contribution to error signals -YUTA

8102   Tue Feb 19 00:21:09 2013 yutaUpdateElectronicsPOP path set up but AS55 is broken

Hmm......
I thought AS55 is broken because it was not responding to the AS beam nor flashlight in DC. What's the DC gain difference between AS55 and POP55 (or REFL55)?

 Quote: I undertook the investigation of the AS55 PD. I found the PD is not broken.

8101   Mon Feb 18 23:41:15 2013 SendhilUpdateAlignmentAligned IPPOS, IPANG and OPLEVS

[Yuta, Sendhil]

We aligned IPPOS, IPANG and all OPLEVs (except for ETMX and SRM).

1. First aligned the IPPOS by tweeking the steering mirrors inside the BS chamber.

2. Aligned the IPANG by tweeking the steering mirrors inside the BS chamber and ETMY chamber.

3. Aligned the OPLEVS for the BS and PRM was done by tweeking the steering mirrors inside the BS chamber and checked that OPLEV beams were not clipped.

4. Centred the OPLEV beams for the ITMY and ETMY.

5. For the OPLEV of ITMX the alignment was done by tweeking the steering mirrors inside the ITMX chamber.

Attachment 1: IPANGIPPOSoplevs.png
8100   Mon Feb 18 21:43:05 2013 KojiUpdateAlignmentPOP path set up but AS55 is broken

I undertook the investigation of the AS55 PD. I found the PD is not broken.

I tested the PD on the PD test bench and it works just fine.

I attatched the characterization result as there has been no detailed investigation of this PD as far as I remember.

The transimpedance gain at 55MHz is 420Ohm, and the shotnoise intercept current is 4.3mA.

Attachment 1: AS55.pdf
8099   Mon Feb 18 18:28:01 2013 yutaBureaucracyAlignmentwe are going to pump down

We will start preparing for pumping down. Main goal for this is to demonstrate PRFPMI using ALS.
Here are to-dos before we pump down.

Feb 18 eveing
- check input beam and Y arm alignment again
- IPPOS/IPANG alignment
- check all oplevs

Feb 19 morning
- open ETMX chamber heavy door
- align BS to X end
- center beam on all AS optics
- make sure AS/REFL is clear
- take picture of flipped PR2 (added by YM)
- make sure green is not clipped by new PRM oplev mirrors  (added by YM)
- center all oplevs

Feb 19 afternoon - Feb 20 morning
- close PSL shutter
- close all heavy doors and put the access connector back
- start pumping down

Feb 20 evening
- start aligning IFO

8098   Mon Feb 18 11:54:15 2013 Max HortonUpdateSummary PagesTiming Issues and Calendars

Crontab: The bug of data only plotting until 5PM is being investigated.  The crontab's final call to the summary page generator was at 5PM.  This means that the data plots were not being generated after 5PM, so clearly they never contained data from after 5PM.  In fact, the original crontab reads:

0 11,5,11,17 * * * /users/public_html/40m-summary/bin/c1_summary_page.sh 2>&1

I'm not exactly sure what inspired these entries.  The 11,5,11,17 entries are supposed to be the hours at which the program is run.  Why is it run twice at 11?  I assume it was just a typo or something.

The final call time was changed to 11:59PM in an attempt to plot the entire day's data, but this method didn't appear to work because the program would still be running past midnight, which was apparently inhibiting its functionality (most likely, the day change was affecting how the data is fetched).  The best solution is probably to just wait until the next day, then call the summary page generator on the previous day's data.  This will be implemented soon.

Calendars: Although the calendar tabs on the left side of the page were fixed, the calendars displayed at: https://nodus.ligo.caltech.edu:30889/40m-summary/calendar/ appear to still have squished together text.  The calendar is being fetched from https://nodus.ligo.caltech.edu:30889/40m-summary/calendar/calendar.html and displayed in the page.  This error is peculiar because the URL from which the calendar is being fetched does NOT have squished together text, but the resulting calendar at 40m-summary/calendar/ will not display spaces between the text.  This issue is still being investigated.

8097   Mon Feb 18 00:03:46 2013 ZachUpdateComputer Scripts / ProgramsARBCAV v3.0

I have uploaded ARBCAV v3.0 to the SVN. The major change in this release, as I mentioned, is the input/output handling. The input and output are now contained in a single 'model' structure. To define the cavity, you fill in the substructure 'model.in' (e.g., model.in.T = [0.01 10e-6 0.01]; etc.) and call the function as:

model = arbcav(model);

Note: the old syntax is maintained as legacy for back-compatibility, and the function automatically creates a ".in" substructure in the output, so that the user can still use the single-line calling, which can be convenient. Then, any individual parameter can be changed by changing the appropriate field, and the function can be rerun using the new, simpler syntax from then on.

The function then somewhat intelligently decides what to compute based on what information you give it. Using a simple option string as a second argument, you can choose what you want plotted (or not) when you call. Alternatively, you can program the desired functionality into a sub-substructure 'model.in.funct'.

The outputs are created as substructures of the output object. Here is an example:

>> th = 0.5*acos(266/271) *180 /pi;

OMC.in.theta = [-th -th th th];

OMC.in.L = [0.266 0.284 0.275 0.271];

OMC.in.RoC = [1e10 2 1e10 2];

OMC.in.lambda = 1064e-9;

OMC.in.T = 1e-6 * [8368 25 8297 33];

OMC.in.f_mod = 24.5e6;

>> OMC

OMC =

in: [1x1 struct]

>> OMC = arbcav(OMC,'noplot')

Warning: No loss given--assuming lossless mirrors

> In arbcav at 274

OMC =

in: [1x1 struct]

FSR: 2.7353e+08

Lrt: 1.0960

finesse: 374.1568

buildup: 119.6956

df: [1000x1 double]

coefs: [1000x4 double]

HOM: [1x1 struct]

>> OMC.HOM

ans =

f: [1x1 struct]

pwr: [1x1 struct]

>> OMC.HOM.pwr

ans =

carr: [15x15 double]

SBp: [15x15 double]

SBm: [15x15 double]

Some other notes:

• The annoying Mdo.m has been internalized; it is no longer needed.
• For the next release, I am working on including:
• Finite mirror thickness/intracavity refractive elements - If, for god knows what reason, you decide to put a mirror substrate within a cavity
• Mode overlap - Calculating the overlap of an input beam to the cavity
• Mode matching - Calculating a mode matching telescope into the cavity for some defined input beam
• Anything else?

I have added lots of information to the help header, so check there for more details. As always, your feedback is greatly appreciated.

8096   Sun Feb 17 19:27:19 2013 ranaUpdateSUSPRM coil balanced

I will check out the AS55 situation tomorrow. Just put it on my desk.

MC Autolocker was disabled - I enabled it.

For the F2P.py, you should look at how we did this with the script written 8 years ago in csh. There we stored the initial values in a file (so they don't get blow away if someone does CTRL-C). Your python script should have a trap for SIGINT so that it dies gracefully by restoring the initial values. In order to have the smooth value adjustment, you must first set the TRAMP field for all the coil gains to 2 and then switch. Make sure that the lockin ignores the first few seconds of data after making this switch or else it will be hugely biased by this transient.

For the PRM OL use as a F2A reference, you also have to take into account that the OL beam is hitting the PRM surface at non-normal incidence. IF it is a large angle, there will be a systematic error in the setting of the F2Y values.

8095   Sat Feb 16 19:23:17 2013 yutaUpdateLSCPR2 flipped PRMI locked

It is my pleasure to announce that the first lock of PR2 flipped PRMI was succeeded.

POP looks very nice. TEM00 and not wobbling.
We need more I/Q phase and gain/filter adjustment and characterization soon.

Some more details:
MICH error signal: AS55_Q_ERR (using POP55 PD; phase rotation angle 70 deg)
PRCL error signal: REFL11_I_ERR (phase rotation angle 80 deg)
MICH feedback: BS (MICH_GAIN = -60)
PRCL feedback: PRM (PRCL_GAIN = -0.5)

8094   Sat Feb 16 18:32:01 2013 yutaSummaryRF Systemphase tracker: OLTF

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.

8093   Sat Feb 16 17:27:26 2013 yutaUpdateSUSPRM coil balanced

PRM coil gains and f2a filters are adjusted for PRMI work.
It seems like UR/LL coil gains were ~10 % larger than others, and f2a filters changed by few %.

What I did:
1. Tried to lock PRMI but when I turn on PRCL lock, PRM reflection looked like it tends to go up and left in REFL camera (last night).

2. So, I set up PRM oplev back, by steering PRM oplev mirrors on the BS table (last night).

3. Turned PRM oplev sero on, f2a filters off, and ran

> /opt/rtcds/caltech/c1/scripts/SUS/F2P_LOCKIN.py -o PRM

I had to fix F2P_LOCKIN.py because it assumed some OUTPUT buttons in LOCKIN1 filters to be ON.
Also, I had to restore filters in LOCKIN1 (8.5 Hz bandpass filter etc.) because their names were changed. To do this, I copied filters needed from /opt/rtcds/caltech/c1/chans/filter_archive/c1sus/C1SUS_110916_162512.txt, renamed LOCKIN1_(I|Q|SIG) with LOCKIN1_DEMOD_(I|Q|SIG), and pasted to the current filter bank file. I checked that they look OK with foton after editing the file.

This measurement takes about 30 minutes. I ran several times to check consistency. There was ~ 0.1 % standard deviation for the measurement results.

4. By putting measured coupling coefficients and PRM pendulum frequency (f0=0.993 Hz) to /opt/rtcds/caltech/c1/scripts/SUS/F2Pcalc.py, I got new f2a filters.

5. Overwrote f2a filters in C1:SUS-PRM_TO_COIL_(1-4)_1 FM1 with new ones, and turned  new f2a filters on.

Result:
Below is the DC gain adjustment result from F2P_LOCKIN.py;

multiplier factors are :
UL = 1.141525
UR = 0.879997
LR = 1.117484
LL = 0.860995
Set C1:SUS-PRM_ULCOIL_GAIN to 1.04990177238
Set C1:SUS-PRM_URCOIL_GAIN to -0.983396190716
Set C1:SUS-PRM_LRCOIL_GAIN to 0.954304254663
Set C1:SUS-PRM_LLCOIL_GAIN to -0.971356852259

So, UR/LL coil gains somehow got ~10 % larger than other two since last coil balancing.

Measured coupling coefficients from F2P_LOCKIN.py were

- measured coupling coefficients are : P2P(POS=>PIT) = 0.014993 P2Y(POS=>YAW) = 0.001363

New f2a filters are plotted below. They look fairly different compared with previous ones.

We need better F2P_LOCKIN.py:
Some one should make F2P_LOCKIN.py better. The main problem is the sudden gain change when starting diagonalization at low frequency. It sometimes trips off the watchdog.

Some elogs related:
Kiwamu made f2a filters in Sep 2011: elog #5417
Koji adjusting DC gains in Jan 2013: elog #7969

8092   Fri Feb 15 21:22:29 2013 yutaUpdateElectronicsAS55 replaced with POP55 PD

I temporarily replaced AS55 PD with PD labeled "POP55(POY55)".
I think POP55 is working because I could lock MI with this PD using AS55_Q_ERR as an error signal. I rotated I/Q phase (C1:LSC-AS55_PHASE_R) to 70 deg by minimizing ASDC during MI lock.

POP55 PD was freely sitting on the ITMX table.
I will leave AS55 PD at free space of the AP table. Someone, please look into it.

8091   Fri Feb 15 20:07:28 2013 yutaUpdateAlignmentPOP path set up but AS55 is broken

[Manasa, Yuta]

We set up POP camera and POPDC PD, and centered REFL PDs.
We also tried to center AS55 PD, but AS55 seems to be broken.

What we did:
1. POP path alignment:
Shot green laser pointer from ITMX table at where POPDC PD was sitting and centered green beam at optics in the POP path. Steered POPM1/M2 mirrors in the ITMX chamber to make green laser overlap with the PRM-PR2 beam as far as I can reach from ITMX chamber. We removed some ND filters and a BS for attenuating POP beam because POP power was somehow so low. Currently, POP is pick-off of the beam which goes from PRM to PR2.

2. POP camera and PD:
We first used camera to find the beam at where POPDC PD was sitting because it is much easier to find focused beam. Put an iris in front of the camera, and put POP DC behind it. Steered a mirror in front of PD to maximize DC output.

3. REFL PDs:
Steered mirrors in the REFL path to center the beam and maximized DC outputs, as usual.

4. AS55:
AS55 was not responding very much to the flashlight nor AS beam. C1:LSC-ASDC_OUT looked funny. By swapping the ribbon cables of AS55, REFL55, and REFL165, I confirmed that AS55 PD itself is broken. Not the ribbon cable nor PD circuit at LSC rack. I don't know what happened. AS55 was working on Feb 8 (elog #8030).

Result:
We aligned PRMI coarsely. POP(right above) looks much better than before. REFL (left below) still looks elliptic, but ellipticity differs with the position on the camera. Some astigmatism is happening somewhere. AS (right below) looks pretty nice with MI aligned.

Next:
1. Fix AS55? Or replace it with POP55 PD, which is currently unused.
2. Confirm we are getting the right error signals or not, and lock PRMI.

8090   Fri Feb 15 17:11:13 2013 ChloeUpdate QPD circuit pictures

I took better pictures of the circuits of the QPD and spent a couple of hours with a multimeter trying to figure out how all the connections worked. I will continue to do so and analyze the circuits over the weekend to try to understand what is going on. I also have an old SURF report that Eric sent me that is similar to the design I was planning to use to sum the pitch and yaw signals. I will try and look at this over the weekend.

Attachment 1: IMG_0337.JPG
Attachment 2: IMG_0338.JPG
8089   Fri Feb 15 16:09:19 2013 KojiUpdateGeneralbeam traps ready to be installed

For the hexagonal one, insert one of the glass plate only half. Use a 1"x.5" piece if exists.

For the diamond one, you don't need the forth glass piece.

Attachment 1: HexBeamDump.pdf
Attachment 2: DiamondBeamDump2in.pdf
8088   Fri Feb 15 15:21:07 2013 JamieUpdateComputersc1iscex IO-chassis dead

I appears that the c1iscex IO-chassis is either dead or in a very bad state.  The PCIe interface card in the IO-chassis is showing four red lights, where it's supposed to be showing a dozen or so green lights.  Obviously this is going to prevent anything from running.

We've had power issues with this chassis before, so possibly that's what we're running into now.  I'll pull the chassis and diagnose asap.

8087   Fri Feb 15 09:58:49 2013 SteveUpdateGeneralbeam traps ready to be installed

Black-green glass traps are ready for light in vacuum. I can assemble more if needed. These three sizes are available.

Attachment 1: IMG_0083.JPG
Attachment 2: IMG_0084.JPG
8086   Fri Feb 15 01:51:43 2013 JenneSummaryAlignmentIFO aligned and ready for PRMI locking

Yuta and Manasa, you guys are awesome!

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".

8085   Fri Feb 15 01:41:02 2013 Manasa, YutaSummaryAlignmentIFO aligned and ready for PRMI locking

[Yuta, Manasa, Jenne, Jamie, Steve]

### IFO aligned and ready for PRMI locking

Alignment procedure

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 face back 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.

Tomorrow

0. REFL still looks like an egg, but leave it .

1. Align PRMI (no more in-vac!) .

2. Align POP/REFL/AS cameras and PDs.

3. Setup PRM/BS/ITMX/ITMY oplevs.

4. Balance the coils on these mirrors.

5. Lock PRMI.

8084   Thu Feb 14 10:42:41 2013 JamieSummaryAlignmentMMT, curved TTs does not explain beam ellipticity at Faraday

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:

8083   Thu Feb 14 08:29:41 2013 SteveUpdateIOOlow MC1 OSEM voltage

MC1 -  LR, LL, UL & UR  OSEMs should be adjusted to get  1.2V

Attachment 1: Feb14_2013.png
8082   Thu Feb 14 00:10:12 2013 yutaSummaryAlignmentREFL is not clipped

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.

8081   Wed Feb 13 22:09:26 2013 JenneUpdateAlignmentREFL is not clipped

We need to calculate whether this level of astigmatism is expected from the new active TT mirrors, but I claim that the beam is not clipped.

As proof, I provide a video (PS, why did it take me so long to be converted to using video capture??).  I'm just showing the REFL camera, so the REFL beam as seen out on the AS table.  I am moving PRM only.  I can move lots in pitch before I start clipping anywhere.  I have less range in yaw, but I still have space to move around.  This is not how a clipped beam behaves.  The clipping that I see after moving a ways is coincident with clipping seen by the camera looking at the back of the Faraday.  i.e. the first clipping that happens is at the aperture of the Faraday, as the REFL beam enters the FI.

Also, I'm no longer convinced entirely that the beam entering the Faraday is a nice circle.  I didn't check that very carefully earlier, so I'd like to re-look at the return beam coming from TT1, when the PRM is misaligned such that the return beam is not overlapped with the input beam.  If the beam was circular going into the Faraday, I should have as much range in yaw as I do in pitch.  You can see in the movie that this isn't true.  I'm voting with the "astigmatism caused by non-flat active TT mirrors" camp.

8080   Wed Feb 13 19:41:07 2013 yutaSummaryGeneralpossible explanations to oval REFL beam

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.

8079   Wed Feb 13 19:30:45 2013 KojiSummaryGeneralpossible explanations to oval REFL beam

>> "What has changed since:"

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.

8078   Wed Feb 13 19:09:32 2013 yutaSummaryGeneralpossible explanations to oval REFL beam

[Jenne, Manasa, Jamie, Yuta]

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.

8077   Wed Feb 13 16:31:08 2013 JenneUpdatePSLPMC pitch input tuned, MC yaw input tuned

[Jenne, Yuta]

I looked at PMCR camera on the MC1 tv, and tweaked up the beam going into the PMC - it only needed a little bit of pitch.

Yuta and I measured the MC spots, determined (consistent with my measurements this morning) that they were only off in yaw.  We touched the 2nd steering mirror in the zigzag on the PSL table in yaw a small amount (top of knob away from me), realigned the MC, and things were good.  The plot is zoomed in to show only measurements taken today.  2 in the morning, before anything in the IFO room was touched.  1 this afternoon after tweaking PMC.  1st attempt at PSL beam tweaking was successful, 2nd measurement confirms it wasn't a fluke.

8076   Wed Feb 13 14:21:19 2013 JenneUpdateLockingPRC cavity gains

 Quote: With 1500ppm loss on both PR2 and PR3, 150ppm arm cavity loss: 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.

With a PR2 loss of 896ppm (from the plot on the wiki), but no loss from PR3 because we didn't flip it, and the same 150ppm round trip arm cavity loss, I get:

Carrier gain = 21.0

Sideband gain = 66.7

(No loss case, with an extra sig-fig, so you can see that the numbers are different:  Carrier = 21.4, Sideband = 68.8 .)

So, this is 1.6% loss of carrier buildup and 3.1% loss of sideband buildup.  Moral of the story - G&H's measured AR reflectivity is less than Rana's guess, and we didn't flip PR3, so we should have even less of a power recycling gain effect than previously calculated.

8075   Wed Feb 13 09:28:56 2013 SteveUpdateOpticsG&H - HR plots

Gooch & Housego optics order specification from 03-13-2010

Side 1: HR Reflectivity >99.99 % at 1064 nm for 0-45 degrees for S & P polarization

Side 2: AR coat R <0.15

The HR coating scans uploaded to 40mwiki / Aux optics today

8074   Wed Feb 13 01:26:08 2013 yutaSummaryGeneralrough analysis of aligned PRM-PR2 mode scan

Koji was correct.

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

dx = sqrt(sum(xi-xavg)/(n-1))
= stdev*sqrt(n/(n-1))

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 Xavg = xavg*n/n = xavg dXavg^2 = n*dx^2/n^2 => dXavg = dx/sqrt(n) Xavg +/- dXavg = xavg +/- dx/sqrt(n)

8073   Tue Feb 12 23:24:17 2013 yutaUpdateAlignmentIFO alignment in prep for in-air PRMI

[Manasa, Yuta]

Lot's of alignment work, still no AS beam. REFL is clipped by Faraday output aperture......
Our guess is that this is because
we skipped MC centering.

Alignment procedure we took:
1. AM work: Aligned input beam using TT1/TT2
such that the beam hits ETMY and ITMY at the center.

2. Coarsely aligned ITMY
such that the ITMY retro-reflected beam hits BS at the center.

3. Aligned ETMY (we didn't actually move ITMY)
such that Y arm flashes.
This tells you that ITMY is aligned well to the incident beam.

4. Aligned BS
such that the beam hits ITMX at the center.

5. Aligned ITMX
such that the ITMX retro-reflected beam hits BS at the center.
At this point, we saw MI fringes at AS port.

6. Fine alignment of ITMX:
MI reflected beam was not overlapping in front of BS after it was reflected by PRM.
We used this longer REFL path to tune alignment of ITMX to ITMY reflected beam.
We saw MI fringe at REFL port coming out of the chamber, but it was clipped.

7. Aligned PRM
by looking at REFL beam from PRM on the back face of Faraday (video FI_BACK).
We fine tuned the alignment such that PRM retro-relfected beam hits BS at the center and REFL beam from PRM overlaps with the MI fringes at the back face of Faraday.

8. Clipping of REFL at the Faraday output aperture:
We confirmed that the shape of the REFL beam from PRM was OK at the back face of Faraday. But some how, it was clipped at the output aperture. So, REFL beam coming out of the chamber is clipped now.

9. Tried to get AS beam out of the chamber:
We tweaked steering mirrors after SRM to get AS beam out of the chamber. But, we lost the AS beam between the very last folding mirrors (OMPO and OM6) in the OMC chamber......

Discussion:
1. Why clipping at the Faraday output aperture?
In principle, if PRM reflects the incident beam at normal incidence, it should pass the Faraday unclipped. But it's not!
Our guess is that the incident beam does not go well centered through the apertures of the Faraday. I think we have to do MC centering to get good pointing to the Faraday.
We also see that MI fringe at the back face of the Faraday is at the edge of its aperture, after all of these alignment work (we even used Y arm!). This tells you that some thing is wrong.

2. Why did you guys lose the AS beam?
AS beam is too weak after reflecting off of OMPO. The beam was neither visible on IR cards nor IR viewers. The beam is weaker than usual because PMC transmission is ~0.7 and MC REFL is getting high (~ 0.7). We didn't want to realign MC after all of this work today.

Tomorrow (my suggestion):
1. Align PMC (for higher power).
2. MC centering.
3. Input beam steering using TTs and redo the same alignment procedure (it shouldn't take longer than today).
==> Center beam on PR2  (Added by Manasa)
4. Maybe we should better check PRM reflection at REFL port after the Faraday, before doing the full alignment work.
5. Align AS, REFL, POP PDs/cameras.
6. Setup PRM/BS/ITMX/ITMY oplevs.
7. Balance the coils on these mirrors.
8. Lock PRMI.

What needs to be done before pumping down:
1. PRMI characterization: PR gain and g-factor
How can we do the g-factor measurement? Use additional laser? Kakeru method (elog #1434; we need to calibrate mirror tilt to do this)?
2. Glitch study in PRMI locking. If still glitchy, we have to do something. How is beam spot motion? (elog #6953)
3. Fine alignment of the flipped PR2.
4. Fine alignment of IFO using both arms.

8072   Tue Feb 12 23:22:14 2013 ManasaUpdateScatteringScattering setup

[Jan, Manasa]

We installed a camera at the ETMY end to look at the scattering pickoff from the ITMY. We were able to see the whole of the beam tube. We need to meditate on where to assemble the camera and use appropriate lenses to narrow the field of view such that we avoid looking at scattering from other sources inside the chamber.

8071   Tue Feb 12 20:57:47 2013 JenneUpdateAlignmentIFO alignment in prep for in-air PRMI

We should check MC spot positions to see what they are.

Also, I'm not thrilled about the idea of a clipped REFL beam.  Haven't we played that game before, and decided it's a crappy game?  Can we recenter the MC, and recover quickly with TT1?

8070   Tue Feb 12 20:42:36 2013 JamieUpdateAlignmentIFO alignment in prep for in-air PRMI

Yuta, Manasa, Jamie, Jenne, Steve, Rana

Starting this morning, we removed the temporary half PRC mirror in front of BS and started to align the IFO in prep for an in-air lock of the PRMI.

This morning, using the new awesome steerable active input TTs, Jenne and I centred the beam on PRM, PR2/3, BS, ITMY and ETMY.

After lunch, Yuta and Manasa aligned the Y ARM, by looking at the multi-pass beam.  The X-end door was still on, so they roughly aligned to the X ARM by centring on ITMX with BS.  They then got fringes at the BS, and tweaked the ITMs and PRM to get full fringes at BS.

We're currently stuck because the REFL beam appears to be clipped coming out of the faraday, even though the retro-reflected beam from PRM is cleanly going through the faraday output aperture.  The best guess at the moment is that the beam is leaving MC at an angle, so the retro-reflected beam is coming out of the faraday at an angle.  We did not center spots on MC mirrors before we started the alignment procedure today.  That was dumb.

We may be ok to do our PRMI characterization with the clipped REFL, though, then we can fix everything right before we close up.  We're going to need to go back to touch up alignment before we close up anyway (we need to get PR2 centered).

Yuta and Manasa are finishing up now by making sure the AS and REFL beams are cleanly existing onto the AS table.

Tomorrow we will set up the PRM oplev, and start to look at the in-air PRMI.  Hopefully we can be ready to close up by the end of the week.

8069   Tue Feb 12 18:28:46 2013 JamieSummaryOpticsCurvature radii of the G&H/LaserOptik mirrors

 Quote: 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?

8068   Tue Feb 12 18:25:43 2013 JamieSummaryGeneralhalf PRC with astigmatic PR2/3

Quote:
 arbcav a la mode measurement g tangential 0.9754 0.9753 0.986 +/- 0.001 g sagital 0.9686 0.9685 0.968 +/- 0.001

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

### case 1: PR3 only

 PR2 RoC (m) PR3 RoC (m) g (half PRC) tangential 706 -420 0.986 sagittal 706 -700 0.969

### case 2: PR3 only

 PR2 RoC (m) PR3 RoC (m) g (half PRC) tangential 5000 -700 0.986 sagittal 706 -700 0.969

### case 3: PR2 and PR3

 PR2 RoC (m) PR3 RoC (m) g parameter tangential 2000 -600 0.986 sagittal 706 -700 0.969

From Koji's post about the scans of the G&H mirrors, it looks entirely reasonable that we could have these levels of astigmatism in the optics.

## What this means for full PRC

These all make the same full PRC situation:

g (tangential):  0.966

g (sagittal):  0.939

ARM mode matching:  0.988

8067   Tue Feb 12 17:26:31 2013 ChloeUpdate QPD circuitry to test mount vibrations

I spent awhile today reading about op-amps and understanding what would be necessary to design a circuit which would directly give pitch and yaw of the QPD I am using. After getting an idea of what signals would be summed or subtracted, I opened up the QPD to take better pictures than last time (sorry, the pictures were blurry last time and I didn't realize). It turns out some of the connections have been broken inside the QPD, which would explain why we saw an unchanging signal in Ch2 on the oscilloscope yesterday when trying to test the laser setup.

I found a couple other QPDs, which I will be using to help understand the circuit (and what is going on). I will be trying to use the same QPD box since it has banana cable and BNC cable adapters, which is helpful to have in the lab. Once I have concluded what the circuitry is like and designed electronics to add and subtract signals, I will build and mount all the circuits within the box (more sturdily than last time) so as to have a quality way of measuring the mount vibrations when I get there.

8066   Tue Feb 12 00:50:08 2013 yutaUpdateLockingPR2 oplev spectra

I wanted to see if PR2 motion makes PRC beam motion or not, using temporary oplev to PR2.
I could not measure the coherence between beam motion and PR2 motion, because I couldn't lock half-PRC today.
But I took spectra of PR2 oplev anyway.

Result:

Below are the spectra of PR2 oplev outputs (taken using C1:SUS-ITMX_OL(PIT|YAW)_IN1). Bottom plot is POP DC during half-PRC locked yesterday.

Discussion:
We see bump in PR2 oplev output at ~ 2-3 Hz. But we cannot say this is a evidence for PR2 motion making PRC beam motion because no coherence measurement was done. Also, oplev might be just seeing the ITMX stack motion.

Resonant frequency of TTs measured were at ~ 1.8-1.9 Hz (elog #8054), but we cannot clearly see these peaks in oplev outputs. Did resonant frequency shifted because of different damping condition?

8065   Tue Feb 12 00:14:00 2013 yutaUpdateLockingPRM coil balancing

We tried to lock half-PRC tonight, but we couldn't. Why?? I could lock yesterday.
It locks for ~ 1 sec, but it beam spot motion freaks out mainly in yaw.
I tried to balance PRM coils, but oplev beam was clipped by MMT1......

What I did:
1. Found elog #5392 and found F2P_LOCKIN.py

2. Modified F2P_LOCKIN.py because LOCKIN channel names are some how changed like this;

LOCKIN1_I -> LOCKIN1_DEMOD_I
LOCKIN1_Q -> LOCKIN1_DEMOD_Q
LOCKIN1_SIG -> LOCKIN1_DEMOD_SIG

3. Running

/opt/rtcds/caltech/c1/scripts/SUS/F2P_LOCKIN.py -o PRM

should adjust (UL|UR|LR|LL)COIL_GAINs by putting some gain imbalance and shaking the mirror in different frequencies. It uses LOCKIN to OL(PIT|YAW).

4. Since there was no PRM oplev beam coming out from the vacuum, I quickly looked into BS-PRM chamber. Oplev beam was clipped by MMT1. If I adjust PRM slider values to avoid clipping, the beam will be clipped by mirrors on oplev table. What happened to the PRM oplev?

5. I also made bunch of /opt/rtcds/userapps/trunk/sus/c1/medm/templates/SUS_SINGLE_LOCKIN(1|2)_DEMOD_(I|Q|SIG).adl because there were missing screens.

Next:
We need to restore the PRM oplev and balance the coils. See, also, elog #7679

8064   Mon Feb 11 21:03:15 2013 yutaUpdateLockingPR2-flipped half-PRC mode scan

To estimate the systematic effects to the g-factor measurement, I changed how to analyze the data in multiple ways.
From the estimation, I get the following g-factors for half-PRC;
tangential: 0.986 +/- 0.001(stat.) +/- 0.008(sys.)
sagittal: 0.968 +/- 0.001(stat.) +/- 0.003(sys.)

The a la mode/arbcav calculation is not so far from the measurement(elog #8059). So, mirror curvatures and lengths are not far from what we expect.

Method:
Method I used to analyze the mode scan data is as follows;

1. Use the spacing between upper sideband and lower sideband to calibrate the data.
2. Measure the position of 00, 1st, 2nd and 3rd mode.
3. Used the following formula to get TMS

nu_TMS = sum((n_i-n)*(nu_i-nu)) / sum((n_i-n)^2)

where n_i is the order of transverse mode, n is average of n_i's, nu_i is the frequency if i-th order mode and nu is average of nu_i's. This is just a linear fitting.

But since it is hard to resolve where the higher order mode is, it is maybe better to use only 00, 1st, and 2nd mode. Also, since cavity sweep is not linear enough, it is maybe better to use spacing between 00 and lower sideband (sideband closer to HOMs) to calibrate the data. Changing the analysis will give us information about the effect of peak choosing and linearity.

How the result differ:
Below are the plots of order of tranverse mode vs measured relative frequency difference from 00 mode. 5 plots on left are when PRM is misaligned in pitch and right are same in yaw. From the plot, you can see using 3rd order mode tend to give larger TMS. Did I picked the wrong one??
left:    right:

Results:
Below table is the result when I changed the analyzing method;

PRM misaligned in pitch
calibration    how many HOMs    measured g-factor
upper-lower    up to 3rd    0.968
upper-lower    up to 2nd    0.974
upper-lower    up to 1st    0.975
00-lower       up to 3rd    0.952
00-lower       up to 2nd    0.962
00-lower       up to 1st    0.963

PRM misaligned in yaw
calibration    how many HOMs    measured g-factor
upper-lower    up to 3rd    0.986
upper-lower    up to 2nd    0.989
upper-lower    up to 1st    0.991
00-lower       up to 3rd    0.964
00-lower       up to 2nd    0.988
00-lower       up to 1st    0.991

Using 00-lower calibration tend to give us smaller g-factor. Using less higer order-mode tend to give us higher g-factor.
By taking standard deviation of these, I roughly estimated the systematic error as above.

Discussion:
I think it is OK to move on to PRMI now.
But I wonder how much astigmatism is needed to get this measurement data. If astigmatism is not so crazy, it's OK. But if it's not, I think it is better to do more measurement like PRM-PR2-TM cavity.

8063   Mon Feb 11 19:55:47 2013 ManasaUpdateOpticsG&H - AR Reflectivity

I adjusted the focal length of the focusing lens and reduced the beam size enough to mask with the razor blade edge while looking at the camera and then making measurements using PD.

I am still not satisfied with this data because the R of the HR surface measured after flipping seems totally unbelievable (at around 0.45).

G&H AR reflectivity

R percentage

11 ppm @4 deg
19.8 ppm @6 deg
20 ppm @ 8 deg
30 ppm @ 20 deg

8062   Mon Feb 11 18:44:34 2013 JamieUpdateComputerspasswerdz changed

 Quote: Be Prepared http://xkcd.com/936/

Password for nodus and all control room workstations has been changed.  Look for new one in usual place.

We will try to change the password on all the RTS machines soon.  For the moment, though, they remain with the old passwerd.

8061   Mon Feb 11 18:39:10 2013 ChloeUpdateGeneralPictures of Circuitry in Photodiode

I am going to be making measurements to find the optical mounts with the least noise. I am using a quadrature photodiode to record intensity of laser light. These are pictures of the circuitry inside (both sides). I will be designing/making some circuitry on a breadboard in the next few days in order to add and subtract the signals to have pitch and yaw outputs.

Attachment 1: IMG_0327.JPG
Attachment 2: IMG_0329.JPG
8060   Mon Feb 11 17:54:02 2013 KojiSummaryOpticsCurvature radii of the G&H/LaserOptik mirrors

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

They are found under this link
https://nodus.ligo.caltech.edu:30889/40m_phasemap/40m_TT/（requires: LVC credentials)
or
/cvs/cds/caltech/users/public_html/40m_phasemap/40m_TT

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)

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???

Attachment 1: TT_Mirrors_RoC.pdf
8059   Mon Feb 11 17:17:30 2013 JamieSummaryGeneralmore analysis of half PRC with flipped PR2

 Quote: 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:

R_eff = -2 / C


When the incident angle in non-zero:

tangential: R_eff = R_eff / cos(\theta)
sagittal:   R_eff = R_eff * cos(\theta)


For flipped PR2, with small 1.5 degree incident angle and RoC of -706 at HR:

M_t = M_s = [1.0000, 0.0131; -0.0028, 1.0000]
R_eff = 705.9


For flipped PR3, with large 41 degree incident angle and RoC of -700 at HR:

M_t = [1.0000, 0; 0.0038, 1.0000]
M_s = [1.0000, 0; 0.0022, 1.0000]
R_eff = 592.4


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

 arbcav a la mode measurement g tangential 0.9754 0.9753 0.986 +/- 0.001 g sagital 0.9686 0.9685 0.968 +/- 0.001

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?

arbcav HOM plot:

ELOG V3.1.3-