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ID Date Author Type Category Subject
2623   Mon Feb 22 10:25:37 2010 JenneUpdateCOCITMY standoff and guiderod epoxied

This work happened on Friday, after Nodus and the elog went down....

[Jenne, Kiwamu]

The guiderod and standoff for ITMY were epoxied, and left drying over the weekend on the flow bench under a foil tent.  The flow bench was off for the weekend, so we made tents which hopefully didn't have any place for dust to get in and settle on the mirrors.

There is a small chance that there will be a problem with glue on the arm of the fixture holding the guiderod to the optic.  Kiwamu and I examined it, and hopefully it won't stick.  We'll check it out this afternoon when we start getting ready for gluing magnets onto optics this afternoon.

2629   Mon Feb 22 21:07:26 2010 JenneUpdateCOCMagnets glued to ITMX

[Kiwamu, Jenne]

The magnets + dumbbell standoffs have been glued to ITMX.  We're waiting overnight for them to dry.

Since I broke one of the magnet + dumbbells on the ITMY set, we've glued another dumbbell to the 6th magnet, and it should be ready for us to glue to ITMY tomorrow, once ITMX is dry and out of the fixture.  This doesn't put us behind schedule at all, so that's good.

We had been concerned that there might be a problem with the arm of the guiderod fixture being glued to ITMY, but it was fine after all.  Everything is going smoothly so far.

[Zach, Mott]

Zach and Mott are almost prepared to start cutting the viton for the earthquake stops.  We need 2 full sets by Wednesday morning, when we expect to begin hanging the ITMs.

2642   Fri Feb 26 01:00:07 2010 JenneUpdateCOCSuspension Progress

This is going to be a laundry list of the mile markers achieved so far:

* Guiderod and wire standoff glued to each ITMX and ITMY

* Magnets glued to dumbbells (4 sets done now).  ITMX has 244 +- 3 Gauss, ITMY has 255 +- 3 Gauss.  The 2 sets for SRM and PRM are 255 +- 3 G and 264 +- 3 G.  I don't know which set will go with which optic yet.

* Magnets glued to ITMX.  There were some complications removing the optic from the magnet gluing fixture.  The way the optic is left with the glue to dry overnight is with "pickle picker" type grippers holding the magnets to the optic.  After the epoxy had cured, Kiwamu and I took the grippers off, in preparation to remove the optic from the fixture.  The side magnet (thankfully the side where we won't have an OSEM) and dumbbell assembly snapped off.  Also, on the UL magnet, the magnet came off of the dumbbell (the dumbbell was still glued to the glass).  We left the optic in the fixture (to maintain the original alignment), and used one of the grippers to glue the magnet back to the UL dumbbell.  The gripper in the fixture has very little slop in where it places the magnet/dumbbell, so the magnet was reglued with very good axial alignment.  Since after the side magnet+dumbbell came off the glass, the 2 broke apart, we did not glue them back on to the optic.  They were reattached, so that we can in the future put the extra side magnet on, but I don't think that will be necessary, since we already know which side the OSEM will be on.

* Magnets glued to ITMY.  This happened today, so it's drying overnight.  Hopefully the grippers won't be sticky and jerky like last time when we were removing them from the fixture, so hopefully we won't lose any magnets when I take the optic out of the fixture.

* ITMX has been placed in its suspension cage.  The first step, before getting out the wire, is to set the optic on the bottom EQ stops, and get the correct height and get the optic leveled, to make things easier once the wire is in place.  Koji and I did this step, and then we clamped all of the EQ stops in place to leave it for the night.

* The HeNe laser has been leveled, to a beam height of 5.5inches, in preparation for the final leveling of the optics, beginning tomorrow.  The QPD with the XY decoder is also in place at the 5.5 inch height for the op lev readout.  The game plan is to leave this set up for the entire time that we're hanging optics.  This is kind of a pain to set up, but now that it's there, it can stay out of the way huddled on the side of the flow bench table, ready for whenever we get the ETMs in, and the recoated PRM.

* Koji and Steve got the ITMX OSEMs from in the vacuum, and they're ready for the hanging and balancing of the optic tomorrow.  Also, they got out the satellite box, and ran the crazy-long cable to control the OSEMs while they're on the flow bench in the clean room.

Koji and I discovered a problem with the small EQ stops, which will be used in all of the SOS suspensions for the bottom EQ stops.  They're too big.  :(  The original document (D970312-A-D) describing the size for these screws was drawn in 1997, and it calls for 4-40 screws.  The updated drawing, from 2000 (D970312-B-D) calls for 6-32 screws.  I naively trusted that updated meant updated, and ordered and prepared 6-32 screws for the bottom EQ stops for all of the SOSes.  Unfortunately, the suspension towers that we have are tapped for 4-40.  Thumbs down to that.  We have a bunch of vented 4-40 screws in the clean room cabinets, which I can drill, and have Bob rebake, so that Zach and Mott can make viton inserts for them, but that will be a future enhancement.  For tonight, Koji and I put in bare vented 4-40 screws from the clean room supply of pre-baked screws.  This is consistent with the optics in our chambers having bare screws for the bottom EQ stops, although it might be nicer to have cushy viton for emergencies when the wire might snap.  The real moral of this story is: don't trust the drawings.  They're good for guidelines, but I should have confirmed that everything fit and was the correct size.

2654   Thu Mar 4 02:25:14 2010 JenneUpdateCOCFurther details on the magnet story, and SRM guiderod glued

[Koji, Jenne]

First, the easy story:  SRM got it's guiderod & standoff glued on this evening.  It will be ready for magnets (assuming everything is sorted out....see below) as early as tomorrow.  We can also begin to glue PRM guiderods as early as tomorrow.

The magnet story is not as short.....

Problem: ITMX and ITMY's side magnets are not glued in the correct places along the z-axis of the optic (z-axis as in beam propagation direction).

ITMX (as reported the other day) has the side magnet placement off by ~2mm.  ITMX side was glued using the magnet fixture from MIT and the teflon pads that Kiwamu and I improvised.

It was determined that the improvised teflon pads were too thin (maybe about 1m thick), so I took those out, and replaced them with the teflon pads stolen from the 40m's magnet gluing fixture.   (The teflon pad from the MIT fixture and the ones from the MIT fixture are the same within my measuring ability using a flat surface and feeling for a step between them.  I haven't yet measured with calipers the MIT pad thickness).  The pads from the 40m fixture, which were used in the MIT fixture to glue ITMY side last night were measured to be ~1.7mm thick.

Today when Koji hung ITMY, he discovered that the side magnet is off by ~1mm.  This improvement is consistent with the switching of the teflon pads to the ones from the 40m fixture.

We compared the 40m fixture with the one from MIT, and it looks like the distance from the edge of where the optic should sit to the center of the hole for the side magnet is different by ~1.1mm.  This explains the remaining ~1mm that ITMY is off by.

We should put the teflon pads back into the 40m fixture, and only use that one from now on, unless we find an easy way to make thicker teflon pads for the fixture we received from MIT.  (The pads that are in there are about the maximum thickness that will fit).  I'm going to use my thickness measurements of SRM (taken in the process of gluing the guiderods) to see what thickness of pads / what fixture we want to actually use, but I'm sure that the fixture we found in the 40m is correct.  We can't use this fixture however, until we get some clean 1/4-28 screws.  I've emailed Steve and Bob, so hopefully they'll have something for us by ~lunchtime tomorrow.

The ITMX side magnet is so far off in the Z-direction that we'll have to remove it and reglue it in the correct position in order for the shadow sensor to do anything.  For ITMY, we'll check it out tomorrow, whether the magnet is in the LED beam at all or not.  If it's not blocking the LED beam enough, we'll have to remove and reglue it too.

Why someone made 2 almost identical fixtures, with a 1mm height difference and different threads for the set screws, I don't know.  But I don't think whoever that person was can be my friend this week.

2820   Tue Apr 20 18:02:22 2010 JenneUpdateCOCNew SRM and PRM Hung

[Jenne, Steve]

We removed the old SRM and PRM from their cages, and are temporarily storing them in the rings which we use to hold the optics while baking.  Steve will work on a way to store them more permanently.

We then hung the new SRM (SRMU03) and new PRM (SRMU04) in the cages.  We were careful not to break the wires, so the heights will not have changed from the old heights.

The optics have not been balanced yet.  That will hopefully happen later this week.

3051   Sun Jun 6 04:48:41 2010 ranaUpdateCOCITM01 HR Phase Map

While trying to set up the SIS-FFT to use our new ITM phase maps, I noticed that the surface of our ITMs looks pretty good actually (even compared to the aLIGO pathfinder optic map on the AIC wiki). I'm attaching it here for your viewing pleasure.

The code to plot it has been added to the SVN in the PhaseMaps/mat directory.

Attachment 1: itm01hr.png
3091   Sun Jun 20 16:07:23 2010 KojiSummaryCOCCalibration of the metrology lab interferometer

Kiwamu and Koji

Summary

We have visited GariLynn's lab to make a calibration of the metrology interferometer.

The newly calibrated value is

RoC(SRMU01) = 153.3+/- 1.6 [m]

This is to be compared with the specification of 142m +/- 5m

Although the calibration deviation from the previous value was found to be 1.3%, it is far from explaining the curvature difference between the spec (142m) and the measured value.

Motivation

The previous measurements of the SRM curvatures showed larger RoCs by ~10% compared with the spec.

It can be caused by the mis-calibration of the pixel size of the CCD in the metrology interferometer.
In order to confirm the calibration value, an object with known dimension should be measured by the instrument.

Method

We've got a flat blank optic from "Advanced Thin Film" together with a metalic ring.
The ring has been attached on the blank optic with 3 fragments of a double sided tape.
The RoC of SRMU1 was also measured in order to obtain "the radius of curvature of the day".

The calibration process is as follows:

1. Measure the diameters of the ring by a caliper in advance to its attachment to the blank.
2. Determine the inner and outer diameter of the ring in the obtained image.
Note that the obtained image is pre-calibrated by the default value given by the measurement program
(i.e. 0.270194mm/pixel for horizontal)
3. Check the ratio of the diameters with the measured value by the caliper. Correct a systematic effect.
4. Compare the image measurement and the caliper measurement.

Results

1. The outer and inner diameters of 2.000" and 1.660" (measured by a caliper, error 0.005"). The ratio is 0.830+/-0.003.
2. The center and radius for the inner circle were estimated to be (79.7924, 91.6372) and 21.4025 [mm].
The center and radius for the outer circle were estimated to be (79.6532, 91.6816) and 25.6925 [mm].

The error would be ~0.01mm considering they sweep 500 pixels by the circle and the pixel size is 0.27mm. i.e. 0.27/Sqrt(500) ~ 0.01mm
3. Ratio of the inner and outer diameter is 0.8330 +/- 0.0005.
The systematic error of x is given by solving (21.4025+x)/(25.6925-x)=0.83 ==> x = -0.042 +/- 0.043 [mm]. This is just a 0.2% correction.
By correcting the above effect, we get (Rin, Rout) = (21.36 +/- 0.046, 25.74 +/- 0.047).
4. By comparing the result with the caliper measurement, we get calibration factor of 1.013 +/- 0.005.
This means we measured "1mm" as "1.013mm". The scale was too small.

We have got the calibration of 0.2737+/-0.0014 [mm/pixel].

Discussion

Because of the calibration error, we measured too long RoC. The same day, we measured the curvature of SRMU01 as 155.26 m.
The newly calibrated value is

RoC(SRMU01) = 153.3+/- 1.6 [m]

This is the value to be compared with the specification of 142m +/- 5m

Attachment 1: ring1_inner_centering.pdf
Attachment 2: ring1_outer_centering.pdf
Attachment 3: SRMU01_pic.png
3684   Sun Oct 10 16:59:20 2010 KojiOmnistructureCOCPRM phase map measurement at Downs SB 014

[Kiwamu, Yuta, Koji]

We went to the new metrology lab at Downs subbasement (Rm014) in order to measure the phase map of the delivered PRMs.

It's brand-new. So we had to measure the reference phase map, calibration as well as the phase map of our mirrors (3 PRMs and 1 spare SRM). It took a whole day...

Attachment 1: IMG_3646.jpg
Attachment 2: IMG_3647.jpg
3685   Sun Oct 10 18:09:02 2010 KojiSummaryCOCPhase map interferometer calibration for the data on Oct 8th, 2010

### Summary:

Calibration of the phase map interferometer was calculated for the data on Oct 8th, 2010.
The calibration value is 0.1905 mm/pixel.

This is slightly smaller than the assumed value in the machine that is 0.192mm/pixel.
This means that the measured radii of curvature must be scaled down with this ratio.
(i.e. RoC(new) = RoC(old) / 0.1922 * 0.19052)

### Motivation:

Our tagets of the phasemap measurement are:

1. Measure the figure errors of the mirrors
2. Measure the curvature of the mirrors

The depth of the mirror figure is calibrated by the wavelength of the laser (1064nm).
However, the lateral scale of the image is not calibrated.
Although Zygo provides the initial calibration as 0.192 mm/pixel, we should measure the calibration by ourselves.

### Method:

We found an aperture mask with a grid of holes with 2mm diameter and 3mm spacing (center-to-center).
Take the picture of this aperture and calibrate the pixel size. The aperture is made of stainless and makes not interference
with the reference beam. Thus we put a dummy mirror behind the aperture. (UPPER LEFT plot)

As the holes are aligned as a grid, the FFT of the aperture image shows peaks at the corresponding pitches. (UPPER MIDDLE plot)
As the aperture was slightly rotated, the grids of the peaks are also slanted.

We can obtain the spacing of the peak grids. How can we can that values precisely? I decided to make an artificial mask image.
The artificial mask (LOWER LEFT plot) has the similar FFT pattern (LOWER MIDDLE plot). The inner product of the two
FFT results (i.e. Sum[abs(fft1) x abs(fft2)]), quite a large value is obtained if the grid pitch and the aperture angle agrees between those images.
Note that the phase information was discarded. The estimated grid spacing of the artificial mask can be mathematically obtained.

### Result:

The grid pitch and the angle were manually set as initial values. Then the parameters to give the local maximum was obtained by fminsearch of Matlab.
UPPER RIGHT and LOWER RIGHT plots show the scan of the evaluation function by changing the angle and the pitch. They behave quite normal.

The obtained values are

Grid pitch: 15.74 pixel
Angle: 1.935 deg

As the grid pitch is 3mm, the calibration is

3 mm / 15.74 pixel = 0.1905 mm/pixel

### Discussion:

A spherical surface can be expressed as the following formula:

z = R - R Sqrt(1-r2/R2)      (note: this can be expanded as r2/(2 R)+O(r3) )

Here R is the RoC and r is the distance from the center. This means that the calibration of r quadratically changes the curvature.
We have measured the RoC of the spare SRM. We can compare the RoCs measured by this new metrology IFO and the old one,
as well as the one by Coastline optics.

Attachment 1: calibration.pdf
3738   Mon Oct 18 18:33:46 2010 KojiSummaryCOCSummary of the main mirrors & their phasemap measurement

I have made a summary web page for the 40m upgrade optics.

https://nodus.ligo.caltech.edu:30889/40m_phasemap/

I made a bunch of RoC calculations along with the phase maps we measured.
Those are also accommodated under this directory structure.

Probably.... I should have used the wiki and copy/paste the resultant HTML?

7385   Fri Sep 14 01:18:51 2012 ranaUpdateCOC2 Layout Changes

After looking at the in-vacuum layout I think we should make two changes during the next vent:

1) Reduce the number of mirrors between the FI and its camera. We install a large silvered mirror in the vacuum flange which holds the Faraday cam (in the inside of the viewport). That points directly at the input to the Faraday. We get to remove all of the steering mirror junk on the IO stack.

2) Take the Faraday output (IFO REFL) out onto the little table holding the BS and PRM Oplevs. We then relocate all 4 of the REFL RFPDs as well as the REFL OSA and the REFL camera onto this table. This will reduce the path length from the FI REFL port to the diodes and reduce the beam clutter on the AS table.

7398   Mon Sep 17 18:04:01 2012 SteveUpdateCOC2 Layout Changes

 Quote: After looking at the in-vacuum layout I think we should make two changes during the next vent: 1) Reduce the number of mirrors between the FI and its camera. We install a large silvered mirror in the vacuum flange which holds the Faraday cam (in the inside of the viewport). That points directly at the input to the Faraday. We get to remove all of the steering mirror junk on the IO stack. 2) Take the Faraday output (IFO REFL) out onto the little table holding the BS and PRM Oplevs. We then relocate all 4 of the REFL RFPDs as well as the REFL OSA and the REFL camera onto this table. This will reduce the path length from the FI REFL port to the diodes and reduce the beam clutter on the AS table.

There is just so much room on this table.

Attachment 1: IMG_1635.JPG
7517   Wed Oct 10 08:36:47 2012 SteveUpdateCOCspecial mirror mounts holder

 Quote: After looking at the in-vacuum layout I think we should make two changes during the next vent: 1) Reduce the number of mirrors between the FI and its camera. We install a large silvered mirror in the vacuum flange which holds the Faraday cam (in the inside of the viewport). That points directly at the input to the Faraday. We get to remove all of the steering mirror junk on the IO stack. 2) Take the Faraday output (IFO REFL) out onto the little table holding the BS and PRM Oplevs. We then relocate all 4 of the REFL RFPDs as well as the REFL OSA and the REFL camera onto this table. This will reduce the path length from the FI REFL port to the diodes and reduce the beam clutter on the AS table.

1)  Mirror mount holder for "large silvered mirror" inside of the 8" OD tube vacuum envelope.

Attachment 1: 10101201.PDF
8211   Sat Mar 2 00:23:19 2013 ranaSummaryCOCPhase Maps measured of the ATF flat mirrors

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)

Attachment 1: 0966_0997_phasemap.pdf
10414   Wed Aug 20 15:31:27 2014 ericqUpdateCOCArm Loss Investigations Continue

[ericq, Gabriele]

Summary: After today's meeting, Gabriele and I looked into the arm loss situation, to see if we should really believe the losses that had been suggested by my previous measurements. We made some observations that we're not sure how to explain, and we're thinking about other ways to try and estimate the losses to corroborate previous findings.

We first looked to see if the ASS had some effective offset, leaving the alignment not quite right. Once ASS'd, we twiddled each arm cavity mirror in pitch and yaw to see if we could achieve higher transmission. We could not, so this suggested that ASS works properly.

We then looked at potential offsets in the Xarm loop. We found that an input offset of 25 counts increased the transmission, but only very slightly. With this offset adjusted, we confirmed the qualitative observation that locking/unlocking the xarm causes a much bigger change in ASDC than doing the same with the harm.

However, we noted that the ASDC data (which is the DC value of the AS55 RFPD) was quite noisy, hovering around 50 counts. Looking at the c1lsc model, we found that we were looking at direct ADC counts, so the signal conditioning was not so great. We went to the LSC rack and stole the SR560 that had been hooked up as a REFLDC offsetter, and used it to give ASDC a gain of 100, and a LP at 100Hz, since we only care about DC values. We then undid the gain in the input FM; and this calmed the trace down a fair bit. The effects due to each arm locking/unlocking was still consistent with previous observations.

At this point, we looked at the arm transmission and ASDC signals simultaneously. Normally, when misaligning a cavity, one would expect the reflected power to rise and the transmission to fall.

However, we saw that when misalignment the Yarm in yaw in either direction, or the Xarm in one direction, both the IR transmission and ASDC would fall. This initially made us think of clipping effects.

So, we checked out the AS beam situation on the AP table. On a card, the beam looks round as we could tell, and the beam spot on AS55 was nice and small. (We tweaked its steering a little bit in pitch to put it at the center of the "falling-off" points) The reflection and transmission falling effect remained.

At this point, we're not really sure what could be causing this effect. After the reflected beams recombine at the BS, the output path is common, so it's strange that this odd effect would be the same for both arms.

Lastly, we discussed other ways that we may be able to see if the Xarm really has ~500ppm loss. Since its transmission is ~1.4%, Gabriele estimated that we may be able to see a ~300Hz difference in the arm cavity pole frequency between the two arms, based on the modification of the cavity finesse due to loss. Since we don't currently have the AOM set up to inject intensity noise, we talked about using frequency noise injection to measure the arm cavity poles, though this would be coupled with the IMC pole, but this could hopefully be accounted for.

11876   Fri Dec 11 23:12:09 2015 KojiSummaryCOCLoss map measurement document

Yutaro left detailed slides for his loss map measurement

https://dcc.ligo.org/LIGO-G1501547

12102   Mon May 2 17:06:58 2016 ranaSummaryCOCG&H optics to Fullerton/HWS for anneal testing

Steve sent 4 of our 1" diameter G&H HR mirrors to Josh Smith at Fullerton for scatter testing. Attached photo is our total stock before sending.

Attachment 1: 20160427_182305.jpg
12103   Mon May 2 17:11:55 2016 ranaUpdateCOCRC folding mirrors

Antonio/Gautam are now developing a more up to date Finesse model of our recycling cavities to see what we can have there before our power recycling gain or cavity geometric stability is compromised. Expect that we will here a progress report on the model on Wednesday.

Some thoughts:

1. RC folding mirrors need to be dichroic to allow green beams to get out.
2. We should look at the specs Jamie used to get the RC folding mirrors last time and figure out what went wrong / what specs to change.
3. T_1064 < 100 ppm. Hopefully < 50 ppm.
4. On the AR side, we mainly want low AR for green, but nothing special for 1064, since that's taken care of by the HR.
5. How much should we wedge these things?
6. Should the wedge be horizontal?
7. Can we get someone in Downs to update the optical layout?
8. What microroughness do we need?
9. The mirrors must be flat, with the  500 m < RoC < 100 km. Part of the Finesse modeling is to figure out what happens if the RoC is in the 300 - 1000 m range. Better stability?
12120   Wed May 18 01:10:22 2016 gautamUpdateCOCFinesse modelling

I've been working on putting together a Finesse model for the current 40m configuration. The idea was to see if I could reproduce a model that is in agreement with what we have been seeing during the recent DRFPMI locks. With Antonio and EricQs help, I've been making slow progress in my forays into Finesse and pyKat. Here is a summary of what I have so far.

• Arm lengths were taken from some recent measurements done by yutaro and me
• Recycling cavity lengths were taken from Gabriele's elog 9590 - it is likely that the lengths I used have errors ~1cm - more on this later. Furthermore, I've tried to incorporate the flipped RC folding mirrors - the point being to see if I can recover, for example, a power recycling gain of ~7 which is what was observed for the recent DRFPMI locks.
• I used Yutaro's most recent arm loss numbers, and distributed it equally between ITM and ETM for modeling purposes.
• For all other optics, I assumed a generic loss number of 25ppm for each surface

Having put together the .kat file (code attached, but this is probably useless, the new model with RC folding mirrors the right way will be what is relevant), I was able to recover a power recycling gain of ~7.5. The arm transmission at full lock also matches the expected value (125*80uW ~ 10mW) based on a recent measurement I did while putting the X endtable together. I also tuned the arm losses to see (qualitatively) that the power recycling gain tracked this curve by Yutaro. EricQ suggested I do a few more checks:

1. Set PRM reflectivity to 0, scan ETMs and look at the transmission - attachment #1 suggests the linewidth is as we expect
2. Set ETM reflectivity to 0, scan PRM - attachment #2 suggests a Finesse of ~60  for the PRC which sounds about right
3. Set ETM reflectivity to 0, scan SRM and verify that only the 55 MHz sidebands resonate - Attachment #3

Conclusion: It doesn't look like I've done anything crazy. So unless anyone thinks there are any further checks I should do on this "toy" model, I will start putting together the "correct" model - using RC folding mirrors that are oriented the right way, and using the "ideal" RC cavity lengths as detailed on this wiki page. The plan of action then is

• Evaluating the mode-matching integrals between the PRC and the arm cavities as a function of the radius of curvature of PR2 and PR3
• Same as above for the SRC
• PRC gain as a function of RoC of folding mirrors
• Mode overlap between the modes from the two arm cavities as a function of the RoC of the two ETMs (actually I guess we can fix RoC of ETMy and just vary RoC of ETMx).

Sidenote to self: It would be nice to consolidate the most recent cavity length measurements in one place sometime...

Attachment 1: arms.pdf
Attachment 2: PRC.pdf
Attachment 3: SRC.pdf
Attachment 4: Finesse_model.zip
12130   Tue May 24 22:49:02 2016 gautamUpdateCOCFinesse modelling - mode overlap scans

Summary:

Having played around with a toy finesse model, I went about setting up a model in which the RC folding mirrors are not flipped. I then repeated the low-level tests detailed in the earlier elog, after which I ran a few spatial mode overlap analyses, the results of which are presented here. It remains to do a stability analysis.

Overview of model parameters (more details to follow):

• PRC length = 6.7727m (chosen using $\dpi{80} l_{PRC} = (N+\frac{1}{2})\frac{c}{2f_1}$, N=0 - I adjusted the position of the PRM to realize this length in the model, while leaving all the other vertex optics in the same positions as in elog 9590
• SRC length = 5.4182 (chosen using $\dpi{80} l_{SRC} = M\frac{c}{2f_2}$ but not $\dpi{80} l_{SRC} = N\frac{c}{2f_1}$, M and N being integers, for M=2 - as above, I adjusted the position of the SRM to realize this in the model, while leaving all other vertex optics in the same positions as in elog 9590. It remains to be verified if it is physically possible to realize these dimensions in vacuum without any beam clipping etc but I think it should be possible seeing as the PRM and SRM had to be moved by less than 2cm from their current positions..
• For the losses, I used the most recent numbers we have where applicable, and put in generic 25ppm loss for all the folding mirrors/BS/AR surfaces of arm cavity mirrors/PRM/SRM. Arm round trip loss was equally distributed between ITMs and ETMs
• Arm lengths used: L_X = 37.79m, L_Y = 37.81m
• To set the "tunings" of the various mirrors, I played around with a few configurations to see where the various fields resonated - it turns out that for PRM, ITMX, ITMY, ETMX and ETMY, the "phase" in the .kat file can be set as 0. while that for the SRM can be set as 90. In the full L1/H1 interferometer .kat files, these are tuned even further to the (tenth?!) decimal place, but I think these values suffice for out purposes.

Results (general note: positive RoC in these plots mean a concave surface as seen by the beam):

• Attachments #1, #2 and #3 reproduce the low-level tests performed earlier for this updated model - i.e. I look at the arm transmission with no PRM/SRM, circulating PRC power with no ETMs, and circulating SRC power with no ETMs. Everything looks consistent here... In Attachment #2, there is no legend, but the (almost overlapping) red and green lines are meant to denote the +f1 and +f2 sidebands.
• Attachments #4 and #5 are a summary of the mode-overlap scans for the PRC and SRC. What I did was to vary the radius of curvature of the RC mirrors (finesse only allows you to vary Rcx and Rcy, so I varied both simultaneously) and calculate the mode overlap between the appropriate pairs of cavities (e.g. PRX and XARM) in the tangential and saggital planes. The take-away here is that there is ~5% mode-mismatch going from an RoC of 1000m to 300m. I've also indicated the sag corresponding to a given RoC - these are pretty tiny, I wonder if it is possible to realize a sag of 1um? I suppose it is given that I've regularly seen specs of surface roughness of lambda/10?
• Attachment #6 shows the PRC gain (calculated as T_PRC * (transmitted arm power with PRM / transmitted arm power without PRM) as a function of the RoC of PR2 and PR3. As a sanity check, I repeated this calculation with lossless HR surfaces (but with nominal 25ppm losses for AR surfaces of ITMs, and BS etc), shown in Attachment #7. I think these make sense too...
• Attachment #8 - in order to investigate possible mode mismatch between the arm modes due to different radii of curvature of the ETMs, I kept the ETMY RoC fixed at 57.6m and varied the ETMY RoC between 50m and 70m (here, I've plotted the mode matching efficiency as a function of the RoC of the ETM in the X and Y directions separately - the mode overlap is computed as $\dpi{80} \frac{1}{\sqrt{2}}(x^2 + y^2)$ where x and y denote the overlap in the tangential and saggital planes respectively. It would seem that we only lose at most a couple of percent even if the RoCs are mismatched by up to 10m...
• Attachment #9 - .kat file and the various pykat scripts used to generate these plots...

Next step is to carry out a stability analysis...

Attachment 1: armTransmission.pdf
Attachment 2: prcFSR.pdf
Attachment 3: srcTransmission.pdf
Attachment 4: modeMatchPRX.pdf
Attachment 5: modeMatchSRX.pdf
Attachment 6: PRCgainScan.pdf
Attachment 7: PRCgainLossless.pdf
Attachment 8: armModeMatchScan.pdf
Attachment 9: Finesse_files.zip
12131   Tue May 24 23:17:37 2016 ericqUpdateCOCFinesse modelling - mode overlap scans

I think you should use the current actual PRC & SRC cavity lengths as measured, as it would be simplest to simply replace the folding mirror optics without changing the macroscopic lengths / optic positions. (EDIT: Gautam rightly points out that we have to move things around regardless, since our current lengths include propagation through the folding mirror subtrates)

Moreover, the recycling cavity lengths you posted are not the right "ideal" lengths to use, as they do not account for the complex reflectivities of the sidebands off of the arm cavities (I have made this mistake myself). See this 40m wiki page for details.

In short, given our current modulation frequency, the ideal lengths to use would be:

• Ideal arm length of 37.795 m
• Ideal PRC length of 6.753 m
• Ideal SRC length of 5.399 m

These are the lengths that the recycling cavity optics were positioned for (though we did not achieve them perfectly). If you do a finer PRC/SRC length scan around the DRFPMI resonance of your model, you would presumably see some undesired sideband splitting.

12190   Thu Jun 16 15:57:46 2016 gautamUpdateCOCContrast as a function of RoC of ETMX

Summary

In a previous elog, I demonstrated that the RoC mismatch between ETMX and ETMY does not result in appreciable degradation in the mode overlap of the two arm modes. Koji suggested also checking the effect on the contrast defect. I'm attaching the results of this investigation (I've plotted the contrast, $C = \frac{P\mathrm{_{max}}-P\mathrm{_{min}}}{P\mathrm{_{max}}+P\mathrm{_{min}}}$  rather than the contrast defect 1-C).

Details and methodology

• I used the same .kat file that I had made for the current configuration of the 40m, except that I set the reflectivities of the PRM and the SRM to 0.
• Then, I traced the Y arm cavity mode back to the node at which the laser sits in my .kat file to determine what beam coming out of the laser would be 100% matched to the Y arm (code used to do this attached)
• I then set the beam coming out of the laser for the subsequent simulations to the value thus determined using the gauss command in finesse.
• I then varied the RoC of ETMX (I varied the sagittal and tangential RoCs simultaneously) between 50m and 70m. As per the wiki page, the spare ETMs have an RoC between 54 and 55m, while the current ETMs have an RoC of 60.26m and 59.48m for the Y and X arms respectively (I quote the values in the "ATF" column). Simultaneously, at each value of the RoC of ETMX, I swept the microscopic position of the ETMX HR surface through 2pi radians (-180 degrees to 180 degrees) using the phi functionalilty of finesse, while monitoring the power at the AS port of this configuration using a pd in finesse. This guarantees that I sweep through all the resonances. I then calculate the contrast using the above formula. I divided the parameter space into a grid of 50 points for the RoC of ETMX and 1000 points for the microscopic position of ETMX.
• I fixed the RoC of ETMY as 57.6m in the simulations... Also, the maxtem option in the .kat file is set to 4 (i.e. higher order modes with indices m+n<=4 are accounted for...)

Result:

Attachment #1 shows the result of this scan (as mentioned earlier, I plot the contrast C and not the contrast defect 1-C, sorry for the wrong plot title but it takes ~30mins to run the simulation which is why I didn't want to do it agian). If the RoC of the spare ETMs is about 54m, the loss in contrast is about 0.5%. This is in good agreement with this technical note by Koji - it tells us to expect a contrast defect in the region of 0.5%-1% (depending on what parameter you use as the RoC of ETMY).

Conclusion:

It doesn't seem that switching out the current ETM with one of the spare ETMs will result in dramatic degradation of the contrast defect...

Misc notes:

1. Regarding the phase command in Finesse - EricQ pointed out that the default value of this is 3, which as per the manual could give unphysical results sometimes. The flags "0" or "2" are guaranteed to yield physical results always according to the manual, so it is best to set this flag appropriately for all future Finesse simulaitons.
2. I quickly poked around inside the cabinet near the EX table labelled "clean optics" to see if I could locate the spare ETMs. In my (non-exhaustive) search, I could not find it in any of the boxes labelled "2010 upgrade" or something to that effect. I did however find empty boxes for ETMU05 and ETMU07 which are the ETMs currently in the IFO... Does anyone know if I should look elsewhere for these?
EDIT 17Jun2016: I have located ETMU06 and ETMU08, they are indeed in the cabinet at the X end...
3. I'm attaching a zip file with all the code used to do this simulation. The phase flag has been appropriately set in the (only) .kat file. setLaserQparam.py was used to determine what beam parameter to assign to be perfectly matched to the Y arm. modeMatchCheck_ETM.py was used to generate the contrast as a function of the RoC of ETMX.
4. With regards to the remaining checks to be done - I will post results of my investigations into the HOM scans as a function of the RoC of the ETMs and also the folding mirrors shortly...
Attachment 1: contrastDefect.pdf
Attachment 2: finesseCode.zip
12193   Thu Jun 16 18:42:12 2016 ranaUpdateCOCContrast as a function of RoC of ETMX

That sounds weird. If the ETMY RoC is 60 m, why would you use 57.6 m in the simulation? According to the phase map web page, it really is 60.2 m.

12194   Thu Jun 16 23:02:57 2016 gautamUpdateCOCContrast as a function of RoC of ETMX
 Quote: That sounds weird. If the ETMY RoC is 60 m, why would you use 57.6 m in the simulation? According to the phase map web page, it really is 60.2 m.

This was an oversight on my part. I've updated the .kat file to have all the optics have the RoC as per the phase map page. I then re-did the tracing of the Y arm cavity mode to determine the appropriate beam parameters at the laser in the simulation, and repeated the sweep of RoC of ETMX while holding RoC of ETMY fixed at 60.2m. The revised contrast defect plot is attached (this time it is the contrast defect, and not the contrast, but since I was running the simulation again I thought I may as well change the plot).

As per this plot, if the ETMX RoC is ~54.8m (the closer of the two spares to 60.2m), the contrast defect is 0.9%, again in good agreement with what the note linked in the previous elog tells us to expect...

Attachment 1: contrastDefect.pdf
12197   Mon Jun 20 01:38:04 2016 ranaUpdateCOCContrast as a function of RoC of ETMX

So, it seems that changing the ETMX for one of the spares will change the contrast defect from ~0.1% to 0.9%. True? Seems like that might be a big deal.

12204   Mon Jun 20 18:07:15 2016 gautamUpdateCOCContrast as a function of RoC of ETMX
 Quote: So, it seems that changing the ETMX for one of the spares will change the contrast defect from ~0.1% to 0.9%. True? Seems like that might be a big deal.

That is what the simulation suggests... I repeated the simulation for a PRFPMI configuration (i.e. no SRM, everything else  as per the most up to date 40m numbers), and the conclusion is roughly the same - the contrast defect degrades from ~0.1% to ~1.4%... So I would say this is significant. I also attempted to see what the contribution of the asymmetry in loss in the arms is, by running over the simulation with the current loss numbers of 230ppm for Yarm and 484ppm for the X arm, split equally between the ITMs and ETMs for both cases, and then again with lossless arms - see attachment #1. While this is a factor, this plot seems to suggest that the RoC mismatch effect dominates the contrast defect...

Attachment 1: contrastDefectComparison.pdf
12219   Tue Jun 28 16:06:09 2016 gautamUpdateCOCRC folding mirrors - further checks

Having investigated the mode-overlap as a function of RoC of the PRC and SRC folding mirrors, I've now been looking into possible stability issues, with the help of some code that EricQ wrote some time back for a similar investigation, but using Finesse to calculate the round trip Gouy phase and other relevant parameters for our current IFO configuration.

To do so, I've been using:

1. Most up to date arm length measurements of 37.81m for the Y arm and 37.79m for the X arm
2. RoCs of all the mirrors from the phase map summary page
3. Loss numbers from our November investigations

As a first check, I used flat folding mirrors to see what the HOM coupling structure into the IFO is like (the idea being then to track the positions of HOM resonances in terms of CARM offset as I sweep the RoC of the folding mirror).

However, just working with the flat folding mirror configuration suggests that there are order 2 22MHz and order 4 44MHz HOM resonances that are really close to the carrier resonance (see attached plots). This seems to be originating from the fact that the Y-arm length is 37.81m (while the "ideal" length is 37.795m), and also the fact that the ETM RoCs are ~3m larger than the design specification of 57m. Interestingly, this problem isn't completely mitigated if we use the ideal arm lengths, although the order 2 resonances do move further away from the carrier resonance, but are still around a CARM offset of +/- 2nm. If we use the design RoC for the ETMs of 57m, then the HOM resonances move completely off the scale of these plots...

Attachment 1: C1_HOMcurves_Y.pdf
Attachment 2: C1_HOMcurves_DR.pdf
12223   Tue Jun 28 20:43:23 2016 KojiSummaryCOCFirst Contact cleaning practice

Made a dry run of the in-situ cleaning for a 3inch optic.

Attachment 1: The Al dummy mass is clamped in the suspension cage.
Attachment 2: The front surface was painted. The nominal brush with the FC bottle was used.
Attachment 3: Zoom in of the front surface.
Attachment 4: The back surface was painted.
Attachment 5: The back surface was peeled.
Attachment 6: The front surface was peeled too.
Attachment 7: The peeled layers.

Findings:

1. To paint a thick layer (particlarly on the rim) is the key to peel it nicely.

2. It was helpful for easier peeling to have mutiple peek tabs. Two tabs were sufficient for ~1" circle.

3. The nominal brush with the bottle was OK although one has to apply the liquid many times to cover such a large area. A larger brush may cause dripping.

4. The nominal brush was sufficiently long once the OSEMs are removed. In any case it is better to remove the OSEMs.

Attachment 1: IMG_20160628_170335196.jpg
Attachment 2: IMG_20160628_171547769.jpg
Attachment 3: IMG_20160628_171607802.jpg
Attachment 4: IMG_20160628_172328190.jpg
Attachment 5: IMG_20160628_174541960.jpg
Attachment 6: IMG_20160628_174556004.jpg
Attachment 7: IMG_20160628_174617198.jpg
12234   Thu Jun 30 16:21:32 2016 gautamUpdateCOCSideband HOMs resonating in arms

[EricQ, gautam]

Last night, we set about trying to see if we could measure and verify the predictions of the simulations, and if there are indeed HOM sidebands co-resonating with the carrier. Koji pointed out that if we clip the transmitted beam from the arm incident on a PD, then the power of the higher order HG modes no longer integrate to 0 (i.e. the orthogonality is broken), and so if there are indeed some co-resonating modes, we should be able to see the beat between them on a spectrum analyzer. The procedure we followed was:

1. Choose a suitable PD to measure the beat. We chose to use the Thorlabs PDA10CF because it has ~150MHz bandwidth, and also the responsivity is reasonable at 1064nm.
2. We started our measurements at the Y-end. There was a sufficiently fast lens in the beam path between the transmon QPD and the high gain PD at the Y end, so we went ahead and simply switched out the high gain thorlabs PDA520 for the PDA10CF. To power the PDA10CF, we borrowed the power cable from the green REFL PD temporarily.
3. We maximized the DC power of the photodiode signal using an oscilloscope. Then to introduce the above-mentioned clipping and orthogonality-breaking, we misaligned the beam on the PD until the DC power was ~2/3 the maximum value.
4. We then hooked up the PD output to the Agilent network analizyer (with a DC block).
5. We measured the spectrum of the PD signal around 11.066MHz (with 100kHz span) and higher harmonics up to 55MHz and used a narrow bandwidth (100Hz) and long integration time (64 averages) to see if we could find any peaks. More details in the results section.
6. Having satisfied ourselves with the Y-end measurements, we
• restored the power cable to the green beat PD
• re-installed the thorlabs PDA520
• verified that both IR and green could be locked to the arm

We then repeated the above steps at the X-end (but here, an additional lens had to be installed to focus the IR beam onto the PDA10CF - there was, however, sufficient space on the table so we didn't need to remove the PDA520 for this measurement).

Results:

Y-end: DC power on the photodiode at optimal alignment ~ 200mV => spectra taken by deliberately misaligning the beam incident on the PD till the DC power was ~120mV (see remarks about these values).

RF sideband (Y-arm) Peak height (uV) Beat power (nW) RF sideband (X-arm) Peak height (uV) Beat Power (nW)
11 1.55 0.52 11 1.2 0.4
22 10.6 3.53 22 none seen N.A.
33 none seen N.A. 33 none seen N.A.
44 22.0 7.33 44 7 2.33
55 8.6 2.97 55 5 1.67

I converted the peak heights seen on the spectrum analyzer in volts to power by dividing by transimpedance (=5*10^3 V/A into a 50ohm load) * responsivity at 1064nm (~0.6A/W for PDA10CF).

Remarks:

1. This effect flagged by the simulations seems to be real. Unfortunately I can't get a more quantitative picture because we can't quantify the mode-overlap between the carrier 00 mode and any higher order mode on the beat PD (as we know nothing about the profile of these modes), but the simulations did suggets that the 2nd order 22MHz and 4th order 44MHz HOMs are the ones closest to the carrier 00 resonance (see Attachments #2 and #3), which is kind of borne out by these results.
2. I disbelieve the conversions into power that I have done above, but have just put them in for now, because a DC power of 200mW at the Y-end suggests that there is >160uW of light transmitted from the arm, which is at least twice what we expect from a simple FP cavity calculation with the best-known parameters. If I've missed out something obvious in doing this conversion, please let me know!
3. For the Y-arm, the region around 55MHz had a peak (presumably from the sideband HOM beating with the carrier) but also a bunch of other weird sub-structures. I'm attaching a photo of the analyzer screen. Not sure what to make of this...
Attachment 1: image.jpeg
Attachment 2: C1_HOMcurves_Y.pdf
Attachment 3: C1_HOMcurves_X.pdf
12325   Fri Jul 22 03:02:37 2016 KojiUpdateCOCFC painting

[Koji Gautam]

We have worked on the FC painting on ITMX and ITMY. We also replaced the OSEM fixing screws with the ones with a hex knob.
This was done except for the SD OSEM as the new screw was not long enough. We left an allen-key version of the screw for the SD OSEM.

All the full-resolution photos can be found on g-photo.

ITMY

Attachment1: The barrel was pretty dusty. Some dusts were observed on the HR face but it was not so terrible. The barrel and the HR face were blown with the ionized N2 and then wiped with IPA. The face wiping was done n a similar way as the drag wiping.

Attachment2: FC was applied to the HR surface.

Attachment3: The AR surface was also painted with FC. The brush touched the coil holder.

Attachment4: The brush touched the coil holder. Another PEEK tab was applied to remove this FC stain on the metal holder.

Attachment5: This is the result of successful removal of the FC stain.

ITMX

Attachment6: The OSEM arrangement before removal. We confirmed that the OSEM arrangement was as described on Wiki.

Attachment7/8: The ITMX was obviously a lot dirtier than ITMY. The barrel accumulated dusts.

Attachment9: This is the HR face picture with large dusts on it.

Attachment10: The HR surface was painted with FC.

Attachment11: This is the AR surface with FC painted.

Attachment 1: ITMY_barrel_dust.jpg
Attachment 2: ITMY_HR_FC.jpg
Attachment 3: ITMY_AR_FC.jpg
Attachment 4: ITMY_drip_removal.jpg
Attachment 5: ITMY_drip_removed.jpg
Attachment 6: ITMX_OSEMS.jpg
Attachment 7: ITMX_barrel_dust1.jpg
Attachment 8: ITMX_barrel_dust2.jpg
Attachment 9: ITMX_HR_dusty.jpg
Attachment 10: ITMX_HR_FC.jpg
Attachment 11: ITMX_AR_FC.jpg
12407   Sat Aug 13 18:25:22 2016 gautamUpdateCOCRC folding mirrors - Numerical review

This elog is meant to summarize my numerical simulations for looking into the effects of curvature on the RC mirrors. I've tried to go through my reasoning (which may or may not be correct) and once this gets a bit more refined, I will put all of this into a technical note.

Motivation:

• Both the G&H (PR2, SR2) and Laseroptik (PR3 SR3) are convex on the HR side with RoCs of approximately -600m and -700m (though as stated in the linked elog, I'm not actually sure if there are measurements of this number) EDIT AUG15: There are measurements for the Laseroptik mirrors here
GV April 8 2017: This elog by Jenne suggests that the installed PR2 has an RoC of approximately -700m. Koji has uploaded the phase map data for the RC TT mirrors to
/users/public_html/40m_phasemap/40m_TT and
/users/public_html/40m_phasemap/40m_TT2. The G&H mirror data seems to be in the former folder, and it looks like there are two mirrors, one with RoC of ~ -700m and the other with RoC of ~ -500m. Does this mean PR2 has RoC -700m and SR2 has RoC -500m?
• As a result, both the PRC and SRC were close to instability
• By flipping the folding mirrors, the instability has been mitigated, but at the expense of the non-ideal situation where the AR coated side and the substrate are now inside the recycling cavity
• We would like to order some new folding mirrors. In order to avoid receiving convex mirrors from the vendor, we want to specify a concave curvature for the HR side
• The aim of this investigation is to look at how concave we should make these mirrors, because although the cavity stability improves with concavity of the HR side, possible disadvantages of having too convex mirrors are:
• ​Mode-mismatch between the recycling cavities and the arms
• Astigmatism

The study:

• I've built a Finesse model for the 40m, which has been used for all the numerical studies quoted here
• In constructing this Finesse model, I've used the following sources to specify various paramaters:
• ​RoCs, R, T and physical dimensions of 4 test-masses, PRM, SRM and BS: Core optics wiki page
• Losses - arm losses from Yutaro's measurements in elog11857 and elog11818 (distributed equally between ITM and ETM). For other optics, a generic value of 25ppm was used
• "Ideal" lengths for our current modulation frequency were used for the various cavities (37.795m for the arms, 6.753m for PRC, 5.399 for SRC)
• The folding mirrors (PR2, PR3, SR2, SR3) are initialized as flat in the model
• I performed some low-level checks (e.g. arm linewidth, PRC FSR etc) to check that the model was sensible
• I then proceeded to investigate the effects of curvature on the folding mirrors. Specifically, I investigated the following:
• What is the mode mismatch between the recycling cavity mode and the arm as a function of the RoC of the folding mirror?
• What is the effect of the RoC of the folding mirrors on the round-trip gouy phase accumulated (and hence the transverse mode spacing) in the recycling cavities?
• For now, the parameter space explored is from 300m concave to 1000m concave. An RoC of 1km for a 2" optic corresponds to a sag of ~0.3 microns. I will explore the 1km-10km concave space and update the results shortly

Results:

• Attachments #1 and #2 show the mode mismatch between the recycling cavity and the arm for various curvatures. The colorbars have been normalized to span the same range in all the plots
• For both the PRC and the SRC, if we have folding mirrors with an RoC of 1000m concave, we will have a mode mismatch of 2-3%. The number gets worse the more convex the mirror
• Attachments #3 and #4 show the one-way accumulated Gouy phase. Here, I have varied the curvature of the folding mirrors along a specific axis at a time (i.e. I've assumed that the folding mirrors are identical). I've also added the transverse mode spacing as a second y-axis. I have yet to check how these numbers compare with the linewidth of the 00-mode for the various fields, but for 1km concave folding mirrors, the TMS is in the region of 2MHz

To do:

• I will extend the range of RoCs explored to 10km concave and post results - but I will have to check with EricG to make sure that it is feasible for us to specify curvatures in this range
• I was trying to use the RT gouy phase as calcluated by my Finesse simulations to plug into some analytical expressions to try and generate plots like this for various RoCs of the folding mirrors, but if the TMS calculations suffice, I will abandon these efforts
• What are the other specifications we need to worry about before placing an order? Some thoughts from Rana's earlier elog:
• The coatings need to be dichroic to allow extraction of the green beam (but only PR3/SR3 is currently dichroic?)
• Wedge angle on the AR side?
• Are there any other obvious sanity checks I should carry out?

Attachment 1: PRX_consolidated.pdf
Attachment 2: SRX_consolidated.pdf
Attachment 3: Gouy_PRC.pdf
Attachment 4: Gouy_SRC.pdf
12413   Tue Aug 16 11:51:43 2016 gautamUpdateCOCRC folding mirrors - Numerical review

Summary of roundtable meeting yesterday between EricG, EricQ, Koji and Gautam:

We identified two possible courses of action.

1. Flip the G&H mirror (PR2/SR2) back such that the (convex) HR face is the right way round. We want to investigate what are the requirements on a new PR3/SR3 optic that will guarantee cavity stability and also give good mode matching.
2. Order two new sets of mirrors (i.e. replace all 4 folding mirrors). In this case, we want to spec a flat (how flat is reasonable to specify? EricG will update us) PR3/SR3, and design a PR2/SR2 with some concavity that will guarantee cavity stability in the event PR3/SR3 deviates from flatness (but still within what we spec). The choice to make PR3 as close to flat as possible is because the angle of incidence in our arrangement means that any curvature on PR3 dominates astigmatism.

I have done some calculations to evaluate the first alternative.

• Based on yesterday's preliminary discussion, we felt it is not reasonable to spec mirrors with RoC > 4km (sag of ~80nm). So I restrict my analyses to the range 300m-4km
• Koji has a measurement of the phase maps for the G&H mirrors. The measured curvature is ~-500m. In my simulations, I've tried to allow for error in this measurement, so I look at the range -450m to -700m for the G&H mirror.
• The Gouy phase analysis suggests we should look for an RoC of +500m (concave) for the new PR3/SR3 to have a TMS of ~1.5 MHz. Anything flatter (but still concave) means the TMS gets smaller.
• The mode-matching in this region also looks pretty good, between 98% and 99%
• I will post results of the analysis for the second alternative here for comparison

Something else that came up in yesterdays meeting was if we should go in for 1" optics rather than 2", seeing as the beam spot is only ~3mm on these. It is not clear what (if any) advantages this will offer us (indeed, for the same RoC, the sag is smaller for a 1" optic than a 2").

Attachments:

Attachment #1: Mode-matching maps between PRX and Xarm cavities, PRY and Yarm cavities with some contours overlaid.

Attachment #2: Mode-matching maps between SRX and Xarm cavities, SRY and Yarm cavities with some contours overlaid.

Attachment #3: Gouy phase calculations for the PRC

Attachment #3: Gouy phase calculations for the SRC

Attachment 1: PRC_consolidated.pdf
Attachment 2: SRC_consolidated.pdf
Attachment 3: GouyPRC.pdf
Attachment 4: GouySRC.pdf
12414   Tue Aug 16 16:38:00 2016 gautamUpdateCOCRC folding mirrors - Numerical review

Here are the results for case 2: (flat PR3/SR3, for purpose of simulation, I've used a concave mirror with RoC in the range 5-15km, and concave PR2/SR2 - I've looked at the RoC range 300m-4km).

• This is where we order two new sets of mirrors, one for use as PR2/SR2, and the other for use as PR3/SR3.
• RoC of flat PR3/SR3 in simulation explored in the range 5km-15km (concave)
• RoC of concave PR2/SR2 in simulation explored in the range 300m-4km (concave)

Attachment #1: Mode matching between PRC cavities and arm cavities with some contour plots

Attachment #2: Mode matching between SRC cavities and arm cavities with some contour plots

Attachment #3: Gouy phase and TMS for the PRC. I've plotted two sets of curves, one for a PR3 with RoC 5km, and the other for a PR3 with RoC 15km

Attachment #4: Gouy phase and TMS for the SRC. Two sets of curves plotted, as above.

Hopefully EricG will have some information with regards to what is practical to spec at tomorrow's meeting.

EDIT: Added 9pm, 16 Aug 2016

A useful number to have is the designed one-way Gouy phase and TMS for the various cavities. To calculate these, I assume flat folding mirrors, and that the PRM has an RoC of 115.5m, SRM has an RoC of 148m (numbers taken from the wiki). The results may be summarized as:

Cavity One-way Gouy phase [rad]           TMS [MHz]
PRX 0.244 1.730
PRY 0.243 1.716
SRX 0.197 1.743
SRY 0.194 1.717

So, there are regions in parameter space for both options (i.e. keep current G&H mirrors, or order two new sets of folding mirrors) that get us close to the design numbers...

Attachment 1: PRC_consolidated.pdf
Attachment 2: SRC_consolidated.pdf
Attachment 3: GouyPRC.pdf
Attachment 4: GouySRC.pdf
12417   Wed Aug 17 14:37:36 2016 gautamUpdateCOCRC folding mirrors - Numerical review
Quote:

Cavity One-way Gouy phase [rad]           TMS [MHz]
PRX 0.244 1.730
PRY 0.243 1.716
SRX 0.197 1.743
SRY 0.194 1.717

So, there are regions in parameter space for both options (i.e. keep current G&H mirrors, or order two new sets of folding mirrors) that get us close to the design numbers...

Keeping these design numbers in mind, here are a few possible scenarios. The "designed" TMS numbers from my previous elog are above for quick reference.

Case 1: Keep existing G&H mirror, flip it back the right way, and order new PR3/SR3.

• Spec PR3 to be concave with RoC 600 +/- 50m
• This means the TMS in the PRC is in the range 1.4 MHz - 1.6 MHz [see this plot]
• The mode matching efficiency for the PRC is > 98.5% [see this plot]
• The TMS in the SRC is in the range 1.6 MHz - 1.8 MHz [see this plot]
• Mode matching efficiency for SRC is > 98.5% [see this plot]
• PRG between 34-38, depending on uncertainty in measurement of RoC of existing G&H mirror [see Attachment #1, added Nov 11 2016]

Case 2: Order two new sets of folding mirrors

• Spec PR3/SR3 to be flat - for purposes of simulation, let's make it concave with RoC 10 +/- 5 km
• Spec PR2/SR2 to be concave with RoC 1500 +/- 500m
• The TMS in the PRC is between 1.7 MHz and 1.85 MHz [see this plot]
• Mode matching efficiency is >98.5% in the PRC [see this plot]
• TMS in the SRC is between 1.7 MHz and 2 MHz
• Mode matching efficiency >99.0% in the SRC

At first glance, it looks like the tolerances are much larger for Case 2, but we also have to keep in mind that for such large RoCs in the km range, it may be impractical to specify as tight tolerances as in the 100s of metres range. So these are a set of numbers to keep in mind, that we can re-iterate once we hear back from vendors as to what they can do.

For consolidation purposes, here are the aLIGO requirements for the coatings on the RC folding mirrors: PR2, PR3, SR2, SR3

Attachment 1: PRG.pdf
12418   Wed Aug 17 16:28:46 2016 KojiUpdateCOCRC folding mirrors - Numerical review

For the given range of the PR3/SR3 RoCs for both cases, all the resulting numbers such as TMSs/mode matching ratios look reasonable to me.

12631   Mon Nov 21 15:34:24 2016 gautamUpdateCOCRC folding mirrors - updated specs

Following up on the discussion from last week's Wednesday meeting, two points were raised:

1. How do we decide what number we want for the coating on the AR side for 532nm?
2. Do we want to adjust T@1064nm on the HR side to extract a stronger POP beam?

With regards to the coating on the AR side, I've put in R<300ppm@1064nm and R<1000ppm@532nm on the AR side. On the HR side, we have T>97% @ 532nm (copied from the current PR3/SR3 spec), and T<50ppm @1064nm. What are the ghost beams we need to be worried about?

• Scattered light the AR side interfering with the main transmitted green beam possibly making our beat measurement noisier
• With the above numbers, accounting for the fact that we ask for a 2 degree wedge on PR3, the first ghost beam from reflection on the AR side will have an angular separation from the main beam of ~7.6 degrees. So over the ~4m the green beam travels before reaching the PSL table, I think there is sufficient angular separation for us to catch this ghost and dump it.
• Moreover, the power in this first ghost beam will be ~30ppm relative to the main green beam. If we can get R<100ppm @532nm on the AR side, the number becomes 3ppm
• Prompt reflection from the HR surface of PR3 scattering green light back into the arm cavity mode
• The current spec has T>97% @532nm. So 3% is promptly reflected at the HR side of PR3
• I'm not sure how much of a problem this really will be - I couldn't find the reflectivities of PR2 and PRM @532nm (were these ever measured?)
• In any case, if we can have T<50ppm @1064nm and R>99.9% @532nm, that would be better

So in conclusion, with the specs as they are now, I don't think the ALS noise performance is adversely affected. I have updated the spec to have the following numbers now.

HR side: T < 50ppm @1064nm, T>99.9% @532nm

AR side: R < 100ppm @1064nm and @532nm

As for the POP question, if we want to extract a stronger POP beam, we will have to relax the requirement on the transmission @1064nm on the HR side. But recall that the approach we are now considering is to replace only PR3, and flip PR2 back the right way around. Currently, POP is extracted at PR2, so if we want to stick with the idea of getting a new PR3 and extracting a stronger POP beam, there needs to be a major optical layout reshuffle in the BS/PRM chamber. Koji suggested that in the interest of keeping things moving along, we don't worry about POP for the time being...

Alternatively, if it turns out that the vendor can meet the specs for our second requirement (which requires 1.5% of lambda @632nm measurement precision to meet the 10+/-5km RoC tolerance on PR3), then we can ast for T<1000ppm @1064nm for the HR coating on PR2, and keep the coating specs on PR3 as above.

Attached is a pdf with the specs updated to reflect all the above considerations...

Attachment 1: Recycling_Mirrors_Specs_Nov2016.pdf
12847   Thu Feb 23 10:59:53 2017 gautamUpdateCOCRC folding mirrors - coating optimization

I've now made a DCC page for the mirror specifications, all revisions should be reflected there.

Over the last couple of days, I've been playing around with Rana's coating optimization code to come up with a coating design that will work for us. The basic idea is a to use MATLAB's particle swarm constrained optimization tool to minimize an error function that is a composite of four penalties:

1. Thermal noise - we use the proxy function from E0900068-v3 to do this
2. Deviation from target T @1064nm, p-pol
3. Deviation from target T @532nm, p and s-pol
4. HR Surface field

On the AR side, I only considered 2 and 3. The weighting of these four components were set somewhat arbitrarily, but I seem to be able to get reasonable results so I am going with this for now.

From my first pass at it, the numbers I've been able to get, for 19 layer pairs, are (along with some plots):

HR Side:

• T = 50ppm, 1064nm p-pol
• T = 99%, 532nm s and p-pol

(in this picture, the substrate is to the right of layer 38)

AR Side:

• R ~50ppm for 532nm, s and p-pol

(substrate to the right of layer 38)

These numbers are already matching the specs we have on the DCC page currently. I am not sure how much better we can get the specs on the HR side keeping with 19 layer pairs...

All of this data, plus the code used to generate them, is on the gitlab coatings page...

Attachment 1: PR3_R_170222_2006.pdf
Attachment 2: PR3_123_TOnoise_170222_2203.pdf
Attachment 3: PR3_123_Layers_170222_2203.pdf
Attachment 4: PR3AR_R_170222_2258.pdf
Attachment 5: PR3AR_123_Layers_170222_2258.pdf
12887   Tue Mar 14 10:56:33 2017 gautamUpdateCOCRC folding mirrors - coating optimization

Rana suggested including some additional terms to the cost function to penalize high sensitivity to deviations in the layer thickness (L). So the list of terms contributing to the cost function now reads:

1. Thermal noise - we use the proxy function from E0900068-v3 to do this
2. Deviation from target T @1064nm, p-pol
3. Deviation from target T @532nm, p and s-pol
4. HR Surface field
5. The ratio $\frac{d\mathcal{T}/\mathcal{T}}{dL/L}$ with dL/L = 1%, evaluated at 1064nm p-pol and 532nm p and s-pol (only the latter two for the AR side)

I did not include other sensitivity terms, like sensitivity to the refractive index values for the low and high index materials (which are just taken from GWINC).

There is still some arbitrariness in how I chose to weight the relative contributions to the cost function, but after some playing around, I think I have a solution that I think will work. Here are the spectral reflectivity and layer thickness plots for the HR and AR sides respectively.

HR side: for a 1% increase in the thickness of all layers, the transmission changes by 5% @ 1064nm p-pol and 0.5% @ 532nm s and p-pol

AR sidefor a 1% change in the thickness of all layers, the transmission changes by <0.5% @ 532nm s and p-pol

(substrate to the right of layer 38)

I've also checked that we need 19 layer pairs to meet the spec requirements, running the code with fewer layer pairs leads to (in particular) large deviations from the target value of 50ppm @ 1064nm p-pol.

Do these look reasonable?

Attachment 1: PR3_R_170313_1701.pdf
Attachment 2: PR3AR_123_Layers_170313_1701.pdf
Attachment 3: PR3AR_R_170313_1752.pdf
Attachment 4: PR3AR_123_Layers_170313_1752.pdf
12936   Mon Apr 10 15:37:11 2017 gautamUpdateCOCRC folding mirrors - v3 of specs uploaded

Koji and I have been going over these calculations again before we send a list of revised requirements to Ramin. I've uploaded v3 of the specs to the DCC page. Here is a summary of important changes.

1. Change in RoC specification - I condensed the mode-matching information previously in 8 plots into the following 2 plots. Between tangential and saggital planes, the harmonic mean was taken. Between X and Y cavities, the arithmetic mean was taken. Considering the information in the following plots, we decided to change the spec RoC from 600 +/- 50m to 1000 +/- 150m. The required sensitivity in sag measurement is similar to the previous case, so I think this should be feasible.

Why this change? From the phase map information at  /users/public_html/40m_phasemap/40m_TTI gather that we have 2 G&H mirrors, one with curvature ~ -700m and the other with curvature ~ -500m. An elog search suggests that the installed PR2 has RoC ~ -700m, so this choice of RoC for PR3 should give us the best chance of achieving optimal modematching between the RCs and arms as per the plots below.

2. Cavity stability checks - these plots confirm that the cavity remains stable for this choice of RoC on PR3...

3. Coating design - I've been playing around with the code and my understanding of the situation is as follows. to really hit low AR of 10s of ppms, we need many dielectric layer pairs. But by adding more pairs, we essentially become more susceptible to errors in layer thickness etc, so that even though the code may tell us we can achieve R_AR(532nm) < 50ppm, the minima is pretty sharp so even small perturbations can lead to much higher R of the order of a few percent. On the HR side, we need a large number of layer pairs to achieve T_HR(1064nm)=50ppm. Anyways, the MC studies suggest that for the HR coating design, with 19 layer pairs, we can be fairly certain of T_HR(1064nm)<100ppm and R_HR(532nm)>97% for both polarizations, which seems reasonable. In order to make the R_HR(532nm) less susceptible to errors, we need to reduce the number of layer pairs, but then it becomes difficult to achieve the 50ppm T_HR(1064nm) requirement. Now, I tried using very few layer pairs on the AR side - the best result seems to be with 3 layer pairs, for which we get R_AR(532nm)<1% and T_AR(1064nm)>95%, both numbers seem reasonable to me. In the spectral reflectivity, we also see that the minima are much broader than with large number of layer pairs.

First row below is for the HR side, second row is for the AR side. For the MC studies, I perturbed the layer thicknesses and refractive indices by 1%, and the angle of incidence by 5%.

If there are no objections, I would like to send this version of the specs to Ramin and get his feedback. Specifically, I have assumed values for the refractive indices of SiOand Ta2O5 from google, Garilynn tells me that we should get these values from Ramin. Then we can run the code again if necessary, but these MC studies already suggest this coating design is robust to small changes in assumed values of the parameters...

Attachment 1: PRC_modematch.pdf
Attachment 2: SRC_modematch.pdf
Attachment 3: TMS_PRC.pdf
Attachment 4: TMS_SRC.pdf
Attachment 5: PR3_HR_spectralRefl.pdf
Attachment 6: PR3_HR_MC_CDF_revised.pdf
Attachment 7: PR3_AR_spectralRefl_new.pdf
Attachment 8: PR3_AR_MC_CDF_new.pdf
13155   Mon Jul 31 23:39:02 2017 ranaUpdateCOCCavity Scan Simulation Code

Hiro Yamamoto has updated SIS (Static Interferometer Simulation) to allow us to do the MCMC based inference of the 40m arm cavity mirror maps.

In the examples directory I have put 3 files:

1. mcmcCavityScans.m - runs many cavity scans using parfor and saves the data
2. plotCavityScans.m - loads the .mat file with the data and plots it
3. plotCavityScans.py - python file which also loads & plots, but nicer since python has a transparency option for the traces.

Attached is the plots and the data. The first attached plot is a low resolution one: 200 scans of 100 frequency points each. Second plot is 200 scans of 300 points each.

The run was done assuming perfect LIGO arm params with a random set of Zernike perturbations for each run. The amplitude of each Zernike was chosen from a Normal distribution with a standard deviation of 10 nm.

We need to come up with a better guess for the initial distribution from which to sample, and also to use the more smart sampling that one does using the MCMC Hammer.

Attachment 1: manyCavityScans-SIS.pdf
Attachment 2: manyCavityScans-SIS.pdf
Attachment 3: MonteCarlo_CavityScans.mat
14148   Thu Aug 9 02:12:13 2018 gautamUpdateCOCSouth East or West?

Summary:

For operating the SRC in the "Signal-Recycled" tuning, the SRC macroscopic length needs to be ~4.04m (compared to the current value of ~5.399m), assuming we don't do anything fancy like change the modulation frequencies and not transmit through the IMC. We're putting together a notebook with all the calculations, but today I was thinking about what the signal extraction path should be, specifically which chamber the SRM should be in. Just noting down the thoughts I had here while they're fresh in my head, all this has to be fleshed out, maybe I'm making this out to be more of a problem than it actually is.

Details:

• For the current modulation frequencies, if we want the reosnance conditions such that the f2 sideband is resonant in the SRC (but not f1, i.e. small Schnupp asymmetry regime) while the carrier is resonant in the arms (required for good sensing of the SRC length), the macroscopic length of the SRC needs to be changed to ~4.04m.
• Practically, this means that the folded SRC would only have one folding mirror (SR2).
• There is a shorter SRC length of ~1.something metres which would work, but that would involve changing the relative position between ITMs and BS (currently ~2.3m) so I reject that option for now.
• So the SR2 would be roughly where it is right now, ~20cm from the BS.
• The question then becomes, where do we direct the reflection from the SR2? We need an optical path length of ~1.5m from SR2. So options are
• ITMY table (East)
• ITMX table (South)
• IMC table (West)
• Moreover, after the SRM, we have to accommodate:
• Some kind of pickoff for in-air PDs.
• OFI.
• OMC MMT.
• OMC.
• Some kind of CBA (as of now I think going to the ITMY table is the best option):
ITMY
• Easy to direct beam from BS/PRM chamber to the ITMY table (i.e. we don't have to worry too much about avoiding other optics in the path etc).
• ITMY table probably has the most room to work out an OFI + OMC MMT + OMC solution.
• AS beam extraction to air will be more complicated, possibly have to do it on ITMY optical table.
• Not sure if the ITMY table can accommodate all of the output optics subsystems I listed above.
• Routing the LO beam to this table would be tricky I guess.
ITMX
• Routing the LO beam for homodyne detection is probably easiest in this chamber.
• Allows for small AoI on folding mirror, reducing the impact of astigmatism.
• Pain to work in this chamber because of IMC tube.
• Steering beam from SR2 to ITMX table means threading the needle between PRM and PR3 possibly.
IMC
• Probably allows the use of (almost) the entire existing OMC chamber for the output optics (OFI, OMC MMT, OMC).
• IMC table is crowded (2 SOS towers, several steering optics for the input beam, input faraday).
• Not sure what is the performance of the seismic isolation stacks on these tables vs the larger optical tables.
• Painful to work in these smaller chambers.
14164   Wed Aug 15 12:15:24 2018 gautamUpdateCOCMacroscopic SRC length for SR tuning

Summary:

It looks like we can have a stable SRC of length 4.044 m without getting any new mirrors, so this is an option to consider in the short-term.

Details:

• The detailed calculations are in the git repo
• The optical configuration is:
• A single folding mirror approximately at the current SR3 location.
• An SRM that is ~1.5m away from the above folding mirror. Which table the SRM goes on is still an open question, per the previous elog in this thread.
• The SRC length is chosen to be 4.044 m, which is what the modeling tells us we need for operating in the SR tuning instead of RSE.
• Using this macroscopic length, I found that we could use a single folding mirror in the SRC, and that the existing (convex) G&H folding mirrors, which have a curvature of -700m, happily combine with our existing SRM (concave with a curvature of 142m) to give reasonable TMS and mode-matching to the arm cavity.
• The existing SRM transmission of 10% may not be optimal but Kevin's calculations say we should still be able to see some squeezing (~0.8 dB) with this SRM.
• Attachment #1 - corner plot of the distribution of TMS for the vertical and horizontal modes, as well as the mode-matching (averaged between the two modes) between the SRC and arm cavity.
• Attachment #2 - histograms of the distributions of RoCs and lengths used to generate Attachment #1. The distributions were drawn from i.i.d Gaussian pdfs.

gautam 245pm: Koji pointed out that the G&H mirrors are coated for normal incidence, but looking at the measurement, it looks like the optic has T~75ppm at 45 degree incidence, which is maybe still okay. Alternatively, we could use the -600m SR3 as the single folding mirror in the SRC, at the expense of slightly reduced mode-matching between the arm cavity and SRC.

Attachment 1: SRC_MCMC_shortTerm.pdf
Attachment 2: SRC_dists_shortTerm.pdf
14314   Wed Nov 21 16:48:11 2018 gautamUpdateCOCEY mini cleanroom setup

With Chub's help, I've setup a mini cleanroom at EY - Attachment #1. The HEPA unit is running on high now. All surfaces were wiped with isopropanol, we can wipe everything down again on Monday and replace the foil.

Attachment 1: IMG_7174.JPG
15374   Thu Jun 4 00:21:28 2020 KojiSummaryCOCITM spares and New PR3 mirrors transported to Downs for phasemap measurement

GariLynn worked on the measurement of E1800089 mirrros.

The result of the data analysis, as well as the data and the codes, have been summarized here:
https://nodus.ligo.caltech.edu:30889/40m_phasemap/#E1800089

15401   Tue Jun 16 13:05:36 2020 KojiUpdateCOCITM spares and New PR3 mirrors transported to Downs for phasemap measurement

ITMU01 / ITMU02 as well as the five E1800089 mirrors came back to the 40m. Instead, the two ETM spares (ETMU06 / ETMU08) were delivered to GariLynn.
Jordan worked on transportation.

Note that the E1800089 mirrors are together with the ITM container in the precious optics cabinet.

Attachment 1: 40m_Optics.jpg
15625   Wed Oct 14 13:28:04 2020 KojiUpdateCOCITM/ETM spares in Downs

The two ITM spares and two ETM spares are together stored in the optic storage (B110) at Downs. c/o Liyuan and GariLynn

Attachment 1: IMG_3073.jpeg
3193   Mon Jul 12 11:20:56 2010 Gopal HowToCOMSOL TipsIntrusions (Negative Extrusions)

For the sake of future users, I have decided to periodically add tips and tricks in using COMSOL that I have figured out, most probably after hours of circuitous efforts. They will always be listed under the new COMSOL Tips category.

Today's topic: Intrusions

COMSOL has a very user-friendly interface for taking objects from 2D to 3D using the "extrusion" feature. But suppose one wants to design an object which contains screw holes or some other indentation. I've found that creating "punctures" in COMSOL is either impossible or very complicated.

Instead, COMSOL encourages users to always "add" to the object. In other words, one must form the lowest level first, then build layers sequentially on top using new work plane and boolean difference operators. This will probably be a bit clearer with an example:

1) First, create the planar projection in a work plane:

2) Extrude the first layer only in the regular fashion:

3) Add a new work plane which is offset in the z-direction to the deepest point of the intrusion.

4) Now, create the shape of the intrusion in this new work plane.

5) Use the Boolean "Difference" to let COMSOL know that, on this plane, the object has a hole.

6) Extrude once more from the second work plane to complete the intrusion.

3194   Mon Jul 12 12:16:50 2010 DmassHowToCOMSOL TipsIntrusions (Negative Extrusions)

An entry on the 40m wiki page might serve you better, and be easier to sift through once all is said and done

3291   Mon Jul 26 11:15:23 2010 GopalHowToCOMSOL TipsPictures from Transfer Function Tutorial on the Wiki

The attached pictures give a brief overview of my transfer function measurement procedure in COMSOL. For more details, please see the Wiki.

3322   Thu Jul 29 17:11:16 2010 GopalUpdateCOMSOL TipsIncluding Gravity in COMSOL

[Gopal, Jan]

For the past couple of days, Jan and I have been discussing a major issue in COMSOL involving modeling both oscillatory and non-oscillatory forces simultaneously while using FDA. It turns out that he and I had run into the same problem at different times and with different projects. After discussing with an expert, Jan had decided in the past that this simple task was impossible via direct means.

The issue could still be resolved if there was a way for us to work on the Weak Form of the differential equations describing the system:

• Usually, one must define weight as a body load in the negative-z direction. However, this problematically instantiates a new force in COMSOL, which is automatically driven over the range of frequencies during FDA.
• Instead, we could define gravity as an anti-restoring force, since we assume that the base of the stack is fixed.
• In other words, Fg = (ρ*g/L)*x + (ρ*g/L)*y for a point mass which is constrained on the bottom (for small angles).
• Working in Weak Form then, we'd never have to define an explicit gravity load-- this could just be an extra couple of terms in the differential equation which are related entirely to the x- and y-vectors (well-defined for each mesh point). This would fool COMSOL into never tacking on the oscillatory term during FDA.

According to current documentation however, Weak Form analysis is not yet possible in COMSOL 4.0. Jan suggested moving my work over to ANSYS or waiting for the 4.0 upgrade, but there's probably not enough time left in my SURF for either of these options. I suggested attempting a backwards-compatibility test to COMSOL 3.5; Jan and I will be exploring this option some time next week.

ELOG V3.1.3-