The OMC #002 is ready for shipment.
Attachment 1: Work done on Sept 19, 2022
Other attachments: Putting the OMC in the pelican case.
Inspected the past LLO add-on mass configuration.
There are unknown masses at the DCPD side. It looks like a small SS mass with an estimated mass of 5g. But the DCC number is unknown.
We are going to add 10g on each corner as well as the damping aterial. We should be able to figure out the fastener / mass configuration.
Here is the balance mass info for the LLO OMC#001 analyzed from the photographs
If we attach the additional mass, longer 1/4-20 screws (1", 1" 1/8, 1" 1/4) are going to be used.
Started July 15, 2022 and finished Aug 30. So it took ~1.5 months (with a couple weeks of break)
Class B special tools
First Contact Kit
Bonding kit (excl EP30-2 bond)
Power meters (excl Power meter controller)
Cable bracket replacement kit
Optics / Optomechanics
=== Action done on Aug 30 ===
Fiber MM setup / Fiber coupler mount
Glass Beamdumps (for optical testing)
Thorlabs fiber coupler tool
General bent nose plier for fiber
Thorlabs collimator tiny allen
Spare High QE PDs
Spare OMC bags / Zip bags
Balance Mass 10g Qty 8 (Different Type D11*** 1.25" dia), 20g Qty 10 / Mass damper D1700301 -04 / Mass damper screws SHCS 1/4-20 x 1.25 Qty 25 / 1" screws and 1 1/8" screws
Shipping request: https://services1.ligo-la.caltech.edu/FRS/show_bug.cgi?id=25002
=== Low supply! ===
Upon the LLO work, the current PD arrangement in the cages are:
B1 OMC1 PDT (A1-23)
B2 OMC1 PDR (A1-25)
B3 original (C1-03)
B4 OMC2 PDT (B1-22)
C1 OMC2 PDR (B1-23)
C2 original (C1-08)
C3 original (C1-09)
C4 original (C1-10)
Fiber matching: 43.2/56.7 = 76%
S/P-pol ratio 0.7/43.2 = 1.6%
Clean Supply Ordered
The measured total optical loss of the OMC was
1st: 0.015 +/- 0.003
2nd: 0.085 +/- 0.005
3rd: 0.0585+/- 0.0008
4th: 0.047 +/- 0.002
In avegrage the estimated loss is
Loss = 0.055 +/- 0.014
This is unchanged from the measurement at LLO after the FC cleaning
Loss = 0.053 +/- 0.010
The damaged black glass was removed from the OMC breadboard leaving the glass base.
The black glass pieces were bonded very tightly on the FS base with EP30-2. The apparent amount of the bond was not so much but it was such hard that removal by hand was not possible.
We decided to give drips of Acetone on the base hoping the gradual dissolving of EP30-2. Using a knife edge, the "filets" of the bonds were removed, but the BD was still tight.
By wedging the black glass-black glass bonding with the nife edge, the left side (the directly damaged one) was taken off from the structure leaving a tiny fragment of the glass on the base.
The remaining one was even stronger. We patiently kept dripping Acetone on the base and finally, the black glass piece was knocked off and removed from the base.
Attachment 1: The base right after the black glass removal.
Attachment 2: The black glass pieces were stored in a container with Al foil + clean cloth bed. The damaged and fogged surfaces faced up.
Attachment 3: The zoom-in shot of the black glass pieces.
Attachment 4: The base was wiped with Acetone and cleaned with FC. We will bond another BD assembly on the base, presumably using the UV epoxy.
Photo of the BS1 AR cleaning process
Attachment 1: Before cleaning. Foggy surface is visible.
Attachment 2: After FC cleaning. The structure of the deposited material is still quite visible.
Attachment 3: Acetone scrubbing. Cotton Q-tip was used so that the stick does not melt with acetone.
Attachment 4: After acetone scrubbing. Nicely clean!
Acetone scrubbing was applied to HR/AR of BS1, FM1, FM2, BS2, and HR of CM1 and CM2. (total 10 surfaces)
Then final FC paint was applied to these 10 surfaces.
We'll come back to the setup on Thu for FC peeling and loss measurement.
- Removed the first contact we left on Monday.
- Measured transmission (Set1) Very high loss! Total optical loss of 18.5%! Observation with the IR viewer indicated that CM1 has bright scattering. We suspencted a remnant of FC.
- Applied the second FC on the four cavity mirrors. This made the CM1 sport darker.
- Measured the transmission (Set1~Set3). We had consistent loss of 4.2~5.0%. We concluded that this is the limitation of this OMC even with the cleaning.
Conclusion on the cleaning of OMC #001
- After a couple of first contact cleaning trials and deep cleaning, the total loss was measured to be 0.045+/-0.004.
This indicated a slight improvement from the loss measured at LLO before any cleaning (0.064+/-0.004).
However, the number did not improve to the level we marked in 2013 (0.028+/-0.004).
- This loss level of 4.5% is comparable to the loss level of OMC #3, which is currently used at LHO.
Therefore, this OMC #1 is still a useful spare for the site use.
- Some notes / to-do regarding this unit:
1) The beam dump with melted black glass was removed. A new beam dump needs to be bonded on the base.
2) The connector bracket still needs to be replaced with the PEEK version.
3) The PZT of CM1 has been defunct since 2013. Combining LV and HV drivers is necessary upon use at the site. (LLO used to do it).
OMC Transmission measurement after the 2nd deep cleaning
The 2nd deep cleaning didn't improve the transmission. (See Attachment 2)
The measured loss was 0.044+/-0.002
Aaron took the set to Cryo lab
We obtained Regent grade DI water. It was poured into a smaller cup.
FC liquid was also poured into a small beaker.
Wash the mirror with a swab. We should have used a smaller swab that GariLynn has in her lab.
As soon as the mirror was wiped with the water, the FC was applied with a large brush. Don't let the water away!
Then more layer of the FC was added as usual.
The quick painting of FC made a mess around the mirrors due to excess liquid (Attachment 2). So, we decided to remove the FC remnants (on non-optic surfaces) with cotton swabs and then applied FC as usual.
This made the mess removed, however, we found the OMC loss was increased to >10%(!) (Attachment 3). We decided to continue tomorrow (Thu) with more weapons loaded consulting with GariLynn.
Another set of FC cleaning was applied to FM1/FM2/CM1/CM2 and SM2. Some FC strings are visible on SM2. So I decided to clean SM2 as well as the cavity mirrors close to SM2 (i.e. FM2 and CM2)
As a result, the bright scattering spot on CM1 is now very dim. And the loss was reduced to 4.0%. This is 0.4% better than the value before the water cleaning.
It'd be interesting to repeat the water cleaning, at least on FM1. FM1 is the closest cavity mirror to the beam dump damaged by the high-power laser pulse.
Maybe we should also clean the AR side of FM1 and BS1, as they were right next to the damaged beam dump. It is not for the loss but for reducing the scattering.
The second trial of the water scrub
A bright scatter is visible on FM1, so I tried water scrub on FM1. This time, both surfaces of FM1 and both surfaces of BS1 were cleaned.
Smaller Vectra swabs were used for the scrub. Then the water was purged by IPA splashed from a syringe. Right after that FC was applied.
This was a bit messy process as the mixture of water/IPA/FC was splattered on the breadboard.
Nevertheless, all the mess was cleaned by FC in the end.
The transmission measurements are shown in Attachment 1, and the analyzed result is shown together with the past results.
The 2nd water scrub didn't improve the transmission and it is equivalent to the one after the two times of deep cleaning.
I concluded that the water scrub didn't change the transmission much (or at all). We reached the cleaning limit.
We started buikding the OMC #4.
Today we tested the functionality of the four remaining PZTs (11,12,13 and 22) . Each PZT was placed within a collimated 500um beam.
Roughly half of the beam was blocked by the PZT. The PZT and a PD then acted as shadow sensor. Each PZT was tested with 0 and
150 V. The resulting power change then could be converted into a displacement of the PZT using the beam diameter.
The open light value for each of these tests was 3.25 V.
0 V supply voltage --> 1.717 V on PD
150 V supply voltage --> 1.709 V on PD
delta = 0.008 V
0 V supply voltage --> 1.716 V on PD
150 V supply voltage --> 1.709 V on PD
delta = 0.007 V
0 V supply voltage --> 1.702 V on PD
150 V supply voltage --> 1.694 V on PD
delta = 0.008 V
0 V supply voltage --> 1.770 V on PD
150 V supply voltage --> 1.762 V on PD
delta = 0.008 V
0.008 V --> 0.24% change in power on PD --> about 3.8 um displacement assuming no light which is blocked
by the PZT is hitting the PD.
We further started to drive all four PZTs over night with 100 V (half of their range) at 100 Hz.
We additionally display the impedance to ensure none of them degrades.
All four PZTs seem to be connected to Teflon coated wires. It needs to be checked if these
fulfill the vacuum compatibility requirements.
[Joe, Koji, Liyuan, Philip, Stephen]
Work done on 16.04.2019
Finishing assembly of transport box
Assembly worked fine except for the clamping structure to clamp the lid of the transport box to the bottom part.
It seemed that some of the plastic of these clamps became brittle during the baking. The plastic was removed and the
clamps where wiped clean. It appears that the clamps can't be locked as they should. Still the transport box should be fine
as the long screws will mainly clamp the two parts together.
Preparing the transport box to mount the breadboard
The lid of the the transport box was placed upside down and clamped to the table. All peak clamping structures where pulled back as far as possible.
Preparation and cleaning of the breadboard
We unpacked the breadboard and found lots of dust particles on it (most likely from the soft paper cover which was used). We used the ionized nitrogen gun
at 25 psi to get rid of the majority of particles and cross-checked with a bright green flash light before and after blowing. The second stage of cleaning was done
below the clean room tent and included the wiping of all surfaces. The breadboard was then placed into the prepared lid of the transport box and clamped with peak
Unpacking of the template
The previously cleaned template was unpacked while the last layer of coverage was removed below the cleanroom tent.
Template adjustment on the breadboard
All peak screws of the clamping structure of the template where removed. The template was placed onto the breadboard only seperated by peak spacers.
All peak screws have been inserted for horizontal clapming. A calipper was used to measure the distance of each edge of the template to the edge of the
breadboard. For documentation the labeled side of the bradboard (facing away from the persons on the pictures) of the upside down breadboard is defined to
be the south side, continuing clockwise with west, north and east. First rough alignment was done by shifting the template on the breadboard and then the
peak screws where used for fine tuning. The caliper values measured where:
North C 8.32mm E 8.52 mm W 8.41 mm
East C 8.08 mm
South C 8.32 mm
West C 8.02 mm
(E indicating east side position, W indicating west side position and C indicating center position)
ach[Joe, Phillip, Koji, Stephen]
Work from 17.04.2019
First contact cleaning of OMC optics
We cleaned the OMC optic with first contact. After a first cleaning run all mirrors except for two looked
fine. One had some first contact residuals on the left at center height and another had some particle sitting
near the center area. As the ionized nitrogen gun didn't help we applied another round of first contact which resolved
the two issues. Unfortutanely the second run of cleaning again left some residuals of first contact at the edges.
We were able to peal these off with tweezers.
Placement of Optics at the breadboard
We cleaned the contact surfaces for the bonds using optic wipes and pure isopropanol. The placement wen't well for 3 of the 5 optics (low number of newtonian rings).
One was recleaned and placed on the breadboard again which seemed fine. For the 5th no newtonian rings could be seen (either verry ood or bad) we planed on trying it in the current set-up. Mirrors used can be seen in attachment 3.
We took apart the unit removed from the 3rd IFO (Unit serial number aLIGO #3, XTAL 10252004) to see what makes it tick. Koji has done a fine job of adding the plots of the impedance data to this log book. Attached are some details of the physical construction showing the capacitor values used in shunt before the coils.
Attached please see my notes summarizing the models for the electrodes and inductors within the 3rd IFO EOM
Attached is a block diagram of the test setup used in the 40m lab to measure the modulation index of the IO modulator
Norna Robertson, Stephen Appert || 29 Nov 2017, 2 pm to 4 pm || 227 Downs, CIT
We made some preparations for modal testing, but did not have enough time to make measurements. Below is an after-the-fact log, including some observations and photos of the current state of the OMC bench.
Preparation for the PZT subassembly bonding (Section 6.2 and 7.3 of T1500060 (aLIGO OMC optical testing procedure)
- Gluing FIxture (Qty4)
- Silica Sphere Powder
- Electric scale
- Toaster Oven for epoxy mixture qualification
- M prisms
- C prisms
- Noliac PZTs
- Cleaning tools (forceps, tweezers)
- Bonding kits (copper wires, steering sticks)
- Thorlabs BA-2 bases Qty2
- Razor Blades
Also brought to the 40m on 10 April, in preparation for PZT subassembly bonding:
- new EP30-2 epoxy (purchased Jan 2019, expiring Jul 2019 - as documented on documents attached to glue, also documented at C1900052.
- EP30-2 tool kit (maintained by Calum, consisting of mixing nozzles, various spatulas, etc)
Already at the 40m for use within PZT subassembly bonding:
- "dirty" ABO A with temperature controller (for controlled ramping of curing bake)
- clean work areas on laminar flow benches
- Class B tools, packaging supplies, IPA "red wipes", etc.
Upon reviewing EP30-2 procedure T1300322 (current revision v6) and OMC assembly procedure E1300201 (current revision v1) it appears that we have gathered everything required.
[Stephen, Philip, Koji, Joe]
Breadboard D1200105 SN06 was selected as described in eLOG 338. This log describes unwrapping and preparation of the breadboard.
Relevant procedure section: E1300201 section 6.1.5
Breadboard was unwrapped. No issues observed during unwrapping.
Visual inspection showed no issues observed in breadboard - no large scratches, no cracks, no chipping, polished area (1 cm margin) looks good.
Initially the breadboard has a large amount of dust and fiber from the paper wrapping. Images were gathered using a green flashlight at grazing incidence (technique typical of optic inspection).
PROCEDURE IMPROVEMENT: Flashlight inspection and Top Gun use should be described (materials, steps) in E1300201.
Top gun was used (with medium flow rate) to remove large particulate. Breadboard was placed on Ameristat sheet during this operation.
Next, a clean surface within the cleanroom was protected with Vectra Alpha 10 wipes. The breadboard, with reduced particulate after Top Gun, was then placed inside the cleanroom on top of these wipes. Wiping with IPA Pre-wetted Vectra Alpha 10 wipes proceeded until the particulate levels were acceptable.
Joe and Koji then proceeded with placing the breadboard into the transport fixture.
As mentioned in eLOG 331, either increased thermal cycling or apparent improvements in cured EP30-2 strength led to fracture of curved mirrors at unintended locations of bonding to the PEEK fixture parts.
The issue and intended resolution is summarized in the attached images (2 different visualizations of the same item).
Redline has been posted to D1600336-v3.
Drawing update will be processed shortly, and parts will be modified to D1600336-v4.
Summary: Beginning on 20 May 2019, two CM PZT assemblies were soaked in Acetone in an effort to debond the EP30-2 bonds between tombstone-PZT and between PZT-optic. Debonding was straightforward after 8 days of soaking. 24 hours of additional acetone soaking will now be conducted in an attempt to remove remnant EP30-2 from bonding surfaces.
Procedure: The assemblies were allowed to soak in acetone for 8 days, with acetone level below the HR surface of the optic. No agitation of the solution, mechanical abrasion of the bond, or other disturbance was needed for the bond to soften.
GariLynn contributed the glassware and fume hood, and advised on the process (similar to debonding of CM and PZT from OMC SN002 after damaging event). The equipment list was (WIP, more detail / part numbers will be gathered today and tomorrow):
Results: Today, 28 May 2019, I went to the lab to check on the optics after 8 days of soaking. Liyuan had monitored the acetone level during the first 4 days, topping up once on 24 May. All bonds were fully submerged for 8 days.
There were 2 assemblies soaked in one crystallizing dish. Debonded assemblies - ref OMC eLOG 328 for specified orientations and components:
PZT Assy #9 - ref. OMC eLOG 334 - M17+PZT#12+C10
PZT Assy #7 - ref. OMC eLOG 332 - M1+PZT#13+C13
PZT Assy #7 was investigated first.
A video of removal of C10 and PZT#12 from PZT Assy #9 was collected (See Attachment 8), showing the ease with which the debonded components could be separated.
Photos and video have been be added to supplement this report (edit 2019/07/08).
Wedge and thickness measurements of PZTs 12 and 13 took place after debonding and cleaning - results are shown in the first image (handwritten post-it format).
These thickness measurements seem to have come back thinner than previous measurements. It is possible that I have removed some PZT material while mechanically removing glue. It is also possible that there is systematic error between the two sets of measurements. I did not run any calculations of wedge ange or orientation on these data.
Note that cleaning of debonded PZTs involved mechanically separating glue from the planar faces of PZTs. The second image shows the razer blade used to scrape the glue away.
There were thick rings of glue where there had been excess squeezed out of the bond region, and there was also a difficult-to-remove bond layer that was thinner. I observed the presence of the thin layer by its reflectivity. The thick glue came off in patches, while the thin glue came off with a bit of a powdery appearance. It was hard to be certain that all of the thin bond layer came off, but I made many passes on each of the faces of the 2 PZTs that had been in the bonded CM assemblies. I found it was easiest to remove the glue in the bonded
I was anticipating that the expected 75-90 micron bond layer would affect the micrometer thickness measurements if it was still present, but I did not notice any irregularities (and certainly not at the 10 micron level), indicating that the glue was removed successfully (at least to the ~1 micron level).
Yesterday I measured the thickness of the PZTs in order to get an idea how much the PZTs are wedged.
For each PZT, the thickness at six points along the ring was measured with a micrometer gauge.
The orientation of the PZT was recognized by the wire direction and a black marking to indicate the polarity.
A least square fitting of these six points determines the most likely PZT plane.
Note that the measured numbers are assumed to be the thickness at the inner rim of the ring
as the micrometer can only measure the maximum thickness of a region and the inner rim has the largest effect on the wedge angle.
The inner diameter of the ring is 9mm.
The measurements show all PZTs have thickness variation of 3um maximum.
The estimated wedge angles are distributed from 8 to 26 arcsec. The directions of the wedges seem to be random
(i.e. not associated with the wires)
As wedging of 30 arcsec causes at most ~0.3mm spot shift of the cavity (easy to remember),
the wedging of the PZTs is not critical by itself. Also, this number can be reduced by choosing the PZT orientations
based on the estimated wedge directions --- as long as we can believe the measurements.
Next step is to locate the minima of each curved mirror. Do you have any idea how to measure them?
Here is a summary of the events of the last week, as they relate to EP30-2.
1) I lost the EP30-2 syringes that had been ordered for the OMC, along with the rest of the kit.
2) The EP30-2 syringes ordered for the OMC Unit 4 build from January had already expired, without me noticing.
3) LHO shipped expired epoxy on Thursday. Package not opened until Monday.
4) Current, unopened syringe of EP30-2 has been received from LHO. Expiration date is 22 Jan 2020. Syringe storage has been improved. Kit has been docked at its home in Downs 303 (Modal Lab) (see attached photo, taken before receipt of new epoxy).
Current Status: Epoxy is ready for PZT + CM subassembly bonding on Monday afternoon 23 September.
The following items are presently staged at the 40m Bake Lab (see photo indicating current location) (noting items broght by Koji as well):
The following item is in its home in Downs 303 (Modal Lab)
The 40m Bake Lab's Dirty ABO's OMEGA PID controller was borrowed for another oven in the Bake Lab, so I have had to play with the tuning and parameters to recover a suitable bake profile. This bake is pictured below (please excuse the default excel formatting).
I have increased the ramp time, temperature offset, and thermal mass within the oven; after retuning and applying the parameters indicated, the rate of heating/cooling never exceeds .5°C/min.
The ABO is controlled by a different temperature readout from the data logger used to collect data; the ABO readout is a small bead in contact with the shelf, while the data logger is a lug sandwiched between two stainless steel masses upon the shelf. I take the data logger profile to be more physically similar to the heating experienced by an optic in a gluing fixture, so I feel happy about the results of the above bake.
I plan to add the data source file to this post at my earliest convenience.
The 40m Bake Lab's Dirty ABO's OMEGA PID controller was borrowed for another oven in the Bake Lab (sound familiar? OMC elog 377), so I have had to play with the tuning and parameters to recover. This bake seemed to inadequately match the intended temperature profile for some reason (intended profile is shown by plotting prior qualifying bake for comparison).
The parameters utilized here are exactly matching the prior qualifying bake, except that the autotuning may have settled on different parameters.
Options to proceed, as I see them, are as follows:
Follow up on OMC elog 379
I was able to obtain the following (dark blue) bake profile, which I believe is adequate for our needs.
The primary change was a remounting of the thermocouple to sandwich it between two stainless steel masses. The thermocouple bead previously was 1) in air and 2) close to the oven skin.
OMC PZT Assy Production Cure Bake (ref. OMC elog 381) for PZT Assy #9 and #10 started 27 September 2019 and completed 28 September 2019. Captured in the below figure (purple trace). Raw data has been posted as an attachment as well.
We have monitored the temperature in two ways:
1) Datalogger thermocouple data (purple trace).
2) Checking in on temperature of datalogger thermocouple (lavender circles) and drive thermocouple (lavender diamonds), only during initial ramp up.
Comments on bake:
This post captures the curing timeline followed by OMC PZT Assys #9 and #10.
Source file posted in case any updates or edits need to be made.
The following is the current status of the epoxies used in assembly of the OMC (excerpt from C1900052)
Re-purchasing efforts are underway and/or complete
[Koji, Jordan, Stephen]
The beam dumps, bonded on Fri 06 Dec 2019, were placed in the newly tuned and configured small dirty ABO at the Bake Lab on Fri 13 Dec 2019.
Images are shared and references are linked below
Bonding log entry - https://nodus.ligo.caltech.edu:8081/OMC_Lab/386
Bake ticket - https://services.ligo-wa.caltech.edu/clean_and_bake/request/992/
OMC Beam Dump - https://dcc.ligo.org/LIGO-D1201285
OMC Unit 4 Build Machined Parts are currently located in Stephen's office. See image of large blue box from office, below.
Loaned item D1100855-V1-00-OMC08Q004 to Don Griffith for work in semi-clean HDS assy.
This includes mass mounting brackets, cable brackets, balance masses, etc. For full inventory, refer to ICS load Bake-9527 (mixed polymers) and Bake-9495 (mixed metals).
Inventory includes all items except cables. Plasma sprayed components with slight chipping were deemed acceptable for Unit 4 use. Cable components (including flex circuit) are ready to advance to fabrication, with a bit more planning and ID of appropriate wiring.
More explicit insights into the inventory for the Unit 4 build. Image of inventory included below.
ref: E1900034 and other associated documents.
EDIT (ZK): All the plots here were generated using my MATLAB cavity modeling tool, ArbCav. The utility description is below. The higher-order mode resonance plots are direct outputs of the function. The overlap plots were made by modifying the function to output a list of all HOM resonant frequencies, and then plotting the closest one as a function of cavity length. This was done for various values of highest mode order to consider, as described in the original entry.
This function calculates information about an arbitrary optical cavity. It can plot the cavity geometry, calculate the transmission/reflection spectrum, and generate the higher-order mode spectrum for the carrier and up to 2 sets of sidebands.
The code accepts any number of mirrors with any radius of curvature and transmission, and includes any astigmatic effects in its output.
As opposed to the previous version, which converted a limited number of cavity shapes into linear cavities before performing the calculation, this version explicitly propagates the gouy phase of the beam around each leg of the cavity, and is therefore truly able to handle an arbitrary geometry.
I expressed concern that arbitrarily choosing some maximum HOM order above which not to consider makes us vulnerable to sitting directly on a slightly-higher-order mode. At first, I figured the best way around this is to apply an appropriate weighting function to the computed HOM frequency spacing. Since this will also have some arbitrariness to it, I have decided to do it in a more straightforward way. Namely, look at the spacing for different values of the maximum mode number, nmax, and then use this extra information to better select the length.
Below are the spacing plots for the bowtie (flat-flat-curved-curved) and non-bowtie (flat-curved-flat-curved) configurations. Points on each line should be read out as "there are are no modes of order N or lower within [Y value] linewidths of the carrier TEM00 transmission", where N is the nmax appropriate for that trace. Intuitively, as more orders are included, the maxima go down, because more orders are added to the calculation.
*All calculations are done using my cavity simulation function, ArbCav. The mode spacing is calculated for each particular geometry by explicitly propagating the gouy phase through each leg of the cavity, rather than by finding an equivalent linear cavity*
Since achievable HOM rejection is only one of the criteria that should be used to choose between the two topologies, the idea is to pick one length solution for EACH topology. Basically, one maximum should be chosen for each plot, based on how how high an order we care about.
For the bowtie, the nmax = 20 maximum at L = 1.145 m is attractive, because there are no n < 20 modes within 5 linewidths, and no n < 25 modes within ~4.5 linewidths. However, this means that there are also n < 10 modes within 5 linewidths, while they could be pushed (BLUE line) to ~8.5 linewidths at the expense of proximity to n > 15 modes.
Therefore, it's probably best to pick something between the red and green maxima: 1.145 m < L < 1.152 m.
By manually inspecting the HOM spectrum for nmax = 20, it seems that L = 1.150 m is the best choice. In the HOM zoom plot below and the one to follow, the legend is as follows
Following the same logic as above, the most obvious choice for the non-bowtie is somewhere between the red maximum at 1.241 m and the magenta maximum at 1.248 m. This still allows for reasonable suppression of the n < 10 modes without sacrificing the n < 15 mode suppression completely.
Upon inspection, I suggest L = 1.246 m
I reiterate that these calculations are taking into account modes of up to n ~ 20. If there is a reason we really only care about a lower order than this, then we can do better. Otherwise, this is a nice compromise between full low-order mode isolation and not sitting directly on slightly higher modes.
One complication that arises is that all of these are highly dependent on the actual RoC of the mirrors. Unfortunately, even the quoted tolerance of ±1% makes a difference. Below is a rendering of the RED traces (nmax = 20) in the first two plots, but for R varying by ±2% (i.e., for R = 2.45 m, 2.50 m, 2.55 m).
The case for the non-bowtie only superficially seems better; the important spacing is the large one between the three highest peaks centered around 1.24 m.
Also unfortunately, this strong dependence is also true for the lowest-order modes. Below is the same two plots, but for the BLUE (nmax = 10) lines in the first plots.
Therefore, it is prudent not to pick a specific length until the precise RoC of the mirrors is measured.
Assuming the validity of looking at modes between 10 < n < 20, and that the curved mirror RoC is the design value of 2.50 m, the recommended lengths for each case are:
HOWEVER, variation within the design tolerance of the mirror RoC will change these numbers appreciably, and so the RoC should be measured before a length is firmly chosen.
EDIT 2 (ZK): As with the previous post, all plots and calculations here are done with my MATLAB cavity modeling utility, ArbCav.
EDIT (ZK): Added input q parameters for OMMT
I found the nice result that the variation in the optimal length vs. variation in the mirror RoC is roughly linear within the ±1% RoC tolerance. So, we can choose two baseline mode definitions (one for each mirror topology) and then adjust as necessary following our RoC measurements.
For R = 2.5 m, the optimal length (see previous post) is LRT = 1.150 m, and the variation in this is dLRT/dR ~ +0.44 m/m.
Here is an illustration of the geometry:
The input q parameters, defined at the point over the edge of the OMC slab where the beam first crosses---(40mm, 150mm) on the OptoCad drawing---are, in meters:
For R = 2.5 m, the optimal length is LRT = 1.246 m, and the variation in this is also dLRT/dR ~ +0.44 m/m.
q parameters, defined as above:
Here is the proposed RoC measurement setup. Koji tells me that this is referred to as "Anderson's method".
We would like to use a linear cavity to measure the RoC of the curved mirrors independently (before forming the ring cavity), since the degeneracy of HOMs will make the fitting easier.
If we decided that the symmetric sidebands are too unwieldy, or that we have issues from sidebands on sidebands, we can accomplish the same style measurement using an AOM-shifted pickoff of the pre-PDH EOM beam. The advantage of the former method is that we don't have to use any polarization tricks.
Here is a more detailed version of the setup, so that we can gather the parts we will need.
EDIT (ZK): Koji points out that (1 - Ti) should really be the non-resonant reflectivity of the aligned cavity, which is much closer to 1. However, it should *actually* be the non-resonant reflectivity of the entire OMC assembly, including the steering mirror (see bottom of post). The steering mirror has T ~ 0.3%, so the true results are somewhere between my numbers and those with (1 - Ti) -> 1. In practice, though, these effects are swamped by the other errors.
More information about the power-dependent visibility measurement:
As a blanket statement, this measurement was done by exact analogy to those made by Sam and Sheon during S6 (c.f. LHO iLog 11/7/2011 and technical note T1100562), since it was supposed to be a verification that this effect still remains. There are absolutely better ways to do (i.e., ways that should give lower measurement error), and these should be investigated for our characterization. Obviously, I volunteer.
All measurements were made by reading the output voltages produced by photodetectors at the REFL and TRANS ports. The REFL PD is a BBPD (DC output), and the TRANS is a PDA255. Both these PDs were calibrated using a Thorlabs power meter (Controller: PM100D; Head: S12XC series photodiode-based---not sure if X = 0,2... Si or Ge) at the lowest and highest power settings, and these results agreed to the few-percent level. This can be a major source of error.
The power was adjusted using the HWP/PBS combination towards the beginning of the experiment. For reference, an early layout of the test setup can be seen in LLO:5978 (though, as mentioned above, the REFL and TRANS PDs have been replaced since then---see LLO:5994). This may or may not be a "clean" way to change the power, but the analysis should take the effect of junk light into account.
Below is an explanation of the three traces in the plot. First:
Now, the traces
The error bars in the measurement were dominated, roughly equally, by 1) systematic error from calibration of the PDs with the power meter, and 2) error from noise in the REFL_L measurement (since the absolute AC noise level in TRANS and REFL_L is the same, and TRANS >> REFL_L, the SNR of the latter is worse).
(1) can be helped by making ALL measurements with a single device. I recommend using something precise and portable like the power meter to make measurements at all the necessary ports. For REFL_L/UL, we can place a beam splitter before the REFL PD, and---after calibrating for the T of this splitter very well using the same power meter---both states can be measured at this port.
(2) can probably be helped by taking longer averaging, though at some point we run into the stability of the power setting itself. Something like 30-60s should be enough to remove the effects of the REFL_L noise, which is concentrated in the few-Hz region in the LLO setup.
One more thing I forgot was the finite transmission of the steering mirror at the OMC input (the transmission of this mirror goes to the QPDs). This will add a fixed error of 0.3%, and I will take it into account in the future.
I found that, in fact, I had lowered the modulation depth since when I measured it to be 0.45 rads --> Psb = 0.1.
Here is the sweep measurement:
This is Psb = 0.06 --> gamma = 0.35 rads.
This changes the "raw transmission" and "coupling", but not the inferred visibility:
I also measured the cavity AMTF at three powers today: 0.5 mW, 10 mW, and 45 mW input.
They look about the same. If anything, the cavity pole seems slightly lower with the higher power, which is counterintuitive. The expected shift is very small (~10%), since the decay rate is still totally dominated by the mirror transmissions even for the supposed high-loss state (Sam and Sheon estimated the roundtrip loss at high power to be ~1400 ppm, while the combined coupling mirrors' T is 1.6%). I have not been able to fit the cavity poles consistently to within this kind of error.