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ID Date Author Type Category Subject
15363   Tue Jun 2 14:05:24 2020 HangUpdateBHDMM telescope actuation range requirments

We computed the required actuation range for the telescope design in elog:15357. The result is summarized in the table below. Here we assume we misalign an IFO mirror by 1 urad, and then compute how many urad do we need to move the (AS1, AS4) or (LO1, LO2) mirrors to simultaneously correct for the two gouy phases.

 [urad/urad] ITMX ITMY ETMX ETMY BS PRM PR2 PR3 SR3 SRM AS1 1.9 2.1 -5.0 -5.5 0.5 0.5 -0.3 0.2 0.1 0.6 AS4 2.9 2.0 -8.8 -5.5 -5.9 -0.7 1.3 -0.7 -0.5 0.7 LO1 -4.0 -3.9 11.0 10.4 1.9 -0.4 -0.2 0.1 0.0 -1.1 LO2 -5.0 -3.7 15.1 10.4 8.7 0.8 1.9 1.1 0.7 -1.3

The most demanding ifo mirrors are the ETMs and the BS, for every 1 urad misalignment the telescope needs to move 10-15 urad to correct for that. However, it is unlikely for those mirrors to move more 100 nrad for a locked ifo with ASC engaged. Thus a few urad actuation should be sufficient. For the recycling mirrors, every 1 urad misalignment also requires ~ 1 urad actuation.

As a result, if we could afford 10 urad actuation range for each telescope suspension, then the gouy phase separations we have should be fine.

================================================================

Edits:

We looked at the oplev spectra from gps 1274418500 for 512 sec. This should be a period when the ifo was locked in the PRFPMI state according to elog:15348. We just focused on the yaw data for now. Please see the attached plots. The solid traces are for the ASD, and the dotted ones are the cumulative rms. The total rms for each mirror is also shown in the legend.

I am now confused... The ITMs looked somewhat reasonable in that at least the < 1 Hz motion was suppressed. The total rms is ~ 0.1 urad, which was what I would expect naively (~ x100 times worse than aLIGO).

There seems to be no low-freq suppression on the ETMs though... Is there no arm ASC at the moment???

Attachment 1: TM_OL_spec_1274418500_512.pdf
Attachment 2: CORNER_OL_spec_1274418500_512.pdf
15379   Sat Jun 6 14:07:30 2020 JonUpdateBHDStock-Part Mode-Matching Telescope Option

## Summary

For the initial phase of BHD testing, we recently discussed whether the mode-matching telescopes could be built with 100% stock optics. This would allow the optical system to be assembled more quickly and cheaply at a stage when having ultra-low loss and scattering is less important. I've looked into this possibility and conclude that, yes, we do have a good stock optics option. It in fact achieves comprable performance to our optimized custom-curvature design [ELOG 15357]. I think it is certainly sufficient for the initial phase of BHD testing.

## Vendor

It turns out our usual suppliers (e.g., CVI, Edmunds) do not have enough stock options to meet our requirements. This is for two reasons:

• For sufficient LO1-LO2 (AS1-AS4) Gouy phase separation, we require a very particular ROC range for LO1 (AS1) of 5-6 m (2-3 m).
• We also require a 2" diameter for the suspended optics, which is a larger size than most vendors stock for curved reflectors (for example, CVI has no stock 2" options).

However I found that Lambda Research Optics carries 1" and 2" super-polished mirror blanks in an impressive variety of stock curvatures. Even more, they're polished to comprable tolerances as I had specificied for the custom low-scatter optics [DCC E2000296]: irregularity < λ/10 PV, 10-5 scratch-dig, ROC tolerance ±0.5%. They can be coated in-house for 1064 nm to our specifications.

From modeling Lambda's stock curvature options, I find it still possible to achieve mode-matching of 99.9% for the AS beam and 98.6% for the LO beam, if the optics are allowed to move ±1" from their current positions. The sensitivity to the optic positions is slightly increased compared to the custom-curvature design (but by < 1.5x). I have not run the stock designs through Hang's full MC corner-plot analysis which also perturbs the ROCs [ELOG 15339]. However for the early BHD testing, the sensitivity is secondary to the goal of having a quick, cheap implementation.

## Stock-Part Telescope Designs

The following tables show the best telescope designs using stock curvature options. It assumes the optics are free to move ±1" from their current positions. For comparison, the values from the custom-curvature design are also given in parentheses.

### AS Path

The AS relay path is shown in Attachment 1:

• AS1-AS4 Gouy phase separation: 71°
• Mode-matching to OMC: 99.9%
 Optic ROC (m) Distance from SRM AR (m) AS1 2.00  (2.80) 0.727  (0.719) AS2 Flat   (Flat) 1.260  (1.260) AS3 0.20  (-2.00) 1.864  (1.866) AS4 0.75  (0.60) 2.578  (2.582)

### LO Path

The LO relay path is shown in Attachment 2:

• LO1-LO2 Gouy phase separation: 67°
• Mode-matching to OMC: 98.6%
 Optic ROC (m) Distance from PR2 AR (m) LO1 5.00  (6.00) 0.423  (0.403) LO2 1000 (1000) 2.984  (2.984) LO3 0.50  (0.75) 4.546  (4.596) LO4 0.15  (-0.45) 4.912  (4.888)

## Ordering Information

I've created a new tab in the BHD procurement spreadsheet ("Stock MM Optics Option") listing the part numbers for the above telescope designs, as well as their fabrication tolerances. The total cost is $2.8k + the cost of the coatings (I'm awaiting a quote from Lambda for the coatings). The good news is that all the curved substrates will receive the same HR/AR coatings, so I believe they can all be done in a single coating run. Attachment 1: ASpathStock.pdf Attachment 2: LOpathStock.pdf 15380 Mon Jun 8 11:50:02 2020 HangUpdateBHDAstigmatism and scattering plots We consider the astigmatism effects of the stock options. The conclusions are: 1. For the AS path, the stock should work fine for the phase-one of BHD, if we could tolerate a few percent MM loss. The window for length adjustment to achieve >99% MM for both s and t is only 1 mm for 1% RoC error (compared to ~ 1 cm in the customized case). 2. The LO path seemed tricky. As LO3 & LO4 are both significantly curved (RoC<=0.5 m), the non-zero angle of incidence makes the astigmatism quite sever. For the t-plane the nominal MM can be 0.98, yet for the s-plane, the nominal MM is only 0.72. We could move things around to achieve a MM ~ 0.85, which is probably fine for the phase-one implementation but not long term. Details: Attachments 1-3 are for the AS path; 4-6 are for the LO path. 1 & 4. Marginalized MM distribution for the AS/LO paths. Here we assumed 5 mm positional error and 1% fractional RoC error. Due to the astigmatism, the nominal s-plane MM is only 0.72 for the LO path. 2 & 5. Scattering plots for the AS/LO paths. We color coded the points as the following: pink: MM>0.99; olive: 0.98<MM<=0.99; grey: MM<=0.98. For the AS path, MM is mostly sensitive to the AS1 RoC and can be adjusted by changing AS1-AS3 distance. For the LO path, the LO3 RoC and LO3-LO4 distance are most critical for the MM. 3 & 6. Assuming +- 1% AS1 (LO3) fractional RoC error, how much can we compensate for it using AS1-AS3 (LO3-LO4) distance. For the AS path, there exists a ~ 1 mm window where the MM for s and t can simultaneously > 99%. For the LO path, the best we can do is to make s and t both ~ 85%. Quote: ## Summary For the initial phase of BHD testing, we recently discussed whether the mode-matching telescopes could be built with 100% stock optics. This would allow the optical system to be assembled more quickly and cheaply at a stage when having ultra-low loss and scattering is less important. I've looked into this possibility and conclude that, yes, we do have a good stock optics option. It in fact achieves comprable performance to our optimized custom-curvature design [ELOG 15357]. I think it is certainly sufficient for the initial phase of BHD testing. ## Vendor It turns out our usual suppliers (e.g., CVI, Edmunds) do not have enough stock options to meet our requirements. This is for two reasons: • For sufficient LO1-LO2 (AS1-AS4) Gouy phase separation, we require a very particular ROC range for LO1 (AS1) of 5-6 m (2-3 m). • We also require a 2" diameter for the suspended optics, which is a larger size than most vendors stock for curved reflectors (for example, CVI has no stock 2" options). However I found that Lambda Research Optics carries 1" and 2" super-polished mirror blanks in an impressive variety of stock curvatures. Even more, they're polished to comprable tolerances as I had specificied for the custom low-scatter optics [DCC E2000296]: irregularity < λ/10 PV, 10-5 scratch-dig, ROC tolerance ±0.5%. They can be coated in-house for 1064 nm to our specifications. From modeling Lambda's stock curvature options, I find it still possible to achieve mode-matching of 99.9% for the AS beam and 98.6% for the LO beam, if the optics are allowed to move ±1" from their current positions. The sensitivity to the optic positions is slightly increased compared to the custom-curvature design (but by < 1.5x). I have not run the stock designs through Hang's full MC corner-plot analysis which also perturbs the ROCs [ELOG 15339]. However for the early BHD testing, the sensitivity is secondary to the goal of having a quick, cheap implementation. ## Stock-Part Telescope Designs The following tables show the best telescope designs using stock curvature options. It assumes the optics are free to move ±1" from their current positions. For comparison, the values from the custom-curvature design are also given in parentheses. ### AS Path The AS relay path is shown in Attachment 1: • AS1-AS4 Gouy phase separation: 71° • Mode-matching to OMC: 99.9%  Optic ROC (m) Distance from SRM AR (m) AS1 2.00 (2.80) 0.727 (0.719) AS2 Flat (Flat) 1.260 (1.260) AS3 0.20 (-2.00) 1.864 (1.866) AS4 0.75 (0.60) 2.578 (2.582) ### LO Path The LO relay path is shown in Attachment 2: • LO1-LO2 Gouy phase separation: 67° • Mode-matching to OMC: 98.6%  Optic ROC (m) Distance from PR2 AR (m) LO1 5.00 (6.00) 0.423 (0.403) LO2 1000 (1000) 2.984 (2.984) LO3 0.50 (0.75) 4.546 (4.596) LO4 0.15 (-0.45) 4.912 (4.888) ## Ordering Information I've created a new tab in the BHD procurement spreadsheet ("Stock MM Optics Option") listing the part numbers for the above telescope designs, as well as their fabrication tolerances. The total cost is$2.8k + the cost of the coatings (I'm awaiting a quote from Lambda for the coatings). The good news is that all the curved substrates will receive the same HR/AR coatings, so I believe they can all be done in a single coating run.

Attachment 1: AS_MM_hist_stock.pdf
Attachment 2: AS_MM_t_scat_stock.pdf
Attachment 4: LO_MM_hist_stock.pdf
Attachment 5: LO_MM_s_scat_stock.pdf
15381   Mon Jun 8 12:49:07 2020 KojiUpdateBHDAstigmatism and scattering plots

Can you describe the mode matching  in terms of the total MM? Is MM_total = sqrt(MM_vert * MM_horiz)?

15382   Mon Jun 8 17:40:22 2020 JonUpdateBHDAstigmatism and scattering plots

MM_total = (MM_vert + MM_horiz) / 2.

The large astigmatic MM loss in the LO case is mainly due to the strong LO4 curvature (R=0.15m) with a 10 deg AOI. I looked again at whether LO1 could be increased from R=5m to the next higher stock value of 7.5m, as this would allow weaker curvatures on LO3 and LO4. However, no, that is not possible---it reduces the LO1-LO2 Gouy phase separation to only 18 deg.

There is, however, a good stock-curvature option if we want to reconsider actuating LO4 instead of LO2 (attachment 1). It achieves 99.2% MM with the OMCs, allowing positions to vary +/-1" from the current design. The LO1-LO4 Gouy phase separation is 72 deg.

Optic ROC (m) Distance from PR2 AR (m)
LO1 10 0.378
LO2 1000 2.984
LO3 10 4.571
LO4 7.5 4.926

Alternatively, we could look at reducing the AOI on LO3 and LO4 (keeping LO1-LO2 actuation).

Attachment 1: LOpathStock2.pdf
15384   Mon Jun 8 21:45:47 2020 JonUpdateBHDAstigmatism and scattering plots

Hmm? T1300364 suggests MM_total = Sqrt(MM_Vert * MM_Horiz)

15386   Tue Jun 9 14:55:43 2020 JonUpdateBHDMM telescope actuation range requirments

I don't think we ever discussed why the angular RMS of the ETMs is so much higher than the ITMs. Maybe that's a separate matter because, even assuming the worst case, the actuation range requirement is

which is still only order 1% of the pitch/yaw pointing range of the Small Optic Suspensions, according to P1600178 (sec. IV. A). Can we check this requirement off the list?

Quote:

We computed the required actuation range for the telescope design in elog:15357. The result is summarized in the table below. Here we assume we misalign an IFO mirror by 1 urad, and then compute how many urad do we need to move the (AS1, AS4) or (LO1, LO2) mirrors to simultaneously correct for the two gouy phases.

 [urad/urad] ITMX ITMY ETMX ETMY BS PRM PR2 PR3 SR3 SRM AS1 1.9 2.1 -5.0 -5.5 0.5 0.5 -0.3 0.2 0.1 0.6 AS4 2.9 2.0 -8.8 -5.5 -5.9 -0.7 1.3 -0.7 -0.5 0.7 LO1 -4.0 -3.9 11.0 10.4 1.9 -0.4 -0.2 0.1 0.0 -1.1 LO2 -5.0 -3.7 15.1 10.4 8.7 0.8 1.9 1.1 0.7 -1.3

The most demanding ifo mirrors are the ETMs and the BS, for every 1 urad misalignment the telescope needs to move 10-15 urad to correct for that. However, it is unlikely for those mirrors to move more 100 nrad for a locked ifo with ASC engaged. Thus a few urad actuation should be sufficient. For the recycling mirrors, every 1 urad misalignment also requires ~ 1 urad actuation.

As a result, if we could afford 10 urad actuation range for each telescope suspension, then the gouy phase separations we have should be fine.

================================================================

Edits:

We looked at the oplev spectra from gps 1274418500 for 512 sec. This should be a period when the ifo was locked in the PRFPMI state according to elog:15348. We just focused on the yaw data for now. Please see the attached plots. The solid traces are for the ASD, and the dotted ones are the cumulative rms. The total rms for each mirror is also shown in the legend.

I am now confused... The ITMs looked somewhat reasonable in that at least the < 1 Hz motion was suppressed. The total rms is ~ 0.1 urad, which was what I would expect naively (~ x100 times worse than aLIGO).

There seems to be no low-freq suppression on the ETMs though... Is there no arm ASC at the moment???

15387   Tue Jun 9 15:02:56 2020 eHangUpdateBHDAstigmatism and scattering plots

Using the updated AOI's for the LO path: (4.8, 47.9, 2.9, 4.5) deg for (LO1, LO2, LO3, LO4), we obtain the following results.

First two plots are scattering plots for the t and s planes, respectively. Note that here we have changed to 0.5% fractional RoC error and 3 mm positional error. We have also changed the meaning of the colors: pink:MM>0.98; olive 0.95<MM<=0.98, and grey MM<=0.95. It seems that both planes would benefit statistically if we make the LO3-LO4 distance longer by a few mm.

We also consider how much we could compensate for the MM error in the last plot. We have a few mm window to make both planes better than 0.95.

Attachment 1: LO_MM_t_scat_stock.pdf
Attachment 2: LO_MM_s_scat_stock.pdf
15389   Thu Jun 11 09:37:38 2020 JonUpdateBHDConclusions on Mode-Matching Telescopes

After further astigmatism/tolerance analysis [ELOG 15380, 15387] our conclusion is that the stock-optic telescope designs [ELOG 15379] are sufficient for the first round of BHD testing. However, for the final BHD hardware we should still plan to procure the custom-curvature optics [DCC E2000296]. The optimized custom-curvature designs are much more error-tolerant and have high probability of achieving < 2% mode-matching loss. The stock-curvature designs can only guarantee about 95% mode-matching.

Below are the final distances between optics in the relay paths. The base set of distances is taken from the 2020-05-21 layout. To minimize the changes required to the CAD model, I was able to achieve near-maximum mode-matching by moving only one optic in each relay path. In the AS path, AS3 moves inwards (towards the BHDBS) by 1.06 cm. In the LO path, LO4 moves backwards (away from the BHDBS) by 3.90 cm.

### AS Path

Interval Distance (m) Change (cm)
SRMAR-AS1 0.7192 0
AS1-AS2 0.5405 0
AS2-AS3 0.5955 -1.06
AS3-AS4 0.7058 -1.06
AS4-BHDBS 0.5922 0
BHDBS-OMCIC 0.1527 0

### LO Path

Interval Distance (m) Change (cm)
PR2AR-LO1 0.4027 0
LO1-LO2 2.5808 0
LO2-LO3 1.5870 0
LO3-LO4 0.3691 +3.90
LO4-BHDBS 0.2573 +3.90
BHDBS-OMCIC 0.1527 0
15456   Mon Jul 6 15:10:40 2020 JonSummaryBHD40m --> A+ BHD design analysis

As suggested last week, Hang and I have reviewed the A+ BHD status (DRD, CDD, and reviewers' comments) and compiled a list of key unanswered questions which could be addressed through Finesse analysis.

In anticipation of others helping with this modeling effort, we've tried to break questions into self-contained projects and estimated their level of difficulty. As you'll see, they range from beginner to Finesse guru.

15464   Thu Jul 9 17:12:52 2020 gautamUpdateBHDIn-air BHD

Summary:

We can probably learn something about the interferometer / top level BHD plan with an in-air BHD setup, even if the noise is bad. Here are some thoughts about how we would do it.

LO delivery:

For this first attempt, we don't really care about the PRC filtering. So possible places to pick off an LO beam are:

LO beam pickoff options
Location Pros Cons
IP POS
• Filtered by IMC
• Medium level of invasiveness
• We lose the IP POS diagnostic, which is kind of useful nowadays given the drifty TTs.
• Only few mW LO power available
PSL table IR beam currently going to green doubling setup
• Least invasive w.r.t. normal IFO operation
• Plenty of light (~100 mW) available. But how much can we safely couple into fiber?
• Beam not filtered by IMC (although it is filtered by the PMC)
POX/POY
• Since this beam is extracted from inside the PRC, probably enjoys the best filtering.
• Possibly drifts a lot, so tricky to reliably couple into a fiber?
• Maximally invasive w.r.t. regular IFO operations.

In all cases, I think the easiest option to actually route whatever beam we choose into a fiber, and then bring it over to whatever cavity we choose to use for an OMC. I'm assuming whatever phase control technique we end up using can cancel the fiber phase noise at relevant frequencies.

LO phase control

• Stress the fiber? This will require us to purchase some custom hardware, and interface it to the CDS system.
• PZT mirror? We should have sufficient hardware available to drive a PI style PZT mirror.

There is a question about the range, but I think these are the only two realistic options we can implement on a reasonable time scale.

OMC:

Again, there are a few options. Here are some pros and cons that come to my mind.

OMC cavity options
Option Pros Cons
Old copper OMC
• Probably the simplest option in terms of the peripherals.
• PZT driver recently verified to work
• We can get the OMMT and DCPDs out as well.
• Allows us to not compromise on the RF darm optical gain (not sure if locking will be as easy if we cut the power to the AS55 photodiode by 50-75%).
• Requires a vent.
• Probably not the most efficient use of the space on the AP table.
• Filtering performance isn't quantified.
Spare PMC
• Doesn't require a vent.
• Compact footprint.
• Need to build the cavity.
• Need to check if the drive electronics from the old copper OMC can easily be interfaced with whatever PZT we use on this cavity.
• Filtering performance kind of unknown?
Custom cavity with spare mirrors
• Doesn't require a vent.
• Probably no more difficult than the spare PMC option?
• We need at least one actuatable mirror, so we'd need some PZT mounted optic + associated drive electronics.

If we can do a vent (we'd just need a single chamber open), I'd go for the option of getting the copper OMC out and using that. Attachment #1 shows the approximate sizes of the various components (OMMT, OMC cavity, DCPDs), while Attachment #2 shows a rough sketch of where things would go on the AP table, with the rectangles approximately to scale.

CDS:

I'd made a c1omc model sometime ago. Basically, I think we have sufficient ADC/DAC channels in the c1ioo machine for any of the options listed above - but using the copper OMC and associated peripherals would allow the easiest interfacing.

Attachment 1: OMCchamber.pdf
Attachment 2: AP_Table_20180328.pdf
15479   Tue Jul 14 15:29:25 2020 gautamUpdateBHDIn-air BHD - DCPD amplifier noise

For the first pass, it's probably easiest to use the existing DCPD amplifier. Looking at the gain and noise performance in Attachment #1, seems totally fine, the electronics noise will not be limiting if we have ~10mW of LO power. I assumed a transimpedance resistor of 1 kohm, and all other numbers as on the schematic (though who knows if the schematic is accurate). The noise should be measured to confirm that the box is performing as expected...

Attachment 1: DCPDamp.pdf
15483   Wed Jul 15 19:11:40 2020 gautamUpdateBHDIn-air BHD - alignment into OMC

I forgot about the pointing - probably we will need another actuator to control the pointing of the AS beam onto the DCPDs. I found a few old PI PZTs (model number is S-320, which is a retired part), one is labelled broken but the others don't indicate a-priori that they are broken. I'll post a more detailed hardware survey later.

Draft   Wed Jul 15 19:17:09 2020 gautamUpdateBHDIn-air BHD - alignment into OMC

You can activate all 3axis

15489   Thu Jul 16 01:12:22 2020 gautamUpdateBHDIn-air BHD - preparing the LO path

Attachment #1 - The 80mW pickoff was getting clipped on a BNC cable, and not making it to the doubling oven. 😢 .

• Since the PSL doubled beam isn't used for locking these days, I just didn't notice.
• I blame the ringdown team, this crazy tee arrangement wasn't the case before.
• I fixed the situation by changing the cabling such that the beam clears the cables comfortably.

Attachment #2 - PSL green shutter removed. Alignment into the doubling oven is extremely tedious, and so I opted to preserve the capability of recovering the green beam by simply removing a single mirror.

Attachment #3 - The beam path for coupling the LO beam into a fiber.

• Primary goal was to have easy access to some steering mirrors so that I can optimize alignment into the fiber collimator.
• I opted to use the NW corner of the PSL table - that's where most of our existing fiber hardware is anyways, and there was sufficient space and easy access over there.
• 3 Y1 mirrors were installed, using the preferred Polaris mounts and 3/4" post + baseplate hardware. They were labelled Y1-1037-45P so that future workers need not be un-necessarily tortured. The third mirror is not visible in this photograph.
• Once the collimator arrives, I will mode match this beam into the fiber. Plan is to use the fiber originally used for the mode spectroscopy project. It needs to be moved to the NW corner of the PSL table, and the other end needs to be routed to the AP table (it was brought back to the PSL table to facilitate Anjali's fiber MZ experiment).
• There is plenty of space in the beam path for mode-matching lens(es) and polarization control optics.

Attachment #4 shows the BHD photodiodes taken from QIL.

• Unfortunately, we could not find the readout electronics.
• In the worst case, we can just interface these PDs with the existing Satellite box (associated with the copper OMC).
• It might be that the OMC cavity can simply be placed on this breadboard, making the whole setup nice and portable.
• We may want to consider having an OFI between the OMC and the IFO AS beam at some point...
Attachment 1: IMG_8626.JPG
Attachment 2: IMG_8627.JPG
Attachment 3: IMG_8628.JPG
Attachment 4: IMG_8629.JPG
15493   Sun Jul 19 15:40:15 2020 gautamUpdateBHDIn-air BHD - CDS and wiring summary

Attachment #1 shows the proposed wiring and CDS topology for the in air BHD setup. The PDF document has hyperlinks you can follow to the DCC entries. Main points:

1. I think we should run the realtime model on c1lsc. This will negate the need for any IPC between c1ioo and c1lsc machines.
2. I think we have most of the electronics we need already, though I am still in the process of testing the various boards, especially the HV ones.
3. We may choose to use the switchable whitening feature for the M2 ISS board
• This would require some BIO channels
• There are plenty spare in c1lsc, so it's not going to be a show stopper
• This is why I've not explicitly included a whitening board for now...
4. The main job seems to be to make a whole bunch of custom cables. For the most part, I think we have the long (~20m) long D9 cables, so I propose just snipping off the connector at one end, and soldering on the appropriate connectors to the correct conductors.
5. For the homodyne phase control - the proposal is to use a PI PZT with 3 piezoelectric elements. We would drive the 3 elements with the same voltage, by shorting the conductors together (at least that's how I understood Koji's comment), so we'd only need a single DAC channel for this purpose.
• Need to confirm that the parallel PZT capacitances (each element is ~300 nF so 3 in parallel would be ~900 nF) still allows sufficient actuation bandwidth.
• If the relative actuation strength of the 3 elements needs to be individually tuned, we may have to use three DAC channels. The D980323 board will allow the driving of 3 independent channels. I have one of these boards in hand, but need to check if it works, and also implement the changes outlined here.
6. The alignment control has not yet been accounted for
• We could consider using the in-vacuum PZTs, these were verified to be working ~2018.
• If we use only 1 steering PZT mirror, we have sufficient free DAC channels available in c1lsc. But if we need both (to avoid clipping for example), then we need more DAC channels - we can either free up one DAFI channel, or install a DAC in the c1lsc expansion chassis
7. We may want to expand to have a second OMC at some point. In which case we'd need, at the very least
• 1 more DAC card
• A HV driver for the second OMC length (could use the Trek driver if we use D980323 for the homodyne phase control).

Please comment if I've overlooked something.

Attachment 1: wiringDiagram.pdf
15495   Mon Jul 20 17:55:15 2020 gautamUpdateBHDIn-air BHD - preparing the LO path

The LO pickoff has been coupled into a fiber with ~90% MM (8 mW / 9 mW input). While I wait for the DCPD electronics to be found in the Cryo lab, I want to monitor the stability of the pointing, polarization etc, so I'd like to clear some space on the AP table that was occupied for the mode spectroscopy project. If there are no objections before 2pm tomorrow July 21 2020, I will commence this work.

15497   Tue Jul 21 00:30:24 2020 gautamUpdateBHDIn-air BHD - LO RIN

Attachment #1 shows the RIN of the local oscillator beam delivered to the AP table via fiber. I used a PDA520 to make this measurement, while the electronics for the DCPDs are pending. I don't really have an explanation for the difference between the locked IFO trace vs the not locked trace - we don't have an ISS running (but this first test suggests we should) and the beam is picked off before any cavities etc, so this is a reflection of the state of the FSS servo at the times of measurement?

Tried locking CARM using the hybrid REFL (for AO path) and POX 11 (for MCL path) scheme a bunch of times today, but I had no luck. When the CARM offset is zeroed, the PRMI lock is lost almost immediately. Maybe this is indicative of some excess noise in the POX data stream relative to the REFL signal? The one thing I haven't tried is to take the IFO all the way to the locked state, and then transition the MCL actuation from CM_SLOW to POX11_I.

An SR785 is sitting on the North side of the AP table in the walkway - I will clear it tomorrow.

Attachment 1: LO_RIN.pdf
15498   Tue Jul 21 16:41:46 2020 gautamUpdateBHDPMC assembly space

I decided to use the old EY auxiliary optics table, which is now stored along the east arm about 10 m from the end, as a workspace for assembling the little PMCs. I wiped everything down with isopropanol for general cleanliness, removed the metal plate on the south edge of the table enclosure to allow access, covered the table with some clean Aluminium foil, and then moved the plastic box with PMC parts to the table - see Attachment #1. I haven't actually done any assembly just yet, waiting for more info (if available) on the procedure and implements available...

Attachment 1: IMG_8635.JPG
15503   Tue Jul 28 13:55:11 2020 HangUpdateBHDExploring bilinear SRCL->DARM coupling

We explore bilinear SRCL to DARM noise coupling mechanisms, and show two cases that by doing BHD readout the noise performance can be improved. In the first case, the bilinear piece is due to residual DHARD motion (see also LHO:45823), and it matters mostly for the low-frequency (<100 Hz) part, and in the second piece the bilinear piece is due to residual SRCL fluctuation and it matters mostly for the a few x 100 Hz part. Details are below:

=================================================

General Model:

We can write the SRCL to DARM transfer function as (Evan Hall's thesis, eq. 2.29)

Z_s2d(f) = C_lf(f) * F^2 * x_D + C_hf(f) * F * dphi_S * x_D    ---- (1)

where

C_lf ~ 1/f^2 and C_hf ~ f are constants at each frequency unless there are major upgrades to the IFO,

F is the finesse of the arm cavity which depends on the alignment, spot position on the TMs, etc.,

dphi_S is the SRCL detuning (wrt the nominal 90 deg value),

x_D is the DC DARM offset.

The linear part of this can be removed with feedforward subtractions and it is the bilinear piece that matters, which reads

dZ_s2d = C_lf * <F>^2 * dx_D + C_hf * <F> * <dphi_S> * dx_D

+ 2C_lf * <F> * <x_D>  * dF + C_hf * <dphi_S> * <x_D> * dF

+ C_hf  * <F> * <x_D> * d(dphi_S).     ---- (2)

The first term in (2) is due to residual DARM motion dx_D. This term does not depends on the DC value of DARM offset <x_D> and thus does not depend on doing BHD or DC readout. On the other hand, the typical residual DARM motion is 1 fm << 1 pm of DARM offset. Since the current feedforward reduction factor is about 10 (see both Den Martynov's thesis and Evan Hall's thesis), clearly we are not limited by the residual DARM motion.

The second term is due to the change in the arm finesse, which can be affected by, e.g., the alignment fluctuation (both increasing the loss due to scattering into 01/10 modes and affecting the spot positon and hence changing the losses), and is likely to be the reason why we see the effect being modulated by DHARD.

The last term in (2) is due to the residual SRCL fluctuation and is important for the ~ a few x 100 Hz band.

=================================================

DHARD effects.

As argued above, the DHARD affects the SRCL -> DARM coupling as it changes the finesse in the arm cavity (through scattering into 01/10 modes; in finesse we cannot directly simulate the effects due to spot hitting a rougher location).

Since in the second term of eq. (2) the LF part depends on the DARM DC offset <x_D>, this effect can be improved by going from DC readout to BHD.

To simulate it in finesse, at a fixed DARM DC offset, we compute the SRCL->DARM transfer functions at different DHARD offsets, and then numerically compute the derivative \partial Z_s2d / \partial \theta_{DH}. Then multiplying this derivative with the rms value of DHARD fluctuation \theta_{DH} we then know the expected bilinear coupling piece.

The result is shown in the first attached plot. Here we have assumed a flat SRCL noise of 5e-16 m/rtHz for simplicity (see PRD 93, 112004, 2016). We do not account for the loop effects which further reduces the high frequency components for now. The residual DHARD RMS is assumed to be 1 nrad.

In the first plot, from top to bottom we show the SRCL noise projection at different DARM DC offsets of (0.1, 1, 10) pm. Since the DHARD alignment only affects the arm finesse starting at quadratic order, it thus matters what DC offset in DHARD we assume. In each pannel, the blue trace is for no DC offset in DHARD and the orange one for a 5 nrad DC offset. As a reference, the A+ sensitivity is shown in grey trace in each plot as a reference.

We can see if there is a large DC offset in DHARD (a few nrad) and we still do DC readout with a few pm of DARM offset, then the bilinear piece of SRCL can still contaminate the sensitivity in the 10-100 Hz band (bottom panel; orange trace). On the other hand, if we do BHD, then the SRCL noise should be down by ~ x100  even compared to with the top panel.

(A 5 nrad of DC offset in DHARD coupled with 1 nrad RMS would cause about 0.5% RIN in the arms. This is somewhat greater than the typically measured RIN which is more like <~ 0.2%. See the second plot).

=================================================

SRCL effect.

Similarly we can consider the SRCL->DARM coupling due to residual SRCL rms. The approach is very similar to what we did above for DHARD. I.e., we compute Z_s2d at fixed DARM offset and for different SRCL offsets, then we numerically evaluate \partial Z_s2d / \partial dphi_S. A residual SRCL rms of 0.1 nm is then used to generate the projection shown in the third figure.

Unlike the DHARD effect, the bilinear SRCL piece does not depend on the DC SRCL detuning (for the 50-500 Hz part). It does still depends on the DARM DC offset and therefore could be improved by BHD.

Since we do not include the LP of the SRCL loop in this plot, the HF noise at 1 kHz is artifical as it can be easily filtered out. However, the LP will not be very strong around 100-300 Hz for a SRCL UGF ~ 30 Hz, and thus doing BHD could still have some small improvements for this effect.

Attachment 1: SRCL_bilin_DHARD.pdf
Attachment 2: ARM_RIN.pdf
Attachment 3: SRCL_bilin_SRCL.pdf
15505   Wed Jul 29 11:57:59 2020 ranaUpdateBHDIn-air BHD - CDS and wiring summary

3. I agree - this whitening will be handy to have for diagnostics.

4. I think in principle, we can ask a company to make the custom cables for us to save us some hand labor. Rich/Chub probably know the right companies to do small numbers of dirty cables.

5. Can't we just a single Noliac PZT in the same way that the OMC does? Or is the lead time too long?

6. Do we need active steering for this in-air test? I'm not even sure how we would get the alignment signal, so maybe that's a good reason to figure this out.

15507   Thu Aug 6 00:34:38 2020 YehonathanUpdateBHDMonte Carlo Simulations

I've pushed an MCMC simulation to the A+ BHD repo (filename MCMC_TFs.ipynb). The idea is to show how random offsets around ideal IFO change the noise couplings of different DOFs to readout.

At each step of the simulation:

1. Random offsets for the different DOFs are generated from a normal distribution. The RMSs are taken from experimental data and some guesses and can be changed later. The laser frequency is tuned to match the CARM offset.

These are the current RMS detunings I use:

 DOF RMS Taken from DARM 10fm PHYSICAL REVIEW D 93, 112004 (2016), Table 2 CARM 1fm PHYSICAL REVIEW D 93, 112004 (2016), Table 2 MICH 3pm PHYSICAL REVIEW D 93, 112004 (2016), Table 2 PRCL 1pm PHYSICAL REVIEW D 93, 112004 (2016), Table 2 SRCL 10pm PHYSICAL REVIEW D 93, 112004 (2016), Table 2 OMCL 0.1pm Guess OMC Breadboard angle 1\mu rad Guess Differential arm loss 15ppm Guess BHD BS imbalance 10% Guess OMC finesse imbalance 5ppm Guess

2. A transfer function is computed for the noisy DOFs.

3. Projected noise is calculated.

These are the noise level for the DOFs:

 DOF Noise Taken from MICH 2e-16 m PHYSICAL REVIEW D 93, 112004 (2016), Fig 9 PRCL 0.5e-17 m PHYSICAL REVIEW D 93, 112004 (2016), Fig 9 SRCL 5e-16 PHYSICAL REVIEW D 93, 112004 (2016), Fig 9 OMCL 2.5e-17*(100/f)^(1/2) LIGO-G1800149 OMC Breadboard angle 1nrad Guess RIN 2e-9 Optics Letters Vol. 34, Issue 19, pp. 2912-2914 (2009)

The attachments show the projected noise levels for the noisy DOFs. Each curve is a different instance of random offsets. The ideal case - "zero offsets" is also shown.

OMC Comm and OMC diff refer to the common and differential length change of the OMCs.

Attachment 1: MICH_Aplus_MCMC.pdf
Attachment 2: PRCL_Aplus_MCMC.pdf
Attachment 3: SRCL_Aplus_MCMC.pdf
Attachment 4: OMC_Comm_Aplus_MCMC.pdf
Attachment 5: OMC_Diff_Aplus_MCMC.pdf
Attachment 6: OMC_Angle_Yaw_Aplus_MCMC.pdf
Attachment 7: OMC_Angle_Pitch_Aplus_MCMC.pdf
Attachment 8: L0_RIN_Aplus_MCMC.pdf
15509   Fri Aug 7 11:23:47 2020 ranaUpdateBHDMonte Carlo Simulations

that's great. I think we would like to figure out how to present this so that its clear what the distribution of TFs is. Maybe we can plot the most likely curve as well as a shaded region indicating the 5% and 95% values?

 Quote: I've pushed an MCMC simulation to the A+ BHD repo (filename MCMC_TFs.ipynb). The idea is to show how random offsets around ideal IFO change the noise couplings of different DOFs to readout.

and then we add the loops

15512   Mon Aug 10 07:13:00 2020 YehonathanUpdateBHDMonte Carlo Simulations

I fixed some stuff in the MCMC simulation:

1. Results are now plotted as shades from minimum to maximum. I tried making the shade the STD around a mean but it doesn't look good on a log scale when the STD is bigger than the mean.

2. Added comparison with aLigo. The OMCL diff and comm motions in A+ are both compared to the single OMCL DOF of aLigo.

3. I fixed a serious error in the code that produced incorrect results.

4. Imbalances in the IFO such as differential arm loss are generated randomly at the beginning and stay fixed for the rest of the simulation instead of being treated as an offset.

5. The simulation now runs with maxtem=2. That is, TEM modes up to 2nd order are considered.

The results are attached.

Attachment 1: MICH_AplusMCMC.pdf
Attachment 2: PRCL_AplusMCMC.pdf
Attachment 3: SRCL_AplusMCMC.pdf
Attachment 4: OMC_Comm_AplusMCMC.pdf
Attachment 5: OMC_Diff_AplusMCMC.pdf
Attachment 6: OMC_Angle_Yaw_AplusMCMC.pdf
Attachment 7: OMC_Angle_Pitch_AplusMCMC.pdf
Attachment 8: L0_RIN_AplusMCMC.pdf
15513   Mon Aug 10 16:52:04 2020 gautamUpdateBHDWorkable setup prepared

All the details are in E2000436, and documents linked from there, I think an elog would be much too verbose. In summary, a workable setup consisting of

• 2 DCPDs interfaced with the realtime CDS system. Note that because this circuit is single-ended, while the AA and ADC are differential receiving, there is an overall gain of 0.5. Explicitly, for the 300 ohm DC transimpedance, the conversion is ~350 cts/mW.
• A local oscillator beam delivered via fiber that is mode-matched (roughly) with the IFO AS beam.
• A PZT mounted mirror to control the homodyne phase. The PZT (S320) is an obsolete part and it's hard to find a datasheet for it, but if its specs are comparable to the more modern S330, the full stroke is 10 um, for a max applied voltage of 100 V DC, so 100nm/V. c.f. 200V for 3um full stroke of the Noliac.

was prepared.

Last night, I locked the PRMI with the carrier resonant, and convinced myself that the DCPD null stream was sensing the MICH degree of freedom (while it was locked on AS55_Q) with good SNR below ~60 Hz. Above ~60 Hz, in this configuration, the ADC noise was dominating, but by next week, I'll have a whitening board installed that will solve this particular issue. With the optical gain of MICH in this configuration, the ADC noise level was equivalent to ~500 nrad/rtHz of phase noise above ~60 Hz (plots later).

Now, I can think about how to commission this setup interferometrically.

15514   Tue Aug 11 23:20:29 2020 gautamUpdateBHDSome first tests with air BHD setup

Some tests done today:

All of these tests were done with the PRMI locked with carrier resonant in the recycling cavity (i.e. sidebands rejected to REFL port). I then actuated the BS length DOF with a sine wave at 311.1 Hz, 40 cts amplitude (corresponding to ~8 pm of peak-to-peak displacement).

1. Attempt to balance the DCPDs
• I tried to tune the digital gains of the two DCPDs so as to minimize the appearance of this line in the SUM channel
• but no matter how I tuned the gains, I couldn't make the line in the SUM channel disappear entirely - in fact, the best I could do was to make the line height in SUM and NULL channels (yes I recognize the poor channel name choice, I'll change "NULL" to "DIFF" at the next model recompile) the same. See Attachment #1.
• The lobes around the main peak are indicative of some scattering?
• Attachment #2 shows a wider frequency range. The homodyne phase isn't controlled, so the "NULL" channel is not necessarily measuring the correct quadrature to be sensing MICH motion.
• I think I can back out something about the contrast defect from this fact, but I need to go back to some modeling.
2. A simple test of the homodyne phase actuator
• I wanted to check that this PI S320 piezo actually allows me to actuate the optical path length of the local oscillator.
• I'm using the OMC HV driver to drive said PZT - so there are two DAC channels available, one to dither the optic and one to apply a control signal. I think mainly this is to avoid using up DAC range for the dither signal, the overall dynamic range is still limited by the HV supply.
• I can't find the maximum voltage that can be applied on the datasheet - so conservatively, I limited the HV output to saturate at 100 V DC, as this is the maximum for the S330 piezos used for green steering, for which there is a manual.
• The S320 manual does say the full stroke of each PZT element is 10 um - so the actuation coefficient is ~100 nm/V. I then drove this actuator with a sine wave of 500 cts amplitude, at 314.1 Hz (corresponding to 15 nm of motion). With only the LO beam incident on the PDs, I saw no signal in either DCPD - as expected, so this was good.
• Then, with the PRMI locked, I repeated the test. If there is no DC light field (as expected for the PRMI in this configuration), I wouldn't expect this drive signal to show up in the DCPDs. But in fact, I do. Again, this supports the presence of some (for now unquantified) contrast defect.

While it would seem from these graphs that the RIN of the LO beam at these frequencies is rather high, it is because of the ADC noise. More whitening (to be installed in the coming days) will allow us to get a better estimate, should be ~1e-6 I think.

I was just playing today, still need to setup some more screens, DTT templates etc to do more tests in a convenient way.

 Now, I can think about how to commission this setup interferometrically.
Attachment 1: PRMI_RFlock.pdf
Attachment 2: PRMI_RFlock_fullscale.pdf
15532   Mon Aug 17 23:41:50 2020 gautamUpdateBHDWhitening and air BHD dark noise

Summary:

With the chosen transimpedance of 300 ohms, in order to be able to see the shot noise of 10 mW of light in the digitized data streams, we'd need all 3 stages of whitening. If we want to be shot noise limited with 1 mW of LO light, we'd need to increase said transimpedance I think.

Details:

The measurements were taken with

1. No light incident on the DCPDs.
2. The flat whitening gain was set to 0 dB.
3. Whitening engaged sequentially, stage by stage, shown as (Blue, Red, Orange and Green) curves corresponding to (0, 1, 2, 3) stages of whitening.

Of course, it's unlikely we're going to be shot noise limited for any configuration in the short run. But this was also a test of

1. My soldering.
2. Change of whitening corner frequencies.
3. Test of the overall whitening board assembly.

All 3 tests passed.

Attachment 1: BHD_whitening.pdf
15535   Fri Aug 21 15:27:00 2020 gautamUpdateBHDBetter BHD mode-matching

Summary:

The mode-matching between the LO and AS beams is now ~50%. This isn't probably my most average mode-matching in the lab, but I think it's sufficient to start doing some other characterization and we can try squeezing out hopefully another 20-30% by putting the lenses on translation stages, tweaking alignment etc.

Details:

The main change was to increase the optical path length of the IFO AS path, see Attachment #1. This gave me some more room to put a lens and translate it.

• The LO path uses two lenses, f=200mm and f=100mm to focus the collimator output beam, which is supposedly ~1200um diameter, to something like 400um diameter (measured using beam profiler but not very precisely).
• This beam is  fairly well collimated, and the beam size is close to what the PMC cavity will want, I opted not to tweak this too much more.
• For the AS beam, the single bounce reflection from ITMY was used for alignment work.
• There is a 2" f=600mm lens upstream (not seen in Attachment #1). This supposedly makes a beam with waist ~80um, but I couldn't numerically find a good solution numerically if this assumption is true, so I decided to do the mode-matching empirically.
• A single f=150mm lens got me a beam that seemed pretty well collimated, and roughly the same size as the LO beam, so I opted to push ahead with that. Later, I measured with the beam profiler that the beam is ~600um in diameter, so the beam isn't very well matched to the LO spot size, but I decided to push ahead nevertheless.
• Patient alignment work enabled me to see interference fringes.
• Note that the ITM reflection registers 30 cts (~80 uW). Assuming 800mW transmission through the IMC, I would have expected more like 800mW * 5.637% * 50% * 98.6% * 50% * 10% * 30% * 50% * 50% = 80uW, so this is reasonable I guess. The chain of numbers corresponds to T_PRM * T_BS * R_ITM * R_BS * T_SRM * T_vac_OMC_pickoff * R_in_air_BS * R_homodyneBS.
• The IFO AS beam appears rather elliptical to the eye (and also on the beam profiler). It already looks like this coming out of the vacuum so not much we can do about it right now I guess. By slightly rotating the f=150mm focusing lens so that the beam going through it at ~10 degrees instead of normal incidence, I was able to get a more circular beam as measured using the beam profiler.
• With the AS beam blocked, the LO beam registers 240 cts on each DCPD (~0.7 mW).
• The expected fringe should then be (sqrt(240) + sqrt(30))^2 - (sqrt(240) - sqrt(30))^2 ~ 440 cts pp.
• The best alignment I could get is ~200 cts pp, see Attachment #2.

Next steps:

Try the PRMI experiments again, now that I have some confidence that the beams are actually interfering.

See Attachment #3 for the updated spectra - the configuration is PRMI locked with carrier resonant and the homodyne phase is uncontrolled. There is now much better clearance between the electronics noise and the MICH signal as measured in the DCPDs. The "LO only" trace is measured with the PSL shutter closed, so the laser frequency isn't slaved to the IMC length. I wonder why the RIN (seen in the SUM channel) is different whether the laser is locked to the IMC or not? The LO pickoff is before the IMC.

Attachment 1: IMG_7548.JPG
Attachment 2: BHD_MM.png
Attachment 3: PRMI_DCPDs.pdf
15539   Tue Aug 25 05:51:29 2020 YehonathanUpdateBHDMonte Carlo Simulations

I re-plotted the MCMC results as semi-transparent lines so that probable lines stick out.

This also reveals what is behind the extreme sparsity in the aLIGO simulation results (In the previous post).

There seem to be some bi-stability/phase transition/whatever in the aLIGO simulation. The aLIGO transfer functions are very sensitive to one or more of the DOFs. Not sure which yet.

Attachment 1: MICH_AplusMCMC.pdf
Attachment 2: PRCL_AplusMCMC.pdf
Attachment 3: SRCL_AplusMCMC(1).pdf
Attachment 4: OMC_Diff_AplusMCMC.pdf
Attachment 5: OMC_Comm_AplusMCMC.pdf
Attachment 6: OMC_Angle_Yaw_AplusMCMC.pdf
Attachment 7: OMC_Angle_Pitch_AplusMCMC.pdf
Attachment 8: Main_Laser_RIN_AplusMCMC.pdf
15540   Wed Aug 26 00:52:55 2020 gautamUpdateBHDBHD activities

Listing some talking points from the last week of activity here.

1. LO delivery fiber cable may be damaged.
• The throughput itself doesn't suggest any problems, I get almost all the light I put in out the other end.
• However, even when I slightly move the fiber, I see huge amplitude fluctuations in the DCPD readouts. This shouldn't be the case, particularly if the light is well matched to one of the special axes of the PM fiber. I checked with a PBS at the output that this is indeed the case, so something else must be funky?
• In any case, I don't think it's a great idea to use this 70m long fiber for bringing the light from the PSL table to the adjacent AP table. Chub has ordered a 10m patch cable.
• I was a bit too hasty this morning, thinking we had a patch cable in hand, and so I removed the fiber from the AP table. So right now, the LO beam doesn't make it to the BHD setup. Depending on the lead time for the new patch cable, I may or may not resurrect this old setup.
• I have also located some foam and rigid plastic tubing which I think will help in isolating the fiber from environmental length(phase) modulation due to acoustic pickup.
2. BHD commissioning activities
• Basically, I've been trying to use the Single Bounce ITM reflection/ Michelson / PRMI with carrier locked to get some intuition about the BHD setup. These states are easily prepared, and much easier to understand than the full IFO for these first attempts.
• One concern I have is the angular stability (or lack thereof). When the PRMI is locked, the DC light level on each DCPD fluctuates between ~0 (which is what it should be), up to ~30 cts (~85uW).
• Using the empirically determined attenuation factor between the DCPDs and the dark port of the beamsplitter, I estimate the power can be as high as 20mW. This is a huge number, considering the input to the interferometer is ~800mW. I assume that all the light is at the carrier frequency, since the PRC should reject all the sideband light in this configuration. In any case, the total amount of sideband light is ~20mW, and the carrier stays resonant in the PRC even when there are these large ASDC excursions, so I think it's a reasonable assumption that the light is at the carrier frequency. Moreover, looking at the camera, one can see a clear TEM10/01 profile, indicative of imperfect destructive interference at the beamsplitter due to beam axis misalignment.
• The effect of such excursions on the BHD readout hasn't yet been quantified (by me at least), but I think it may be hampering my attempts to dither the homodyne phase to estimate the LO phase noise.
3. High voltage coil driver project - see thread for updates.
4. Trek HV driver has arrived.
• I haven't opened the box yet, but basically, what this means is that I can dither the mirror intended for homodyne phase control in a reasonable way.
• Previously, I was using the OMC HV driver to drive the PZTs - but this dither signal path has a 2kHz high pass filter (since the OMC length dither is a kHz dither). I didn't want to futz around with the electronics, particularly since the unit was verified to be working.
• So the plan now would be to drive the input of the Trek with a DAC output (an appropriate AI chassis has been prepared to interface with the CDS system).
• Hopefully, there's enough DAC dynamic range to dither the PZT and also do the homodyne phase locking using a single channel. Else, we'd need to use two channels and install a summing amplifier.
• We definitely need more high-voltage amplifiers/supplies in the lab:
• Any Thorlabs HV drivers we can recover?
• Eventually, we will need HV for coil drivers, OMC PZTs, steering PZTs, homodyne phase control PZT.
5. PMC bases have arrived.
• Joe Benson from the machine shop informed me today afternoon that the bases were ready for pickup.
• We have 3 bases in hand now. The finish isn't the greatest in the world, but I think it'll work. You can see some photos here.
• I will hold off on putting this together while I work on the basic airBHD commissioning tests. We can install the PMCs later.
6. AS port WFS project
• We now have in hand almost all the components for stuffing the ISC whitening and LSC demod boards.
• Rich, Chub, Luis and I had a call on Monday. The advise from Rich/Luis was:
• Choose an inductance that has Z~100 ohms at the frequency of interest, for the resonant transimpedance part.
• Choose a capacitance that gives the appropriate resonant frequency.
• Don't stuff more notches than you need - start with just a 2f notch (so 110 MHz for us), and make sure to place the highest frequency notch closest to the photodiode.
• Rich also suggested looking at the optical signal with a non-optimized head, get an idea of what the field content is, and then tune the circuit as necessary. There are obviously going to be many issues that only become apparent once we do such a test.
• The aLIGO modulation frequencies are only 20% different from the 40m modulation frequencies. So I thought it is best if for our first pass, we stick to the inductance values used in the aLIGO circuits (same footprint, known part etc etc). Then, we will change the capacitance so that we have a tuning range that is centered our modulation frequencies.
• The parts have been ordered.
7. ISS project
• Half of the LO light on the BHD breadboard is diverted for the purpose of sensing the LO intensity noise, for eventual stabilization. Right now, it is just getting dumped.
• A PD head has been located. It has a minimalist 1kohm transimpedance amplifier circuit integrated into the head.
• Our AOM driver has an input range of 0-1V DC. We want to map the servo output of +/-10V DC (or +/-4V DC if we use an SR560 based servo for a first pass) to this range.
• I wanted to do this for once in a non-hacky way so I drew up a circuit that I think will serve the purpose. It has been fabricated and will be tested on the bench in a couple of days.
• Once I get a feel for what the signal content is, I will also draw up a interface board to the PD head that (i) supplies the reverse bias voltage and +/-15 V DC to the PD head and (ii) applies some appropriate HPF action and provides a DC monitor as well.
8. Summary pages are dead.
9. General lab cleanup
• I moved all the PPE from the foyer area into the designated cabinets along the east arm.
• Did some basic cleanup of the lab in preparation for crane inspection. Walkways are clear.
• I de-cluttered the office area a bit, but today I received ~10 packages from Digikey/FrontPanelExpress etc. So, in fact, it got even more cluttered. Entropy will go down once we ship these off to screaming circuits for stuffing the PCBs.
15545   Fri Aug 28 23:33:38 2020 gautamUpdateBHDSome more hardware changes

Just a quick set of notes detailing changes so that there are no surprises, more details to follow.

1. Trek driver has been temporarily placed on top of the KEPCO supply east of the OMC electronics rack. Cabling to it has been laid out as well. I turned both off so neither should be energized now.
2. A new AI chassis (and associated cabling including the DAC SCSI cable and +/-24 V DC cable) has been installed in 1X2.
3. To map the DAC range to what the Trek driver wants, I've configured the inverting summing amplifier with gain of 1/8. The offset voltage is set to 5V DC instead of 10V as intended, because the DAC can only drive +/-5 V when connected to a single ended receiving/sending unit.
4. The LO delivery fiber was re-laid, and the interference between the IFO AS beam and LO beams were restored.

I briefly tried some LO PZT mirror dithering tonight, but didn't see the signal. Needs more troubleshooting.

15549   Sat Aug 29 22:46:29 2020 gautamUpdateBHDNew homodyne-phase control electronics

Summary:

The electronics chain used to drive the three elements of the PI PZT on which a mirror is mounted with the intention of controlling the LO phase has been changed, to now use the Trek Mode603 power amplifier instead of the OMC high voltage driver. Attachment #1 shows the new configuration.

Details:

The text of Attachment #1 contains most of the details. The main requirement was to map the DAC output voltage range, to something appropriate for the Trek amplifier. The latter applies a 50V/V gain to the signal received on its input pin, and also provides a voltage monitor output which I hooked up to an ADC channel in c1ioo. The gain of the interfacing electronics was chosen to map the full output range of the DAC (-5 to +5 V for a single-ended receiving config in which one pin is always grounded) to 0-2.5 V at the input of the Trek amplifier, so that the effective high voltage drive range is 0-125 V. I don't know what the damage threshold is for the PI PZT, maybe we can go higher. The only recommendation given in the Trek manual is to not exceed +/-12 V on the input jack, so I have configured D2000396 to have a supply voltage of 11.5 V, so that in the event of electronics failure, we still don't exceed this number.

On the electronics bench, I tested the drive chain, and also measured the transfer function, see Attachment #2. Seems reasonable (the Trek amplifier was driving a 3uF capacitive load used to protect the SR785 measurement device from any high voltage, hence the roll-off). The gain of D2000396 was changed from 1/8 to 1/4 after I realized that the DAC full range is only +/- 5 V when the receiving device is single-ended at both input and output. Maybe the next iteration of this curcuit should have differential sending, to preserve the range.

Testing:

To test the chain, I used the single bounce beam from the ITM, and interfered it with the LO. Clear fringing due to the seismic motion of the ITM (and also LO phase noise) is visible. In this configuration, I drove the PZT mirror in the LO path at a higher frequency, hoping to see the phase modulation in the DCPD output. However, I saw no signal, even when driving the PZT with 50% of the full DAC range. The voltage monitor ADC channel is reporting that the voltage is faithfully being sent to the PZTs, and I measured the capacitance of the PZTs (looked okay), so not sure what is going on here. Needs more investigation.

Update Aug 30 5pm: Turns out the problem here was a flaky elbow connector I used to pipe the high voltage to the PI PZT, it had some kind of flaky contact in it which meant the HV wasn't actually making it to the PZT. I rectified this and was immediately able to see the signal. Played around with the dark fringe Michelson for a while, trying to lock the homodyne phase by generating a dither line, but had no success with a simple loop shape. Probably needs more tuning of the servo shape (some boosts, notches etc) and also the dither/demod settings themselves (frequency, amplitude, post mixer LPF etc). At least the setup can now be worked on interferometrically.

Attachment 2: trekTFs.pdf
15553   Wed Sep 2 00:49:47 2020 gautamUpdateBHDSome notes about homodyne phase

Summary:

Using a heterodyne measurement setup to track both quadratures, I estimated the relative phase fluctuation between the LO field and the interferometer output field. It may be that a single PZT to control the homodyne phase provides insufficient actuation range. I'll also need to think about a good sensing scheme for controlling the homodyne phase, given that it goes through ~3 fringes/sec - I didn't have any success with the double demodulation scheme in my (admittedly limited) trials.

For everything in this elog, the system under study was a simple Michelson (PRM, SRM and ETMs misaligned) locked on the dark fringe.

Details:

​This work was mainly motivated by my observation of rapid fringing on the BHD photodiodes with MICH locked on the dark fringe. The seismic-y appearance of these fringes reminded me that there are two tip-tilt suspensions (SR2, SR3), one SOS (SRM) + various steering optics on seismic stacks (6+ steering mirrors) between the dark port of the beamsplitter and the AS table, where the BHD readout resides. These suspensions modulate the phase of the output field of course. So even though the Michelson phase is tightly controlled by our LSC feedback loop, the field seen by the homodyne readout has additional phase noise due to these optics (this will be a problem for in vacuum BHD too, the question is whether we have sufficient actuator range to compensate).

To get a feel for how much relative phase noise there is between the LO field and the interferometer output field (this is the metric of interest), I decided to set up a heterodyne readout so that I can simultaneously monitor two orthogonal quadratures.

• The idea is that with the Michelson locked, there is no DC carrier field from the interferometer.
• The field incident on the DCPD from the interferometer should be dominated by the 55 MHz sideband transmitted to the dark port given the Schnupp asymmetry.
• The LO field is picked off before any RF sidebands are added to it (the PMC modulation sideband should be suppressed by the cavity transmission).
• Therefore, the LO field should be dominantly at the carrier frequency.
• By placing a broadband RFPD (PDA10CF) in place of one of the DCPDs, I can demodulate the optical beat between this 55 MHz sideband, which shares the same output path to the location of the DCPD as the audio-frequency sidebands on the carrier from the dark Michelson, to estimate the relative phase noise between the LO and IFO output fields.
• The point is that with the heterodyne readout, I can track the fringe wrapping, which is not an option for the BHD readout with two DCPDs, and uncontrolled LO phase.

Attachment #1 shows the detailed measurement setup. I hijacked the ADC channels normally used by the DCPDs (along with the front-end whitening) to record these time-series.

Attachments #2, #3 shows the results in the time domain. The demodulated signal isn't very strong despite my pre-amplification of the PDA10CF output by a ZFL-500-HLN, but I think for the purposes of this measurement, there is sufficient SNR.

This would suggest that there are pretty huge (~200um) relative phase excursions between the LO and IFO fields. I suppose, over minutes, it is reasonable that the fiber length changes by 100um or so? If true, we'd need some actuator that has much more range to control the homodyne phasethan the single PZT we have available right now. Maybe some kind of thermal actuator on the fiber length? If there is some pre-packaged product available, that'd be best, making one from scratch may be a whole project in itself. Attachment #3 is just a zoomed-in version of the time series, showing the fringing more clearly.

Attachment #4 has the same information as Attachment #2, except it is in the frequency domain. The FFT length was 30 seconds. The features between ~1-3 Hz support my hypothesis that the SR2/SR3 suspensions are a dominant source of relative phase noise between LO and IFO fields at those frequencies. I guess we could infer something about the acoustic pickup in the fibers from the other peaks.

Attachment 1: heterodyneMICH.pdf
Attachment 2: unwrappedPhase.pdf
Attachment 3: unwrappedPhase_zoom.pdf
Attachment 4: phaseNoisePSD.pdf
15554   Thu Sep 3 00:00:57 2020 gautamUpdateBHDNew patch cable installed
• 10m PM1064 cable was installed. I tried a double shielding approach (photos tmrw here), but I suspect the real weak point is where the fiber is plugged into the collimator - it's hard to imagine we can stabilize this sort of arrangement to better than 100um absolute length over long periods of time, I'd think thermal/mechanical strains in the fiber will modulate the length by ~mm (?). Anyways, let's see what the heterodyne measurement tells us.
• This work required (i) realignment at the input coupler and (ii) change of position of mode matching lenses in the LO path on the AS table to see any interference with the IFO beam. This indicates something was seriously wrong with the old patch cable, as the collimator should set the mode. The MFD of the two fibers may have been different, but I don't know if that alone can account for it.
• As of now, I have fringes between the ITM single bounce and the LO, but the fringe pk-pk is only 10% of the theoretical pk-pk based on DC values of the LO and AS beams. So the mode matching can be improved significantly (I preivously had ~60%).

To be continued tomorrow. I think it's a good idea to let the newly installed fiber relax into some sort of stable configuration overnight.

15555   Thu Sep 3 15:55:04 2020 gautamUpdateBHDPhase drift between LO and IFO after fiber replacement

Summary:

After replacement of the fiber delivering the LO beam to the airBHD setup (some photos here), I repeated the measurement outlined here. There may be some improvement, but overall, conclusions don't change much.

Details:

The main addition I made was to implement a digital phase tracker servo (a la ALS), to make sure my arctan2 usage wasn't completely bonkers (the CDS block can be deleted later, or maybe it's useful to keep it, we will see). I didn't measure it today, but the UGF of said servo should be >100 Hz so the attached spectrum should be valid below that (loop has not been done, so above the UGF, the control signal isn't a valid representative of the free running noise). Attachment #1 shows the result. The 1 Hz and 3 Hz suspension resonances are well resolved. Anyways, what this means is that the earlier result was not crazy. I don't know what to make of the high frequency lines, but my guess is that they are electronic pickup from the Sorensens - I'm using clip-mini-grabbers to digitize these signals, and other electronics in that rack (e.g. ALS signals) also show these lines.

It is pretty easy to keep the simple Michelson locked for several minutes. Attachment #2 shows the phase-tracker servo output over several minutes. The y-axis units are degrees. If this is to be believed, the relative phase between the two fields is drifting by 12um ove an hour. This is significantly lower than my previous measurement, while the noise in the ~0.5-10 Hz band is similar, so maybe the shorter fiber patch cable did some good?

I think there is also correlation between the PSL table temperature, but of course, the evidence is weak, and there are certainly other effects at play. At first, I thought the abrupt jumps are artefacts, but they don't actually represent jumps >360 degrees over successive samples, so maybe they are indicative of some real jump in the relative phase? Either fiber slippage or TT suspension jumps? I'll double check with the offline data to make sure it's not some artefact of the phase tracker servo. If you disagree with these conclusions and think there is some meaurement/analysis/interpretation error, I'd love to hear about it.

Next steps:

1. Budget the offline inferred phase noise spectrum, overlay a seismic noise model, to see if we can disentangle the contributions from the suspensions and that from the LO fiber.
2. I'll see if I can setup an LO pickup with some RF sidebands on it in parallel to this setup so we can try some of the ideas discussed on the call this week. There are several beams available, but the question is whether I can get this into a fiber without 1 week of optical layout work.

I have left the heterodyne electronics setup at the LSC rack, but it is not powered (because there are some exposed wires). Please leave it as is.

Attachment 1: LOphaseDrift.pdf
Attachment 2: phaseDrift_tempCorr.png
15562   Mon Sep 7 23:49:14 2020 gautamUpdateBHDA first look at RF44 scheme

Summary:

Over the last couple of days, I've been working towards getting the infrastructure ready to test out the scheme of sensing (and eventually, controlling) the homodyne phase using the so-called RF44 scheme. More details will be populated, just quick notes for now before I forget.

• LO beam with RF sidebands needed to be re-coupled into collimator, it wasn't seated tightly and just touching the fiber completely destroyed the alignment.
• HWP installed before said collimator - IMC wants s-polarized light whereas the IFO field is p-polarized.
• After my work, the numbers were: ~1.47mW input to collimator, ~1.07mW out of collimator on AS table, ~1mW making it to the BHD board. All seem like reasonable numbers to me.
• 44 MHz signal synthesis - for now, I use a Marconi (10 MHz synced to Rb clock), I think we could also use a mixer+SLP50 to mix 11 and 55 MHz signals (which are easily available at the LSC rack) to generate this. I looked at Wenzel quadruplers, the specs don't suggest a quadrupler will do much better.
• CDS model was modified to accept the phase-tracker output as an error signal for the homodyne phase control servo. Compile and install went smooth but I opted against a model restart tonight, I'll do it tmrw.
• Some trials were done with the Michelson locked to a dark fringe (as was done for the case of the DC LO field beating with the 55 MHz sideband). While the overall spectrum lines up fairly well with earlier trials, the signal looks somewhat more "discontinuous" in its traversal of I/Q space, and it never quite goes to 0. Some offset? What does this mean for locking? More investigations needed....
15563   Tue Sep 8 01:31:43 2020 KojiUpdateBHDA first look at RF44 scheme

- Loose fiber coupler: Sorry about that. I could not detect something was loose there, although some of the locks were not tightened.

- S incident instead of P: Sorry about that too. I completely missed that the IMC takes S-pol.

15565   Wed Sep 9 00:05:18 2020 gautamUpdateBHDMore notes on the RF44 scheme

Summary:

1. With the Michelson locked on a dark fringe, the f2-f1 signal at ~44 MHz does not seem to ever vanish, it seems to bottom out at ~2mV DC. Is this just an electronics offset? Not sure of the implications on using this as a locking signal for the homodyne phase yet.
2. The inferred relative phase fluctuations between the LO and RF fields using this 44 MHz signal is consistent with that from previous tests.
3. The laying out of the new, shorter, fiber patch cable seems to have helped to reduce the phase drift over minute time scales.
4. So far, I have not had any success in using the 44 MHz signal to close a servo loop and keep the homodyne phase locked for more than a few seconds at a time, and even then, the loop shape is sub-optimal as the in-loop error signal is not clean. Maybe some systematic loop shaping will help, but I think the dynamic range requirement on the actuator is too high, and I'm not sure what to make of the fact that the error signal does not vanish.

Details:

Attachment #1 shows the optical setup currently being used to send the LO field with RF sidebands on it to the air BHD setup.

• You can find a video of the large power fluctuations mentioned in my previous elog here. After tightening the collimator in the mount, the arrangement is still rather sensitive, but at least I was able to see some light on the DCPD on the AS table, at which point I could use this signal and tweak the alignment to maximize it.
• It is well known that the input beam to the IMC drifts during the day, either due to temperature fluctuations / PMC PZT stroke L2A / some other reason (see Attachment #4 for the power drift over ~12 hours, it is not monotonic with temperature). The fact that our collimating setup is so sensitive to the input pointing isn't ideal, but I noticed the power had only degraded by ~5% today compare to yesterday, so maybe the occassional touch up is all that is required.

Attachment #2 shows spectra of the relative phase drift between LO and IFO output field (from the Dark Michelson).

• I still haven't overlaid a seismic model. There was some discussion about the TTs having a 1/f roll-off as opposed to 1/f^2, I don't know if there was any characterization at the time of installation, but this SURF report seems to suggest that it should in fact be 1/f^2 because the passive eddy current dampers are mounted to the main suspension cage on springs rather than being rigidly attached.
• The noise at ~100 Hz is ~x2 higher if the spectra is collected during the daytime, when the seismic activity is high. Although this shouldn't really matter at 100 Hz?
• There are also huge power-line harmonics - I suspect these are making it difficult to close a feedback loop, as I couldn't add a 60 Hz comb which doesn't affect the loop stability for a UGF of ~30-50 Hz. But if they aren't notched out, the control signal RMS is dominated by these frequencies.

Attachment #3 shows the signal magntiude of the signals used to make the spectra in Attachment #2, during the observation time (10 minutes) with which the spectra were computed. The dashed vertical lines denote the 1%, 50% and 99% quantiles.

• Koji asked me about the 55 MHz signal and why it doesn't vanish - for the dark Michelson, where the ITMs don't apply any relative phase on reflection to the carrier and RF sideband fields, we expect that the upper and lower sidebands cancel, and so there should be no intensity modulation at 55 MHz (just like we don't expect any for a pure phase modulated light field incident on a photodiode).
• However, from the I/Q demodulated data that is collected, it would appear that while the size of the signal does vary, it doesn't ever completely vanish. This implies some asymmetry in the sidebands (or at least, the transmission of the sidebands by the Michelson). I didn't estimate the effect of the Schnupp asymmetry, or if this asymmetry is coming from elsewhere, but the point is that for the conclusions drawn from Attachment #2 remain valid even though both the amplitude and phase of the 55 MHz signal is changing.
• I also plot the corresponding histogram for the 44 MHz signal. You can see that it never goes to 0 (once I fix the x-label ticks). I don't know if this is consistent with some electronics offset.

Attempts to close a feeddback loop to control the homodyne phase:

• A digital PLL (a.k.a. Phase Tracker) servo was used to keep the demodulated 44 MHz signal in one (demodulated) quadrature, which can then be used as an error signal.
• Unlike the ALS case, the quantity to be servoed to 0 is the magnitude of the 44 MHz signal, and not its phase, so that's how I've set up the RTCDS model.
• I played around with the loop shape to try and achieve a stable lock by actuating on the PZT mounted mirror in the LO path - however, I've not yet had any success so far.
Attachment 1: IMG_3397.JPG
Attachment 2: phaseNoisePSD.pdf
Attachment 3: magnitudeHist.pdf
Attachment 4: LOpowerDrift.png
15567   Thu Sep 10 15:43:22 2020 JonUpdateBHDInput noise spectra for A+ BHD modeling

As promised some time ago, I've obtained input noise spectra from the sites calibrated to physical units. They are located in a new subdirectory of the BHD repo: A+/input_noises. I've heavily annotated the notebook that generates them (input_noises.ipynb) with aLOG references, to make it transparent what filters, calibrations, etc. were applied and when the data were taken. Each noise term is stored as a separate HDF5 file, which are all tracked via git LFS.

So far there are measurements of the following sources:

• L1 SRCL
• H1 SRCL
• L1 DHARD PIT
• L1 DSOFT PIT
• L1 CSOFT PIT
• L1 CHARD PIT

These can be used, for example, to make more realistic Hang's bilinear noise modeling [ELOG 15503] and Yehonathan's Monte Carlo simulations [ELOG 15539]. Let me know if there are other specific noises of interest and I will try to acquire them. It's a bit time-consuming to search out individual channel calibrations, so I will have to add them on a case-by-case basis.

15569   Mon Sep 14 07:50:01 2020 YehonathanUpdateBHDMonte Carlo Simulations

Turns out what was causing the instability in the aLIGO plots were the lock commands which I forgot to remove before running the simulation. Removing these also made the simulation much faster.

Other than that I improved other stuff in the simulations:

• The LO phase in the aPlus simulation is now optimized for the lowest noise at 100Hz.
• Added RF PDs diagnostics (see attachments 8 for aPlus and 9 for aLIGO). The thresholds (red dashed lines in attachments 8,9) for cutting marginal simulations are set such that roughly 30% of the simulations are discarded.
• Removed DHARD because it jacks up the RF PD readings in aPlus for some reason.
• Fixed the sign of laser frequency shift in response to CARM offset.

Still need to do:

• Incorporate Jon’s noise curves.
• Add phase noise for LO beam.
• Add arm reflectivity imbalance.
• Add mirror curvature imbalance.
• Include feedback loops using Pytickle.

Feel free to add to the todo list.

Attachment 1: MICH_AplusMCMC.pdf
Attachment 2: PRCL_AplusMCMC.pdf
Attachment 3: SRCL_AplusMCMC(1).pdf
Attachment 4: OMC_Comm_AplusMCMC.pdf
Attachment 5: OMC_Diff_AplusMCMC.pdf
Attachment 6: OMC_Angle_Yaw_AplusMCMC.pdf
Attachment 7: OMC_Angle_Pitch_AplusMCMC.pdf
Attachment 8: Main_Laser_RIN_AplusMCMC.pdf
Attachment 9: aPlus_RF_Diagnostics.pdf
Attachment 10: aLIGO_RF_Diagnostics.pdf
15575   Tue Sep 15 22:11:52 2020 gautamUpdateBHDMore notes on the RF44 scheme

Summary:

After more trials, I think the phase tracker part used to provide the error signal for this scheme needs some modification for this servo to work.

Details:

Attachment #1 shows a block diagram of the control scheme.

I was using the "standard" phase tracker part used in our ALS model - but unlike the ALS case, the magnitude of the RF signal is squished to (nearly) zero by the servo. But the phase tracker, which is responsible for keeping the error signal in one (demodulated) quadrature (since our servo is a SISO system) has a UGF that is dependent on the magnitude of the RF signal. So, I think what is happening here is that the "plant" we are trying to control is substantially different in the acquisition phase (where the RF signal magnitude is large) and once the lock is enabled (where the RF signal magnitude becomes comparitively tiny).

I believe this can be fixed by dynamically normalizing the gain of the digital phase tracking loop by the magnitude of the signal = sqrt(I^2 + Q^2). I have made a modified CDS block that I think will do the job but am opting against a model reboot tonight - I will try this in the daytime tomorrow.

I'm also wondering how to confirm that the loop is doing something good - any ideas for an out-of-loop monitor? I suppose I could use the DCPD - once the homodyne phase loop is successfully engaged, I should be able to drive a line in MICH and check for drift by comparing line heights in the DCPD signal and RF signal. This will requrie some modification of the wiring arrangement at 1Y2 but shouldn't be too difficult...

The HEPAs, on the PSL table and near ITMY, were dialled down  / turned off respectively, at ~8pm at the start of this work. They will be returned to their previous states before I leave the lab tonight.

Attachment 1: RF44.pdf
15579   Fri Sep 18 10:47:48 2020 gautamUpdateBHDSensing scheme for homodyne phase

eSummary:

I don't think the proposed scheme for sensing and controlling the homodyne phase will work without some re-thinking of the scheme. I'll try and explain my thinking here and someone can correct me if I've made a fatal flaw in the reasoning somewhere.

Field spectrum cartoon:

Attachment #1 shows a cartoon of the various field components.

• The input field is assumed to be purely phase modulated (at 11 MHz and 55 MHz) creating pairs of sidebands that are in quadrature to the main carrier field.
• The sideband fields are drawn with positive and negative imaginary parts to indicate the relative negative sign between these terms in the Jacobi-Anger expansion.
• For our air BHD setup, the spectrum of the LO beam will also be the same.
• At the antisymmetric (= dark) port of the beamsplitter, the differential mode signal field will always be in the phase quadrature.
• I'm using the simple Michelson as the test setup:
• The ITMs have real and (nearly) identical reflectivities for all frequency components incident on it.
• The sideband fields are rotated by 90 degrees due to the i in the Michelson transmission equation.
• The Schnupp asymmetry preferentially transmits the 55 MHz sideband to the AS port compared to the 11 MHz sideband - note that in the simple Michelson config, I calculate T(11 MHz) = 0.02%, T(55 MHz) = 0.6% (both numbers not accounting for the PRM attenuation).
• I think the cartoon Hang drew up is for the DRFPMI configuration, with the SRC operated in RSE.
• The main difference relative to the simple Michelson is that the signal field picks up an additional 90 degrees of phase propagating through the SRC.
• For completeness, I also draw the case of the DRFPMI where the SRC is operated at nearly the orthogonal tuning.
• I think the situation is similar to the simple Michelson

So is there a 90 degree relative shift between the signal quadrature in the simple Michelson vs the DRFPMI? But wait, there are more problems...

Closing a feedback loop using the 44 MHz signal:

We still need to sense the 44 MHz signal with a photodiode, acquire the signal into our CDS system, and close a feedback loop.

• The 44 MHz signal is itself supposed to be generated by the interference between the TEM00 55 MHz sideband from the IFO output with the TEM00 11 MHz sideband from the LO field (let's neglect any mode mismatch, HOMs etc for the moment).
• By splitting this beat signal photocurrent in two, mixing each part with an electrical 44 MHz signal, and digitizing the IF output of said mixers, we should in principle be able to reconstruct the magnitude and phase of the signal.
• The problem is that we know from other measurements that this signal is going to go through multiple fringes, and hence, we don't have a signal that is linear in the quantity we would like to control, namely the homodyne phase (either quadrature signal can be a candidate linear signal around a zero crossing, but when the signals are going through multiple fringes, neither signal stays linear).
• One possible way to get around this problem is to use a phase tracker servo - basically, close a purely digital feedback loop, using one of the demodulated quadratures as an error signal, and changing the demodulation phase digitally such that the signal stays entirely in the orthogonal quadrature. However, such a scheme relies on the signal magnitude remaining constant. If the "error signal" goes to zero for multiple reasons (rotation out of the quadrature being considered, or just that the signal itself goes to zero), then this technique won't work. Of course, the phase tracker doesn't know what the "phase" of the signal is, when it's magnitude is (nearly) zero.
• It is true that we always expect a "background" level of 44 MHz signal, from the 11 MHz and 55 MHz sidebands in the LO beam directly interfering, but this doesn't contain any useful information, and in fact, it'd only contaminate the phase tracker error signal I think.
• So we can't rely on the error staying in one quadrature (like we do for the regular IFO PDH signals, where there is no relative phase propagation between the LO and RF sideband optical fields and so once we set the demodulation phase, we can assume the signal will always stay in that quadrature, and hence we can close a feedback loop), and we can't track the quadrature. What to do? I tried to dynamically change the phase tracker servo gain based on the signal magnitude (calculated in the RTCDS code using sqrt(I**2 + Q^2), but this did not yield good results...

Next steps:

I don't have any bright ideas at the moment - anyone has any suggestions?🤔

Aside:

I wanted to check what kind of signal the photodiode sees when only the LO field is incident on the photodiode. So with the IFO field blocked, I connected the PDA10CF to the Agilent analyzer in "Spectrum" mode, through a DC block. The result is shown in Attachment #2. To calculate the PM/AM ratio, I assumed a modulation depth of 0.2. The RIN was calculated by dividing the spectrum by the DC value of the PDA10CF output, which was ~1V DC. The frequencies are a little bit off from the true modulation frequencies because (i) I didn't sync the AG4395 to a Rb 10 MHz signal, and (ii) the span/BW ratio was set rather coarsely at 3kHz.

I would expect only 44 MHz and 66 MHz peaks, from the interference between the 11 MHz and 55 MHz sideband fields, all other field products are supposed to cancel out (or are in orthogonal quadratures). This is most definitely not what I see - is this level of RIN normal and consistent with past characterization? I've got no history in this particular measurement.

Attachment 2: PMAMratio.pdf
15596   Tue Sep 22 22:38:11 2020 gautamUpdateBHDSensing scheme for homodyne phase - some analytic calcs

I got some feedback from Koji who pointed out that the phase tracker is not required here. This situation is similar to the phase locking of two lasers together, which we frequently do, except in that case, we usually we offset the absolute frequencies of the two lasers by some RF frequency, and we demodulate the resulting RF beatnote to use as an error signal. We can usually acquire the lock by simply engaging an integrator (ignoring the fact that if we actuate on the laser PZT, which is a frequency actuator, just a proportional feedback will be sufficient because of the phase->frequency conversion), the idea being that the error signal is frequently going through a zero-crossing (around which the sinusoidal error signal is approximately linear) and we can just "catch" one of these zero crossings, provided we don't run of actuation range.

So the question here becomes, is the RF44 signal a suitable error signal such that we can close a feedback loop in a similar way? To try and get more insight, I tried to work out the situation analytically. I've attached my thinking as a PDF note. I get some pretty messy complicated expressions for the RF44 signal contributions, so it's likely I've made a mistake (though Mathematica did most of the heavy lifting), it'll benefit from a second set of eyes.

Anyways, I definitely think there is some additional complications than my simple field cartoon from the preceeding elog would imply - the relative phases of the sidebands seem to have an effect, and I still think the lack of the PRC/SRC make the situation different from what Hang/Teng et. al. outlined for the A+ homodyne phase control analysis. Before the HEPA failed, I had tried closing the feedback loop using one quadrature of the demodulated RF44 signal, but had no success with even a simple integrator as the loop (which the experience with the PLL locking says should be sufficient, and pretty easily closed once we see a sinusoidally oscillating demodulated error signal). But maybe I'm overlooking something basic conceptually?

 Quote: eSummary: I don't think the proposed scheme for sensing and controlling the homodyne phase will work without some re-thinking of the scheme. I'll try and explain my thinking here and someone can correct me if I've made a fatal flaw in the reasoning somewhere.
Attachment 1: simpleMich.pdf.zip
15611   Mon Oct 5 00:37:19 2020 gautamUpdateBHDSingle bounce interferometer locked

Summary:

The simple interferometer, composed of a single bounce reflection from ITMY and the LO beam deilvered via fiber to the AS table, can be locked - i.e. the phase of the LO beam can be controlled such that the DC light level on the DCPDs after the two beams are interfered can be stabilized. This test allows us to confirm that various parts of the sensing and actuation chain (e.g. PI PZT for homodyne phase control, Trek amplifier etc etc) are working.

I will post more quantitative analysis tomorrow.

Optical configuration:

• LO beam is a pickoff of the main PSL beam from just before it goes into the vacuum. The optical power arriving on each DCPD after the various beamsplitters, coupling loss etc is ~200 uW.
• IFO beam is the single bounce reflection from ITMY. For this test, ETMY, ITMX and ETMY are misaligned. Optical power arriving on each DCPD is ~80uW.
• The two beams are interfered on a 50-50 beamsplitter. The mode-matching efficiency was estimated to be ~50% which isn't stellar, but should be fine for this test.
• So, at half-fringe, we expect the signal on each DCPD to be linearly proportional to the phase difference between the two fields, and so we can use that as an error signal.

Servo topology:

Attachment #2 shows the servo topology.

• For a first attempt to close the feedback loop, we can consider the two blocks labelled "Sensing Chain" and "Actuation chain" to have a flat frequency response. While this isn't true, for a taget loop with ~100 Hz UGF, I think the approximation is reasonable.
• From the peak-to-peak value (160 cts) of the DCPD signals when the homodyne phase is uncontrolled, I estimate a sensing response (at half-fringe) of approximately 0.3 ct/nm, since this corresponds to 532nm of relative phase between the two beams.
• An inverting summing amplifier is used to map the +/- 2^15 ct DAC range to 0-125V on the PI PZT. Assuming the full stroke of the PZT is 10um per the datasheet, and that this voltage range drives half of the full stroke (this is just a guess since all the old PI PZT circuits were designed to work at 0-250 V), we get an actuation coefficient of 0.075 nm/ct.
• Using these two numbers, we can then design a digital feedback loop that gives an open loop transfer function with ~100 Hz UGF, and sufficient stability margin.
• From the earlier measurements, we have an estimate for the amount of phase fluctuations caused by (i) seismic disturbances and (ii) fiber phase noise. This is the quantity we wish to suppress, and the suppression factor will be 1/(1+L), where L is the open loop gain.
• I didn't do this in any systematic way, but the loop in Attachment #3 seemed like a reasonable shape that would suppress the error signal RMS by ~10x, as shown in Attachment #4. So I decided to try this out.

Other notes:

1. The idea of offloading the DC control voltage to the ITMY suspension seemed to work fine.
2. It also seems like the relative phase between the two beams doesn't drift by so large an amount in short time scales, at least at night/quiet seismic conditions. So it is possible to maintain the lock for several seconds without having to offload the DC signal to the suspensions.
3. I didn't bother adapting the FSS Slow PID script to do this offloading in an automated way, seemed like more trouble than was just doing it by hand. But we may want to automate this in the future.
4. I couldn't make a clean measurement of the loop transfer function using the usual IN1/IN2 method. Introducing a step offset at the error point, the servo is able to track it (I didn't fit the step response time, but it's not as if the loop bandwidth is <1 Hz or something). I have to compare the measured in-loop error signal ASD to the free-running one to get a feel for what the UGF is, I guess, to rule out a weird loop.
5. Update 1100 Oct 6 2020: I have now added measured, in-loop, error point spectra to Attachment #4. Looks like there might be significant sensing noise re-injection.
• Initially, I forgot to turn the HEPA on the PSL down for the measurement. So I have the two traces to compare. Looks like with the HEPA turned up to full, there is more noise in the 50-200 Hz range.
• The trace marked "highGain" was taken with an overall loop gain that was 3dB higher than the nominal value - I could see some oscillations start to appear, and in the spectrum, maybe the feature at ~150 Hz is evidence of some gain peaking?

Conclusions:

1. The PI PZT seems to work just fine.
2. Need to look into the loop shape. I guess it's not reasonable to expect a UGF much higher than 100-200 Hz, because of the various delays in the system, but maybe the low frequency suppression can be made better.
3. What are the next steps?? What does this mean for the RF44 sensing scheme?
Attachment 1: simpleHomodyne.png
Attachment 2: singleBounceIFO.pdf
Attachment 3: proposedController.pdf
Attachment 4: freeRunningSuppressed.pdf
15612   Mon Oct 5 00:53:16 2020 KojiUpdateBHDSingle bounce interferometer locked

🤘🤘🤘

15623   Tue Oct 13 11:13:54 2020 gautamUpdateBHDInvestigation into RF44 sensing

Attachment #1: spectra of the phase noise between LO and IFO output fields sensed using the RF44 signal.

• Measurement setup:
• LO an IFO fields are combined on a beamsplitter, with ~60% mode-matching efficiency.
• One port of the BS goes to a DCPD.
• The other port goes to an RF sensing photodiode, PDA10CF. The spec-ed dark noise NEP is ~12 pW/rtHz at 1.6 um, (so let's say 25 pW/rtHz) and transimpedance is 5kohms into a 50 ohm load. We can convert this to an equivalent sensing noise at the error point of this loop, though it's more likely that the electronics (demod, ADC etc) noise downstream dictate the sensing limit, which I measure by blocking light on the photodiode.
• The demodulation is done on one of the newly received D0902745 boards - this was just a more compact setup than many cascaded minicircuit components. We don't have the hardware to package this into a chassis to shield against electronics noise pickup yet, so I'm using a bench supply to power this for now (via a voltage regulation board, D1000217.
• "Dark Noise" = ASD with no light incident on the photodiode. "LO field only" = ASD with only the LO field incident on the photodiode.
• The "Dark noise" trace and "LO field only" traces are converted from cts/rtHz to rad/rtHz by noting that when the Michelson is locked on a dark fringe, the demodulated RF44 quadratures have a pk-pk amplitude of ~160 cts (corresponding to pi radians of phase shift). Since in these conditions the demodulated quadratures do not undergo any fringe wrapping, I converted the spectra by simple multiplication.
• For the "RF44 open loop" trace:
• The DC offset in the demodulated signal (due to the RF44 signal from the LO field only) is digitally compensated, so that the fringing has (roughly) zero offset.
• The Michelson was locked on a dark fringe, and the demodulated RF44 quadratures were monitored for ~5 mins. Then arctangent (specifically, arctan2 to get the correct quadrant in the IQ plane) of the two signals was taken to convert the fringing signals to phase noise.

Closing a feedback loop:

• Since it seems like we are sensing a signal (below ~1kHz at least), I tried to close a feedback loop (modelled loop shape shown in Attachment #2, it's just a model because I have to guess what the sensing and actuation gains are, and they're both assumed to be flat, digital delays etc aren't accounted for). I've also added the inferred loop gain by taking the ratio of the in loop and unsuppressed ASDs (though of course I don't account for the flat sensing noise at higher frequencies). At least qualitatively, things line up...
• While I can get the light level on the DCPD to stabilitze somewhat, the loop is not at all stable, and the suppression isn't very good at all.
• Not sure how meaningful any of the spectra with the loop closed are, but FWIW, I've put in the spectra of the demodulated RF44 signals with the loop engaged (RF44 Q is used as the error signal). A clear problem is evident at ~120 Hz, and the forest of lines isn't helping for sure. Also unclear to me why the I and Q signals don't have the same profile at low frequencies.

Conclusions/Questions:

1. What is the reason for the huge forests of lines in the "RF44 open loop" ASD, that are absent in the other two traces? If this were electrical pickup, it should be there in all three traces?
2. Is the shape of the spectrum reasonable? The roll-off above ~5 Hz doesn't seem quite steep enough to be seismic noise from the suspensions. Can it really be that the Michelson dark field has such high phase noise?
3. How can we get this scheme to give us cleaner sensing?
4. The actuation chain was verified to work fine with the single bounce beam from an ITM interfered with the LO field, and using the DC light level as an error signal and locking to the half-fringe point. So the problem is not due to insufficient actuation range. Seems like the error signal is so polluted with these forests of lines that even though there is some suppression of the error signal at low frequencies, the unsuppressed noise is still significant. I can't solve the problem by simply increasing the loop gain...
5. It is not shown here, but with only the LO field incident on the RFPD, I see a drift of the demodulated signals on the ~5 minute timescale - is this just due to fiber length change? If so, this is potentially problematic, as on long time scales, the true zero of the error point of the servo would be changing on the ~5 minute timescale. This would be true even for the final suspended scheme - if the path length between PR2 and the homodyne BS changes by some microns, we would have to correct this at DC?
Attachment 1: phaseNoisePSD.pdf
Attachment 2: loopTF.pdf
15628   Thu Oct 15 10:42:39 2020 gautamUpdateBHDMore investigation into RF44 sensing

Summary of discussion between Koji and gautam on 14 Oct:

1. Koji questioned the accuracy of the "open loop" ASD shown here. While it may not be entirely accurate to compute the free-running (homodyne) phase noise simply by taking the arctangent of the I and Q signals (because the magnitude of the signal is also changing), gautam claims the estimate is probably still close to the true homodyne phase, especially since the ratio of the "in-loop" and free-running ASDs gives something that closely approximates the magnitude of the supposed OLG of the system.
2. Koji suggested the following tests:
• Investigate the relative stability of the two RF signal generators involved in this system. Since the 44 MHz electrical LO signal (for demodulation) is generated by a separate IFR from the one used to imprint 11 MHz and 55 MHz phase modulation sidebands on the main PSL beam, we want to investigate what the drift is.
• Try implementing an analog feedback loop using LB1005 - the idea being we should be able to implement higher bandwidth control, for better suppression of the high frequency noise (which looking at the ASD is not only due to seismic phase modulation of the IFO output field). Maybe some combination of this and the Marconi investigation would suggest why we have these forests of lines in the ASDs of the error signal?
• Turn off the HEPAs on the PSL enclosure completely as a test, to see if that improves (i) phase noise due to air currents and (ii) mechanical pickup on the fiber producing  phase noise.

I tried all of these last night / overnight, here are my findings.

Analog locking of the homodyne phase:

See Attachment #1

• RF44_I was used as the error signal.
• The "C1:OMC-ZETA_IMON_OUT" channel is actually looking at the error signal monitor from the LB1005, and is uncalibrated in this plot.
• The "monitor" port on the demodulator board provides a convenient location for us to route the demodulated signal to an LB1005 box, while simultaneously digitizing both demodulated quadratures.
• Empirically, I found settings that could engage the lock. I also found that I couldn't increase the gain much more without destroying the lock.
• The time domain signals look much "cleaner" in this analog feedback loop than when I achieved similar stabilization using the digital system. But I will quantify this more when I post some spectra of the in loop error signals.
• I will do some more characterization (loop TF measurement, error point spectrum in lock etc), but in summary, it looks like we still only have ~100 Hz UGF. So something in the loop is limiting the bandwidth. What could it be?
• The main problem is that the LB1005 isn't well suited to remote enabling/disabling of the lock, so this isn't such a great system.

Relative stability of two IFR2023s synchronized to the same FS725 Rb standard:

The electrical LO signal for demodulation of the 44 MHz photocurrent is provided by an IFR2023 signal generator. To maintain a fixed phase relation between this signal, and the phase modulation sidebands imprinted on the interferometer light via a separate IFO2023 signal generator, I synchronize both to the same Rb timing standard (a 10 MHz signal from the FS725 is sent to the rear panel frequency standard input on the IFR). We don't have a direct 44 MHz electrical signal available from the main IFO Marconi at the LSC rack (or anywhere else for that matter). So I decided to do this test at 55 MHz.

• RF input of the demodulator was driven by 5*11.066209 MHz pickoff from the LSC rack.
• LO input of the demodulator was driven by 5*11.066209 MHz signal from the IFR2023 used for the RF44 demodulation setup.
• The outputs were monitored overnight. The RF44_Q channel had a DC level of nearly 0. So this channel is nearly a linear sensor of the phase noise between LO and RF signals.
• To convert ADC counts to radians, I offset the LO Marconi frequency by 100 Hz, and saw that the two quadratures showed pk-pk variation of ~24000cts. So, at the zero crossing, the conversion is 1/(24000/2) rad/ct ~83urad/ct.
• The result is shown in Attachment #2. The "measurement noise" trace corresponds to the RF. input of the demodulator being terminated to ground with a 50 ohm terminator.
• For comparison, I also overlay the phase noise estimate of an individual IFR from Rana. In his investigation, the claim is that the PLL that locks the IFR to the Rb timing standard has ~1kHz UGF, but if my measurement is correct, the relative stability between the two signal generators synchronized to the same timing standard already. degrades at ~1 Hz. Could be just a cts/rad calibration error I guess.
• In any case, we are far from saturating this limit in the homodyne phase lock.
• There are several sharp lines in this measurement too - but I don't know what exactly the source is. Of course the two marconis are plugged into separate power strips, so that may explain the 60 Hz lines and harmonics, but what about those that aren't a multiple of 60 Hz?

A look at the time domain signal:

With the Michelson locked on the dark fringe, the RF44 I and Q signals in the time domain are shown in Attachment #3 for a 1 minute stretch.

• The RF44 signal level bottoms out at ~40 cts. Okay, so this is the offset.
• However, the maximum value of the RF44 signal amplitude seems to be modulated in time. How can we explain this?
Attachment 1: analogZetaLock.png
Attachment 2: relPhaseNoise.pdf
Attachment 3: sigMagPhase.pdf
15631   Fri Oct 16 09:16:37 2020 YehonathanUpdateBHDMonte Carlo Simulations

Pushed another update to MCMC simulation. This includes:

• Added new imbalances: ITM transmission, ITM & ETM RoCs.
• Added new static offsets: DHARD, DSOFT, CHARD, CSOFT. All pitch. The RMS is calculated from the data Jon fetched with /input_noises/input_noises.ipynb.
• SRCL noise ASD and RMS are now taken from data in /input_noises.
• RF PD diagnostics were redone: Instead of post-discarding marginal simulations, simulations are now discarded when one or more of the RF PDs demodulated signal does not cross zero when the associated DOFs are scanned by 1um in the offset state.

The DOFs<->RFPD associations I use are:

 DARM AS_f2_I CARM REFL_f1_I MICH POP_f2_Q PRCL POP_f1_I SRCL REFL_f2_I

However, one thing that bothers me is that for some reason ~ 15 out of 160 aLigo simulations are discarded while none for A+. It can also be seen that the A+ simulations are more spread-out which might be related.

The new simulation results are attached.

Attachment 1: MICH_AplusMCMC.pdf
Attachment 2: PRCL_AplusMCMC.pdf
Attachment 3: SRCL_AplusMCMC.pdf
Attachment 4: OMC_Comm_AplusMCMC.pdf
Attachment 5: OMC_Diff_AplusMCMC.pdf
Attachment 6: OMC_Angle_Yaw_AplusMCMC.pdf
Attachment 7: OMC_Angle_Pitch_AplusMCMC.pdf
Attachment 8: Main_Laser_RIN_AplusMCMC.pdf
15637   Thu Oct 22 11:48:08 2020 YehonathanUpdateBHDMonte Carlo Simulations

I found this H1 alog  entry by Izumi confirming that the calibrated channels CAL-CS_* need the same dewhitening filter.

This encouraged me to download the PRCL and MICH data and using Jon's example notebook. I incorporated these noise spectra into the MCMC simulation. The most recent results are attached.

I am still missing:

• Laser frequency noise
• Laser RIN
• Estimation of the LO phase noise
• Estimation of the BHD breadboard angular noise

Also, now the MCMC repeats a simulation if it doesn't pass the RF PDs test so the number of valid simulations stays the same. I'm still not sure about why the A+ simulations are much more robust to these tests than aLigo simulations.

Attachment 1: MICH_AplusMCMC.pdf
Attachment 2: PRCL_AplusMCMC.pdf
Attachment 3: SRCL_AplusMCMC.pdf
Attachment 4: OMC_Comm_AplusMCMC.pdf
Attachment 5: OMC_Diff_AplusMCMC.pdf
Attachment 6: OMC_Angle_Yaw_AplusMCMC.pdf
Attachment 7: OMC_Angle_Pitch_AplusMCMC.pdf
Attachment 8: Main_Laser_RIN_AplusMCMC.pdf
15684   Mon Nov 23 12:25:14 2020 gautamUpdateBHDBHD MMT Optics delivered

Optics --> Cabinet at south end (Attachment #1)

Scanned datasheets--> wiki. It would be good if someone can check the specs against what was ordered.

Attachment 1: IMG_8965.HEIC
ELOG V3.1.3-