Plotte below are the resultant subtractions for YARM using different witness configurations,

The best subtraction happens with all the channels of both the GUR1 and T240 seismometers, but one gets just as good subtraction without using the z channels as witnesses. 

Also, why is the T240 seismometer better at subtracting noise for YARM compared to what GUR1 alone can acomplish? Using only the X and Y channels for the T240 gave the third best subtraction(purple trace). 

My plan for now is as follows:

1) Measure the transfer function from the ETMY actuator to the YARM control signal

2) Collect data for YARM when FF for MCL is on in order to see what kind of subtractions can be done.

- IMC PDH demodulation phase adjustment

- Permanent setup for green transmission DC PDs  on the PSL table

Suresh reported to Den, who reported to me (although no elogs were made.....) that something was funny with the FB.  I went to look at it, and it's actually the RAID array rebuilding itself.  I have called in our guru, Jamie, to have a look-see.

The RAID (JetStor SATA 416S) is indeed resyncing itself after a disk failure.  There is a hot spare, so it's stable for the moment.  But we need a replacement disk:

    RAID disks:  1000.2GB Hitachi HDT721010SLA360

Do we have spares?  If not we should probably buy some, if we can.  We want to try to keep a stock of the same model number.

Other notes:

The RAID has a web interface, but it was for some reason not connected.  I connected it to the martian network at 192.168.113.119.

Viewing the RAID event log on the web interface silences the alarm.

I retrieved the manual from Alex, and placed it in the COMPUTER MANUALS drawer in the filing cabinet.

 Alex logged in around 10:30 this morning and, at our request, adjusted the configuration of fb40m to have 20 days of lookback.

I wasn't able to get him to elog, but he did email the procedure to us:

1) create a bunch of new "Data???" directories in /frames/full
2) change the setting in /usr/controls/daqdrc file
       set num_dirs=480;

my guess is that the next step is:

3) telnet fb0 8087

    daqd>  shutdown

I checked and we do, in fact, now have 480 directories in /frames/full and are so far using up 11% of our 13TB capacity. Lets try to remember to check up on this so that it doesn't get overfull and crash the framebuilder.

There were 2 open outputs on the splitter in the RAMmon (formerly known as Stochmon) box underneath the BS oplev table.  The input to the splitter comes from the Thorlabs PD that we're using as our RAM monitoring PD.  2 of the outputs go to the RMS detection of 11 and 55 MHz.  Now the other 2 (previously terminated) outputs go over to the LSC rack via SMA cable.  The signal on both channels is ~200mV pk-pk, so -10dBm.  One is plugged into the AS11 demod board (which didn't have a PD input yet), and the other goes to POP55's demod board, so POP55 is not what you think it is for now.

Koji is working on checking out the Rich box, which has 4 demodulators, which we will use eventually.  Right now we're just using the already-plugged-in demod boards so we can start looking at some trends of RAM.  We're going to need to find some channels when we're ready for the switchover.

Zach is nearing completion of the mini-update to the temp sensing system.  Once we have the new more sensitive temp sensor in place, we can have a look-see at the similarities between EOM temperature and RAM levels.

Monitoring good, but remember that the EOM alignment must be done carefully to minimize the RAM before we can use these trends.

It seems like there is some confusion---or disagreement---amongst the lab about how to proceed with the RAM work (as Rana mentioned at the TAC meeting, we will henceforth refer to it only as "RAM" and never as "RFAM"; those who refuse to follow this protocol will be taken out back and shot).

I would like to provide a rough outline and then request that people reply with comments, so that we can get a collective picture of how this should work. I have divided this into two sections: 1) Methodology, which is concerned with the overall goal of the testing and the procedure for meeting them, and 2) General Issues, which are broadly important regardless of the chosen methodology.

1. Methodology

There are two broad goals:

• Characterization of extant RAM
  • Measuring the RAM levels existing in an aLIGO-type interferometer without any suppression systems
  • Modeling to estimate the effect on IFO control and corroboration with measurements where possible
    • DC RAM levels contributing offsets to IFO operating point
    • Quasi-DC RAM levels affecting long term detector tuning (e.g., sensing matrix, MICH -> DARM feedforward, etc.)
    • Audio-frequency RAM contributing noise directly via error point modulation
  • Modeling to scale/adapt results from 40m -> aLIGO
• Mitigation
  • Developing and assessing systems for suppressing RAM
    • Passive: thermal shielding and isolation
    • Active: EOM temperature control
      • Simple temperature stabilization
      • RAM error signal

The question is: which is our goal? The first, the second, or both? If both, what priority is given to which and can/should they be done in parallel? Also, task distribution.

2. General Issues

These are loosely related, so they are in random order:

• Sensing
  • Temperature
    • What is the priority/urgency of a precision AC-bridge-readout temperature sensor?
    • If priority/urgency is low, what is the priority/urgency of upgrading breadboard controller to protoboard version? The common answer will be "make the protoboard version now", but if the urgency of the final AC sensing is high, it may make sense to focus on finalizing that design (after all, other experiments are waiting on a precision temperature controller, and it is not cost-effective to make many temporary controllers as I have done for the 40m).
    • Sensor noise issues
      • What is the sensor-noise-limited temperature stabilization level?
      • What is our willingness to tolerate the thermal low-passing of the EOM can itself (i.e., what is our sensitivity to gradients)?
      • To answer the above questions, we need to perform stabilization tests with several sensors on the same can, with some in loop (averaged) and some out of loop.
      • If we determine that gradients are a problem, we may need to:
        • Design a casing for outside the EOM (inside the foam box) to make the heating uniform, or
        • We may be able to get away with a more customized heater (instead of heating the can from one side as we do now).
  • Optical RAM
    • Stochmon is a nice diagnostic tool, but do we want something better? In particular, we want to have linear signals about a zero-DC-RAM point, which requires phase
      • Where will this sensor be located?
      • What kind of PD will it be? Broadband? Multi-resonant?
      • What sort of electronics will we need? If we are going to use this as an error signal for controlling the EOM temperature, it is just as important as any other IFO readout, since it may couple into all of them.
        • RF pickup is a BIG ISSUE HERE
        • How will the demodulation phases be selected? It should be possible to take TF measurements in certain misaligned (i.e., non-resonant) conditions and adjust the relative phase between the RAM readouts and standard IFO RF readouts such that they are in phase, but this will require some thinking.
        • Lots more, I'm sure
• Control
  • Method (overlaps some with methodology portion)
    • What is better, simple temperature stabilization or RAM feeback? (More likely, "how much better is RAM feedback?")
    • If RAM feedback is difficult or impossible to implement effectively (see below), is temperature stabilization good enough?
  • Regime
    
    • Depending on extant RAM levels and on achievable sensing noise, it will be unwise and/or unnecessary to have a RAM control bandwidth above some relatively low frequency (~sub Hz)
      • Gain where RAM suppression is not needed only injects noise into the system
      • This cutoff frequency is largely determined by the thermal response of the system, but additional filtering will likely be necessary to reduce higher-frequency noise coupling (e.g., nonlinear downconversion of high-frequency signals into heater dissipation, etc.)
  • Efficacy
    • If we do RAM feedback, which signal (i.e. which frequency and quadrature) do we minimize?
      • Do we achieve large common-mode reduction across all RF signals, or is there some differential component?
      • In particular, do we make some or all other control signals noisier by stabilizing/minimizing RAM in one channel?
      • If the answer is yes, can we derive an effective control signal from a linear combination of some or all individual RAM signals?

There are probably many other issues I have neglected, so please comment on this rough draft as you see fit!

Since no one has made any comments, I will assume that everyone is either 100% satisfied with the outline or they have no interest in the project. Under this assumption, I will make decisions on my own and begin planning the individual steps in more detail.

In particular, I will assume that our goal comprises BOTH characterization of RAM levels and mitigation, and I will try to find the best way that both can be achieved as simultaneously as possible. 

Last night I measured our RAM offsets and looked at how those affect the PRMI situation.  It seems like the RAM is not creating significant offsets that we need to worry about.

Words here about data gathering, calibration and calculations.

Step 1:  Lock PRMI on sideband, drive PRM at 675.13Hz with 100 counts (675Hz notches on in both MICH and PRCL).  Find peak heights for I-phases in DTT to get calibration number.

Step 2:  Same lock, drive ITMs differentially at 675.13Hz with 2,000 counts.  find peak heights for Q-phases in DTT to get calibration number.

Step 3:  Look up actuator calibrations.  PRM = 19.6e-9/f^2 meters/count and ITMs = 4.68e-9/f^2 meters/count.  So, I was driving PRM about 4pm, and the ITMs about 20pm.

Step 4:  Unlock PRMI, allow flashes, collect time series data of REFL RF siganls.

Step 5: Significantly misalign ITMs, collect RAM offset time series data.

Step 6: Close PSL shutter, collect dark offset time series data.

Step 7: Apply calibration to each PD time series.  For each I-phase of PDs, calibration is (PRM actuator / peak height from step 1).  For each Q-phase of PDs, calibration is (ITM actuator / peak height from step 2).

Step 8:  Look at DC difference between RAM offset and dark offset of each PD.  This is the first 4 rows of data in the summary table below.

Step 9:  Look at what peak-to-peak values of signals mean.  For PRCL, I used the largest pk-pk values in the plots below.  For MICH I used a calculation of what a half of a fringe is - bright to dark.  (Whole fringe distance) = (lambda/2), so I estimate that a half fringe is (lambda/4), which is 266nm for IR.  This is the next 4 rows of data in the table.

Step 10: Divide.  This ratio (RAM offset / pk-pk value) is my estimate of how important the RAM offset is to each length degree of freedom. 

Summary table:

Plots (Left side is several PRMI flashes, right side is a zoom to see the RAM offset more clearly):

In the last post, I showed that SRCL element in the MICH sensor (AS55I-mich) is chaned 1% due to RAM.

Here I calculated how is this 1% residual in MICH sensor (AS55 I-mich) shown in MICH sensitivity. The senario is:

(1) we assume we are canceling SRCL in MICH by feed forward first (original matrix (2,3) element).

(2) SRCL in MICH (matrix(2,3) is changed 1% due to RAM, but you keep the same feed forward with the same feedforward gain

(3) You get 1% SRCL residual motion in MICH sensor. This motion depends on how SRCL is quiet/loud. The assumed level is

Pollution level = SRCL shot noise level in SRCL sensor  x  SRCL closed loop TF  x  1% residual .... the following plot.

AS sensor = AS55I-mich  --- SN level 2.4e-11 W/rtHz ------- MICH SN level 6e-17 m/rtHz

SRCL sensor = AS55 I-SRCL --- SN level 2e-11 W/rtHz ---  SRCL SN level 5e-14 m/rtHz

 I extended my RAM script from DRMI (3DoF) to the full IFO (5DoF).

Again, it calculates the operation point offsets for each DoF from the opt model with RAM. Then the position offsets are added to the model, and calculates the LSC matrix. RAM level is assumed as 0.1% of the PM modulation level, as usual, and lossless for a simple model.

Original matrix without RAM:

REFL f1 : 1.000000    0.000000    0.000008    -0.000005    0.000003 

  AS f2 : 0.000001    1.000000    0.000005    -0.003523    -0.000001 

 POP f1 : -3956.958708    -0.000183    1.000000    0.019064    0.000055 

 POP f2 : -32.766392    -0.154433    -0.072624    1.000000    0.024289 

 POP f2 : 922.415913    -0.006625    1.488912    0.042962    1.000000 

(MICH and SRCL uses the same sensor, with optimised demodulation phase for each DoF.) 

Operation position offsets are:

PRCL   -3.9125e-11 m

SRCL    9.1250e-12 m

CARM  5.0000e-15 m  

and no position offsets for DARM and MICH (because they are differential sensor and not affected by RAM offsets).

Resulting matrix with RAM + RAM offsets, normalised by the original matrix:  

REFL f1 : 0.001663    -0.000000    0.003519    0.000005    -0.000003 

  AS f2 : 0.000004    0.514424    0.000004    -0.001676    -0.000001 

 POP f1 : 7.140984    -0.001205    15.051807    0.019254    0.000417 

 POP f2 : 0.029112    -0.319792    0.042583    1.000460    0.024298 

 POP f2 : -0.310318    -0.014385    -1.761519    0.043005    0.999819 

As you can see in the second matrix, the CARM and DARM rows are completely destroyed by the RAM offsets! The signals are half reduced in the DARM case, so the mixture between DARM and MICH are about 50% degraded.

 I also would like to extend this script to use the DC readout, but don't know how to calculate the postion offset for AS_DC because the error signal is not zero-crossing for AS_DC anymore. Do you have any suggestions for me?

 I don't think I understand the question. AS_DC should not have a zero crossing, correct?

 That's right. I calculate the offset of the operation point (when you have RAM) from the zero-crossing point of the PDH signals. I don't know how to do that for AS_DC, because it doesn't cross zero anymore anytime.

I add a flow-chart drawing what the scripts do and how the scripts calculate the LSC matrix.

(1) First, you calculate the LSC matrix WITHOUT RAM or anything, just for a reference. This is the first matrix shown in the quoted post.

(2) The script calculates the LSC matrix with RAM. Also, the heterodyne signals for all 5 DoF are calculated. The signals have offsets due to the RAM effect. The operating position offsets are saved for the next round.

(3) The script calculates the LSC matrix again, with RAM plus the offset of the operation points. The matrix is shown in the last part of the quoted post.

Now I am going to check (A) LSC matrices (matrix 2, the second matrix of above chart) with different RAM levels (B) Are pos-offsets degrade the CARM and DARM so much (See, the quated result below), is that true?

Oops, Yesterday's results for DARM was wrong!

I got more convincing results now. 

> (B) Are pos-offsets degrade the CARM and DARM so much (See, the quoted result below), is that true? 

• CARM got a small position offset which degrades CARM signal 2 orders of mag (still the biggest signal in the sensor, though).
• DARM was not so bad, and probably the change of the DoF mixture is mostly not changed.
• Matrices don't change only with 1e-4 RAM. It changes with position offsets.
• I'll see how the matrix changes without position offsets but only with RAM effects, changing RAM levels.
• Again, above is C1 configuration, 1e-4 RAM level of PM level.

Koji and Jamie suggested me to include the coupling between DoFs when I calculate the last matrix. So far, I just add all the pos-offsets of 5 DoFs and re-calculate the matrix again. However, once I add one DoF pos-offset, it could already change the LSC matrix therefore different pos-offset to the other four DoF, we must iterate this process until we get the equilibrium pos-offsets for 5 DoFs.

I also noticed an error in the optical configuration file. AM mod levels were smaller than that supposed to be because of the hald power going through the AM-EOMs in the MZI paths. Also I have put PM-Mods in the MZT path which gives the smaller mod indexes. So, smaller mod levels were applied both for PM and AM. As PM-AM ratio is still kept in this, so the matrices were not very wrong, I assume. I'll modify that and post the results again.

 I'm still wondering whether iteration version or simple version is closer approximation to the real situation. Sorry for few explanations here. I will try to present those on Friday.

Anyway, here is the results for both:

%*.*.*. Original matrix w/o RAM .*.*.*

REFL f1 : 1.000000        0.000000    -0.000003    -0.000005    0.000007 

  AS f2 : 0.000002        1.000000    0.000009    -0.003522    -0.000002 

 POP f1 : -3954.521443    -0.000965    1.000000    0.019081    -0.000152 

 POP f2 : -32.770726    -0.154433    -0.072594    1.000000    0.024284 

 POP f2 : 922.393978    -0.006608    1.488319    0.042948    1.000000 

*** Iteration *** 

%*.*.*. Resulting matrix w/ RAM .*.*.*

REFL f1 : 0.039125    -0.000000    0.003665       0.000005    -0.000007 

  AS f2 : 0.000010    1.000431    0.000009       -0.003500    -0.000002 

 POP f1 : 156.420221    -0.000246    15.586838    0.019406    -0.000154 

 POP f2 : 1.255806    -0.154275    0.047313       1.000008    0.024285 

 POP f2 : -34.814720    -0.006600    -1.884850    0.042950    1.000000 

Offsets converged to:

PRCL =  2.1e-15, MICH = 1.1e-17, SRCL = -3.8e-15, CARM = 2.2e-16, DARM = 0 

(POP CARMs became so much smaller compared with the other matrix below, because the offsets are added al of 5 DoFsl at once here.)

*** no iteration, offsets added for each DoF separately ***

REFL f1 : 0.020611        -0.000000    0.003600    0.000005    -0.000007 

AS f2   : 0.000002        1.000000    0.000009    -0.003522    -0.000002 

POP f1  : 1842.776419    -0.000198    21.533358    0.019404    -0.000132 

POP f2  : -32.700639    -0.153095    -0.072481    0.999995    0.024360 

 POP f2 : 922.393862    -0.006435    1.488298    0.042949    0.999982 

Added offsets:

PRCL =  7.5e-15, MICH = 6.25e-16, SRCL = -1.4e-14, CARM = 4.5e-16, DARM = 0

* So far, I used to add all the offsets at once. This time I add CARM and get the CARM row, add PRCL and get the PRCL row... and so on.

I 

I didn't understand how CARM can be decreased 2 orderes of magnitude and PRCL can be INCREASED by such small offsets (see the matrix quoted).

Apparently it was because of an optical-spring ish effect from the "detuning" (which is actually RAM position offsets). I put two plots which are CARM and PRCL tranfer functions to REFL f1 or POP f1, when there is a slight PRCL offset (0, 1e-14m, and 1e-15m cases are plotted). Looking at these plots, it was not a good idea to calculate the LSC matrix in DC because they are affected by this detuning a lot. I'll try f = 150 Hz for the matrix.

 I wrote an RAM simulation script ... it calculates the LSC signal offset and the operation point offset depending on the RAM modulation index.

Configuration : RAM is added on optC1, by the additional Mach-Zehnder ifo before the PRM.

 Both are for PRCL sweep result. Note that REFL33I is always almost zero. Next step: Check the LSC matrix with matrix at the offset operation point.

 On the right figure, you see the non-zero operation points even when RAM mod index = 0. Apparently they come from non-zero loss of the model.  (Each mirror of 50ppm loss was assumed).

 I calculated the DRMI RAM LSC matrix with RAM and the operation point offsets.

• configuration: C1 DRMI
• RAM is added by an Mach-Zehnder ifo placed before the PRM
• demodulation phases are optimised for each DoF
• the operation points offset from the PDH signals are calculated and added to the optical configuration as mirror position offsets
• Then the matrix is calculated with the offsets and the RAM
• The set of the scrips are found as RAMmatrix.m, normMAT.m, newGetMAT.m,  on CVS/ifomodeling/40m/fullIFO_Optickle. They are a bit messy scripts at this moment.

Results:

(1) No RAM LSC matrix

(2) With 1% RAM mod index of PM (normalised by (1) )

(3) With 5% RAM mod index of PM (normalised by (1) )

Adding some more results with more realistic RAM level assumption.

(4) With 0.1% RAM mod index of PM (normalized by (1) )

(5) With 0.5% RAM mod index of  PM (normalized by (1) )

I have been looking at the swings in the RAMmon channels since the heater was reengaged, to compare them to the data from beforehand (with and without the foam box). With the large grains of salt that I will list after, it appears that the EOM temperature controller does in fact reduce the amplitude of the swings by a measurable factor.

Salt:

1. The reason I have not included any plots here is because the data suck. What we should ideally have is a continuous stream of RAMmon signals split into three chunks: 1) no foam, no heat, 2) foam, no heat, and 3) foam and heat. Instead, we have pieces of each kind of data on different days, before and after the MC has been realigned, some in old channels and some in new so that the calibration is different, etc. This piecemeal shit will not do.
2. I realized that the LF boost was not engaged on the heater when I turned it on most recently. For this reason, the EOM temperature has not been stabilized as well as it might have been on diurnal timescales, and so with the boost it could be that the noise reduction is greater. For posterity, the DC suppression level is ~20x without the boost.

It seems impractical to try and rope off essentially 3 straight days where nothign major can be done to the IFO just to take RAM data. Instead, I think we should figure out a way to mimic the diurnal temperature swings on ~hour timescales. The EOM can temperature follows PSL-FSS_RMTEMP almost exactly and with a very short delay, so we can probably even accomplish this by stepping the lab A/C temperature. If this won't work, we can use an incandescent lamp or something similar to heat up the area around the EOM by a noticeable amount.

I'll try to come up with a good way to do this so that we can get some reliable data...

EOM was aligned to minimize the 11 and 55 MHz peaks in the RAMmon PD the other day (elog 6089), and was left with just the temperature sensor attached, no heater, no foam box.

Here is a 4 day trend:

I don't have a whole lot to say about this, other than there's a lot of stuff going on.  The craziness at the end is me realigning the PMC and MC since, as you can see, MC trans was way down.  The foam box was put on earlier today (elog 6104), so we'll see how that changes things over night.

Now we've got another day of data, with the foam box on for the last 24hrs.

First plot is a 5 day trend so you can see that the RAM has gotten a little bit smaller, as has the temperature drift, but not by a whole lot.

Second plot is the last 19 hours (so excluding much of the time while I was realigning beams on the PSL table yesterday), to zoom in on just the time when the foam box was installed.

After lunch Zach and I are going to engage the heater to temperature stabilize the system, to see how that affects things.

In other news, the MC looks like it was fine for a good long time, and ~3 hours ago it went bad.  The mode that's flashing is really bad in both pitch and yaw.  I don't know what happened, but something is not so awesome. Edit: Steve said that he opened the PSL table at some point this morning to look around but not touch, and also it's Janitor Day, and Kevin comes in around 8ish. That doesn't mean I know the actual cause, but those are the only things that happened in the IFO room this morning that anyone is aware of.

In order to measure the transfer function of the RC cavity's foam, I've turned off the servo so that the room temperature noise can excite it.

The attached plot shows a step response test from 2 weeks ago. Servo is nominally still working fine.

 I've just now re-enabled the temperature control of the reference cavity can. Trend of the last 8 days is attached.

 My attempt to passively measure the transfer function of the foam failed fantastically.

As it turns out, the room temperature fluctuations inside the PSL box reach the 1 mK/rHz noise floor of the  AD590 (or maybe the ADC) at ~1-2 mHz. Everything at higher frequencies is noise.

So to see what the foam is doing we will have to do something smarter - we need a volunteer to disable the RC temperature servo from the EPICS screen and then cycle the PSL table lights every hour in the morning.

We'll then use our knowledge of the Laplace transform to get the TF from the step responses.

 more detailed instructions needed....

We've turned off the RC temperature stabilization and the lights will supply the quasi-random heat input to the table and the cavity. Alberto and Kiwamu will be turning the lights on and off at random times.

The attached plot is the spectrum of temperature fluctuations of the room and the vacuum can with no stabilization from this weekend. I think the rolloff above 10 mHz is kind of fake - I had the .SMOO parameter set to 0.99 for both of these channels. I've just now set the .SMOO to 0 for both channels, so we should now see the true ADC or sensor noise level. It should be ~1 mK/rHz.

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

Some thoughts:

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

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

Motivation: 

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

The study:

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

Results:

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

To do:

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

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

We identified two possible courses of action.

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

I have done some calculations to evaluate the first alternative. 

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

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

Attachments:

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

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

Attachment #3: Gouy phase calculations for the PRC

Attachment #3: Gouy phase calculations for the SRC

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

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

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

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

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

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

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

EDIT: Added 9pm, 16 Aug 2016

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

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

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

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

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

Case 2: Order two new sets of folding mirrors

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

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

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

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

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

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

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

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

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

HR Side:

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

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

AR Side:

• R ~50ppm for 532nm, s and p-pol

   (substrate to the right of layer 38)

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

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

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

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

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

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

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

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

  (substrate to the right of layer 38)

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

Do these look reasonable? 

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

To do so, I've been using:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

1. Change in RoC specification - I condensed the mode-matching information previously in 8 plots into the following 2 plots. Between tangential and saggital planes, the harmonic mean was taken. Between X and Y cavities, the arithmetic mean was taken. Considering the information in the following plots, we decided to change the spec RoC from 600 +/- 50m to 1000 +/- 150m. The required sensitivity in sag measurement is similar to the previous case, so I think this should be feasible.
   
   Why this change? From the phase map information at  /users/public_html/40m_phasemap/40m_TT, I gather that we have 2 G&H mirrors, one with curvature ~ -700m and the other with curvature ~ -500m. An elog search suggests that the installed PR2 has RoC ~ -700m, so this choice of RoC for PR3 should give us the best chance of achieving optimal modematching between the RCs and arms as per the plots below.
   
   
2. Cavity stability checks - these plots confirm that the cavity remains stable for this choice of RoC on PR3...
     
3. Coating design - I've been playing around with the code and my understanding of the situation is as follows. to really hit low AR of 10s of ppms, we need many dielectric layer pairs. But by adding more pairs, we essentially become more susceptible to errors in layer thickness etc, so that even though the code may tell us we can achieve R_AR(532nm) < 50ppm, the minima is pretty sharp so even small perturbations can lead to much higher R of the order of a few percent. On the HR side, we need a large number of layer pairs to achieve T_HR(1064nm)=50ppm. Anyways, the MC studies suggest that for the HR coating design, with 19 layer pairs, we can be fairly certain of T_HR(1064nm)<100ppm and R_HR(532nm)>97% for both polarizations, which seems reasonable. In order to make the R_HR(532nm) less susceptible to errors, we need to reduce the number of layer pairs, but then it becomes difficult to achieve the 50ppm T_HR(1064nm) requirement. Now, I tried using very few layer pairs on the AR side - the best result seems to be with 3 layer pairs, for which we get R_AR(532nm)<1% and T_AR(1064nm)>95%, both numbers seem reasonable to me. In the spectral reflectivity, we also see that the minima are much broader than with large number of layer pairs.
   
   First row below is for the HR side, second row is for the AR side. For the MC studies, I perturbed the layer thicknesses and refractive indices by 1%, and the angle of incidence by 5%.
       
      

If there are no objections, I would like to send this version of the specs to Ramin and get his feedback. Specifically, I have assumed values for the refractive indices of SiO₂ and Ta₂O₅ from google, Garilynn tells me that we should get these values from Ramin. Then we can run the code again if necessary, but these MC studies already suggest this coating design is robust to small changes in assumed values of the parameters...

Here is the transfer function and cutoff frequency (pole) of the first stage low pass circuit of the Pentek whitening board.

Circuit:

R1 = R2 = 49.9 Ohm, R3 = 50 kOhm, C = 0.01uF. Given a differential voltage of 30 volts, the voltage across the 50k resistor should be 29.93 volts.

Transfer Function: 

Given by, 

So low pass RC filter with one pole at 1 MHz.

I have updated the schematic, up to the changes mentioned by Rana plus some notes, see the DCC link here: [PLACEHOLDER]

I should have done this by hand...

I stepped the RC can temperature to see the response in the laser frequency. This gives a true measure of the thermal time constant of the RC. Its ~4 hours.

Since the RCPID screen now has a setpoint field, I can remotely type in 1 deg steps. The NPRO SLOW actuator locks the NPRO to the RC at long time scales and so we can use C1:PSL-FSS_SLOWDC to measure the RC length. By knowing what the step response time constant is, we can estimate the transfer function from can temperature to frequency noise and thereby make a better heater circuit.

 Does the observed temperature shift make any sense? Well, John Miller and I measured the SLOW calibration to be 1054 +/- 30 MHz / V.

We know that the thermal expansion coefficient of fused silica, alpha = 5.5 x 10^-7 (dL/L)/deg. So the frequency shift ought to be alpha * c / lambda = 155 MHz / deg.

Instead we see something like 110 MHz / deg. We have to take more data to see if the frequency shift will actually asymptote to the right value or not. If it doesn't, one possibility is that we are seeing the effect of temperature on the reflection phase of the mirror coatings through the dn/dT and the thermal expansion of the dielectric layers. I don't know what these parameters are for the Ta2O5 layers.

A more useful measure of the frequency noise can be gotten by just looking at the derivative in the first 30 minutes of the step, since that short time scale is much more relevant for us. Its 0.04 V / hour / (2 deg) =>  860 (Hz/s)/deg.

In the frequency domain this comes out to be dnu/dT = 860 Hz/deg @ 0.16 Hz or dnu/dT = 137 *(1/f) Hz / deg.

Our goal for the reference cavity frequency noise is 0.01 * (1/f) Hz/rHz. So the temperature noise of the can needs to be < 0.1 mdeg / rHz.

The overnight triangle wave I ran on the AOM drive turns out to have produced no signal in the FAST feedback to the PZT.

The input power to the cavity was ~10 mW (I'm totally guessing). The peak-peak amplitude of the triangle wave was 50% of the total power.

The spectral density of the fast signal at the fundamental frequency (~7.9 mHz) is ~0.08 V/rHz. The FAST calibration is ~5 MHz/V. So, since we

see no signal, we can place an upper limit on the amount of frequency shift = (5 MHz/V) * (0.08 V/rHz) * sqrt(0.0001 Hz) = 4 kHz.

Roughly this means that the RIN -> Hz coefficient must be less than 4 kHz / 5 mW or ~ 1 Hz/uW.

For comparison, the paper on reference cavities by the Hansch group lists a coefficient of ~50 Hz/uW. However, they have a finesse of 400000

while we only have a finesse of 8000-10000. So our null result means that our RC mirrors' absorption is perhaps less than theirs. Another possibility

is that their coating design has a higher thermo-optic coefficient. This is possible, since they probably have much lower transmission mirrors. It would be

interesting to know how the DC thermo-optic coefficient scales with transmission for the standard HR coating designs.

This first plot shows the RC temperature channels' performance from 40 days ago, before we disabled the MINCO PID controller. Although RCTEMP is supposed to be the out of loop sensor, what we really care about is the cavity length and so I've plotted the SLOW. To get the SLOW on the same scale, I've multiplied the channel by 10 and then adjusted the offset to get it on the same scale.

 The second plot shows a period after that where there is no temperature control of the can at all. Same gain scaling has been applied to SLOW as above, so that instead of the usual 1 GHz/V this plot shows it in 0.1 GHz/V.

The third plot shows it after the new PID was setup.

Summary: Even though the PID loop has more gain, the true limit to the daily fluctuations in the cavity temperature and the laser frequency are due to the in-loop sensors measuring the wrong thing. i.e. the out-of-loop temperature is too different from the in-loop sensor. This can possibly be cured with better foam and better placement of the temperature sensors. Its possible that we're now just limited by the temperature gradients on the can.