[Lydia, gautam]

To measure the modulation depth of the 29.5 MHz sideband, we plan to connect a bidirectional coupler between the EOM and the triple resonant circuit box. This will let us measure the power going into the EOM and the power in the reflection. According to the manual for the EOM (Newport 4064), the modulation depth is 13 mrad/V at a wavelength of 1000 nm. Before disconnecting these we will turn off the Marconi.

Hopefully we can be gentle enough that the EOM can be realigned without too much trouble. Before touching anything we'll measure the beam power before and after the EOM so we know what to match after.

If anyone has an objection to this plan, speak now or we will proceed tomorrow morning.

I'm afraid that the bidirectional coupler, designed to be 50ohm in/out, disturbs the resonant circuit designed for the EOM which is almost purely capacitive.

One possible way could be to measure the transfer function using the active FET probe from the triple resonant input to the output with the EOM attached.

Another way: How about to measure the reflection before the resonant circuit? Then, of course, there is the triple resonant interface circuit between the power combiner and the EOM. This case, we will see how much power is consumed in EOM and the resonant circuit. Then we can use the previous measurement to see the conversion factor between the power consumption to the modulation depth. Kiwamu may give us his measurement.

Just collecting some links from my elog searching today here for easy reference later.

• EOM datasheet: Newfocus 4064 (according to this, the input Impedance is 10pF, and can handle up to 10W max input RF power).
• An elog thread with some past measurement details: elog 5339. According to this, the modulation depth at 29.5 MHz is 4mrad. The EOM's manual says 13mrad/V @1000nm, so we expect an input signal at 29.5MHz of 0.3V(pk?). But presumably there is some dependance of this coefficient on the actual modulation frequency, which I could not find in the manual. Also, Kiwamu's note (see next bullet) says that the EOM was measured to have a modulation depth of 8 mrad/V
• A 2015 update from Kiwamu on the triple resonant circuit: elog 11109. In this elog, there is also a link to quite a detailed note that Kiwamu wrote, based on his analysis of how to make this circuit better. I will go through this, perhaps we want to pursue installing a better triple resonant circuit...

I couldn't find any details of the actual measurement technique, though perhaps I just didn't look for the right keywords. But Koji's suggestion of measuring powers with the bi-directional coupler before the triple resonant circuit (but after the power combiner) should be straightforward. 

[gautam, Lydia]

We set out to measure the 29.5 MHz power going to the EOM today but decided to start by looking at the output of the RF AM stabilizer box first. We wanted to measure the AM noise with a mixer, so we needed to know the power it was giving. We looked at the ouput that goes to the power combiner on the PSL table and found it was putting out only -2.0 dBm (~0.5 Vpp)! This was measured by taking a spectrum with the AG4395 and confirmed by looking on a scope.

To find out if this could be adjusted, we found an old MEDM screen (/opt/rtcds/caltech/c1/medm/c1lsc/master/C1LSC_RFADJUST.adl) and moved the 29.5 MHz EOM Mod Index Adjust slider while measuring the voltage coming in to the MOD CONTOL connection on the front of the AM stabilizer box. Moving the slider from 0 to 10 changes the input voltage linearly from -10 V to 10 V measured with a DMM at the cross-connects as we couldn't find an appropriate adapter for the LEMO cable. The 29.5 MHz modulation only appeared for slider values between 0 and 5, after which it abruptly shuts off. However, changing the slider value between 0 and 5 (Voltage from -10 to 0) does not change the amplitude of the output.

This seems like a problem; further investigation into the AM stabilizer box is neccessary. This DCC document outlines how to test the box, but we can't find a schematic. Since we don't have any mixers that can handle signals as small as -2 dBm, we gave up trying to measure the AM noise and will attempt to measure that and the reflection power from the EOM + resonant circuit once this problem has been diagnosed and fixed.

GV: After some digging, I found the schematic for the RF AM stabilization box (updated wiki and added it to the 40m document tree). According to it, there should be up to +22dBm of RF AM stabilized output to the EOM available, though we measured -2dBm yesterday, and could not vary this level by adjusting the EPICS voltage value. Neglecting losses in the cabling and the power combiner on the PSL, this translates to a paltry 0.178Vrms*0.6*8mard/Vrms ~ 0.85 mrad of modulation depth (gain at 29.5 MHz of the triple resonant circuit taken from this elog)... I think we need to pull this 1U chassis out and debug more thoroughly...

Some more details of our investigation:

1. Here is a spectrum of the signal to the power combiner on the PSL table, measured on the output of the RF AM Stabilization box.
   
   Perhaps these sidebands were the ones I observed while looking at the input to the WFS demod board.
2. The signal looked like a clean sinusoid when viewed on an oscilloscope with input impedance set to 50ohms. There were no sharp features or glitches in the time we observed, except when the 29.5 MHz MEDM slider was increased beyond 5, as noted by Lydia.
3. We couldn't find a schematic for this RF AM Stabilization servo, so we are not sure what RF output power to the EOM we should expect. Schematic has since been found.
4. I measured the power level at the input side (i.e. from the crystal) and found that it is ~12dBm, which seems reasonable (the front panel of the box housing the 29.5 MHz oscillator is labelled 13dBm). The schematic for the RF AM stabilization box says we should expect +10dBm at the input side, so all this points to a problem in the RF AM stabilization circuit...
5. There is an attenuator dial on the front panel of the said RF AM stabilization servo that allows one to tune the power to the LO input of the WFS. Right now, it is set to approximately 7dB of attentuation, which corresponds to -12dBm at the WFS demod board input. I did a quick check to see if turning the dial changed the signal level at the LO input of the WFS board. The dial moves in clicks of 1dB, and the RF power at the LO input of the demod board increased/decreased by ~1dBm for each click the dial was rotated (I only explored the region 3dB-11dB of atttentuation). So it should be possible to increase the LO level to the WFS demod boards, is there any reason we shouldn't increase this to -8bBm (~0.25Vpp into 50ohms, which is around the level Koji verified the mixer to be working well at)?
6. There were a couple of short ribbon cables which were just lying around on top of the cards in the eurocrate, Koji tells me that these were used as tester cables for checking the whitening filters and that they don't serve any purpose now. These have been removed.
7. Added a button to IMC MEDM screen to allow easy access to the MEDM screen with slider to control the 29.5MHz modulation depth - though as mentioned in Lydia's elog, at the moment, this slider has no effect on the 29.5MHz power level to the EOM...
   

[johannes, gautam]

We pulled out the RF AM stabilization box from the 1X2 rack. PSL shutter was closed, marconi output, RF distribution box and RF AM stabilization box were turned off in that order. We had to remove the 4 rack nut screws on the RF distribution box because of the stiff cables which prevented the RF AM stabilization box extraction. I've left the marconi output and the RF distribution boxes off, and have terminated all open SMA connections with 50 ohm terminators just in case. Rack nuts for RF distribution box have been removed, it is currently sitting on a metal plate that is itself screwed onto the rack. I deemed this a stable enough ledge for the box to sit on in the short run, while we debug the RF AM stabilization box. We will work on the debugging and re-install the box as soon as we are done...

[gautam, Lydia]

We looked at the RF AM stabilizer box to see if we could find out 1) Why the output power is so low, and 2) Why it can't be changed with the DC input "MOD CONT IN." Details to follow, attached is the annotated schematic from DCC document D000037. 

We are not returning the box tonight so the PSL shutter remains closed. 

1. What is the probe situation? Ought to use a high impedance FET probe to measure this or else the scope would load the circuit.
2. The ERA amplifiers are known to slowly die over ~10 year times scales. Search our ELOG for ERA-5. We'll have to replace some; ask Steve to order if we don't have many in the Plateau Tournant.
3. What kind of HELA are the HELA amplifiers? Please a link to the data sheet if you can find it. I wonder what the gain and NF are at 30 MHz. I think the HELA-10D should be a good variant.

> What is the probe situation? Ought to use a high impedance FET probe to measure this or else the scope would load the circuit.

We did indeed use the active probe, with the 100:1 attenuator in place. The values Lydia has quoted have 40dB added to account for this.

> What kind of HELA are the HELA amplifiers? Please a link to the data sheet if you can find it. I wonder what the gain and NF are at 30 MHz. I think the HELA-10D should be a good variant

The HELA is marked as HELA-10. It doesn't have the '+' suffix but according to the datasheet, it seems like it is just not RoHS compliant. It isn't indicated which of the varieties (A-D) is used either on the schematic or the IC, only B and D are 50ohms. For all of them, the typical gain is 11-12dB, and NF of 3.5dB.

I've added the schematic of the RF AM stabilization board to the 40m PSL document tree, after having created a new DCC document for our 40m edits. Pictures of the board before and after modification will also be uploaded here...

[rana, gautam, lydia]

Today we looked at the schematics for the RF AM stabilizer box and decided that there were an unnecessary amount of attenuators and amplifiers cancelling each other out and adding noise. At the end of the path are 2 HELA-10D amplifiers which we guessed based on the plots for the B version would have an acceptable amount of compression if the output of the second one is ~27dBm. This means the input to the first one should be a few dBm. This should be achieved with as simple a path as possible.

This begged the question, do we need the amplitude to be stabilized at all? Maybe it's good enough already when it comes into this box from the RF distribution box. So I tried to measure the AM noise of the 29.5 MHz signal that usually goes into the AM stabilizer:

• I first measured the power to be 12.8 dBm with the AG4395.
• I sent the signal through a splitter, then sent one side attenuated by 3 dB to the LO side of a level 7 mixer, and the other side attenuated by 10 dB to the RF side of the mixer.
• The output of the mixer went through a lowpass filter at 1.9 MHz (with a 50Ω inline terminator). Initially I connected this directly to a DAQ channel (C1:ALS-FC_X_F_IN), but the ADC noise was stronger than the AM signal.
• To fix this I used the SR560, AC coupled with a gain of 10^4. Attachment 1 is a spectrum of the noise measured with everything connected as described, and also for separate portions of the signal chain:
  • I measured the ADC noise by connecting a terminator to the cable going to DAQ.
  • I measured the mixer noise by putting a terminator on the RF input (and the end of the cable that was connected to it), while still driving LO.
  • I measured the SR560 noise by putting a terminator on the input.

It seems like I'm getting mostly noise from the SR560. Maybe it would be better to use an SR785 to take data instead of DAQ, and then skip the SR560? At low frequencies it seems like the AM noise measurement may be actually meaningful. In any case, if the actual AM noise from the crystal is lower than any of these other noise sources, it means we probably don't need to stabilize the amplitude with a servo, which means we can simplify the AM stabilizer board considerably to just amplify what it gets to 27 dBm.

For a comparison: OMC ELOG 238

Here's what I'm planning to do to the RF AM stabilizer box. I'm going to take out several of the components along the path to the EOM (comments in green), including the dead ERA-4 and ERA-5 amplifiers, the variable attenuator which is controlled by a switch that can't be accessed outside the box, and the feedback path from the daughter board servo. I'm arranging things so that the output of the HELA-10 does not exceed the maximum output power. 

I wasn't quite as sure what to do about the path to the ASC box (comments in blue). I talked with Gautam and he said this gets split equally between several singals, one of which goes to the LO of the demod board which expects -10 dBm and currently gets -12 dBm (can go up to -8 by turning switch). So maybe we don't actually want the signal to be anywhere near +27 dBm at the output. The plans for the box are here, it looks like +27 in will end up with +10 at each output, which is way more than what's currently coming out. But maybe this needs to be increased to match the other path? 

Also we haven't measured the actual response of the variable attenuator U4 for various switch positions; it's the same model as the one I'm removing from the EOM path and that one had slightly different behavior for different switch positions than what the spec sheet says. Same goes for the HELA-10 units along this path: what is their actual gain? So perhaps these should be measured and then a single attenuator should be chosen to get the right output signal level. Alternatively it could just be left alone, if it is at an OK level right now. Advice on what to do here would be appreciated.  

I'll work on the EOM path tonight and wait for feedback on the rest of it. 

EDIT: Gautam pointed out that there's some insertion loss from the components I'll be removing that hasn't been accounted for. Also the plans have been updated to reflect that I'm replacing AT5 with a 1dB attenuator (from 6 dB). 

I suggest:

1. Disable the path which goes to the two spare outputs. Replace the ERA-5 with a 50 Ohm resistor to terminate that path. Make sure the ERA bias voltage is not shorting into something.
2. Remove the ERA amps from the ASC path and remove the switch. Make it fixed gain such that we get +27 dBm out of the front.
3. Put the ASC output into the 1U multi-splitter box and attenuate those outputs so that they supply ~0 dBm to the 2 WFS and the LSC Demod board.

I think this then allows us to have the low noise OCXO signals everywhere with enough oomph.

I made some of the changes. Gautam and I will finish tomorrow. 

While I was soldering the sharpest tip of the soldering iron (the one whose power supply shows the temperature) stopped working and I switched to a different one. Not sure how to fix this. 

Do we want to replace all of the removed ERA's with 50 Ohm resistors, or just the one along the spare output path? I shorted one of them with a piece of wire and left all the others open. 

I couldn't get one of the attenuators off (AT1, at beginning of ASC path). In trying I messed up the solder pad. Part of the connecting trace on the PCB board is exposed so we should be able to fix it. 

Rana motivated me to take a step back and reframe the objectives and approach for this project, so I am collecting some thoughts here on my understanding of it. As I write this, some things still remain unclear to me, so I am leaving these as questions here for me to think about...

Objectives: 

1. The PSL is locked to the IMC cavity - but at frequencies near 1 Hz, the laser frequency is forced to follow the IMC cavity length fluctuations, even though the free-running PSL frequency noise at those frequencies is lower. This excess is also imprinted on the arms when locked to the IR. We would like to improve the situation by feeding back a portion of the MC PDH error signal to the cavity length actuator to stabilize the MC cavity length at low frequencies. Moreover, we would like this loop to not imprint additional control noise in the arm control signals, which is a problem we have observed with the existing MCL loop. 
    
2. The borader goal here is to use this project as a case study for designing the optimal loop and adaptive feedback. Can we come up with an algorithm, which takes
   • A model of our system (made with measured data where possible)
   • A list of our requirements (e.g. in this case, frequency noise requirements in various frequency bands, smooth crossovers between the various loops that enable locking the PSL to the IMC cavity and avoid injecting excess control noise into the plant)

and come up with the best loop that meets all our rquirements? What constitutes the "best" loop? How do we weight the relative importance of our various requirements? 

Proposed approach:

For the specific problem of making the MCL feedback loop better, the approach I have in mind right now is the following:

1. Build a model of the 40m IMC loop. Ultimately the performance of the loop we implement will depend on the transfer function from various additive noise sources and disturbances in the feedback loop (e.g. electronics noise) to the output (i.e. laser frequency). Building an accurate model will allow us to quantify the performance of the proposed control loop, and hence, optimize it with some algorithm. I did some work on a simplistic, purely analytical model of the two MC loops (MCF and MCL), but Rana pointed out that it is better to have something more realistic for this purpose. I have inherited his Simulink models, which I will now adapt to reflect the 40m topology. 
2. Come up with a list of requirements for the MCL controller. Some things that come to mind:
   • Reduce the arm control signal spectral amplitude below 20 Hz
   • Not increase the arm control signal spectral amplitude above 20 Hz
   • Crossover smoothly with the FSS slow temperature control loop and the MCF loop. 
   • What factor of suppression are we looking for? What is achievable? Once I build the model, it should shed some light on these..
   • Is the PMC a more stable frequency reference than the NPRO crystal at low frequencies? This measurement by Koji seems to suggest that it isn't (assuming the 1e4 product for the NPRO free-running frequency noise)..
3. Once we have a model and a satisfactory list of requirements, design a control loop that meets these using traditional techniques, i.e. desired tracking error in the control band of 0.1-20 Hz (is this possible? The model will tell us...), gain and phase margin requirements etc. But this need not necessarily be the optimal controller that meets all of our requirements
4. Optimize the controller - how? Can we define an objective function that, for example, rewards arm control signal suppression and penalizes injection of control noise, and just fminsearch in the [z,p,k] parameter space of the controller? Is there a smarter way to do this?
5. Can this algorithm be adaptive, and optimize the controller to adapt to prevailing seismic conditions for example? Is this the same as saying we have a model that is accurate enough for us to predict the response of the plant to environmental disturbances? 

My immediate goal is to have the Simulink model updated.

Thoughts/comments on the above will be appreciated...

In working on automatic DARM loop design, we have this code:

https://git.ligo.org/rana-adhikari/ModernControls/tree/master/OptimalFeedback/GlobalCost

the things in there like mkCost*, etc. have examples of the cost functions that are used. It may be useful to look at those and then make a similar cost function calculation for the MCL/MCF loop.

Since the "stablizer box" doesn't really need to stabilize, it just needs to amplify, I decided to replace it with an off the shelf amplifier we already had, ZHL-2. I worked on getting it set up today, but didn't connect anything so that people have a chance to give some feedback. 

• The gain we expect is 18 dB, and the maximum output with 1dB of compression is 29 dBm. To avoid compression, I'm aiming for ~26 dBm output, so ~8 dBm input. We measured the output of the source to be 12.8 dBm before, so I attached a 5dB attenuator to the input side of the amplifier. 
• Across the 24V power input and the ground pin, I soldered a 100 uF, 50V electrolytic capacitor and a .27 uF, 50V metal film capacitor. Note that unlike the other similar amplifiers we have, the ground and +24 pins are separated (see image on datasheet). I wasn't sure if that changed what to do so I just found comparable caps to the ones that were there on another model. 
• I twisted and soldered wires to the +24 and ground, making sure they were long enough to reach the clips where the power from the Sorensens gets split up. I placed the amplifer in the rack on top of the RF distribution box and ziptied the power cable in place. 
• I connected a splitter to the output of the amplifier. Should I use a 10dB coupler instead, to maximize the power to the EOM?

So, I think the remaining thing to do is to connect the splitter to ASC out and to the line to the EOM, the +24V supply to the amplifier, and the 29.5 MHz input to the attenuator. I wanted to wait on this to get confiration that the setup is OK. Eventually we can put all of this in a box. 

Also, I noticed that in the clear cabinet with the Sorensens next to this rack, the +24 V unit is not supplying any voltage and has a red light that says "OVP." 

I've edited Rana's Simulink model to reflect the current IMC servo topology (to the best of my understanding). I've tried to use Transfer Function blocks wherever possible so that we can just put in the appropriate zpk model in the script that will linearize the whole loop. I've also omitted the FSS SLOW loop for now.

I've been looking through some old elogs and it looks like there have been several modifications to both the MC servo board (D040180) and the TT FSS Box (D040105). I think it is easiest just to measure these TFs since the IMC is still down, so I will set about doing that today. There is also a Pomona Box between the broadband EOM and the output of the TT FSS box, which is meant to sum in the modulation for PMC locking, about which I have not yet found anything on the elog.

So the next steps are:

1. Measure/estimate all the unknown TFs and gains in this schematic
2. Linearize the model, get the OLG, see if the model matches previously measured OLGs (with the MCL part disabled)
3. Once the model is verified to be correct, look at couplings of various noise sources in the MCL part of the loop, and come up with a suitable controller.

If anyone sees something wrong with this topology, please let me know so that I can make the required changes.

It is more accurate to model the physical frequency noises at various places.

cf. See also 40m ALS paper or Shigeo Nagano PDH thesis on https://wiki-40m.ligo.caltech.edu/40m_Library

- The output 4 should be "Laser frequency"

- Seismic path should be excluded from the summing node

- The output after the PMC: "Laser frequency after the PMC"

- "Laser frequency after the PMC" is compared (diffed) with the output 1 "mirror motion in Hz"

- The comparator output goes to the cav pole, the PD, and the PDH gain: This is the output named "PDH Error"

- Tap a new path from "Laser frequency after the PMC" and multiply with the cav pole (C_IMC)
- Tap a new path from "Mirror motion" and multiply with the cavity high pass  (s C_IMC/omega)
- Add these two: This is the output named "Frequency noise transmitted by IMC"

A few minutes back, I glanced up at the control room StripTool and noticed that the MCREFL PD DC level had gone up from ~0 to ~0.7, even though the PSL shutter was closed. This seemed bizzare to me. Strangely, simply cycling the shutter returned the value to the expected value of 0. I wonder if this is just a CDS problem to do with c1iool0 or c1psl? (both seem to be responding to telnet though...)

Since things look to be back to normal, I am going to start with my characterization of the various TFs in the IMC FSS loop...

I tested the amplifier with the Agilent network analyzer and measured 19.5 dB of gain between 29 and 30 mHz. The phase only changed by 1 degree over this same 1 MHz span. Since everything seems to be in order I'll hook it up this afternoon, unless there are any objections. 

I set everything up and connected it as shown on the block diagram attached to the previous entry, with the exception of the DC power. This is becuase there is no place open to connect to on the DIN rail where the DC power is distributed, so the +24V power will have to be shut off to the other equipment in 1X1 before we can connect the amplifier. (The amplifier is in 1X2, but the DC power distribution was more accessible in 1X1.) I also added 3 new +24 V clips with fuses despite needing only one, so next time we need to connect something new it's not such a hassle. 

The RF distribution box where the 29.5 MHz signal originates should not be turned on until the amplifer has DC power. Since we may have a power interruption tomorrow, the plan is to wait until things are shut down in preparation, and then shut off anyhting else necessary before connecting the new clips on the rail to the existing ones. 

Quick summary elog, details to follow. I did the following:

• Updated the Simulink model based on Koji's feedback. 
• Today morning, I measured the (electronic) open-loop TFs of
  • MC Servo Board
  • FSS Fast path (PZT)
  • FSS PC Drive path
• The summing amplifiers in the latter two paths are assumed to be broadband for the purposes of this model.

The measurements I have look reasonable. But I had a hard time trying to look at the schematic and determine what is the appropriate number and locations of poles/zeros with which to fit the measured transfer function. Koji and I spent some time trying to go through the MC Servo board schematic, but looks like the version uploaded on the 40m DCC tree doesn't have changes made to it reflected (we compared to pictures on the 40m google photos page and saw a number of component values were different). Since the deviation between fit and measurement only occurs above 1MHz (while using poles/zeros inferred from the schematic), we decided against pulling out the servo board and investigating further - but this should be done at the next opportunity. I've marked the changes we caught on a schematic and will upload it to the 40m DCC page, and we can update this when we get the chance.

So it remains to fit the other two measured TFs, and add them to the Simulink model. Then the only unknown will be the PDH discriminant, which we anyway want to characterize given that we will soon have much more modulation.  

Data + plots + fits + updated schematics to follow...

Here are the details as promised.

Attachment #1: Updated simulink model. Since I haven't actually run this model, all the TF blocks are annotated "???", but I will post an updated version once I have run the model (and fix some of the questionable aesthetic choices)

Attachment #2: Measured and fitted transfer functions from the "IN1" input (where the demodulated MC REFL goes) to the "SERVO" output of the MC servo board (to FSS box). As mentioned in my previous elog, I had to put in a pole (fitted to be at ~2MHz, called pole 9 in the plot) in order to get good agreement between fit an measurement up to 10MHz. I didn't bother fitting all the high frequency features. Both gain sliders on the MEDM screen ("IN1 Gain" and "VCO gain") were set to 0dB for this measurement, while the super boosts were all OFF.

Attachment #3: Measured and fitted transfer function from "TEST 1 IN" to "FAST OUT" of the FSS box. Both gains on the FSS MEDM screen ("Common gain adjust" and "fast gain adjust") were set to 0dB for this measurement. I didn't need any ad-hoc poles and zeros for this fit (i.e. I can map all the fitted poles and zeros to the schematic), but the fit starts to deviate from the measurement just below 1 MHz.. perhaps I need to add a zero above 1MHz, but I can't see why from the schematic...

Attachment #4: Measured TF from "TEST 1 IN" to "PC OUT" on the FSS box. MEDM gains were once again 0dB. I can't get a good fit to this, mainly because I can't decipher the poles and zeros for this path from the schematic (there are actually deviations from the schematic posted on the 40m DCC page in terms of component values, I will try and correct whatever I notice) . I'll work on this...

Attachment #5: Data files + .fil files used to fit the data with LISO

Most of the model has come together, I am not too far from matching the modelled OLG to the measured OLG. So I will now start thinking about designing the controller for the MCL part (there are a couple of TFs that have to be measured for this path).

Lydia finished up installing the new RF amplifier, and will elog the details of the installation.

I wanted to try and measure the IMC OLG to compare against my Simulink model. So I went about performing a few checks. Summary of my findings:

1. The amplifier seems to be working fine. I checked powers at the input, output to EOM and output to distribution box (that serves the various LOs) first with a 30dB attenuator at the input, and subsequently with the design choice of 5dB attenuator at the input. Everything seemed in order.
2. I installed a 30 dB attenuator at the MC REFL PD input to the demod board since my (rough) calculations suggested that our modifications would have resulted in the RF beat power between carrier and sideband increasing in power by ~27dB.
3. I then opened the PSL shutter and tried locking the IMC - with manual tweaking of the various gains, I was able to lock.
4. But getting to this point took me a while so I couldn't get an OLG measurement in.

TBC tomorrow, I'm leaving the PSL shutter closed and the RF source off for tonight...

To install the replacement amplifier, I did the following:

• Mounted the amplifier in a 2U chassis, with a metal plate between the amplifier and the bottom of the box. The plate is separated from the box and the amplifier with 2 sets of Nylon screws. I did it this way to make use of the holes that were already in the chassis bottom and just drill holes into a plate instead. 
• Cannibalized mounting brackets and back panel from old ALS Beatbox. The back panel has an on/off switch and a 3W3 feedthrough for power. 
• Made a power cable to reach from the 1X1 fuse blocks to the back panel of my box. Goes up through the top of the rack and then back down. 
• Installed the chassis in the rack. The lid is currently off and there is no front panel yet. 
• Changed the +5dB attenuator to +30 to be able to check things first before supplying a way stronger signal. 
• Installed 4 new +24 V fuse blocks on the adjacent rack (1X1). 
  • Put the new fuses on the DIN rail and wired them together. Connected the new power cable to one of them. 
  • Blocked PMC transmission and made sure all RF sources in 1X1 and 1X2 were turned off
  • Turned off the + 24 V and -24 V Sorensens, trying to keep them fairly balanced as I turned them to 0. 
  • At this point Rana suggested I turn off the other DC power supplies in the rack, which I did.
  • Connected the new fuse blocks to the existing +24 V ones. Note that they are not contiguous but they follow the color code and will be labeled. 
  • I'm only using one of the new +24 outputs, but I made more for future use to minimize the number of times we have to turn the power off. 
• Connected the output of the amplifier to the EOM, and the coupled signal to the distribution box (which splits it and sends it to the demod boards). 
• Turned on the power switch and checked that the amplifier was in fact getting 24 V. 
• Connected the input from the 29.5 MHz source and measured the power coming from the amplifier. I measured -12 dBm instead of the expected ~0 dBm, but Gautam was able to see the expected power later, so maybe something just wasn't connected right.
• Double checked the power coming into the amplifier, which was consistent with earlier measurements at about 12.8 dBm. 

Still to be done:

• Label/relabel several things (fuse blocks, back panel, etc) 
• Current label on +24 Sorensen needs to be updated
• Order front panel and install
• Install power indicator lights on front and back 
• Readjust gains (analog and digital) to use full signal output and measure (hopefully) improved WFS performance
• Insert bi-directional coupler and measure modulation depth and reflections from EOM

To remind myself about how to put filter caps on the mini-circuits RF Amps, I looked at Koji's recent elog. Its mostly about op-amps, but the idea holds for us.

We want a big (~100 uF) electrolytic with a 50V rating for the +24V RF Amp. And then a 50V ceramic capacitor of ~0.1 uF close to the pins. Remember that the power feed through on the Mini-circuits case is itsself a capacitive feedthrough (although I guess its a ~100 pF).

Later, we should install in this box an active EMI filter (e.g. Vicor)

Rana and I spent some time looking at the IMC demod board earlier today. I will post the details shortly, but there was a label on the front panel which said that the nominal LO level to the input should be -8dBm. The new 29.5MHz routing scheme meant that the LO board was actually being driven at 0dBm (that too when the input to the RF distribution box was attenuated by 5dB).

An elog search revealed this thread, where Koji made some changes to the demod board input attenuators. Rana commented that it isn't a good idea to have the LO input be below 0dBm, so after consulting with Koji, we decided that we will

• Remove the 5dB attenuator to the input of the distribution box such that the LO is driven at ~5dBm
• Remove the input 10dB attenuator, first ERA-5SM amplifier, and the mini circuits power splitter from the demod board (schematic to follow).

After implementing these changes, and testing the board with a Marconi on the workbench, I found that the measured power levels (measured with an active FET probe) behave as expected, up till the ERA-5SM immediately prior to the LO (U4 and U6 on the schematic). However, the power after this amplifier (i.e. the input to the on-circuit LO, Minicircuits JMS-1H, which we want to be +17dBm), is only +16dBm. The input to these ERA-5SMs, which are only ~2years old, is -2dBm, so with the typical gain of +20dB, I should have 18dBm at their output. Moreover, increasing the input power to the board from the Marconi doesn't linearly increase the output from the ERA-5SM. Just in case, I replaced one of the ERA-5SMs, but observed the same behaviour, even though the amplifier shouldn't be near saturation (the power upstream of the ERA-5SM does scale linearly).

This needs to be investigated further, so I am leaving the demod board pulled out for now...

The input impedance of the mixer is not constant. As the diode switches, it changes dynamically. Because of this, the waveform of the LO at the mixer input (i.e. the amplifier output) is not sinusoidal. Some of the power goes away to harmonic frequencies. Also, your active probe is calibrated to measure the power across the exact 50Ohm load, which is not in this case. The real confirmation can be done by swapping the mixer with a 50Ohm resistor. But it is too much. Just confirm the power BEFORE the amp is fine. +/-1dB does not change the mixer function much.

Instead, we should measure
- Orthogonality
- Gain imbalance
of the I/Q output. This can be checked by supplying an RF signal that is 100~1kHz away from the LO frequency and observe I&Q outputs.

29.5 MHz RF Modulation Source

• The +13dBm from the Wenzel oscillator gets amplified to +27dBm by a ZHL-2-S. There is a 5dB attenuator on the input to the amplifier to avoid compression/saturation.
• The amplified output goes to the EOM (+26dBm measured at the rack, no measurement done at the input to the triple-resonant circuit box yet), while a 10dB coupled part goes to the RF distribution box which splits the input into 16 equal parts. The outputs were measured to spit out +5dBm.
• 2 of these go to the WFS demod boards - it was verified that this level of drive is okay for the comparator chips on the demod board.
• A third output goes to the IMC Demod board. The demod board was modified so that the nominal LO input level is now +5dBm (details below).
• The remaining outputs are all terminated with 50ohms.

IMC Demodulation Board

• The input attenuator, amplifier and power splitter were removed.
• Schematic with changes marked and power levels measured, along with a high-res photograph (taken with our fancy new Macro lens + LED light ring) has been uploaded to a page I made to track changes for this part on the DCC (linked to 40m document tree).
• After making the changes, it was verified that the power levels in the signal chain were appropriate up till the input to the ERA-5SM amplifier directly before the LO. These levels were deemed appropriate, and also scaled in a predictable manner with the input power. As Koji mentions in the previous elog, the dynamically changing input impedance of the mixer makes it difficult to measure the LO level at this point, but I am satisfied that it is within ~1dBm of the nominal +17dBm the mixer wants.
• The board was further checked for gain imbalance and orthogonality of the I and Q outputs. The graphic below show that there is negligible gain imbalance, but the relative phase between the I and Q channels is ~78 degrees (they should be 90 degrees). Of course this doesn't matter for the IMC locking as we only use the I phase signal, but presumably, we want to understand this effect and compensate for it. 
  
  
• The label on the front panel has been updated to reflect the fact that the nominal LO input is now +5dBm
• The demodulation phase had changed since the RF signal change was modified - Rana and I investigated this effect on Monday morning, and found that a new ~1.5m long cable was needed to route the signal from the RF distribution box to the LO input of the demod board, which I made. Subsequent modifications on the demod board meant that an extra ~10cm length was needed, so I just tacked on a short length of cable. All of the demodulated signal is now in the I output of the demod board (whereas we had been using the Q output).
• The graphics below confirms that claim above. Note the cool feature on the digital scopes that the display persistence can be set to "infinity"!
      

I wanted to do a quick check to see if the observed signal levels were in agreement with tests done on the workbench with the Marconi. The mixers used, JMS-1H, have an advertised conversion loss of ~7dB (may be a little higher if we are not driving the LO at +17dBm). The Lissajous ellipse above is consistent with these values. I didn't measure powers with the MC REFL PD plugged into the demod board, but the time series plot above suggest that I should have ~0dBm power in the MC REFL PD signal at 29.5MHz for the strongest flashes (~0.3Vpp IF signal for the strong flashes). 

MC Servo Board

• As mentioned above, we now use the I phase signal for lMC PDH locking.
• This has resulted in an overall sign change of the servo. I have updated the MEDM screen to reflect that "MINUS" is the correct polarity now..
• To set the various gains, I measured the OLTF for various configurations using the usual IN1/IN2 prescription on the MC Servo Board (using the Agilent analyzer). 
• I started at 0dBm "In1 Gain", and the nominal (old) values for "VCO gain", "FSS Common Gain" and "FSS FAST gain"  and found that though I could lock the MC, I couldn't reliably turn on the boosts.
• After some tweaking, I settled on +10dB "In1 Gain". Here, locking was much more reliable, and I was able to smoothly turn on the Super Boosts. The attached OLTF measurement suggests a UGF of ~118kHz and phase margin of a little more than 30 degrees. There is room for optimization here, since we have had UGFs closer to 200kHz in the recent past. 
  
• I didn't get around to measuring the actual PZT/EOM crossover yesterday. But I did measure the OLTF for various values of the FSS gains. At the current value of +20dBm, the PC drive signal is hovering around 1.5V. This bit of optimization needs to be done more systematically. 
• I've edited mcup and mcdown to reflect the new gains. 
  

Some general remarks

• The whole point of this exercise was to increase the modulation depth for the 29.5MHz signal. 
• By my estimate, assuming 8mrad/V modulation index for the EOM and a gain of 0.6 at 29.5 MHz in the triple resonant box, we should have 100mrad of modulation after installing the amplifier (compared to 4mrad before the change). 
• The actual RF power at 29.5 MHz at the input/output of the triple resonant box has not yet been measured. 
• The WFS input error signal levels have to be re-measured (so I've turned off the inputs to the digital WFS filters for now)

I would think that we want to fix the I/Q orthog inside the demod board by trimming the splitter. Mixing the Q phase signal to the I would otherwise allow coupling of low frequency Q phase junk from HOMs into the MC lock point.

I was a little confused why the In1 Gain had to be as high as +10dB - before the changes to the RF chain, we were using +27dB, and we expect the changes made to have increased the modulation depth by a factor of ~25, so I would have expected the new In1 Gain to be more like 0dB.

While walking by the PSL table, I chanced upon the scope monitoring PMC transmission, and I noticed that the RIN was unusually high (see the scope screenshot below). We don't have the projector on the wall anymore, but it doesn't look like this has shown up in the SLOW monitor channel anyways. Disabling the MC autolocker / closing the PSL shutter had no effect. I walked over to the amplifier setup in 1X2, and noticed that the SMA cable connecting the output of the amplifier to the EOM drive was flaky. By touching the cable a little, I noticed that the trace on the scope appeared normal again. Turning off the 29.5MHz modulation source completely returned the trace to normal.

So I just made a new cable of similar length (with the double heat shrink prescription). The PMC transmission looks normal on the scope now. I also re-aligned the PMC for good measure. So presumably, we were not driving the EOM with the full +27dBm of available power. Now, the In1 Gain on the MC servo board is set to +2dB, and I changed the nominal FSS FAST gain to +18dB. The IMC OLTF now has a UGF of ~165kHz, though the phase margin is only ~27 degrees.. 

I made a tentative front panel design for the newly installed amplifier box. I used this chassis diagram to place the holes for attaching it. I just made the dimensions match the front of the chassis rather than extending out to the sides since the front panel doesn't need to screw into the rack; the chassis is mounted already with separate brackets. For the connector holes I used a caliper to measure the feedthroughs I'm planning to use and added ~.2 mm to every dimension for clearance, because the front panel designer didn't have their dimensions built in. Please let me know if I should do something else. 

The input and coupled output will be SMA connectors since they are only going to the units directly above and below this one. The main output to the EOM is the larger connector with better shielded cables. I also included a hole for a power indicator LED. 

EDIT: I added countersinks for 4-40 screws on all the screw clearance holes. 

Johannes, if you're going to be putting a front panel order in soon, please include this one. 

Also, Steve, I found a caliper in the drawer with a dead battery and the screws to access it were in bad shape- can this be fixed? 

Following the discussion at the meeting today, I wanted to finish up the WFS tuning and then hand over the IFO to Johannes for his loss stuff. So I did the following:

1. First I set the dark offsets on the WFS (with PSL shutter closed). Then I hand aligned the MC to maximize transmission, centered the beam on the WFS, and set the RF offsets with the MC unlocked.
2. Given that the demod phase for the IMC PDH demodulation board changed by |45 degrees|, I tried changing the digital demod phases in each of the WFS quadrant signals by +/- 45 degrees. Turns out +45 degrees put all the error signal into the I Phase, which is what we use for the WFS loops.
3. Then I attempted to check the WFS loops. I estimated that we have ~25 times the modulation depth now, so I reduced the WFS1/2 P/Y gains by this factor (but left the MC2 TRANS P/Y gains as is). The loop gain seemed overall too low, so I upped the gain till I saw instability in the loop (error signals ringing up). Then I set the loop gains to 1/3 of this value - it was 0.01 before, and I found the loop behaved well (no oscillations, MC TRANS stabilized) at a gain of 0.002.

At this point, I figured I would leave the WFS in this state and observe its behaviour overnight. But abruptly, the IMC behaviour changed dramatically. I saw first that the IMC had trouble re-acquiring lock. Moreover, the PC Drive seemed saturated at 10.0V, even when there was no error signal to the MC Servo board. Looking at the MEDM screen, I noticed that the "C1-IOO_MC_SUM_MON" channel had picked up a large (~3V) DC offset, even with In1 and In2 disabled. Moreover, this phenomenon seemed completely correlated with opening/closing the PSL shutter. Johannes and I did some debugging to make sure that this wasn't a sticky button/slider issue, by disconnecting all the cables from the front panel of the servo board - but the behaviour persisted, there seemed to be some integration of the above-mentioned channel as soon as I opened the PSL shutter.

Next, I blocked first the MC REFL PD, and then each of the WFS - turns out, if the light to WFS2 was blocked and the PSL shutter opened, there was no integrating behaviour. But still, locking the MC was impossible. So I suspected that something was wrong with the LO inputs to the WFS Demod Boards. Sure enough, when I disconnected and terminated those outputs of the RF distribution box, I was able to re-lock the MC fine.

I can't explain this bizzare behaviour - why should an internal monitor channel of the MC Servo board integrate anything when the only input to it is the backplane connector (all front panel inputs physically disconnected, In1 and In2 MEDM switches off)? Also, I am not sure how my work on the WFS could have affected any hardware - I did not mess around at the 1X1 rack in the evening, and the light has been incident on the WFS heads for the past few days. The change in modulation depth shouldn't have resulted in the RF power in this chain crossing any sort of damage threshold since the measured power before the changes was at the level of -70dBm, and so should be at most -40dBm now (at the WFS demod board input). The only thing different today was that the digital inputs of the WFS servos were turned on...

So for tonight I am leaving the two outputs of the RF distribution box that serve as the LO for the WFS demod boards terminated, and have also blocked the light to both WFS with beam blocks. The IMC seems to be holding lock steady, PC drive levels look normal...

Unrelated to this work, but I have committed to the svn the updated versions of the mcup and mcdown scripts, to reflect the new gains for the autolocker...

[Koji, gautam]

Turns out the "problem" with WFS2 and the apparent offset accumulation on the IMC Servo board is probably a slow machine problem.

Today, Koji and I looked at the situation a little more closely. This anomalous behaviour of the C1:IOO-MC_SUM channel picking up an offset seems correlated with light being incident on WFS2 head. Placing an ND filter in front of WFS 2 slowed down the rate of accumulation (though it was still present). But we also looked at the in-loop error signal on the IMC board (using the "Out 2" BNC on the front panel), and this didn't seem to show any offset accumulation. Anyways, the ability of the Autolocker doesn't seem to be affected by this change, so I am leaving the WFS servo turned on.

The new demod phases (old +45degrees) and gains (old gains *0.2) have been updated in the SDF table. It remains to see that the WFS loops don't drag the alignment over longer timescales. I will post a more detailed analysis here over the weekend...

Also, we thought it would be nice to have DQ channels for the WFS error signals for analysis of the servo (rather than wait for 30 mins to grab live fine resolution spectra of the error signals with the loop On/Off). So I have added 16 DQ channels [recorded at 2048 Hz] to the c1ioo model (for the I and Q demodulated signal from each quadrant for the 8 quadrants). The "DRATE" for the c1ioo model has increased from ~200 to 410. Comparing to the "DRATE" of c1lsc, which is around 3200, we think this isn't significantly stretching the DAQ abilities of the c1ioo model...

Yikes. Please change the all teh WFS DQ channels sample rates from 2048 down to 512 Hz. I doubt we ever need anything about 180 Hz.

There is sometimes an issue with this: if our digital AA filters are not strong enough, the noise about above 256 Hz can alias into the 0-256 Hz band. We ought to check this quantitatively and make some elog statement about our AA filters. This issue is also seen in DTT when requesting a low frequency spectrum: DTT uses FIR filters which are sometimes not sharp enough to prevent this issue.

Here is a comparison of the error signal spectra after increasing the IMC modulation depth, to the contribution with RF inputs / whitening inputs terminated (which I borrowed from Koji's characterization of the same in Dec 2016, these shouldn't have changed).

Some general observations:

1. This data was taken with the WFS servos disabled, but with the IMC hand-aligned to a good state (MC_TRANS ~15,000). The error signal spectra are from the new DQ channels (but still sampled at 2048Hz, I had not implemented the change to 512Hz).
2. The error signals seem to have increased by ~25x , which is consistent with how much we expect the modulation depth to have increased
3. The bump around 1 Hz is now cleaerly visible in all 16 channels, as is the bounce peak at 16Hz (relative to Dec 2016). In general, between 0.1Hz and 5Hz, there is now a fair bit of daylight between the error signals and the electronics noise contribution. 

I will update with the in-loop error signal spectra, which should give us some idea of the loop bandwidth.

I will look into lowering the sampling rate, and how much out-of-band power is aliasing into the 0-256 Hz band and update with my findings.

I installed the front panel today. While I had the box out I also replaced the fast decoupling capacitor witha 0.1 uF ceramic one. I made SMA cables to connect to the feedthroughs and amplifier, trying to keep the total lengths as close as possible to the cables that were there before to avoid destroying the demod phases Gautam had found. I didn't put in indicator lights in the interest of getting the mode cleaner operational again ASAP. 

I turned the RF sources back on and opened the PSL shutter. MC REFL was dark on the camera; people were taking pictures of the PD face today so I assume it just needs to be realigned before the mode cleaner can be locked again. 

I've attached a schematic for what's in the box, and labeled the box with a reference to this elog. 

The alignment wasn't disturbed for the photo-taking - I just re-checked that the spot is indeed incident on the MC REFL PD. MC REFL appeared dark because I had placed a physical beam block in the path to avoid accidental PSL shutter opening to send a high power beam during the photo-taking. I removed this beam block, but MC wouldn't lock. I double checked the alignment onto the MC REFL PD, and verified that it was ok.

Walking over to the 1X1, I noticed that the +24V Sorensen that should be pushing 2.9A of current when our new 29.5MHz amplifier is running, was displaying 2.4A. This suggests the amplifier is not being powered. I toggled the power switch at the back and noticed no difference in either the MC locking behaviour or the current draw from the Sorensen.

To avoid driving a possibly un-powered RF amplifier, I turned off the Marconi and the 29.5MHz source. I can't debug this anymore tonight so I'm leaving things in this state so that Lydia can check that her box works fine...

[gautam, lydia]

I pulled out the box and found the problem: the +24 V input to the amplifier was soldered messily and shorted to ground. So I resoldered it and tested the box on the bench (drove with Marconi and checked that the gain was correct on scope). This also blew the fuse where the +24 power is distributed, so I replaced it. The box is reinstalled and the mode cleaner is locking again with the WFS turned on.

Since I tried to keep the cable lengths the same, the demod phases shouldn't have changed significantly since the amplifier was first installed. Gautam and I checked this on a scope and made sure the PDH signals were all in the I quadrature. In the I vs. Q plot, we did also see large loops presumably corresponding to higher order mode flashes.

I've been sitting on some data for a while now which I finally got around to plotting. Here is a quick summary:

Attachment #1: I applied a step input to the offset of each of the six WFS loops and observed the step response. The 1/e time constant for all 4 WFS loops is <10s suggesting a bandwidth a little above 0.1Hz. However, the MC2 P and Y loops have a much longer time contant of ~150s. Moreover, it looks like the DC centering of the spot on the QPD isn't great - the upper two quadrants (as per the MEDM screen) have ~3x the cts of the lower pair.
I did not (yet) try increasing the gain of this loop to see if this could be mitigated. I accidentally saved this as a png, I will put up the pdf plot

Attachment #2: This is a comparison of the WFS error signals with the loops engaged (solid lines) vs disabled (dashed lines). Though these measurements were taken at slightly different times, they are consistent with the WFS loop bandwidths being ~0.1Hz.

Attachment #3: Comparison of the spectra of the testpoint channels and their DQ counterparts at the same time which are sampled at 512Hz. It does not look like there is any dramatic aliasing going on, although it is hard to tell what exactly is the order of the digital AA filter implemented by the RCG. Further investigation remains to be done... For reference, here are some notes: T1600059, T1400719

GV 7 March 2017 6pm: It looks like we use RCG v2.9.6, so it should be the latter document that is applicable. I've been going through some directories to try and find the actual C-code where the filter coeffs are defined, but have been unsuccessful so far...

[valera, gautam]

Last night, Valera and I looked into two aspects of the IMC:

1. How can we accurately set the offset at the error point of the PDH servo such that we lock to the true center of the resonance?
2. What's up with the large common mode offset on the WFS?

I will post a more detailed elog about last night's work, but Valera also thought it might be a good idea to try and improve the mode-matching into the IMC. I couldn't find anything on the wiki/elog about the mode matching situation on the PSL table, so I quickly went over yesterday to measure some lengths. From looking at the MCREFL DC levels when the mode cleaner is locked (~0.37V) and unlocked (~5.7V), the current mode matching efficiency seems to be about 88%, so there is definitely some headroom for improvement.

Here is my cartoon of the situation on the PSL table. All lengths are measured in mm, and I would say correct to +/- 5 mm, so there could be considerable error here...

  (L1 : f=+200mm. L2: f=-150mm. L3:  f=+400mm)

I extracted the lengths from the edge of the PSL table to IM1 and MC1 from (what I think are) the latest CAD drawings on the DCC. I then put all this into an a la mode script [Attachment #5] - I assumed a waist of 370um at the PMC output mirror, and a waist of 1.78mm at MC1. I neglected the passage through the in-vac Faraday, EOM and BS1 (on the sketch above) and the MC1 substrate. I was able to achieve a theoretical mode-matching efficiency of 1 by just moving the positions of L2 and L3. 

Given that there are probably errors of the order 0.5cm in the lengths on the PSL table, and also the in-vacuum distance to MC1, I figured it would be ideal to just move one lens and see if we can improve the efficiency. It looks like it may be more effective to move L2 than L3. The plot on the right shows that the sensitivity is approximately equal to the positioning of L2 and L3. Judging by this plot, looks like w.r.t. the coordinates in this plot, we are somewhere around (0.02,-0.02).

It looks like if we want to do this, moving L2 (f = -150mm) may be the best way to go.

[valera, gautam]

We implemented the plan outlined in the previous elog. The visibility (Pmax-Pmin)/(Pmax+Pmin) calculated with the MC REFL PD levels with the MC locked/unlocked is now ~96% (up from 88%). The MC REFL DC level in lock is now ~0.12V (compared to 0.4V). Assuming a modulation depth of 0.1 @ 29.5MHz, about 25% of this (i.e. 0.03V) is from sideband light.

The procedure followed was (see sketch in previous elog for various optic labels):

1. Move L2 back (towards PMC) by ~2cm.
2. Walk the beam using M3 and M4 to minimize MCREFL, re-lock IMC, run WFS. 
3. Move L3 back (towards PMC) by ~2cm.
4. Repeat steps 2 and 3, the latter with smaller steps, monitor MCREFL DC level.

We could probably tweak the fine positioning of L2 and L3 and improve the efficiency a little more, but the primary objective here was to see if there was any effect on the large common mode offset on the WFS demodulated "SUM" output. Unfortunately, we saw no effect.

Here are two photos of the relevant section of the PSL table before (left) and after (right) our work there:

[valera, gautam]

Motivation: see this elog

I was fiddling around for a few days trying to implement the method outlined in this paper to null this offset - I will post a separate elog about my efforts but Valera pointed out that we could try injecting an AF modulation at the IN2 input of the MC Servo Board. Last night, we hooked up an SR function generator (f = 312Hz, A = 0.01Vpp, IN2 gain = -5dB) to the unused BNC IN2 input of the MC Servo board. To avoid any additional offsets from the AO path during this measurement, I disconnected the LEMO cable (it is labelled).

We looked at the spectrum of the MC transmission around 312Hz and also 2*f = 624Hz. As a result of this modulation, we expect in the transmitted power, dP/P, a 2f term with amplitude ~(X_mod/X_0)^2 and a term at f with amplitude ~(X_offset * X_mod / X_0^2) - I may have missed out some numerical factors of order 1. So the latter should vanish if the offset at the error point is truly zero and the lock-point is the center of the resonance. Last night, we found that an offset in the range of -0.25 V to -0.19 V nulled this peak in the DTT spectrum. Today, the number was -0.05V. So the true offset seems to vary from lock to lock. Here are spectra around f=312Hz for a few different values of the offset slider (the center of the resonance seems to be -0.05V on the MEDM slider at this time).

Do these numbers make sense? Some time ago, I had pulled out the MC Servo board to find out what exactly is going on at this offset summing point. The MEDM slider goes from -10V to 10V, and by measuring the voltage at TP5 (see schematic below), I found that there is a 1/40 scaling factor between what is actually applied and the number on the MEDM slider (so for example, the numbers in the legend in the above plot have to be divided by 40). I've modified the MC Servo Board MEDM screen to reflect this. When I had pulled the board out, I noticed that in addition to the offset voltage applied via the backplane connector, there was also a potentiometer (R50 in the schematic below). I had nulled the voltage at TP5 using this potentiometer, but I guess drifts of ~5mV are possible. 

Discussion on calibration of offset slider in Hz/V:

I've yet to do a rigorous calibration of this slider into Hz, but looking at the spectrum of the transmitted intensity at 2f, we estimated the coefficient (X_mod/X_0) ~ 3e-3 for an offset of 0.2V. dP/P ~1 when the applied modulation equals the linewidth of the cavity, which is 3.6kHz. So 0.2V of offset slider corresponds to ~ 10Hz frequency offset. In other words, I estimate the slider calibration to be 50Hz/V. So with the full range of +/- 10V, we should be able to scan ~1kHz of frequency offset. What does this imply about the variation of the offset slider value that removes the peak at 1f between locks? As mentioned above, this variation is ~0.2V over a day - with the calibration mentioned above, this corresponds to a change in cavity length of ~10um, which seems reasonable to me...

So how did all of this tie in with WFS SUM offsets? We did the following:

• After nulling the length offset using the procedure detailed above, we noticed non-zero offsets on both WFS1 and WFS2 "I" SUM outputs
• So we set the dark offsets and RF offsets for the WFS, with no light incident on the WFS (PSL shutter closed). 
• Re-locking the IMC and closing the WFS loops, we noticed that WFS2 SUM offset was still hovering around 0, but WFS1 SUM offset was ~ -2000cts.
• Looking at some trends on dataviewer, this offset seems to drift around over a few days timescale by a few thousand counts - for example, the WFS1 offset today was +2000cts. Moreover, the WFS1 offset seems to drift around by ~factor of 3 times as much as WFS2 offset in the 24 hour period I looked up (plot to follow)...
• Misaligned MC2 and looked at the sum offset with just the single bounce beam off MC1 onto the WFS

I neglected to screenshot the StripTool from the times we were doing these trials but I have the times, I will pull up some dataviewer plots and upload them here tomorrow...

I've taken a bunch of transfer function measurements from the MC ASC PIT and YAW channels to the WFS error signals using the same set of DTT templates Koji used while characterizing the WFS loops a couple of months ago, before the IMC RF changes. Analysis is underway and I will post the results here shortly...

As an aside, Rana had added 10dB and 20dB gains to all of the WFS filter banks yesterday. I tried engaging the 10dB gains on the two MC2_TRANS PD loops, and this did not seem to induce any instability. I stepped both loops and saw that as expected, the 1/e times for both of these loops is about 45 seconds now (compared to ~150 seconds at the nominal gain). These have been running all day today, and the IMC seems well behaved, so I am going to leave these on for now... Jacking up the gain on the MC2_TRANS_QPD loops by 20dB induced instability - same story for the 4 WFS loops with 10dB additional gain...

Thanks to Koji's nice MATLAB script using DttData functions, I was able to quickly analyze the TF data. Essentially, this measurement was a repetition of what was done here. The difference is that the modulation depth has been increased by ~25x compared to that measurement from December 2016. Here are the measured TFs (before accounting for the 1/f^2 normalization) for the various quadrants and the PIT/YAW channels:

The plots above are just to illustrate that the measurement was clean between the band over which the averaging will be done to compute the TF amplitude - i.e. 7-15Hz. The full summary of TF amplitudes, standard deviations, and the sensing matrix in the style of the referenced elog (the actual excel spreadsheet is Attachment #4, minus some of the graphics Koji had on his excel sheet):

Inverting those matrices, we get the matrices that diagonalize the sensor-actuator chain:

PITCH:

YAW:

I will try implementing these matrices tomorrow and take a look at the step responses of the loops - the idea is that perhaps the system wasn't optimally diagonalized before and perhaps we can now improve the bandwidths of all the loops.

For sensing matrix, better to use single frequency sine response. We don't want to measure around the bounce or above the 28 Hz cutoff filters in the MC SUS.

I've reduced the gains of the damping on all 3 MC SUS by a factor of 3 for overnight observation as part of the ongoing feedforward noise cancellation investigations. I will return them to the nominal values tomorrow morning.

I've restored the damping loop gains to their nominal values. Analysis of the coherence between MCL and seismometer channels under this reduced gain setting is underway, results to follow.