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:
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"
Today I finished fitting the transfer function to a vectfit model for seismometers T240_X and T240_Y, and then used these to filter noise online from the mode cleaner.
The Bode plot for T240_X is in figure 1, and T240_Y is in figure 2. I made sure to weight the edges of the fit so that no DC coupling or excessive injection of high frequency noise occurs at the edges of the fit.
I used C1:IOO-MC_L_DQ as the first channel I filtered, with C1:IOO-MC_L_DQ(RMS) for RMS data. I took reference data first, without my filter on. I then turned the filter on and took data from the same channel again. The filtered data, plotted in red, subtracted from the reference and did not inject noise anywhere in the mode cleaner.
I also looked at C1:LSC-YARM_OUT_DQ and C1:LSC-YARM_OUT_DQ(RMS) for its RMS to see if noise was being injected into the Y-Arm when my filter was implemented. I took reference data here also, shown in blue, and compared it to data taken with the filter on. My filter, in pink, subtracted from the Y-Arm and injected no noise in the region up to 10 Hz, and only minimal noise at frequencies ~80 Hz. Frequencies this high are noisy and difficult to filter anyways, so the noise injection was minimal in the Y-Arm.
After fighting relentlessly with the mode cleaner, I believe I have achieved final results.
I have mostly been focusing on Wiener filtering MCL with a SISO Wiener filter for a reason, simplicity. This simplicity allowed me to understand the dificulties of getting a filter to work on the online system properly and to develope a systematic way of making this online Wiener filters. The next logical step after achieving my final SISO Wiener filter using the T240-X seismometer as witness for MCL (see elog:11535) and learning how to produce good conditioned Wiener filters was to give MISO Wiener filtering of MCL a try.
I tried performing some MISO filtering on MCL using the T240-X and T240-Y as witnesses but the procedure that I used to develope the Wiener filters did not work as well here. I made the decision to ditch it and use some of the training data I saved when the SISO (T240-X) filter was runing overnight to develope another SISO Wiener filter for MCL but this time using T240-Y as witness. I will compare how much more we gain when doing MISO Wiener filtering compared to just a bunch of SISO filtering in series, maybe a lot, or little.
I left both filters running overnight in order to get trainining data for arm and WFS yaw and pitch subtractions.
The SISO filters for MCL are shown below:
The theoretical FIR and IIR subtractions using the above filters:
Running the filters on the online system gave the following subtractions for MCL and YARM:
Comparing the subtractions using only the T240-X filter versus the T240-X and T240-Y:
Somehow it seems like the ELOG makes all of the thumbnails way too big by default. Did we get some sneaky upgrade recently?
I would only plot your results below 50 Hz. We don't care about the RMS at high frequencies and it can make the RMS misleading.
We definitely need to include one vertical Wilconox at each MC chamber so that it can subtract all of that junk at 10-20 Hz.
Big thumbnails? Could it have been this? elog:11498.
Anyways, I fixed the plots and plotted an RMS that can actaully be read in my original eLOG. I'll see what can be done with the MC1 and MC2 Wilcoxon (z-channel) for online subtractions.
Ignacio is correct; I forgot to shrink the value back down after testing the PDF thumbnails. Default thumbnail size is now back to 600px.
I'm not totally sure, but by eyeball, this seems like the best online MCL reduction we've ever had. Nice work.
The 3 Hz performance is the same as usual, but we've never had such good 1 Hz reduction in the online subtraction.
I would like to see a plot of the X & Y arm control signals with only the MCL filter ON/OFF. This would tell us how much of the arm signals were truly frequency noise.
We took data for the mode cleaner a while ago, June 30th I believe. This data contained signals from the six accelerometers and the three seismometers. In here I have only focused on the seimometer signals as witnesses in order to construct Wiener filters for each of the three seismometer signals (x,y,z) and for the combined seismometers signal. The following plot showing the ASD's shows the results,
Wiener filtering works beautifully for the seismometers. Note that subtraction is best when we use all three seismometers as the witnesses in the Wiener filter calculation, as can be clearly seen in the first plot above.
Now, I used vectfit to conver the Wiener FIR filters for each seismometer to their IIR versions. The following are the bode plots for the IIR filters,
For the x-direction seismometer,
For the y-direction seismometer
And for the z-direction seismometer,
The IIR filters were computed using 5 zeros and 5 poles using vectfit. That was the maximum number of poles that I could use wihtout running into trouble with matrices being almost singular in Matlab. I still need to figure out how to deal with this issue in more detail as fitting the y-seismometer was a bit problematic. I think having a greater number of poles will make the fitting a bit easier.
(updateAfter Eric gave me feedback on my previous elog post, I went back and fixed some of the silly stuff I stated.
First of all, I have come to realized that it makes zero sense to plot the ASD's of the mode cleaner against the seismometer noise. These measurements are not only quite different, but elementary, they posess different units. I have focused my attention to the MCL being Wiener filtered with the three siesmometer signals.
One of the major improvements that I make in the following analysis is,
1) Prefiltering; a band pass filter from 1 to 5 Hz, in order to emphasize subtraction of the bump shown in the figure below.
2) I have used vectfit exclusively in the 1 to ~5 Hz range, in order to model the FIR filter properly, as in, the kind of subtraction that we care about. Limiting myself to the 1 - 5 Hz range has allowed me to play freeley with the number of poles, hence being able to fit the FIIR filter properly with an IIR rational transfer function properly,
The resulting ASD's are shown below, in blue we show the raw MCL output, in blac the Wiener filter (FIR) result, and finally in black, the resultant data being filtered with the calculated IIR Wiener filter.
Now, in the following plots I show the IIR Wiener filters for each of the three seismometers,
For the Y seismometer,
and for the Z seismometer,
The matlab code for this work is attached: code.zip
As MCL is disturbing arm locking by injecting a lot of noise, I have modified 'mcup' to disable MCL
As MC WFS keeps failing to start up when it is locked, the lines in 'mcwfsoff' to clear WFS filter history were restored.
MC down script is too slow to block MC_L when the cavity goes out of lock. As a result the loop strongly kicks MC2. We decided to make a threshold inside MCS model on MC TRANS that will block MC_L during lock loss. This is a lower threshold. Upper threshold can be slow and is implemented inside MC up script.
Fast threshold can be set inside MC2 POS. I did not correct MC2 top level medm screen as it is the same for all core optics.
Note: Fast trigger will also block ALS signal if MC loose lock.
I turned on some filters and gain in the SUS-MC2_MCL filter bank tonight so as suppress the seismic noise influence on MC_F. This may help the MC stay in lock in the daytime.
Koji updated the mcdown and mcup scripts to turn the MCL path on and off and to engage the Boost filters at the right time.
The attached PNG shows the MCL screen with the filters all ON. In this state the crossover frequency is ~45 Hz. MC_F at low frequencies is reduced by more than 10x.
I also think that this may help the X-Arm lock. The number of fringes per second should be 2-3x less.
I did a raw calibration of MCL and GUR. Accuracy is a factor of 2.
GUR path : 800 V/m/s => readout box (G~100) => ADC (0.7 mV/count)
MCL path : laser 1 MHz / V, cavity length ~ 25 m
I measured feedback signal before the laser with SR and avoided whitening filters for MC_F.
I've added MCL and WFS stop triggers into C1MCS/SUS model. Threshold value of MC_TRANS can be changed in the text entry located in MC2_POSITION medm screen. I tried 2 cases: trigger either blocks signal before MCL filter bank input or after output. Due to filter history in the 1 case MC2 was still slightly disturbed (C1:SUS-MC2_ULPD_VAR ~= 15) right after unlock. In the second case there was no disturbance as we zero output signal, but then I had to add "clear history" command to the mcup script.
WFS triggers block the signal before ASCPIT/YAW filter bank.
I've redone the WFS triggers. I left the MCL trigger alone (for now....I'll come back to it).
The trigger was setup such that (a) it was totally unclear what was going on, by looking at the WFS screen. Koji and I spent some time confused before I remembered that Den did this work recently. Also, for some reason, the triggers were just plain thresholding, not a schmidt trigger, so any time the cavity flashed, the WFS came on. Since the cavity can flash before the mcdown script has a chance to turn off the WFS servos, the outputs of the WFS filters are trying to output thousands of counts, and the signal goes through any time the cavity flashes. Not so good.
I have removed the triggering for the angular DoFs from the mcs model (leaving the MCL triggering for now). I have put new triggering into the ioo model, at the error point of the WFS loops. The idea is that if the cavity unlocks, we don't want to lose the current pointing of the mirrors. If the WFS servos were doing a lot of DC work, the bias sliders won't have the full information about where we want the mirrors to point. Since we have the integrators in FM1, removing the input signal should freeze the output signal. I need to modify the WFS on / off script so that this doesn't get turned off every lockloss.
Also, I have implemented (for the first time in a useful model, although I've done some testing in the tst model) the "wait" delay between a cavity locking and the trigger going through. The idea is that we don't necessarily want the WFS to come on simultaneously with the cavity lock. Since the wait delay resets any time it is un-triggered, this also prevents any signals from going through during cavity flashes. The wait block has 3 inputs: (1) a trigger, the output of some kind of trigger block, (2) a number of seconds to wait and (3) the model rate in Hz. The model rate should be set with a constant in the model, the trigger passed from the trigger block, and the wait time in seconds should be available as an epics input.
So far it looks like it's working as I expect, although I'm honestly too tired to do enough testing that I'm satisfied with, so I'm leaving the WFS off for the night.
I've redone the WFS triggers. I left the MCL trigger alone (for now....I'll come back to it).
Your schmitt trigger has 2 threshold values - min and max. Set thresholding value in my trigger to the max of your schmitt trigger and you get the same behavior for MC, triggers are not supposed to turn anything on in this realization as they do for locking with flashing.
The problem is that the WFS were being engaged with your triggers every time the MC flashed. That wasn't a schmidt trigger thing, but I like the schmidt trigger better anyway.
Anyhow, it's turned on, and it works really well. It's kind of awesome. I'm really excited to start using the wait block to start pushing even more of the locking out of scripts and into the real time system.
Riju did the measurement of the MCREFL PD.
I found data files in her directory on the control machine.
I was not sure how much was the transimpedance of the DC out.
I assumed the default number from the circuit diagram which was 66.7Ohm.
This may cause the error in absolute caribration of the transimpedance but the shape does not change.
The RF preamp is gain-peeking at 250MHz.
Here is further characterization of the PD response.
As you can see in the second attachment, the 3dB cut off of the resonance is about 2.3MHz.
The game plan file in dropbox was also modified.
Gautam and Steve,
Our MCREFL rfpd C30642GH 2x2mm beeing investigated for burned spots.
Atm1, unused - brand new pd
Atm2,3,4 MCREFL in place was not moved
More pictures will be posted on 40m Picassa site later.
I did a quick measurement of the beam size on the MC REFL PD today morning. I disabled the MC autolocker while this measurement was in progress. The measurement set up was as follows:
This way I was able to get right up to the heat sink - so this is approximately 2cm away from the active area of the PD. I could also measure the beam size in both the horizontal and vertical directions.
The measured and fitted data are:
The beam size is ~0.4mm in diameter, while the active area of the photodiode is 2mm in diameter according to the datasheet. So the beam is ~5x smaller than the active area of the PD. I couldn't find anything in the datasheet about what the damage threshold is in terms of incident optical power, but there is ~100mW on th MC REFL PD when the MC is unlocked, which corresponds to a peak intensity of ~1.7 W / mm^2...
Even though no optics were intentionally touched for this measurement, I quickly verified that the spot is centered on the MC REFL PD by looking at the DC output of the PD, and then re-enabled the autolocker.
Kevin, Gautam and Arijit
We did a optical measurement of the MCREFL_PD transimpedance using the Jenny Laser set-up. We used 0.56mW @1064nm on the NewFocus 1611 Photodiode as reference and 0.475mW @1064nm on the MCREFL_PD. Transfer function was measured using the AG4395 network analyzer. We also fit the data using the refined LISO model. From the optical measurement, we can see that we do not have a prominent peak at about 300MHz like the one we had from the electrical transimpedence measurement. We also put in the electrical transimpedence measurement as reference. RMS contribution of 300MHz peak to follow.
As per Rana`s advice I have updated the entry with information on the LISO fit quality and parameters used. I have put all the relevant files concerning the above measurement as well as the LISO fit and output files as a zip file "LISO_fit" . I also added a note describing what each file represents. I have also updated the plot with fit parameters and errors as in elog 10406.
Today we performed the in-loop noise measurements of the MCREFL-PD using the SR785 to ascertain the effect of the Noise Eater on the laser. We took the measurements at the demodulated output channel from the MCREFL-PD. We performed a series of 6 measurements with the Noise Eater ''ON'' and ''OFF''. The first data set is an outlier probably, due to some transient effects. The remaining data sets were recorded in succession with a time interval of 5 minutes each between the Noise Eater in the ''ON'' and ''OFF'' state. We used the calibration factor of 13kHz/Vrms from elog 13696 to convert the V_rms to Hz-scale.
The conclusion is that the NOISE EATER does not have any noticeable effect on the noise measurements.
ALS beat spectrum and also the arm control signal look as they did before. coherence between arm control signals (in POX/POY lock) is high between 10-100Hz, so looks like there is still excess frequency noise in the MC transmitted light. Looking at POX as an OOL sensor with the arm under ALS control shows ~10x the noise at 100 Hz compared to the "nominal" level, consistent with what Koji and I observed ~3weeks ago.
We tried swapping out Marconis. Problem persists. So Marconi is not to blame. I wanted to rule this out as in Jan, Steve and I had installed a 10MHz reference to the rear of the Marconi.
the noise eater on/off measurements should be done for 0-100 kHz and from the demod board output monitor
We redid the measurement measuring the voltage noise from the REFL PD demod board output monitor with an SR785 with the noise eater on and off. We used a 100x preamp to amplify the signal above the SR785 noise. The SR785 noise floor was measured with the input to the preamp terminated with 50 ohms. The spectra shown have been corrected for the 100x amplification.
This measurement shows no difference with the noise eater on or off.
I found that MCT QPD has a dependence of the total output on the position of the spot. Since the QPD needs the supply and bias voltages from the sum/diff amp, I could not separate the problems of the QPD itself and the sum/diff amplifier by the investigation on Tuesday. On Wednesday, I investigated a generic quad photodiode interface module D990692.
...I was so disappointed. This circuit was left uninvestigated and used so long time with the following sorrowful conditions.
- This circuit has 4 unbuffered inputs with input impedance of 300~400 Ohm. It's way too low!
- Moreover, those channels have different input impedances. Ahhhh.
- Even worse, the QPD circuit D990272 has output impedance of 50 Ohm.
- The PCB of this circuit has four layers. It is quite difficult to make modifications of the signal route.
- It is a headache: this circuit is "generic" and used in many places.
D990692 has 4 channel inputs that are not buffered. Each channel has two high impedance buffers but they are used only for the monitors. The signal paths have no buffer.
The differential amplifier is formed by R=1k Ohm. The inverted side of the input has 1kOhm impedance. The non-inverted side has 1.5kOhm impedance.
CH1: 10K // 1.5k // 1.5k // 1k = 411 Ohm
CH2: 10K // 1.5k // 1k // 1k = 361 Ohm
CH3: 10K // 1k // 1k // 1k = 323 Ohm
CH4: 10K // 1k // 1.5k // 1k = 361 Ohm
Considering the output impedance of 50Ohm for the QPD, those too low input impedances result in the following effect:
- Because of the voltage division, we suffer absolute errors of 10.8~13.4%. This is huge.
- Because of the input impedance differences, we suffer a relative error of 1.5%~3%. This is also huge.
Unfortunately, the circuit has no room to modify; the signal paths are embedded in the internal layer.
I decided to replace the resistors of the sum/diff amps from 1k to 10k. Also the input impedance of the buffer was removed as the input is terminated by the sum/diff amps in any case.This changes the input inpedance to the followings:
CH1: 15k // 15k // 10k = 4286 Ohm
CH2: 15k // 10k // 10k = 3750 Ohm
CH3: 10k // 10k // 10k = 3333 Ohm
CH4: 10K // 15k // 10k = 3750 Ohm
These yield the absolute error of 1.2-1.5%. The relative error is now 0.3%. I can accept these numbers, but later I should put additional terminating resistors to compensate the differencies.
So far I have modified the resistors for the MCT as the modification for a QPD needs 17 10k resistors.
Next thing I have to check is the dependence of the QPD outputs on the spot positions.
Edit: Feb 11, 2010
I talked with Frank and he pointed out that the impedances are not the matter but the gains of the each channels are the matters (after considering the output impedance of the QPD channels).
If we assume the ideal voltage sources at the QPD and the symmetric output impedances of 50Ohm, the gain of the each circuit are affected but the change should be symmetric.
He found that several things:
- The analog switch (MAX333) used in the QPD unit adds more output impedance (somewhat randomly!).
- The resistance of the sum/diff circuits may vary each other unless we use 0.1% resistors.
I found that MCT QPD has dependence of the total output on the position of the spot. Since the QPD needs the supply and bias voltages from the sum/diff amp, I could not separate the problems of the QPD iteself and the sum/diff amplifier by the investigation on Tuesday. On Wednesday, I investigated a generic quad photodiode interface module D990692.
This is indeed sad. But, we can perhaps bypass all of this by just using the individual segment outputs. According to the circuit diagram and the c1iool0 .db file, we should be able to just do the math on the segments and ignore the VERT/HOR/SUM signals completely. In that case, we can just use high impedance for the sum/diff buffers as Koji says and not suffer from the calibration errors at all I think.
Unfortunately, the signals for individual segments also suffer from the voltage drop as all of the low impedance amplifiers are hung from the same input.
In order to utilize the individual channels, we anyway have to remove the resistors for the VERT/HOR/SUM amps.
That is possible. But does it disable some fast channels for future ASC purposes?
For a certain investigation of the sum/diff module for MCT QPD/MC REFL QPD, I removed it from the system.
I undid Yuta's temporary setup, and put beam back on both WFS. Since Koji had just aligned the Mode Cleaner, I centered the beam on the WFS using the WFS QPD screen, while watching the WFS Head screen, to make sure that the beam was actually hitting the QPD, and not off in lala land.
- We must check the MCWFS path alignment and configuration.
* Noticed that the MCWFS path is totally wrong. Someone (Yuta?) wanted to use the MCWFS as a reference, but the steering mirror in front of WFS1 was switched out, and now no beam goes to WFS2 (it's blocked by part of the mount of the new mirror). I have not yet fixed this, since I wasn't using the WFS tonight, and had other things to get done. We will need to fix this.
Not satisfactory work of adaptive filtering make us to think about the signals that we use. Now we try to deal with mode cleaner and analize its length. We take MC_F channel. We know that MC_F is used as a feedback signal to the laser frequency and laser changes it's frequency linear to the input modulation signal up to ~1kHz. Than is MC_F is length of MC, not velocity or acceleration. If so, it's form due to seismic noise + company of other noises + stacks and wires should be approximately like the left plot. Instead we see the right plot.
Possibly, left-plot form signal is not possible to transmit through the wires and adc. Most signal at medium and high frequencies would be lost because of wire and adc noise. For that reason mode cleaner length signal might be amplified at frequecnies >~20 Hz by some bandpass filter.
Where is this highpass filter and what is the form of this filter?
It might be just after the photodetector in order not to transmit real mode cleaner length through the wires. But if wires and not very noisy, it could be somewhere before ADC.
But anyway, for the laser frequency feedback the corresponding low pass filter should be used.
Where is this lowpass filter and what is the form of the filter?
We followed the mode cleaner length signal up to TT FSS and measured the mode cleaner length, that is used as an input to TT FSS. As shown http://nodus.ligo.caltech.edu:8080/40m/5867 MC_F is different from the signal that is given to TT FSS. This is not clear because we do not have smth that could effect on the signal that much before branch node and recording of MC_F. The main difference is the cut off at the MC_F signal at 3 Hz. It might be a digital filter but we do not see any filters between adc_0_0 up to MC_F test point - straight line. This means that we have an analog filter somewhere between that blue box where the branch point is and ADC. We need to find it. But at least, we do not have a lowpass filter before FSS. So it is probably after it.
So, we need to find the 3 filters that we think affect on the MC_F channel in order to figure out why we have such a bad coherence between seismic signal and mode cleaner length.
There should be a whitening filter in the Pentek Generic DAQ board (Eurocard with 8 differential LEMO inputs). It used to be that the MC_L channel came in through here and I believe it has 2 stages of 150:15 pole:zero filters.
I don't remember if it is one or two stages, but this should be easy to measure with a function generator or by driving this input using the MC2 UL Coil monitor and doing the transfer function in DTT (as Koji and Jenne did for the demod boards).
- Saved BURT backup in /users/anchal/BURTsnaps/
- Copied existing code for mode cleaner noise budget from /users/rana/mat/mc. Will work on this from home to convert it inot new pynb way.
Get baseline IMC measurements (passive):
- What is MC_F? Let's find out.
- On MC_F Cal window titled 'C1IOO-MC_FREQ', we turned off ON/OFF and back on again.
- Using diaggui, we measured ASD of MC_F channel in units of counts/rtHz.
- Using diaggui, measured ASD from a template (under /users/Templates) and overlay the 1/f noise of the NPRO (Attachment 1)
- WFS Master
- Went through the schematic and tried to understand what is happening.
- Accidentally switched on MC WF relief (python 3). Bunch of things were displayed on a terminal for a while and then we Ctrl-C it.
- The only thing we noticed that change is a slight increase in WFS1 Yaw, and a corresponding decrease in WFS1 Pitch, WFS2 Pitch, and WFS2 Yaw.
- We need to find out what this script does.
The last MC_F calibration was done by Ayaka : Elog 7823
And does anyone know what the MC_F calibration is?
I saw that entry, but it doesn't state what the calibration is in units of Hz/counts. It just gives the final calibrated spectrum.
It's railed. This is what halted locking progess on Monday night, as this channel is used for the offloadMCF script, which slowly feeds back a CARM signal to the ETMs to prevent the VCO from saturating.
Attached is a 5 day trend, which shows that the channel went dead a few days ago. All the channels shown are being collected from the same ICS110B (I think), but only some are dead. It looks like they went dead around the time of the "All computers down" from Sunday.
Attached are the channels being recorded from the ICS110B in 1Y2 (the IOO rack). Channels 12, 13, 16, 17, 22, 24, 25 appear to have gone dead after the computer problems on Sunday.
This has been fixed by one of the two most powerful & useful IFO debugging techniques: rebooting. I keyed the crate in 1Y2.
Sometimes I like to plot the spectrum of MC_F. Its a good diagnosis of whether something is wrong.
The red trace is noisier than the blue reference. What is the cause of this?
MC_F low frequency noise might be due to local damping electronics. I did not measure OSEM noise, but even without it electronics (AA -> ICS 110 -> ADC) provide sufficient amount of noise.
These 2 image show electronics noise and coherence between OSEM signal / seismic
From these 2 plots we might think that SNR > 10 and coherence OSEM / GUR is high at the frequency range 0.1 - 10 Hz and this is not a big problem.
However, at low frequencies the length of seismic waves becomes large enough and relative oscillations of MC2 and MC13 decrease.
For 1 wave ( u(MC2) - u(MC1) ) / u(MC2) = sin(2 * pi * L * f / c), L - distance between MC1 and MC2 where 2 seismometers are located. So MC123 move according to seismic motion and electronics noise is not seen unless we look at MC Length. Here this noise is seen, because mirrors move in a synchronistic manner.
To check this I measured seismic noise with 2 guralps at distance 12 meters - at MC1 and MC2. Then I've computed the difference between these signals. And indeed at low frequencies, relative motion is much less.
Green, blue - GUR1,2_X
Red - differential motion GUR1_X - GUR2_X
The following plot illustrates how electronics noise effects MC_F. Green is the signal to coils. Red - electronics noise. Blue, black, cyan - simulated contribution to MC_F for different seismic waves speed. Most probably seismic waves have waves in the range 50 - 800 m/s, others are deep. The plot shows that electronics noise is big enough to disturb coherence between MC_F and seismic noise.
Here is a rough calculation of the seismic waves speed. The following plot shows the ratio of psd of differential MC2-MC1 motion to MC2 motion.
If seismometers would be very far, ratio would be 1 if we neglect the difference in transfer function SEISMOMETER -> ADC for each channel. The drift of the ratio from 1 to 1.3 demonstrates this effect. Ratio starts to decrease at 15 Hz according to sin (2*pi*L*f/c) ~ 2*pi*L/c * f. So 2*pi*L/c * f_0 = pi/2 => c = 4 * L * f = 600 m / sec.
We looked at the different outputs of the MC servo board to make sure they make some kind of sense. As per my elog 6625, the names of the channels were wrong, but we wanted to confirm that we have something sensible.
Currently, OUT1 of the servo board is called "MC_F" and the SERVO out is called "MC_SERVO". We looked at the spectrum of each, and the transfer function between them.
You can see that in addition to a 2kHz pole, MC_L also seems to have a 10-100 zero-pole pair.
Also, while cleaning things up in the models, I fixed the names of these MCL/MCF channels. OUT1 is now called MC_L, and is connected to ADC0_0, and SERVO is called MC_F and is connected to ADC0_6. Both MC_L and MC_F go to the RFM, and thence on to the OAF. MC_L (which used to be mis-named MC_F) still goes both to the MCS model for actuation on MC2, and to the OAF for MC-OAF-ing. Right now MC_F is unused in the OAF model, but we can change that later if we want.
I grabbed the a plot of the iLIGO PSL frequency noise spectrum from the Rana manifesto:
Rana's contention is that this spectrum (red trace) is roughly the same as for our NPRO.
From the jenne/mevans/pepper/rana paper Active noise cancellation in a suspended interferometer I pulled a plot of the calibrated MC_L noise spectrum:
The green line on this plot is a rough estimate of where the above laser frequency noise would fall on this plot. The conversion is:
L / f = 10 m / 2.8e14 Hz = 3.5e-14 m/Hz
which at 10 Hz is roughly 1.5e-11 m. This puts the crossover somewhere between 1 and 10 Hz.