We have been discussing how does the parameter estimation depends on the length per FFT segment. In other words, after we collected a series of data, would it be better for us to divide it into many segments so that we have many averages, or should we use long FFT segments so that we have more frequency bins?
My conclusions are that:
1). We need to make sure that the segment length is long enough with T_seg > min[ Q_i / f_i ], where f_i is the resonant frequency of the i'th resonant peak and the Q_i its quality factor.
2). Once 1) is satisfied, the result depends weakly on the FFT length. There might be a weak hint preferring a longer segment length (i.e., want more freq bins than more averages) though.
To reach the conclusion, I performed the following numerical experiment.
I considered a simple pendulum with resonant frequency f_1 = 0.993 Hz and Q_1 = 6.23. The value of f_1 is chosen such that it is not too special to fall into a single freq bin. Additionally, I set an overall gain of k=20. I generated T_tot = 512 s of data in the time domain and then did the standard frequency domain TF estimation. I.e., I computed the CSD between excitation and response (with noise) over the PSD of the excitation. The spectra of excitation and noise in the readout channel are shown in the first plot.
In the second plot, I showed the 1-sigma errors from the Fisher matrix calculation of the three parameters in this problem, as well as the determinant of the error matrix \Sigma = inv(Fisher matrix). All quantities are plotted as functions of the duration per FFT segment T_seg. The red dotted line is [Q_1/f_1], i.e., the time required to resolve the resonant peak. As one would expect, if T_seg <~ (Q_1/f_1), we cannot resolve the dynamics of the system and therefore we get nonsense PE results. However, once T_seg > (Q_1/f_1), the PE results seem to be just fluctuating (as f_1 does not fall exactly into a single bin). Maybe there is a small hint that longer T_seg is better. Potentially, this might be due to that we lose less information due to windowing? To be investigated further...
I also showed the Fisher estimation vs. MCMC results in the last two plots. Here each dot is an MCMC posterior. The red crosses are the true values, and the purple contours are the results of the Fisher calculations (3-sigma contours). The MCMC results showed similar trends as the Fisher predictions and the results for T_seg = (32, 64, 128) s all have similar amounts of scattering << the scattering of the T_seg=8 s results. Though somehow it showed a biased result. In the third plot, I manually corrected the mean so that we could just compare the scattering. The fourth plot showed the original posterior distribution.
Koji and I have prepared the vacuum system for the power outage on Saturday.
From here, we shutdown electronics.
/sbin/shutdown -h now
Koji and I began starting that Vacuum system up.
- Once the FRG gauge readings are back (see next elog by Tega), I could open V1 to pump down the main vacuum manifold.
- TP2/TP3 were brought back to stand-by mode (slower spinning)
- V7 was closed to separate the annuli side and TP1
During the vacuum recovery, I saw TPs were automatically turned on as soon as the backing pumps were engaged. I could not figure out what caused this automation.
Also, I saw some gate valve states changed while I was not touching them. e.g. V7 was close / VM3 was open / etc
I really had no idea what/who was handling these.
As of ~18:00 local, the main volume pressure is ~2e-5 torr and ready to open the PSL shutter.
[Paco, Chris Stoughton, Leo -- remote]
This morning Chris came over to the 40m lab to help us get the RFSoC board going. After checking out our setup, we decided to do a very basic series of checks to see if we can at least get the ADCs to run coherently (independent of the DACs). For this I borrowed the Marconi 2023B from inside the lab and set its output to 1.137 GHz, 0 dBm. Then, I plugged it into the ADC1 and just ran the usual spectrum analyzer notebook on the rfsoc jupyter lab server. Attachment #1 - 2 shows the screen captured PSDs for ADCs 0 and 1 respectively with the 1137 MHz peaks alright.
The fast ADCs are indeed reading our input signals.
Before this simple test, we actually reached out to Leo over at Fermilab for some remote assistance on building up our minimally working firmware. For this, Chris started a new vivado project on his laptop, and realized the rfsoc 2x2 board files are not included in it by default. In order to add them, we had to go into Tools, Settings and add the 2020.1 Vivado Xilinx shop board repository path to the rfsoc2x2 v1.1 files. After a little bit of struggling, uninstalling, reinstalling them, and restarting Vivado, we managed to get into the actual overlay design. In there, with Leo's assistance, we dropped the Zynq MPSoC core (this includes the main interface drivers for the rfsoc 2x2 board). We then dropped an rf converter IP block, which we customized to use the right PLL settings. The settings, from the System Clocking tab were changed to have a 409.6 MHz Reference Clock (default was 122.88 MHz). This was not straightforward, as the default sampling rate of 2.00 GSPS was not integer-related so we had to also update that to 4.096 GSPS. Then, we saw that the max available Clock Out option was 256 MHz (we need to be >= 409.6 MHz), so Leo suggested we dropped a Clocking Wizard block to provide a 512 MHz clock input for the rfdc. The final settings are captured in Attachment # 3. The Clocking Wizard was added, and configured on its Output Clocks tab to provide a Requested Output Freq of 512 MHz. The finall settings of the Clocking wizard are captured in Attachment #4. Finally, we connected the blocks as shown in Attachment #5.
We will continue with this design tomorrow.
I found this interesting entry by Rana in the old (deprecated) elog : here
I wonder if Rolf has ever written the mentioned GUI that explained the rationale behind the test point number mapping.
I'm just trying to add the StochMon calibrated channels to the frames. Now I remember why I kept forgetting of doing it...
At ITMX, on the CES side, 5 Ft from the wall the jackhammer is on. The susses are holding well.
We are celebrating Rob's promotion to thesis poetry. These pictures were taken on December 9, 2009
Rob has finished all his measurements in the lab and is officially well prepared to graduate.
There is a planned power outage tomorrow, Saturday from 7am till midnight.
I vented all annulies and switched to ALL OFF configuration. The small region of the RGA is still under vacuum.
The vac-rack: gauges, c1vac1 and UPS turned off.
It turns out that we perfecly timed the big one
In the process of finding the signal of the big chilean earthquake I just realized that we were all off
There's several more of the this vintage in one of the last cabinets down the new Y-arm.
Hold on, did the arms get re-baptized?
John Miller has arrived from Australia with 3 bags of Wagonga Coffee. Trade bargaining has started on
250 mgs of Sumatran Mandehling, Timur and Papua New Guine.
I'm cleaning out to make room for our new optical cabinet. Are we keeping these? There are ~20 pieces of 10" od 1" wide tapes and large number of cassettes.
AJW, Zucker, Stuart A and Koji were notified in this matter.
Alan suggested to save data of Bruce Allen paper of observation of binary neutron stars in the 40m on 1994 November 14-20 and save back up tapes of his period in the 40m.
Mike: reels are not readable any more, it is time to let go
After Kiwamu set the REFL11 phases in the PRMI configuration (maximized PRM->REFL11I reesponse) I tried to measure the MC length and the 11 MHz frequency missmatch by modulating the 11 MHz frequency and measuring the PM to AM conversion after the MC using the REFL11Q signal. The modulation appears in the REFL11Q with a good snr but the amplitude does not seem to go through a clear minimum as the 11 MHz goes through the MC resonance.
We could not relock the PRMI during the day so I resorted to a weaker method - measuring the amplitude of the 11 MHz sideband in the MC reflection (RF PD mon output on the demod board) with a RF spectrum analyzer. The minimum frequency on the IFR is 11.065650 MHz while the nominal setting was 11.065000 MHz. The sensitivity of this method is about 50 Hz.
Elog crashed a couple times, restarted it a couple times.
Just a reminder that a film crew will be here Monday morning, filming Christian Ott for some Discovery channel show.
They are slated to be here from 8am to 12:30pm or so. They will take a couple of shots inside the lab, and the rest of the filming should be of Christian in the control room (which they will "clean up" and fit with "sexy lighting"). I will try to be here the whole time to oversee everything.
Also, according to Steve, there will be some crane guys for fixing the Y end crane issue (#5124) Monday morning.
a film crew will be here Monday morning. They are slated to be here from 8am to 12:30pm or so.
Konecrane Fred was early this morning. He diagnosed the ETMY crane horizontal drive gear box dead and left just before the film crew showed up.
New gear box should be here by the end of this week for installation.
The lab air quality is high ~20,000 counts of particles of 0.5 micron. Keep an eye on this before you open the chamber.
Elog did not respond despite running the /cvs/cds/caltech/elog/start-elog.csh script two times.
It worked the after the third restart.
It seems like there is some confusion---or disagreement---amongst the lab about how to proceed with the RAM work (as Rana mentioned at the TAC meeting, we will henceforth refer to it only as "RAM" and never as "RFAM"; those who refuse to follow this protocol will be taken out back and shot).
I would like to provide a rough outline and then request that people reply with comments, so that we can get a collective picture of how this should work. I have divided this into two sections: 1) Methodology, which is concerned with the overall goal of the testing and the procedure for meeting them, and 2) General Issues, which are broadly important regardless of the chosen methodology.
There are two broad goals:
The question is: which is our goal? The first, the second, or both? If both, what priority is given to which and can/should they be done in parallel? Also, task distribution.
2. General Issues
These are loosely related, so they are in random order:
There are probably many other issues I have neglected, so please comment on this rough draft as you see fit!
Since no one has made any comments, I will assume that everyone is either 100% satisfied with the outline or they have no interest in the project. Under this assumption, I will make decisions on my own and begin planning the individual steps in more detail.
In particular, I will assume that our goal comprises BOTH characterization of RAM levels and mitigation, and I will try to find the best way that both can be achieved as simultaneously as possible.
I know it's really hard to remember, but our future selves will thank us dearly if we remember to commit all of our code changes to the svn with nice log messages. At the moment there's a LOT of modified stuff in the userapps working directory that needs to be committed:
controls@pianosa:/opt/rtcds/userapps/release 0$ svn status | grep '^M'
This doesn't even include things that haven't even been added yet. It doesn't take much time. Just copy and paste what you elog about the changes.
Let's see if the ripples observed in the MC ringdown can be due to tilt motion of the mirrors.
The time it takes to produce a phase shift corresponding to N multiples of 2*pi is given by:
t = sqrt(2*N*lambda/(L*omega_T^2*(alpha_1+alpha_2)))
L is the length of the MC (something like 13m), and alpha_1, alpha_2 are the DC tilt angles of the two mirrors "shooting into the long arms of the MC" produced by the MC control with respect to the mechanical equilibrium position. omega_T is the tilt eigenfrequency of the three mirrors (assumed to be identical). lambda = 1.064e-6m;
The time it takes from N=1 to N=2 (the first observable ripple) is given by: tau1 = 0.6/omega_T*sqrt(lambda/L/(alpha_1+alpha_2))
The time it takes from N=2 to N=3 is given by: tau2 = 0.77*tau1
First, we also see in the measurement that later ripples are shorter than early ripples consistent with some accelerated effect. The predicted ripple durations tau seem to be a bit too high though. The measurements show something like a first 14us and a late 8us ripple. It depends somewhat on the initial tilt angles that I don't know really.
In any case, the short ripple times could also be explained if the tilt motions start a little earlier than the ringdown, or the tilt motion starts with some small initial velocity. The next step will be to program a little ringdown simulation that includes mirror tilts and see what kind of tilt motion would produce the ripples exactly as we observe them (or maybe tilt motion cannot produce ripples as observed).
Isn't it just a ringing of the intracavity power as you shifted the laser frequency abruptly?
Hmm. I don't know what ringing really is. Ok, let's assume it has to do with the pump... I don't see how the pump laser could produce these ripples. They have large amplitudes and so I always suspected something happening to the intracavity field. Therefore I was looking for effects that would change resonance conditions of the intracavity field during ringdown. Tilt motion seemed to be one explanation to me, but it may be a bit too slow (not sure yet). Longitudinal mirror motion is certainly too slow. What else could there be?
Laser frequency shift = longitudinal motion of the mirrors
Ok, so the whole idea that mirror motion can explain the ripples is nonsense. At least, when you think off the ringdown with "pump off". The phase shifts that I tried to estimate from longitudinal and tilt mirror motion are defined against a non-existing reference. So I guess that I have to click on the link that Koji posted...
Just to mention, for the tilt phase shift (yes, there is one, but the exact expression has two more factors in the equation I posted), it does not matter, which mirror tilts. So even for a lower bound on the ripple time, my equation was incorrect. It should have the sum over all three initial tilt angles not only the two "shooting into the long arms" of the MC.
With a curvature radius of about 57m for the ETMs, flat ITMs at the beam waist, and using 39m for the arm lengths, one finds that the beam radius at the ETMs is about 5.3mm. The clipping power loss of a 5.3mm beam through a 20mm radius baffle hole would be less than a ppm of a ppm if the beam was perfectly centered. If the baffle hole had 15mm radius, the clipping loss would be 0.01ppm. If the baffle hole had 10mm radius, the loss would be 810ppm. The loss values are calculated using the formula of the "Gaussian beam" Wikipedia article, "Power through an aperture" section. So I did not check if that one is ok.
I finally managed to get long stretches of PRMI lock, up to many minutes. The lock is not yest very stable, it seems to me that we are limited by some yaw oscillation that I could not trace down. The oscillation is very well visible on POP.
Presently, PRCL is controlled with REFL55_I, while MICH is controlled with AS55_Q. This configuration is maybe not optimal from the point of view of phase noise couplings, but at least it works quite well. I believe that the limit on the length of locks is given by the angular oscillation. I attach to this entry few plots showing some of the lock stretches. The alignment is not optimal, as visible from a quite large TEM01 mode at the dark port.
Here are the parameters I used:
MICH gain -10 PRCL gain -0.1
Normalization of both error signal on POP22_I with factor 0.004
Triggering on POP22: in at 100, out at 20 for both MICH and PRCL.
POP55 demodulation phase -9
MICH and PRCL control signal limits at 2000 counts
There is a high frequency (628 Hz) oscillation going on when locked (very annoying on the speakers...), but reducing the gain made the lock less stable. I could go down to MICH=-1.5 and PRCL=-0.02, still being able to acquire the lock. But the oscillation was still there. I suspect that it is not due to the loops, but maybe some resonance of the suspension or payload (violin mode?). There is still some room for fine tuning...
Lock is acquired without problems and maintained for minutes.
Have a nice week-end!
I put a notch in FM10 for both MICH and PRCL at 628Hz, to try to prevent us from exciting the mode that Gabriele saw on Friday. Since those filter banks were all full, I have removed an ELP50 (ellip("LowPass",4,1,40,50)). I write it down here, so we can put it back if so desired.
Koji asked me to perform a simulation of the response of POP QPD DC signal to mirror motions, as a function of the CARM offset. Later than promised, here are the first round of results.
I simulated a double cavity, and the PRC is folded with parameters close to the 40m configuration. POP is extracted in transmission of PR2 (1ppm, forward beam). For the moment I just placed the QPD one meter from PR2, if needed we can adjust the Gouy phase. There are two QPDs in the simulation: one senses all the field coming out in POP, the other one is filtered to sense only the contribution from the carrier field. The difference can be used to compute what a POP_2F_QPD would sense. All mirrors are moved at 1 Hz and the QPD signals are simulated:
This shows the signal on the POP QPD when all fields (carrier and 55 MHz sidebands) are sensed. This is what a real DC QPD will see. As expected at low offset ETM is dominant, while at large offset the PRC mirrors are dominant. It's interesting to note that for any mirror, there is one offset where the signal disappears.
This is the contribution coming only from the carrier. This is what an ideal QPD with an optical low pass will sense. The contribution from the carrier increases with decreasing offset, as expected since there is more power.
Finally, this is what a 2F QPD will sense. The contribution is always dominated by the PRC mirrors, and the ETM is negligible.
The zeros in the real QPD signal is clearly coming from a cancellation of the contributions from carrier and sidebands.
The code is attached.
const Pin 1 # input power
const Lprc 6.752 # power recycling cavity length
const d_BS_PR3 0.401 # folding mirror distances
const d_PR2_PR3 2.081
const d_PRM_PR2 1.876
const c 299792458 # speed of light
const fmod 5*c/(4*Lprc) # modulation frequency, matched to Lprc
% compile simulation class
m = MIST('foldeddoublecavity.mist');
% create simulation object
s = FoldedDoubleCavity(8);
% set angulat motion
When I got back to the lab, there was enough water that it was seeping under the wall, and visible outside. Physical plant says it will take an hour before they can come, so I'm getting dinner, then will let them in.
The guy from physical plant came, and turned off the water to the kitchen sink. He is putting in a work order to have the plumbers come look at it on Monday morning. It looks like something is wrong with the water heater, and we're getting water out of the safety overpressure valve / pipe.
The wet things from under the sink are stacked (a little haphazardly) next to the cupboards.
Last supper before departing at "Grazie" El Portal. All the best on your journey!
While tightening the bolts on the ETMX wire clamp, the wire broke. All four face magnets broke off.
Fortunately, no pieces were lost.
For the rest of this vent, at least, we need to start using the EQ stops more frequently. Whenever the suspension is being worked on clamp the optic. When you need it to be free back off the stops, but only by a few hundred microns - never more than a millimeter.
Best to take our time and use the stops often. With all the magnets being broken off, its not clear now how many partially cracked glue joints we have on dumbells which didn't completely fall off.