Over the weekend, I ran Relay Tuning method for the PID of beatnote frequency control. After CTN:2426 this needed to be done to fix the PID constants to appropriate value. The results of the tuning were:
Critical period Tc = 45.900000000000006
Critical gain Kc = 18.382414309527164
Suggested kp, ki, kd are 3.676482861905433, 0.16019533167343933, 56.25018778715313
RXA: Wah! precision help here
The relay amplitude was set to 0.5 W and I could see very good sustained oscillations which the code used to get above calculated values.
I tested the performance of PID today. Attached is the convergence of beatnote frequency, which happened in about 20 minutes only to 40 kHz offset value. After that point, the proportional gain of the PID is so high, that the actuator response essentially copies the fluctuations in the beatnote frequency itself. So no more stabilization happens. The integral constant is very low (I think it is required for quick convergence with no overshoot), so to travel this 40 kHz distance, it will probably take hours. But that's fine with us as our photodetectors work well enough with this offset too.
If you see the second plot, the beatnote did not drift beyond +/- 2kHz for over 40 min. I want to see if tonights beatnote will get any better due to this good stabilization.
Code And Data
Attached is a first attempt at tracing the rays on reflection from the wedged and tilted window together with the cavity mirror.
I used Sean Leavey's zero and created a ray tracing module for simple purposes which is fast and easy to use. Check out the examples to see the capabilities.
To use, git pull labutils to update and keep labutils /traceit in your python path.
More info about each ray can be seen by layout['R4'] kind of statements. Or just write layout.rays to see info about all rays. This includes their vector positions, the origin phenomenon, and ray etc.
I know a lot can be done to make this look better. But I'm not going to dive into developing this module right now. However, suggestions on how to make the ray trace diagram more useful are welcome so that I can make it more informational.
Seems like most of the reflections would be bunched together in two directions where we should put the beam dumps.
Today I ran the two codes with the same parameter values to check if the effective reflectivities calculated during the calculation of thermo-optic nose matches. They do match exactly actually. Attached is an over plot.
Coating effective coefficient of thermo-refractive effect comes out to be:
Old Code: 8.61(46)e-05 K**-1
New Code: (8.59+/-0.21) e-05 K**-1
So this discrepancy was not really there. I was just comparing apples with oranges earlier.
The effective coating CTR in the previous code was 7.9e-5 1/K and in the new code, it is 8.2e-5 1/K. Since this value is calculated after a lot of steps, it might be round off error as initial values are slightly off. I need to check this calculation as well to make sure everything is right. Problem is that it is hard to understand how it is done in the previous code as it used matrices for doing complex value calculations. In new code, I just used ucomplex class and followed the paper's calculations. I need more time to look into this too. Suggestions are welcome.
Also, I found that the effective reflectivities from the top surface of layers calculated in Evans et a. PRD 78, 102003 (2008) were different from reflectivities calculated by matrix method in Hong et al. PRD 87, 082001 (2013). It turned out that the sign before phase in Eq. B3 and B4 in Evans et a. PRD 78, 102003 (2008) were opposite to what comes from the matrix method. After discussions with Gabriele, I came to the conclusion that this sign only creates a difference of giving complex conjugates of effective reflectivity. But to have consistency, I have corrected the sign of phase in the new code. Attached is a comparison of old effective reflectivity and the new one. One can see that the imaginary values are opposite in sign but everything else matches perfectly. Also, this has no effect on the effective coating coefficient of thermo-refraction.
Gabriele suggested that I plot the estimated coating Brownian noise for different values of bulk and shear loss angles and compare with the old code. The expectation is that the estimated noise should vary smoothly and should agree with old result where bulk and shear loss angles are taken the same. In the first plot, I have plotted estimate coating Brownian noise for CTN experiment over the nominal range of bulk and shear loss angles. Since this range doesn't really have an overlap with equal bulk and shear loss angle case, I made another plot in which such a square region is chosen. We can see that the estimated coating Brownian noise is slightly higher (roughly 2.5% from CTN:2390 figure 2).
Let me know if someone can think of a better viewing angle or more insights to take out from this. Code is attached.
Better Plots attached.
2D Heat Maps
Edit: Added comparison plot as well.
With comparison with old estimates:
Variation of the estimate of coating Brownian noise as beam spot radius on the mirror changes. Plotted in displacement noise as the frequency conversion factor is dependent on cavity length and beam radius also depends on that.
I used the method described in Section V of https://arxiv.org/abs/1406.4467, to do a bayesian inference using mechanical ring-down measurements of coating loss angles by Steve Penn (recently reported in https://dcc.ligo.org/LIGO-G1901676) as a prior. I assumed all probability distributions to be gaussian. We are clearly not close to measuring the Brownian noise as with present uncertainty limits reported by Penn et al, the prior distribution and the likelihood distribution do not overlap with each other at all, giving us no meaningful result. Note the different limits in x-axis on first and second plot.
This was a quick run of this though, just to set up the method. Ideally, I should use integrated noise in some frequency range around 300 Hz to use as the measurement. Also, Steve Penn actually did not report any uncertainty value with his measurements, so I assumed the uncertainty the same as his previous measurement. Looking forward to the more formal release of his data.
Liquid Instrument's Application Engineer at La Jolla told me that connection with moku might be mroe stable if it is directly connected to the computer through a USB cable. It still gets identified with Name, Serial Number or IP address, just the connection is mroerobust. So today, I have connected our moku with USB. I have seen in past couple of weeks that every few days the moku data transfer gets stuck or it fails to connect through LAN. So trying this out.
After the new PID parameters were tuned (CTN:2428), I waited for some time and the beatnote was stably locked to its setpoint of 27.34 MHz for over 2 weeks now. It is a good time to assess the beatnote frequency stabilization. Here I took data of 10 days and plotted it in three different timescales. The standard deviation plotter in light blue is calculated by standard deviation over 10 s of averaging of data. Green background means everything was locked at that time. Other than green would mean that either something was unlocked or there is a gap in the channel data (this case).
How good is good? We were so bad, I never did this calculation. Are we hitting boundaries of how good the thermal controls can anyway do? Is the remaining noise in beatnote spectrums just scatter noise or there is still room for improvement in beatnote stabilization. Food for thought.
Code and Data
I updated this calculation by adding curves for contribution through bulk loss angle and shear loss angle separately. Rana suspected that shear loss and bulk loss should behave differently with the change in beam radius on the mirrors. But apparently the Hong et al. calculations do not suggest that way. I checked this analytically too. The definitions of Eq. (96) of power spectral densities of coating thickness fluctuation of a particular layer due to Bulk or Shear loss angles have the same dependence on the effective area of the beam on the layer.
The only thing different between the final contribution from these different fluctuations is in the transfer functions mentioned in Table I from bulk and shear noise fields to layer thicknesses and surface height of coating-substrate interface. These are also plotted in a second curve to get an idea of these transfer functions.
Along with the effects of layer thickness and surface height changes to final mirror displacement (effective) via phase change of reflected light is given by parameters q^B and q^S as defined in Eq. (94). These are plotted in the third plot and show the real difference in contribution from bulk and shear. This is in stark contradiction with what Ian just told me. They believe that for a Gaussian pressure profile, the energy stored in shear strain is 3 times higher than that stored in bulk strain. For comparison with a figure of the paper (fig.7.), I plotted the square root of these transfer functions in the fourth plot. However, the paper plots these for Silica and Tantla, not AlGaAs.
My conclusion is that at least in Hong et al.'s treatment, the effect of beam area on the mirror is equal to both bulk and shear contributions (Eq. 96).
I repeated the measurement done by Tara and Evan to update residual NPRO noise in our noise budget.
Acutally it does look like it's a 50 Ω loading issue. I find that when 50 Ω inline terminators are added to OUT1 and OUT2, the measured OLTF is reduced by a factor of 1.6. This explains the discrepancy between the SR785 and HP4395 measurements. I've attached the corrected OLTF plots, along with plots of a vector fit, and the expected residual frequency noise [assuming a free-running NPRO noise of 104 Hz/Hz1/2 × (1 Hz / f)].
I and Ian discussed what the transfer functions would look like. Then today, using some old calculations, I put up this notebook which does the calculations for us. The notebook has the calculations typed up in latex too.
This is the first attempt. We have to work on making the EOM path's transfer function closer to the expected model transfer function. And we should use a faster opamp as well, I think.
Edit Fri Oct 4 14:44:33 2019 anchal:
The nodes at input and output of buffer in the PZT path are connected together. That is wrong. Also, If possible, you should name the elements same as the zero model in the notebook. Anyways, I think we are ready to solder a circuit board.
Whoever commented last, suggested a good idea. So I've here plotted the NPRO slow control voltage signals, converted into the inferred temperature of the cavities (see CTN:2415). I'm not so sure which CMRR the anonymous commentator is talking about. More clarification on that would be helpful.
I have updated the plant model to contain the cavity pole also. Cavity pole is a pair of positive and negative real poles, so it is hard (or maybe impossible) to imitate it exactly with an electronic circuit. Or maybe, my analysis is wrong.
Nevertheless, I have for now made this circuit which has a second-order pole, so it correctly matches the magnitude of the model transfer function up to 1 MHz for both PZT and EOM paths. Note that the elliptical filter is not included in this as we can connect the circuit to Test port 1 which injects just before the filter in LIGO-D0901894. Also, for the gains in EOM path, I had to add some factors to make it the same as the model transfer function. All components are calculated for E12 series resistors and capacitors.
Attached is a pdf of the notebook which contains all the mathematics in latex and a zip file with all files to recreate and further work on this. Ian can use these as support to learn zero further.
On Oct 11th at 15:04:04, the south laser switched off on its own. I would like to know if anyone entered the lab around this time. Koji did mention that our Laser Safety sign outside was blinking, but I have no more information than that. Attached is the data of south PMC reflection DC, which is the first photodiode that measures the laser. It suddenly went to zero, indicating the laser was switched off and the locks did not drive it to this point. I'm also finding that the laser intensity is reducedasit used to saturate the South PMC reflection photodiode when unlocked but presently shows around 5V. I'm trying to put the experiment back to same parameters as before.
South PMC Error signal is showing huge weird capacitor charging type oscillations. Attached is an oscilloscope measurement of it. A more weird thing is that this peak is appearing at random frequencies, that is, if I take single sequence measurements of 1 ms length, I see these peaks occurring at a difference from 100 us to 500 us, randomly.
Following up after CTN:2452, the laser safety sign is not working. Hence the lab has been shut down now. All lasers are switched off with key turned to off position. I'll fix the laser safettysign before turning the experiment back one. Possible reasons might be an interlock glitch or bulb fuse.
I have taken the bulb from ATF lab inside sign for now. I'm ordering a new one to replace that soon.
With Laser actuation not connected, I see that the South PMC Servo board is acting up. Firstly, it is not responding to changes made on the ramp when engage is off. This shows that maybe the engage DAC channel is faulty and PMC lock is always on. Need to investigate more on this so for now I have disconnected the PMC PZT from the servo board so that nothing further happens. North side is completely happy and sound.
I have a wierd observation. The following two combination work:
But when I connect the South PMC to its own South PMC Servo Card, the PZT output voltage does not change with changes made to Ramp. The other side, works.
I checked the capacitance of the South PMC PZT and it came to about 395 nF which is same as specifications with the error bars. So the PZT isn't bad.
But if I disconnect the South PMC PZT from the South PMC Servo Card, the output voltage at the servo card changes as expected with ramp voltage.
This is very perplexing. I think I need second opinion here to do sanity checks otherwise I'll go mad in the basement.
Updated schematics for reference: South PMC Servo Card
Yeah, the cables are isolated and no inversion could happen.
Are you sure that all the cables involved are isolated and there is no polarity inversion? e.g. The unfunctional combination provides HV to GND directry at the cable, for example.
Even more bizzarething is that it works now! I'm not halucinating here but the same thing was not working before.I even have lab notes from yesterday when it wasn't working.
This is pretty bad as I don't want to be unaware of something in the lab that caused this. The only other clue here in all this is that the laser intensity changed. We control the intensity of light going into the experiment at (24,110) through the half waveplate before a PBS. Rana told me that the polarization direction of laser coming from NPRO shouldn't change, but since the incident of last Friday, I have had to change the rotation of this half waveplate in both directions to ensure same amound of light reaches the cavity as on North. since no alignment was changed at the south PMC, there is no reason for the mode matching to change drastically there or during the day. but this is the only fishy clue I've got for now.
Both cavities are locked. with same amount of gains in the FSS and PMC loops in both paths as before. The can's temperature as reached to the setpoint and the beatnote frequency PID is working to take it to 27.34 MHz. I'll set trigger for tonight for beatnote frequency noise measurement if the frequency reaches in the range of the photodiode.We then will know what is the impact on the experiment noise.
Latest BN Spectrum: CTN_Latest_BN_Spec.pdf
Daily BN Spectrum: CTN_Daily_BN_Spec.pdf
I ran the code for aLIGO coating structure and tried to reproduce fig5 and fig7 of Hong et al. paper. It turned out that the derivatives of the complex reflectivity were not matching with the paper. I rewrote the code, with a fresh mind without looking at previous code and voila, after increasing computation time slightly due to more brute force calculations, I was able to reproduce the figures. These figures are attached. Since I do not have access to the data of the figures in the paper (I tried to email the authors but got no replies), I could only try to plot it on the same scale and limits and check the values by eyes. The values seem to match. So I am more confident now to declare that this code completely follows the paper's calculations.
However, this does not change the coating Brownian noise. I have updated the noise budgets at the Daily and Latest plots.
The same thing happened again. This time, not just with the SPMC actuation voltage, but the South Laser slow voltage control was also unresponsive. However, I am not very sure about the latter. This was resolved once the restarted the whole lab. This narrows down the problem to following possibilities:
These still don't explain CTN:2456. Again, since this is an irreproducible error, I will just have to wait for it to happen to gather more clues. Right now, everything is fine and beatnote is traveling towards set frequency.
Today, this problem happened again (check history for details). I have done the following investigative steps:
I'll take another inspection with a fresh mind next time. This problem needs to be resolved as we can't leave some unexplained phenomenon to keep happening in the lab.
I reduced the power falling on the PMC to ensure the high signal level isn't causing this problem. It was not. The problem still persisted.
Then, I did this reproducible step (quoted below)again, but this time I had a small 10 mV signal from SR785 going into FP2TEST and I was taking transfer function to TP2. If the U5A AD602 is switched off by the Blanking pin, the transfer function should remain null. This gave me a way of checking if the AD602 is wrongly getting switched on on its own.
This is good evidence in my opinion that the AD602 at U5A is faulty. I need comments on this conclusion. If I don't hear otherwise by tomorrow noon, I'll start working on replacing it.
Edit Thu Oct 31 10:26:50 2019
Issue fixed. See CTN:2469.
I brought a new AD602AR from 40m and replaced the U5A AD602 which from the previous post seemed like the culprit, but it wasn't.
I'll think of some new way of figuring out the point of the problem. It would be nice if someone can help me with this. All the history of the issue is on this thread starting at CTN:2451.
It turns out I did not have a full understanding of the problem and it was not really a problem. The blanking (pin 4) on U5A AD602 doesn't shut down the channel, it just reduced the gain by 100. So if the gain in previous stage is large enough, the lock can still be acquired. And that's what was happening.
Ideally, we need to keep the AD602 on all the time and lock by scanning the offset with low gain. The loop will catch the lock (the exact same thing I thought was a problem) and once that has happened, we can just increase the loop gain the set value.
Presently, the gain behind the U5A AD602 is 101, which is kind of high. I just need to check if the above-mentioned locking method would work robustly without wrongly getting locked to any higher-order modes with the gain slider set to some threshold value within -10 dB to 30 dB. If that can't be done, I might have to reduce the gain in the first stage. For now, the cavities are locked and beatnote is traveling towards set point.
First step in FSS Diagnostics was to see RF output from the RFPDs in FSS when they are locked. I ran some extensive measurements to cover all the information about this signal. The RF out is sent to the FSS box through ZFDC-20-5-S+ 19.5 dB directional coupler. The coupled output's spectrum is measured at different frequency ranges using both AG4395A and SR785. The measurement configuration files are included with data for metadata of the measurement. The signal is also analyzed in time series with measurement upto 1 GSa/s with TDS 3034C and one measurement at 5 GSa/s with TDS 3052B. Both measurements were done manually setting minimum possible voltage resolution and using DC coupling with 50 Ohm impedance. All data is attached raw here for now. More interpretation and analysis to come soon.
Rana told me that in 40m, the PMCs are autolocked by reducing the gain of the loop and changing the ramp until the lock is acquired. Then the gain is increased back to operation point. I tried this method with our South PMC as the usual method being used of 'changing Blanking state' wasn't working anymore. However, even with the gain set all the way to -10 dB, the loop was not locking exactly at the center of the TEM00 mode. And was unable to skip higher-order modes. There is a header H1 which changes the input stage gain. Removing this header pin, reducing the input stage gain by a factor of 100. Even after doing this, I was unable to robustly acquire the lock by this method. Besides, this reduced gain was the case earlier (CTN/2427) and it was too low as the VCA U5A AD602 had to be kept at maximum 30dB gain. So I did not want to reduce this first stage gain.
Somewhat similar to our FSS loops, I find it much cleaner to just not close the loop until we have reached near the lock point. This could be done fairly easily with the existing code. I just had to change the loopStateEnable variable from Engage (which changes the Blanking pin on U5A AD602) to input switch (FP1TEST for South and FP2TEST for North). So now, when finding a lock point, the input is changed to terminated inputs and the loop is closed when lock point is found. This works very nicely, just like the FSS autolocks.
This has finally fixed any problems with PMC autolocks.
I raised the North TTFSS box by 6 inches to make way for working on South box and to reduce the congestion of connectors in front of the two boxes. I have also clamped the boxes to a fixed position now, so they can't move. This would ensure the cables are not hitting the end of the platform and face any severe strain.
The next step towards improving lab cable hygiene and layout is to replace all RF cables with RG-405 Belden-N 1671J cables. However, the effects of this change would be less significant then fixing the sick FSS. So I'll first focus on that.
South Common Gain: 24 dB! , Fast Gain: 14 dB
North Common Gain: 10 dB, Fast Gain: 10 dB
I've wrote this script, nonlinTF.py which controls a Marconi 2023A and SR785 together. Marconi is used to providing a carrier frequency which is mixed with the Source Out signal from SR785 before feeding into the TEST2 input port on D040105 of TTFSS boxes. Then OUT1 port on D040105 of TTFSS box is used to read back at channel two of SR785 (channel one being fed with a copy of the Source Out signal). So SR785 is effectively measuring any downconversion in the loop (due to some nonlinearity) from micing of CF-IF, CF and CF+IF probe signals injected into the loop. The effectively closed-loop transfer function between TEST2 and OUT1 should be G/(1+G), so this injected signal should not suffer any suppression, nor should it affect the locks. The locks were maintained without any problems during the whole measurement. The CF frequency was stepped by 100 kHz from 100kHz to 10 MHz and then by 1 Mhz upto 100 MHz.
Mixer ZX05-1LHW (level +13 dBm) was used for the mixing and IF peak voltage was set to 30 mV. The configuration of the measurement for the transfer function is present in the configuration file in the folder.
But what now?
I calculated these values by integrating in the 8 MHz neighborhood around the marked harmonic peak, the power spectral density using the frequency at the point as the lower edge of the bin. Slew rate is calculated by multiplying the rms voltage level with the frequency and the fraction is calculated against the datasheet value for Max 4107.
SFSS RFPD Output Slew Rate Usage (MAX 4107, SR: 500 V/us)
These calculations at least show that MAX 4107 should be much far away from reaching its slew rate limit in both RFPDs.
In line with industrial practices, I did two tone third order intermodulation test today on the FSS RFPDs. This test was inspired by procedure described in this technical note by MiniCircuits and this paper at IEEE.
Datasheet for MAX4107
I did some theoretical calculations using the datasheet value of second harmonic SFDR from MAX4107 and the transfer function I measured from Test IN ports of RFPDs (using 100 kOhm series resistance).
Edited Wed Nov 20 14:43:07 2019: Corrected an error in code.
I took time-series data at TP1 on NFSS. This is just after the elliptical filter which is after the demodulation on board.
As also seen in the spectrum measurement at this testpoint in CTN:2474, there is a lot of power at around 435 kHz. But this is not noise!
As seen on the oscilloscope, this is a near-perfect sinusoid. So this must be either of the following:
This measurement was taken with a 500 MHz 10x Probe with a 300MHz TDS 3034C oscilloscope at 0.5 GSa/s sampling rate.
Interestingly, there is no such oscillation or peak on the South side. However, the south sides COM Gain is 24 dB and Fast Gain is 14 dB. So it could be because it is just suppressing this non-linear effect properly or just has a very high UGF.
I quickly took a high-frequency Open Loop Gain measurement of NFSS loop at 10 dB COM Gain and 10 dB FAST gain, using the same measurement method as in CTN:2443. The UGF has not changed much but there is a dip at 435 kHz. This was there before too, I was just not paying enough attention to this part of OLTF before. So, we can say with some confidence that the 435 kHz signal seen in the oscilloscope in CTN:2482 at TP1 is actually due to some non-linear effect most probably and does not get suppressed at all. The phase margin near UGF looks about 135 degrees so there is no solid reason to believe this could be due to loop oscillation.
So I got to think of what combination of RF frequencies might be mixing down to create this oscillation and where. This oscillation is also visible in Plot 6 and 7 of NFSS_RFPD_Output_Oscilloscope.pdf of the measurements done in CTN:2470.
This has happened few times now that acromag channel for the can heater driver stopped updating according to the PID script and the can gets heated to a very high temperature. This pushes the temperature out of the ranges of the current AD590 temperature sensor board. I have changed the range of channel 2 (this was being used for out-of-loop) to ensure we can still see some meaningful temperature value when such incidents happen. I have replaced R18 from 100k to 27k. The updated table is:
I took a spectrum of PMC error signal when the FSS loop is not closed. This should provide a rough estimate of the free running laser noise. We had earlier seen a peak at 435 kHz in the Northside, hence I wanted to take this data with some references. First of all, this peak is very similar in the description of relaxation-oscillation peaks of these NPRO lasers mentioned on page 52 of this manual. The "Noise Eater (NE)" is supposed to suppress this peak significantly. However, in the spectrum of the PMC error signal, there is no difference when noise eater was ON or OFF.
I took a spectrum of Southside as well, just to see if I could see action of Noise eater there. For south laser, the noise eater suppressed noise only till 100 kHz or so and probably this side also has a similar relaxation-oscillation peak problem but is shadowed by a large feature at 30 kHz. Not, the absolute value of the spectrum between North and south are vastly different due to different amount of light, different transimpedances od the PDs and different gain values in the feedback circuit.
However, the noise eater is supposed to reduce relative intensity noise only. And the error signals of PMC should really be telling us noise in the frequency of the laser. So maybe I'm connecting two dots in different Hilbert spaces. But Rana suggested that a busted Noise Eater could be the reason for the 435 kHz peak, I just do not understand how RIN would cause frequency noise so badly. I thought photothermal transfer functions from RIN to frequency noise were very small.
I'm trying to think hard with my small brain how the distortion would affect the PDH functioning and inject noise in the frequency of the laser. I have a line of reasoning which starts with a question.:
Of course, all this depends on the RF sidebands interfering constructively upon reflection. I remember (I don't know from where) that it is the opposite. Either there is a fault in my calculations or this is indeed what is happening. I need to understand this properly to go further. Need help.
I put laser settings on both North and South Cavities back to default. From this point onwards, all settings about the lasers would be known and kept track of. The red values are the settings that were changed.
While turning the nominal diode current of south laser all the way clockwise, I found that the laser power peaks before the maximum diode current is reached. This diode current is about 1.9 A. This is unexpected. Any explanations on this would be helpful.