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  1494   Fri Aug 29 19:56:06 2014 EvanDailyProgressBEATBeat breadboard in place


Beat breadboard is slid back into place. North transmission appears on north camera. Still need to do south transmission.

Tara has found south transmission on camera. I steered the transmitted beams onto the beat PD and then made the k-vectors as parallel as I could as seen on an IR card.

The DC voltage on the PD is okay (ca. 50 mV from each beam), but I cannot see a beat note on the AC path using the HP4395. Tara will give a temperature kick which hopefully will bring the beat note within the range of the 1811.

  2186   Tue May 15 14:29:47 2018 awadeDailyProgressTempCtrlBeat drift over the last few weeks

We haven't been paying attention to the beat frequency or its control in the last few weeks.  Yesterday it was apparent that the beat had drifted to ~2 GHz.  When I tuned the differential heating to ~0.42 W with a common offset of 0.56831 W I found that this had almost no effect on the beat note.

Initially I thought maybe the shield heater driver box was broken.  On closer inspection it seems that the Acromag IOC channels had been moved to a different output channel and the IOC process was only very recently reset to enact those changes.  

I've relabeled the cables and BNC ports to make it clear which components should plug into which.  I've set the differential heating to 0.422991 W and both lasers seem to be tracking in the right direction towards a 26 MHz beat note now.  It will take a few more hours to get close enough to stabilized. Currently at 250 MHz.

  1499   Wed Sep 3 12:02:19 2014 Tara, EvanDailyProgressBEATBeat found

Tara added some more juice to the north cavity heater last night. Now we can lock both cavities to TEM00 and get a beat within the bandwidth of the 1811.

  • North laser slow: 5.020 V
  • South laser slow: 0.722 V
  • Beat frequency: 49.3 MHz
  800   Thu Jan 26 00:34:23 2012 frank, taraDailyProgressBEATBeat improvement

 We investigated the beat noise, and found out a few issues we have to fix to improve the sensitivity.

  •  Periscopes

Resonant peaks from periscopes around 800 Hz are high. We use an aluminum bar to tighten the periscopes together. This bring down the peaks. However, the peaks are still high. We certainly have to work on the design for the periscope to get rid of the mechanical peaks.


upper beam for dual periscope. This help reducing resonant peak around 800 Hz a lot.


  • Marconi's phase noise for ACAV loop.

The local oscillator we use for driving the AOM in ACAV loop is Marconi. We are sitting on its phase noise at 10kHz tuning range .When the tuning range is set to 1kHz, noise at frequency above 1kHz drops. However, with 1kHz tuning range setup, we don't have enough gain to suppress noise at lower frequency and noise around 100Hz goes up.

We need to characterize ACAV loop to project LO's phase noise on the noise budget (this has not been done yet). We might have to add another EOM for feedback on ACAV loop.

  •  Acoustic coupling

 We also noticed that talking noise can easily couple to the beat signal, but we are not certain where it happens. All mounts and posts will be checked if they are loosen or can be improved.



  577   Tue Apr 12 19:49:39 2011 taraDailyProgressBEATBeat measurement is back

I realigned the beam on the beat path and measured the beat. With new eddy current damping, the peaks at 3.73 Hz now becomes smaller.



  929   Sat Apr 21 00:55:00 2012 frank, taraDailyProgressBEATBeat measurement update

We measured the beat after a few changes in the setup (modulation index, air spring, small enclosure around the beat). We update the noise budget with suppressed laser frequency noise and Marconi's frequency noise in ACAV loop as well. There is not much improvement in the overall beat noise.

A few changes in the setup:

  •  Air Springs: We activated the air springs (it was off because we though it causes the vacuum chamber to move too much during the work), so there is one more seismic isolation stage. The peak at 58 Hz disappears.  However, there are peaks around 6-12 Hz showing up this time. They are probably from the table and the legs that are not set to float the table properly*.
  • Modulation index: now the modulation index is 0.18. I measured the power in the carrier and sideband to calculate the mod index, see PSL:855 . This is the maximum we can have with the 13dBm from Marconi with 4-way splitter (-6dBm),-0.5 dBm loss from the cable, so the power to EOM is 6.5dBm.  With the new mod index, the frequency discriminator gain (inverse) for RCAV/ACAV become 22 and 31 kHz/V.
  • A prototype enclosure box around beat setup: PSL:925.


Updated Traces:

  •   Suppressed Laser frequency noise: Since we changed the OLG of TTFSS by changing the modulation index, we remeasured the OLG of TTFSS, applied to the laser frequency noise (estimated to be 1e4/f Hz/rtHz). Good news, we have enough gain in RCAV loop to suppress the laser noise to coating level. The gain setup for common/fast is 750/750
  •  Frequency noise of Marconi for ACAV: We had not done this so far, so we wanted to make sure that it would not be the limiting source. This is done by dividing the frequency noise of marconi by ACAV OLG TF. We assume that the frequency noise is the same as we measured from the marconi for PLL plotted in the noise budget.
  • Shot noise is updated with the current modulation index (0.18) and cavities visibilities (~80%). It is not shown in the nb because I included it in the PDH detection noise.

* The table legs have small leaks, so we have air compressor to keep the pressure high, PSL:880. It works once every hour when the pressure is low.  The change of pressure can screw up the beam alignment a lot (for example, DC readout from RCAV RFPD can be varied from 100mV - 1.2V, with 1.7V maximum value (off resonance). I think it affects the alignment to AOM and change the diffraction efficiency/ beam shape as well.  It also changes the seismic isolation property. The peaks around 10 Hz show up when the pressure is low.  I'll find new legs from New Port and ask for the quote.


==Plan for the next few days==

1) Try using DAQ to measure beat signal, see if we can get rid off the frequency noise from PLL

2) Find out about the new legs(prices/availability)

3) Make the acoustic enclosure box around the whole setup

4) Work on the design for new vacuum windows.


  1373   Sat Oct 26 15:35:42 2013 EvanDailyProgressBEATBeat measurement with ISS

Summary: No good so far. Engaging the ISS seems to have basically zero effect on the beat. The beat overall looks worse than it did a month ago, and the shape seems to mimic the shape of the north cavity RIN. More optimization of the north EOAM is necessary.

Details: Having set up the north EOAM on Thursday (PSL:1372), I spent most of yesterday trying to get a RIN-suppressed beat measurement.

The continual drift of the laser frequency control signals was irritating, so I spent some time getting the slow digital PID controls for the lasers back up and running. At first only KP seemed to have no effect on the laser control signals; it turns out this is because the PID Perl scripts that run on the Sun machine rescale the KI and KD coefficients by a timestep variable, which had been set to zero. I've set it to 1. I've chosen KP = KD = 0 and KI = 0.0002 (with appropriate choice of sign for the two loops). The system is probably overdamped, but it manages to integrate the control signals down to zero in a resonable amount of time (<30 s) and I don't think it's a high priority to optimize it right now.

The south PDH error signal has noticeable 250 kHz oscillations which get worse as the common TTFSS gain is increased. The north PDH error signal is much quieter. Are we perhaps hitting a mechanical resonance of the EOM crystal? Or (dare I say it) do we have the wrong sign for the common path of the PDH loop?

I took out the hand-soldered integrating board that I built for the ISS loops; it was railing too often. The ISS setup for each path is now as follows: each ISS PD goes into the A input of an SR560, and a programmable voltage reference (Calibrators Inc. DVC–350A) goes into the B input. The voltage is chosen to match the dc voltage from the ISS PD. The SR560 is dc coupled and set to take the difference A − B. The gain is set to 5×103 V/V, with a single-pole low-pass at 1 kHz. The output from the SR560 is fed into the EOAM.

The suppressed and unsuppressed RIN measurements are given in the first two plots. Evidently, these simple ISS loops are able to suppress the RIN by a factor of 50 or so. Also, the north RIN is much worse than the south RIN, and the hump from 100 Hz to 10 kHz is reminiscent of a poorly aligned EOAM (as seen in PSL:1311, for example). So I'd like to spend some more time fiddling with the north EOAM to see if I can improve the RIN suppression. Alternatively, perhaps we are suffering because the north path has no PMC to stabilize the pointing into the EOM, EOAM, etc.

Anyway, I pressed ahead and looked at the beat. To convince myself of the repeatability of the setup, I took a measurement with the ISS loops on, then a measurement with the ISS loops off, and then a measurement with the ISS loops on again. The result is given in the third plot. Below a few hertz, the ISS may have a positive effect. Above this, there is either no effect or a small worsening effect.

Note that the shape of the beat follows the shape of the north cavity RIN. I think we should spend a little time noise hunting and optimizing on the north path to see if we can make this go away. Note also that the beat is worse than it was back in September (PSL:1321). Two immediate culprits that I can think of are (a) the installation of the EOAM or (b) the fact that the vacuum can is no longer floated. But it could just as well be that there's something else (e.g., PDH offsets) that I neglected to optimize.

Attachment 1: north_iss.pdf
Attachment 2: south_iss.pdf
Attachment 3: beat.pdf
  1375   Mon Oct 28 22:55:11 2013 EvanDailyProgressBEATBeat measurement with ISS

I've taken Tara's farsi.m and changed the values of finesse F and absorption α in order to fit the magnitude of the TF measurement in PSL:1368. I've chosen 7500 for the finesse and 5 ppm for the absorption, although for this calculation they are degenerate (entering into the TF as F/α).

Using this, I've taken the RIN measurements from Friday and used them to estimate the induced frequency fluctuation in the beat readout, assuming a transmitted power of 1 mW from each cavity.

In the case when the ISS is off, the estimated effect of RIN on the current beat is significant only below 10 Hz. When the ISS is on, the RIN is insignificant over the entire measurement range. This perhaps explains the observed reduction in the beat PSD below 10 Hz when the ISS is on.

Attachment 1: rin_to_beat.pdf
Attachment 2: expected_rin-to-beat.pdf
Attachment 3: expected_rin-to-beat_iss.pdf
  1395   Wed Jan 15 10:56:08 2014 EvanSummaryNoiseBudgetBeat measurement: residual

I've taken the total noise trace, interpolated it so that it uses the same frequency array as the measurement trace, and performed the quadrature subtraction of the two to get the residual. I've also converted the beat to single-cavity length noise by multiplying by Lλ/sqrt(2)c, with L = 3.7 cm.

Attachment 1: short_nb_residual.pdf
Attachment 2: short_nb_residual.fig
  1605   Wed Nov 4 11:28:37 2015 AntonioDailyProgressBEATBeat noise did not improve with the ISSs ON



I have measured the noise at the beat note with both the ISS servo activated —>

NO improvement compared to the past. It is actually a bit worse. However with the EAOM

in the South path I had to change sluggishly the PDH gain settings.


- I took two measurements with different Fdev at the Marconi (1kHz and 10kHz) and the noise

is the same mostly. It seems that the limitation at moment relies NOT in the Marconi noise.






Attachment 1: PLL_noise_comparison_20151104.pdf
  1692   Fri Jul 29 16:52:06 2016 awade and AntonioDailyProgressBEATBeat note signal

We have a beat-note.

For the last few days we have been able to bring the two lasers to within the 125 MHz bandwidth of the Newfocus 1811 detector at the output of the vacuum tank. By tuning the length of the North cavity (turning the temperature up) we were able to also bring the resonance of the cavities to within this bandwidth.  

Using the beat note detector setup we assembled at the start of the laser path (PSL_Lab/1689), we can see that the frequency offset of the north and south cavity resonance settled at 70 MHz for a north heater voltage set point of 11.5 V (74 mA). We still don't know what temperature that is because we have no thermistor monitor setup yet. However, it seems that with enough settling time it is stable enough for these initial diagnostic tests.

However, until today we had trouble finding a beat note after the two ref cavities.  We checked polarization, co-alignment of the beams as well as switching the detector in and out with the NF-1611 (1 GHz) detector borrowed from the 40-m.  It turns out there are some neutral density filters installed right before the final focusing lens in the post refcav beatnote setup. When I checked the specs for the NF-1811 it looked like we were well below the RF saturation point with a lot of room to increase power.

For the NF-1811 saturation power @ 1550 nm is 55 uW. The responsively at 1064 nm looks like about 0.6 of this.  So saturation at our wavelength is about 91.7 uW. I measured the total power after the combining beamsplitter, it was 227 uW, so with 13 dB worth of ND filters this was brought down to about 11.3 uW.  We first switched the ND filters (ND1.0+ND0.3) for a single ND0.5 and a beat note could be see 3 dB above the dark noise (75 dBm) of the detector. We then removed the ND filter completely at got a beat note (at 70 MHz) that had a clearance of 17 dB above dark noise.  Not sure if this is enough to make a 'good' measurement but at least we can now see something at the combined transmission of the cavities. The damage threshold is of course way above this.

There is quite a bit of work to be done improving on this and getting the PLL loop setup.  We also need to start work on getting a calibration together. The PDH loops also need some optimizing.


On another side note:

We can see the 14.75 MHz  side bands at the beat note output (and one 2x harmonic of this). I'm not sure if this is ok as I would have through the ref cavities would filter this out and I'm not sure if maybe HOM or other would let this to pass the cavity. 

  796   Tue Jan 24 02:47:41 2012 frank, taraDailyProgressBEATBeat with 14.75 Mhz sideband

After switching to 14.75 MHz sideband setup, aside from the RFPDs, we did not change anything yet. We use TTFSS setup on the table. The seismic stack is still the same. The table is not floated. So we measure the beat  noise as a reference.



we use 14.75 resonant EOM for adding sideband, and the broadband EOM for feedback.  The resonant EOM is driven by an LO at 14.75 MHz @ 20dBm. The broadband EOM is supplied with 25V power supply, it is operated at low voltage because of the limited current source. 

RCAV is locked by TTFSS, ACAV is locked by UPDH, the phase shift for both loop is done by cable length adjustment.

 Note that we removed the Faraday isolator from the setup due to the limited space. It will be installed back later once we change the EOM base.

The power input is 0.2 mW on both cavities. The visibility is more than 80%.

==Problem and Plan==

We saw that beam alignment caused the bump around 1kHz to change significantly, so we will re-align everything to make sure that we have good mode matching.

The power input was chosen to be around 0.2 mW because at 1mW the error signal is irregular.  It might be the RFPD problem, we will look into it.

  798   Wed Jan 25 03:05:57 2012 frank, taraDailyProgressBEATBeat with 14.75 Mhz sideband

We added a ccd camera to monitor the reflected beam from the locked cavity. The shape of the beam(turns out to be LG10) tells us that we have to do a better mode matching.


We found that bad alignment can cause extra noise in the beat noise, see  (psl:796).So we monitored the reflected beam from the locked cavity to check what kind of misalignment we have to fix. Currently, the shape of LG10 is the dominant one which tells us that we do not have a good spotsize/spot position match which can be fixed by moving the lenses in front of the cavity.


above, top right panel, the shape of the beam reflected from the locked RefCav.


==To Do==

  So we will move the lenses in front of the cavity to optimize the mode matching.   The current value is ~ 96.5%, we want to improve it without spending too much time, not more than a day. We will mount the lenses on translational stages for better position adjustment.

  1500   Wed Sep 3 16:34:37 2014 Tara, EvanDailyProgressBEATBeat, mode-matching


Tara added some more juice to the north cavity heater last night. Now we can lock both cavities to TEM00 and get a beat within the bandwidth of the 1811.

  • North laser slow: 5.020 V
  • South laser slow: 0.722 V
  • Beat frequency: 49.3 MHz

Beat frequency drifted to 61 MHz over the course of a few hours. We need to wait for the cavity temperatures to settle.

I improved the mode-matching a little bit on the south cavity; it's about 50% (the theoretical max is 71%). The south lenses are now on translation stages.

I've attached a beat spectrum. Nothing is floated, RAM is not optimized, etc.; this is just a rough indicator of where things stand.

Here is what I think should happen next, in rough order of importance:

  1. Float chamber
  2. Measure RIN
  3. Measure photothermal TF (I also need to recheck my photothermal code — I don't believe the coating TE part)
  4. Put photothermal noise on noise budget
  5. Reduce RAM.
  6. Measure residual frequency noise.
  7. Measure PLL noise. Use ATF DAQ and make spectral histogram.
  8. Measure seismic noise (with Guralp or T240), with table floated and unfloated. Use ATF DAQ and make spectral histogram.
Attachment 1: noiseBudget.pdf
  1966   Tue Oct 31 22:56:29 2017 CraigDailyProgressTempCtrlBeatnote Fluctuations

We have to figure out why our beatnote is flying around if we are going to do science down here.  It's preventing us from taking a low actuator noise spectrum off of our PLL, and that is required for measuring our true noise of our cavity beatnote.

Tonight I have set up the Agilent to always be taking spectra and recording them with acromag1.  This will allow us to track the beatnote motion and peak strength overnight with a data point coming once every 45 seconds. I'll have to write a peakTracker.py script which takes in a spectrum.txt and finds the peak, should be easy.

I have also written a channelLogger.py directly on acromag1, which is logging the channels for slow control voltages for both cavities, the in-loop and out-of-loop vaccan temp sensors, and an environmental temp sensors overnight.

The point of all of this is to look for obvious correlations between beatnote motion and temperature controls.

One thought I had today was the power difference in the laser cavities.  If I recall correctly, the North cavity has about 2.5 times as much power as the South cavity.  Also, our slow voltage laser temperature controls change both the laser frequency and the laser power.  This means that any large swings in the slow voltage laser control will result in significantly different power resonanting in the cavities, which could result in significant differential temperature changes.  Our cavity finesse is like 10000, so this effect is multiplied.  Perhaps we should think about evening out the power in the cavities, AKA putting a ND filter in front of the North cav?

  2416   Thu Sep 5 16:59:36 2019 anchalDailyProgressBEATBeatnote Frequency long time series data

Attached is captured beatnote frequency between Aug 27th 2019 to Today, Sep 5th 2019.

I have attached a few more zoomed-in plots as well. This code will serve us in the future as well. Only the green regions are where both cavities were locked and cavity heater PID was engaged. This data involves the experiment time of CTN:2406 and hence have the disturbances of that time as well.

Essentially, there is no fixed stability number one can really quote for this PID. It looks stable in regions, but at times it shoots up or down randomly. Maybe some of them are because of me doing something on the table, but some are late at night which can only be explained by the movement of ghosts.

fromFBread.py updated

fromFBread.py now has an optional flag -d for decimating the read data, so that smaller files are created. Example: -d 160 will decimate the data by a factor of 160 making a sampling rate of 0.1 Hz. It calculates mean of the data, for a block size of 160 (corresponding to 10s) and also calculates standard deviation in this block and adds that as additional columns in the read data. Hence the plots attached here have uncertainties as well.

Code and Data

Attachment 1: BeatnoteLongTimeSeries.pdf
BeatnoteLongTimeSeries.pdf BeatnoteLongTimeSeries.pdf BeatnoteLongTimeSeries.pdf
  2441   Wed Oct 2 12:22:44 2019 anchalDailyProgressBEATBeatnote Frequency long time series data

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).


  • Over 10 days, the beatnote hardly left +/- 2 kHz zone from the setpoint. Even with one standard deviation far away, the beatnote does note leave +/- 2.5 kHz zone. We are using Moku at 2.5 KHz bandwidth right now.
  • Over a day, here it was Sep 28th (Saturday), the beatnote is within +/- 2kHz even up to one standard deviation point. 
  • Over 1 hour which was between 1 am to 2 am on Sep 28th, the beatnote was similarly calm.
  • In the last plot, I have plotted drift over 60s in beatnote frequency which is our measurement duration. This drift doesn't even cross 1.5 kHz mark.


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

Attachment 1: BeatnoteLongTimeSeries.pdf
BeatnoteLongTimeSeries.pdf BeatnoteLongTimeSeries.pdf BeatnoteLongTimeSeries.pdf BeatnoteLongTimeSeries.pdf
  2448   Tue Oct 8 16:48:07 2019 putInYourRealNameDailyProgressBEATBeatnote Frequency long time series data

comment on goodness of Temperature controls:

Since the frequency is wandering by ~3 kHz at the hours time scales, we can estimate the differential cavity temperature to be:

delta T = (1/CTE) * df / (c / lambda) = (1 / 5e-7) * (3 kHz / 300 THz) = 20 micro-K

If someone can plot the NPRO SLOW signals at the similar time scales, we would know what the CMRR is. But I think 20 uK is probably just fine. 

  2449   Wed Oct 9 16:08:39 2019 anchalDailyProgressBEATBeatnote Frequency long time series data

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.


  • As the anonymous commentator said, the ideal temperature difference between the cavities would be around 20 uK, but that is clearly not the case as North Cavity varies more than 0.1 K while the South Cavity is relatively more stable.
  • This could also indicate that some external low-frequency noise source drifts the North Lasers frequency by corrupting the FSS.
  • The thermal dynamics of the two cavities should be similar unless same driven current causes starkly different emission of heat from the coil heaters (which are supposedly of same length).
  • Some more help in understanding these results are required, or atleast a person who can bounce back ideas with me.
  • So the can upgrade might be useful afterall. If anything, it will reduce the mysteries related to the cavities locked inside there for the last 5 years.

Code and Data

Attachment 1: BeatnoteLongTimeSeriesPart2.pdf
BeatnoteLongTimeSeriesPart2.pdf BeatnoteLongTimeSeriesPart2.pdf BeatnoteLongTimeSeriesPart2.pdf BeatnoteLongTimeSeriesPart2.pdf BeatnoteLongTimeSeriesPart2.pdf BeatnoteLongTimeSeriesPart2.pdf BeatnoteLongTimeSeriesPart2.pdf BeatnoteLongTimeSeriesPart2.pdf
  2428   Mon Sep 16 17:05:00 2019 anchalSummaryBEATBeatnote Frequency stabalization

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! crying 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.

Testing performance

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

Attachment 1: BeatnotePIDPerformance.pdf
BeatnotePIDPerformance.pdf BeatnotePIDPerformance.pdf
  2077   Wed Feb 7 17:37:10 2018 CraigDailyProgressBEATBeatnote Required

Some quick settings:

North visibility: 39%
Power on RFPD in trans: 200 µW (TOO MUCH)
Power on RFPD in trans with ND filter: 20 µW
Beatnote Freq: 17.945 MHz (Slewing down at 1 kHz/min)
Beatnote Strength: -1 dBm with ND filter on
South Slow Volts: -6.0375 V
North Slow Volts: 3.5596 V

Next step: Beatnote spectra, then vent and dump scatterers.

  2151   Thu Mar 22 17:41:24 2018 CraigDailyProgressBEATBeatnote Spectrogram jupyter notebook

I've created a spectrogram (Fig 1) ipython notebook in ~/Git/cit_ctnlab/ctn_labdata/scripts/SeismicAndScatteringStudy.ipynb. I also attached a median beatnote ASD (Fig 2) for reference.
This is the beginnings of a study to look for coherence between our accelerometers and beatnote to figure out the velocity of our scatterers.

It takes a little while for nds2 to acquire the data from Gabriele's cymac3, because the data is sampled at 65536 Hz.  For 300 seconds of data it takes the script 172 seconds to retrieve the data. 

I'm currently thinking about ways to make this spectrogram plot on the order of days as opposed to minutes so we can get a long-term idea about our beatnote.  Even looking at this, it seems like the scattering shelf does oscillate a bit at around 10 Hz.  Our 500 Hz hump seems pretty constant on this time scale as well.

Attachment 1: CTNLabBeatnoteSpectrogram_TimeLength_300s_gpsStart_1205785966.pdf
Attachment 2: CTNLabBeatnoteASD_gpsStart_1205785966.pdf
  2095   Sat Feb 17 00:23:38 2018 Craig, awadeDailyProgressBEATBeatnote Stabilization PID results from today

Top plot is smoking gun that awade's new PID beatnote controller works on a timescale of half a day.

I've been trying to relock the North path tonight, so I looked at the North slow volts to get an idea of where the resonance frequency should be.  I also plotted the beatnote for good measure, to see if there was any slewing going on. 

Turns out, the nice damped oscillation in the beatnote frequency you see is due to awade's PID loop controlling the North cavity shield temperature this morning.  Pretty cool.

This is incredibly useful, because it means that when we get a beatnote again, once it settles down, we'll always be able to take low-range, low noise PLL measurements because the Ncav shield temp is being actuated to keep the beatnote from moving around.

It seems like awade can probably do even better, what with all the overshooting.  Get down from under-coupled to critically coupled PID control.

EDIT:  The NCAV Shield Heater PID loop settings were
P = 0.02500
I  = 0.00001
D = 0.00000

Attachment 1: Screenshot_from_2018-02-17_00-23-28.png
  2167   Mon Apr 9 20:44:41 2018 awadeDailyProgressTempCtrlBeatnote Stabilization: Configuring heaters to actuate differentially

In an effort to improve the CTN experiment's temperature control I've reconfigured the cavity heaters to operate with differential and common mode heating.  By making the actuation symmetric and elevating both cavities well above the vaccan temperature hopefully this will improve the linearity of the actuator.

The heating wire on the north path is 156.8 Ω and south is 85.6 Ω (don't know why they are different). I've configured an additional channels for the south heater (previously not hooked up).  Units of the new channel are in watts.  Two additional calcout channels were made that set the common heating value (in watts) for both channels and a difference between the heaters (in watts) that ranges from -1.1 W to +1.1 W.  After rebooting the IOC and setting the common and diff heating to produce 0 W on south and 0.7734 W on north I get roughly the same beat note frequency as before.

After the change PID feedback to the differential heater channel, it was possible to use PI feedback to drive the beat note to a set point of 100 MHz but tweaking gain values to kill oscillations was takes a very long time (still not there yet).  I reattempted to implement the relay auto tuning method from before (see PSL:2142). However, I had the same converging cycle limit to zero after a few hours.  I think that the large lag on the actuator/sensor/plant in these temperature tuning situations may rule out finding objective Kp, Ki, Kd values using relay tuning methods: the lag puts us away from the -pi first real axis crossing the nyquist curve and estimates of the plant's critical gain and frequency are bogus.  

Short of making some really smart controls that can anticipate the trajectory of the temperature and make more optimal estimates for the feedback I may need to vent the can and get some low noise platinum RTD sensors on the shields.

  2142   Fri Mar 16 13:09:35 2018 awade, CraigDailyProgressTempCtrlBeatnote Stabilization: Relay tuning of PID feedback coefficients

Beat note slewing is still a problem and it will be some time before Shruti (this year's summer SURF) is here to tackle it with some intelligent controls: i.e. neural networks/machine learning, Kalman filters, Wiener filters (?) etc.

This post is an intermediate one, I will post something in more detail about using relay tests to find PID parameters at some later time.

PID controlling beat note still not well tuned

In a previous test of controlling the beat note frequency with PID feedback to the north cavity heat shield I guessed P, I and D values.  Reaching optimal values based on the usual human methods of driving the loop close to instability and then backing off prove to be very difficult.  For the cavity-heater system the time constants for settling to thermal equilibrium are very long.  The critical dampening period appears to be on the order of 20 minutes (see below).  However, with the loop engaged and very close to point of inducing instability the oscillations can extend out to many hours. Its difficult to keep track of movements of the various gains and their impact, especially when many other parts of the experiment are dropping lock, drifting, ringing, etc. I found it difficult to discriminate the goodness of the last adjustment when there are a bunch of spurious step functions induced from humans interacting in the lab and outside.

It is also really difficult to assess whether one has truly hit the optimal critically dampened condition with no long term instability causing oscillations.  Lots of people offer advice and rules of thumb on how to tune to 'good enough'.  If tolerances are relatively loose then it might be ok. But we can do better. Ideally we would actively drive the system to probe the plant's properties and come up with an optimization that set the values in an objective way.  An active optimization will maximize the useful information for the given integration time and remove the human biases in tuning PID for plants with very large time lag.

You can see an example of one set of values I chose in PSL:2095.  It took some 12 hours to fully dampen down, this was a bad choice of values.  After this I gave up on manual tuning to work on other things.

The Relay Test

There is a way of probing the plant under control to estimate appropriate values for P, I and D values: a relay test.  There is some information for this auto tuning method in [1]. It basically consists of switching out the PID block for a relay function.  The relay does a hard switch from +a to -a depending on the sign of the error signal: it is a step function set about some mean operating point.  This active feedback induces an oscillation in the plant and, once the system settles into regular oscillations, the relay function leads the plant by 90°.  Although the square wave hard switch will induce Fourier components at higher harmonics of the lowest natural frequency of the plant, in almost all non-pathological plants there is a dominant pole that filters these frequency components out.  Thus, the dominant oscillations induced during a relay test give some clear information about the characteristic response of the plant in a relatively robust way.

This method is similar to the step function test that people sometimes do.  That is a much older method from the 1940's.  You provide a step kick in the actuation and fit the impulse response to retrieve the critical period and amplitude of the plant's response.  The disadvantage of this method is that one is only getting information from a single kick, you also have to fit the plant response along with any sensor noise etc.  It is much better to integrate for a longer period and lock-in on the frequency of interest. 

From the induced relay oscillations we can extract a critical dampening period (Tc) and critical dampening coefficient (Kc) from the ratio of the relay amplitude and induced peak-to-peak error signal amplitude. These values give the frequency at which the plant's Nyquist curve first cuts the real axis. This represents the first frequency at which the plant lags the driving signal by -180°.  This is all the information we need to make a critically dampen PID loop (in principle). There is a standard lookup table for choices of Kp, Ki and Kd gain values for Tc and Kc given in most text books.  It turns out these 'standard' values are well known to be bad and frequently give a loop tuning that have excessive oscillations.  They get copied from textbook to textbook as part of the canon of PID tuning wisdom. Values that I found to work well with initial test on the laser slow controls were that given in Table 1 of [2]. For clarity I've tabulated these values below (in case the link dies).

Improved Zeigler-Nichols tuning constants
Type Kp Ti Td
Original textbook values 0.6Kc Tc/2 Tc/8
Little overshoot 0.33Kc Tc/2 Tc/3
No overshoot 0.2Kc Tc/2 Tc/3

Where Ti and Td are integral and derivative terms in the 'standard' form of the PID controller, hence 

K_i = \frac{K_p}{T_i}; \qquad K_d = K_pT_d

Initial tests

I did an initial test of this auto tuning method on the laser slow controls.  It pretty much guessed first time the PID values that we had set manually with only 120 seconds of integration time. The typical characteriztic impulse response time is on the order of 4.5 seconds in that case.  That isn't a bad effort.

In my initial test on the cavity shield-beat note feedback I chose a relay amplidue of 0.05 W, an average actuator offset of 0.775 W and a setpoint of 26.5 MHz and triggered the autotune function for 4 hours.  See attachment 1 for what happened (sorry no proper plot, not worth it at this stage).  Basically the initial average actuator point was set a little too high for the set point (producing an asymmetric response) and the whole system was below the critical dampening amplitude and converges on the set point. The relay amplitude needs to be turned up to induce a much larger response.  I would also guess that there should be an extremely slow feedback to the actuator mean value to keep the plant response symmetric.   

This initial test was a failure.   For reference the suggested loop adjustment based on median period and amplitude was  kp, ki, kd = 0.76544, 0.01486, 26.28024. Bad.F


Gradient descent on PID values

This was a failure in my initial tests on laser slow controls.  For a cost function I integrated the error function over the course of a step test that was roughly 10 times the characteristic response time of the plant (laser slow frequency input). I sampled two values for the proportional term and performed a step test on each.  I then computed a local gradient of the cost function.  This cost function I was using was too susceptible to sensor noise and gave more or less 50:50 guesses in either direction for the next move in tuning parameters even when it was clear it needed to be moved down.  So it was as good as a random walk simulation. 

Might get back to this later.  There might be more time efficient ways that extract information more efficiently.


Integration into the PIDLocker_beta.py python script

I have integrated the relay test into the beta version of our python locker.  Its called with the --autotune flag, use age is something like 

>  python PIDLocker_beta.py PIDConfig_NCAVHeater.ini --autotune -d 0.05 -t 14400

For more information run  

> python PIDLocker_beta.py --help

You can get the script from our ctn_scripts git repo here: https://git.ligo.org/cit-ctnlab/ctn_scripts, its called PIDLocker_beta.py.  I have also attached a snapshot of the current version below for future reference. All the auto tune functionality is contained within a function called RelayAutoTune.  It isn't truely 'auto' as you can see from above section, but with a bit of playing around with offset and relay amplitude you can get it to work.

More to come later. For some future reading, mostly for interesting ideas, see [3].


[1]  Åström, K. J. & Murray, R. M. Feedback Systems: An Introduction for Scientists and Engineers, Control And Cybernetics 36, (2008) (link). There many versions, they are not equal.

[2]  Wilson, D. I. Relay-based PID Tuning, Autom. Control Feb/March, 10–12 (2005) (link).

[3]  Hornsey, S., A Review of Relay Auto-tuning Methods for the Tuning of PID-type Controllers, Reinvention: an International Journal of Undergraduate Research 2, issue 2 (2012) (link)


Attachment 1: RelayTest_BNtoCavShieldHeater_Failure2018-03-16_at_3.05.48_PM.png
Attachment 2: PIDLocker_beta_snapshot20180316.tar.gz
  2413   Wed Sep 4 15:08:51 2019 anchalDailyProgressBEATBeatnote Timeseries from Oscilloscope

For record, I took data of beatnote timeserieswith fasted sampling rate on Tektronix TDS 3034C (CTN_OSC_SN01).

  • I do see that that positive half cylce looks better than negative half cycle.
  • There might be some clipping happing on the negative peak, but can't say for sure.
  • Right now, it is 3.48 Vpp, so running moku with 10Vpp input range.
  • To the wise people around me, please let me know if there is something glaringly wrong with this signal.

Code and Data

Attachment 1: BeatnoteOsc.pdf
  2283   Wed Jan 16 11:07:41 2019 anchalDailyProgressNoiseBudgetBeatnote after RF AM and RIN tuneup

Intensity noise to the beatnote transfer function

  • I resurrected the AEOM power control lines with SMA cables to junction plate on the north side.
  • AEOM was driven in linear amplitude modulation regime by aligning input polarization to s (vertical) and making output polarization circular by a quarter waveplate and dumping the s (vertical) polarization through a PBS.
  • I_o = \frac{I_i}{2} \left( 1 + \sin(\frac{V_i}{V_\pi}\pi) \right )
  • For the New Focus 4103 models, we have, V_\pi = 300 V . I used source signal for amplitude modulation of V_i = 5 V . This gives modulation index \beta = 0.052 \, rad and maximum deviation from linearity by I_i \times 1.17 \times 10^{-5} .
  • The measurement was done as a swept sine with input at reference signal as the modulation signal to the AEOM and output as PLL control voltage.
  • The TF is then converted to units of Hz/W using PLL actuation slope of 5 kHz/V. The gain in the PLL loop was set to 100.
  • Beat note frequency during the measurement was near 135 MHz.
  • For the measurement in the North path, Settle Cycle was set to 10 and integration cycle was set to 10.
  • During the measurement in the South path, the beatnote started drifting faster so Settle Cycle was set to 2 and integration cycle was set to 4 and average of 3 measurements is taken.
  • PFA transfer functions. Note, transfer functions are mentioned from different initial points for future use. They were converted by scaling down by the ratio of the DC power measured at Cavity input, PMC output, and AEOM output.

Transmission RIN:

I measured transmission RIN before the beatnote measurement. Unfortunately, we can not compare with earlier intensity noise measurement I took because I didn't take transmission power measurements then.

These measurements were taken in 4 steps of frequency ranges and stitched together. See the attached notebook for further details.

Beat Note Frequency Noise Spectrum

I used the same measurement method as explained in (PSL:2272). Following are some experiment state measurements I made:

Experiment State
Parameter North Path South Path Common Unit
PLL Gain     100 -
PLL Actuation Slope     5 kHz/V
BN Frequency    

~ 130 MHz

drifting down

PMC Input Power 1.82 2.404   mW
PMC Output Power 1.615 1.619   mW
PMC Overlap 89% 67%   %
Incident Power on Cavity 1.497 1.497   mW
Transmitted Power from Cavity 0.96 0.82   mW
Cavity overlap 64% 55%   %

PMC Reflection RFAM

(@ PMC loop RFPM frequecy)

-52 dBm

@ 21.5 MHz

<-71 dBm

@ 14.75 MHz


Cavity Reflection RFAM

(@ PMC loop RFPM frequency)

<-87 dBm

@ 21.5 MHz

< -77 dBm

@ 14.75 MHz


Cavity Reflection RFAM

(@ FSS loop RFPM frequency)

-76 dBm

@ 36 MHz

-75 dBm

@ 37 MHz


Cavity Reflection RFAM

(@ 2x PMC loop RFPM frequency)

< -87 dBm

@ 43 MHz

-54 dBm

@ 29.5 MHz























Note: I also found that half waveplate behind North FSS EOM had no marked order and was probably multi-order. I replaced it with a zero-order half waveplate and found significant improvement in RFAM at Cavity Reflection RFPD. Above mentioned numbers were taken after this change.

Updated Noise Budget:

I'm still using the old code here as there are some unresolved questions with the new code I want to be sure about first.

  • The new spectrum is lower at noise at lower frequencies. This might be due to the unmeasured amount of light falling on the cavities in the previous measurement.
  • RFAM and RIN tuneup decreased noise slightly at 2 and 3 kHz.
  • However, the method used for taking these measurements keeps the uncertainty high. So maybe the effects of our changes are actually negligible and something else is more pressing.
  • Clearly, the growth of noise beyond 1 kHz is still happening and this is one major difference between earlier noise measurements and new measurements.
  • I think installing ISS should be the next step in the queue because these high-frequency bump is probably coming from there.
  • I will also work on tuning up the FSS loop parameters to see if that changes anything.


Attachment 1: LaserPowerNoise_to_BNFreqNoise_TF.pdf
Attachment 2: IN_to_BN_TF.zip
Attachment 3: Transmission_RIN_Jan15_2019.pdf
Attachment 4: RIN_Measurement_20190115.zip
Attachment 5: 20190116_130937noiseBudget.pdf
  2399   Fri Aug 23 18:15:49 2019 anchalDailyProgressBEATBeatnote after a while

The cavity temperature control (aftter the last fixes by Andrew) seem to be working good actually now that the Vacuum Can temperature is stabilized nicely. SO I didn't want to interfere with the PID's job which it seems is trying to reach to the set point almost critically. However, today, the beatnote came below 125 MHz, so we were in range with New Focus 1811 to take the spectrum. So I did it.

Two measurements

I used the coupled output from 20 dB coupler to feed the moku and use it's phase meter along with SR785 witht he previous PLL setup. Since the beatnote was still drifitng by around 10 kHz/24 sec, I took spectrum with linewidth of 1 Hz and used 20 averages to catch the PLL frequency noise in between its jumps. Simultaneously (almost), I took measurements with moku also to see if we can reliably switch over to moku. Good thing about moku is that it is faster in adjusting it's carrier frequency to lock to the signal and hence the jumps are unnoticeable. The attached plots are the measurements.

Uncertainty in moku's ASD plots!

Scott and I have written a modified PSD calculation function, which does everything same as a normal weltch function would do, but on top of it, it provides 15.865% and 84.135% percentile of all the individual segments the function used to calculate PSD. Also, the reported value is median and not mean. Further, this function implements welch function with different sizes of npersegment to ensure more averaging at higher frequencies and equal number of points in each decade. All this is done in mokuReadFreqNoise.py which uses modeifiedPSD.py. Linear detrending of data is also used before calculating the PSDs from the timeseries data provided by moku.


  • I think we can safely switch over to using Moku for measuring beatnote frequency noise, given it is available.
  • Beatnote obviously doesn't look so good. But at the point, the FSS aren't working as expected.
  • There is a weird peak at around 500 Hz which wasn't there before.
  • I'll add the noisebudget with new calculations using different values of Shear and Bulk Loss Angles soon. It is kind of difficult to get these values though.
  • My plan is to keep this functioning state all the time. I'll make sure the cavities are locked with good mode matching and near the desired beatnote frequency.
  • Then I'll focus on the known issues and sources of error and will keep monitoring the beatnote changes every 2-3 days.

Code and Data

Attachment 1: ComparisonOfMokuandSR785BeatnoteSpectrum.pdf
ComparisonOfMokuandSR785BeatnoteSpectrum.pdf ComparisonOfMokuandSR785BeatnoteSpectrum.pdf ComparisonOfMokuandSR785BeatnoteSpectrum.pdf ComparisonOfMokuandSR785BeatnoteSpectrum.pdf ComparisonOfMokuandSR785BeatnoteSpectrum.pdf
  2566   Mon Apr 13 16:52:30 2020 anchalDailyProgressBEATBeatnote measurements back on track

Since this morning atleast, I'm not seeing the North Path unstability (see CTN:2565) and the beatnote is stable and calm at the setpoint. Maybe the experiment just needed some distance from me for few days.

So today, I took a general single shot measurement and even after HEPA filers being on at 'Low', the measurement is the lowest ever, especially in the low-frequency region. This might be due to reduced siesmic activity around the campus. I have now started another super beatnote measurement which would take measurement continuously every 10 min is the transmission power from the cavities look stable enough to the code.

there is a new broad bump though arounf 250-300 Hz which was not present before. But I can't really do noise hunting now, so will just take data until I can go to the experiment.

Latest BN Spectrum: CTN_Latest_BN_Spec.pdf

Daily BN Spectrum: CTN_Daily_BN_Spec.pdf

Relevant post:

CTN:2565: North path's buggy nature NOT solved

Attachment 1: CTN_Latest_BN_Spec.pdf
  2535   Fri Feb 14 10:59:13 2020 anchalDailyProgressBEATBeatnote noise lowered in low frequency region

With some of the changes done recently, the beatnote noise has lowered in the low-frequency region indicating reduction in scatter.

Latest BN Spectrum: CTN_Latest_BN_Spec.pdf

Daily BN Spectrum: CTN_Daily_BN_Spec.pdf

Relevant elog post:

CTN:2530 : Increased sampling rate to 125kSa/s; lowest noise in higher frequencies

CTN:2533 : blocked NF1811 with hex beam dump

CTN:2535 : BN Detector was saturated. Reduced laser powers.

CTN:2531 : Further iterated back and forth to optimized FSS Gains.

  2540   Mon Feb 17 16:08:23 2020 anchalDailyProgressBEATBeatnote noise lowered in low frequency region with ISS

After installing the preliminary ISS, which I'll change tomorrow as per Rana's suggestions, we see some reduction in the beatnote noise in the lower frequency region. I think I should also have an estimate curve for the coupling of laser intensity noise into the final result. I can maybe make some sort of transfer function measurement from actuation on intensity to the beatnote frequency itself using moku.

Latest BN Spectrum: CTN_Latest_BN_Spec.pdf

Daily BN Spectrum: CTN_Daily_BN_Spec.pdf

Relevant elog post:

CTN: 2538 : Installed ISS on both paths using SR560s

CTN:2539 : Rana's suggestion on ISS.

Attachment 1: CTN_Noise_Budget_Effect_ISS_ON.pdf
  2543   Fri Feb 21 16:22:04 2020 anchalDailyProgressBEATBeatnote noise lowered in low frequency region with ISS

After installing the new ISS, the noise is even lower in lower frequencies. Still no change in the noisy peaks at 400 Hz and around 800 Hz. There is also no difference in noise floor above 200 Hz.

Latest BN Spectrum: CTN_Latest_BN_Spec.pdf

Daily BN Spectrum: CTN_Daily_BN_Spec.pdf

Relevant elog post:

CTN: 2542: Installed New ISS on both paths using SR560s

Attachment 1: CTN_Noise_Budget_Effect_ISS_ON_New.pdf
  1330   Mon Sep 9 15:00:19 2013 EvanDailyProgressISSBeefier ISS loop

I made a quick inverting op-amp integrator which kicks in at 860 Hz at has gain 10 at infinity. The feedback is a 5.6 kΩ resistor in series with a 33 nF capacitor. On the inverting input there is a 560 Ω resistor.

I put this after the SR560 with gain set to 100 and bandwidth set to 30 kHz. It seems like this gives good RIN suppression.

Attachment 1: ctn_rin_clopen.pdf
  1333   Wed Sep 11 00:07:04 2013 EvanDailyProgressISSBeefier ISS loop


I made a quick inverting op-amp integrator which kicks in at 860 Hz at has gain 10 at infinity. The feedback is a 5.6 kΩ resistor in series with a 33 nF capacitor. On the inverting input there is a 560 Ω resistor.

I put this after the SR560 with gain set to 100 and bandwidth set to 30 kHz. It seems like this gives good RIN suppression.

I changed the values so that the feedback is 13 kΩ in series with 1.2 nF, and the inverting input is 1.3 kΩ. This puts the zero at 10 kHz.

I duplicated this with a second OP27 on the same circuit board, so now there is an integrator for each cavity.

Last night the best results seemed to be achieved with the SR560s set to G = 100 with a pole at 10 kHz.

  2584   Mon Jun 15 16:43:58 2020 AnchalDailyProgressNoiseBudgetBetter measurement on June 14th

Final result of CTN experiment as of June 15th 5 pm:

\huge \Phi_B = (8.28 \pm 1.45)\times 10^{-4}\quad rad

with shear loss angle taken from Penn et al. which is 5.2 x 10-7. The limits are 90% confidence interval.

The analysis is attached.

Adding Effecting Coating Loss Angle (Edit Fri Jun 5 18:23:32 2020 ):

If all layers have an effective coating loss angle, then using gwinc's calculation (Yam et al. Eq.1), we would have an effective coating loss angle of:

\huge \Phi_c = (4.69 \pm 0.82) \times 10^{-4} \quad rad

This is worse than both Tantala (3.6e-4) and Silica (0.4e-4) currently in use at AdvLIGO.

Also, I'm unsure now if our definition of Bulk and Shear loss angle is truly the same as the definitions of Penn et al. because they seem to get an order of magnitude lower coating loss angle from their bulk loss angle.

Analysis Code


Attachment 1: CTN_Bayesian_Inference_Final_Analysis.pdf
CTN_Bayesian_Inference_Final_Analysis.pdf CTN_Bayesian_Inference_Final_Analysis.pdf CTN_Bayesian_Inference_Final_Analysis.pdf CTN_Bayesian_Inference_Final_Analysis.pdf
  2586   Tue Jun 23 17:28:36 2020 AnchalDailyProgressNoiseBudgetBetter measurement on June 22nd (as I turned 26!)

Final result of CTN experiment as of June 23  5 pm:

\huge \Phi_B = (8.18 \pm 1.42) \times 10^{-4} \quad rad

with shear loss angle taken from Penn et al. which is 5.2 x 10-7. The limits are 90% confidence interval.

The analysis is attached.

Adding Effecting Coating Loss Angle (Edit Fri Jun 5 18:23:32 2020 ):

If all layers have an effective coating loss angle, then using gwinc's calculation (Yam et al. Eq.1), we would have an effective coating loss angle of:

\huge \Phi_c = (4.13 \pm 0.80) \times 10^{-4} \quad rad

This is worse than both Tantala (3.6e-4) and Silica (0.4e-4) currently in use at AdvLIGO.

Also, I'm unsure now if our definition of Bulk and Shear loss angle is truly the same as the definitions of Penn et al. because they seem to get an order of magnitude lower coating loss angle from their bulk loss angle.

Analysis Code


Attachment 1: CTN_Best_Measurement_Result.pdf
  2587   Wed Jun 24 21:14:58 2020 AnchalDailyProgressNoiseBudgetBetter measurement on June 24th

Final result of CTN experiment as of June 24  9 pm:

\huge \Phi_B = (7.75 \pm 1.35) \times 10^{-4} \quad rad

with shear loss angle taken from Penn et al. which is 5.2 x 10-7. The limits are 90% confidence interval.

The analysis is attached.

Adding Effecting Coating Loss Angle (Edit Fri Jun 5 18:23:32 2020 ):

If all layers have an effective coating loss angle, then using gwinc's calculation (Yam et al. Eq.1), we would have an effective coating loss angle of:

\huge \Phi_c = (4.39 \pm 0.76) \times 10^{-4} \quad rad

This is worse than both Tantala (3.6e-4) and Silica (0.4e-4) currently in use at AdvLIGO.

Also, I'm unsure now if our definition of Bulk and Shear loss angle is truly the same as the definitions of Penn et al. because they seem to get an order of magnitude lower coating loss angle from their bulk loss angle.

Analysis Code

Automatically updating results from now on:

  1544   Sat Apr 4 18:15:39 2015 ranaDailyProgressPMCBeware the Bow-Tie

Recall the horrible sadaftermath of using the bow-tie configurationno for the green laser ALS setup at the 40m:angry

All of the supposedly HR mirrors leaked through enough lightcrying to make the table into a Christmas tree. The bow-tie should only be allowed when using the super HR mirrors from G&H which have T < 100 ppm over a wide range of angles.cheeky

  2358   Mon Jun 24 14:00:40 2019 ScottADailyProgressEOMBias Tee Addition

EOM Bias Tee:

  • I will make use of the RF Monitoring Circuit present on the driver for high impedance probing, which should have a coupling factor of about -36db at 37MHz. 
  • I want to model the EOM as a capacitive load, which from the data sheet is 20pF. We will use a board to solder a BNC port to this capacitor, and short the other side to ground. 
  • We want to measure the transfer function before and after the addition of a Bias Tee, and use the RF Monitor to tune the inductor to create an impedance peak at 37MHz.

    The first diagram shows the set-up without the Bias Tee. Here we will confirm the monitoring out channel is functional and the dummy EOM acts as expected. After we will add the Bias Tee as shown in the second diagram. Using the monitoring channel again we can then see the effect of adding the Bias Tee to the output of the amplifier circuit, but before the dummy EOM.

Attachment 1: EOM_driver_schematic.pdf
Attachment 2: EOM_driver_schematic_with_bias_tee.pdf
  2360   Tue Jul 2 17:22:16 2019 ScottADailyProgressRFAMBias Tee Data Analysis


  • First I calculated the transfer function for the ideal condition of the bias tee having one capacitor and one inductor with 50-ohm impedances on each output.
  • Using this function I used both scipy.optimize.curve_fit  and scipy.optimize.least_squares to try and pull out approximate values for C and L, as well as their parasitic resistances.
  • The data was taken from S31 and S32, where the S31 fit should tell us more about the capacitors value, while the S32 fit tells more about the inductor value. This is more relevant for the curve_fit function as it acts on the S31 data and S32 data separately. The least_squares used a cost function that attempts to fit both curves simultaneously, so it should give us good information on both components.
  • While curve_fit outputs the covariance matrix, the least_squares does not.  For least_squares I used its Jacobian to estimate the Hessian and from there calculated the covariance matrix.
  • In order to calculate the strength of randomness in residuals, I used the procedure defined on slides 26-29 from http://www2.compute.dtu.dk/~pcha/LSDF/LinDataFit.pdf. These were implemented as functions within the code "RandomSignTest" and "AutoCorrelationTest". 


  • Our best value for C is from the S31 fit and LSQ fits, which both fall within the range of 211nF. 
  • The value for L taken from the LSQ fit, which should be better correlated than the S31 fit and has a smaller error bar than the S32 fit, is around 694 uH.
  • The parasitic resistance of the inductor given by the LSQ fit is around 3 ohms, while S31 fit yields 530 ohms. In this case, because the LSQ fit uses data from both and is more reasonable, we will take the value from the LSQ fit.
  • It is important to note here that the test to determine the strength of randomness in the residuals failed for all fits used. This indicates we may be oversimplifying the electrical schematic of the bias tee.  
  • The values for the parasitic resistance of the capacitor vary wildly and seems to make little difference in the fitting.

Next Step 

I will add the simplified model of the bias tee into the EOM driver Circuit simulation within LTspice. I will include the parasitic resistance of the inductor, but due to the reason mentioned above will not include the parasitic resistance of the capacitor. Then I will see if it is possible to maintain the impedance peak at 37MHz by using the tuning inductor within the circuit.

Attachment 1: Bias_Tee_Fitting_Analysis_to_Single_C_and_L.zip
Attachment 2: Fitting_Analysis.pdf
  2359   Thu Jun 27 17:06:57 2019 ScottADailyProgressRFAMBias Tee S Matrix

In order to better characterize the Bias Tee, I measured the non-diagonal components of it's S matrix using the network analyzer(NA). I did not measure the reflection coefficients due to the inability of the NA to measure this without specialized components, and attempts at solving numerically were unsuccessful. Bias Tee's model number is ZFBT-4R2GW-FT (Link: https://www.minicircuits.com/WebStore/dashboard.html?model=ZFBT-4R2GW-FT%2B).

Measurement Details:

  • My first step was to solder a BNC connection onto the DC Port of the Bias Tee, and attach SMA to BNC connectors on the RF and RF+DC Ports to connect to the NA. 
  • I split the signal out of RF OUT on the NA and plugged one side into R, and the other into the port on the Bias Tee I was interested in inserting a signal into. The port I wanted to measure the signal out of was connected to A through BNC.
  • The port which was not in use was terminated with 50 ohms.
  • Utilizing WideTFMeas.py and its param and config file I acquired the data to be plotted in a jupyter notebook. 
  • I repeated this process 6 times until every port of the Bias Tee had both been injected with and received the signal from RF OUT.


  • I defined the RF port as Port 1, DC as Port 2 and RF+DC as Port 3.
  • I made 4 plots from this data, three showing the data for each port individually and one showing the transfer functions that will apply when using the bias as expected.
  • The first three plots give the signals read from the two alternate ports when the signal is injected into the port mentioned in the title.
  • The last plot shows the coupling between the RF and RF+DC ports as well as between the DC and RF+DC ports, which characterizes the transfer functions we expect to see in practice.


  • It is clear that any signal from the RF to RF+DC port will pass at high frequencies, but will be attenuated near DC.
  • Also, any signal from the DC port to RF+DC will pass at low frequencies but will be attenuated at high frequencies.
  • The DC attenuation in the RF port should be on the order of 10^(-3) at our operating RF frequency of 37 Megahertz, or around -60db.
  • The RF attenuation in the DC port should be around 10^(-2) up to 400Hz, or around -40 dB.
Attachment 1: Bias_Tee_S_Matrix_6_27_2019.pdf
Bias_Tee_S_Matrix_6_27_2019.pdf Bias_Tee_S_Matrix_6_27_2019.pdf Bias_Tee_S_Matrix_6_27_2019.pdf Bias_Tee_S_Matrix_6_27_2019.pdf
Attachment 2: Bias-Tee.jpg
Attachment 3: Bias_Tee_S-matrix_Data_6-27-2019.zip
  1573   Wed Aug 19 10:34:33 2015 AidanSummaryDAQBinary IO control of TTFSS box working - can lock PDH remotely

I've worked out how to get the binary IO to work with the TTFSS box so that we can activate switches in that unit. It wasn't working in the setup yesterday because of physics. Actually - there is a 10K pulldown resistor in the Acromag unit that attaches the output to ground. The actual circuit looks like this:


VCC (5V) --- (4.99K) --- T1EN -----|-----DIO0 ----(6.2V if DOUT set to 1)---- (10K) ------ | GND

.........   TTFSS...................................| ..............................ACROMAG ...............................................|

T1EN is measured by the switch-chip (SN74HCT157D, chip U3 in D040423) to determine whether it should be open or closed. We need to bring T1EN below 0.8V to get the TTL logic to work.

If DOUT is set to 1, then DIO0 and T1EN become the excitation voltage, 6.2V, and the switch circuit reads high. If DOUT is set to 0, the excitation voltage is removed and we just end up with a voltage divider and around 3.33V at T1EN - which does not register as low.

We can get around this by adding a smaller resistor, say 810 Ohms, in parallel to the 10K, to lower the effective resistance of the pull-down resistor to 750 Ohms. The maximum current the Acromag unit will have to supply is 6.2V/750 Ohms = 8.4mA.

So that's what I did. Now, when I switch DOUT to 1, I see 6.2V at T1EN and when I switch DOUT to 0, I see 0.669V at T1EN. The TTFSS box registers these as two different states and I can lock and unlock the PDH loop from EPICS.

  256   Thu Aug 5 11:33:20 2010 MeganDailyProgress BluePhase 1000

The cavities were still too far off to lock simultaneously, but they should hopefully be better today.

Instead, we played with the Wenzel BluePhase 1000 phase noise test system.


Following the directions in the manual, we locked an IFR/Marconi 2023A to an IFR/Marconi 2023B, calibrated according to the manual, and got a curve very similar to what we had before . This means it's probably working correctly!

So then, just to be adventurous, we decided to connect the VCO in place of the 2023B to measure its phase noise. Apparently that was too adventurous for the BluePhase 1000 . We couldn't lock it (with the feedback loop going to the 2023A) with any input range below roughly 100 kHz and the output (after calibration as per the manual) was a flat line. After readjusting cables and reconnecting cables and finally reverting back to the 2023A vs 2023B to make sure the machine still worked, we decided the unity gain frequency was probably pretty high and the manual calibration did not take that into account. So we used a swept sine measurement to find the transfer function of the system with the VCO connected and locked. The UGF was around 5.3 kHz with the 100 kHz input range . This means that the calibration doesn't account for everything when the UGF is high . But it also means we may have found the problem with our data when the VCO is connected ! So I have to take the data we have, apply a zero at 5.3 kHz, and see if that gets it to line up correctly.

Meanwhile, we installed a program on the computer that, when connected to the BluePhase 1000, can control all the knobs and buttons and locking remotely. And we discovered you can do more on the computer than with the switches on the front! Like change the capacitor value.

So the summary of yesterday's activities is: don't ever completely trust the calibration the manufacturers tell you to use. They might not be taking something (UGF) into account.

And the calibration as per the manufacturers:

1) Adjust the offset until exactly 1 period is displayed on the oscilloscope

2) Divide the time divisions on the oscilloscope to 1/100th the original (this gives 0.02Pi radians)

3) Measure the voltage difference across the two ends of the line

4) Calculate your slope! (gives V/rad)

5) Noise [dBc/Hz] = [PSD]-[20log(slope)]-[amp gain]-[correction for SSB measurement]

Attachment 1: GraphCompare.png
  2475   Sat Nov 9 13:46:08 2019 shrutiMiscElectronics EquipmentBorrowed

I've borrowed a Marconi VCO, a mini-circuits LPF and mixer from the CTN lab for use at the WB EEshop.

AG Mon Dec 30 10:24:28 2019 : Has been returned to CTN now.

  1698   Thu Aug 4 13:33:39 2016 awadeNotesInventoryBorrowed SRS DB64 delayer box from Crackle Lab

Borrowed SRS DB64 delayer box from Crackle Lab.  

Has a set of binary switches in increments of 0.5,1,2,4,8,16,32 ns.  This should be useful in varifying if we have the optimal phase delay for the error signal.  Distance from cavities to PDs has changed but the cabling is the same.  We might as well know that we are opimised rather than trust that it is just OK.

  2383   Wed Aug 7 14:42:58 2019 Nathan HollandMiscElectronics EquipmentBorrowed SRS DB64.

I have borrowed the SRS DB64. It is in QIL.

  2336   Mon May 6 20:12:22 2019 AnjaliSummaryEquipment loanBorrowed components

I borrowed the following components from PSL lab to QIL lab 

1. Mixer (Minicircuit, ZFM-3-S+)

2. RF amplifier (Minicircuit, ZFL-500LN)

3. IFR/Marconi 2023 A (# BD9020)

  2325   Wed Apr 17 10:40:54 2019 KojiSummaryEquipment loanBorrowing an IPA/Acetone glass bottoles CTN->OMC

I borrowed a small isopropanol glass bottle from CTN to OMC (Apr 17, 2019)

I borrowed a small acetone glass bottle, which was in the yellow solvent cabinet, from CTN to OMC (Apr 19, 2019)

  269   Tue Aug 10 21:40:42 2010 Megan and FrankDailyProgress Both Cavities Locked!

We got both cavities locked today!

They stayed locked for at least an hour and were still locked when we left. Hopefully they'll still be locked tomorrow morning!

We aligned both beams into the photodiode (they were already pre-aligned) and maximized the alignment to get the largest signal out of the photodiode. We locked the signal from the photodiode with the IFR/Marconi 2023B signal generator and took some measurements of noise and transfer functions to determine UGFs, which I will post graphs of when I put them together. The plan is to let the temperatures really settle down (they were still settling a bit when we left) and take a good measurement of the noise and measure the transfer functions to determine UGF tomorrow. Then we will pull everything apart (not really) to replace the two cables that have extensions on them to see if something in the connection can be fixed to give better stabilization.

*I added a graph of the noise we measured yesterday at 3 different times*

Attachment 1: BeatSignal.png
  2205   Mon Jun 18 14:42:45 2018 anchalPhotosISSBreadboard circuit testing

Attached is the image of circuit implemented on breadboard with modelled AOM and cavity as phase shifter and low pass filter respectively.
In the image, all red/orange wires are at +15V, all white/grey wires are GND, all green wires are at -15V, all yellow wires are carrying signal and one violet wire is the voltage offset set to 0V right now. All the opamps are OP27G except the adder and an inverter which are OP27E. The circuit corresponds to the attached LTspice circuit.

Attachment 1: Breadboard_Circuit_Labeled.jpg
Attachment 2: ISSAOMCavity.pdf
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