Question for Craig: What does the SNR of our lines have to be? IF we're only trying to calibrate the actuator in the audio band over long time scales, it seems we could get by with more frequency noise. Assuming we want a 1% calibration at 50-500 Hz, what is the requirement on the frequency noise PSD curve?

We get SNR in two ways: the amplitude of applied force and the integration time.  So we are limited in two ways: stability of the lock to applied forces and time of locklosses / calibration fluctuations.

At the sites, you probably know that we blow our spectrum out of the water with the calibration lines, with SNRs of about 100 on the scale of about 10 seconds.  For us this might be impossible, since we aren't as quiet.

If we want 1% calibration on our sweeps, we'll need  0.01 = Uncertainty = sqrt( (1 - COH^2)/(2 * Navg * COH^2) ), where COH is the coherence of the transfer function measurement and Navg is the number of measurements at a specific frequency.  This equation comes from Bendat and Piersol, and is subject to a bunch of assumptions which may not be true for us (particularly, that the plant is stationary in time).

If we let Navg = 10, then COH ~ 0.999.

Coherence = Gxy^2/(Gxx * Gyy), where x(t) and y(t) are the input signal and output signal of the transfer function measurement, Gxx and Gyy are the spectral densities of x and y, and Gxy is the cross-spectral density.  

Usually SNR = P_signal / P_noise, but for us SNR = A_signal / A_noise.

Eric Q and Evan H helped me find the relationship between Coherence and SNR:

P = Pn + Pc, Pn = P * (1 - Coh), Pc = P * Coh

==> SNR = sqrt( Pc / Pn ) = sqrt( Coh / 1 - Coh )

From Coh ~ 0.999, SNR ~ 30.

OK, but the questions still stands: "Assuming we want a 1% calibration at 50-500 Hz, what is the requirement on the frequency noise PSD curve?"

I looked in the optics cabinet to see what lenses we have available, and re-ran the mode-matching calculation to see if we could find a better solution - I'm attaching a plot for what looks like a good candidate (optimized mode-matching efficiency for the X mode is 100%, and for the Y mode, it is 97.98%), though it does involve switching "L1", which is currently a 175mm efl lens, for a 125mm efl lens. I've also indicated on the plot where the various other components are relative to the optimized positions of the lens, and it doesn't look like anything is stacked on top of each other. Also, the beam width throughout is well below 4.7mm, which is the maximum cited width the Faraday can handle, as per its datasheet. "L1" doesn't quite get the waist of the beam to coincide with the geometrical center of the Faraday, but I don't think this is requried? Also, I've optimized the mode matching using the measured X width of the beam (red curve in Attachment #1), and have overlaid the calculated Y width of the beam for the optimized position of the lenses (red curve in Attachment #1). The target waist was 35um at the center of the doubling oven, which the X profile achieves, but the Y profile has a width of 32 um at the same point.

In all the calculations, I've not accounted for possible effects of the HWPs and the Faraday on the beam profile....

I installed and activated Altium, a PCB design software, on the Windows machine M2.

With Altium I am going to design the triple resonant circuit for the broadband EOM.

I found the sensor that we used to measure the tmeperature in the lab. It is a SensorGateway (BASE-WIRED) and according to its datasheet it has a temperature resolution of 0.1 Celsius and an accuracy of 1 Celsius. Regardless, I also let it collect some data overnight to get a better grasp of the noise.

I put the sensor in a box, wrapped around two towels. I tried closing the box as much as possible, but the cables connecting to the sensor prevented me from closing the box all the way. I put the box in the same spot where the sensor sat when the environment data was collected. Here is the picture of the device:

I started the data collection yesterday at around 5pm. Here is the raw temperature data collected by the sensor:

The temperature first increased due to the heat put out by the sensor unit itself (this is a server temp sensor, which has its network server for easy access among other features). We can see that the temperature peaked around 4 hours after the experiment started, which is to be expected, around that time (9pm) the temperature in the lab starts to decrease dramatically. The sensor reached a fairly stable equilibrium around hour 10 which would translate to around 3am, which is again to be expected considering our environment temperature measurements. I used the stable region between hours 10 and 13 for noise estimates:

We can see here that the sensor kept "jumping" between two values: 30.9592 Celsius and 30.8967 Celsius. The difference between these readings is 0.0625 Celsius, and it can be seen that there are no intermediary values between these 2 values. I also performed a spectrum analysis just to see what happens:

The dip at around 0.9 Hz is also visbile in the environment temperature spectrum.

The goal was to characterise the new amplifier (AP1053). For a practice, I did the characterisation of the old amplifier.This test is similar to that reported in Elog ID 13602.

• Attachment #1 shows the schematic of the setup for gain characterisation and Attachment #2 shows the results of gain characterisation. 
• The gain measurement is comparable with the previous results. From the data sheet, 10 dB gain is guaranteed in the frequency range 10-450 MHz. From our observation, the gain is not flat pver this region. We have measured a maximum gain of 10.7 dB at 6 MHz and it has then decreased upto 8.5 dB at 500 MHz
• Attachement #3 shows the schematic of the setup for the noise characterisation and Attachment # 4 shows the results of noise measurment. 
• The noise measurement doesn't look fine. We probably have to repeat this measurement.

I just realized that I forgot to elog this, but yesterday afternoon I bypassed the amplifier in the BeatX path, and now the X beatnote is about -27dBm.  Arms lock nicely with ALS.

And the out-of-loop level of the ALSX compared with the previous measurement is ...?

Sorry, I had been in a hurry when I worked on this last week, and again when I wrote the elog, but I wanted to at least put in a note for any weekend workers.

The ALS beatnote setups need alignment on the PSL table.  However, even at very low RF beat frequency, the X beatnote now at low frequencies matches our best measurement from last week.  The "HEPA off" (teal and purple) measurements are from last week, and the red and blue are from this week.  The X beatnote was 10MHz and the Y beatnote today was 31MHz.

The top plot shows a sweep from 10 kHz to 5 MHz of the ratio of the voltage output of the PD detecting power from the NPRO laser beam and the RF source voltage (the magnitude of the complex transfer function). The black trace was taken with the laser beam blocked. For runs 2 and 3 I changed the laser temperature set point by 10 mK and 100 mK respectively to see if there was a significant change in the AM response. The bottom plots shows runs 2 and 3 compared to run 1 plotted in dB (to be explicit, i'm plotting 10 times the base 10 log of the magnitude of the ratio of two complex transfer functions). Changing the temperature seems to have only a minor effect on the output except at around 450kHz, where the response has a large peak in run 1 and much smaller peaks in runs 2 and 3. 

The traces in the top plot consist of 16 averages taken with a 300Hz IF bandwidth, 15 dBm source power (attenuated with a 6 dB attenuator) and with 20dB attenuation of the input power from the PD.

Next I'm going to probe a narrow band region where the response is low (2.0MHz or 2.4MHz perhaps) and choose a bandwidth for the dither frequency for the PDH locking.

Last Tuesday evening, while attempting the PRFPMI locking, I noticed a strange feature in the LSC signals, which is shown in Attachment #1 (the PDF exported by dataviewer is 14MB so I upload the jpeg instead). As best as I can tell, the REFL33 and POP22 channels show an abrupt jump in the signal levels, while the other channels do not. POP110 shows a slight jump at around the same time, and the large excursion in AS110_Q actually occurs a few seconds later, and is probably some angular excursion of the PRC/BS. I'm struggling to interpret how this can be explained by some interferometric mechanism, but haven't come up with anything yet. The LO for the 3f error signals is the 2f field, but then why doesn't the POP110 channel show a similar jump if there is some abrupt change in the resonant condition? Is such a change even feasible from a cavity length change point of view? Or did the sideband frequency somehow abruptly jump? But if so, why is the jump much more clearly visible in one sideband than the other?

Does anyone have any ideas as to what could be going on here? This may give some clue as to what's up with the weird sensing matrices, but may also be something boring like broken electronics... 

 The new RF cables arrived. But unfortunately we did not realize that RG405 was a Semi-rigid coax cable, with a copper shielding. These are meant to be installed in setups that will not be changed / disturbed. We need to order a different set of cables. The new cables have joined the other cables in the plastic box mentioned above.

For now to check if the old setup is still working, I have installed an RF cable (that we earlier pulled out and looks like in good shape, labelled REFL33) between the AS55 Demodulator output PD RF MON in rack 1Y2 and the network analyzer input. Since Manasa and the others were busy working with the interferometer, I did not switch on the laser and did not take any readings. The power supply to REF DET remains off.

I will continue with the measurements tomorrow morning and also try to get the data wirelessly using Alex's code. 

I've fallen down the rabbit hole of trying to reconcile our desire for newer versions of the Numpy and Scipy python packages with the use of our handy cdsutils tools. 

I've set up an installation of Anaconda python in /ligo/apps/anaconda. Installing pyepics, nds2, and cdsutils was straightforward, but there were a myriad of odd python packages that cdsutils depends on, that are typically installed at the OS level (python-gst, gobject, glib) which I just manually copied over to the anaconda directories. Also, the version of readline that anaconda ships with is somewhat borked (dark voodoo fix was found here: github link. The issue mentioned there wasn't why I needed the fix. Somehow libreadline was causing pyepics initialization to fail). 

I was initially hoping this kind of exercise would be useful, as having a separate python environment that we control buffers us from the system installation and allows us to use whatever version of packages we want, but the amount of hackery I did to get to get cdsutils to work probably didn't result in the most robust solution. (Maybe there was a better way!)

In any case, I have not changed any of our machines' default paths or environment variables. Instead, I have simply created an alias that points to Anaconda python: "apython"

Example:

Thus, Diego should now be able to complete his script that needs the newer Scipy, as well as CDSutils. 

Final note: I've tested z (read|write|avg) with $PATH modified to have /ligo/apps/anaconda/bin at the start, and they seem to work. If things seem to hold up, maybe we can replace the default command-line python, but its not strictly necessary. 

 Avoid rabbit holes! What I did at LLO which works is to install an Anaconda in some shared directory and then just make an alias which puts that directory at the head of the path when running the more advanced SciPy installs. It works fine and cannot interfere with our usual operation since its only sourced when running peak find.

The anaconda distribution used by the control room workstations is actually installed on the shared drive (/cvs/cds/ligo/apps/anaconda/) for consistency reasons. The version was 4.5.11. I ran the following commands to update it today. Now it is version 4.7.12.

The second command takes a while to resolve conflicts, so I've left it running inside a tmux session for now.

Recall that the bash alias for using the anaconda managed python is "apython". I recommend everyone set up a virtual environment when trying out new package installs, to avoid destroying the locking scripts.

This diagram shows the setup of the analog Mixer-Frequency Discriminator (MFD).

The idea is similar to the one of the Schnupp Asymmetry for our Michelson interferometers. The signal from the PD (or any signal source for which you want to know the frequency) is split into two legs; one leg is much longer than the other. The two legs are recombined at a mixer/demodulator. The demodulator output varies sinusoidally with the phase difference of two legs, the same as when we try to measure the phase noise of an oscillator, for example. This is the same concept as the digital frequency discriminator that Aidan and Joe put into the GFD FE system recently.

With a ~1m cable length asymmetry, we get 180 deg of phase shift for a ~100 MHz signal (recall that the speed of light in most of our cables is ~2 x 10^8 m/s). The mixer gives a linear output at 50 MHz (and 150 MHz, 250 MHz, etc.).

This single mixer based setup is fine for most everything we do. In order to get even more resolution, one can just use 2 mixers by splitting the signal with a 4-way instead of 2-way mixer. One setup can have a 0.5-1 m asymmetry to have a large range. The other can have a ~10-30m asymmetry to get a comb of linear readouts.

Typically, we will have some kind of weak signal at the photodiode and will use a 20 or 40 dB gain RF amp to get the signal into the mixer. In this case, the mixer output noise will be at the level of tens of nV/rHz. Any usual low noise audio amplifier (SR560 variety) will be enough to read out the signal.

Why the 50 Ohm terminator? If you look at the specs of the BLP-1.9 filter from Mini-Circuits (its the same for almost all of their LP filters) you see that there's ~90 dB of attenuation above ~30 MHz (where our signals 2*f product will show up). If we use an RF input signal of ~0 dBm, this means that we get a high frequency product of -95 dBm (~10 uVrms) which is OK. But the return loss is 0 dB above 5 MHz - this means that all of the high frequency content is reflected back into the mixer! The 50 Ohm terminator is there to absorb the RF signals coming out of the mixer so as to prevent them from going back into the mixer and mixing with the RF/LO signals. The 50 Ohm terminator does attenuate the DC/audio frequency signals we get out of the mixer by a factor of two, but that's OK since we are not limited by the mixer's thermal noise.

Noise Measurement:

To checkout the noise, we used a 6m RG-58 cable in one leg. We used the DS345 signal generator for the source. We adjusted the frequency to (~21 MHz) give a ~zero mean signal at the demod output. The 6m cable makes the demod output's peak-peak swing correspond to ~16 MHz. We then used an SR560, DC coupled, G=1000, low-noise, 2pole low pass at 1 kHz, to get the signal into the ADC.

The attached plot shows the noise. We have caibrated the digital gain in the channel to make the output into units of Hz. The high frequency noise floor is ~0.3 Hz/rHz and the 1/f knee is at 10 Hz. This setup is already good enough for all of the green locking work at the 40m. In order to make this useful for the reference cavity work or the gyro, we will have to use a longer cable and a lower noise audio amplifier.

As can be seen from the plot, the ADC noise is below the measured noise. The noise of the SR560 with the input terminated is shown in grey - the measured noise of the MFD is very close to this. In order to improve the performance, the next step should be to use a longer cable. There's clearly going to be some trade-off between the temperature dependent effects which come with long cables (dphi/dT gets bigger) and trying to use a high gain ~1 nV/rHz amplfier at the mixer output.

Temperature Drift of the long cable:

This 24-hour minute-trend shows the frequency wander as well as the room temperature. This is not proof of a temperature dependence, but if it is then we get ~3 kHz/deg for the sensitivity. If this is actually the cable and not the amplifier, then we'll have to hunt for a lower tempco cable and put it in a box to isolate it.

I swapped over to a 3x longer cable (old 65 ft. Pasternak cable from ancient 40m days). The old one was 6m, the new one is 18.2 m. It was already coiled up so I put it into a tupperware box to shield it somewhat from the HVAC wind.

The noise went down nearly proportional to the length (after I recalibrated the DAQ channel for the ~3x higher phase->voltage gain). With this length, the peak-peak mixer range is 5.5 MHz, so still enough to go an FSR here.

I give credit to the low frequency improvement entirely to Tupperware for their excellent containers. The current noise limit is most likely the SR560.

[Jenne, EricQ]

I told Koji that I wanted to play with the common mode servo this evening, and he pointed out that we only get the signals after the digital demod phase angle in the digital system (obviously).  So, if I want to use either REFL11 or REFL55 for my CARM signal, I want to do something in analog-land so that my digital demod phase is close to 0 or 90. 

While we had the PRFPMI locked (with CARM offset of 2 or 3 nm), we set the demod phases of REFL11 and REFL55 to minimize a CARM line in the Q-phase.  This gave us -34 degrees for REFL11, and -75 degrees for REFL55. 

We calculated that about 1 degree of phase shift is about 1/(2 * pi * freq), or about 1.4e-8 seconds of delay for 11MHz.  We took the speed of light in the cables to be about 2/3*c, so 1.4e-8 * 2e8 = 2.9 meters per degree for 11MHz.  Since REFL11 was 34 degrees from 0, we estimate that we need to add about 98 meters of cable to the REFL11 signal path.  The same calculation for 55 MHz, but with a 15 degree shift required, gives 8.8 meters of cable to be added to the REFL55 signal path. 

I connected up some long BNC cables, and inserted them between the heliax breakout board on the LSC rack, and the respective PD inputs of the REFL11 and REFL55 demod boards.  I used (45 meters + 45 meters + a little bit) for REFL11, and used about 9 meters for REFL55. 

When we relocked the PRFPMI, and redid the phasing, we were very close to zero for both REFL11 and REFL55!  REFL11's digital demod phase is now +1 degree, and REFL55's digital demod phase is -5 degrees.

We changed the input of the CM servo board from POY (which Den and Koji had been using in December - see elog 9500) to REFL11 I MON. 

Q locked the FPMI (separate reply elog), and then we tried engaging the CM analog servo.  We were not successful. 

These settings were mostly copied from elog 9500, so they are almost surely not correct. 

CM servo screen:  In1 gain = 31dB, switch on, offset = -2.7V, boost off, super boosts off, option=disable, 79:1.6k switch disabled, polarity minus, option disable, AO gain=8dB, limiter enable.

For the slow path, CM_SLOW -> MC LSC servo had a +1 in the input matrix. 

CM filters in the AUX_ERR screen:  FM1 (unwhite) on, all others off, gain = 2.6. 

MC servo filters:  FM7, FM10 on, all others off (no triggered filter modules).  Gain = 0 initially.

MC servo board AO path disabled initially, G=-32dB initially.

Once Q had the FPMI locked, I tried increasing just the CM analog gain (by enabling the AO path on the MC board, and increasing the gain).  Doing this, I lost lock at -3 dB. 

I then tried again, this time alternating increasing the analog gain, and increasing the MC LSC servo gain.  I got up to 3e-3 for the MC digital gain, and -7 dB for the analog gain before we lost lock again.

We have determined that we should probably try just locking one of the arms with POX or POY, as Den and Koji did, to get a feel for how the system works.

For future reference:

As we were poking around with the common mode servo in an FPMI configuration, we locked CARM/DARM with ALS as in recent ELOGs.

MICH was locked on ASDC: ASDC -> MICH = 10.0 in the DCPD DoF Matrix (I couldn't easily get AS55Q working, ASDC worked quickly and good enough)

MICH gain +25, FM4 FM5 On, FM2 switched on once locked. Offset was manually adjusted to get closer to dark fringe.

Actuated on BS: MICH->BS = 0.5 in Output Matrix.

I have never used such a long cable for RF phase adjustment. The speed of the signal is 2e8 m/s and the frequency is ~10e6 Hz.
This means that the wavelength is only about 20m. How could you end up with ~100meters?
The convenient way to remember the cable delay is "1m, 1MHz, 2deg". This gives us ~1.5m for 11MHz and 34deg.

In fact, 1 degree of phase shift is not 1/(2 pi freq) second of delay, but f/360.

For such a precise phase adjustment, it is better to calibrate the delay with the network analyzer.

There turned out to be a few analog signals for the vacuum system after all. The TP2/3 foreline pressure gauges were never part of the digital system, but we wanted to add them, as some of the interlock conditions should be predicated on their readings. Each gauge connects to an old Granville-Phillips 375 controller which only has an analog output. Interfacing these signals with the new system required installing an Acromag XT1221 8-channel A/D unit. Taking advantage of the extra channels, I also moved the N2 delivery line pressure transducer to the XT1221, eliminating the need for its separate Omega DPiS32 controller. When the new high-pressure transducers are added to the two N2 tanks, their signals can also be connected.

The XT1221 is mounted on the DIN rail inside the chassis and I have wired a DB-9 feedthrough for each of its three input signals. It is assigned the IP 192.168.114.27 on the vacuum subnet. Testing the channels in situ revealed a subtley in calibrating them to physical units. It was first encountered by Johannes in a series of older posts, but I repeat it here in one place.

An analog-input EPICS channel can be calibrated from raw ADC counts to physical units (e.g., sensor voltage) in two ways:

1. Via LINR="LINEAR" by setting the engineering-units fields EGUF="[V_max_adc]", EGUL="[V_min_adc]"
2. Via LINR="NO CONVERSION" by manually setting the gain ASLO="[V/count]" and offset AOFF="[V_offset]"

From the documentation, under the engineering-units method EPICS internally computes:

where EGUF="eng units full scale", EGUL="eng units low", and "full scale A/D counts" is the full range of ADC counts. EPICS automatically infers the range of ADC counts based on the data type returned by the ADC. For a 16-bit ADC like the XT1221, this number is 2^16 = 65,536.

The problem is that, for unknown reasons, the XT1221 rescales its values post-digitization to lie within the range +/-30,000 counts. This corresponds to an actual "full scale A/D counts" = 60,001. If a multiplicative correction factor of 65,536/60,000 is absorbed into the values of EGUF and EGUL, then the first term in the above summation can be corrected. However, the second term (the offset) has no dependence on "full scale A/D counts" and should NOT absorb a correction factor. Thus adjusting the EGUF and EGUL values from, e.g., 10V to 10.92V is only correct when EGUL=0V. Otherwise there is a bias introduced from the offset term also being rescaled.

The generally correct way to handle this correction is to use the manual "NO CONVERSION" method. It constructs calibrated values by simply applying a specified gain and offset to the raw ADC counts:

calibrated val = (measured A/D counts)  x ASLO + AOFF

The gain ASLO="[(V_max_adc - V_min_adc) / 60,001]" and the offset AOFF="0". I have tested this on the three vacuum channels and confirmed it works. Note that if the XT1221 input voltage range is restricted from its widest +/-10V setting, the number of counts is not necessarily 60,001. Page 42 of the manual gives the correct counts for each voltage setting.

We discovered that the analog whitening filter of the REFL55_I board is not switching when we operate the button on the user interface. We checked with the Stanford analyzer that the transfer function always correspond to the whitening on.

The digital one is actually switching. We decided to keep the digital de-whitening on to compensate for the analog one. Otherwise we get a very bad shape of the PDH signal. Sorry Rana...

 I forgot to say that the analog gain of the REFL55 channels has been reduced to 9db

 I have been trying to use an ADC with the Raspberry Pi to be able to measure the phase difference between FC input and output signals.I had a hard time interfacing the ADC  with the Pi (setup attached) even after trying to debug the issue for last two days. So I and Eriq Q performed a system reboot on the Pi and tried all the possible ways for the Pi to detect the ADC but we were not able to. At the end we decided to order another IC(Microchip MCP 3008) which we hope can be interfaced with the Pi. Till then I will finish to write data from the FC into pipes so that the control computers can access the real time data. I will also look the correctness of the sampling time that is provided by the spec of the MCL-Mini circuits that is if we could really achieve 0.1 s sampling time with the FC.

Joe let me use the resonant EOM for GigE phase camera for a while.
Then, I immediately started to open it :)

it uses the MiniCIrcuits T5-1T transformer and a TOKO RCL variable inductor.

The photos are on the Picasa 40m album.

http://lhocds.ligo-wa.caltech.edu:8000/40m/40m_Pictures

 Trying to take an image or movie of the ETMY Transmon cam, we got instead this attached image.

I think it is just some scattered green light, but others in the control room think that it is a message from somewhere or someone...

 It is not an angel, it is clearly a four leaf clover (also known as "quadrifoglio"). It is very rare, it brings good luck!

[J, Q]

Alignment is making it tough for locks to last more than 10 minutes. Many (but not all) locklosses correlate with some optic drifting away, and taking all of the light with it. The other locklosses are the quick ones that seem to pop up out of nowhere; we haven't made any headway on these. We wanted to get to a state where we could just let the interferometer sit for some minutes, to explore the data, but got caught up with alignment and PRMI things.

We're finding that both ITMs experience some DC force when entering full PRFPMI lock. I will calculate the torque expected from radiation pressure + offset beam spot, especially for ITMX, where we choose the spot position to be uncontrolled by ASS. 

I set up the QPD ASC servos to act in a common/differential way on the ETMs. The C1:ASC-XARM_[PIT/YAW] filter modules act on the common alignment, whereas the C1:ASC-YARM_[PIT/YAW] filter modules act on the differential alignment. This can soon be cleaned up with some model renaming to reduce confusion. 

Using DC oplev values as a guide, we are hand tuning ITM alignment once the AO path is engaged and we see the DC drift occurring. Then, we set the QPD servo offsets and engage them. 

In this manner, we were able to lock the interferometer at:

• Arm transmission 150 x single arm power
• POPDC indicated a recycling gain of ~5.5
• ASDC/POPDC indicated a contrast of 99.8%
• REFLDC indicated a visibility of 80%

We made the PRMI transition to 1f numerous times, but found that the sideband power fluctuations would get significantly worse after the transition. 

We found that the gains that were previously used were too small by a factor of a few. There is a DC change visible in REFL165 before and after the transition (Also POP55, aka REFL55, is not DQ'd ). Really, it isn't certain that we've zero'd the offset in the CARM board either, so REFL55's zero crossing isn't necessarily more trustworthy that REFL165's. We can go back in the data and do some 2D histograming to see where in the error signal space the sideband power is maximized. 

Jenne reports:

• The all RF transition succeeded 13/29 times. 
• PRMI 1f transision succeeded 10/10 times. 

Here's my first attempt at doing angular actuation calibration for IMC mirrors using the method descibed in /users/OLD/kakeru/oplev_calibration/oplev.pdf by Kakeru Takahashi. The key is to see how much is the cavity mode misaligned from the input mode of beam as the mirrors are moved along PIT or YAW.

There two possible kinds of mismatch:

• Parallel displacement of cavity mode axis:
  • In this kind of mismatch, the cavity mode is simply away from input mode by some distance .
  • This results in transmitted power reduction by the gaussian factor of where is the beam waist of input mode (or nominal waist of cavity).
  • For some mismatch, we can approximate this to
                                                                            
• Angular mismatch of cavity mode axis:
  • The cavity mode axis could be tilted with respect to input mode by some angle .
  • This results in transmitted power reduction by the gaussian factor of   where is the beam divergence angle of input mode (or nominal waist of cavity) given by .
  • or some mismatch, we can approximate this to
                                                                             

Kakeru's document goes through cases for linear cavities. For IMC, the mode mismatches are bit different. Here's my take on them:

MC2:

• MC2 is the easiest case in IMC as it is similar to the end mirror for linear cavity with plane input mirror (the case of which is already studies in sec 0.3.2 in Kaker's document).
• PIT:
  • When MC2 PIT is changed, the cavity mode simple shifts upwards (or downwards) to the point where the normal from MC2 is horizontal.
  • Since, MC1 and MC3 are plane mirrors, they support this mode just with a different beam spot position, shifted up by .
  • So the mismatch is simple of the first kind. In my calculations however, I counted the two beams on MC1 and MC3 separately, so the factor is twice as much.
  • Calling the coefficient to square of angular change , we get:
                                  
  • Here, R is radius of curvature of MC1/3 taken as 21.21m and L is the cavity half-length of IMC taken as 13.545417m.
• YAW:
  • For YAW, the case is bit more complicated. Similar to PIT, there will be a horizontal shift of the cavity mode by .
  • But since the MC1 and MC3 mirrors will be fixed, the angle of the two beams from MC1 and MC3 to MC2 will have to shift by .
  • So the overall coefficient would be:
                                  
  • The factor of 4 in denominator of seconf term on RHS above comes because only half og angular actuation is felt per arm. The factor of 2 in numerator for for the 2 arms.

MC1/3:

• First, let's establish that the case of MC1 and MC3 is same as the cavity mode must change identically when the two mirrors are moved similarly.
• YAW:
  • By tilting MC1 by , we increase the YAW angle between MC1 and MC3 by .
  • Beam spot on both MC1 and MC3 moves by .
  • The beam angles on both arms get shifted by .
  • So the overall coefficient would be:
                                  
  • Note, this coefficient is same as MC2, so it si equivalent to moving teh MC2 by same angle in YAW.
• PIT:
  • I'm not very sure of my caluculation here (hence presented last).
  • Changing PIT on MC1, should change the beam spot on MC2 but not on MC3. Only the angle of MC3-MC2 arm should deflect by .
  • While on MC1, the beam spot must change by and the MC1-MC2 arm should deflect by .
  • So the overall coefficient would be:
                                  

Test procedure:

• We first clicked on MC WFS Relief (on C1:IOO-WFS_MASTER) to reduce the large offsets accumulated on WFS outputs. This script took 10 minutes and reduced the offsets to single digits and IMC remained locked throughout the process.
• Then we switched off the WFS to freeze the outputs.
• We moved the MC#_PIT/YAW_OFFSET up and down and measured the C1:IOO-MC_TRANS_SUMFILT_OUT channel as an indicater of IMC mode matching.
• Attachement 1 are the 6 measurements and there fits to a parabola. Fitting code and plots are thanks to Paco.
• We got the curvature of parabolas from these fits in units of 1/cts^2.
• The coefficients calculated above are in units of 1/rad^2.
• We got the angular actuation calibration from these offsets to physical angular dispalcement in units of rad/cts by .
• AC calibration:
  • I parked the offset to some value to get to the side of parabola. I was trying to reduce transmission from about 14000 cts to 10000-12000 cts in each case.
  • Sent excitation using MC#_ASCPIT/YAW_EXC using awg at 77 Hz and 10000 cts.
  • Measured the cts on transmission channel at 77 Hz. Divided it by 2 and by the dc offset provided. And divided by the amplitude of cts set in excitation. This gives analogous to above DC case.
  • Then angular actuation calibration at 77 Hz from these offsets to physical angular dispalcement in units of rad/cts by .
• Following are the results:

  Optic Act	Calibration factor at DC [µrad/cts]	Calibration factor at 77 Hz [prad/cts]
  MC1 PIT	7.931+/-0.029	906.99
  MC1 YAW	5.22+/-0.04	382.42
  MC2 PIT	13.53+/-0.08	869.01
  MC2 YAW	14.41+/-0.21	206.67
  MC3 PIT	10.088+/-0.026	331.83
  MC3 YAW	9.75+/-0.05	838.44

   

• Note these values are measured with the new settings in effect from 16120. If these are changed, this measurement will not be valid anymore.
• I believe the small values for MC1 actuation have to do with the fact that coil output gains for MC1 are very weird and small, which limit the actuation strength.
• TAbove the resonance frequencies, they will fall off by 1/f^2 from the DC value. I've confirmed that the above numbers are of correct order of magnitude atleast.
• Please let me know if you can point out any mistakes in the calculations above.

Alex, Anchal, and I did the following experiment to obtain calibration constants by oscillating IMC mirrors.

Theory

In previous experiment, we measured transmission counts at some offset values, and fitted the curve in order to get the curvature of transmitted power at MC2. In this time, we use not offset but AC oscillation to get the curvature .

The shape of the transmitted power is quadratic with respect to the tilt of each mirror:

Here  is the parameter including the tilt of each mirror, and  is the signal of the transmitted power at MC2. Oscillating the mirror shows that  has a time-dependance  using an angular frequency , an initial phase , and an amplitude . What we want to get is the curvature of the quadratic function, that is, the coefficient . So we focus on the frequency-doubled term. By substituting  to , we get the time-dependent 

.

We can get  value as  by multipling  and taking time average. This  is the same as  used in 16125 by Anchal when the unit of  is cts.

Method

Before the experiment, we changed some settings

• Turn off servo in the WFS servo,
• Turn off limits in MC SUS ASC inputs,
• Turn off ELP28 FH6 in MC2 Damp Filter.

After the experiment, we restored all the changed settings.

We decided the oscillation frequency, 27.25 Hz and 37 Hz, by monitoring the background PSD at MC2. But we totally took the time-dependent datas using 37 Hz because the pole frequency of some filters is around 27.25 Hz. We used python script that Alex wrote (MC_TRANS_SUM_PLOTS.ipynb, URL: /opt/rtcds/caltech/c1/Git/40m/measurements/IMC) for taking the datas. We took each data by oscillating PIT or YAW of each mirror in IMC. Measuring time was set as 10 s. The time is longer than the 100 times of 1/37 Hz. Oscillating amplitude is tabled below.

In order to analyze the datas, we make python script named MC_TRANS_SUM_ANALYZE.ipynb (URL: /opt/rtcds/caltech/c1/Git/40m/measurements/IMC). We can get  but I have some questions as listed below:

• How can we treat error of ?
• What is the unit of ? and How much value is it? If the unit of  is cts, we can use each oscillating amplitude.

In this time, we use the error of  as the quadrature component. And we use  as the oscillating amplitude as listed above. 

Result

The result is shown in the table.

Comparing with the Anchal's result, we get much smaller error and different order... We have to reconsider the calculation method.

Den made a nice elog about the PRMI RIN that we see a few weeks ago:  8464.  The RIN that we're seeing is typically about ~30%.  The question at hand is: what is causing this power fluctuation, and more specifically, is it the angular motion of the mirrors?

I find that no, the angular motion that we see does not explain the RIN that we see.

In the attached Mathematica notebook, I calculate the power lost due to angular misalignments of one or more mirrors.  (Math comes from Appendix A of Keita's thesis.)

From calibrated oplev spectra, our mirrors are moving about 1 microradian (RMS, which is dominated by low frequencies).  From a super sophisticated "draw on the TV, then measure" method (details below), I have estimated that the maximum static misalignment that we're seeing is about 2 microradians.

With all of this, I find that for a g-parameter of 0.94, the power lost due to misalignments should, at maximum, be 0.6%.  I need a g-parameter of 0.995 to get a power loss of 23%.  Alternatively, if I take the derivative of the power coupling function, to find the static misalignment at the steepest slope of the curve (and thus, the place where any AC misalignment would have the most effect), for 1urad of AC misalignment, I get 40% power loss. 

So, in order for the AC angular motion that we see to explain the RIN that we see, either our mirrors are very, very misaligned (so much so that we couldn't really be locking), or our cavity is much closer to unstable than expected from Jamie's calculations.  Since both of these cases (static misalignment or incorrect g-parameter calculation) have to be taken to extremes before they approximate the RIN that we see, I do not think that this power loss is due to angular fluctuations.

This means that we have to think of another potential cause for this RIN that we're seeing.

Details on the "draw on TV and measure" technique for determining static cavity misalignments:  Looking at the POP camera view, with the PRM significantly misaligned, I traced the straight-through beam spot.  I then restored the PRM, and during several momentary locks, I traced the beam spot, which I took to be the saturated area of the camera.  The idea here is that the straight-through beam represents the incident beam axis, while the locked beam represents the cavity axis.  I'm assuming that the camera image plane is at the face of PR2. I approximately found the center of each of my tracings, and found them to be ~1/4 inch apart.  I also measured the "spot size" of the sideband-locked PRMI, and found it to be ~3.5 inches.  So, very roughly, the ratio of (distance between spots)/(size of beam) is ~0.07. This corresponds to a static misalignment of either the ITM or the PRM of ~2urad, rounding up. (I use the Jamie's calculated g-parameters from elog 8316, the case of flipped PR2, tangential = 0.94 to calculate the effective RoC of the PRM). 

[steve, gautam]

We added the following channels to C0EDCU.ini and restarted the daqd processes. Channels seem to have been added successfully, we will check trend writing later today. Motivation is to have a long term record of annulus pressure (even though we are not currently pumping on the annulus).

C1:Vac-PASE_status

C1:Vac-PASV_status

C1:Vac-PABS_status

C1:Vac-PAEV_status

C1:Vac-PAEE_status

plot next day

Previously, I had gotten the same results for the conductive and the isolated front panels. Today, I sanded off the anodized part on the back of the conductive front panel. I checked afterwards with a mulitmeter to ensure that it was indeed conductive through all the SMA connectors. 

I drove a frequency of 29.359 Hz through the X Arm cable and 29.3592 Hz through the Y Arm cable, giving a difference of 200 Hz. Previously, there would only be a spike in the Y Arm at the difference, while the X Arm did not change if the Y arm was on or off. Now that the panel is fully conductive, a spike can also be seen in the X arm, indicating that crosstalk may possibly be happening with this panel, now that the spike corresponds to both the X arm and Y arm. These results are only after one set of data. Tomorrow I'll take two more sets of data with this panel and do a more in depth comparison of these results to what had been previously seen.  

Around 9:30 we noticed IMC going out of lock with MC1 swinging hard. It seems like the coil output shut down.

It looks like the same situation as last Monday http://nodus.ligo.caltech.edu:8080/40m/17315.

Following that elog I restarted all the models by sshing into all computers and running

Then I burt restored all models to yesterday evening point doing following on rossa:

That seemed to have worked.

 I also had to clear the WFS output to restore MC1 back to its place. Once the IMC got restored I turned the WFS again.

Stopped by lab today. Found all suspensions undamped (even though watchdogs never tripped), same symptom as CDS crash from earlier this month. Fixed as per last ocurrence--- by restarting all models and burt restoring.

I've taken the MC2 analog camera down and put another GigE (unit 151) in its place. This is just temporary and I'll put the analog camera back once I finish the MC2 loss map calibration. I'm using a 25mm focal length camera lens with it and it gives a view of MC2 similar to the analog camera one. But I don't think it is completely focused yet (pictures attached).

...more to follow

gautam - Attachment #3 is my (sad) attempt at finding some point scatterers - Kruthi is going to play around with photUtils to figure out the average size of some point scatterers.

[Kruthi, Koji]

Koji came to the lab to align the IMC/IFO, but found the mirrors are dancing around. Kruthi told me that there was M7.1 EQ at Ridgecrest. Looks like there are aftershocks of this EQ going on. So we need to wait for an hour to start the alignment work.

ITMX and ETMX are stuck.

- ITM unstuck now
- IMC briefly locked at TEM00

A series of aftershocks came. I could unstick ITMX by turning on the damping during one of the aftershocks.
Between the aftershocks, MC1~3 were aligned to the previous dof values. This allowed the IMC flashing. Once I got the lock of a low order TEM mode, it was easy to recover the alignment to have a weak TEM00.
Now at least temporarily the full alignment of the IMC was recovered.

In fact, ETMX was not stuck until the M7.1 EQ today. After that it got stuck, but during the after shocks, all the OSEMs occasionally showed full swing of the light levels. So I believe the magnets are OK.

There were another couple of earthquakes at about 9:30am and 9:50am local.

All but MC2 were off the watchdogs.  I damped and realigned everything and everything looks ok now.

OK, how about this:

• Attachment #1 shows the proposed schematic.
  • It consists of a second order section with Gain x10 to map the +/-10V DC range of the DAC to +/- 100V DC such that we preserve roughly the same amount of DC actuation range.
  • Corner frequency of the SOS is set to ~0.7 Hz. In hindsight, maybe this is more aggressive than necessary, we can tune this.
  • DC gain is 20 dB (typo in the text where I say the DC gain is x15, though we could go with this option as well I think if we want a larger series resistance).
  • A first order passive low-pass stage is added to filter out the voltage noise of the PA91, which dominates the output voltage noise (next bullet).
• Attachment #2 shows the transfer function from input to output
  • The two traces compare having just a single SOS filtering stage vs the current topology of having two SOS stages.
  • The passive output RC network is necessary in either case to filter the voltage noise of the PA91 OpAmp.
  • For the DAC noise, I just assumed a flat noise level of , I don't actually know what this is for the Acromag DACs.
• Attachments #3 shows a breakdown of the top 5 noise contributions.
  • The PA91 datasheet doesn't give current noise information so I just assumed , which was what was used for the PA85 in the existing opamp.lib file.
  • The voltage noise is modelled as , which seems to line up okay with the plot on Pg4 of the datasheet.
  • So the model suggests we will be dominated by the voltage noise of the PA91.
• Attachment #4 translates the noise into current noise seen by the actuator.
  • I add the Johnson noise contribution of the series resistance for this path, which is assumed to be .
  • For comparison, I add the filtered DAC noise contribution, and Johnson noise of the proposed series resistance in the fast path.
  • For the bias path, we are dominated by the Johnson noise of the series resistor from ~60 Hz upwards.
  • It's not quite fair to say that the Johnson noise of the resistance in the fast path dominates, the quadrature sum of fast and bais paths will be ~1.2 times of the former alone. 
  • Bottom line: we will be in the regime of total current noise of ~2.2 pA/rtHz, where I think Kevin's modeling suggests we can see some squeezing.

The question still remains of how to combine the fast and bias paths in this proposed scheme. I think the following approach works for prototyping at least:

• Remove the series resistance on the existing coil driver boards' bias path, hence isolating this from the coil.
• Route the DB15 output connector from the coil driver board (which is now just the fast actuation signals) into a sub-sattelite box housing the bias path electronics.
• Sum the two signals as it is done now, by simply having a conductor (PCB trace) merge the two paths after their respective series resistances.

In the longer term, perhaps the Satellite Box revamp can accommodate a bias voltage summation connector.

I have neglected many practical concerns. Some things that come to mind:

1. Is it necessary to protect the upstream DAC from some potential failure of the PA91 in which the high voltage appears at the input?
2. What is the correct OpAmp for this purpose? This chart on Apex's page suggests that PA15, PA85, PA91 and PA98 are all comparable in terms of drive capability, and the spec sheets don't suggest any dramatic differences. Some LIGO circuits use PA85, some use PA90, but I can't find any that use PA91. Perhaps Rana/Koji can comment about this.
3. What kind of protection is necessary for the PA91 power?
4. What is the correct way to do heat management? Presumably we need heatsinks, and in fact, there is a variant of the packaging style that has "formed" legs, which from what I can figure out, allow the heat sink plane on the PA91 to be parallel to the PCB surface. But I think the heat-sink wisdom suggests vertical fins are the most efficient (not sure if this holds if the PCB is inside a box though). What about the PCB itself? Are some kind of special traces needed?
5. Can we use the current-limiting resistor feature on the PA91? The datasheet seems to advice against it for G>10 configurations, which is what we need, although our requirement is only at DC so I don't know if that table is applicable to this circuit.
6. Are 3W resistors sufficient? I think we require only 10mA maximum current to preserve the current actuation range, so 100 V * 10mA = 1W, so 3W leaves some safety margin.
7. All capacitors should be rated for 500 V per the datasheet.  

Today while Rich Abbott was here, Koji and I had a brief discussion with him about the HV amplifier idea for the coil driver bias path. He gave us some useful tips, perhaps most useful being a topology that he used and tested for an aLIGO ITM ESD driver which we can adapt to our application. It uses a PA95 high voltage amplifier which differs from the PA91 mainly in the output voltage range (up to 900V for the former, "only" 400V for the former. He agrees with the overall design idea of 

• Having a LN opamp with the HV amp inside the feedback loop for better voltage noise at low frequencies.
• Having a passive RC network at the output of the HV amp to filter out noise at high frequencies.

He also gave some useful suggestions like 

• Using the front panel of the box that as a heatsink for the HV amps.
• Testing the stability of the nested opamp loop by "pinging" the output of the opamp with some pulses from a function generator and monitoring the response to this perturbation on a scope.

I am going to work on making a prototype version of this box for 5 channels that we can test with ETMX. I have been told that the coupling from side coil to longitudinal motion is of the order of 1/30, in which case maybe we only need 4 channels.