We have to change the sample rate and AA filter for the mic channels before going too far with the circuit design.

 To save the mic channels at higher than 2k (which we should do), we either have to move them to a different model, change the rate of the PEM model, or see if you can save data faster than the model runs (which I can't imagine is possible).

 PEM model is running at 64K now. It turned out to be tricky to increase the rate:

• BLRMS are computationally expensive and original pem model did not start at any frequency higher then 16k ( at 16k cpu meter readings were 59/60 ). Also when we go higher then 16k, front-end gives the model less resources. I guess it is assumed that this model is iop and won't need too much time. So in the end I had to delete BLRMS blocks for all channels except for GUR2Z and MIC1.
• Foton files are modified during model compilation: lines with sampling rate and declaration of filters in the beginning of the file are changed only. Sos-representation and commands are the same. I hoped that filter commands will let me change sos-representation quickly. I've opened Foton and saved the file. However, Foton modified commands in such a way that the ratio of poles and zeros to sampling rate is preserved. I guess all filters have to be replaced or this process should be done in another way.
• BLRMS block uses low-pass filters below 0.01 Hz, increasing the sampling rate by a factor of 32 might make calculations incorrect. I'll check it.

We should also increase cut off frequency of the low-pass filter in the microphone pre-amplifier from 2 kHz up to ~20-30 kHz.

 Thank you for changing the sample rate!
Also we have to change the Anti-Aliasing filter, as Jamie said.

Now my question is, whether S/N ratio is enough at high frequencies or not. The quality of EM172 microphone is good according to the data sheet. But as you can see in previous picture, the S/N ratio around 1kHz is not so good, though we can see some peaks, e.g. the sound that a fan will make. I have to check it later.
And, is it possible to do online adaptive noise cancellation with a high sampling rate such that computationally expensive algorithms cannot be run?

  That's no good - we need BLRMS channels for many PEM channels, not just two. And the channel names should have the same name as they had in the past so that we can look at long term BLRMS trends.

I suggest:

1. Have a separate model for Mics and Magnetometers. This model should run at 32 kHz and not have low frequency poles and zeros. Still would have acoustic frequency BLRMS.
2. Have a low frequency (f_sample = 2 kHz) model for seis an acc. Seismometers run out of poop by 100 Hz, but we want to have the ACC signal up to 800 Hz since we do have optical mount resonances up to there.
3. Never remove or rename the BLRMS channels - this makes it too hard to keep long term trends.
4. Do a simple noise analysis to make sure we are matching the noise of the preamps to the noise / range of the ADCs.
5. Immediately stop using bench supplies for the power. Use ONLY fused, power lines from the 1U rack supplies.

Ayaka, Den

 C1PEM model is back to 2K.

We created a new C1MIC model for microphones that will run at 32K. C1SUS machine is full, we have to think about rearrangement.

For now, we created DQ channels for microphones inside iop model, so we can subtract noise offline.

We provided 0-25 kHz bandwidth noise to AA board and saw the same signal in the output of ADC in the corresponding channel. So cut-off frequency is higher then 25 kHz. There is a label on the AA board that all filters are removed. What does this mean?

We've turned off AA bench power supply, prepare to use fused from 1U.

[Raji, Ayaka]

Thanks to Den, power supplies for microphone circuit are changed.
So I measured the microphone noise again by the same way as I did last time.

  solid lines: acoustic noise
 dashed lines: un-coherent noise
black line: circuit noise (microphone unconnected)

The circuit noise improves so much, but many line noises appeared.
Where do these lines (40, 80, 200 Hz...) come from?
These does not change if we changed the microphones...

Anyway, I have to change the circuit (because of the low-pass filter). I can check if the circuit I will remake will give some effects on these lines.

I do not think that 1U rack power supply influenced on the preamp noise level as there is a 12 V regulator inside. Lines that you see might be just acoustic noise produced by cpu fans. Usually, they rotate at ~2500-3000 rpm => frequency is ~40-50 Hz + harmonics. Microphones should be in an isolation box to minimize noise coming from the rack. This test was already done before and described here. 

I think we need to build a new box for many channels (32, for example, to match adc). The question is how many microphones do we need to locate around one stack to subtract acoustic noise. Once we know this number, we group microphones, use 1 cable with many twisted pairs for a group and suspend them in an organized way.

 I do not think they are acoustic sounds. If so, there should be coherence between three microphones because I placed three at the same place, tied together. However, there are no coherence at lines between them.

For a last few days I've been working on oaf and simulink model to simulate it. First I did online subtraction from MC when MC_L path was enabled. Inside my code I've added a sum of squares of filter coefficients so we can monitor convergence of the filter.

To to this I've measured path from OAF output to input without AA and AI filters. Then made a vectfit using 2 poles and zeros. Foton command

zpk( [-2.491928e+03;5.650511e-02], [-4.979872e+01;-3.278776e+00], 6.011323e+00)

My simulink model consists of 3 parts:

• cavity with seismic noise at low frequencies, 1/f^2 noise at medium frequencies and white noise at high frequencies
• this cavity is locked using feedback compensation filters that we use to lock arms
• locked cavity with adaptive filter

Adaptive filter in the model uses online c-code. It is connected to simulink block through an S-function. Sampling frequency of the model is 10 kHz. It works fairly fast - 1 sec of simulation time is computed in 1 sec.

I've tested FxLMS algorithm and MFxLMS algorithm that is faster. I plan to test 2 iir adaptive algorithms that are already coded.

I've applied FIR adaptive filter to YARM control. Feedback signal of the closed loop was used as adaptive filter error signal and OAF OUT -> IN transfer function I assumed to be flat because of the loop high gain at low frequencies. At 100 Hz deviation was 5 dB so I've ignored it.

I've added a filter bank YARM_OAF to C1LSC model to account for downsampling from 16 kHz to 2 kHz and put low-pass filter inside.

I've used GUR 1&2 XYZ channels as witnesses. Bandpass filters 0.4-10 Hz we applied to each of them. Error signal was filters using the same bandpass filter and 16 Hz 40 dB Q=10 notch filter. As an AI filter I used 32 Hz butterworth 4 order low-pass filter. Consequently, AI, bandpass and notch filters were added to adaptive path of witness signals.

I've used an FIR filter with 4000 taps, downsampling = 16, delay = 1, tau = 0, mu = 0.01 - 0.1. Convergence time was ~3 mins.

This is interesting. I suppose you are acting on the ETMY.
Can you construct the compensation filter with actuation on the MC length?
Also can you see how the X arm is stabilized?

This may stabilize or even unstabilize the MC length, but we don't care as the MC locking is easy.

If we can help to reduce the arm motion with the MCL feedforward trained with an arm sometime before,
this means the lock acquisition will become easier. And this may still be compatible with the ALS.

Why did you notched out the 16Hz peak? It is the dominant component for the RMS and we want to eliminate it.

 I actuate on ETMY for YARM and ETMX for XARM. For now I did adaptive filtering for both arms at the same time. I used the same parameters for xarm as for yarm.

I've notched 16 Hz resonance because it has high Q and I need to think more how to subtract it using FIR filter or apply IIR.

I'll try MC stabilazation method.

 Adaptive filtering was applied to MC and X,Y arms at the same time. I used a very aggressive (8 order) butterworth filter at 6 Hz as an AI filter for MC not to inject noise to ARMS as was done before

Mu for MC was 0.2, downsample = 16, delay = 1. I was able to subtract 1 Hz. Stack subraction is not that good as for arms but this is because I used only one seismometer for MC that is under the BS. I might install accelerometers under MC2.

EDIT, JCD, 18Feb2013:  Den remembers using mu for the arms in the range of 0.01 to 0.1, although using 0.1 will give extra noise.  He said he usually starts with something small, then ramps it up to 0.04, and after it has converged brings it back down to 0.01.

[Jon, Keerthana, Sandrine]

Thu.-Fri. we continued with PRC scans using the AUX laser, but now the "scanned" parameter is the frequency of AM sidebands, rather than the frequency of the AUX carrier itself. The switch to AM (or PM) allows us to coherently measure the cavity transfer as a function of modulation frequency.

In order to make a sentinel measurement, I installed a broadband PDA255 at an unused pickoff behind the first AUX steering mirror on the AS table. The sentinel PD measures the AM actually imprinted on the light going into the IFO, making our measurement independent of the AOM response. This technique removes not only the (non-flat) AOM transfer function, but also any non-linearities from, e.g., overdriving the AOM. The below photo shows the new PD (center) on the AS table.

With the sentinel PD installed, we proceeded as follows.

• Locked IFO in PRMI on carrier.
• Locked AUX PLL to PSL.
• Tuned the frequency of the AUX laser (via the RF offset) to bring the carrier onto resonance with the PRC.
• Swept the AOM modulation frequency 0-60 MHz while measuring the AUX reflection and injection signals.

The below photo shows the measured transfer function [AUX Reflection / AUX Injection]. The measurement coherence is high to ~55 MHz (the AOM bandwidth is 60 MHz). We clearly resolve two FSRs, visible as Lorentzian dips at which more AUX power couples into the cavity. The SURFs have these data and will be separately posting figures for the measurements.

With the basic system working, we attempted to produce HOMs, first by partially occluding the injected AUX beam with a razor blade, then by placing a thin two-prong fork in the beam path. We also experimented with using a razor blade on the output to partially occlude the reflection beam just before the sensor. We were able to observe an apparent secondary dip indicative of an HOM a few times, as shown below, but could not repeat this deterministically. Besides not having fine control over the occlusion of the beams, there is also large few-Hz angular noise shaking the AS beam position. I suspect from moment to moment the HOM content is varying considerably due to the movement of the AS beam relative to the occluding object. I'm now thinking about more systematic ways to approach this.

How much was the osc freq of the marconi? And then how much was the resulting freq offset between PSL and AUX?

Are we supposed to see two dips with the separation of an FSR? Or four dips (you have two sidebands)?

And the distance between the dips (28MHz-ish?) seems too large to be the FSR (22MHz-ish).
cf https://wiki-40m.ligo.caltech.edu/IFO_Modeling/RC_lengths

(Jon, Keerthana, Sandrine)

I am attaching the plots of the Reflected and transmitted AUX beam. In the transmission graph, we are getting peak corresponding to the resonance frequencies, as at that frequency maximum power goes to the cavity. But in the Reflection graph, we are obtaining dips corresponding to the resonance frequency because maximum power goes to the cavity and the reflected beam intensity becomes very less at those points.

I made the first successful AUX laser scan of a 40m cavity last night.

Attachment #1 shows the measured Y-end transmission signal w.r.t. the Agilent drive signal, which was used to sweep the AUX carrier frequency. This is a distinct approach from before, where the carrier was locked at a fixed offset from the PSL carrier and the frequency of AM sidebands was swept instead. This AUX carrier-only technique appears to be advantageous.

This 6-15 MHz scan resolves three FSR peaks (TEM00 resonances) and at least six other higher-order modes. The raw data are also enclosed (attachment #2). I'll leave it as an excercise for the SURFs to compute the Y-arm cavity Gouy phase.

More progress on the AUX-laser cavity scans.

Changes to the Setup

• For scans, the Agilent is now being used as a standalone source of the LO signal provided to the AUX PLL (instead of the Marconi), which sets the RF offset. We discovered that when the sweep is "held" in network analyzer mode, it does not turn off the RF drive signal, but rather continues outputting a constant signal at the hold frequency. This eliminates the need to use the more complicated double-deomdulation previously in use. The procedure is to start and immediately hold the sweep, then lock the PLL, then restart the sweep. The PLL is able to reliably remain locked for frequency steps of up to ~30 kHz. The SURFs are preparing schematics of both the double- and single-demodulation techniques.
• Both the Marconi and Agilent are now phase-locked to the 10 MHz time reference provided by the rabidium clock. This did noticeably shift the measured resonance frequencies.
• I raised the PI controller gain setting to 4.5, which seems to better suppress the extra noise being injected.
• I've procured a set of surgical needles for occluding the beam to produce HOMs. However, I have not needed to use them so far, as the TEM00 purity of the AUX beam appears to already be low. The below scans show only the intrinisic mode content.

New Results

• YARM scan at 70 uW injection power (Attachment #1). The previously reported YARM scan was measured with 9 mW of injected AUX power, 100x larger than the power available from the SQZ laser at the sites. This scan repeats the measurement with the AUX power attenuated to uW. It still resolves the FSR and at least three HOMs.
• PRC scan (Attachment #2) at 9 mW injection power. It appears to resolve the FSR and at least three HOMs. Angular injection noise was found to cause large fluctuations in the measured signal power. This dominates the error bars shown below, but affects only the overall signal amplitude (not the peak frequency locations). The SQZ angular alignment loops should mitigate this issue at the sites.

Both data sets are attached.

This note reports analysis of cavity scans made by directly sweeping the AUX laser carrier frequency (no sidebands). The measurement is made by sweeping the RF offset of the AUX-PSL phase-locked loop and demodulating the cavity reflection/transmission signal at the offset frequency.

Y-Arm Scan

Due to the simplicity of its expected response, the Y-arm cavity was scanned first as a test of the AUX hardware and the sensitivity of the technique. Attachment 1 shows the measured cavity transmission with respect to RF drive signal.

The AUX laser launch setup is capable of injecting up to 9.3 mW into the AS port. This high-power measurement is shown by the black trace. The same measurement is repeated for a realistic SQZ injection power, 70 uW, indicated by the red curve. At low power, the technique still clearly resolves the FSR and six HOM resonances. From the identified mode resonance frequencies the following cavity parameters are directly extracted.

PRC Scan

An analogous scan was performed for the PRC, with the IFO locked on PSL carrier in PRMI. Attachment 2 shows the measurement of PRC transmission with respect to drive signal.

The scan resolves HOM resonances to at least ~13th order, whose frequencies yield the following cavity parameters.

SRC Scan

Ideally (and at the sites) the SRC mode resonances will be measured in SRMI configuration. Because every other cavity is misaligned, this configuration provides an easily-interpretable spectrum whose resonances can all be attributed to the SRC.

Due to time constraints at the 40m, the IFO could not be restored to lockability in SRMI. It has been more than two years since this configuration was last run. For this reason the scan was made instead with the IFO locked in DRMI, as shown in Attachment 3. The quantity measured is the AUX reflection with respect to drive signal.

This result requires far more interpretation because resonances of both the SRC and PRC are superposed. However, the resonances of the PRC are known a priori from the independent PRMI scan. The SRC mode resonances identified below do not conincide with any of the first five PRC mode resonances.

Based on the identified mode resonance frequencies, the SRC parameters are measured as follows.

Lessons Learned

From experience with the 40m, the main challenges to repeating this measurement at the sites will be the following.

• Pointing jitter of the input AUX beam. This causes the PSL-AUX beam overlap to vary at transmission (or reflection), causing variation in the amplitude of the AUX-PSL beat note. As far as we can tell, the frequency of the resonances (the only object of this measurement) is not changing in time, only the relative amplitudes of the diferent mode peaks. I believe the SQZ alignment loops will mitigate this problem at the sites.
• Stabilization of the network analyzer time base. We found the intrinsic frequency stability of the network analyzer (Agilent 4395A) to be unacceptably large. We solved this problem by phase-locking the Agilent to an external reference, a 10-MHz signal provided by an atomic clock.

From the Measurement Jon made, FSR is 3.967 MHz and the Gouy phase is 52 degrees. From this, the length of the Y-arm cavity seems to be 37.78 m and the radius of curvature of the mirror seems to be 60.85 m.

FSR = Free spectral Range

L = Lenth of the arm

R = Radius of curvature of the mirror (R1 =  , R2= unknown)

[Annalisa, Terra, Koji, Gautam]

Summary: We find a configuration for arm scans which significantly reduces phase noise. We run several arm scans and we were able to resolve several HOM peaks; analysis to come.

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As first, we made a measurement with the already established setup and, as Jon already pointed out, we found lots of phase noise. We hypothesized that it could either come from the PLL or from the motion of the optics between the AUX injection point (AS port) and the Y arm. 

• We first characterized the PLL loop phase noise by comparing the beat signal against the Agilent reference signal, and we found that the beat had lots of phase noise with respect to the reference. Decreasing the PLL gain, we got rid of the phase noise in the beat signal.
• Next, for the optical path length induced phase noise, we took the transfer function between TransMon and REFL signal rather than TransMon and Agilent reference signal. This takes advatage of the fact that the TransMon and REFL both see optical path length phase noise, which therefore gets canceled out in the transfer function. 

In this configuration, we were able to do arm scans where the phase variation at each peak was pretty clear and well defined. We took several 10MHz scan, we also zoomed around some specific HOM peak, and we were able to resolve some frequency split. 

We add some pictures of the setup and of the scan.

The data are saved in users/OLD/annalisa/Yscans. More analysis and plots will follow tomorrow. 

I recently realized that the PLL is only using about 20% of the available actuation range of the AUX PZT. The +/-10 V control signal from the LB1005 is being directly inputted into the fast AUX PZT channel, which has an input range of +/-50 V.

I recommend to install a PZT driver (amplifier) between the controller and laser to use the full available actuator range. For cavity scans, this will increase the available sweep range from +/-50 MHz to +/-250MHz. This has a unique advantage even if slow temperature feedback is also implemented. To sample faster than the timescale of most of the angular noise,  scans generally need to be made with a total sweep time <1 sec. This is faster than the PLL offset can be offloaded via the slow temperature control, so the only way to scan more than 100 MHz in one measurement is with a larger dynamic range.

[anjali, gautam]

To facilitate the 1um MZ frequency stabilization project, I decided that the AUX laser was a better candidate than any of the other 3 active NPROs in the lab as (i) it is already coupled into a ~60m long fiber, (ii) the PSL table has the most room available to set up the readout optics for the delayed/non-delayed beams and (iii) this way I can keep working on the IR ALS system in parallel. So we moved the end of the fiber from the AS table to the SE corner of the PSL table. None of the optics mode-matching the AUX beam to the interferometer were touched, and we do not anticipate disturbing the input coupling into the fiber either, so it should be possible to recover the AUX beam injection into the IFO relatively easily.

Anjali is going to post detailed photos, beam layout, and her proposed layout/MM solutions later today. The plan is to use free space components for everything except the fiber delay line, as we have these available readily. It is not necessarily the most low-noise option, but for a first pass, maybe this is sufficient and we can start building up a noise budget and identify possible improvements.

The AUX laser remians in STANDBY mode for now. HEPA was turned up while working at the PSL table, and remains on high while Anjali works on the layout.

• Attachment #1 shows the schematic of the experimental setup for the frequency noise measurement of 1 um laser source.

• AUX laser will be used as the seed source and it is already coupled to a 60 m fiber (PM980). The other end of the fiber was at the AS table and we have now removed it and placed in the PSL table.

• Attachment # 2 shows the photograph of the experimental setup. The orange line shows the beam that is coupled to the delayed arm of MZI and the red dotted line shows the undelayed path.

• As mentioned, AUX is already coupled to the 60 m fiber and the other end of the fiber is now moved to the PSL table. This end needs to be collimated. We are planning to take the same collimator from AS table where it was coupled into before. The position where the collimator to be installed is shown in attachment #2. Also, we need to rotate the mirror (as indicated in attachment #2) to get the delayed beam along with the undelayed beam and then to combine them. As indicated in attachment #2, we can install one more photo diode to perform  balanced detection.

• We need to decide on which photodetector to be used. It could be NF1801 or PDA255.

• We also performed the power measurement at different locations in the beam path. The different locations at which power measurement is done is shown attachment #3

• There is an AOM in the beam path that coupled to the delayed arm of MZI. The output beam after AOM was coupled to the zero-order port during this measurement. That is the input voltage to the AOM was at 0 V, which essentially says that the beam after the AOM is not deflected and it is coupled to the zero-order port. The power levels measured at different locations in this condition are as follows. A)282 mW B)276 mW C)274 mW D)274 mW E)273 mW F)278 mW G)278 mW H)261 mW I)263 mW J)260 mW K)131 mW L)128 mW M)127 mW N)130 mW

• It can be seen that the power is halved from J to K. This because of a neutral density filter in the path of the beam

• In this case, we measured a power of 55 mW at the output of the delayed fiber. We then adjusted the input voltage to the AOM driver to 1 V such that the output of AOM is coupled to the first order port. This reduced the power level in the zero-order port of AOM that is coupled to the delayed arm of the MZI. In this case we measured a power of 0.8 mW at the output of delayed fiber.

•  We must be careful about the power level that is reaching the photodetector such that it should not exceed the damage threshold of the detector.

• The power measured at the output of undelayed path is 0.8 mW.

• We also must place the QWP and HWP in the beam path to align the polarisation.

We measured the Xend green laser PDH Open loop transfer function by following method:

• We first measured the feedback transfer function 'K' directly.
  • See attachment 2 for this measurement. We measured Out2/exc here.
• Then, we closed the loop as shown in attachment 1with SR560 as a summing juntion at error point.
  • We injected excitation through B channel in SR560 and measured transfer function Out1/Out2.
  • This measurement should give us by loop alegbra.
• Then we multiplied the two transfer function measurements to get open loop transfer function.

Result:

• Our measurement gives the same UGF of 10kHz and phase margin of 53.5 degrees as reported in 13238.
• The shape of measurement also follows 1/f above 10 Hz atleast.
• Our measurement might not be correct below 10 Hz but we did not see any saturation or loss of lock in 1Hz to 10 Hz measurement.
• This OLTF is different from the modelled OLTF here even though the UGF matches.
• The feedback gain is supposed to roll-off faster than 1/f in 30Hz to 1kHz region but it does not seem to in our measurement.
• This suggests that the actual uPDH box is shaping the loop different from what schematic suggests. This might mean that the gain is much lower in the low frequency region than we would like it to be.
• We will investigate the reason of difference between model and measurement unless someone has a better explaination for the descripancy.

Attachment 1 shows the closed loop of Xend Green laser Arm PDH lock loop. Free running laser noise gets injected at laser head after the PZT actuation as . The PDH error signal at output of miser is fed to a gain 1 SR560 used as summing junction here. Used in 'A-B mode', the B port is used for sending in excitation where .

We have access to three ports for measurement, marked at output of mixer, at output of SR560, and at PZT out monitor port in uPDH box. From loop algebra, we get following:

, where is the open loop transfer function of the loop.

So measurement of can be done in following two ways (not a complete set):

1. , if excitation amplitude is large enough such that over all frequencies.
   • In this method however, note that SR785 would be taking ratio of unsuppresed excitation at with suppressed excitation at
   • If the closed loop gain (suppression) is too much, the excitation signal might drop below noise floor of SR785 while measuring .
   • This would then appear as a flat response in the transfer function.
   • This happened with us when we tried to measure this transfer function using this method. Below few hundered Hz, the measurement will become flat at around 40 dB.
   • Increasing the excitation amplitude where suppression is large should ideally work. We even tried to use Auto level reference option in SR785.
   • But the PDH loop gets unlocked as soon as we put exciation above 35 mV at this point in this loop.
2. , if excitation amplitude is large enough such that over all frequencies.
   • In this method, channel 1 (denominator) on SR785 would remain high in amplitude throughout the measurement avoiding the above issue of suppression below noise floor.
   • We can easily measure the feedback transfer funciton with the loop open. Then multiplying the two measurements should give us estimate of open loop transfer function.
   • This is waht we did in 16194. But we still could not increase the excitation amplitude beyond 35 mV at injection point and got a noisy measurement.
   • We checked yesterday coherence of excitation signal with the three measurment points and it was 1 throughout the frequency region of measurement for excitation amplitudes above 20 mV.
   • So as of now, we are not sure why our signal to noise was so poor in lower frequency measurement.

Working in Xend with mask on has become unbearable. It is very hot there and I would really like if we fix this issue.

Today, the Xend Green laser was just unable to hold lock for longer than 10's of seconds. The longest I could see it hold lock was for about 2 minutes. I couldn't find anything obviously wrong with it. Attached are noise spectrums of error and control points. The control point spectrum shows good matching with typical free running laser noise.

Are the few peaks above 10 kHz in error point spectrum worrysome? I need to think more about it in a cooler place to make sure.

I wanted to take a high frequency spectrum of error point to make sure that higher harmonics of 250 kHz modulation frequency are not leaking into the PDH box after demodulation. However, the lock could not be maintained long enough to take this final measurement. I'll try again tomorrow morning. It is generally cooler in the mornings.

This post is just an update on what's happening. I need to work more to get some meaningful inferences about this loop.

Attachment 1 shows the case when excitation is sent at control point i.e. the PZT output. As before, free running laser noise  in units of Hz/rtHz is added after the actuator and I've also shown shot noise being added just before the detector.

Again, we have a access to three output points for measurement. right at the output of mixer (the PDH error signal), the feedback signal to be applied by uPDH box (PZT Mon) and the output of the summing box SR560.

Doing loop algebra as before, we get:

So measurement of can be done by

• For frequencies, where is large enough, to have an SNR of 100, we need that ratio of to integrated noise is 100.
• Assuming you are averaging for 'm' number of cycles in your swept sine measurement, time of integration for the noise signal would be where f is the frequency point of the seeping sine wave.
  • This means, the amplitude of integrated laser frequency noise at either or would be
  • Therefore, signal to laser free running noise ratio at f would be .
  • This means to keep a constant SNR of S, we need to shape the excitation amplitude as
  • Putting in numbers for X end Green PDH loop, laser free-running frequency noise ASD is 1e4/f Hz/rtHz, laser PZT actuation is 1MHz/V, then for 10 integration cycles and SNR of 100, we get:
• Assuming you are averaging for a constant time  in swept sine measurement, then the amplitude of integrated laser free noise would be
  • In this case, signal to laser free-running noise ratio at f would be
  • This means to keep a constant SNR of S, we need to shape the excitation amplitude as
  • Again putting in numbers as above and integration time of 1s, we need an excitation amplitude shape

This means at 100 Hz, with 10 integration cycles, we should have needed only 3 mV of excitation signal to get an SNR of 100. However, we have been unable to get good measurements with even 25 mV of excitation. We tried increasing the cycles, that did not work either.

This post is to summarize this analysis. We need more tests to get any conclusions.

We did the measurement of OLTF for Xend green laser PDH loop with excitation added at control point using a SR560 as shown in attachment 1 of 16202. We also measured coherence in our measurement, see attachment 1.

Measurement details:

• We took the measurement as per 16202.
• We did measurement in two pieces. First in High frequency region, from 1 kHz to 100 kHz.
  • In this setup, the excitation amplitude was kept constant to 5 mV.
  • In this region, the OLTF is small enough that signal to noise ratio is maintained in (SR560 sum output, measured on CH1). The coherence can be seen to be constant 1 throughout for CH1 in this region.
  • But for (PZT Mon, measured on CH2), the low OLTF actually starts damping both signal and noise and to elevate it above SR785 noise floor, we had a high pass (z:0Hz, p:100kHz, k:1000) SR560 amplifying before measurement (see attachment 2). This amplification has been corrected in Attachment 1. This allowed us to improve the coherence on CH2 to above 0.5 mostly.
• Second region is from 3 Hz to 1 kHz.
  • In this setup, the excitation was shaped with a low pass (p: 1Hz, k:5) SR560 filter with SR785 source amplitude as 1V.
  • We took 40 averaging cycles in this measurement to improve the coherence further.
  • In this freqeuency region, is mostly coherent as we shaped the excitation as  and due to constant cycle number averaging, the integrated noise goes as (see 16202 for math).
  • We still lost coherence in (CH1) for frequencyes below 100 Hz. the reason is that the excitation is suppressed by OLTF while the noise is not for this channel. So the shaping of excitation only helps fight against the suppression of OLTF somewhat and not against the noise.
    
  • We need shaping for this purpose but we were loosing lock with that shaping so we shifted back to shaping and captured whatever we could.
  • It is clear that the noise takes over below 100 Hz and coherence in CH1 is lost there.

Inferences:

• Yes, the OLTF does not look how it should look but:
• The green region in attachment 1 shows the data points where coherence on both CH1 and CH2 was higher than 0.75.  So the saturation measured below 1 kHz, particularly in 100 Hz to 500 Hz (where coherence on both channels is almost 1) is real.
• This brings the question, what is saturating. As has been suggested before, our excitation signal is probably saturating some internal stage in the uPDH box. We need to investigate this next.
  • It is however very non-intuitive to why this saturation is so non-uniform (zig-zaggy) in both magnitude and phase.
  • In past experiences, whenever I saw somehting saturating, it would cause a flat top response in transfer function.
• Another interesting thing to note is the reduced UGF in this measurement.
• UGF is about 40-45 kHz. This we believe is due to reduced mode matching of the green light to the XARM when temperature of the end increases too much. We took the measurement at 6 pm and Koji posted the Xend's temperature to be 30 C at 7 pm in 16206. It certainly becomes harder to lock at hot temperatures, probably due to reduced phase margin and loop gain.

Here I describe efforts to cancel the AUX laser PZT mechanical resonances from ~200 kHz-400kHz. While these may not be the resonances we end up wanting to suppress, I chose this region as an exercise because it contains the most significant peaks.

The PZT transfer measurement was taken on 09/06 by myself and Anchal. The Moku:Go outputted a swept-sine (1kHz - 1MHz) I sent to the AUX laser PZT. The beat note between the AUX and frequency-doubled PSL was sent to the DFD, and the I and Q channels were routed back as input to the Moku:Go. We also took a calibration transfer function of the Moku:Go, sending output 1 to inputs 1 and 2. 

Almost all of the signal was present in the I channel, so I proceeded to use the I data for fitting/next steps. After normalizing the measured frequency response by the calibration measurement (and adjusting for the calculated time delays in the loop - see [17131]), I fit the resulting data using vectfit [Attachment 1]. I supplied the function with n_poles=16, which in reality fit for 16 complex pairs of poles. This complexity of fit was not necessary to capture the 3 prominent peaks, but would likely be needed to fit any of the more heavily-damped resonances. 

I chose to invert all fitted poles between 200 kHz and 367 kHz and the corresponding fitted zeros. The result of this filter applied to the original frequency response data can be seen in Attachment 2, where the blue-shaded region contains the inverted poles/zeros. In total, 9 pairs of poles and 9 pairs of zeros were inverted. 

Next steps:

This looks really good to me. Rather than fully invert the plant, what we would like to do is now design a filter which allow this loop to have a high UGF and a high gain below 1 kHz. Anchal and Paco probably have gain requirements for this loop in the ALS-CAL paper they are writing. The loop would have the cavity transfer function, as well as the demod electronics for the green PDH loop.

In addition to the gain requirements, we would also like to have a phase margin > 30 deg, and a gain margin of > 10 dB.

Moku:Go used for full locking of green laser - OLTF to come

Picking up from where Reuben left off, I used the Moku:Go in multi-instrument mode to replace the signal generator and uPDH box entirely (Moku:Go setup shown in Attachments 1+2). The lock-in amplifier sourced the modulation for the PZT: 210.5 kHz, 1.4 Vpp amplitude (consistent with 7dBm used by the uPDH box) This LO was used to demodulate the REFL signal input. I coarsely tuned the demodulation phase to 90 degrees until the PDH error signal looked reasonable. The PDH error signal was passed to the digital filter box using the same filter as before. After slightly adjusting the gain knob in the filter module (-8 dB), the lock seemed reasonably stable - transmission screenshot in Attachment 3. I got transmission to ~0.8 with the analog loop today, so it was exciting to see this level maintained with the Moku:Go lock (ignoring oscillations from test mass motion). The system remains locked to TEM00 for 5-10 minutes before mode hopping, which is qualitatively comparable to the analog loop as well.

An OLTF of the Moku:Go loop still needs to be taken. Since the loop error point isn't outputted from the Moku (passed direclty between instruments), I'll need to inject an excitation at the control point. When I fed the control signal to input A of the SR560 and tried to lock with the direct output, the lock would repeatedly break. I noticed that the BATT light of the SR560 was on - I'll repeat this with another SR560, but the lock might be breaking due to an offset. Once this is debugged, I can inject an excitation and measure the loop OLTF.

[Radhika, Yuta, Hiroki, Paco]

During YAUX noise measurements, we also locked IR and green lasers in xarm (using Moku:Go lock-in amplifier + digital controller) to look at ALS noise in XARM. I adjusted the controller gain until green transmission looked tightly controlled (less fuzzy). We measured the out-of-loop ALS X beat note fluctuations at 2 gain levels: -12 dB and -14 dB down from the uPDH box fitted response. These are Attachments 1 and 2 respectively.

Note that there was some mirror motion at 1 Hz that is reflected in the spectral densities (coil balancing of ETMX had just been taking place). The -12dB gain adjustment causes frequency noise ~3x higher than the reference above ~70Hz. The -14dB gain adjustment has higher noise from 70-400 Hz, but has slightly suppressed noise above 1 kHz (relative to -12dB gain).

Moku:Go delay measurements will help clarify if this excess noise is a fundamental limitation of the device, or if there is room for improvement by optimizing the controller or further tweaking the gain/offset.

[Jenne & Sanjit]

Good news: We could successfully send filtered output to MC1 @ SUS.

We used 7 channels (different combinations of 3 seismometer and six accelerometer)

We tried some values of \mu (0.001-0.005) & gain on SUS_MC1_POSITION:MCL and C1ASS_TOP_SUS_MC1 (0.1-1).

C1:ASS-TOP_SUS_MC1_INMON is huge (soon goes up to few times 10000), so ~0.1 gains at two places bring it down to a reasonable value.

Bad news: no difference between reference and filtered IOO-MC_L power spectra so far.

Plan of action: figure out the right values of the parameters (\mu, \tau, different gains, and may be some delays), to make some improvement to the spectra.

 ** Rana: there's no reason to adjust any of the MCL gains. We are not supposed to be a part of the adaptive algorithm.

After a lot of headache, I got the OAF working again - read on for details.....................

Sometime last week, Jenne, Kiwamu, and I tried to update the OAF model to include the IIR "feed-around" path.

This path is in parallel to the existing FIR-based adaptive FXLMS stuff that Matt put in earlier. The reason for the

new path is that we want to try emulating the same FF technology which has been successful lately at LLO.

However, we were unable to make the ASS work after this work. Mostly, the build stuff worked fine, but we couldn't get DTT

to make a transfer function. The excitation channels could be selected and the excitation would actually start and get all the

way into MC1, but DTT would just hang on the first swep-sine measurement with no time-out error. Clearly our ASS building

documentation is no good. We tried using the instructions that Koji gave us for AAA, but that didn't completely work.

In particular, the 'make-uninstall-daq-ass' command gave this command:

[controls@c1ass advLigo]$ make uninstall-daq-ass
grep: target/assepics/assepics*.cmd: No such file or directory
Please make ass first
make: *** [uninstall-daq-ass] Error 1

re-arranging the order to do 'make-ass' first fixes this issue and so I have fixed this in the OAF Wiki.

The there's the whole issue with the tpchn_C3.par file. This contains all the test point definitions for the ASS/OAF machine. The main

IFO numbers are all in tpchn_C1.par and the OMC is all in tpchn_C2.par. When we do the usual build, in the 'make install-daq-ass' part:

[controls@c1ass advLigo]$ make install-daq-ass
Installing GDS node 3 configuration file
/cvs/cds/caltech/target/gds/param/tpchn_C3.par
Updating DAQ configuration file
/cvs/cds/caltech/chans/daq/C1ASS.ini
we get this .par file installed in the target area. The ACTUAL param file seems to actually be in /cvs/cds/caltech/gds/param  !!

Of course, it still doesn't work. That's because the standard build likes to point to /cvs/cds/caltech/gds/bin/awgtpman and the one that runs on

linux is actually /opt/gds/awgtpman. So I've now made a file called startup_ass.cmd.good which runs the correct one. However, the default build

will try to start the wrong one and we have to fix the 'startass' script to point to the correct one on each build. Running the correct awgtpman

allows us to get the TP data using tools like tdsdata, so far no luck with DTT.\

UPDATE (23:33): It turns out that it was my old nemesis, NTPD. c1ass had a /etc/ntp.conf file that was pointing at an ntp server called rana113. I

am not an NTP server; I don't even know what time it is. I have fixed the ntp.conf file by making it the same ass c1omc (it now points to nodus). After

this I set the date and time manually (sudo date -s "20 DEC 2009 23:27:45") and then restarted NTPD. It should now be fine even when

we reboot c1ass.

After all of this nonsense, I am able to get TP data from c1ass and take transfer functions between it and the rest of the world !

This allowed measuring the MC1 -> MCL TF finally. Its mostly flat. Data saved as Templates/OAF/OAF-MCLTF.xml

 What does OAF stand for? The entry doesn't say that. Also the acronym is not in the abbreviation page of the wiki.

Can anyone please explain that?

I fit the MC1 -> MCL TF using vectfit4.m (from mDV). The wrapper file is mDV/extra/C1/ fitMC12MCL.m.

Plotted here are the data (RED), the fit (BLUE), and the residual x10 (GREEN).

For the magnitude plot, residual is defined as ------   res = 1 - fit / data

For the phase plot the residual is defined as -------    res =  phase(data)-phase(fit)

You can see that the agreement is very good. The phase match is better than 5 deg everywhere below 10 Hz.

This TF is so smooth that we could have probably done without using this, but its good to excercise the method anyway.

Kiwamu made the OAF screen functional today - screenshot attached.

After this, I used the measured TF of the MC1 to MCL to filter the signals from the Wilcoxon accelerometers and feed them into the MC.

The noise at 3 Hz went down by a factor of ~3. There's a little excess created at 100 Hz. Its good to see that our intuition about feed-forward is OK.

I did all of the filter calculations by adapting the scripts that Haixing, Valera, and I got going at LLO. They're all in the mDV/extra/C1 SVN.

The Wiener code predicts much better performance from using more than just 2 horizontal accelerometers, but I was too lazy to do more channels today.

I also added the Rai box to the Ranger readout today - the noise at 0.1 Hz went down by a factor of 10 and the noise at 1 Hz is close to 10^-11 m/rHz.

The Rai box ran out of batteries a couple of days ago and so the data is no good. I've put the Ranger back on the SR560 for now (but with the damping resistor removed, so the gain is 2x more than before).