This feels reminiscent of the Hartmann wavefront sensor camera refresh rate.  Team TCS is going to look at this as soon as they are finished with their currently-ongoing maintenance tasks.

EDIT: Never mind, Danny looked, and all of the refresh rates are correctly set to be much lower frequency than this.

Gabriele, Hang

Gabriele pointed out that the f-domain subtraction using coherence could easily lead to over subtraction, as the finite amount of average could over-estimate the coherence. For example, the improvement above 30 Hz in the previous attached plot could hardly be real as the ASC noise should have been rolled off there. 

We thus looked at a longer data stretch of 10240 sec (~ 3 hrs; 5 times what we used in the previous study) starting at gps 1236511818. Again we use 8 sec per fft and 50% overlaps, and therefore 2559 averages. This should mitigate the errors due to finite averaging.  The result is attached to this entry. 

In the first plot we show the DARM noise spectra before and after subtracting the linear/quadratic ASC channels.

In the second plot we present the largest contributions' projection to DARM (ranked by the contribution at 25 Hz).

In the last one we compute the SISO coherence between [CH_Y(t)xCS_P(t)] and DARM as a sanity check for result plotted in the second figure. 

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Some conclusions based on the plot:

    1. We still see a significant (visible by eyes) improvement in the 15-30 Hz band by including the quadratic terms such as DH_P(t) x CS_P(t). The level of noise reduction is roughly comparable to what we had in the previous entry in this band. 

    2. Below 20 Hz the dominating nonlinear correction comes from [CH_P(t) x DH_P(t)] which is more or less expected. On the other hand, the largest contribution at 25 Hz is from [CH_Y(t) x CS_P(t)]. This is a bit surprising. Nonetheless, we also looked at the SISO coherence and saw a similar amount of projection to DARM. Thus the coupling should be real. It suggests that we may have large P/Y and C/D cross-coupling simultaneously.

    3. Above 30 Hz, the quadratic subtraction matches the linear subtraction. This should be viewed as a reduction in the systematic error in our approach. 

    4. In the 10-15 Hz band, even linear subtraction can still improve the noise performance. This is an indication that in addition to the geometrical a2l coupling (that is freq independent), we also have a path of angle->power->length coupling (that scales ~ 1/f^2 and thus is visible only at low frequencies; this path also cannot be subtracted by the dithering soft loop which handles only the geometrical one). This is consistent with the previous observations that as we decreased the dithering frequency (thus locking pt was more biased by the radiation P effect), the ASC->DARM coupling got worse at ~20 Hz.

Was unsuccessful in damping the mode.  It made the spectrum really terrible.  I tried increasing the ADS dithers so that they wouldn't get drown out, and that wasn't good.  I turned off the ADS, but we still lost lock.

Kara and I had a look, and the phase rotator filters in ITMX Mode 2 weren't at the correct phases (+40 deg and -70 deg, rather than +/- 60 deg, and their magnitudes weren't unity at the violin frequency).  She used Patrick's gui to put in +/-30 deg and +/-60 deg filters, so that we can hopefully find something that more reliably damps this mode.  For now, it is also commented out of the lscparams so that it won't turn on with totally different filters than it used to have.

Anamaria changed the Mode2 filter to also catch the Mode 4 frequency, and turned off the gain for Mode4. 

Also, we made the Mode3 filter much more narrow, so that the tail of it isn't hitting its neighbors and potentially driving them up.

Ensured that Mode9 is very narrow (it was already an 8th order butterworth), and made mode1 more narrow (4th order to be 6th order) to help prevent it from hitting the mode9 frequency.

I've adjusted the guardian damping settings for ITMX modes 2 and 4.  

Mode 2 now uses filters FM5, FM9, and FM10 with gain=-25.

Mode 4 now has gain=0.

I've commented out both ITMX modes 1 and 9 so that we can make it to NLN now, and find the best damping settings later after we've had a chance to check consistency.

Here I am trying to build a model of the scattering. If you don't have time to read all of it, jump directly to the last plot, which gives what I believe is a reasonably good model that we could use for noise projections.

Here's a spectrogram of DARM during times around the OMC ANG X injections. It is evident that even without any injection, there are scattering shelves in DARM going up to 20-30 Hz. 

I selected four periods: two before the injection (fist at T=100s in the spectrogram above: almost no scatter visible, second at T=600s, some scattering visible) and two during the injection (T=850s: low amplitude injection, T=1000s: high amplitude injection). 

Using H1:OMC-ASC_ANG_X_INMON as a proxy for the scatterer motion, I can fit a scattered light noise model based on the "phase wrapping" model (from Accadia 2010 and Canuel 2013), including a single bounce and a double bounce. The model simply assumes that the fringe wrapping gives a noise in h(t) that can be modeled by

where f_1 and f_2 are the two coupling coefficients for the single and double bounces (related to the amount of light which is scattered back) and k_1 is a factor converting the OMC_ANG_X into the actual length change in the scattering path. 

If I use the medium amplitude injection, I can find coefficients that described quite well the spectrum of scattered light. The parameters are f_1 = 1e-19, f_2 = 1e-21, k_1 = 22e-7. In the plot below I use those parameters to "project" the scattered light noise for all four periods. The bottom left plot shows that the fit is good for the medium amplitude injection, but clearly fails for all other cases.

I can't reproduce the scattered light noise for both medium and hgh amplitude using any of the H1:OMC-ASC_[AND/POS]_[X/Y]_INMON signals. In particular for the high amplitude injection I can't reproduce the rising edge of the shelf. Typically one gets such rising edges when the RMS of the motion is concentrated at almost a single frequency.

If we assume that only the 0.5 Hz motion is responsible for the scattering, we can proceed as follows:

1. First, I apply a narrow band filter to H1:OMC-ASC_ANG_X_INMON, composed of a zero at 0 Hz plus a complex pole at -0.1 +- 0.5j Hz, scaled to maintain a gai of 1 at 0.5 Hz. 
2. Then I can use the filtered signal to fit the high amplitude injection noise.

The best parameters are: f_1=3.5e-20, f_2=5e-22, k_1=1.6e-5. The resulting noise projects well for both the high and medium injection amplitude, and it is also in the right ballpark for the high scattering period without injection. So this seems to be a good model.

We can apply the same scattered light model to the noisy period reported in 47399. It looks like the same parameters over-estimate the up-conversion (i.e. the corner frequency of the scattered light is too high). So I had to reduce the k_1 coefficient from 1.5e-5 to 1.0e-5, while I could use the same coupling factors f_1 and f_2.

I ran some 0.5 Hz line injections in the other OMC ASC degrees of freedom to see if there were any differences in the coupling.

First attached figure shows DARM and the control signals for (clockwise from top left) POS_X, POS_Y, ANG_Y and ANG_X. Red is ambient noise, blue with a moderate excitation and yellow with a larger excitation. Apologies for the different excitation amplitudes. POS_X has the strongest coupling.

Second attached figure is the control signals and corresponding RMSs.

I haven't done the work of projecting these into DARM yet, but in case anyone wants to the template can be found here:

/ligo/cds/lho/exports/georgia.mansell/Scattering/20190311_OMC_ASC_to_DARMscatter2.xml

Ran some more injections into OMC ASC ANG X, this time with a BB Inj 0.1 to 1 Hz.  Stored at https://lhocds.ligo-wa.caltech.edu/exports/craig.cahillane/Scatter/
Continuing work on the scattering projection into DARM in the live noisebudget.  It's not too far away, needs more work though.

If you have an opportunity over the weekend, what you need to do is:

Set the laser power to 30W. Go to ISS_DC_COUPLED (IMC_LOCK guardian). Confirm that the VGA gain slider is at 7dB.

Go to the floor. At the back of the ISS 2nd loop chassis on the rightmost PSL rack, there are four BNC connectors labeled as ERR1, ERR2, EXC and board OUT.

Connect the excitation of SR785 to EXC, CHA to ERR2, CHB to ERR1.

In the MEDM screen, enable excitation input.

EXC voltage of 1000mV is OK. There's a 1/10 attenuation in the EXC path so this is not excessive. You'll have to integrate long (e.g. 0.1 sec or some such) to get a decent measurement.

Measure the OLTF. Note that the measured quantity is OLTF/10.

Disable EXC, disconnect EXC, connect ERR2 and ERR1 and OUT to a scope and measure the voltages. If you still see a huge gain peaking you want to lower the gain further.

This morning when H1 lost lock, I quickly went to the floor and made the same measurements, and things look OK.

At 30W with 7dB VGA slider, UGF~28kHz, phase margin~37deg, which look good to me (first attachment).

Moving the slider back up to 12dB, the servo immediately started the oscillation at about 50kHz. Bringing it down to 11dB already quenched the oscillation.

With the nominal gain of 7dB, the residual noise at around 50kHz was ~1Vpp after the x10 summation stage with maybe another 1+Vpp or so at around UGF (second attachment blue) which is larger than I'd like. However, the output of VGA with 7dB gain will be ~4.5+Vpp which would be large but OK. The output of the board was measured to be about 15~20mVpp or so (2nd attachment green), this is no problem for the 1st loop.

(The reason why the board output is small is because two fixed boost type filters downstream has about 2E-3 attenuation combined for f>20kHz.)