L. Dartez, J. Kissel, S. Dwyer

With the first long lock stretch we've had in a week, we took the time to explore the relationship between the large amount of detuning we've seen in the last full IFO sensing measurement (aka optical plant, aka DARM plant, see LHO:67063). 

We see a dramatic, though not unexpected, change in the optical plant with the addition of a SRCL offset (literally, turning on the digital offset H1:LSC-SRCL1_OFFSET). No other magic to the setup of the measurement. 

Attached are the results.
pdf attachment: This shows the processed sensing functions during each offset. 

    Here, we clearly see the evolution from "anti-" spring to "pro-" spring ... though once we get past -200 ct offset, the story begins to get confusing, like's it had been during O3, where we think we begin to expose L2A2L cross-coupling between the DARM loop and ASC loops (see e.g. LHO:55274). From this, we conclude that we can remove detuning with a SRCL offset of (about) -175 ct = -0.532 [deg] = -1.575 [nm] (see discussion of calibration of the offset below). Recall, in O3B, we ran with a +100 ct offset.

Image 1: this shows the systematic error in the DELTAL_EXTERNAL calibration change as a function of the offset in the same color scheme. 

    What's dramatic to see here is that the SRC detuning in the sensing function has an impact on the calibration all the way down at 20-30 Hz. This also should not be so terribly surprising given that the sensing function still contributes ~10% of the response function at 10 Hz, and given that the "deviation from flat" is about a factor of 2 at 20 Hz, it's no surprise that 50% * 10% = a 5% shift. 

As usual, this DTT display of the systematic error comes with all the caveats about us not understanding how to re-calibrate this template for the super-Nyquist corrections. We're now able to process this offline and get more sensible information, so expect a follow up on that in the comments below. However, in the mean time, we can at least admire the *change* in systematic error.

Now that we've found a SRCL Offset we think we like, we'll further investigate mitigating what L2A2L DARM to ASC cross-coupling we see remaining by pushing around the DHARD ASC gains; pitch at least of which has been proven to also have an impact (see LHO:52983).

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Image 2: this shows the typical metrics for power build up in the IFO. The cursor is dropped where we started the measurement, about an hour and 10 minutes from when we hit nominal low noise. One can see an 11% exponential increase in the arm cavity power build up from landing at 60 W to the lock-loss, but only a 2% increase in power from the start of the calibration measurements. It's not perfectly thermalized, but we can't wait for ever. 
Here're the list of IFO Configurations that might impact DARM (or might be relevant when we change them in the future):
- Input Power: 60 W from the PSL input to the IMC, 57.3 W into PRM
- LSC: No DARM length to Arm Cavity angle ("L2A") control decoupling the ETMX PUM stages
- ASC GAIN (P/Y): DHARD -30/-40, CHARD 1/125, DSOFT 2.5/30, CSOFT 20/20
- QUADs: ESD bias voltage is at -9.3 DAC volts, PUM drivers are in State 3, 
- TCS: Ring heaters on are IX (0.4 W), EY (1.4 W), C02 lasers are X = Annular 4.0 W, Y = Central 1.7 W
- SQZ: Frequency dependent squeezing was ON.

Image 3: This shows that running with a SRCL offset does not come without cost. The sensor for SRCL is POP_A, and as one applies as SRCL offset then more power is pushed out towards the POP sensor. As such, we watch the raw ADC signals that capture the analog DEMOD outputs, POP_A_RF9 and POP_A_RF45, to make sure they're not saturating. With a -250 ct offset, POP_A_RF_9_I, peaking at around ~26000 [ct] with a mean of ~22000 [ct]. Given that we recommend running at -175 [ct] offset, it's not that bad, but it means we might prefer to "solve" the detuning in another way (e.g. with an *ASC* SRC offset, or with the SR3 ring heater). 

While we've not fit for any spring frequency, we can at least turn the SRCL offset counts into physical units of displacement, dl-, given the 'to_um' calibration found within the H1:CAL-CS_SUM_SRCL_ERR bank = 9.0e-6 [um/ct] and then to amount of change in phase detuning with phase_deg = (180/pi) * dl- [ (2*pi)/ lambda ] as in LHO:51592.
Here're the table of offsets in physical units:

         [ct]       [nm]      [deg]
           50       0.45      0.152
           25      0.225      0.076
            0          0          0
          -25     -0.225     -0.076
          -50      -0.45     -0.152
         -100       -0.9     -0.305
         -200       -1.8     -0.609
         -250      -2.25     -0.761
which gives a calibration of the SRCL1_OFFSET as 3.04e-3 deg/ct or 9.00e-3 nm/ct.