On Saturday, I was able to get some data on the effect of different blend filters on DARM. It looks like we probably don't want to be using the 45mhz blends, or they need some re-working to reduce their low frequency performance. The attached plots are DARM from 2 lock stretches on Saturday. This is the CAL CS DELTAL spectra, which Jeff helped me calibrate, hopefully he'll explain in a comment. Blue traces are both end stations with 45mhz blends, orange traces are both end stations with 90 mhz blends, black is the ground. Ground was pretty similar between the 2 cases, range was similar, though slightly higher with the 90mhz blend, possibly better alignment? First plot is .01 hz to 3 hz, where most of the action is, the second plot is 1hz to 100hz.
The first plot shows the 90 mhz blend does as well as the 45mhz blend down to .3 hz, then does a factor of several worse until ~50mhz, where the gain peaking on the 45mhz blend causes more motion. Above 1 hz the 90mhz blend shows more RMS, I'm not sure of the cause, but there are features visible in the second plot at about 8-15hz that I don't understand. But they are probably not due to the blend change.
The method for calibrating the CAL-DELTAL_EXTERNAL_DQ DARM spectrum and getting it "right" around and below 10 [Hz]: (1) undo the 5 zeros at 1 [Hz], 5 poles at 100 [Hz] whitening DAQ filter LHO aLOG 16702 as one would normally do for this channel at all frequencies. (2) compensate for the digital UIM control filter (FM1 & 2, "int" and "lowboost", two poles at 0 [Hz], two zeros at 0.1 and 0.3 [Hz]) that we don't replicate in the CAL-CS actuation path because of numerical precision noise. (See LHo aLOG 17528) That means, in DTT, one has to apply the following calibration filter: Gain: 0.03 Poles: 1,1,1,1,1, 0, 0 Zeros: 100,100,100,100,100, 0.3, 0.1 where the gain of (exactly) 0.03 is to normalize the z:p = ([0.3 0.1] : [0 0]) filter necessary for getting the actuation at low frequencies correct in step (2) -- i.e. prod(2*pi*[0.3 0.1]) / (2*pi)^2 = 0.03 Why (2) works: Remember that DELTAL_EXTERNAL is the sum of the calibrated DARM_ERR and DARM_CTRL channels, DELTAL_EXTERNAL = (1 / C) * DARM_ERR + A * DARM_CTRL where C is the sensing function (i.e. the IFO's "test mass DARM displacement sensor" calibration) and A is the actuation function (i.e. the ETMY transfer function). A dominates this sum below the DARM UGF at ~40 [Hz]. As such, well below 40 [Hz], DELTAL_EXTERNAL ~ A * DARM_CTRL. Since we're using hierarchical feed back to ETMY, where the UIM/TST or L1/L3 cross-over frequency is ~1 [Hz], then well below *that*, DELTAL_EXTERNAL ~ A_{uim} * DARM_CTRL, i.e. the total calibration for DELTAL_EXTERNAL "well" below 1 [Hz] is dominated by how accurately we reproduce / calibrate / model the UIM actuation path. Since the UIM digital filters we've intentionally left out in CAL-CS have frequency content below ~0.5 [Hz], they're simply "missing" from the calibration of DELTAL_EXTERNAL, and we can, offline, just multiply all of DARM by these filters, and get the "right" answer. This being said, *all* calibration below 10 [Hz] still should be treated with some skepticism, because we have little-to-no precision measurements of the scale factor, DARM OLGTF frequency dependence, and/or TST/UIM cross-over frequency in this band (and we don't plan on making any). I could say it's "within a factor of two," because I think we've done everything right, but I have no measured proof to bound the uncertainty quantitatively. Above 10 [Hz], the latest estimate of precision and accuracy are described in detail in LHO aLOG 18186.