As we are considering running with a detuned signal recycling. I went back to this simple parametric model of the DARM response with SR detuned, which has two free parameters, the pole of the response when SR is tuned (in Hz), and the angle of detuning on the circle in the complex parameter space of the pole (which monotonic but not directly related to the SR detuning phase). A question is how to use that model for Hrec, which currently relies on two lines, one at 70Hz and at 360Hz.
Figure 1 shows the changes in the amplitude of the response at 70Hz, for a reasonable range we would explore in both parameters of the model. The changes are very small, at most 1.5%, and depend mostly on the SR detuning angle. The amplitude of that line should remain a good parameter for measuring the absolute scaling of the optical response, that can be affected by the power in the arms, the maching with the OMC, or other type of detection losses.
Figure 2 shows the changes in the amplitude of the response at 360Hz. In that case the amplitude is mostly affected by the pole frequency of the model. In principle it should remain around ~430Hz when detuning, but that gives the freedom for the calibration to follow any changes, for example due to SR misalignment.
Figure 3 shows the changes in the phase of the response at 360Hz. The phase is mostly affected by the SR detuning. So that will be a good measure of the SR detuning for the optical model.
Figure 4 looking at the line at 491.3Hz the phase change of 0.2 rad that was measured during the experiment of Feb 24 corresponds to roughly ~1 of detuning in this parametric model.
This model doesn't include the optical spring at low frequency. In principle the parameters should be related with the SR detuning, in practice I doubt it will be reliable, as the optical spring frequency also depends on the power in the arms, and simulations show it is also affected by the PR and SR RoC mistuning. So there the only solution that seems reasonable to me is to measure the frequency and Q factor of that pole using additional lines at low frequency.
/users/mwas/calib/detunedSRfit/SR_TF_parameter_scan.m