Andrei, Naoki, Sheila
For the upcoming measurement of the FC backscattering, we need to calibrate the length change of the FC. To do this, we calculated the transfer function from the GS_SL FC control signal [Hz] to FC2 displacement [μm]. We followed the steps in Diagram.png to get to result. The plot bode_all_datasets.png contains all the used datasets.
The resulting transfer function is presented here: Tranfer_func.png (where Result curve is the transfer function). The result was exported to frequency/magnitude/phase dataset and can be found in result_data.txt. The remaining .txt files contain all the used datasets for this calculation.
Assuming that the frequency of the FC resonance shift Δf equal to c/2L corresponds to the FC length change ΔL equal to λ/2. (λ = 532 nm, L = 300 m), then Δf/ΔL = c/(L * λ) = 1.88*1012 [Hz/m] = 1.88*106 [Hz/μm]. Multiplying Transfer function by this coefficient will get us the open loop unity gain frequency of 39.4 Hz. Open-loop gain plot (after multiplication) can be found in the following figure: openloop_gain.png.
For FC2 suspension plant, we used sus_um in H1:CAL-CS_SUM_PRCL_PRM filter bank. The sus_um is the PRM suspension plant in the unit of um/count. Although the FC2 and PRM are the same HSTS suspensions, FC2/PRM M2 and M3 actuation strength is different by 0.326/2.83 according to the suspensions control design summary table on the door of control room as shown in the attachment (TACQ for FC2, TACQ*** for PRM). So we added this factor for FC2 M3 path.
