[Elenna, Gabriele]
Elenna did two PRCL noise injections, at times separated by about 1h40m. We measured the transfer function to the other LSC loops and to REFL_RIN, since we observed coherence of DARM with RIN and DARM with PRCL.
The most striking observations are:
- most transfer functions are very smooth with 1/f or 1/f^2 shape
- they changed significantly between the two measurements
The transfer function PRCL_IN1 / PRCL_OUT should be a good measurement of the optical gain. The gain measured the second time is ~0.75 the gain measured the first time. So we're losing PRCL optical gain over time. Not a new story. Probably thermal effects.
PRCL to MICH and SRCL coupling got smaller.
PRCL to CHARD_P got smaller, but PRCL to CHARD_Y got larger (by a factor 3-4, depending on frequency). This might be explained if the beam spot is moving on the PRM over time, in yaw, to increase the length to angle coupling. It's interesting that this is happening in yaw and we know we have a yaw alignment problem in the PRC.
Another interesting coupling is from PRCL to REFL_RIN. Ideally we should not have any linear coupling from PRCL to REFL power. This could happen if PRCL or CARM were locked off resonance. The fact that the coupling RIN / PRCL is getting larger (by a factor 2) might indicate that the PRCL (or CARM) offset is changing over time. Probably thermal effects? Maybe also related to the change in optical gain?
Following up on the PRCL to RIN coupling. From a measurement in 68899, I estimate that the PRCL actuation strenght is 1e-7 microns/cts at 4 Hz, assuming the SUS-ISCINF counts are the same as PRCL_OUT counts and that the OSEM L witness is calibrated in microns. This allows me to convert the REFL_RIN / PRCL_OUT in REFL_RIN / PRCL displacement. It is fairly flat, and in the two measurements it changed from 200 1/um to 400 1/um
From a simply double cavity model, one can compute the RIN in reflection as a function of the PRCL and CARM offsets from resonance. The actual REFL power depends a lot on the losses and reflectivity of the mirrors, and here I haven't included any sidebands. So this is at best an order of magnitude guess.
This simple model shows as expected a linear dependency of PRCL > RIN coupling with the PRCL offset. To explain the measured coupling one should have a PRCL offset between 0.025 and 0.050 nm. This seems small enough to be realistic.
My guess is that this offset is probably due to higher order modes created by the yaw misalignment in the PRC
Using the same actuation strenght estimate, and the measured TFs from PRCL_OUT to PRCL_IN1, we can estimate the PRCL optical gain in the two cases: 2.3e6 and 1.7e6 cts/micron, where cts are measured at PRCL_IN1.
So the offsets that minimize PRCL to RIN would be 58 and 85 counts.
