In elog2187, we measured FDS with CCFC loop locked. Meanwhile, there were no GR automatic alignment (AA) and input mirror feed back (InputFB). And we have seen detuning changed by about 10Hz, which should not happen since CCFC works to remove the detuning change with precision of 1Hz (could be a bit worse in elog2187). I have thought about this in more detail, and I found misalignment can impact on CCFC lock.

I have a code Aritomi-san provided about CCFC error signal calculation. By using this code, as elog2300, I added mode matching influence for this error signal and found the shape change of this signal, which was confirmed with experiment. I made this simulation again with mode matching level of 100%, 95%(our current situation), and 90%. The simulation result is shown in the attached figure (figure 1 is the zoom in of figure 2). We can see that the CCFC error signal zero crossing point changes with different mode matching level. Let's remind that when CCFC is used to lock filter cavity, we lock filter cavity to the zero point of CCFC error signal. Since CCFC zero crossing point changes with mode matching level, a misalignment for squeezing field will translate into FDS detuning change.

Attached figures show zero crossing point changes from 1.954 to 1.895, which are normalized by detuning frequency 54Hz. Therefore, this corresponds to a frequency change of 3.2Hz. Without automatic alignment, and considering the experience of our mirror suspension system change, this misalignment induces detuning change and prevents us from the goal of 1Hz detuning stabilization. Even with GR automatic alignment, the alignment is actually fluctuating and results in ~95% misalignment, which should introduce already 3.2Hz detuning change.

To achieve really detuning change less than 1Hz, IR automatic alignment will be necessary!