When cavity mirror alignment changes, the optical axis of cavity will change. This makes intra-cavity beam hits on different points on cavity mirrors. For example, when a pitch pertubation 'x' is introduced to cavity end mirror, according to cavity geometry, the intra-cavity beam will change beam hitting position on end mirror by 'x*(R-L)/2' while change beam hitting position on input mirror by 'x*(R+L)/2'. In our case, R~440m and L~300m.
When FC is locked with GR both in length and alignment, we can introduce the pertubation for input\end pitch\yaw. The detuning change is taken simulatenously. However, it is noticed that only small amount of misalignment can be introduced (about 5urad), otherwise, cavity get unlock. This introduced misalignment corresponds to a beam position change on the other cavity mirror by about 2mm.
The misalignment and detuning change is attached. We can see that the input mirror misalignment introduce more detuning change. This can be reasonable since the end mirror has more layers of coatings, which is more probably to have difference for phase error between GR and IR.
The detuning measurement had some problems. The main issue is that pointing loop was not kept to be zero while these scanning.
When pointing loop is kept to be zero, either we introduce pertubation to input or end mirror yaw/pitch, the beam hitting position can change only on input mirror. Therefore, when we do this scan, we are doing a map similar to elog2615. But instead of end mirror in elog 2615, this scan is for input mirror. Attached figure 1 shows the schematic of this scanning process.
Since the PR/BS pointing loop has angular scanning range of about 200urad, which can scan a range only about 0.8mm on input mirror. After doing these scan on input/end mirrors y/p, we got detuning change, input/end mirror oplev signal, and pointing error signal as attached figure 2-5.
With position change of about 0.8mm on input mirror, the detuning change is less than 5Hz. (This is a detuning change smaller than the flat region found on filter cavity end mirror in elog2615.)