Lessons learned on the beam spot centering (so far)
The spot position on MC2 can be adjusted by the alignment of the mirror while maintaining the best overlapping between the beam and the cavity axes.
In general, there are two methods:
1) Use the cavity as a reference:
Move the MC mirrors such that the cavity eigenmode hits the centers of the mirrors.
-> Then adjust the incident beam to obtain the best overlapping to the cavity.
2) Use the beam as a reference:
Move the incident beam such that the aligned cavity has the spots at the centers of the mirrors.
-> Then adjust the incident beam to obtain the best spot position while the cavity mirrors keep tracking
the incident beam.
Found the method 1) is not practical.
This is because we can move the eigenmode of the cavity only by very tiny amount if we try to keep the cavity locked.
How much we can move by mirror alignment is smaller than the waist radius or the divergence angle.
For the MC, the waist radius is ~2mm, the divergence angle is 0.2mrad. This means the axis
translation of ~1mm is OK, but the axis rotation of ~4mrad is impractical.
Also it turned out that adjustinig steering mirror to the 10-m class cavity is quite difficult.
A single (minimum) touch of the steering mirror knob is 0.1mrad. This already change the beam position ~0.1mm.
This is not an enough resolution.
Method 2) is also not so easy: Steering mirrors have singular matrix
Indeed! (Remember the discussion for the IMMT)
What we need is the pure angle change of 4mrad at the waist which is ~2m distant from the steering mirror.
This means that the spot at the steering mirror must be moved by 8mm (= 4mrad x 2m). This is the result of the
nearly-singular matrix of the steering mirrors.
We try to avoid this problem by moving the in-vac mirror (IM1), which has somewhat independent move.
The refl beam path also has the big beam shift.
But once the vacuum manifold is evacuated we can adjust very little angle.
This can also be a good news: once the angle is set, we hardly can change it at the PSL side.