Out of the 4 DoF (arm optical axis pos and angle, green input beam pos and angle, 2x for pitch and yaw not counted), 3 DoF will likely need a frequent initial alignment - the input beam position at the ETM is the one DoF that remains fixed.

Below is a short description of the suggested alignment loops. Attached is a draft RTCDS model block for e.g. X-arm pitch (we need 4 of them for X/Y P/Y).

Signals to be demodulated:
L: cavity PDH length error signal (green)
R: cavity reflected power (green)
T: cavity transmitted power (green)

Actuation basis (in rad):
(ITM, ETM, TMS)

g-factors:
g1=1-L/R1;
R1= RoC of ITM
g2=1-L/R2;
R2= RoC of ETM

Dither drive frequencies:
f1: ITM dither frequency
fT: TMS dither frequency

Control loops:
1) Fix ITM actuation node
L --->x ---> CTRL_FILT -----> (g1,1,1)
      ^
      |
      f1

Remark:
- Actuation at 1.65-2Hz or above 4Hz seems possible in pitch
- Pitch centering offset at 1.7Hz: ~2.3mm (slightly freq. dependent)
- Pitch centering offset above 4Hz: ~4.7mm
- Could provide a slight additional length drive to compensate this offset
- no such issues for yaw
- Actuation leaves the following quantities unchanged:
  - arm axis position on ETM
  - angle between arm axis and input beam


2) Input beam to arm axis angle overlap at ETM focal point
R or T ---> x ---> CTRL_FILT -----> (1,g2,g2)
            ^
            |
            f1
Remark:
- Actuation leaves the following quantities unchanged:
  - arm axis position on ITM
  - arm axis to input beam separation at ETM focal point
  - input beam position at ETM (trivial)

3) Input beam to arm axis angle overlap at ETM
R or T ----> x ---> CTRL_FILT ----->  (0,0,1)
             ^
             |
             fT
Remark:
- Actuation leaves the following quantities unchanged:
  - arm axis position and angle
  - input beam position at ETM (trivial)

Alternatives:
- GigE camera centering on ITM (instead of 1)
- ETM dither possible, but due to the steep drop-off of the Quad actuation, I expect reasonable drive amplitudes (producing a decent dip in power buildup) to only be possible at very low frequencies. As a result, since the dither frequency separation dictates the achievable bandwidth, it might be difficult to run all dither loops at the same time.

General Remarks:
- The dither drive is done in the optics basis, because any other basis would require significant attention to the relative phase of different actuation functions.
- To be able to run the loops in sequence, an orthogonal actuation function is desirable.
- repeat procedure of X- and Y -arm, pitch and yaw
- Once both arms are aligned, turn this feed-back off.