Sheila, Stefan

The low-finesse in the green cavity poses a problem for stabilizing the x-arm length:
 - The PDH error signals of 00-mode and 01-mode overlap.
 - Alignment fluctuations lead (to the first non-trivial order) to a fluctuation in 01-mode power. I.e. the relative contribution of the 10-mode-PDH-signal to the main PDH-signal varies.
 - If the 10-mode-PDH-signal at the main locking point is non-zero, this will couple into frequency fluctuations (relative between arm length and green light). These can be a significant fraction of the line width (about 1.5kHz ?).
 - To avoid this we need the 10-mode-PDH-signal to have a co-located zero-crossing, leading to only gain modulation, but no frequency fluctuations.

 - I can think of two strategies to achieve that:
   1) Set the modulation frequency to exactly 1 transverse mode spacing off the resonance. This lines up the zero-crossings of the PDH signals.
      Setting the demodulation phase exactly will guarantee that the large q-signal does not couple.
      Disadvantages: - The slope of the 10-mode-PDH-signal is large, leading to large gain fluctuations, and requiring an exact knowledge of the transverse mode spacing. (Problem with thermal heating later on?)
                     - The q-signal is maximal - setting the demod phase accurately is crucial.
   2) Pick the modulation frequency at some different value, but set the demod phase such that on the locking point the contribution of the 10-mode-PDH-signal is zero. This will need some more modeling.

For now we chose solution 1): We set the modulation frequency to 24.424281MHz (5099Hz below the co-resonant point of 24.429380MHz). 5099Hz is our current best guess of the transverse mode spaceing - we will need to measure that accurately. Using our phasing table from alog 9386, we set the delay phase shifter to 18.8125nsec (switches up: 1/16, 1/4, 1/2, 2, 16; down: 1/8, 1, 2, 4). As expected, when locked on the 00-mode, we now get a big q-phase offset.