EDIT 2 (ZK): As with the previous post, all plots and calculations here are done with my MATLAB cavity modeling utility, ArbCav.
EDIT (ZK): Added input q parameters for OMMT
I found the nice result that the variation in the optimal length vs. variation in the mirror RoC is roughly linear within the ±1% RoC tolerance. So, we can choose two baseline mode definitions (one for each mirror topology) and then adjust as necessary following our RoC measurements.
For R = 2.5 m, the optimal length (see previous post) is LRT = 1.150 m, and the variation in this is dLRT/dR ~ +0.44 m/m.
Here is an illustration of the geometry:
The input q parameters, defined at the point over the edge of the OMC slab where the beam first crosses---(40mm, 150mm) on the OptoCad drawing---are, in meters:
For R = 2.5 m, the optimal length is LRT = 1.246 m, and the variation in this is also dLRT/dR ~ +0.44 m/m.
q parameters, defined as above: