As I was a little dissatisfied with the inaccuracy in the distance numbers in Kiwamu's sketch, I went back to the 18 Dec 2010 table layout drawing for more accurate numbers. These are now included in this round of plots.
Also, I include astigmatism due to the incident angles on MMT1 (~3.5 deg) and MMT2 (~1 deg).
First plot, IPPOS path, using the recent (fixed) measurements from Suresh to fix the beam width. Note that the old 2010 measurements of the MC waist are consistent with this measurement.
Second plot, Main IFO path all the way to the ITM (average) position, using the 2010 MC waist measurements to fix the beam width.
Third plot, Main IFO path all the way to the ITM position, but with PRM flipped (negative RoC), using the 2010 MC measurement to fix beam width.
With the PRM correctly oriented (2nd plot), I get beam waists of (x = 2.529 mm, y = 2.646 mm), which corresponds to a mode matching to the arm cavity of (eta = 97.43%, PRM correct).
With the PRM flipped (3rd plot), I get beam waists of (x = 3.176 mm, y = 3.3 mm), which corresponds to a mode matching to the arm cavity of (eta = 99.55%, PRM flipped).
Second plot (this is how the MMT was designed to be, before the ETMs were moved, which made the ideal waist larger):
For both the 2nd and 3rd plot, we can't look at the post-MMT waist measurements, since that distance on the plots is after the PRM, which is a curved optic. So the fact that the post-MMT measurements match the correct-PRM plot better than the flipped-PRM plot can't be taken to be meaningful.
Moral of the story: I'm not sure how to interpret any of this to tell us if the PRM is flipped or not, since the measurements are all of the beam profile before the beam sees the PRM. We'd have to measure the profile after the PRM somehow in order to get that information. We have okay but not great mode matching to the arm if the PRM is correct, but I don't know that we readjusted the MMT after we moved the ETMs. I don't remember recalculating any optimal telescope lengths after the arm length change. If we need better mode matching, I can do that calculation, although given how much space we don't have, it would be hard in practice to move the MMT mirrors by much at all.