I measured eight of the 45P mirrors from the 40m. The transmission doesn't look as high as we realistically need it to be. They were: 57ppm, 38ppm, 46ppm, 36ppm, 48ppm, 64ppm, 34ppm, 55ppm, with some ~10ppm error.
Using combinations of these mirrors the best we could do is a transmission through the cavity of 20% with losses at 40% and a contrast defect of 0.22, the rest being lost in transmission through the turning mirrors.
We are starting to get quotes back in for coating runs. It seems that they may not be able to get exactly the transmission we want, but instead will have +- 30ppm. It may be that we want to be a bit cautious in our transmission choice since 100ppm -30 would end up with a transmission much lower than we want. If we go for a higher transmission in the first place then we reduce that risk but may get a slightly lower finesse, for example 130ppm would give a finesse of 15k instead of 18k for 100ppm. The extra upside is that we get a better contrast defect (0.12).
The C_d is never going to be zero since the input and output mirrors will have very similar transmissivity.
I've put in requests for quotes to a number of companies now for 100ppm coatings. I also checked through our history of measured transmissions, and notices that these mirrors have some that are very close to what we want. The Y145P 2" mirrors that I previously measured seem to have much higher transmission for 45S than the ones in the Mott measurements. I'm going to go across and dig these out again so we can repeat the measurement.