Looking at intensity noise in reflection of the interferometer allows us to measure the mode matching as well as the reflection coefficient.

The idea is that fluctuations above the cavity pole are promptly reflected by the interferometer, whereas the DC field will be resonant and have a reflectivity smaller than unity. In our case, where we are close to critically matched but still over-coupled, the reflected DC field also picks up a minus sign. Any field that is not mode matched will simply be prompt reflected and not acquire a minus sign. The later is true for both the fluctuations and the DC field.

Including the total reflected power, one can then invert the equation and determine both mod matching and reflectivity. A note detailing the derivation can be found in LIGO-T2300249.

Using the values measured in alog 70982, we get

For this derivation we neglected to include the RF sidebands. Typically, they are small, but the note details how they can be included if the power is measured as function of the modulation index. The 75W interferometer wasn't thermalized yet, when the measurement was taken and we can expect an additional 1.2% of power increase in reflection. If we attribute all to mode mismatch, we would have a total of ~4.4% of the input power not mode matched.

The mode mismatch power is important for figuring out the impedance matching of the PRM, see alog 68451.