LHO ALOG 28765 said: "We reached 30 (as measured by LSC-PR_GAIN - Evan claims this is more like 35)."

I have the same impression based on the IFO visibility (reflectivity) estimation from the power recycling gain. My rough estimation says LSC-PR_GAIN is ~15% underestimated, which is quite consistent with Evan's claim. His estimation of the PRG is based on the difference of the transmitted light level between the single arm lock and the full IFO.

The first attached plot shows the comparison of the measured and estimated IFO reflectivity (or visibility). The data was taken from four lock stretches on Jul 26. The measured value (magenta) was normalized to have the unity when the IFO was not locked. Also it was normalized by the incident power. This visibility includes the power of the modulation sidebands and the rejected junk light. So even if the IFO is critically coupled, it does not go down to zero. In stead, it goes to 0.018, which is an empirical number came from the second analysis.

Basically, I couldn't reproduce the measured visibility with the power recycling taken from LSC-PR_GAIN. The red curve was estimated from LSC-PR_GAIN using a Fabry-Perot model formed by the PRM (T=0.031) and the perfect mirror with a loss between them. The blue curve is the estimated loss (or say, the reflectivity defect of the compound mirror by FPMI+SR). When the incident power (not shown here) was increased in every lock stretch, the power recycling gain went down and thus the estimated loss went up. But more reflection was expected because of severe undercoupling. In reality, we didn't have such amout of reflection. Also during the power up, it seemed that the IFO was still undercoupled, while the estimation showed less reflection.

If the power recycling gain is scaled by +15% (times 1.15), we can explain the measured visibility better. The second attachment is the same analysis with the PRG scaled. We have better explanation of the initial overcoupling part, the dip at the critical coupling, and the low reflectivity at high power.

The same effect can be obtained by changing the PRM transmissivity from 0.031 to 0.036. However, it is an unlikely assumption.

We probably can imprve the model by taking the sideband recycling gains and the modulation depths into account. If the model is made precise enough, we might become able to estimate the ammount of the junk light due to thermal lensing, for example. Also this analysis gives us realtime monitor of the internal loss in the IFO and this gives us more sensitive measure how good the IFO alignment/lensing is, compared to looking at the power recycling gain which is a small change of a high number like 30.