## page was renamed from Upgrade 09/IFO Modeling/Curvature Mismatch
= Effect of the end mirror curvature error to the contrast of ¥¥a Fabry-Perot based Michelson interferometer =

We found that one of the ETMs of the 40m interferometer could be delivered with a curvature error of 5¥% from the nominal radius. The effect of this curvature error to the contrast of a FPMI was investigated by analytical calculation and simulations with FINESSE.

[[attachment:curvature_mismatch.pdf|Here]] is the document.

For the parameter similar to the 40m interferometer with nominal end mirror curvature of 57 m,  the contrast defect of the FPMI is given by: 

 . dC = 3.61 x 10^-4^ dR^2^ + O^3^(dR)

and this is dominated by the higher-order modes.

The result was confirmed with simulations on FINESSE.

{{attachment:curvature_mismatch_plot.png}}

Relationship between the curvature error and the contrast defect.
Red dots show the simulated results. The blue line is the curve for the analytical calculation.