Estimating the off resonance thermal noise in mirrors, Fabry-Perot interferometers, and delay lines: The half infinite mirror with uniform loss

We present an analysis comparing the thermal noise in Fabry-Perot and delay-line interferometers with half-infinite mirrors. With a center to center spot spacing of at least twice the Gaussian beam spot size a delay line produces significantly less phase noise than a comparable Fabry-Perot interferometer for the case of half infinite mirrors at frequencies where test mass thermal noise usually dominates. When the delay-line spots overlap substantially the delay-line produces approximately the same noise as the Fabry-Perot interferometer. For a single bounce these results agree with those based on the method of Levin.