Thermal noise computation of arbitrary masses in optical interferometers from first principles

Thermal noise of optical components is one of the sensitivity limiting effects in gravitational wave detectors, laser stabilization cavities and many other experiments in basic research. However, current methods for the computation of thermal noise are limited for an application in either infinitely large or symmetrically illuminated masses. I present a general method of computing thermal noise of arbitrary finite-sized masses in optical interferometers. The presented approach generalizes state-of-the-art methods for an application in arbitrary shaped optical elements illuminated by arbitrary spatial light distributions. Furthermore, I show the application of the presented approach to compute thermal noise of maladjusted mirrors in Fabry-Perot interferometers. It is shown that the noise can be reduced by off-axis illumination in the case of thin mirrors.