  Grating reflectors have been repeatedly discussed to improve the noise
performance of metrological applications due to the reduction or absence of any
coating material. So far, however, no quantitative estimate on the thermal
noise of these reflective structures exists. In this work we present a
theoretical calculation of a grating reflector's noise. We further apply it to
a proposed 3rd generation gravitational wave detector. Depending on the grating
geometry, the grating material and the temperature we obtain a thermal noise
decrease by up to a factor of ten compared to conventional dielectric mirrors.
Thus the use of grating reflectors can substantially improve the noise
performance in metrological applications.
