Reception frequency bandwidth of a gravitational resonant detector with optical readout

A gravitational resonant bar detector with a large scale Fabry-Perot cavity as an optical read out and a mechanical displacement transformer is considered. We calculate, in a fully analytical way, the final receiver bandwidth in which the potential sensitivity, limited only by the bar thermal noise, is maintained despite the additional thermal noise of the transformer and the additive noise of the optical readout. We discuss also an application to the OGRAN project, where the bar is instrumented with a 2m long FP cavity.