  Diffraction gratings have been proposed as core elements in future
laser-interferometric gravitational-wave detectors. In this paper, we use a
steady-state technique to derive coupling of lateral grating displacement to
the output ports of a diffractive Fabry-Perot cavity. By introducing a signal
to noise ratio (SNR) for each of the three cavity output ports the magnitude of
the noise sidebands originating from lateral grating displacement are compared
to the magnitude of a potential gravitational wave signal. For the example of a
3km long Fabry-Perot cavity featuring parameters similar to the planned
Advanced Virgo instrument, we found that the forward-reflecting grating port
offers the highest SNR at low frequencies. Furthermore, for this example
suspension requirements for lateral isolation were computed, and a factor of
twenty relaxation at a frequency of 10Hz can be gained over the transmitted
port by observing the forward-reflected port.
