  We use beam tracing -- implemented with a newly-written code, Scotty -- and
the reciprocity theorem to derive a model for the linear backscattered power of
the Doppler Backscattering (DBS) diagnostic. Our model works for both the
O-mode and X-mode in tokamak geometry (and certain regimes of stellarators). We
present the analytical derivation of our model and its implications on the DBS
signal localisation and the wavenumber resolution. To determine these two
quantities, we find that it is the curvature of the field lines and the
magnetic shear that are important, rather than the curvature of the cut-off
surface. We also provide an explicit formula for the hitherto poorly-understood
quantitative effect of the mismatch angle. Consequently, one can use this model
to correct for the attenuation due to mismatch, avoiding the need for empirical
optimisation. This is especially important in spherical tokamaks, since the
magnetic pitch angle is large and varies both spatially and temporally.
