  The coherent reflectivity of a dense, relativistic, ultra-thin electron layer
is derived analytically for an obliquely incident probe beam. Results are
obtained by two-fold Lorentz transformation. For the analytical treatment, a
plane uniform electron layer is considered. All electrons move with uniform
velocity under an angle to the normal direction of the plane; such electron
motion corresponds to laser acceleration by direct action of the laser fields,
as it is described in a companion paper. Electron density is chosen high enough
to ensure that many electrons reside in a volume \lambda_R^3, where \lambda_R
is the wavelength of the reflected light in the rest frame of the layer. Under
these conditions, the probe light is back-scattered coherently and is directed
close to the layer normal rather than the direction of electron velocity. An
important consequence is that the Doppler shift is governed by
\gamma_x=(1-(V_x/c)^2)^{-1/2} derived from the electron velocity component V_x
in normal direction rather than the full \gamma-factor of the layer electrons.
