  The generation of laser-driven dense relativistic electron layers from
ultra-thin foils and their use for coherent Thomson backscattering is
discussed, applying analytic theory and one-dimensional particle-in-cell
simulation. The blow-out regime is explored in which all foil electrons are
separated from ions by direct laser action. The electrons follow the light wave
close to its leading front. Single electron solutions are applied to initial
acceleration, phase switching, and second-stage boosting. Coherently reflected
light shows Doppler-shifted spectra, chirped over several octaves. The Doppler
shift is found to be proportional to \gamma_x^2=1/(1-\beta_x^2), where \beta_x
is the electron velocity component in normal direction of the electron layer
which is also the direction of the driving laser pulse. Due to transverse
electron momentum p_y, the Doppler shift by
4*\gamma_x^2=4*\gamma^2/(1+(p_y/mc)^2) ~= 2*\gamma is significantly smaller
than full shift of 4*\gamma^2. Methods to turn p_y -> 0 and to recover the full
Doppler shift are proposed and verified by 1D-PIC simulation. These methods
open new ways to design intense single attosecond pulses.
