  A novel method is proposed to determine the carrier-envelope phase (CEP) of a
relativistic few-cycle laser pulse via the central frequency of the isolated
light generated from Thomson backscattering (TBS). We theoretically investigate
the generation of a uniform flying mirror when a few-cycle drive pulse with
relativistic intensity ($I > 10^{18} {{\rm{W}} \mathord{/
  {\vphantom {{\rm{W}} {{\rm{cm}}^{\rm{2}}}}}.
  \kern-\nulldelimiterspace} {{\rm{cm}}^{\rm{2}}}}$) interacts with a target
combined with a thin and a thick foil. The central frequency of the isolated
TBS light generated from the flying mirror shows a sensitive dependence on the
CEP of the drive pulse. The obtained results are verified by one dimensional
particle in cell (1D-PIC) simulations.
