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