A method is proposed to determine the carrier-envelope phase (CEP) of a relativistic few-cycle laser pulse via the frequency of the Thomson backscattering (TBS) light. We theoretically investigate the generation of a flying mirror when a few-cycle drive pulse with relativistic intensity interacts with a target combined with a thin and a thick foil. The frequency of the 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 simulations and are explained by an analytical model.
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