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With the aim to determine the spectral phase of an optical pulse, we develop a new method based on the superimposition of two slightly shifted replicas of the spatial representation of the pulse spectrum. We record, at each point of the spectrum, the beating signal due to the superimposition of the two spectra. Knowledge of the phases of the beating signals allows for the reconstruction of the spectral phase. An additional measurement of the spectral intensity leads to the complete characterization of the pulse. Our setup does not involve any nonlinear optical process.