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Effects of external optical feedback from a reflection grating on the linewidth of a GaAlAs semiconductor laser operating at 780 nm are investigated. Accurate linewidth measurements as a function of the laser frequency tuning have been performed by applying the self-homodyne technique with a short delay line. A realistic coupled-cavity model, which incorporates the frequency-dependent reflection from the grating, is used to explain the measured data. The agreement between the theoretical and experimental results was found to be good.