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A new method for the measurement of the linewidth enhancement factor of semiconductor lasers is presented, based on the interferometric self-mixing effect. It is a fast and easy to perform method that does not require radio frequency nor optical spectrum measurements. A small fraction of the emitted light is backreflected into the laser cavity by a remote target driven by a sine waveform. The mixing of the returned and the lasing fields generates a modulation of the optical output power in the form of an interferometric waveform, with a shape that depends on the optical feedback strength and the linewidth enhancement factor α, according to the well-known Lang-Kobayashi theory. We show that the value of α can be retrieved from a simple measurement of two characteristic time intervals of the interferometric waveform. Experimental results obtained on different laser diodes show an accuracy of ±6.5%.