We present a linear self-referenced measurement of the spectral amplitude and phase of a free-running quantum-dash modelocked laser diode. The technique is suitable for measuring optical signals with repetition rates up to 100 GHz. In contrast to many other linear techniques it requires no external electronic clock synchronized to the signal under test. Using this method we are able to compensate for the intracavity dispersion of the diode to demonstrate 500 fs pulses at a repetition rate of 39.8 GHz. We also use the technique to characterize the dependence of the diode’s intracavity dispersion on the applied current.