Tunable laser diodes are now widely used in dense wavelength division multiplexing (DWDM) optical fiber networks. A wide tunability range and good frequency stability are generally required, without mode hopping. Special applications require fast frequency measurement. Unfortunately, commercially available classical spectral measurement systems are much too slow for that purpose. In this paper, we present a new and low-cost system dedicated to fast spectral measurements based on a Michelson interferometer. The free spectral range (FSR) of the interferometer must be carefully optimized. We have designed optimized and tested an experimental system that can quickly analyze with good accuracy the tunability range of tunable distributed Bragg reflector (DBR) laser diodes, and their possible mode hopping. Our set-up can also be used for other spectral measurements (linewidth, chirp, Henry's alpha enhancement factor, spectral and power monitoring). After theoretical analysis of our experimental set-up, we finally present the fast spectral measurements results obtained with a typical 1550 nm two sections DBR QW (quantum well) laser diode. Our measurements have been obtained within less than 500 ps, which is much faster than limits induced by switching thermal effects in laser diodes, and that speed could still be increased.