We report on a method to obtain dispersion measurements from spectral-domain low-coherence interferograms which enables high accuracy (approximate to ps/(nm.km)), broadband measurements and the determination of very dense (up to 20 points/nm over 500 nm) data sets for both dispersion and dispersion slope. The method exploits a novel phase extraction algorithm which allows the phase associated with each sampling point of the interferogram to be calculated and provides for very accurate results as well as a fast measurement capability, enabling close to real time measurements. The important issue of mitigating the measurement errors due to any residual dispersion of optical elements and to environmental fluctuations was also addressed. We performed systematic measurements on standard fibers which illustrate the accuracy and precision of the technique, and we demonstrated its general applicability to challenging problems by measuring a carefully selected set of microstructured fibers: a lead silicate W-type fiber with a flat, near-zero dispersion profile; a hollow core photonic bandgap fiber with strongly wavelength dependent dispersion and dispersion slope; a small core, highly birefringent index guiding microstructured fiber, for which polarization resolved measurements over an exceptionally wide (approximate to 1000 nm) wavelength interval were obtained. (C)2014 Optical Society of America