We propose to use low-coherence-length cw optical sources with a broad spectrum in heterodyne near-field scanning microscopy in order to imitate optical pulse propagation and to obtain information about spectrally variant properties of nanophotonic components. The dispersion difference in the interferometer arms for a symmetric acousto-optic modulator arrangement is shown to be negligible over appreciable bandwidths. Demonstration of the principle of operation and viability of this approach is provided by measurement of the group refractive index of a silicon channel waveguide.