Picosecond pulses from a tunable mode-locked visible dye laser are injected into a 603-m few-mode optical fiber. Measurements of the output power temporal profile with 35-ps resolution show six clearly resolved modes. Time-profile measurements over a two-dimensional array of points in the fiber output far field yield a picture of each mode that identifies it. Measurements as a function of wavelength and fitting to waveguide dispersion calculations are used to model the fiber core refractive-index profile. As a result for the nominal step-index fiber used in this work, the presence of an index dip at the center of the core was detected.