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Group velocity dispersion spectra have been determined for 7.8-m lengths of a single-mode optical fiber. The dispersion spectra are derived from measurement of the transit delay time of picosecond pulses (4-10 ps) from optically pumped ultrashort cavity semiconductor film lasers. The delay time spectra have been measured to 1 ps precision over the range from 1.11 to 1.53 μm for single-mode step-index and quadruple-clad fibers. This is the highest temporal resolution achieved for any pulse delay measurement in optical fibers. The resulting dispersion spectra are in good agreement with measurements made for the same fibers by other techniques.