We present a new approach to investigating ionospheric irregularities, using the temporal structure function of totally reflected radio echo phase variations. Modern digital ionosondes (e.g., the dynasonde) measure the echo phase with very high resolution and precision, at closely spaced antennas, frequencies, and times. A stringing procedure gives continuous and unambiguous phase variation data for time intervals of any desired length. Quasi-periods of tens of seconds up through several minutes are caused by large-scale movements of the ionospheric plasma, while shorter-period phase variations result from the interaction of the sounding signal with small-scale irregularities. The relevant irregularity spatial domain extends from decameter radio wavelengths to the first Fresnel scale, a few kilometers. We obtain a theoretical relation between structure functions of the temporal phase variations and spatial irregularities with a simple model of frozen horizontal drift. The relation permits solutions of both the direct and inverse problems. Although long-period phase measurements are practicable and essential to exploring larger irregularity scales, they require observing modes dedicated to multiple fixed-frequency time series, and this undesirably limits the number of altitudes that can be monitored simultaneously. An alternative rudimentary structure function is obtainable from standard dynasonde B-mode ionograms; it offers good altitude and time resolution for irregularity studies while permitting other established diagnostics (electron density profiles, vector velocities, critical frequencies, etc.) with the same data. We show some example analyses by these methods as applied to auroral and magnetic-equatorial dynasonde observations. We find irregularity amplitudes in the range 0.001<ΔN/N<0.1 (for a nominal scale of 1 km) and spectral indices in the range 2<&ngr;<4, with evidence of diurnal variation in both quantities at both locations. ¿ 2001 American Geophysical Union