  High resolution (~1 arcminute) astronomical imaging at low frequency (below
150 MHz) has only recently become practical with the development of new
calibration algorithms for removing ionospheric distortions. In addition to
opening a new window in observational astronomy, the process of calibrating the
ionospheric distortions also probes ionospheric structure in an unprecedented
way. Here we explore one aspect of this new type of ionospheric measurement,
the differential refraction of celestial source pairs as a function of their
angular separation. This measurement probes variations in the spatial gradient
of the line-of-sight total electron content (TEC) to 0.001 TECU/km accuracy
over spatial scales of under 10 km to over 100 km. We use data from the VLA
Low-frequency Sky Survey (VLSS; Cohen et al. 2007, AJ 134, 1245), a nearly
complete 74 MHz survey of the entire sky visible to the Very Large Array (VLA)
telescope in Socorro, New Mexico. These data comprise over 500 hours of
observations, all calibrated in a standard way. While ionospheric spatial
structure varies greatly from one observation to the next, when analyzed over
hundreds of hours, statistical patterns become apparent. We present a detailed
characterization of how the median differential refraction depends on source
pair separation, elevation and time of day. We find that elevation effects are
large, but geometrically predictable and can be "removed" analytically using a
"thin-shell" model of the ionosphere. We find significantly greater ionospheric
spatial variations during the day than at night. These diurnal variations
appear to affect the larger angular scales to a greater degree indicating that
they come from disturbances on relatively larger spatial scales (100s of km,
rather than 10s of km).
