  In this paper, we consider random phase fluctuations imposed during wave
propagation through a turbulent plasma (e.g. ionosphere) as a source of
additional noise in interferometric visibilities. We derive expressions for
visibility variance for the wide field of view case (FOV$\sim10$ deg) by
computing the statistics of Fresnel diffraction from a stochastic plasma, and
provide an intuitive understanding. For typical ionospheric conditions
(diffractive scale $\sim 5-20$ km at $150$ MHz), we show that the resulting
ionospheric `scintillation noise' can be a dominant source of uncertainty at
low frequencies ($\nu \lesssim 200$ MHz). Consequently, low frequency widefield
radio interferometers must take this source of uncertainty into account in
their sensitivity analysis. We also discuss the spatial, temporal, and spectral
coherence properties of scintillation noise that determine its magnitude in
deep integrations, and influence prospects for its mitigation via calibration
or filtering.
