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In radio astronomy, holography is a commonly used technique to create an image of the electric field distribution in the aperture of a dish antenna. The image is used to detect imperfections in the reflector surface. Similarly, holography can be applied to phased array telescopes, in order to measure the complex gains of the receive paths of individual antennas. In this paper, a holographic technique is suggested to calibrate the digital beamformer of a phased array telescope. The effectiveness of the technique was demonstrated by applying it on data from the Engineering Development Array 2, one of the prototype stations of the low frequency component of the Square Kilometre Array. The calibration method is very quick and requires few resources. In contrast to holography for dish antennas, it works without a reference antenna. We demonstrate the utility of this technique for initial station commissioning and verification as well as for routine station calibration., 14 pages, 10 figures. Accepted for publication in Radio Science

Low-frequency, wide field-of-view (FoV) radio telescopes such as the Murchison Widefield Array (MWA) enable the ionosphere to be sampled at high spatial completeness. We present the results of the first power spectrum analysis of ionospheric fluctuations in MWA data, where we examined the position offsets of radio sources appearing in two datasets. The refractive shifts in the positions of celestial sources are proportional to spatial gradients in the electron column density transverse to the line of sight. These can be used to probe plasma structures and waves in the ionosphere. The regional (10-100 km) scales probed by the MWA, determined by the size of its FoV and the spatial density of radio sources (typically thousands in a single FoV), complement the global (100-1000 km) scales of GPS studies and local (0.01-1 km) scales of radar scattering measurements. Our data exhibit a range of complex structures and waves. Some fluctuations have the characteristics of travelling ionospheric disturbances (TIDs), while others take the form of narrow, slowly-drifting bands aligned along the Earth's magnetic field.

Detection of the fluctuations in 21 cm line emission from neutral hydrogen during the Epoch of Reionization in thousand hour integrations poses stringent requirements on calibration and image quality, both of which necessitate accurate primary beam models. The Murchison Widefield Array (MWA) uses phased array antenna elements which maximize collecting area at the cost of complexity. To quantify their performance, we have developed a novel beam measurement system using the 137 MHz ORBCOMM satellite constellation and a reference dipole antenna. Using power ratio measurements, we measure the {\it in situ} beampattern of the MWA antenna tile relative to that of the reference antenna, canceling the variation of satellite flux or polarization with time. We employ angular averaging to mitigate multipath effects (ground scattering), and assess environmental systematics with a null experiment in which the MWA tile is replaced with a second reference dipole. We achieve beam measurements over 30 dB dynamic range in beam sensitivity over a large field of view (65\% of the visible sky), far wider and deeper than drift scans through astronomical sources allow. We verify an analytic model of the MWA tile at this frequency within a few percent statistical scatter within the full width at half maximum. Towards the edges of the main lobe and in the sidelobes, we measure tens of percent systematic deviations. We compare these errors with those expected from known beamforming errors.