| Abstract
| - Next generation radio observatories such as the Murchison Widefield Array (MWA), the Long Wavelength Array (LWA), the LOw Frequency ARray (LOFAR), the Combined Array for Research Millimeter-wave Astronomy (CARMA) and the Square Kilometer Array (SKA) provide a number of challenges for interferometric data analysis. These challenges include heterogeneous arrays, direction-dependent instrumental gain, and refractive and scintillating atmospheric conditions. From the analysis perspective, this means that calibration solutions cannot be described using a single complex gain per antenna. In this paper, we use the optimal map-making formalism developed for cosmic microwave background analyses to extend traditional interferometric radio analysis techniques - removing the assumption of a single complex gain per antenna and allowing more complete descriptions of the instrumental and atmospheric conditions. Due to the similarity with holographic mapping of radio antenna surfaces, we call this extended analysis approach software holography. The resulting analysis algorithms are computationally efficient, unbiased and optimally sensitive. We show how software holography can be used to solve some of the challenges of next generation observations, and how more familiar analysis techniques can be derived as limiting cases.
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