  Next generation radio observatories such as the MWA, LWA, LOFAR, CARMA and
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 can not be described using a
single complex gain per antenna. In this paper we use the optimal map-making
formalism developed for CMB 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.
