Optical Physics of Imaging and Interferometric Phased Arrays
  Microwave, submillimetre-wave, and far-infrared phased arrays are of considerable importance for astronomy. We consider the behaviour imaging phased arrays and interferometric phased arrays from a functional perspective. It is shown that the average powers, field correlations, power fluctuations, and correlations between power fluctuations at the output ports of an imaging or interferometric phased array can be found once the synthesised reception patterns are known. The reception patterns do not have to be orthogonal or even linearly independent. It is shown that the operation of phased arrays is intimately related to the mathematical theory of frames, and that the theory of frames can be used to determine the degree to which any class of intensity or field distribution can be reconstructed unambiguously from the complex amplitudes of the travelling waves at the output ports. The theory can be used to set up a likelihood function that can, through Fisher information, be used to determine the degree to which a phased array can be used to recover the parameters of a parameterised source. For example, it would be possible to explore the way in which a system, perhaps interferometric, might observe two widely separated regions of the sky simultaneously. 
Stafford Withington, George Saklatvala, and Michael P. Hobson