Partially coherent analysis of imaging and interferometric phased arrays: noise, correlations, and fluctuations

Phased arrays are of considerable importance for far-infrared, submillimeter-wave, and microwave astronomy; they are also being developed for areas as diverse as optical switching, radar, and radio communications. We present a discretized, modal theory of imaging and interferometric phased arrays. 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 determined for a source in any state of spatial coherence and polarization, once the synthesized beam patterns are known. It is not necessary to know anything about the internal construction of the beam-forming networks; indeed, the beam patterns can be taken from experimental data. The synthesized beams can be nonorthogonal and even linearly dependent. Our theory leads to many conceptual insights and opens the way to a range of new design and simulation techniques.