As has been mentioned in Section 1, the basic distinction between a phased array
and a multi-element interferometer is that in a phased array the signals from all
the elements are added in phase before (or after) being put through a square-law
detector, where as in a multi-element interferometer, the signals from the
elements are correlated in pairs for each possible combination of two elements and
these outputs are further processed to make a map of the brightness distribution.
Thus, if the signal from element i is given by , the output of
the (coherent) phased array can be written as
Expansion of the right hand side of eqn 6.5.10 produces terms of the kind and . The first kind are all available from the correlator outputs and, if the correlator also records the self products of all the elements, the second kind are also provided by the correlator. Thus, by appropriate combinations of the outputs of the correlator used in the multi-element interferometer, the phased array output can be synthesised. Even the steering of the beam of the phased array can be achieved by combining the visibilities from the correlator after multiplying with appropriate phase factors. Also, the incoherently phased array output can be synthesised by combining only the self product outputs from the correlator.
However, the network of multipliers required to implement the correlator is a much more complicated hardware than the adder and square law detector needed for the phased array. Further, the net data rate out of the correlator is much higher than that from the phased array output, for data with the same time resolution. Thus, the interferometer achieves the phased array response in a very expensive manner. This is especially true for very compact, point-like sources where observations with an interferometer do not provide any extra information about the nature of the source. For example, observations of pulsars are best suited to a phased array, as these are virtually point sources for the interferometer and the requirement for high time resolution that is relevant for their studies is more easily met with a phased array output.