  The recent demonstration of a real-time direct imaging radio interferometry
correlator represents a new capability in radio astronomy. However wide field
imaging with this method is challenging since wide-field effects and array
non-coplanarity degrade image quality if not compensated for. Here we present
an alternative direct imaging correlation strategy using a Direct Fourier
Transform (DFT), modelled as a linear operator facilitating a matrix
multiplication between the DFT matrix and a vector of the electric fields from
each antenna. This offers perfect correction for wide field and non-coplanarity
effects. When implemented with data from the Long Wavelength Array (LWA), it
offers comparable computational performance to previously demonstrated direct
imaging techniques, despite having a theoretically higher floating point cost.
It also has additional benefits, such as imaging sparse arrays and control over
which sky co-ordinates are imaged, allowing variable pixel placement across an
image. It is in practice a highly flexible and efficient method of direct radio
imaging when implemented on suitable arrays. A functioning Electric Field
Direct imaging architecture using the DFT is presented, alongside an
exploration of techniques for wide-field imaging similar to those in visibility
based imaging, and an explanation of why they do not fit well to imaging
directly with the digitized electric field data. The DFT imaging method is
demonstrated on real data from the LWA telescope, alongside a detailed
performance analysis, as well as an exploration of its applicability to other
arrays.
