  We introduce a new technique for imaging the polarized radio sky using
interferometric data. The new approach, which we call Faraday synthesis,
combines aperture and rotation measure synthesis imaging and deconvolution into
a single algorithm. This has several inherent advantages over the traditional
two-step technique, including improved sky plane resolution, fidelity, and
dynamic range. In addition, the direct visibility- to Faraday-space imaging
approach is a more sound foundation on which to build more sophisticated
deconvolution or inference algorithms. For testing purposes, we have
implemented a basic Faraday synthesis imaging software package including a
three-dimensional CLEAN deconvolution algorithm. We compare the results of this
new technique to those of the traditional approach using mock data. We find
many artifacts in the images made using the traditional approach that are not
present in the Faraday synthesis results. In all, we achieve a higher spatial
resolution, an improvement in dynamic range of about 20%, and a more accurate
reconstruction of low signal to noise source fluxes when using the Faraday
synthesis technique.
