  We present a method for imaging small scatterers in a homogeneous medium from
polarization measurements of the electric field at an array. The electric field
comes from illuminating the scatterers with a point source with known location
and polarization. We view this problem as a generalized phase retrieval problem
with data being the coherency matrix or Stokes parameters of the electric field
at the array. We introduce a simple preprocessing of the coherency matrix data
that partially recovers the ideal data where all the components of the electric
field are known for different source dipole moments. We prove that the images
obtained using an electromagnetic version of Kirchhoff migration applied to the
partial data are, for high frequencies, asymptotically identical to the images
obtained from ideal data. We analyze the image resolution and show that
polarizability tensor components in an appropriate basis can be recovered from
the Kirchhoff images, which are tensor fields. A time domain interpretation of
this imaging problem is provided and numerical experiments are used to
illustrate the theory.
