  We present a theoretical study of ghost imaging based on correlated beams
arising from parametric down-conversion, and which uses balanced homodyne
detection to measure both the signal and idler fields. We analytically show
that the signal-idler correlations contain the full amplitude and phase
information about an object located in the signal path, both in the near-field
and the far-field case. To this end we discuss how to optimize the optical
setups in the two imaging paths, including the crucial point regarding how to
engineer the phase of the idler local oscillator as to observe the desired
orthogonal quadrature components of the image. We point out an inherent link
between the far-field bandwidth and the near-field resolution of the reproduced
image, determined by the bandwidth of the source of the correlated beams.
However, we show how to circumvent this limitation by using a spatial averaging
technique which dramatically improves the imaging bandwidth of the far-field
correlations as well as speeds up the convergence rate. The results are backed
up by numerical simulations taking into account the finite size and duration of
the pump pulse.

Quantum Physics