  Time-harmonic far-field source array imaging in a two-dimensional waveguide
is analyzed. A low-frequency situation is considered in which the diameter of
the waveguide is slightly larger than the wavelength, so that the waveguide
supports a limited number of guided modes, and the diameter of the antenna
array is smaller than the wavelength, so that the standard resolution formulas
in open media predict very poor imaging resolution. A general framework to
analyze the resolution and stability performances of such antenna arrays is
introduced. It is shown that planar antenna arrays perform better (in terms of
resolution and stability with respect to measurement noise) than linear
(horizontal or vertical) arrays and that vertical linear arrays perform better
than horizontal arrays, for a given diameter. However a fundamental limitation
to imaging in waveguides is identified that is due to the form of the
dispersion relation. It is intrinsic to scalar waves, whatever the complexity
of the medium and the array geometry.
