  Filled arrays of bolometers are currently being employed for use in astronomy
from the far-infrared through millimeter parts of the electromagnetic spectrum.
Because of the large range of wavelengths for which such detectors are
applicable, the number of modes supported by a pixel will vary according to the
specific application of a given available technology. We study the dependence
of image fidelity and induced polarization on the size of the pixel by
employing a formalism in which diffraction due to the pixel boundary is treated
by propagating the second-order statistical correlations of the radiation field
through a model optical system. We construct polarized beam pattern images of
square pixels for various ratios of p/\lambda where p is the pixel size and
\lambda is the wavelength of the radiation under consideration. For the limit
in which few modes are supported by the pixel (p/\lambda<1), we find that the
diffraction due to the pixel edges is non-negligible and hence must be
considered along with the telescope diffraction pattern in modeling the
ultimate spatial resolution of an imaging system. For the case in which the
pixel is over-moded (p/\lambda>1), the geometric limit is approached as
expected. This technique gives a quantitative approach to optimize the imaging
properties of arrays of planar detectors in the few-mode limit.
