Direct-view microscopes use multiple-aperture arrays in the source and
detector planes. We develop a theory for brightfield and fluorescence
direct-view microscopy which allows us to determine the optical secti
oning strength for finite-sized, multiple-pinhole arrays with an arbit
rary distribution of apertures. We specialize to the cases of square,
hexagonal and interleaving Archimedean spiral arrays and consider the
implications of the array configuration on both the optical sectioning
strength and the light budget.