  While near-field scanning optical microscopy (NSOM) can provide optical
images with resolution much better than the diffraction limit, analysis and
interpretation of these images is often difficult. We present a theory of
imaging with transmission NSOM that includes the effects of tip field,
tip/sample coupling, light propagation through the sample and light collection.
We apply this theory to analyze experimental NSOM images of a nanochannel glass
(NCG) array obtained in transmission mode. The NCG is a triangular array of
dielectric rods in a dielectric glass matrix with a two-dimensional photonic
band structure. We determine the modes for the NCG photonic crystal and
simulate the observed data. The calculations show large contrast at low
numerical aperture (NA) of the collection optics and detailed structure at high
NA consistent with the observed images. We present calculations as a function
of NA to identify how the NCG photonic modes contribute to and determine the
spatial structure in these images. Calculations are presented as a function of
tip/sample position, sample index contrast and geometry, and aperture size to
identify the factors that determine image formation with transmission NSOM in
this experiment.
