Direct observations of free-standing single-wall carbon nanotubes (SWNTs), either as individual tubes or bundled in ropes, are performed using a Fresnel projection microscope (FPM). The analysis is done with the support of systematic numerical simulations of Fresnel diffraction images. The images of individual SWNTs are characterized by bright lines, while semitransparency wire fringe patterns are observed for thin ropes. Ropes with a higher number of individual tubes present the conventional Fresnel fringe patterns of an opaque wire. This differentiation in the FPM images between fringe patterns and bright line patterns allows for an easy detection of individual SWNTs. FPM also allows us to detect the presence of localized defects along SWNTs, and, in particular, the characterization of nanotube junctions. Although the exact structure of the junctions cannot be deduced presently from the images they, at least, indicate the presence of strong electric fields associated with the structural connections between the SWNTs.