  We develop the theoretical foundation for primary objective grating (POG)
telescopy. In recent years, a wide range of telescope designs that collect the
light over a large grating and focus it with a secondary receiving optic that
is placed at grazing exodus have been proposed by Thomas D. Ditto, and are
sometimes referred to as Dittoscopes. Applications include discovery and
characterization of exoplanets, discovery of near-Earth asteroids, and
spectroscopic surveys of the sky. These telescopes would have small aerial
mass, and therefore provide a path forward to launch large telescopes into
space. Because this series of telescope designs departs from traditional
telescope designs, it has been difficult to evaluate which applications are
most advantageous for this design. Here, we define a new figure of merit, the
"modified etendue," that characterizes the photon collection capability of a
POG. It is demonstrated that the diffraction limit for observations is
determined by the length of the grating. We evaluate the effects of atmospheric
seeing for ground-based applications and the disambiguation of position vs.
wavelength in the focal plane using a second dispersing element. Finally, some
strategies for fully reaping the benefits of POG optical characteristics are
discussed.
