  MUSTANG is a bolometer camera for the Green Bank Telescope (GBT) working at a
frequency of 90 GHz. The detector has a field of view of 40 arcseconds. To
cancel out random emission change from atmosphere and other sources, requires a
fast scanning reflecting system with a few arcminute ranges. In this paper, the
aberrations of an off-axis system are reviewed. The condition for an optimized
system is provided. In an optimized system, as additional image transfer
mirrors are introduced, new aberrations of the off-axis system may be
reintroduced, resulting in a limited field of view. In this paper, different
scanning mirror arrangements for the GBT system are analyzed through the ray
tracing analysis. These include using the subreflector as the scanning mirror,
chopping a flat mirror and transferring image with an ellipse mirror, and
chopping a flat mirror and transferring image with a pair of face-to-face
paraboloid mirrors. The system analysis shows that chopping a flat mirror and
using a well aligned pair of paraboloids can generate the required field of
view for the MUSTUNG detector system, while other systems all suffer from
larger off-axis aberrations added by the system modification. The spot diagrams
of the well aligned pair of paraboloids produced is only about one Airy disk
size within a scanning angle of about 3 arcmin.
