  Calculations are performed for the spectral line profiles and images of
astrophysical maser radiation that emerges from isolated spheres and thin disks
viewed edge-on. In contrast to previous investigations where various
approximations are made, the full equations are solved here for the
frequency-dependent radiative transport that includes the thermal motion of the
molecules. The spectral line profiles for spheres and disks are found to
rebroaden to the full thermal Doppler breadth with increasing saturation in
essentially the same way as is well known to occur for a linear maser. The
variation with frequency in the apparent angular sizes of masing spheres and
thin disks is found to be negligible at frequencies within the spectral line
where the flux is significant. Calculations also are performed for spherical
and disk masers that are not isolated, but for which the seed radiation for the
masers is incident from one side as would occur when a strong continuum source
is on the far side of the masers. Again, the spectral line profiles are found
to rebroaden to the full thermal breadths with increasing saturation and there
are no significant variations in the apparent angular sizes with frequency.
However, the full rebroadening does occur at somewhat higher saturation and the
variation of the apparent angular sizes as a function of the degree of
saturation is quite different from that of the isolated masers. Spheres and
disks have served as idealized geometries with which to examine possible
deviations from the linear approximation for astrophysical masers.
