  Astronomical imaging with micro-arcsecond ($\mu$as) angular resolution could
enable breakthrough scientific discoveries. Previously-proposed $\mu$as X-ray
imager designs have been interferometers with limited effective collecting
area. Here we describe X-ray telescopes achieving diffraction-limited
performance over a wide energy band with large effective area, employing a
nested-shell architecture with grazing-incidence mirrors, while matching the
optical path lengths between all shells. We present two compact nested-shell
Wolter Type 2 grazing-incidence telescope designs for diffraction-limited X-ray
imaging: a micro-arcsecond telescope design with 14 $\mu$as angular resolution
and 2.9 m$^2$ of effective area at 5 keV photon energy ($\lambda$=0.25 nm), and
a smaller milli-arcsecond telescope design with 525 $\mu$as resolution and 645
cm$^2$ effective area at 1 keV ($\lambda$=1.24 nm). We describe how to match
the optical path lengths between all shells in a compact mirror assembly, and
investigate chromatic and off-axis aberrations. Chromatic aberration results
from total external reflection off of mirror surfaces, and we greatly mitigate
its effects by slightly adjusting the path lengths in each mirror shell. The
mirror surface height error and alignment requirements for diffraction-limited
performance are challenging but arguably achieveable in the coming decades.
Since the focal ratio for a diffraction-limited X-ray telescope is extremely
large ($f/D$~10$^5$), the only important off-axis aberration is curvature of
field, so a 1 arcsecond field of view is feasible with a flat detector. The
detector must fly in formation with the mirror assembly, but relative
positioning tolerances are on the order of 1 m over a distance of some tens to
hundreds of kilometers. While there are many challenges to achieving
diffraction-limited X-ray imaging, we did not find any fundamental barriers.
