You've got it! With today's telescopes, most stars are so
far away that they appear to be point sources to a telescope detector.
Point sources have angular sizes that are smaller than the distortions
introduced by the detector. What telescope limitations prevent us from
measuring the angular sizes of stars?
Limitations of Point Spread Functions
One distortion light suffers when it is seen through a telescope is called
a point spread function. The point spread function
of a telescope is the pattern that a point of emission appears as. Each
telescope has its own point spread function. The point spread function has
the effect of equalizing the size of any objects whose angular size is
fewer pixels across than the point spread function.
Limitations of Resolution
Telescopes are also limited by their resolution. A telescope's resolution
is the angular size of the sky that each pixel represents (this is often a
function of wavelength). If the resolution of the telescope is larger than
the angular size of the star, it is impossible for the star to look
"clearer" than a single pixel.
At best, a distant star that is unresolved will appear as a single pixel
(at least the location will be well constrained!). At worst, it will
appear as a blurry blob, the telescope's point spread function. In any
case, unless the star is lare and nearby (so that its angular size is
larger than the telescope's resolution and its point spread function),
little information can be gained from an optical image of a star taken by
today's telescopes. Perhaps in the future telescope resolution and point
spread functions will improve to the point where we can image many stars
other than our own Sun!