  Microlensing is a powerful tool for studying stellar atmospheres because as
the source crosses regions of formally infinite magnification (caustics) the
surfaceof the star is resolved, thereby allowing one to measure the radial
intensity profile, both photometrically and spectroscopically. However, caustic
crossing events are relatively rare, and monitoring them requires intensive
application of telescope resources. It is therefore essential that the
observational parameters needed to accurately measure the intensity profile are
quantified. We calculate the expected errors in the recovered radial intensity
profile as a function of the unlensed flux, source radius, spatial resolution
the recovered intensity profile, and caustic crossing time for the two
principle types of caustics: point-mass and binary lenses. We demonstrate that
for both cases there exist simple scaling relations between these parameters
and the resultant errors. We find that the error as a function of the spatial
resolution of the recovered profile, parameterized by the number of radial
bins, increases as $N_R^{3/2}$, considerably faster than the naive $N_R^{1/2}$
expectation. Finally, we discuss the relative advantages of binary
caustic-crossing events and point-lens events. Binary events are more common,
easier to plan for, and provide more homogeneous information about the stellar
atmosphere. However, a sub-class of point-mass events with low impact
parameters can provide dramatically more information provided that they can be
recognized in time to initiate observations.
