  In this paper we analyze the stellar populations present in M31 using nine
sets of adjacent HST-NICMOS Camera 1 and 2 fields with galactocentric distances
ranging from 2' to 20'. These infrared observations provide some of the highest
spatial resolution measurements of M31 to date; our data place tight
constraints on the maximum luminosities of stars in the bulge of M31. The tip
of the red giant branch is clearly visible at Mbol ~ -3.8, and the tip of the
asymptotic giant branch (AGB) extends to Mbol ~ -5. This AGB peak luminosity is
significantly fainter than previously claimed; through direct comparisons and
simulations we show that previous measurements were affected by image blending.
We do observe field-to-field variations in the luminosity functions, but
simulations show that these differences can be produced by blending in the
higher surface brightness fields. We conclude that the red giant branch of the
bulge of M31 is not measurably different from that of the Milky Way's bulge. We
also find an unusually high number of bright blueish stars (7.3/arcmin^2) which
appear to be Galactic foreground stars.
