  We have obtained HST-NICMOS observations of five of M31's most metal rich
globular clusters. These data allow photometry of individual stars in the
clusters and their surrounding fields. However, to achieve our goals -- obtain
accurate luminosity functions to compare with their Galactic counterparts,
determine metallicities from the slope of the giant branch, identify long
period variables, and estimate ages from the AGB tip luminosity, we must be
able to disentangle the true properties of the population from the
observational effects associated with measurements made in very crowded fields.
  In this paper we present a careful analysis of photometry in crowded regions,
and show how image blending affects the results and interpretation of such
data. Although this analysis is specifically for our NICMOS observations in
M31, the techniques we develop can be applied to any imaging data taken in
crowded fields; we show how the effects of image blending will even limit NGST.
We use three different techniques to analyze the effects of crowding on our
data, including the insertion of artificial stars (traditional completeness
tests) and the creation of completely artificial clusters. They are used to
derive threshold- and critical-blending radii for each cluster, which determine
how close to the cluster center reliable photometry can be achieved. The
simulations also allow us to quantify and correct for the effects of blending
on the slope and width of the RGB at different surface brightness levels.
