Baade's Window at 2.2 microns - The luminosity function and a comparison with the bulge of M31

We have obtained H-band (2.2 micron) photometry of ~ 17000 stars in a 604 arcmin^2^ field of Baade's Window. The derived luminosity function is consistent with that obtained from unbiased samples of grism-selected M giants in the same region. There is no evidence that the bulge contains a significant number of stars that are bright at K and missed by grism surveys. We synthesized images of the bulge field as it would appear at the distance of M31 and show that image crowding will produce an artificial enhancement of the bright end of the measured luminosity function. We conclude that the upper part of the luminosity function in M31's bulge may be identical to that in Baade's Window.