A method is presented for obtaining accurate photometry (sigma less than or similar to 0.1 mag) of stars in the dense cores of Galactic globular clusters using images taken with the Planetary Camera of the Hubble Space Telescope (HST). The principal challenge is due to the fact that the wings of the point spread function (PSF) extend much further than the typical separation between stars. Further complications arise from the complex structure of the PSF, significant variations of the PSF across the field, and the limited dynamic range of the data compared to the range in stellar brightnesses. If the variation of the PSF across the image is not taken into account, one introduces systematic photometric errors of order 0.2 mag. The core of the HST PSF, however, is about five times sharper than the best angular resolution available in ground based images. Detailed and realistic simulations have been carried out to estimate photometric accuracy and completeness. The technique of empirically modeling the variable PSF and determining stellar brightnesses by PSF fitting has been applied to HST PC images of the dense, metal-rich, disk globular cluster 47 Tuc obtained with the F555W and F785LP filters (similar to V and I). An accurate color-magnitude diagram is constructed for post-main-sequence stars brighter than V approximately 18-a task that has proved impossible from the ground due to the high degree of crowding in the core of 47 Tuc. The region within 1' of the center of 47 Tuc contains a centrally concentrated population of blue stragglers. The projected distribution of giant stars has a core radius r(c)=23"+/-2" (0.52 pc). The diffuse light from fainter stars (just below turnoff) has a core radius (approximately 26") that is slightly larger than that of the giants. No central cusp of light or signature of core collapse is seen in 47 Tuc. The data place a 95% upper limit of 2.6 X 10(3)(v(rms)/12 km s-1)2 M. on the mass of any compact object at the center of the cluster. There is no detectable color gradient in 47 Tuc; DELTA(V-I) < 0.1 between the center and r=1'.
