We present a detailed discussion of how to obtain precise stellar photometry in crowded fields using images from multi-conjugate adaptive optics (MCAO) systems, with the intent of informing the scientific development of this key technology for the Extremely Large Telescopes. We use deep J and K_s exposures of NGC 1851 taken with the Gemini Multi-Conjugate Adaptive Optics System (GeMS) on Gemini South to quantify the performance of the instrument and to develop an optimal strategy for stellar photometry using PSF-fitting techniques. We judge the success of the various methods we employ by using science-based metrics, particularly the width of the main sequence turn-off region. We also compare the GeMS photometry with the exquisite HST data in the visible of the same target. We show that the PSF produced by GeMS possesses significant spatial and temporal variability that must be accounted for during the analysis. We show that the majority of the variation of the PSF occurs within the control radius of the MCAO system and that the best photometry is obtained when the PSF radius is chosen to closely match this spatial scale. We identify photometric calibration as a critical issue for next generation MCAO systems such as those on TMT and E-ELT. Our final CMDs reach K_s~22---below the main sequence knee---making it one of the deepest for a globular cluster available from the ground. Theoretical isochrones are in remarkable agreement with the stellar locus in our data from below the main sequence knee to the upper red giant branch.
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