Optimal stellar photometry for multi-conjugate adaptive optics systems using science-based metrics

We present a detailed discussion of how to obtain precise stellar photometry in crowded fields using images obtained with multi-conjugate adaptive optics (MCAO), with the intent of informing the scientific development of this key technology for the Extremely Large Telescopes. We use deep J and K$_\mathrm{s}$ exposures of NGC 1851 obtained using the Gemini Multi-Conjugate Adaptive Optics System (GeMS) on Gemini South to quantify the performance of the system and to develop an optimal strategy for extracting precise stellar photometry from the images using well-known PSF-fitting techniques. We judge the success of the various techniques 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 of the same target in the visible. We show that the PSF produced by GeMS possesses significant spatial and temporal variability that must be accounted for during the photometric analysis by allowing the PSF model a reasonably high degree of spatial variability and by treating all exposures independently. We identify photometric calibration as a critical issue for next generation MCAO systems such as those on TMT and the E-ELT. Our final CMDs reach K$_\mathrm{s}\sim$23, below the main sequence knee of this cluster, and theoretical isochrones provide remarkable agreement with the stellar locus in our data from the main sequence knee to the red giant branch.