Since I had only one image to analyze, reductions were performed with the DAOPHOT II generation of ALLSTAR (see Stetson &Harris 1988; Stetson, Davis, &Crabtree 1990; Stetson 1994a). I tried reducing the field with five different model point-spread functions (PSFs): (1) a spatially invariant PSF derived from ten bright stars in the test image itself; (2) a quadratically varying PSF derived from the NGC 1850 frames discussed by Stetson (1994b); and (3) spatially invariant, (4) quadratically varying, and (5) cubically varying PSFs derived from grids of model profiles generated with Tiny TIM by Shaun M. Hughes. These Tiny TIM simulations were for a different focus setting and jitter history than assumed in the simulation. For each of (2)-(5), I added the 256256 simulation back into the middle of an 800800 blank image, so that the variations in the PSF would be correctly mapped into the frame.
Actually, there were two tests: one where the stars were exactly centered in their respective central pixels, and one where stars could effectively fall anywhere with respect to the centers of pixels. I analyzed these separately. I used the ``truth'' files to provide initial estimates of the stars' positions, but not of their magnitudes. This is fair because in most cases of interest the astronomer would have multiple images of a given star field, and would be able to generate a more complete list of detections than could be derived from any one frame alone.