Testing the Responses of Three PSF Fitting Methods

We present an analysis of prototype code designed to fit point-spread functions to point-like astronomical objects appearing in images taken by DECam, or the Dark Energy Camera. We test three methods, each of which yields a maximum likelihood estimate for a different likelihood function. We call these methods Poisson likelihood, χ2 with background error, and χ2 with data error, and describe their differences mathematically. Each is used to construct a fit involving up to four parameters characterizing the raw pixel data. We measure biases in the signal and background levels under a variety of conditions. We test the variance and error estimate of the fits as a function of signal strength, outline areas of sensitivity, and demonstrate the effects of incomplete or inaccurate information on the Poisson fit. We conclude that the Poisson likelihood fitting method is best, as it is successful in all circumstances under which the χ2 series are, and displays other favorable attributes where the others do not.