Estimation of the location of an optical object with photodetectors limited by quantum noise

We study the maximum likelihood estimation of the location of an incoherent object, the light from which is distorted by an optical system and detected by photoelectric detectors with quantum noise. The noise is treated as a set of uncorrelated Gaussian variables with variances proportional to the signal plus background at their corresponding detectors. By the simulation of the noise, a large number of cases are tested and curves for the probability distribution of the error distance are obtained.