The detection of two-dimensional optical signals which have been corrupted by noise is considered. Discussion is limited to the detection of a known object in a known location. The problem is approached from the classical statistical technique of hypothesis testing. Initially the solution is formulated in very general terms. The decision rule is derived for a signal distorted by noise of an unspecified type which may include signal dependent noise. Once the decision rule is obtained, the probabilities of false alarm and detection are evaluated from a{\sl a priori}knowledge of the noise and imaging system. The general results are applied to Poisson noise, signal dependent Gaussian noise, and binomial noise.