Model-based optical two-point resolution

The classical criteria for optical two-point resolution consider intensity observations that are exactly describable by a mathematical two-component model. This paper considers an alternative resolution criterion, which concerns detected images. These images can never be exactly described by the model adopted. This is caused by both systematic and random errors. It is shown that two distinct classes of sets of observations can be distinguished. For the one class, the model fitting solutions for the component locations are distinct. Then the components are resolved. For the other class, the solutions exactly coincide and resolution is impossible. It is shown how these classes can be determined for any two-component model. Furthermore, for statistical observations, the probability of resolution can be computed as a function of the SNR. This probability can be used to compare the performance of different imaging systems