Resolution limits in astronomical images

A method is introduced to derive resolution criteria for various a priori defined templates of brightness distribution fitted to represent structures and objects in astronomical images. The method is used for deriving criteria for the minimum and maximum resolvable sizes of a template. The minimum resolvable size of a template is determined by the ratio of (SNR-1)/SNR, and the maximum detectable size is determined by the ratio of 1/SNR. Application of these criteria is discussed in connection to data from filled-aperture instruments and interferometers, accounting for different aperture shapes and the effects of Fourier sampling, tapering, apodization and visibility weighting. Specific resolution limits are derived for four different templates of brightness distribution: (1) two-dimensional Gaussian, (2) optically thin spherical shell, (3) disk of uniform brightness, and (4) ring. The limiting resolution for these templates changes with SNR similarly to the quantum limit on resolution. Practical application of the resolution limits is discussed in two examples dealing with measurements of maximum brightness temperature in compact relativistic jets and assessments of morphology of young supernova remnants.