Resolution limits in astronomical images

TL;DR

This paper introduces a method to determine resolution limits for astronomical images based on brightness distribution templates, considering SNR and instrument effects, with practical applications to jets and supernova remnants.

Contribution

It develops a novel approach to derive resolution criteria for different brightness templates in astronomical imaging, incorporating SNR and instrument characteristics.

Findings

Resolution limits depend on SNR and template type.

Maximum and minimum resolvable sizes are quantified.

Application to real astronomical data demonstrates practical utility.

Abstract

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.