Natural resolution limit
V. Yu. Terebizh · Astronomical and Astrophysical Transactions · 2001
Numerical simulations are used to study the well-known problem of a limiting detectable separation between two point-like components of a double source. Three versions of the problem are considered: (I) The Point Spread Function (PSF) is given a priori; (II) For a specified analytical form of the PSF, its parameters are to be estimated from observations of a single star; (III) The PSF is not known at all. The images of single and close binary stars are simulated by taking into account photon noise, the pixel structure of the detector and other factors that are common in real experiments. We generate large-sized samples of randomly blurred images of single and binary stars, and obtain maximum-likelihood estimates of 6 parameters for each binary image: the binary's total brightness, the relative brightness of its components, and 4 of their Cartesian coordinates. Monte Carlo simulations are consistent with the previously found analytical solution of the problem, according to which the limiting detectable separation between the components is , where Δ80 is the characteristic width of the PSF, and ψ is the signal-to-noise ratio within the image. Thus, the rough pixel structure of the detector and the presence of noise do not hinder the achievement of a resolution in the visual spectral range of order 0.001″–0.1″ with moderate-sized astronomical telescopes.