Localisation error, due to finite fluorescence Signal and camera Noise, means that multiple independent localisations of a fluorophore produce a blurred map of fluorescence density, analogous to a Point Spread Function. 104 images of a single fluorophore were simulated, each with N = 103 photons, and parameters (b = 10, and a = s = 160 nm) such that Equation 1 predicts a localisation error of 9.6 nm. After applying a super-resolution algorithm to these simulated images in MATLAB (using sparse Gaussian fitting similar to (Wolter et al. 2010)), the localised positions were found to have a standard deviation of 9.8±0.25 nm. The average Thompson precision estimated from the image data (without using the known parameters N and b) was similar, at 9.3 nm – with the difference due to slight overestimation of signal, N. This localisation error, normally-distributed, implies the Sparrow criterion of resolution is about 20 nm. (b) A simulated object (i) consists of 2 lines of fluorophores, at 5 nm spacing, crossing at 45º. Its diffraction limited image is shown in (ii), and in (iii) a super-resolution image of the localised fluorophore density was reconstructed from data simulated as for the single fluorophore images used in (a), but with random activation of fluorophore subsets. A mean of 80 localisations were obtained per fluorophore, which avoids significant sampling limitation. Cross sections through the super-resolved image show that a limiting Sparrow resolution of about 20 nm was achieved (blue line), at the Precision Limit expected from Equations 1 and 8 (iv). (c) Nyquist-limited resolution: if the localisation precision supports a resolution finer than the fluorescent label spacing, the microscope will (correctly) resolve a pointillist image. This means finer scale information about the underlying specimen is not found, and the size of features smaller than about twice the label spacing cannot be reliably measured.