  Widefield stochastic microscopy techniques such as PALM or STORM rely on the
progressive accumulation of a large number of frames, each containing a scarce
number of super-resolved point images. We justify that the redundancy in the
localization of detected events imposes a specific limit on the temporal
resolution. Based on a theoretical model, we derive analytical predictions for
the minimal time required to obtain a reliable image at a given spatial
resolution, called image completion time. In contrast to standard assumptions,
we find that the image completion time scales logarithmically with the ratio of
the image size by the spatial resolution volume. We justify that this
non-linear relation is the hallmark of a random coverage problem. We propose a
method to estimate the risk that the image reconstruction is not complete,
which we apply to an experimental data set. Our results provide a theoretical
framework to quantify the pattern detection efficiency and to optimize the
trade-off between image coverage and acquisition time, with applications to
$1$, $2$ or $3$ dimension structural imaging.
