  We propose to use intensity correlation microscopy in combination with
structured illumination to image quantum emitters that exhibit antibunching
with a spatial resolution reaching far beyond the Rayleigh limit. Combining
intensity measurements and intensity auto correlations up to order $m$ creates
an effective PSF with FWHM shrunk by the factor $\sqrt{m}$. Structured
Illumination microscopy on the other hand introduces a resolution improvement
of factor 2 by use of the principle of moir\'e fringes. Here, we show that for
linear low-intensity excitation and linear optical detection the simultaneous
use of both techniques leads to an in theory unlimited resolution power with
the improvement scaling favorably as $m + \sqrt{m}$ in dependence of the
correlation order $m$. Hence, yielding this technique to be of interest in
microscopy for imaging a variety of samples including biological ones. We
present the underlying theory and simulations demonstrating the highly
increased spatial superresolution, and point out requirements for an
experimental implementation.
