  Second order intensity correlations of speckle illumination are extensively
used in imaging applications that require going beyond the Rayleigh limit. The
theoretical analysis shows that significantly improved imaging can be extracted
from the study of increasingly higher order intensity cumulants. We provide
experimental evidence by demonstrating resolution beyond what is achievable by
second order correlations. We present results up to 20th order. We also show an
increased visibility of cumulant correlations compared to moment correlations.
Our findings clearly suggest the benefits of using higher order intensity
cumulants in other disciplines like astronomy and biology.
