  Here, we show that, contrary to the common opinion, the super-resolution
optical fluctuation microscopy might not lead to ideally infinite
super-resolution enhancement with increasing of the order of measured
cumulants. Using information analysis for estimating error bounds on the
determination of point sources positions, we show that reachable precision per
measurement might be saturated with increasing of the order of the measured
cumulants in the super-resolution regime. In fact, there is an optimal
correlation order beyond which there is practically no improvement for objects
of three and more point sources. However, for objects of just two sources, one
still has an intuitively expected resolution increase with the cumulant order.
