Abstract
Here, we show that superresolution optical fluctuation microscopy might not lead to ideally infinite superresolution enhancement with increasing of the order of measured cumulants. Using information analysis for estimating error bounds on the determination of point-source positions, we show that reachable precision per measurement might be saturated with increasing of the order of the measured cumulants in the superresolution 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.