We propose a method for estimating the thickness of ultra thin histological sections by image statistics alone. Our method works for images, that are the realisations of a stationary and isotropic stochastic process, and it relies on the existence of statistical image-measures that are strictly monotonic with distance. We propose to use the standard deviation of the difference between pixel values as a function of distance, and we give an extremely simple, linear algorithm. Our algorithm is applied to the challenging domain of electron microscopic sections supposedly $45\text{ nm}$ apart, and we show that these images with high certainty belong to the required statistical class, and that the reconstructions are valid.