Motivated by applications in electron microscopy, we study the situation where a stationary and isotropic random field is observed on two parallel planes with unknown distance. We propose an estimator for this distance. Under the tractable, yet flexible class of Léevy-based random field models, we derive an approximate variance of the estimator. The estimator and the approximate variance perform well in two simulation studies.

Keywords: Léevy-based modelling, Monte Carlo methods, random fields, stereology, section distance, systematic sampling, variance, variogram.