Autocorrelations of random fractal apertures and phase screens
arXiv:1612.06201 · doi:10.1142/S0218348X17500050
Abstract
We introduce a new product representation for general random binary fractal apertures defined by removing voids from Euclidean space, and use it to derive a simple closed-form expression for ensemble-averaged correlations. Power-law scaling at short distance follows almost immediately. Similar techniques provide easy constructions of objects with fractional Brownian short-distance behavior for phase screens and other applications.
This article has been accepted for publication by the journal Fractals (World Scientific Publishing). Acceptance dated November 17, 2016