Moiré patterns between aperiodic layers: quantitative analysis and synthesis

Moiré effects that occur in the superposition of aperiodic layers such as random dot screens are known as Glass patterns. Unlike classical moiré effects between periodic layers, which are periodically repeated throughout the superposition, a Glass pattern is concentrated around a certain point in the superposition, and farther away from this point it fades out and disappears. I show that Glass patterns between aperiodic layers can be analyzed by using an extension of the Fourier-based theory that governs the classical moiré patterns between periodic layers. Surprisingly, even spectral-domain considerations can be extended in a natural way to aperiodic cases, with some straightforward adaptations. These new results allow us to predict quantitatively the intensity profile of Glass patterns; furthermore, they open the way to the synthesis of Glass patterns that have any desired shapes and intensity profiles.