Glass patterns in the superposition of random line gratings

摘要

Moire effects ('Glass patterns') that occur in the superposition of correlated random layers have long been studied. However, only little is known of Glass patterns which occur in the 1D random case: namely, when the superposed layers consist of random line gratings, straight or curved. In this paper we study the properties and the behaviour of such Glass patterns, and we compare them with those of the analogous moire effects between periodic line gratings. We provide for each case a detailed mathematical analysis of the fringe shapes and locations, along with illustrative figures which clearly compare the behaviour of the corresponding random and periodic (or repetitive) superpositions. Publisher's note. We believe the moire images in this article will print faithfully from the online pdf file but some spurious fringing will probably occur on-screen, depending on the screen resolution. To minimize that effect, we recommend viewing on-screen at 200% or higher magnification in Acrobat or Acrobat Reader.