Microstructures: dot trajectories and their morphology

Abstract

Perhaps the most striking property of moiré effects between aperiodic screens, which clearly distinguishes them from their periodic or repetitive counterparts, is the appearance in the superposition of intriguing microstructure dot alignments, also known as “dot trajectories”. These dot trajectories may have various geometric shapes, depending on the transformations undergone by the superposed layers. In the case of simple linear transformations such as layer rotations, layer scalings, etc. the resulting dot trajectories are rather simple (circular, radial, spiral, elliptic, hyperbolic, linear, etc.); see Figs. 2.1-2.3. But when the layer transformations are more complex, the resulting dot trajectories may have more interesting and sometimes even quite spectacular shapes. And yet, if the same layer transformations are applied to periodic layers, no dot trajectories are visible in the superposition, and the resulting moiré effects look completely different, as we can clearly see in the right hand side of each of the figure pairs throughout this book. What is the reason for this surprising difference?