Background and basic notions

Abstract

Several mathematical approaches can be used to explore the moiré phenomenon. The classical geometric approach [Nishijima64; Tollenaar64; Yule67] is based on a geometric study of the properties of the superposed layers, their periods and their angles. By considering relations between triangles, parallelograms, or other geometric entities generated between the superposed layers, this method leads to formulas that can predict, under certain limitations, the geometric properties of the moiré patterns. Another widely used classical approach is the indicial equations method (see Sec. 11.2); this is a pure algebraic approach, based on the equations of each family of lines in the superposition, which also yields the same basic formulas [Oster64]. A more recent approach, introduced in [Harthong81], analyzes the moiré phenomenon using the theory of non-standard analysis. This approach can also provide the intensity levels of the moiré in question, in addition to its basic geometric properties.