Superimposition
Superimposition of 2D images containing correlated periodic grid structures may produce moiré patterns. Superimposition of two correlated layers comprising parallel lines or curves may give rise line moiré patterns. The movement of one of the layers results in a faster movement of the line moiré superimposition image. Such optical acceleration is known as moiré speedup (check for the formulas of optical speedup for curved patterns). When superimposing two identical layers comprising randomly spaced parallel lines, at a small angle or with a small scaling difference random line moiré patterns, namely line Glass patterns (after Leon Glass, 1969) appear. Similarly, when superimposing two identical layers of randomly scattered dots at a small angle or with a small scaling difference random dot Glass patterns, namely random dot moiré, appears. When one of the layers embeds complex shapes, such as sequences of symbols forming a text, and another layer contains parallel lines or curves, the superimposition image may gives rise to magnified shapes, called shape moiré patterns.