Unified approach for the explanation of stochastic and periodic moires

Moire phenomena of different types are frequently encountered in electronic imaging. Most common are moire effects that occur between periodic structures. These effects have been intensively investigated in the past, and their mathematical theory is today fully understood. The same is true for moire effects between repetitive layers (i.e., between geometric transformations of periodic layers). However, although moire effects that occur between random layers (Glass patterns) have long been recognized, only little is known today about their mathematical behavior. In this work we study the behavior of such moires, and compare it with analogous results from the periodic case. We show that all cases, periodic or not, obey the same basic mathematical rules, in spite of their different visual properties. This leads us to a unified approach that explains both the behavior of Glass patterns in the stochastic case, and the well-known behavior of the moire patterns in periodic or repetitive cases