Variational approach to moiré pattern synthesis.
Moiré phenomena occur when two or more images are nonlinearly combined to create a new superposition image. Moiré patterns are patterns that do not exist in any of the original images but appear in the superposition image, for example as the result of a multiplicative superposition rule. The topic of moiré pattern synthesis deals with creating images that when superimposed will reveal certain desired moiré patterns. Conditions that ensure that a desired moiré pattern will be present in the superposition of two images are known; however, they do not specify these images uniquely. The freedom in choosing the superimposed images can be exploited to produce various degrees of visibility and ensure desired properties. Performance criteria for the images that measure when one superposition is better than another are introduced. These criteria are based on the visibility of the moire patterns to the human visual system and on the digitization that takes place when the images are presented on discrete displays. We propose to resolve the freedom in moire synthesis by choosing the images that optimize the chosen criteria.