A Generalized Fourier-based Method for the Analysis of 2D Moiré Envelope-forms in Screen Superpositions

When repetitive structures such as line-gratings or dot-screens are superposed, a new pattern may become clearly visible in the superposition, although it does not exist in any of the original structures. This phenomenon, which in some cases appears to be very spectacular, is known as the superposition Moiré effect. In this article we analyse the 2D envelope-forms of these Moiré patterns, based on the Fourier theory, and we show how they can be derived analytically from the original superposed structures, either in the spectral domain or directly in the image domain. This approach not only offers a qualitative geometric analysis of each superposition Moiré, but also enables the intensity levels of each Moiré to be determined quantitatively. We first develop this analysis method for the simple case of line-grating superpositions, and then we generalize it to the superposition of doubly periodic structures such as dot screens, for any order Moiré. We finally show how, by means of this analysis method, we can fully explain (and predict) the surprising envelope-forms generated in the superpositions of screens with any desired dot-shapes, for any order of Moiré.