Superposition of Cantor gratings II: Fractality of the moiré profiles

Here, we treat the fractality condition for the moiré fringe profiles obtained from the superposition of two Cantor gratings. These Cantor structures are built through the product of periodic components. We restrict the study to the case in which both gratings have the same fractal parameters (dimension and lacunarity). However, the period of each component can be different. The contribution of each periodic component is also shown, and the total moiré is expressed as a product of the moiré from pairs of such components (Optik 113 (2002) 13-24). Considering the normalized fringe profiles as sets and based on the theory of dynamical systems, the fixed points are obtained. Finally, the calculation of the perimeter-yardstick relation (Richardson method) permits to obtain a power law and the fractality condition is accomplished for such normalized fringe profiles.