Superposition of planar Cantor gratings and directional self-similarity I: General considerations

Author: Lehman, M.

Source: Optik – International Journal for Light and Electron Optics, Volume 113, Number 1, 1 April 2002 , pp. 13-24(12)

Publisher: Urban & Fischer

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Abstract:

Studying the properties of the diffracted field, when two Cantor diffraction gratings are superimposed are important in order to establish the relationships between the geometry of each fractal grating and the corresponding structure of the diffracted field. Here, we consider two interesting cases, the first related with the Moiré effect, since the Cantor gratings used are built through periodic functions. The second case for studying is the characterization of field in the Fraunhofer region, into each envelope of diffraction, using the self-similarity function. For this case it is shown that it is more appropriate the calculation on the modulus of the electromagnetic field, instead of using the intensity distribution. To exemplify, we use Cantor gratings with fractal dimensions D = ln (2)/ln (3) and D = 0.5, which have scaling factor 3 and 4 respectively.

Keywords: Diffraction; fractals; Cantor bars; superposition; Moiré; effect; selfsimilarity; Fraunhofer region

Document Type: Original article

DOI: http://dx.doi.org/10.1078/0030-4026-00107

Affiliations: 1: Sofilab SACV, México DF (México) and Instituto Nacional de Astrofísica, Optica y Electrónica (INAOE), Tonantzintla, Puebla, México

Publication date: 2002-04-01