In this paper, the case for studying is the characterization of field in the Fraunhofer region, into each envelope of diffraction, using the self-similarity function as a function of the angular direction. 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. Also, we use a Cantor set obtained as a product superposition of cosine functions.
We extend the results obtained for different cases of the product superposition between periodic functions to the case of circular symmetry. The characteristics of focalization for such case is studied. We name Fresnel-Cantor zone plate to the structures obtained.
The study of properties of the diffracted field, when two Cantor diffraction gratings are superimposed is important for establishing the relationships between the geometry of each fractal grating and the corresponding structure of the diffracted field. Here, we consider simple examples related with the Moire effect, since the Cantor gratings used are built through periodic functions.
We are interested in the study of the diffraction from complex apertures with the use of conformal mapping transformation. We use polygonal structures and the Riemann mapping theorem to transform these structures into a circular region and so to develop the calculation of the diffracted fields along the Fresnel region. We show some cases for fractal apertures with Koch boundary.
In this work, we superimpose tow and more random images of irregular particles, using different statistics and concentration for the texture distributions. This is achieved using different random generators to obtain binary images in the distribution of these particles. For these case, the box counting dimension is calculated and we obtain the relation between this dimension and the corresponding structure. In this way, we obtain a fractal characterization for the superposition of these binary images.
The method of conformal mapping, through the Schwartz-Christoffel transformation, is applied to solve the scattering of electromagnetic beams from planar surface with a Koch corrugation. We use the integral method with the calculation of admittance of the transformed plane which is the kernel in the equations. The problem is planted for both polarization for the far field.
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