Search results for "Cantor set"
showing 5 items of 15 documents
Ophthalmic: Laboratorio virtual para el diseño de nuevas lentes oftálmicas
2013
This work presents a new virtual laboratory, OPHTALMIC, developed with MATLAB GUI for using in Optics and Optometry courses as a computer tool for studying the focusing properties of multifocal diffractive both on unconventional structures both periodic and aperiodic. This virtual laboratory enables students to quickly and easily analyze the influence of the different parameters of construction and find the best solution for a user.
Cantor Dust Zone Plates
2013
In this paper we use the Cantor Dust to design zone plates based on a two-dimensional fractal for the first time. The pupil function that defines the coined Cantor Dust Zone Plates (CDZPs) can be written as a combination of rectangle functions. Thus CDZPs can be considered as photon sieves with rectangular holes. The axial irradiances produced by CDZPs of different fractal orders are obtained analitically and experimentally, analyzing the influence of the fractality. The transverse irradiance patterns generated by this kind of zone plates has been also investigated.
Polyadic devil's lenses.
2009
Devil’s lenses (DLs) were recently proposed as a new kind of kinoform lens in which the phase structure is characterized by the “devil’s staircase” function. DLs are considered fractal lenses because they are constructed following the geometry of the triadic Cantor set and because they provide self-similar foci along the optical axis. Here, DLs are generalized allowing the inclusion of polyadic Cantor distributions in their design. The lacunarity of the selected polyadic fractal distribution is an additional design parameter. The results are coined polyadic DLs. Construction requirements and interrelations among the different parameters of these new fractal lenses are also presented. It is …
Axial behaviour of Cantor ring diffractals
2003
Cantor ring diffractals describe rotationally symmetric pupils constructed from a one-dimensional polyadic Cantor set. The influence on the axial irradiance of several fractal descriptors of such pupils, including fractal dimension, number of gaps and lacunarity, are investigated. It is shown that, contrary to their transversal response, the axial behaviour of these pupils does not resemble the fractal structure of the aperture. The sensitivity of such pupils to the spherical aberration is also analysed.
Free vs. Locally Free Kleinian Groups
2015
Abstract We prove that Kleinian groups whose limit sets are Cantor sets of Hausdorff dimension < < 1 are free. On the other hand we construct for any ε > > 0 an example of a non-free purely hyperbolic Kleinian group whose limit set is a Cantor set of Hausdorff dimension < < 1 + + ε.