Search results for "Number"
showing 10 items of 3939 documents
Apparent magic numbers in embedded Ti-O clusters
2003
Stable clusters constituted of four ${\mathrm{TiO}}_{2}$ entities have been evidenced in nanometer-sized spinel oxides by a combination of diffraction and x-ray-absorption experiments. Contrary to free clusters, the size of the embedded clusters is strongly determined by the constraints imposed by the surrounding matrix so that the magic number of four is in fact specific to the matrix and only then apparent.
Fractal zone plates with variable lacunarity.
2009
Fractal zone plates (FZPs), i.e., zone plates with fractal structure, have been recently introduced in optics. These zone plates are distinguished by the fractal focusing structure they provide along the optical axis. In this paper we study the effects on this axial response of an important descriptor of fractals: the lacunarity. It is shown that this parameter drastically affects the profile of the irradiance response along the optical axis. In spite of this fact, the axial behavior always has the self-similarity characteristics of the FZP itself.
Devil’s vortex-lenses
2009
In this paper we present a new kind of vortex lenses in which the radial phase distribution is characterized by the "devil's staircase" function. The focusing properties of these fractal DOEs coined Devil's vortex-lenses are analytically studied and the influence of the topological charge is investigated. It is shown that under monochromatic illumination a vortex devil's lens give rise a focal volume containing a delimited chain of vortices that are axially distributed according to the self-similarity of the lens.
Diffraction by m-bonacci gratings
2015
We present a simple diffraction experiment with m-bonacci gratings as a new interesting generalization of the Fibonacci ones. Diffraction by these nonconventional structures is proposed as a motivational strategy to introduce students to basic research activities. The Fraunhofer diffraction patterns are obtained with the standard equipment present in most undergraduate physics labs and are compared with those obtained with regular periodic gratings. We show that m-bonacci gratings produce discrete Fraunhofer patterns characterized by a set of diffraction peaks which positions are related to the concept of a generalized golden mean. A very good agreement is obtained between experimental and …
Multifractal zone plates
2010
We present multifractal zone plates (MFZPs) as what is to our knowledge a new family of diffractive lenses whose structure is based on the combination of fractal zone plates (FZPs) of different orders. The typical result is a composite of two FZPs with the central one having a first-order focal length f surrounded by outer zones with a third-order focal length f. The focusing properties of different members of this family are examined and compared with conventional composite Fresnel zone plates. It is shown that MFZPs improve the axial resolution and also give better performance under polychromatic illumination.
Wavelength-compensated Fourier and Fresnel transformers: a unified approach
2007
We recognize that one can adapt any dispersion-compensated broadband optical Fourier transformer to achieve wavelength compensation in the Fresnel diffraction region just by inserting a diffractive lens at the input plane and vice versa. This unification procedure is employed in a second stage in the design of a novel hybrid (diffractive-refractive) optical setup that provides, in a sequential way, nearly wavelength-independent Fresnel diffraction patterns in the irradiance of the object transmittance.
Focal shift in optical waves with off-axis focus
2003
We present a formulation for a suitable description of the focal shift in optical waves that have an off-axis focus. This shift that is primarily produced along the chief axis is given in terms of the focal distance and depends only on a parameter that is named as the generalized Fresnel number. Any non-uniform, either truncated and non-apertured optical beam with off-axis focus may be considered.
Single-zone-plate achromatic fresnel-transform setup: Pattern tunability
1997
Abstract White-light point-source illumination results in the chromatic blurring of the optical field diffracted by an aperture. In this paper, broadband dispersion compensation for a continuous set of Fresnel diffraction patterns associated with an arbitrary input transparency is carried out, in a sequential way, by means of a single on-axis blazed zone plate. The input is illuminated with a white-light converging spherical wavefront and the diffractive lens is inserted at the virtual source plane. We recognize that the position of the input along the optical axis permits to achieve a different achromatic Fresnel diffraction pattern with low residual chromatic aberrations. The theory deriv…
Three-dimensional behavior of apodized nontelecentric focusing systems.
2002
The scalar field in the focal volume of nontelecentric apodized focusing systems cannot be accurately described by the Debye integral representation. By use of the Fresnel–Kirchhoff diffraction formula it is found that, if the aperture stop is axially displaced, the focal-volume structure is tuned. We analyze the influence of the apodizing function and find that, whereas axially superresolving pupil filters are highly sensitive to the focal-volume reshaping effect, axially apodizing filters are more inclined to the focal-shift effect.
Effective Fresnel-number concept for evaluating the relative focal shift in focused beams
1998
We report on an analytical formulation, based on the concept of effective Fresnel number, to evaluate in a simple way the relative focal shift of rotationally nonsymmetric scalar fields that have geometrical focus and moderate Fresnel number. To illustrate our approach, certain previously known results and also some new focusing setups are analytically examined.