Related papers: Fourier Transform of Annular Beams
Fraunhofer diffraction plays a vital role in experimental physics not only because it accurately describes the behaviour of light in the usual propagation limit, but also because it links the diffracted light with the scattering object…
These informal notes consider Fourier transforms on a simple class of nice functions and some basic properties of the Fourier transform.
In this paper we show an alternative way of defining Fourier Series and Transform by using the concept of convolution with exponential signals. This approach has the advantage of simplifying proofs of transforms properties and, in our view,…
We describe the range of the attenuated ray transform of a unitary connection on a simple surface acting on functions and 1-forms. We use this to determine the range of the ray transform acting on symmetric tensor fields.
Researchers from a broad spectrum of scientific and engineering disciplines are increasingly using near-field infrared spectroscopic techniques to characterize materials nondestructively and with nanoscale spatial resolution. However,…
Some properties of the fractional Fourier transform, which is used in information processing, are presented in connection with the tomography transform of optical signals. Relation of the Green function of the quantum harmonic oscillator to…
Fourier and fractional-Fourier transformations are widely used in theoretical physics. In this paper we make quantum perspectives and generalization for the fractional Fourier transformation (FrFT). By virtue of quantum mechanical…
We report a new experimental technique for quantifying the angular distribution of light scattered by single plasmonic and metamaterial nanoscatterers, based on Fourier microscopy in a dark field confocal set up. This new set up is a…
Nonuniform Fourier data are routinely collected in applications such as magnetic resonance imaging, synthetic aperture radar, and synthetic imaging in radio astronomy. To acquire a fast reconstruction that does not require an online inverse…
We propose a fractional variant of Mellin's transform which may find an application in the Conformal Field Theory. Its advantage is the presence of an arbitrary parameter which may substantially simplify calculations and help adjusting…
Finite field transforms have many applications and, in many cases, can be implemented with a low computational complexity. In this paper, the Z Transform over a finite field is introduced and some of its properties are presented.
When an optical beam propagates through a turbulent medium such as the atmosphere or ocean, the beam will become distorted. It is then natural to seek the best or optimal beam that is distorted least, under some metric such as intensity or…
With the help of a simple model, we analyze Scanning Tunneling Microscopy images of simple and double moir\'e patterns resulting from misoriented bi- and tri-layers graphene stacks. It is found that the model reproduces surprisingly well…
An extension may be proposed to the intensity interferometer of Hanbury Brown and Twiss to provide the Fourier phase measurement by the use of third-order intensity correlations. It is well known that interferometric reconstruction of…
Fourier imaging is an indirect imaging method which records the diffraction pattern of the object scene coherently in the focal plane of the imaging system and reconstructs the image using computational resources. The spatial resolution,…
In this article, we compare a set of Wave Front Sensors (WFS) based on Fourier filtering technique. In particular, this study explores the "class of pyramidal WFS" defined as the 4 faces pyramid WFS, all its recent variations (6, 8 faces,…
Fourier analysis plays a major role in the analysis and understanding of many phenomena in physics and contemporary engineering. However, students, who have often discovered this notion through numerical tools, do not necessarily understand…
We study Fourier theory on quantum Euclidean space. A modified version of the general definition of the Fourier transform on a quantum space is used and its inverse is constructed. The Fourier transforms can be defined by their Bochner's…
Many phenomena are described by bivariate signals or bidimensional vectors in applications ranging from radar to EEG, optics and oceanography. The time-frequency analysis of bivariate signals is usually carried out by analyzing two separate…
The present chapter [submitted for publication in "Fourier Transforms, Theory and Applications", G. Nikolic (Ed.), InTech (Open Access Publisher), Vienna, 2011] is concerned with the introduction and study of a quadratic discrete Fourier…