Related papers: Fourier Transform of Annular Beams
We study the properties of different type of transforms by means of operational methods and discuss the relevant interplay with many families of special functions. We consider in particular the binomial transform and its generalizations. A…
We present both experimentally and theoretically the transformation of radially and azimuthally polarized vector beams when they propagate through a biaxial crystal and are transformed by the conical refraction phenomenon. We show that, at…
Fourier transform (FT) plays a crucial role in a broad range of applications, from enhancement, restoration and analysis through to security, compression and manipulation. The Fourier transform (FT) is a process that converts a function…
We consider finite approximations of a fractal generated by an iterated function system of affine transformations on $\mathbb{R}^d$ as a discrete set of data points. Considering a signal supported on this finite approximation, we propose a…
We show that with an appropriate surface modification, a slab of photonic crystal can be made to allow wave transmission within the band gap. Furthermore, negative refraction and all-angle-negative-refraction (AANR) can be achieved by this…
Directional transforms have recently raised a lot of interest thanks to their numerous applications in signal compression and analysis. In this letter, we introduce a generalization of the discrete Fourier transform, called steerable DFT…
In this brief note we repeat an earlier calculation of the Fourier transformed scanning tunneling spectra of the $d$-density wave (DDW) phase using a different band structure, which is more realistic and consistent with the angle resolved…
Optical two-dimensional Fourier-transformed (2DFT) spectroscopy is used to study the coherent optical response of potassium vapor in a thin transmission cell. Rephasing and non-rephasing spectra of the D1 and D2 transitions are obtained and…
The parametric fluorescence from a nonlinear crystal forms a conical radiation pattern. We measure the angular and spectral distributions of parametric fluorescence in a beta-barium borate crystal pumped by a 405-nm diode laser employing…
This report will explore and answer fundamental questions about taking Fourier Transforms and tying it with recent advances in AI and neural architecture. One interpretation of the Fourier Transform is decomposing a signal into its…
The spectral analysis of the operator Fourier truncated on the positive half-axis is done.
In this paper, we define a new transform called the Gabor quaternionic Fourier transform (GQFT), which generalizes the classical windowed Fourier transform to quaternion valued-signals, we give several important properties such as the…
Scalar diffraction calculations such as the angular spectrum method (ASM) and Fresnel diffraction, are widely used in the research fields of optics, X-rays, electron beams, and ultrasonics. It is possible to accelerate the calculation using…
The fractional Fourier transform (FrFT), a fundamental operation in physics that corresponds to a rotation of phase space by any angle, is also an indispensable tool employed in digital signal processing for noise reduction. Processing of…
In this work, we present the theoretical and experimental study of the propagation of Airy beams when passing through two convex lenses with different focal distances. The theoretical analysis is presented from a matrix optical model for an…
In the present paper, the wavelet transform of Fractal Interpolation Function (FIF) is studied. The wavelet transform of FIF is obtained through two different methods. The first method uses the functional equation through which FIF is…
As an appropriate analog of the Euclidean short-time Fourier transform, we study a windowed version of the Helgason-Fourier transform on the complex unit ball and translate the theory of modulation/coorbit spaces. As a result, atomic…
The effect of the laser linewidth on the resonance fluorescence spectrum of a two-level atom is revisited. The novel spectral features, such as hole-burning and dispersive profiles at line centre of the fluorescence spectrum are predicted…
We consider a topological integral transform of Bessel (concentric isospectral sets) type and Fourier (hyperplane isospectral sets) type, using the Euler characteristic as a measure. These transforms convert constructible $\zed$-valued…
We survey and investigate some computational aspects of the Fourier-Mukai transform.