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The Replica Fourier Transform is the generalization of the discrete Fourier Transform to quantities defined on an ultrametric tree. It finds use in con- junction of the replica method used to study thermodynamics properties of disordered…
Discrete trigonometric transformations, such as the discrete Fourier and cosine/sine transforms, are important in a variety of applications due to their useful properties. For example, one well-known property is the convolution theorem for…
Most research on astrophysical lensing has been conducted using the geometric optics framework, where there exists a clear concept of lensing images. However, wave optics effects can be important for coherent sources, e.g. pulsars, fast…
We describe the change of the spatial distribution of the state of polarisation occurring during two-dimensional imaging through a multilayer and in particular through a layered metallic flat lens. Linear or circular polarisation of…
A method to create instructive, nonuniform aperture functions using spatial frequency filtering is described. The diffraction from a single slit in the Fresnel limit and the interference from a double slit in the Fraunhofer limit are…
Point Spread Function (PSF) modeling is a central part of any astronomy data analysis relying on measuring the shapes of objects. It is especially crucial for weak gravitational lensing, in order to beat down systematics and allow one to…
The basic principle of astronomical interferometry is to derive the angular distribution of radiation in the sky from the Fourier transform of the electric field on the ground. What is so special about the Fourier transform? Nothing, it…
We propose a method based on sinc series approximations for computing the Rayleigh-Sommerfeld and Fresnel diffraction integrals of optics. The diffraction integrals are given in terms of a convolution, and our proposed numerical approach is…
The Fractional Fourier Transform (FrFT) has widespread applications in areas like signal analysis, Fourier optics, diffraction theory, etc. The Holomorphic Fractional Fourier Transform (HFrFT) proposed in the present paper may be used in…
The availability of neutron spallation-source instruments that provide total scattering powder diffraction has led to an increased application of real-space structure analysis using the pair distribution function. Currently, the analytical…
Based on diffraction theory and the propagation of the light, Fourier optics is a powerful tool allowing the estimation of a visible-range imaging system to transfer the spatial frequency components of an object. The analyses of the imaging…
Typically the use of the Rayleigh-Sommerfeld diffraction formula as a photon propagator is widely accepted due to the abundant experimental evidence that suggests that it works. However, a direct link between the propagation of the…
We present a theoretical study of a spectral filter, which consists of a diffraction grating, a coupling lens, and an optical fiber. As the diffracted beam is highly dispersed spatially, coupling into an optical fiber naturally creates a…
After launching and deploying a sparse space telescope, fine tuning is required to correct for inaccurate initial placement of its elements. We selected unique shapes and locations of these telescope aperture segments, to be able to…
Within the expansive domain of optical sciences, achieving the precise characterization of light beams stands as a fundamental pursuit, pivotal for various applications, including telecommunications and imaging technologies. This study…
A new definition of a fractional derivative has recently been developed, making use of a fractional Dirac delta function as its integral kernel. This derivative allows for the definition of a distributional fractional derivative, and as…
A problem of scattering by a Dirichlet right angle on a discrete square lattice is studied. The waves are governed by a discrete Helmholtz equation. The solution is looked for in the form of the Sommerfeld integral. The Sommerfeld…
The spread of valence band Wannier functions in semiconductors and insulators is a characteristic property that gives a rough estimation of how insulating is the material. We elaborate that the gauge-invariant part of the spread can be…
The problem of diffraction by a Dirichlet quarter-plane (a flat cone) in a 3D space is studied. The Wiener-Hopf equation for this case is derived and involves two unknown (spectral) functions depending on two complex variables. The aim of…
The Point Spread Function (PSF) is a key figure of merit for specifying the angular resolution of optical systems and, as the demand for higher and higher angular resolution increases, the problem of surface finishing must be taken…