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We introduce a novel framework for upsampled Point Spread Function (PSF) modeling using pixel-level Bayesian inference. Accurate PSF characterization is critical for precision measurements in many fields including: weak lensing, astrometry,…
We consider the two-point correlation function of the photodissociation cross section in molecules where the fragmentation process is indirect, passing through resonances above the dissociation threshold. In the limit of overlapping…
We present a new purely equilibrium microscopic approach to the description of liquid-glass transition in terms of space symmetry breaking of three- and four-particle distribution functions in the cases of two and three dimensions,…
We consider an optical diffraction grating in which the spatial distribution of open slits forms a fractal set. The Fraunhofer diffraction patterns through the fractal grating are obtained analytically for the simplest triad Cantor type and…
The boost-invariant longitudinal space, defined by the parameter $\sigma=\frac{1}{2}b^-P^+$ can be studied from the Fourier transformation of distributions over the conjugate variable skewness $\xi$. We investigate quark Wigner…
A novel approach to 3D surface imaging is proposed, allowing for the continuous sampling of 3D surfaces to extract localized perspective transformation coefficients from Fourier spectrum analysis of projected patterns. The mathematical…
Fourier methods well known in signal processing are applied to three-dimensional wave propagation problems. The Fourier transform of the Green function, when written explicitly in terms of a real-valued spatial frequency, consists of…
In this Chapter we review the challenges of, and opportunities for, 3D spectroscopy, and how these have lead to new and different approaches to sampling astronomical information. We describe and categorize existing instruments on 4m and 10m…
In this paper are reviewed various designs of advanced, multi-aperture optical systems dedicated to high angular resolution imaging or to the detection of exo-planets by nulling interferometry. A simple Fourier optics formalism applicable…
We propose a compact snapshot monocular depth estimation technique that relies on an engineered point spread function (PSF). Traditional approaches used in microscopic super-resolution imaging such as the Double-Helix PSF (DHPSF) are…
Uncertainty in the wide-angle Point Spread Function (PSF) at large angles (tens of arcseconds and beyond) is one of the dominant sources of error in a number of important quantities in observational astronomy. Examples include the stellar…
Multi-wavelength study of extended astronomical objects requires combining images from instruments with differing point spread functions (PSFs). We describe the construction of convolution kernels that allow one to generate…
By use of window functions, time-frequency analysis tools like Short Time Fourier Transform overcome a shortcoming of the Fourier Transform and enable us to study the time- frequency characteristics of signals which exhibit transient os-…
Diffraction of coherent x-ray beams is treated through the Fractionnal Fourier transform. The transformation allow us to deal with coherent diffraction experiments from the Fresnel to the Fraunhofer regime. The analogy with the…
In this paper we show how the spectral theory based on the notion of $S$-spectrum allows us to study new classes of fractional diffusion and of fractional evolution processes. We prove new results on the quaternionic version of the…
The distribution of radiation is investigated for the modeless laser having a multilobe mirror with the lobes (planes) inclined by small angles to optical axis. It is shown that change of the direction resulting from many passages of a ray…
Different theoretical methods used for the description of diffractive processes in small-x deep inelastic scattering are reviewed. The semiclassical approach, where a partonic fluctuation of the incoming virtual photon scatters off a…
Consider the incidence of a time-harmonic electromagnetic plane wave onto a biperiodic dielectric grating, where the surface is assumed to be a small and smooth perturbation of a plane. The diffraction is modeled as a transmission problem…
We investigate the point spread function of a multimode fiber. The distortion of the focal spot created on the fiber output facet is studied for a variety of the parameters. We develop a theoretical model of wavefront shaping through a…
Spectral functions of symmetric matrices -- those depending on matrices only through their eigenvalues -- appear often in optimization. A cornerstone variational analytic tool for studying such functions is a formula relating their…