Search results for "Functional analysis"

Impact of a temporal sinusoidal phase modulation on the optical spectrum

2018

International audience; We discuss the effects of imparting a temporal sinusoidal phase modulation to a continuous wave on the frequency spectrum. While a practical analytical solution to this problem already exists, we present here a physical interpretation based on interference processes. This simple model will help the students better understand the origin of the oscillatory structure that can be observed in the resulting spectrum and that is characteristic of Bessel functions of the first kind. We illustrate our approach with an example from the field of optics.

Sub-wavelength and non-periodic holes array based fully lensless imager

2011

Abstract We present a novel concept for microscopic imaging. The proposed microscope-like device does not include an objective lens neither a condenser. Instead, a metallic plate of sub-wavelength hole-array with a varying pitch is used to illuminate the inspected object that is mounted very close to it. As a result, the transmitted spectrum through each hole differs from the others and therefore, each spot of the detected object is illuminated with a unique spectrum. By measuring a single spectrum that is the sum of all the spectra that are transmitted through the sample and by using spectral decomposition algorithms, the spatial transmission pattern of the object can be extracted.

Compact all-diffractive setup for spectral synthesis with non-uniform illumination

2009

Optical filters based on diffractive optical elements (DOE) have received increased attention since the development of the first synthetic spectrum as a tool for correlation spectroscopy [1]. The production of a synthetic spectrum requires the design of a DOE that transforms the spectrum associated with the incident light into the spectrum of interest. Based on this procedure, several approaches have been reported in the literature [1–4]. In general, these configurations employ angular dispersion elements for spectrum tailoring, so they are restricted to working off-axis, and most of them need an extra focusing refractive lens.

Line Identification of Atomic and Ionic Spectra of Holmium in the Visible Spectral Range. I. Spectrum of Ho i

2019

Molecular correlation functions for uniaxial ellipsoids in the isotropic state

2006

We perform event-driven molecular dynamics simulations of a system composed by uniaxial hard ellipsoids for different values of the aspect-ratio and packing fraction . We compare the molecular orientational-dependent structure factors previously calculated within the Percus-Yevick approximation with the numerical results. The agreement between theoretical and numerical results is rather satisfactory. We also show that, for specific orientational quantities, the molecular structure factors are sensitive to the particle shape and can be used to distinguish prolate from oblate ellipsoids. A first-order theoretical expansion around the spherical shape and a geometrical analysis of the configura…

The broad-band spectrum of Cyg X-2 with INTEGRAL

2005

We study the broad band (3-100 keV) spectrum of Cygnus X-2 with INTEGRAL. We find that the spectrum is well fitted by a Comptonized component with a seed-photons temperature of ~1 keV, an electron temperature of ~3 keV and an optical depth tau ~ 8. Assuming spherical geometry, the radius of the seed-photons emitting region is ~17 km. The source shows no hard X-ray emission; it was detected only at a 3 sigma level above 40 keV. We also analyzed public ISGRI data of Cyg X--2 to investigate the presence of a hard X-ray component. We report the possible presence of hard X-ray emission in one data set.

Star-products, spectral analysis, and hyperfunctions

2000

We study the ⋆-exponential function U(t;X) of any element X in the affine symplectic Lie algebra of the Moyal ⋆-product on the symplectic manifold (ℝ × ℝ;ω). When X is a compact element, a natural specific candidate for U (t;X) to be the exponential function is suggested by the study we make in the non-compact case. U (t;X) has singularities in the t variable. The analytic continuation U(z;X),z = t + iy, defines two boundary values δ+ U (t;X) = limy↓0 U(z;X) and δ-(t;X) = limy↑0 U(z; X). δ+ U (t;X) is a distribution while δ- U (t;X) is a Beurling-type, Gevrey-class s — 2 ultradistribution. We compute the Fourier transforms in t of δ± U (t;X). Both Fourier spectra are discrete but different …

Theoretical study of the discrete and continuum spectrum of BeH

2008

The transition intensities supplied in this Letter are directly connected with a description of the discrete and continuum spectrum of BeH. An attempt to meet our goal requires the calculation of the absorption oscillator strengths of several transitions to Rydberg states of BeH, together with differential oscillator strengths which give rise to different dipole-allowed photoionization channels from the molecular ground state. The calculations have been performed with the molecular-adapted quantum defect orbital (MQDO) approach. Predictions of new spectroscopic data on BeH at energies where high Rydberg transitions can take place, including the continuum region of the spectrum have been mad…

States of 13C with abnormal radii

2016

Differential cross-sections of the elastic and inelastic 13C + α scattering were measured at E(α) = 90 MeV. The root mean-square radii () of 13C nucleus in the states: 8.86 (1/2−), 3.09 (1/2+) and 9.90 (3/2−) MeV were determined by the Modified diffraction model (MDM). The radii of the first two levels are enhanced compared to that of the ground state of 13C, confirming the suggestion that the 8.86 MeV state is an analogue of the Hoyle state in 12C and the 3.09 MeV state has a neutron halo. Some indications to the abnormally small size of the 9.90 MeV state were obtained. peerReviewed

Cluster rotational bands in 11B

2016

Differential cross-sections of 11B+α inelastic scattering at E(α) = 65 MeV leading to most of the known 11B states at excitation energies up to 14 MeV were measured [1]. The data analysis was done using Modified diffraction model (MDM) [2] allowing determining radii of excited states. Radii of the states with excitation energies less than ∼ 7 MeV coincide with the radius of the ground state with an accuracy not less than 0.1 - 0.15 fm. This result is consistent with traditional view on shell structure of low-lying states in 11B. Most of the observed high-energy excited states are distributed among four rotational bands. Moments of inertia of band states are close to the moment of inertia of…