The small-slope approximation method applied to a three-dimensional slab with rough boundaries

75 pages, 45 figuresInternational audienceIn this paper we present new results on the small-slope approximation method. We consider different three-dimensional structures like a randomly rough surface separating two different media and a slab delimited by one or two rough surfaces. We extend the small-slope approximation to the fourth order terms of the perturbative development, and give the expression of the cross-sections for the different polarization states. Numerical examples are treated for the studied structures and a comparison with the small-perturbation is discussed

Theoretical model for diffuse optical wave scattering from a three-dimensional slab bounded by randomly rough surfaces

7 pages, 2 figures. Contribution to the 23rd International Review of Progress in Applied Computational Electromagnetics (ACES 2007) March 19-23, 2007 Verona, Italy.Our purpose is to show how light can interact with slab bounded by rough surfaces. In this paper, we consider three-dimensional structures bounded by two-dimensional weakly rough surfaces or by two-dimensional randomly rough surfaces with small-slope. We discuss the extension of the small-slope approximation method to slabs with two randomly rough surfaces. The fourth order terms of the perturbative development are required in order to take into account the interactions between the randomly rough surfaces

Heuristic imaging from generic projections: backprojection outside the range of the Radon transform

Reflective tomography is an efficient method for optical imaging in the visible and near infrared ranges. It computes empirical reconstructions based on algorithms from X-ray tomography. This subject introduces mathematical gaps to be filled, about the meaning of the reconstructions, and about their artifacts. To tackle these questions, we study more generally the filtered backprojection on projections outside the range of the Radon transform. We consider generic projections that can involve any kind of physical and geometric parameters. We claim that the backprojection contains partially the geometry of the original scene. More precisely, we compare the singularities of the backprojection with the singularities of a representation of the scene. This comparison of wavefront sets, inspired by studies of the artifacts in X-ray tomography, is based on microlocal analysis. It gives a precise meaning to the well-reconstructed geometry, describes the invisible parts, and the artifacts. We illustrate the heuristic and the analysis principle on canonical cases that belong to various fields: shape from silhouettes, constructible tomography, cloaking, reconstruction from cartoon images, imaging of occluded lambertian objects. Numerical results show the relevance of the heuristic and its analysis. In a word, this study provides a mathematical framework that covers the solver of reflective tomography, and exhibits an imaging method whose range of application is wide

Imagerie laser

We derive an original direct imaging method of an object. It is based on topological derivatives, and aims at inverting the amplitude of waves that are retropropagated after laser illuminations

Reflective filtered backprojection

AbstractThis note introduces reflective tomography in a mathematical framework. The effect of the filtered backprojection on reflective-kind projections is studied: a reflective projection is defined, tomographic filtering of such a projection is analysed, and so is the filtered backprojection. The results emphasize the role of the contrasts: we get a decomposition in which the contributions of the discontinuities and of the tangential variations are enlightened

A Numerical Study of Absorption by Multilayered Biperiodic Structures

10 pages, revtex, osa aps sty, 13 eps figuresInternational audienceWe study the electromagnetic scattering by multilayered biperiodic aggregates of dielectric layers and gratings of conducting plates. We show that the characteristic lengths of such structures provide a good control of absorption bands. The influence of the physical parameters of the problem (sizes, impedances) is discussed

Near-infrared active polarimetric and multispectral laboratory demonstrator for target detection

International audienceWe report on the design and exploitation of a real-field laboratory demonstrator combining active polarimetric and multispectral functions. Its building blocks, including a multiwavelength pulsed optical parametric oscillator at the emission side and a hyperspectral imager with polarimetric capability at the reception side, are described. The results obtained with this demonstrator are illustrated on some examples and discussed. In particular it is found that good detection performances rely on joint use of intensity and polarimetric images, with these images exhibiting complementary signatures in most cases

Excited state absorption : a key phenomenon for the improvement of biphotonic based optical limiting at telecommunication wavelengths

International audienceSpectroscopic properties, two-photon absorption (TPA) and excited state absorption (ESA), of two organic cyanine dyes and of a ruthenium based organometallic cyanine are compared in order to rationalize their similar ns-optical power limiting (OPL) efficiency in the telecommunication wavelength range. The TPA contribution to the ns-OPL behavior is higher for both organic cyanines, while the main process is a TPA-induced ESA in the case of the organometallic system, in which the ruthenium induces a broadening of the NIR-ESA band and resulting in a strong spectral overlap between TPA and ESA spectra

A new application of reduced Rayleigh equations to electromagnetic wave scattering by two-dimensional randomly rough surfaces

The small perturbations method has been extensively used for waves scattering by rough surfaces. The standard method developped by Rice is difficult to apply when we consider second and third order of scattered fields as a function of the surface height. Calculations can be greatly simplified with the use of reduced Rayleigh equations, because one of the unknown fields can be eliminated. We derive a new set of four reduced equations for the scattering amplitudes, which are applied to the cases of a rough conducting surface, and to a slab where one of the boundary is a rough surface. As in the one-dimensional case, numerical simulations show the appearance of enhanced backscattering for these structures.Comment: RevTeX 4 style, 38 pages, 16 figures, added references and comments on the satellites peak