Perturbative methods in theory of phase gratings

Perturbative methods are generally invoked for problems in which there is a small parameter. In the theory of phase gratings, the small parameter is the modulation amplitude of the refractive index, and the classical perturbative method is then the Born approximation. But it is well-known that the Born approximation fails at the Bragg resonance, however small the modulation amplitude is. In this paper a perturbative method is presented, which is working at Bragg resonance as well. A sequence of numbers (called the eigenvalues of the problem) are introduced; they depend on the geometrical configuration (incidence angle, grating parameters). It is shown that the Bragg resonance occurs if (and only if) two eigenvalues become equal. These eigenvalues – and the corresponding solutions of the equations – can be expanded in powers of the modulation amplitude. The expansions are different according to whether the corresponding eigenvalue is simple or double. Explicit formulae or algorithms are given. Computing programs have been written from them. These programs are efficient

Analyse de formes par moiré

We present a mathematical analysis of moiré phenomena for shape recognition. The basic theoretical concept - and tool - will be the $contour function$. We show that the mathematical analysis is greatly simplified by the systematic recourse to this tool. The analysis presented permits a simultaneous treatment of two different modes of implementing the moiré technique : the direct mode (widely used and well-known), and the converse mode (scarcely used). The converse mode consists in computing and designing a grating especially for one model of object, in such a manner that if (and only if) the object is in conformity with the prescribed model, the resulting moiré fringes are parallel straight lines. We give explicit formulas and algorithms for such computations.
Nous présentons une analyse mathématique du moiré permettant une reconnaissance des formes. Le concept théorique de base est celui de “ fonction de contour ”. Nous montrons que l'analyse mathématique est simplifiée en faisant appel à ces fonctions. De plus, la méthode proposée permet de traiter d'une manière unifiée les deux différents modes d'utilisation des techniques de moiré : le mode direct (le plus utilisé et le mieux connu), et le moiré inverse, qui consiste, pour un modèle d'objet donné, à calculer et réaliser un réseau spécifique, tel que si (et seulement si) un objet est conforme au modèle, les franges de moiré obtenues seront des lignes droites parallèles. Nous proposons des formules explicites et des algorithmes pour ces traitements.

Innovative fiber optic sensor for hydrogen detection

A new design of a fiber optic sensor using Palladium as a sensitive layer is presented. In this new configuration, a transducer layer is deposited on a multimode fiber (without the optical cladding). The transducer layer is a multilayer stack based on a silver, a silica and a Pd layer. The spectral modulation of the light transmitted by the fiber allows to detect hydrogen. The sensor is only sensitive to the Transverse Magnetic polarized light and the Transverse Electric polarized light can be used as a reference signal. The multilayer thickness defines the sensor performance. The Silica thickness tunes the resonant wavelength, whereas the silver and Pd thickness determines the sensor sensitivity. We present some results obtained for different multilayer Pd configuration

Detailed spectral monitoring of different combustible blends based on gasoline, ethanol and methanol using FT-Raman spectroscopy

The use of mixtures of oil-based fuels with organic chemical components (e.g. ethanol, methanol) has been gaining ground in recent years. Several countries try nowadays to replace part of the fossil fuels for various reasons including economics, sustainability or optimization of resources. The characteristics of these combustiblerelated chemical component blends can be analyzed by different means. Optical spectral analysis (e.g. Raman, Fourier-transforminfrared, etc.) can extract inmany casesmost of the required information concerning themolecular structure of a determined chemical sample in an effective and clean manner. Experimental detailed Raman spectra fromvarious gasoline-ethanol blends and a gasoline-ethanolmethanol blend are presented. The Raman spectral information obtained has been used for approximated quantitative analysis with no additional chemical marker or complicated calibration methods. The analysis has been performed using a self-designed, low-cost, robust and frequency precise Fourier transform Raman (FT-Raman) spectrometer. This proposed FT-Raman spectrometer has been constructed with a Michelson interferometer, an in-house designed photon counter, and a sensitive trans-impedance photo-detector. Additional complex hardware was not used to compensate the mechanical or thermal drifts disturbances in the interferometer. For accurate spectral calculation an interference pattern generated by a low-power Helium-Neon laser (wavelength λ=632.816nm)was used. The resulting spectral data are in the range of 0*cm-1 to 3500*cm-1. The resolution of these Raman spectra is 1.66*cm-1. Higher resolutions are possible since the scanning distances in the Michelson interferometer can be extended substantially before instrumental effects appear. A comparison of the experimental results obtained with standard Raman shift values revealed a satisfactory accuracy and precision in frequency detection