The Point Spread Function (PSF) indirectly encodes the wavefront aberrations of an optical system and therefore is a metric of the system performance. Analysis of the PSF properties is useful in the case of diffractive optics where the wavefront emerging from the exit pupil is not necessarily continuous and consequently not well represented by traditional wavefront error descriptors such as Zernike polynomials. The discontinuities in the wavefront from diffractive optics occur in cases where step heights in the element are not multiples of the illumination wavelength. Examples include binary or N-step structures, multifocal elements where two or more foci are intentionally created or cases where other wavelengths besides the design wavelength are used. Here, a technique for expanding the electric field amplitude of the PSF into a series of orthogonal functions is explored. The expansion coefficients provide insight into the diffraction efficiency and aberration content of diffractive optical elements. Furthermore, this technique is more broadly applicable to elements with a finite number of diffractive zones, as well as decentered patterns.

A series of sol-gel based photopolymerizable silica glass for holographic storage have been synthesized via a facile chemical design in an effort to overcome the cracking problem incurred during the irradiation stage. The holographic composite material includes a low molecular weight polydimethylsiloxane (PDMS) with end-capped hydroxyl groups, an epoxide-containing coupling agent, a photopolymerizable acrylate monomer, and the sol-gel-derived silica matrix. Inclusion of PDMS provides improved compression stress and strain and toughness over the original unmodified samples, without deterioration on the diffraction efficiency (£b). A plateau value of £b ~ 40 % can be found under a beam power of 5.02 mW. Correlation between the molecular weight of acrylate polymer and £b of the holographic composite material is described and the discrepancies analyzed. The premature saturation of polymerization in the holographic system is attributed to the retarded free radical polymerization within the silica matrix. Minor variation of £b with photoinitiator concentration is observed, indicating that only moderate molecular weight is required for a reasonably high £b. The crack-free mechanism is based on the chemical and physical interactions within the material system. We also investigated the pore size and volume effect for optical properties, especially in studies of diffraction efficiency. With mixing rubber additives, the pore characteristics change via measurement of BET technique. The results indicated that moderate pore size made high diffraction efficiency for porous matrix and some characterizations also were presented. On the other hand, the optical application of this recording medium was described via 3D projected fringes profilometry (PFP) measurement. We recorded coded pattern on medium by employing fiber devices as light source. Using endoscope as image-derived tool, we get double-projected fringe images on tiny object. By PFP technique, a performed retrieved image can be achieved.

A series of photopolymerizable silica for optical storage has been prepared using sol-gel process in this study. The inorganic-organic hybrid materials were based on methacroloxy-propyl-trimethoxysilane (MPTS) and tetraethylorthosilicate (TEOS). Thin films of the hybrids were prepared using spin coating, knife coating, and the closed-mold methods, while the knife coating showing better film flatness and controlled film thickness. Results indicate crack-free polymerizable silica can be obtained using a recipe with 1 wt% photoinitiator. Samples after irradiation shows increased transmittance, suggesting that photopolymerization did take place with the aid of photoinitiators. Spectroscopic study from FTIR indicates C=C conversion in the acrylic part of MPTS reaches 57.51%. The grating period is observed by the optical microscopy. The maximum diffraction efficiency is 48.21%, as obtained from the sample of pure MPTS. From BET measurements, the pore size of the polymerizable silica increases with the increasing amount of MPTS, consistent with the results from measurements of apparent density. Factors affecting the diffraction efficiency are analyzed; these include sample flatness, sample thickness, the conversion of monomer, and concentration of the photoinitiator. Formation mechanism of the periodic grating is proposed based on this study. Addition of MPTS can greatly alleviate problem of phase separation; yet, movement acrylic segment in MPTS is severely limited. On the other hand, samples with more TEOS tend to be densified more with decreased diffraction efficiency

No description available.

No / In recent years there has been growing interest in the use of noise barrier profiles that can enhance the diffraction efficiency of plane barriers. These are placed on the top of the barrier in order to reduce sound diffracted into the shadow zone. A variety of shapes have been tested including T-shapes, multiple-edges and various cylindrical configurations. Despite numerous demonstrations that the profiles enhance performance there is no universal agreement on how the improvements can be quantified and incorporated into noise prediction models. Without such quantification it is likely that such profiles will not receive widespread acceptance. TRL has carried out an experimental investigation of the performance of novel-shaped barriers for the Transport Research Foundation. The approach relies on quantifying diffraction efficiency in the near field using a novel application of the Maximum Length Sequence (MLS)-based method. Measurements on 4 different profiles were taken in the vertical plane perpendicular to the barrier face. Two source and four receiver positions were used and results were obtained under a range of wind conditions. Results show large differences between the efficiency of the different options with the absorptive T-shaped and multiple-edge profiles performing best.

No description available.

In dieser Arbeit werden elektrodynamische Untersuchungen von diffraktiven Röntgenoptiken mit hohen Aspektverhältnissen - sog. Volumenzonenplatten - für hochauflösende Röntgenmikroskopie im Photonenenergiebereich von 0.1-10 keV behandelt. Des Weiteren werden Verfahren zur Realisierung solcher Optiken dargestellt. Das Auflösungsvermögen von Röntgenmikroskopen ist weitgehend durch die numerische Apertur der verwendeten Objektive bestimmt. Die Apertur hängt von der äußeren Zonenbreite der Zonenplatte und der gewählten Beugungsordnung ab. Eine Auflösungssteigerung kann nur durch Verringerung der äußeren Zonenbreiten oder Abbildung in hohen Ordnungen erzielt werden. Neben hoher Ortsauflösung ist ein hinreichender Beugungswirkungsgrad die Grundlage für röntgenmikroskopische Abbildungen. Elektrodynamische Rechnungen zeigen, dass geneigte Zonenstrukturen mit hohen Aspektverhältnissen zum signifikanten Anstieg der Effizienz in hohen Beugungsordnungen führen. Diese Volumenbeugungseffekte an Zonenplatten werden mit Hilfe der rigorosen Theorie gekoppelter Wellen untersucht. Praktisch können dreidimensionale, geneigte Nanostrukturen aufgrund der extremen nanotechnologischen Anforderungen nur durch Approximierung des Neigungswinkels realisiert werden. Zur Herstellung von Zonenplatten mit hohen Aspektverhältnissen und geneigten Zonen wird ein sog. Stack-Prozess eingeführt, der auf der Überlagerung von einzelnen Zonenplattenlagen basiert. Um den Neigungswinkel der Zonen anzunähern, werden die Zonenradien dabei mit jeder Lage verringert. Die erfolgreiche Realisierung der erforderlichen Nanotechnologien führt erstmalig zur Herstellung von Multi-Lagen-Zonenplatten mit minimalen Zonenbreiten bis zu 25 nm. Multi-Lagen- und Volumenzonenplatten bieten zukünftig das Potential für gesteigerte Auflösungsvermögen im sub-10 nm Bereich für die Mikroskopie im weichen Röntgenbereich und für die Fokussierung von harter Röntgenstrahlung auf bis zu 20 nm bei gleichzeitig hohen Beugungseffizienzen. / In this thesis, electrodynamical calculations of diffractive x-ray optics with high aspect ratios – so-called volume zone plates – for high resolution x-ray microscopy in the photon energy range from 0.1 - 10 keV are presented. In addition, methods for the realization of this optics are described. The resolution of an x-ray microscope is limited by the numerical aperture of the objective. Thereby the aperture depends on the outermost zone width of the zone plate and the diffraction order which is used for imaging. Hence, the resolution can only be increased by decreasing the minimum zone width or imaging in high orders of diffraction. Besides the resolving power, the diffraction efficiency needs to be sufficiently high for zone plate based x-ray microscopy. Electrodynamical calculations show that tilted zone structures with high aspect ratios significantly increase the diffraction efficiency in selected high orders. These volume diffraction effects on zone plates were investigated by the rigorous coupled wave theory. Due to very high nanotechnological requirements, such three-dimensional, tilted nanostructures can only be realized by multiple-step zone plates. For the fabrication of zone plates with high aspect ratios and tilted zones the so-called stack process is introduced in this thesis, which is based on a superposition of single zone plate layers. For an approximation of the tilt angle of the structures the zone radii are thereby decreased with each layer. For the first time multilayer zone plates with minimum zone widths down to 25 nm were fabricated by the successful realization of the stack process in this thesis. In the future, multilayer and volume zone plates have the potential for an increased spatial resolution in the sub-10 nm range for soft x-ray microscopy and for focusing hard x-rays down to 20 nm with high diffraction efficiencies.

L’utilisation de réseaux optiques dans la géométrie de diffraction conique a connu ces dernières décennies un essor remarquable dans les domaines UV et X grâce à ses propriétés particulières: absence de l’écrantage derrière les traits du réseau aux incidences rasantes, faible dispersion angulaire limitant l’étirement temporel, efficacité de diffraction élevée. Son usage s’est imposé pour la monochromatisation d’impulsions ultra-brèves. C’est aussi l’une des deux options retenues par la Nasa pour le spectrographe à réseau de l’Observatoire à rayon X de la future mission Lynx. Ce travail de thèse contribue au développement de méthodes numériques pour modéliser les effets de diffraction par des réseaux dans une géométrie encore peu étudiée sous cet aspect. La complexité de cette étude réside dans le couplage inhérent entre les deux états fondamentaux de polarisation. Du point de vue numérique, il impose un calcul ‘’vectoriel’’, là où, en géométrie classique des calculs scalaires suffisent. Notre travail s’est appuyé sur les méthodes numériques de calcul de diffraction par des structures périodiques déjà développées dans le cadre de la géométrie classique. Ces méthodes sont basées sur la théorie différentielle, qui consiste à propager une série d’ondes planes au travers de la zone modulée. La méthode différentielle employée est complétée par l’usage de l’algorithme de propagation de la matrice réflectivité. On contourne ainsi certains problèmes de convergence. Dans la partie théorique de ce travail, ces algorithmes sont étendus pour s’adapter aux cas de géométrie oblique. Sur cette base théorique, nous avons pu développer un code de calcul, nommé COROX, fonctionnant dans toutes les géométries d’utilisation. Un certain nombre de réseau types ont été étudiés, tant en géométrie oblique que classique, pour mettre en évidence, non seulement les efficacités de diffraction mais encore les effets de polarisation, (paramètres de Stokes et matrice de Müller) ainsi que les phases spectrales. Des propriétés intéressantes ont été remarquées, comme l’existence d’une composante circulaire non négligeable diffractée par réseau lamellaire quand l’onde incidente polarisée à 45° par rapport au plan du réseau. Le comportement de la phase spectrale est également une donnée significative pour une future gestion d’impulsions ultra-brèves. Des mesures de diffraction ont été effectuées sur la ligne Métrologie du Synchrotron SOLEIL, sur un réseau blazé de 150 traits/mm. Un accord raisonnable entre efficacités mesurées et calculées est constaté si l’on tient compte de la forte rugosité du réseau étudié. / The conical geometry of optical grating diffraction has been suggested and studied, in the last 10 years, for cutting edge applications in the VUV and X-ray domains, due to its specific properties such as: absence of screen inside the grating grooves at grazing incidence, low angular dispersion which limits the temporal spread of short pulses, very high diffraction efficiencies. It has been accepted as the first choice technology for VUV short pulses monochromatization. It is also one of the two options selected by NASA, for the grating spectrograph of the future X-ray Observatory of the Lynx mission. This thesis reports our contribution to the development of numerical methods in order to model the effects of diffraction by optical gratings in this still little studied geometry. This study is made more complex by an inherent coupling between the two fundamental polarization modes. From the numerical aspect, it requires performing “vectorial” computations, whereas, in a classical diffraction geometry, scalar computations are sufficient. Our work is based on numerical methods already developed for modeling optical diffraction by periodic structures in the framework of classical geometry. These methods are using on the differential theory, whose main concept is propagating a set of plane waves throughout the modulated area. We use the differential method together with an algorithm of reflectivity matrix propagation. It overcomes some of the convergence issues. In the theoretical part of this work, reflectivity matrix algorithms are extended to the case of oblique geometry. On these theoretical grounds, we developed a computation code, named COROX, which can be applied in any geometry. A number of typical grating cases have been studied, both in the conical and of le classical one. The output is not only the diffraction efficiencies, but also the polarization properties (Stokes parameters, Müller matrix), as well as the spectral phases. Interesting properties have been noticed, such as the presence of a non-negligible circularly polarized component diffracted from a lamellar grating when the incident wave is linearly polarized at 45° from the grating plane. The spectral phase behavior is also a significant data for an eventual shape tayloring of ultrashort pulses. Diffraction efficiency measurements have been performed on the Metrology beamline of Synchrotron SOLEIL, using a 150 lines/mm blazed grating as a test object. A reasonable agreement between measured and computed efficiencies has been obtained, provided that the rather high roughness of this grating is taken into account.

The theory of stretching and compressing of short light pulses by the chirped volume Bragg gratings (CBG) is reviewed based on spectral decomposition of short pulses and on the wavelength-dependent coupled wave equations. The analytic theory of diffraction efficiency of a CBG with constant chirp and approximate theory of time delay dispersion are presented. Based on those, we performed comparison of the approximate analytic results with the exact numeric coupled-wave modeling. We also study theoretically various definitions of laser beam width in a given cross-section. Quality of the beam is characterized by the dimensionless beam propagation products (?x???_x)?? , which are different for each of the 21 definitions. We study six particular beams and introduce an axially-symmetric self-MFT (mathematical Fourier transform) function, which may be useful for the description of diffraction-quality beams. Furthermore, we discuss various saturation curves and their influence on the amplitudes of recorded gratings. Special attention is given to multiplexed volume Bragg gratings (VBG) aimed at recording of several gratings in the same volume. The best shape of a saturation curve for production of the strongest gratings is found to be the threshold-type curve. Both one-photon and two-photon absorption mechanism of recording are investigated. Finally, by means of the simulation software we investigate forced airflow cooling of a VBG heated by a laser beam. Two combinations of a setup are considered, and a number of temperature distributions and thermal deformations are obtained for different rates of airflows. Simulation results are compared to the experimental data, and show good mutual agreement.