Scattering of electromagnetic waves by rough interfaces and inhomogeneous layers

We consider a two-dimensional problem of scattering of a time-harmonic electromagnetic plane wave by an infinite inhomogeneous conducting or dielectric layer at the interface between semi-infinite homogeneous dielectric half-spaces. The magnetic permeability is assumed to be a fixed positive constant. The material properties of the media are characterized completely by an index of refraction, which is a bounded measurable function in the layer and takes positive constant values above and below the layer, corresponding to the homogeneous dielectric media. In this paper, we examine only the transverse magnetic (TM) polarization case. A radiation condition appropriate for scattering by infinite rough surfaces is introduced, a generalization of the Rayleigh expansion condition for diffraction gratings. With the help of the radiation condition the problem is reformulated as an equivalent mixed system of boundary and domain integral equations, consisting of second-kind integral equations over the layer and interfaces within the layer. Assumptions on the variation of the index of refraction in the layer are then imposed which prove to be sufficient, together with the radiation condition, to prove uniqueness of solution and nonexistence of guided wave modes. Recent, general results on the solvability of systems of second kind integral equations on unbounded domains establish existence of solution and continuous dependence in a weighted norm of the solution on the given data. The results obtained apply to the case of scattering by a rough interface between two dielectric media and to many other practical configurations.

Acoustic scattering by an inhomogeneous layer on a rigid plate

The problem of scattering of time-harmonic acoustic waves by an inhomogeneous fluid layer on a rigid plate in R2 is considered. The density is assumed to be unity in the media: within the layer the sound speed is assumed to be an arbitrary bounded measurable function. The problem is modelled by the reduced wave equation with variable wavenumber in the layer and a Neumann condition on the plate. To formulate the problem and prove uniqueness of solution a radiation condition appropriate for scattering by infinite rough surfaces is introduced, a generalization of the Rayleigh expansion condition for diffraction gratings. With the help of the radiation condition the problem is reformulated as a system of two second kind integral equations over the layer and the plate. Under additional assumptions on the wavenumber in the layer, uniqueness of solution is proved and the nonexistence of guided wave solutions of the homogeneous problem established. General results on the solvability of systems of integral equations on unbounded domains are used to establish existence and continuous dependence in a weighted norm of the solution on the given data.

Cosmological constant and the speed of light

By exploring the relationship between the propagation of electromagnetic waves in a gravitational field and the light propagation in a refractive medium, it is shown that, in the presence of a positive cosmological constant, the velocity of light will be smaller than its special relativity value. Then, restricting again to the domain of validity of geometrical optics, the same result is obtained in the context of wave optics. It is argued that this phenomenon and the anisotropy in the velocity of light in a gravitational field are produced by the same mechanism.

Advances in phase-stepping real-time holography using photorefractive sillenite crystals

This work presents a review of recent developments in phase-stepping real-time holographic interferometry with photorefractive sillenite crystals. Quantitative results are shown in micro-rotation, micro-displacement, and micro-deformation measurements, and in wave-optics and surface analysis as well. The phase stepping was carried out in a four-frame process and the resulting phase map was unwrapped by applying a sin/cos filter. The experimental results are in good agreement with the ones obtained through other means, showing the promising potentialities of phase-stepping real-time holographic interferometry for in situ visualisation, monitoring and analysis in non-destructive testing.

Sparse Signal Representation of Ultrasonic Signals for Structural Health Monitoring Applications

Assessment of the integrity of structural components is of great importance for aerospace systems, land and marine transportation, civil infrastructures and other biological and mechanical applications. Guided waves (GWs) based inspections are an attractive mean for structural health monitoring. In this thesis, the study and development of techniques for GW ultrasound signal analysis and compression in the context of non-destructive testing of structures will be presented. In guided wave inspections, it is necessary to address the problem of the dispersion compensation. A signal processing approach based on frequency warping was adopted. Such operator maps the frequencies axis through a function derived by the group velocity of the test material and it is used to remove the dependence on the travelled distance from the acquired signals. Such processing strategy was fruitfully applied for impact location and damage localization tasks in composite and aluminum panels. It has been shown that, basing on this processing tool, low power embedded system for GW structural monitoring can be implemented. Finally, a new procedure based on Compressive Sensing has been developed and applied for data reduction. Such procedure has also a beneficial effect in enhancing the accuracy of structural defects localization. This algorithm uses the convolutive model of the propagation of ultrasonic guided waves which takes advantage of a sparse signal representation in the warped frequency domain. The recovery from the compressed samples is based on an alternating minimization procedure which achieves both an accurate reconstruction of the ultrasonic signal and a precise estimation of waves time of flight. Such information is used to feed hyperbolic or elliptic localization procedures, for accurate impact or damage localization.

Fading pdf of free-space optical communication system with pointing error

A free-space optical (FSO) laser communication system with perfect fast-tracking experiences random power fading due to atmospheric turbulence. For a FSO communication system without fast-tracking or with imperfect fast-tracking, the fading probability density function (pdf) is also affected by the pointing error. In this thesis, the overall fading pdfs of FSO communication system with pointing errors are calculated using an analytical method based on the fast-tracked on-axis and off-axis fading pdfs and the fast-tracked beam profile of a turbulence channel. The overall fading pdf is firstly studied for the FSO communication system with collimated laser beam. Large-scale numerical wave-optics simulations are performed to verify the analytically calculated fading pdf with collimated beam under various turbulence channels and pointing errors. The calculated overall fading pdfs are almost identical to the directly simulated fading pdfs. The calculated overall fading pdfs are also compared with the gamma-gamma (GG) and the log-normal (LN) fading pdf models. They fit better than both the GG and LN fading pdf models under different receiver aperture sizes in all the studied cases. Further, the analytical method is expanded to the FSO communication system with beam diverging angle case. It is shown that the gamma pdf model is still valid for the fast-tracked on-axis and off-axis fading pdfs with point-like receiver aperture when the laser beam is propagated with beam diverging angle. Large-scale numerical wave-optics simulations prove that the analytically calculated fading pdfs perfectly fit the overall fading pdfs for both focused and diverged beam cases. The influence of the fast-tracked on-axis and off-axis fading pdfs, the fast-tracked beam profile, and the pointing error on the overall fading pdf is also discussed. At last, the analytical method is compared with the previous heuristic fading pdf models proposed since 1970s. Although some of previously proposed fading pdf models provide close fit to the experiment and simulation data, these close fits only exist under particular conditions. Only analytical method shows accurate fit to the directly simulated fading pdfs under different turbulence strength, propagation distances, receiver aperture sizes and pointing errors.

Integrated electronic system for ultrasonic structural health monitoring

A fully integrated on-board electronic system that can perform in-situ structural health monitoring (SHM) of aircraft?s structures using specifically designed equipment for SHM based on guided wave ultrasonic method or Lamb waves? method is introduced. This equipment is called Phased Array Monitoring for Enhanced Life Assessment (PAMELA III) and is an essential part of overall PAMELA SHM? system. PAMELA III can generate any kind of excitation signals, acquire the response signals that propagate throughout the structure being tested, and perform the signal processing for damage detection directly on the structure without need to send the huge amount of raw signals but only the final SHM maps. It monitors the structure by means of an array of integrated Phased Array (PhA) transducers preferably bonded onto the host structure. The PAMELA III hardware for SHM mapping has been designed, built and subjected to laboratory tests, using aluminum and CFRP structures. The 12 channel system has been designed to be low weight (265 grams only), to have a small form factor, to be directly mounted above the integrated PhA transducers without need for cables and to be EMI protected so that the equipment can be taken on board an aircraft to perform required SHM analyses by use of embedded SHM algorithms. Moreover, the autonomous, automatic and on real-time working procedure makes it suitable for the avionic field, sending the corresponding alerts, maps and reports to external equipment.

Design of spherical symmetric gradient index lenses

Spherical symmetric refractive index distributions also known as Gradient Index lenses such as the Maxwell-Fish-Eye (MFE), the Luneburg or the Eaton lenses have always played an important role in Optics. The recent development of the technique called Transformation Optics has renewed the interest in these gradient index lenses. For instance, Perfect Imaging within the Wave Optics framework has recently been proved using the MFE distribution. We review here the design problem of these lenses, classify them in two groups (Luneburg moveable-limits and fixed-limits type), and establish a new design techniques for each type of problem.

Monitorización de estructuras aeronáuticas mediante técnicas de inteligencia artificial

Una de las barreras para la aplicación de las técnicas de monitorización de la integridad estructural (SHM) basadas en ondas elásticas guiadas (GLW) en aeronaves es la influencia perniciosa de las condiciones ambientales y de operación (EOC). En esta tesis se ha estudiado dicha influencia y la compensación de la misma, particularizando en variaciones del estado de carga y temperatura. La compensación de dichos efectos se fundamenta en Redes Neuronales Artificiales (ANN) empleando datos experimentales procesados con la Transformada Chirplet. Los cambios en la geometría y en las propiedades del material respecto al estado inicial de la estructura (lo daños) provocan cambios en la forma de onda de las GLW (lo que denominamos característica sensible al daño o DSF). Mediante técnicas de tratamiento de señal se puede buscar una relación entre dichas variaciones y los daños, esto se conoce como SHM. Sin embargo, las variaciones en las EOC producen también cambios en los datos adquiridos relativos a las GLW (DSF) que provocan errores en los algoritmos de diagnóstico de daño (SHM). Esto sucede porque las firmas de daño y de las EOC en la DSF son del mismo orden. Por lo tanto, es necesario cuantificar y compensar el efecto de las EOC sobre la GLW. Si bien existen diversas metodologías para compensar los efectos de las EOC como por ejemplo “Optimal Baseline Selection” (OBS) o “Baseline Signal Stretching” (BSS), estas, se emplean exclusivamente en la compensación de los efectos térmicos. El método propuesto en esta tesis mezcla análisis de datos experimentales, como en el método OBS, y modelos basados en Redes Neuronales Artificiales (ANN) que reemplazan el modelado físico requerido por el método BSS. El análisis de datos experimentales consiste en aplicar la Transformada Chirplet (CT) para extraer la firma de las EOC sobre la DSF. Con esta información, obtenida bajo diversas EOC, se entrena una ANN. A continuación, la ANN actuará como un interpolador de referencias de la estructura sin daño, generando información de referencia para cualquier EOC. La comparación de las mediciones reales de la DSF con los valores simulados por la ANN, dará como resultado la firma daño en la DSF, lo que permite el diagnóstico de daño. Este esquema se ha aplicado y verificado, en diversas EOC, para una estructura unidimensional con un único camino de daño, y para una estructura representativa de un fuselaje de una aeronave, con curvatura y múltiples elementos rigidizadores, sometida a un estado de cargas complejo, con múltiples caminos de daños. Los efectos de las EOC se han estudiado en detalle en la estructura unidimensional y se han generalizado para el fuselaje, demostrando la independencia del método respecto a la configuración de la estructura y el tipo de sensores utilizados para la adquisición de datos GLW. Por otra parte, esta metodología se puede utilizar para la compensación simultánea de una variedad medible de EOC, que afecten a la adquisición de datos de la onda elástica guiada. El principal resultado entre otros, de esta tesis, es la metodología CT-ANN para la compensación de EOC en técnicas SHM basadas en ondas elásticas guiadas para el diagnóstico de daño. ABSTRACT One of the open problems to implement Structural Health Monitoring techniques based on elastic guided waves in real aircraft structures at operation is the influence of the environmental and operational conditions (EOC) on the damage diagnosis problem. This thesis deals with the compensation of these environmental and operational effects, specifically, the temperature and the external loading, by the use of the Chirplet Transform working with Artificial Neural Networks. It is well known that the guided elastic wave form is affected by the damage appearance (what is known as the damage sensitive feature or DSF). The DSF is modified by the temperature and by the load applied to the structure. The EOC promotes variations in the acquired data (DSF) and cause mistakes in damage diagnosis algorithms. This effect promotes changes on the waveform due to the EOC variations of the same order than the damage occurrence. It is difficult to separate both effects in order to avoid damage diagnosis mistakes. Therefore it is necessary to quantify and compensate the effect of EOC over the GLW forms. There are several approaches to compensate the EOC effects such as Optimal Baseline Selection (OBS) or Baseline Signal Stretching (BSS). Usually, they are used for temperature compensation. The new method proposed here mixes experimental data analysis, as in the OBS method, and Artificial Neural Network (ANN) models to replace the physical modelling which involves the BSS method. The experimental data analysis studied is based on apply the Chirplet Transform (CT) to extract the EOC signature on the DSF. The information obtained varying EOC is employed to train an ANN. Then, the ANN will act as a baselines interpolator of the undamaged structure. The ANN generates reference information at any EOC. By comparing real measurements of the DSF against the ANN simulated values, the damage signature appears clearly in the DSF, enabling an accurate damage diagnosis. This schema has been applied in a range of EOC for a one-dimensional structure containing single damage path and two dimensional real fuselage structure with stiffener elements and multiple damage paths. The EOC effects tested in the one-dimensional structure have been generalized to the fuselage showing its independence from structural arrangement and the type of sensors used for GLW data acquisition. Moreover, it can be used for the simultaneous compensation of a variety of measurable EOC, which affects the guided wave data acquisition. The main result, among others, of this thesis is the CT-ANN methodology for the compensation of EOC in GLW based SHM technique for damage diagnosis.

Ultrasonic measurement technique of burning metals in normal and reduced gravity

The in situ real time measurement of the regression rate of a melting interface (RRMI) is performed by the ultrasonic measurement system reported here. The RRMI is the rate at which a solid/liquid interface (SLI) moves along a metallic rod while burning in an oxygen-enriched atmosphere and is an important flatnmability indicator. The ultrasonic transducer and associated equipment used to drive the transducer and record the echo signal is described, along with the process that transforms the acquired signals into a RRMI value. Test rods of various metals and geometric shapes were burned at several test conditions in different test facilities. The RRMI results with quantified errors are presented and reviewed. The effect of reduced gravity on burning metals is important to space-applications and RRMI results obtained in a reduced gravity environment are also presented.

Two-dimensional nonlinear dynamics of evanescent-wave guided atoms in a hollow fiber

We describe the classical and quantum two-dimensional nonlinear dynamics of large blue-detuned evanescent-wave guiding cold atoms in hollow fiber. We show that chaotic dynamics exists for classic dynamics, when the intensity of the beam is periodically modulated. The two-dimensional distributions of atoms in (x,y) plane are simulated. We show that the atoms will accumulate on several annular regions when the system enters a regime of global chaos. Our simulation shows that, when the atomic flux is very small, a similar distribution will be obtained if we detect the atomic distribution once each the modulation period and integrate the signals. For quantum dynamics, quantum collapses, and revivals appear. For periodically modulated optical potential, the variance of atomic position will be suppressed compared to the no modulation case. The atomic angular momentum will influence the evolution of wave function in two-dimensional quantum system of hollow fiber.

Fourier optics study of traveling-wave excitation at short- wavelength plasma-lasing

Traveling-wave excitation close to the speed of light implies small-angle target-irradiation. Yet, short-wavelength lasing needs large irradiation angles. Pulse-front back-tilt is considered to overcome such trade-off. Pulse-front tilt by means of compressor misalignment was found effective only if coupled with a strong front-end imaging/focusing component.

Diffractive optics-based heterodyne-detected four-wave mixing signals of protein motion: From “protein quakes” to ligand escape for myoglobin

Ligand transport through myoglobin (Mb) has been observed by using optically heterodyne-detected transient grating spectroscopy. Experimental implementation using diffractive optics has provided unprecedented sensitivity for the study of protein motions by enabling the passive phase locking of the four beams that constitute the experiment, and an unambiguous separation of the Real and Imaginary parts of the signal. Ligand photodissociation of carboxymyoglobin (MbCO) induces a sequence of events involving the relaxation of the protein structure to accommodate ligand escape. These motions show up in the Real part of the signal. The ligand (CO) transport process involves an initial, small amplitude, change in volume, reflecting the transit time of the ligand through the protein, followed by a significantly larger volume change with ligand escape to the surrounding water. The latter process is well described by a single exponential process of 725 ± 15 ns at room temperature. The overall dynamics provide a distinctive signature that can be understood in the context of segmental protein fluctuations that aid ligand escape via a few specific cavities, and they suggest the existence of discrete escape pathways.