Computational Algorithms for Improved Synthetic Aperture Radar Image Focusing

High-resolution radar imaging is an area undergoing rapid technological and scientific development. Synthetic Aperture Radar (SAR) and Inverse Synthetic Aperture Radar (ISAR) are imaging radars with an ever-increasing number of applications for both civilian and military users. The advancements in phased array radar and digital computing technologies move the trend of this technology towards higher spatial resolution and more advanced imaging modalities. Signal processing algorithm development plays a key role in making full use of these technological developments.In SAR and ISAR imaging, the image reconstruction process is based on using the relative motion between the radar and the scene. An important part of the signal processing chain is the estimation and compensation of this relative motion. The increased spatial resolution and number of receive channels cause the approximations used to derive conventional algorithms for image reconstruction and motion compensation to break down. This leads to limited applicability and performance limitations in non-ideal operating conditions.This thesis presents novel research in the areas of data-driven motion compensation and image reconstruction in non-cooperative ISAR and Multichannel Synthetic Aperture Radar (MSAR) imaging. To overcome the limitations of conventional algorithms, this thesis proposes novel algorithms leading to increased estimation performance and image quality. Because a real-time imaging capability is important in many applications, special emphasis is placed on the computational aspects of the algorithms.For non-cooperative ISAR imaging, the thesis proposes improvements to the range alignment, time window selection, autofocus, time-frequency-based image reconstruction and cross-range scaling procedures. These algorithms are combined into a computationally efficient non-cooperative ISAR imaging algorithm based on mathematical optimization. The improvements are experimentally validated to reduce the computational burden and significantly increase the image quality under complex target motion dynamics.Time domain algorithms offer a non-approximated and general way for image reconstruction in both ISAR and MSAR. Previously, their use has been limited by the available computing power. In this thesis, a contrast optimization approach for time domain ISAR imaging is proposed. The algorithm is demonstrated to produce improved imaging performance under the most challenging motion compensation scenarios. The thesis also presents fast time domain algorithms for MSAR. Numerical simulations confirm that the proposed algorithms offer a reasonable compromise between computational speed and image quality metrics

Numerical Modelling of Extreme Waves: The Role of Nonlinear Wave-Wave Interactions

The real monsters of the ocean, extreme waves, haunted mariners since the early days of human activities in the sea. Despite having caused numerous accidents and casualties, their systematic study began only in 2000s. Many mechanisms have been proposed to simulate these rare but catastrophic events, with the most prominent being wave focusing. This is connected to the NewWave theory, which has been used extensively in experimental and numerical modelling. However, the majority of the studies fail to capture the distinguishing characteristics of extreme waves, due to the inherent high nonlinearity of the problem and shortcomings of the modelling practice, but also due to inadequate knowledge of the underlying physics. Overcoming these issues is unquestionably necessary for understanding extreme waves and including them in the engineering design practice. The nonlinearity of the problem lies upon the nonlinear wave-wave interactions, which violate the fundamental linear assumptions of NewWave and pose challenges to numerical models. The present work aims at contributing in both understanding the nature of nonlinear wave-wave interactions during the formation of extreme wave events, and examining the applicability and performance of numerical solvers via their systematic validation with state-of-the-art techniques that give new insights into the problem. A range of phase-resolving and phase-averaged models are employed to cover different scales and examine the undergoing physical processes. Through the study of limiting breaking unidirectional dispersive wave groups in finite water depth, it is demonstrated that the free-wave spectrum undergoes considerable transformation and a large portion of energy is transferred to higher and lower harmonics. These effects can be attributed to the action of near-resonant and bound nonlinearities, which have however robust mathematical description. As such, a large part of the thesis is devoted to analytical methods towards establishing an efficient integrated framework for estimating extreme wave profiles, going beyond the classic NewWave. Overall, the present work is a balance of physics and numerics to tackle parts of the challenging problem of extreme waves and improve safety at sea

Investigation of plenoptic imaging systems: a wave optics approach

Conventional imaging devices only capture a part of the total information carried by the light. A new generation of imaging devices, plenoptic systems, use an array of micro lenses to codify the light coming from an object into a four dimensional function called the light field. The final image is then obtained after post processing computations on the light field. In this work plenoptic imaging devices are analysed using a wave optics approach. A platform to simulate light propagating under the Fresnel approximation in a generic optical system was developed in MATLAB. An optical system can be modelled as the composition of two basic operators: the free space propagation and the lens. The first one was implemented developing an original method derived from the angular spectrum of plane waves theory of propagation. The second was implemented using a phase mask. The code was developed to optimize the signal to noise ratio and the computational time. Two different configurations of plenoptic imaging systems were simulated. The first is the plenoptic 1.0 configuration. The general theory of plenoptic 1.0 and the post processing algorithms presented in the literature were verified using the simulation platform. The effects of diffraction were also evaluated and an original refocusing method is presented. For the second configuration, plenoptic 2.0, a full study of the optical resolution has been made and a detailed analysis of the effects of diffraction is presented. The results achieved with the simulations have been used to design a working prototype of a plenoptic microscope. This novel wave optics approach enables us to quantify for the first time in the literature the effects of diffraction on this class of devices. In plenoptic 1.0 diffraction is a source of noise due to the crosstalk between neighbouring lenslets. In plenoptic 2.0 systems the optical resolution is directly proportional to the magnification of the lenslet array. A small magnification leads to a high directional sampling but at the same time to a loss of optical resolution. The finite dimensions of the lenslets together with the wave nature of light produce a physical limit to the amount of information that can be achieved sampling the optical fields with those kind of devices

Filamentation in air : evolution, control and applications

Les travaux présentés dans cette thèse portent sur la propagation non linéaire, sous forme de filaments laser, d'impulsions laser ultra-courtes dans l'atmosphère. Les résultats, principalement obtenus à partir d'expériences réalisées en laboratoire, apportent des éléments de compréhension clés en lien avec la la projection de filaments laser dans l'air. Trois aspects distincts de la filamentation sont abordés, à savoir l'évolution, le contrôle et les applications de la filamentation laser. Dans la section évolution, un filament unique a été rigoureusement caractérisé sur plusieurs dizaines de mètres. Plusieurs mesures ont été effectuées pour obtenir une image détaillée du phénomène global. En effet, la caractérisation inclut la mesure de la distribution de plasma du filament et l'évolution spectrale des impulsions laser. Également, des canaux de lumière intense, exempte d'ionisation, ont été observés et caractérisés sur plusieurs dizaines de mètres. La section sur le contrôle présente des méthodes qui pourraient éventuellement résoudre plusieurs problèmes liés à la projection de filaments puissants à longue distance. La plupart de ces méthodes se concentrent sur la fusion de filaments multiples afin d'obtenir un plus grand nombre d'électrons libres ou, un plus grand élargissement spectral. Ces méthodes comprennent l'utilisation de masques spéciaux, la diffraction d'une ouverture circulaire et un système d'optique adaptative. Enfin, la troisième partie présente deux applications prometteuses de la filamentation dans l'air. La première est la télédétection de polluants. Plusieurs cibles (gaz, cibles métalliques, nuages de fumée, aérosols, traces d'explosifs) ont été exposées à la radiation des filaments et la fluorescence caractéristique de ces cibles a été recueillie à l'aide de la technique LIDAR. Un système d'optique adaptative a été utilisé pour améliorer de façon significative les signaux de fluorescence émise. La deuxième application discutée est la génération d'impulsions dans l'infrarouge moyen via le mélange à quatre ondes durant la filamentation à deux couleurs. Le développement de nouvelles sources laser dans l'infrarouge moyen est de première importance pour résoudre des problèmes importants pour la défense et la sécurité civile. En utilisant cette méthode, des impulsions à large bande centrées entre 4-7 [Mu]m de longueur d'onde ont été produites