A general framework for the evaluation of shock-capturing schemes

We introduce a standardized procedure for benchmarking shock-capturing schemes which is intended to go beyond traditional case-by-case analysis, by setting objective metrics for cross-comparison of flow solvers. The main idea is that use of shock-capturing schemes yields both distributed errors associated with propagation of wave-like disturbances in smooth flow regions, and localized errors at shocks where nonlinear numerical mechanisms are most active. Our standardized error evaluation framework relies on previous methods of analysis for the propagation error with associated cost/error mapping, and on novel analysis of the shock-capturing error based on a model scalar problem. Amplitude and phase errors are identified for a number of classical shock-capturing schemes with different order of accuracy. Whereas all schemes are found to be, as expected, first-order accurate at shocks, quantitative differences are found to be significant, and we find that certain schemes in wide use (e.g. high-order WENO schemes) may yield substantial over-amplification of incoming disturbances at shocks. Illustrative calculations are also shown for the 1D Euler equations, which support sufficient generality of the analysis, although nonlinearity suggests caution in straightforward extrapolation to other flow cases

Snapshot hyperspectral imaging : near-infrared image replicating imaging spectrometer and achromatisation of Wollaston prisms

Conventional hyperspectral imaging (HSI) techniques are time-sequential and rely on temporal scanning to capture hyperspectral images. This temporal constraint can limit the application of HSI to static scenes and platforms, where transient and dynamic events are not expected during data capture. The Near-Infrared Image Replicating Imaging Spectrometer (N-IRIS) sensor described in this thesis enables snapshot HSI in the short-wave infrared (SWIR), without the requirement for scanning and operates without rejection in polarised light. It operates in eight wavebands from 1.1μm to 1.7μm with a 2.0° diagonal field-of-view. N-IRIS produces spectral images directly, without the need for prior topographic or image reconstruction. Additional benefits include compactness, robustness, static operation, lower processing overheads, higher signal-to-noise ratio and higher optical throughput with respect to other HSI snapshot sensors generally. This thesis covers the IRIS design process from theoretical concepts to quantitative modelling, culminating in the N-IRIS prototype designed for SWIR imaging. This effort formed the logical step in advancing from peer efforts, which focussed upon the visible wavelengths. After acceptance testing to verify optical parameters, empirical laboratory trials were carried out. This testing focussed on discriminating between common materials within a controlled environment as proof-of-concept. Significance tests were used to provide an initial test of N-IRIS capability in distinguishing materials with respect to using a conventional SWIR broadband sensor. Motivated by the design and assembly of a cost-effective visible IRIS, an innovative solution was developed for the problem of chromatic variation in the splitting angle (CVSA) of Wollaston prisms. CVSA introduces spectral blurring of images. Analytical theory is presented and is illustrated with an example N-IRIS application where a sixfold reduction in dispersion is achieved for wavelengths in the region 400nm to 1.7μm, although the principle is applicable from ultraviolet to thermal-IR wavelengths. Experimental proof of concept is demonstrated and the spectral smearing of an achromatised N-IRIS is shown to be reduced by an order of magnitude. These achromatised prisms can provide benefits to areas beyond hyperspectral imaging, such as microscopy, laser pulse control and spectrometry

Waymark in the Depths: Baseband Signal Transmission and OFDM in Underwater Acoustic Propagation Channel Models

In the intricate environment of underwater acoustic propagation, establishing reliable communication channels stands as a formidable challenge, primarily due to the medium's inherent properties, such as high path loss, multipath propagation, and time-varying channel characteristics. "Waymark in the Depths: Baseband Signal Transmission and OFDM in Underwater Acoustic Propagation Channel Models" presents an innovative exploration into enhancing underwater communication systems by leveraging advanced signal processing techniques and channel modeling strategies. At the core of this research lies the integration of Orthogonal Frequency Division Multiplexing (OFDM) with baseband signal transmission, aiming to mitigate the detrimental effects of the underwater acoustic environment on signal integrity and throughput. By dissecting the acoustic channel's unique attributes, the study devises a comprehensive channel model that encapsulates the dynamic nature of underwater acoustics, including the impact of temperature, salinity, and pressure on sound speed and signal dispersion. This model serves as a waymark, guiding the development of tailored OFDM techniques that are optimized for the underwater medium, focusing on maximizing spectral efficiency and minimizing error rates. The research meticulously examines the interplay between baseband signal processing and OFDM in this context, illustrating how their synergistic application can overcome the bandwidth limitations and frequency-selective fading characteristic of underwater channels. Through extensive simulation and experimental validation, the study demonstrates the feasibility of achieving high-speed, reliable underwater communication, highlighting significant improvements in data rates and link stability. Furthermore, the research delves into adaptive modulation schemes and coding strategies, optimized for the derived channel model, to bolster the robustness of the communication link against the unpredictable underwater environment. This pioneering work not only sheds light on the complexities of underwater acoustic signal transmission but also charts a path forward for the next generation of underwater communication systems. By pushing the boundaries of current technological capabilities and offering a solid theoretical foundation, this research contributes significantly to the field of underwater acoustics and opens new horizons for marine exploration, environmental monitoring, and submarine communication networks. Through its comprehensive analysis and innovative approaches, "Waymark in the Depths" not only addresses the technical challenges of underwater signal transmission but also lays down a crucial waymark for future endeavors in the uncharted territories of the ocean's depths

Resolution Study of a Hyperspectral Sensor Using Computed Tomography in the Process of Noise

Recently, a new type of hyperspectral imaging sensor has been proposed which simultaneously records both spectral data and multiple spatial dimensions. Unlike dispersive imaging spectrometers, chromo-tomographic hyperspectral imaging sensors (CTHIS) record two spatial dimensions as well as a spectral dimension using computed tomography (CT) techniques with only a finite number of spatially-spectrally diverse images. To date, the factors affecting resolution of these sensors have not been examined. This research examines factors affecting resolution, specifically the number of the focus planes needed to resolve a particular object calculated from a theoretical lower bound, determine a method of reconstructing a hyperspectral object in the presence of noise and background and verify the proposed method of reconstruction and the lower bound applying the proposed reconstruction method to laboratory data. Finally, a simple method is proposed and tested to use this sensor in the presence of atmospheric turbulence with a modified reconstructor to blindly estimate the seeing parameter

Interactive animation of ocean waves

International audienceWe present an adaptive scheme for the interactive animation and display of ocean waves far from the coast. Relying on a procedural wave model, the method restricts computations to the visible part of the ocean surface, adapts the geometric resolution to the viewing distance and only considers the visible waves wavelengths. This yields real-time performances, even when the camera moves. The method allows the user to interactively fly over an unbounded animated ocean, which was not possible using previous approaches

Extended-Path Intensity Correlation: Microarcsecond Astrometry with an Arcsecond Field of View

We develop in detail a recently proposed optical-path modification of astronomical intensity interferometers. Extended-Path Intensity Correlation (EPIC) introduces a tunable path extension, enabling differential astrometry of multiple compact sources such as stars and quasars at separations of up to a few arcseconds. Combined with other recent technological advances in spectroscopy and fast single-photon detection, a ground-based intensity interferometer array can achieve microarcsecond resolution and even better light-centroiding accuracy on bright sources of magnitude $m \lesssim 15$. We lay out the theory and technical requirements of EPIC, and discuss the scientific potential. Promising applications include astrometric lensing of stars and quasar images, binary-orbit characterization, exoplanet detection, Galactic acceleration measurements and calibration of the cosmic distance ladder. The introduction of the path extension thus significantly increases the scope of intensity interferometry while reaching unprecedented levels of relative astrometric precision.Comment: 58+21 pages, 22 figures; companion paper to arXiv:2307.0322

Nonlinear pulse shaping in fibres for pulse generation and optical processing

The development of new all-optical technologies for data processing and signal manipulation is a field of growing importance with a strong potential for numerous applications in diverse areas of modern science. Nonlinear phenomena occurring in optical fibres have many attractive features and great, but not yet fully explored, potential in signal processing. Here, we review recent progress on the use of fibre nonlinearities for the generation and shaping of optical pulses and on the applications of advanced pulse shapes in all-optical signal processing. Amongst other topics, we will discuss ultrahigh repetition rate pulse sources, the generation of parabolic shaped pulses in active and passive fibres, the generation of pulses with triangular temporal profiles, and coherent supercontinuum sources. The signal processing applications will span optical regeneration, linear distortion compensation, optical decision at the receiver in optical communication systems, spectral and temporal signal doubling, and frequency conversion