Dissertations / Theses on the topic 'High angle diffraction theory'

In recent years, optical near-field has received an ever-increasing attention owing to its ability to localise optical signals beyond the diffraction limit. Optical near-field is a non-propagating field existing in the close vicinity of a matter within a range less than the wavelength of the illumination light and it carries the high spatial frequency information showing the fine details of the matter. An optical near-field can be generated by a near-field optical microscope with a nano-aperture or a metal-coated fibre tip. However, common difficulties associated with this approach, such as a fragile probe, a low throughput and signal-to-noise ratio, and a slow response of gap controlling between the probe and the sample, make it less applicable. Alternatively, optical near-field can be produced by total internal reflection (TIR) occurring at the interface of a prism, which is capable of localising the electromagnetic (EM) field in the close vicinity of the interface. However, in this geometry, no confinement of the field can be achieved in the transverse direction, whereas, in most applications such as optical trapping, micro-fabrication and optical data storage, a transverse confinement of the light field is essential. In order to achieve a transverse confinement of the light field, maintaining the high spatial resolution of the optical near-field, and at the same time eliminating the drawbacks associated with the conventional near-field optical microscope, a novel near-field probe based on a high numerical aperture (NA) TIR objective combined with annular illumination has been developed recently. In this arrangement, an obstruction disk is inserted at the back aperture of the objective to block the light with a convergence angle lower than the critical angle determined by the refractive indices of the two media, resulting in a pure focused evanescent field in the second medium. The evanescent field produced by this method provides a useful tool for studying light-matter interaction at the single molecule level not only because of its high resolution but also due to its inherent merits such as no distance regulation, no heating effect and simple experimental setup. But, the most significant advantage that makes this method unique and superior to the other approaches in terms of producing the optical near-field is that it allows the dynamic control of the focal field by simply modulating the phase or amplitude or even the polarisation state of the incident beam before it enters the objective so that complex illumination beams can be generated, whereas in other fibre probe based approaches this goal is extremely difficult to achieve. To make use of such a novel near-field probe, a thorough theoretical and experimental investigation is required. A complete knowledge of the focused evanescent field is a prerequisite for a wide range of applications including single molecule detection, Raman spectroscopy, near-field non-linear imaging and near-field trapping. Therefore, it is not only necessary but also urgent to exploit the focusing properties of a focused evanescent field under complex field illumination both experimentally and theoretically and this is the major aim of this thesis. The complex fields, which are of particular interest in this thesis, are the radially polarised beam and the Laguerre-Gaussian (LG) beam, because the former owns a more compact circularly symmetric field distribution in the focal region when focused by a high NA objective, while the latter is capable of rotating a trapped particle by transferring the orbital angular momentum. Combining them with the focused evanescent field is potentially able to induce novel functions in the near-field region, which cannot be fulfilled by other near-field approaches. In this thesis, in order to generate these two types of beams, a single liquid crystal spatial light modulator (LCSLM) is employed to produce useful phase modulation to the incident beam. Experimental characterisation of an evanescent focal spot is performed with scanning near-field optical microscopy (SNOM), which is capable of providing the direct mapping of the focused evanescent field not only because of its high spatial resolution and its ability to detect the near-field and far-field signals simultaneously, but also due to the motion of the piezzo-stage enables a three-dimensional characterisation of the evanescent focal spot. In this thesis, a SNOM system with an aluminum coated aperture probe is implemented. The field distributions at both the interface and parallel planes with a small distance away from the interface are obtained. To verify the applicability of SNOM as a characterisation methodology, the field distribution in the focal region of a high NA objective illuminated by a linearly polarised plane wave is measured first. A focus splitting along the direction of incident polarisation is observed threedimensionally near the interface under such a circumstance. It has been demonstrated that the depolarisation effect plays an important role in determining the coupling behaviour of the light into the fibre probe of SNOM. The good match between the experimental results and theoretical predications confirms the validity of SNOM. Theoretical investigation of a tightly focused radially polarised beam is undertaken based on the vectorial-Debye diffraction theory because under the tight focusing of a high NA objective, the vectorial nature of the highly localised field has to be carefully considered in order to represent the field distribution accurately. The calculations on the focusing properties of a radially polarised beam suggest that the longitudinal field component in the focal region plays a dominant role in determining the overall field distribution. Direct measurement of the focused evanescent radially polarised beam in a three-dimensional manner near the interface is performed with SNOM. A highly localised focal spot is achieved in the close vicinity of the coverglass. The measured intensity distributions from SNOM show that correction of the focal spot deformation associated with a linearly polarised beam is achieved by taking advantage of the radially symmetric focal spot of a radially polarised beam. A smaller focal spot is acquired due to the dominant longitudinal polarisation component in the focal region, which possesses a more compact focal intensity distribution than that of the overall field. The experimental results demonstrate a good agreement with the theoretical expectations. The fact that a radially polarised beam is capable of eliminating the focus deformation often presented in the focal region of a high NA objective when a linearly polarised beam is employed can be very useful in many applications, including microfabrication using two-photon photopolymerisation technique. The theoretical study on the two-photon point spread function (PSF) of a radially polarised beam indicates that the focus elongation and splitting associated with a linearly polarised beam are eliminated and the achievable lateral size of the focal spot is approximately a quarter of the illumination wavelength, which is less than half of that under the illumination of a linearly polarised beam. A further reductiont of the lateral size can be expected by using annular radial beam illumination. The investigation on the focusing properties of LG beams has also been one of the major tasks of this thesis. Theoretical investigations of a focused evanescent LG beam suggest that the phase shift induced by the boundary effect when a light beam passes the interface satisfying TIR condition plays a vital role in determining the overall shape of the total field distribution. A severe focal intensity deformation is predicted theoretically in the case of focused evanescent LG beam illumination, which might involve new physical phenomena when applied in the near-field trapping. Such a focal intensity deformation is evidenced experimentally by the direct mapping result obtained from the SNOM probe. A quantitative cross-section comparison with the theoretical predication is conducted, which demonstrates a good agreement. To achieve a controllable optical trap and rotation in the near-field region, complex optical fields such as LG beams carrying orbital angular momentum, have been induced for the manipulation of a polystyrene particle. The influence of the focal intensity deformation on a near-field trapping has been thoroughly investigated. Rotation motion of the particle is examined by mapping the two-dimensional (2D) transverse trapping efficiency of the particle. Theoretical investigation reveals that a significant tangential force component is generated on the particle when it is illuminated by a focused evanescent LG beam. Such findings may prove useful in introducing a rotation mechanism in near-field trapping. The research investigations and methodologies described in this thesis provide a new approach to characterise the near-field focal spot under complex field illumination. It enhances the understanding of the novel near-field probe, thus opening the pathway for numerous near-field applications including optical trapping, two-photon excitation (photopolymerisation) and spectroscopy. The focal field rotation phenomena demonstrated in this thesis may prove particularly beneficial in introducing a rotation mechanism in near-field trapping using a focused evanescent field.

This thesis examines certain aspects of diffraction and scattering of high frequency waves, utilising and extending upon the Geometrical Theory of Diffraction (GTD). The first problem considered is that of scattering of electromagnetic plane waves by a perfectly conducting thin body, of aspect ratio O(k^1/2), where k is the dimensionless wavenumber. The edges of such a body have a radius of curvature which is comparable to the wavelength of the incident field, which lies inbetween the sharp and blunt cases traditionally treated by the GTD. The local problem of scattering by such an edge is that of a parabolic cylinder with the appropriate radius of curvature at the edge. The far field of the integral solution to this problem is examined using the method of steepest descents, extending the recent work of Tew [44]; in particular the behaviour of the field in the vicinity of the shadow boundaries is determined. These are fatter than those in the sharp or blunt cases, with a novel transition function. The second problem considered is that of scattering by thin shells of dielectric material. Under the assumption that the refractive index of the dielectric is large, approximate transition conditions for a layer of half a wavelength in thickness are formulated which account for the effects of curvature of the layer. Using these transition conditions the directivity of the fields scattered by a tightly curved tip region is determined, provided certain conditions are met by the tip curvature. In addition, creeping ray and whispering gallery modes outside such a curved layer are examined in the context of the GTD, and their initiation at a point of tangential incidence upon the layer is studied. The final problem considered concerns the scattering matrix of a closed convex body. A straightforward and explicit discussion of scattering theory is presented. Then the approximations of the GTD are used to find the first two terms in the asymptotic behaviour of the scattering phase, and the connection between the external scattering problem and the internal eigenvalue problem is discussed.

This thesis describes the analysis, design and implementation of a high performance DSP-based servo drive for a limited-angle torque motor used in thermal imaging applications. A limited-angle torque motor is an electromagnetic actuator based on the Laws' relay principle, and in the present application the rotation required was from - 10° to + 10° in 16 ms, with a flyback period of 4 ms. To ensure good quality picture reproduction, an exceptionally high linearity of ±0.02 ° was necessary throughout the forward sweep. In addition, the drive voltage to the exciting winding of the motor should be less than the +35 V ceiling of the drive amplifier. A research survey shows that little literature was available, probably due to the commercial sensitivity of many of the applications for torque motors. A detailed mathematical model of the motor drive, including high-order linear dynamics and the significant nonlinear characteristics, was developed to provide an insight into the overall system behaviour. The proposed control scheme uses a multicompensator, multi-loop linear controller, to reshape substantially the motor response characteristic, with a non-linear adaptive gain-scheduled controller to compensate effectively for the nonlinear variations of the motor parameters. The scheme demonstrates that a demanding nonlinear control system may be conveniently analysed and synthesised using frequency-domain methods, and that the design techniques may be reliably applied to similar electro-mechanical systems required to track a repetitive waveform. A prototype drive system was designed, constructed and tested during the course of the research. The drive system comprises a DSP-based digital controller, a linear power amplifier and the feedback signal conditioning circuit necessary for the closed-loop control. A switch-mode amplifier was also built, evaluated and compared with the linear amplifier. It was shown that the overall performance of the linear amplifier was superior to that of the switch-mode amplifier for the present application. The control software was developed using the structured programming method, with the continuous controller converted to digital form using the bilinear transform. The 6- operator was used rather than the z-operator, since it is more advantageous for high speed sampling systems. The gain-scheduled control was implemented by developing a schedule table, which is controlled by the DSP program to update continuously the controller parameters in synchronism with the periodic scanning of the motor. The experimental results show excellent agreement with the simulated results, with linearity of ±0.05 ° achieved throughout the forward sweep. Although this did not quite meet the very demanding specifications due to the limitations of the experimental drive system, it clearly demonstrates the effectiveness of the proposed control scheme. The discrepancies between simulated and experimental results are analyzed and discussed, the control design method is reviewed, and detailed suggestions are presented for further work which may improve the drive performance.

Abstract Charge density studies have been conducted on ten CB1 cannabinoid receptor antagonists via high resolution x-ray crystallography. Bond critical point values and various other properties derived from these studies including the electrostatic potential were analyzed in correlation to the affinity of each compound with the CB1 receptor. Correlation/anti-correlation was found between several properties and Ki. The data was also interpreted by principal component analysis with three principal components accounting for 85% of the data variation. Data mining was limit due to the low sample count and the requirements set for the inclusion of correlated/anti-correlated variables left fewer variables to analyze. The model presented is left for future interpretation.

In high frequency computational electromagnetics, rigorous numerical methods be come unrealistic tools due to computational demand increasing with the frequency. Instead approximations to the solutions of the Maxwell equations can be employed to evaluate th electromagnetic fields. In this thesis, we present the implementations of three high frequency approximat methods. The first two, namely the Geometrical Theory of Diffraction (GTD) and th Physical Optics (PO), are commonly used approximations. The third is a new invention that will be referred to as the Surface Current Extraction-Extrapolation (SCEE). Specifically, the GTD solver is a flexible and modular software package which use Non-Uniform Rational B-spline (NURBS) surfaces to model complex geometries. The PO solver is based on a triangular description of the surfaces and includes fas shadowing by ray tracing as well as contribution from edges to the scattered fields. GTD ray tracing was combined with the PO solver by a well thought-out software architecture Both implementations are now part of the GEMS software suite, the General ElectroMag netic Solvers, which incorporates state-of-the-art numerical methods. During validations both GTD and PO techniques turned out not to be accurate enough to meet the indus trial standards, thus creating the need for a new fast approximate method providing bette control of the approximations. In the SCEE approach, we construct high frequency approximate surface currents ex trapolated from rigourous Method of Moments (MoM) models at lower frequency. T do so, the low frequency currents are projected onto special basis vectors defined on th surface relative to the direction of the incident magnetic field. In such configuration, w observe that each component displays systematic spatial patterns evolving over frequenc in close correlation with the incident magnetic field, thus allowing us to formulate a fre quency model for each component. This new approach is fast, provides good control of th error and represents a platform for future development of high frequency approximations. As an application, we have used these tools to analyse the radar detectability of a new marine distress signaling device. The device, called "Rescue-Wing", works as an inflatabl radar reflector designed to provide a strong radar echo useful for detection and positionin during rescue operations of persons missing at sea.
QC 20101004

Description de la diffraction des electrons par les solides ordonnes a longue distance. Le formalisme necessite d'exprimer l'hamiltonien de diffraction sur une base discrete d'ondes planes. Le spectre des etats propres de l'hamiltonien de diffraction est dense non uniforme. Les calculs dynamiques peuvent donc etre effectues en echantillonant le spectre par valeurs discretes. Application de la methode a la simulation des images de microscopie electronique en haute resolution sur une phase icosaedrique en utilisant la description 6d de la structure. Interpretation des resultats experimentaux par la representation 6d

Bragg scattering of optical waves in thick gratings at extreme angles, where the scattered wave propagates parallel (extremely asymmetric scattering - EAS) or nearly parallel (grazing angle scattering - GAS) to the grating boundaries, is associated with many unique and practically important resonant phenomena. It has been demonstrated that one of the main physical mechanisms for these resonant phenomena is the diffractional divergence of the scattered wave inside and outside the grating region. This thesis fills the gaps in the theoretical and experimental understanding of Bragg scattering in gratings at extreme angles by investigating EAS and GAS in structures where diffractional divergence of waves is significantly affected by anisotropy and/or non-uniformities of the dielectric permittivity. Unusually high sensitivity of wave scattering in thick periodic gratings to small step-like variations of mean structural parameters at the grating boundaries is predicted and described for the case when the scattered wave (the +1 diffracted order) propagates almost parallel to the front grating boundary (the geometry of GAS). A unusual pattern of strong multiple resonances for bulk electromagnetic waves is predicted and analysed numerically in thick periodic holographic gratings in a guiding slab with mean permittivity that is greater than that of the surrounding media. It is demonstrated that these resonances are related to resonant generation of a new type of eigenmodes in a thick slab with a periodic grating. These eigenmodes are generically related to the grating -- they do exist not if the grating amplitude is zero. A new type of resonant coupling of bulk radiation into the conventional guided modes of a slab with a thick holographic grating is predicted and explained theoretically. It occurs in the presence of strong frequency detunings of the Bragg condition by means of interaction of the strongly non-eigen +1 diffracted order with the slab-grating boundaries. Therefore, it is only in the presence of step-like variations of the mean permittivity at the grating boundaries that this type of resonant coupling can occur. A new method for the analysis of EAS and GAS in anisotropic gratings is developed. This method is based on the consideration of the diffractional divergence of the scattered wave and the two-wave approximation in anisotropic gratings. Special efforts are focused on the analysis of EAS and GAS of extraordinary waves in uniaxial gratings. In particular, it is demonstrated that increasing curvature of the normal surface in the direction of propagation of the scattered wave results in increase of its diffraction divergence and the resonant amplitude. A theoretical model is developed for comparison of the theoretical predictions with data obtained from experimental observations of EAS in a holographic grating written in a photorefractive medium. The developed model is applied for the interpretation of experimental observations of EAS in BaTiO3 photorefractive crystals. Good agreement with the theoretical predictions is demonstrated.

Adaptive control designs using neural networks (NNs) based on dynamic inversion are investigated for aerospace vehicles which are operated at highly nonlinear dynamic regimes. NNs play a key role as the principal element of adaptation to approximately cancel the effect of inversion error, which subsequently improves robustness to parametric uncertainty and unmodeled dynamics in nonlinear regimes. An adaptive control scheme previously named composite model reference adaptive control is further developed so that it can be applied to multi-input multi-output output feedback dynamic inversion. It can have adaptive elements in both the dynamic compensator (linear controller) part and/or in the conventional adaptive controller part, also utilizing state estimation information for NN adaptation. This methodology has more flexibility and thus hopefully greater potential than conventional adaptive designs for adaptive flight control in highly nonlinear flight regimes. The stability of the control system is proved through Lyapunov theorems, and validated with simulations. The control designs in this thesis also include the use of pseudo-control hedging techniques which are introduced to prevent the NNs from attempting to adapt to various actuation nonlinearities such as actuator position and rate saturations. Control allocation is introduced for the case of redundant control effectors including thrust vectoring nozzles. A thorough comparison study of conventional and NN-based adaptive designs for a system under a limit cycle, wing-rock, is included in this research, and the NN-based adaptive control designs demonstrate their performances for two highly maneuverable aerial vehicles, NASA F-15 ACTIVE and FQM-117B unmanned aerial vehicle (UAV), operated under various nonlinearities and uncertainties.

Lithium-ion batteries have transformed energy storage and technological applications. They stand poised to convert transportation from combustion to electric engines. The discharge/charge rate is a key parameter that determines battery power output and recharge time; typically, operation is on the timescale of hours but reducing this would improve existing applications and open up new possibilities. Conventionally, the rate at which a battery can operate has been improved by synthetic strategies to decrease the solid-state diffusion length of lithium ions by decreasing particle sizes down to the nanoscale. In this work, a different approach is taken toward next-generation high-power and fast charging lithium-ion battery electrode materials. The phenomenon of high-rate charge storage without nanostructuring is discovered in niobium oxide and the mechanism is explained in the context of the structure–property relationships of Nb2O5. Three polymorphs, T-Nb2O5, B-Nb2O5, and H-Nb2O5, take bronze-like, rutile-like, and crystallographic shear structures, respectively. The bronze and crystallographic shear compounds, with unique electrochemical properties, can be described as ordered, anion-deficient nonstoichiometric defect structures derived from ReO3. The lessons learned in niobia serve as a platform to identify other compounds with related structural motifs that apparently facilitate high-rate lithium insertion and extraction. This leads to the synthesis, characterisation, and electrochemical evaluation of the even more complicated composition–structure–property relationships in ternary TiO2–Nb2O5 and Nb2O5–WO3 phases. Advanced structural characterisation including multinuclear solid-state nuclear magnetic resonance spectroscopy, density functional theory, X-ray absorption spectroscopy, operando high-rate X-ray diffraction, and neutron diffraction is conducted throughout to understand the evolution of local and long-range atomic structure and changes in electronic states.

Volume overload is a common feature in patients on haemodialysis (HD). This contributes significantly to the cardiovascular disease burden seen in these patients. Clinical assessments of the volume state are often inaccurate. Techniques such as interdialytic blood pressure, relative blood volume monitoring, bioimpedance are available to improve clinical effectives. However all these techniques exhibit significant shortcomings in their accuracy, reliability and applicability at the bed side. We evaluated the usefulness of a dual compartment monitoring technique using Continuous Segmental Bioimpedance Spectroscopy (CSBIS) and Relative Blood Volume (RBV) as a tool to assess hydration status and determine dry weight. We also sought to evaluate the role of Atrial Natriuretic Peptide (ANP) and B-type Natriuretic Peptide (BNP) as a volume marker in dialysis patients. The Retrospective analysis of a historical cohort (n = 376, 55 Diabetic) showed a significant reduction in post-dialysis weights in the first three months of dialysis (72.5 to 70kg, p<0.027) with a non-significant increase in weight between months 6-12. The use of anti-hypertensive agents reduced insignificantly in the first 3 months, increased marginally between months 3-6 and significantly increased over the subsequent 6 months. The residual urea clearance (KRU) fell and dialysis times increased. The cohort was very different to that dialysing at Tassin and showed a dissociation between weight reduction and BP control. This may relate to occult volume overload. CSBIS-RBV monitoring in 9 patients with pulse ultrafiltration (pulse UF) showed distinct reproducible patterns relating to extra cellular fluid (ECF) and RBV rebound. An empirical Refill Ratio was then used to define the patterns of change and this was related to the state of their hydration. A value closer to unity was consistent with the attainment of best achievable target weight. The refill ratio fell significantly between the first (earlier) and third (last) rebound phase (1.97 ± 0.92 vs 1.32 ± 0.2). CSBIS monitoring was then carried out in 31 subjects, whilst varying dialysate composition, temperature and patient posture to analyse the effects of these changes on the ECF trace and to ascertain whether any of these interventions can trigger a change in the slope of the ECF trace distinct to that caused by UF. Only, isovolemic HD caused a change in both RBV and ECF in some patients that was explained by volume re-distribution due to gravitational shifts, poor vascular reactivity, sodium gradient between plasma and dialysate and the use of vasodilating antihypertensive agents. This has not been described previously. These will need to be explored further. The study did demonstrate a significant lack of comparability of absolute values of RECF between dialysis sessions even in the same patient. This too has not been described previously. This is likely to be due to subtle changes in fluid distribution between compartments. Therefore a relative changes must be studied. This sensitivity to subtle changes may increase the usefulness of the technique for ECF tracking through dialysis. The potential of dual compartment monitoring to track volume changes in real time was further explored in 29 patients of whom 21 achieved weight reductions and were able to be restudied. The Refill Ratio decreased significantly in the 21 patients who had their dry weights reduced by 0.95 ± 1.13 kg (1.41 ± 0.25 vs 1.25 ± 0.31). Blood pressure changes did not reach statistical significance. The technique was then used to examine differences in vascular refill between a 36oC and isothermic dialysis session in 20 stable prevalent patients. Pulse UF was carried out in both these sessions. There were no significant differences in Refill Ratios, energy removed and blood pressure response between the two sessions. The core temperature (CT) of these patients was close to 36oC and administering isothermic HD did not confer any additional benefit. Mean BNP levels in 12 patients during isovolemic HD and HD with UF did not relate to volume changes. ANP concentrations fell during a dialysis session in 11 patients from a mean 249 ± 143 pg/ml (mean ± SD) at the start of dialysis to 77 ± 65 pg/ml at the end of the session (p<0.001). During isolated UF levels did not change but fell in the ensuing sham phase indicating a time lag between volume loss and decreased generation. (136±99 pg/ml to 101±77.2 pg/ml; p<0.02) In a subsequent study ANP concentrations were measured throughout dialysis and in the post-HD period for 2 hours. A rebound in ANP concentration was observed occurring at around 90 min post-HD. The degree of this rebound may reflect the prevailing fluid state and merit further study. We have shown the utility of dual compartment monitoring with CSBIS-RBV technique and its potential in assessing volume changes in real time in haemodialysis patients. We have also shown the potential of ANP as an independent marker of volume status in the same setting. Both these techniques merit further study.

碩士
國立成功大學
航空太空工程學系
87
An autopilot system for the heading reversal maneuvering (HRM) phase in missile engagement with high off-boresight angle up to 180 degrees has been successfully synthesized with the combination of aerodynamic control and thrust vector control (TVC). The application of H∞ control theory has provided the missile robustness (including robust stability and robust performance) properties in the presence of model uncertainty caused by aerodynamic coefficient variation. Simultaneously, autopilot has enabled the missile to resist the maximal possible yawing moment with any switching frequency induced by the vortex shedding during high angle-of-attack flight. Performance of this autopilot system was validated with a high-fidelity nonlinear six degree-of-freedom simulation. Excellent results have been brought out and the results manifest the feasibility of robust control for various missile control problems.