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The properties and imaging performance of the computed tomographicimaging spectrometer (CTIS) have been investigated with Fourierand wavelet crosstalk matrices. These matrices and theircorresponding datacube reconstruction algorithms explicitly usedsensitivity equations describing the CTIS imaging system. Theseequations derived from Franhofer diffraction theory of thecomputed generated hologram (CGH) disperser, serve as themathematical model of the CTIS.The Fourier crosstalk matrix (FCTM) was primarily used to analyzethe CTIS imaging system. The FCTM describes which spatial andspectral frequencies contribute to object cube data entering thesystem and whether or not these frequencies give distinctcontributions with respect to each other. Furthermore, since theCTIS is a limited angle tomographic imaging system the missingcone of frequencies which is a feature of this instrument isclearly shown using the FCTM. Subsequently, Fourier-basedestimates of the reconstructed object cube (i.e. the datacube)will be missing this frequency information even if the CTIS is aperfect optical system.The wavelet crosstalk matrix (WCTM) was used primarily for efficient datacubereconstruction only. The datacube reconstruction calculations areprimarily proof-of-concept and reproduce the Fourier results withsome absence of Fourier related artifacts. The waveletdecomposition of the object cube is useful for studying multipleobjects in a parallel processing environment withoutreconstructing the entire datacube, thus reducing overall complexity.Datacube reconstructions of actual astronomical observations withthe CTIS, using the techniques of this research, were consistentwith previous independent datacube estimates from the same datausing existing conventional techniques. Furthermore these objectsfurnish natural point-spread functions that supplementcomputational simulations of the CTIS by describing actual imagingsystem performance.The computational tools for the study ofthe CTIS imaging system provide the additional bonus of ananalysis of object detectability by the computation of receiveroperator characteristic (ROC) curves. We used a synthetic binarystar to simulate this in the presence of both detector and objectnoise.Some suggestions for future research directions are given.

The single-scattering properties of six non-spherical ice crystals, droxtals, plates, solid columns, hollow columns, aggregates and 6-branch bullet rosettes are simulated. The anomalous diffraction theory (ADT) is applied to the simulation of the extinction efficiency and the absorption efficiency. Because the first order reflection is considered, the accuracy of the absorption efficiency increases with the increasing of the size parameter. Compared with the reference single-scattering properties from an improved geometric optics method (IGOM), the errors in the extinction and absorption efficiencies are small. In addition, the asymmetry factor is formulated within the framework of diffraction and external reflection. The asymmetry factor based on the ADT matches very well with the IGOM counterpart when the absorption is strong, but needs an improvement in the solar region. The errors in conjunction with the application of the ADT-based optical properties to the computation of atmospheric fluxes and heating rates, based on the Fu-Liou model also are investigated. Two cases, one for tropical cirrus clouds and the other for mid-latitude cirrus clouds, are designed. It is found that the errors of bulk asymmetry factor between ADT-based and IGOM-based result in an overestimation of downward infrared (IR) fluxes and upward solar fluxes, and an underestimation of upward IR fluxes and downward solar fluxes. The errors of the fluxes and heating rates based on two sets of single-scattering properties are caused mainly by the underestimation of the bulk absorption efficiency based on ADT. It is also shown that ADT-based optical properties generate more accurate radiative properties for tropical cirrus clouds than for the mid-latitude cirrus clouds. In conclusion, the ADT-based method can generate reasonably accurate single-scattering properties of ice crystals, and can result in reasonable upward IR and solar fluxes at top of atmosphere (TOA), downward IR fluxes at the surface, and net heating rates.

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.

<p>Two new methods for calculating the double differential scattering cross-section (DDSCS) in electron energy loss spectroscopy (EELS) have been developed, allowing for simulations of sample geometries which have been unavailable to earlier methods of calculation. The new methods concerns the calculations of the <em>thickness function</em> of the DDSCS. Earlier programs have used an analytic approximation of a sum over the lattice vectors of the sample that is valid for samples with parallel entrance and exit surfaces.The first of the new methods carries out the sum explicitly, first identifying the unit cells illuminated by the electron beam, which are the ones needed to be summed over. The second uses an approach with Fourier transforms, yielding a final expression containing the <em>shape amplitude</em>, the Fourier transform of the <em>shape function</em> defining the shape of the electron beam inside the sample. Approximating the shape with a polyhedron, one can quickly calculate the shape amplitude as sums over it’s faces and edges. The first method gives fast calculations for small samples or beams, when the number of illuminated unit cells is small. The second is more efficient in the case of large beams or samples, as the number of faces and edges of the polyhedron used in the calculation of the shape amplitude does not need to be increased much for large beams. A simulation of the DDSCS for magnetite has been performed, yielding diffraction patterns for the L₃ edge of the three Fe atoms in its basis.</p>

Two new methods for calculating the double differential scattering cross-section (DDSCS) in electron energy loss spectroscopy (EELS) have been developed, allowing for simulations of sample geometries which have been unavailable to earlier methods of calculation. The new methods concerns the calculations of the thickness function of the DDSCS. Earlier programs have used an analytic approximation of a sum over the lattice vectors of the sample that is valid for samples with parallel entrance and exit surfaces.The first of the new methods carries out the sum explicitly, first identifying the unit cells illuminated by the electron beam, which are the ones needed to be summed over. The second uses an approach with Fourier transforms, yielding a final expression containing the shape amplitude, the Fourier transform of the shape function defining the shape of the electron beam inside the sample. Approximating the shape with a polyhedron, one can quickly calculate the shape amplitude as sums over it’s faces and edges. The first method gives fast calculations for small samples or beams, when the number of illuminated unit cells is small. The second is more efficient in the case of large beams or samples, as the number of faces and edges of the polyhedron used in the calculation of the shape amplitude does not need to be increased much for large beams. A simulation of the DDSCS for magnetite has been performed, yielding diffraction patterns for the L3 edge of the three Fe atoms in its basis.

Aspheric and freeform surfaces are becoming more common as optical designs become more sophisticated and new generations of fabrication tools reduce cost. Unlike spherical surfaces, these surfaces are fabricated with processes that leave a signature or "structure" that is primarily in the mid-spatial frequency region. Tolerancing aspheric and freeform surfaces requires attention to both surface form and structured mid-spatial frequency fabrication errors. These structured surface errors are shown to create image artifacts such as ghosts, and ripples in the MTF profile. Spatial frequencies beyond "form" errors are often ignored or are modeled with statistical descriptors, which do not account for structured errors.This work explores and develops the theory to describe these errors without statistical assumptions. The analytic source of these artifacts in the image Point Spread Function and the Modulation Transfer Function are compared with computational models. The magnitudes of the image artifacts arising from structured surface errors are shown to be non-linear with surface height. It is also shown that multiple structured surface frequencies mix to create sum and difference diffraction orders that are not present in statistical models.An algorithm is developed that enables an optical designer to determine the important spatial frequencies and magnitudes of allowable errors given an MTF performance budget.

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