Shaping the focal field in three dimensions using polarisation and phase
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Vectorial polarimetry is a novel high-resolution microscopy technique with potential applications in the characterisation of nano-materials, sub-diffraction limit microscopy, and single molecule imaging. Previous work had concentrated on using homogeneous polarisation distributions in the pupil plane of a high numerical aperture objective lens, as well as analysing the scattered and re-collimated light from a nano-scale sample. It has been shown that sub-resolution information can be obtained by measurement of the Stokes parameters of the scattered light. The novel aspect of the vectorial polarimetry system described in this thesis lay in its ability to generate a completely arbitrary polarisation and phase distribution in the pupil of an objective lens. Three passes on two liquid crystal spatial light modulators were used to achieve this; the first pass controlled the absolute phase, while the remaining two were used to tailor the polarisation distribution across the beam. The system focused a laser beam using a high numerical aperture objective lens; the focal field of such a lens is affected by both the polarisation and phase distributions across the entrance pupil. The field at the focus of the microscope lens was modelled using both the Debye-Wolf integrals and a Fourier transform method. Results from these two methods using similar inputs were found to be sufficiently similar for most applications. This modelling was used to investigate the extent to which the focal field could be shaped using polarisation and phase. Experiments were carried out by placing a specimen in the focal plane, and collecting and re-collimating the light scattered from the sample. The polarisation state of the field in the exit pupil was then analysed. Sub-resolution displacements of a nano-sphere could be measured, where a change in one of the Stokes parameters increased as the sphere was moved away from the focus. The second sample investigated was a set of gratings with pitches smaller than the diffraction limit. The Mueller matrices of each of the gratings were measured. Decomposition of these matrices showed that polarimetric properties, such as retardance, depended on the pitch of the gratings; the retardance of a 45 nm grating was different than that for a 32 nm grating, suggesting that polarisation can reveal sub-wavelength structural changes.
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