Refractive index tomography using spherical optical transmission

This thesis describes the theory, experimental development, and results from a novel refractive index (RI) tomographic microscope suitable for laterally unbounded objects. A spherically diverging incident beam is used with lateral object translation in one or two dimensions, allowing different object regions to be sequentially illuminated at different angles. This work was motivated by the need in Brillouin spectromicroscopy (BSM) to combine Brillouin frequency shifts with RI measurements, for objects measuring up to order 100 µm in depth and order 1 mm in width, with a spatial resolution of order 1 µm. In this thesis, a review of the fields of RI tomography and BSM is given, including an overview of the theory, modelling, and results of other RI reconstruction techniques, as well as the theory and experimental developments in BSM. The geometry and theory of the new technique — spherical-transmission RI tomography (ST-RIT) — are presented with modelling and reconstruction methods, where the small-wavelength limiting regime is employed with a specialised implementation of backprojection techniques. Details of a proof-of-concept experimental system are given, before details of the design and construction of µm-scale RI test objects and biologically relevant cartilage samples. The procedure of data collection, processing, and reconstruction is then presented, before the results of reconstructing RI are shown and discussed. Like other tomographic techniques, ST-RIT is limited by the range of incident wave angles transmitted through the object, giving rise to an effect known as the missing cone problem. For this reason, while the constructed system produced reconstructions which conformed to the theory over ~mm lateral scales, it fell short of µm-scale RI localisation. The thesis concludes with a discussion of the efficacy of ST-RIT for the intended application and others, with suggestions for further development of the technique in the future. Open Access