Computational methods in vectorial imaging

In the search for higher resolution, modern day imaging systems frequently employ objective lenses with a high numerical aperture. Propagation of light through such lenses introduces a spatial variation in the polarisation across the beam profile, whilst the inherently large propagation angles also necessitates inclusion of additional transverse and axial electric field components in modelling. A full treatment of polarisation effects including such considerations has implications at all stages in the image formation process, namely; illumination, scattering from the sample, imaging and detection. This tutorial review considers each stage in turn and details the theories required for rigorous modelling and analysis. In particular a generalisation of the well known Jones calculus and ray tracing methods are shown to conveniently and accurately allow rigorous studies of high numerical aperture confocal and conventional polarised light microscopes, imaging samples of arbitrary complexity. Generalisation of the illumination to partially coherent, partially polarised systems is also briefly given. Whilst rigorous modelling techniques can prove time consuming a number of simplifications and approximations can be adopted, allowing computational gains to be achieved. Discussion in this vein is hence also presented.