Mie calculations of the scattered light from a spherical particle traversing a fringe pattern produced by two intersecting laser beams

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Abstract
Mie scattering calculations are described for a transparent spherical particle traversing a stationary fringe pattern produced by two intersecting laser beams as in a conventional, real fringe, LDA system. The scattered intensity and its modulation (visibility) are calculated for a range of different optical geometries and states of polarisation of the beams. In forward scatter the visibility is shown to be virtually independent of polarisation and refractive index, but strongly dependent on the geometry of the optical set-up. Optimum on-axis apertures incorporating stops are calculated for particle sizing. The authors demonstrate numerically that the dynamic range can be extended by the use of an off-axis aperture, or by the use of the intensity function which varies smoothly with particle size. In back scatter the authors show that the visibility technique can in fact be used for particle sizing provided the correct polarisations are used. The intensity function however shows strong irregularities in back scatter due to interference effects and cannot readily be used with monochromatic beams. A regularity in the back-scattered intensity distribution has been found for circularly polarised light and a simple explanation has been given. A particle sizing technique based on this principle is shown to be theoretically feasible.