A study of the influence of absorption on the spatial distribution of fluorescence intensity within large droplets using Mie theory, geometrical optics and imaging experiments

The dependence of energy distributions within droplets on internal absorption effects has been investigated by calculations based on Mie theory and the geometrical optics approximation and experiments. The objective was to evaluate the accuracy of the geometrical optics approximation in calculating droplet volume to fluorescence intensity proportionality, required for planar droplet sizing measurements in sprays based on Mie scattering and fluorescence intensity from droplets. A geometrical optics approach was used to calculate the energy-density distribution in the meridional plane of a droplet and this was compared to the Mie theory solution for a range of imaginary refractive indices m i = 1 × 10 -5 to m i = 5 × 10 -4 . Integration of the energy density distribution over the droplet volume provided a method to compare experimental and theoretical results. Good agreement was found for the energy density and volume integrated energy distribution patterns obtained from both calculation methods and the experimental results. Quantitative comparison of the volume integrated energy results shows that for the investigated range of absorptivity Mie theory calculations lead to results that are ≈30% higher than in the geometrical optics case. This discrepancy is independent of light absorption and droplet size. Tunnelling waves were identified as the cause for the discrepancies between Mie theory and geometrical optics; these contribute to high energy density in the rim region of the droplet images.