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

Abstract

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 mi = 1×10-5 to mi = 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.

Quantitative Measurement of Planar Droplet Sauter Mean Diameter in Sprays using Planar Droplet Sizing

“…The theoretical approach makes use of the geometrical optics approximation Van de Hulst [7] to calculate the scattered light and the fluorescence light emitted by a droplet, following the approach reported in Domann [4 ± 6], which has been successfully compared with Mie theory in Domann [8]. The intensity of the light scattered by a sphere located in a single laser beam was calculated with the geometrical optics approach with proper account of the phases between surface reflection, refraction, 1 st and 2 nd internal reflection.…”

Numerical evaluation of droplet sizing based on the ratio of fluorescent and scattered light intensities (LIF/Mie technique)

“…While the fundamental hypothesis of the LIF/Mie technique is intuitively convincing and in some cases true, it has been demonstrated that its validity is not guaranteed in all situations. For example, the fluorescent light is indeed emitted from within the droplet volume but its intensity distribution has been shown to vary within the droplet volume [33][34]. It has also been demonstrated that the light absorbed by a droplet [29,35] and the fluorescent light emitted from it [15,21,[36][37], are not always proportional to the volume of the droplet.…”

Temperature and chemical composition of droplets by optical measurement techniques: a state-of-the-art review

“…The Mie theory and geometrical optics were used to rigorously calculate the excitation field inside the droplet and the fluorescence signal emerging toward the detector (Castanet et al 2005a;Domann and Hardalupas 2001;Domann et al 2002;Frackowiak and Tropea 2010a, b;Zhang and Melton 1993). In the case of a laser beam arbitrary shaped like a Gaussian beam, the Generalized Lorenz-Mie theories (Gouesbet and Gréhan 2011) can be used as an extension of the Mie theory.…”

“…Paraxial approximation and ray transfer matrix analysis have been also used to describe the internal excitation field (Lavieille et al 2000). Among all the calculations, there is general agreement on the fact that the fluorescence signal from a droplet is not proportional to the droplet volume (Domann et al 2002;Frackowiak and Tropea 2010a). Due to the lens effect induced by the droplet surface and the absorption losses, the excitation field of fluorescence is not uniform within the droplet which means fluorescence is emitted by different points with different probabilities of reaching the detector.…”