Data inversion algorithms for droplet characterization based on simulated rainbows

Abstract

In characterizing droplets, the rainbow reveals information about the size of individual drops, their refractive index, temperature, and in some instances composition. Previous experience in exploiting rainbow scattering for this purpose has led to classical rainbow refractometry, but also to the global rainbow technique. To improve on these existing techniques, a highly focused Gaussian illumination beam offers some advantages for achieving higher spatial resolution in dense spray situations. This is explored in the present study, using simulations of rainbow scattering from a spherical droplet in the primary and secondary rainbow regions. These simulations are performed using the generalized Lorenz-Mie theory (GLMT), allowing for a focused Gaussian beam illumination. For droplet characterization, three inversion algorithms are investigated, designated as the peak-trough method, inflection-inflection method and trough-trough method. The effect of the incident position of the beam on the droplet characterization is considered, as are effects of white noise superimposed on the rainbow. For a spherical water droplet in the size range 50–200 μm, an accuracy of the measured relative refractive index up to 4 decimal places and a relative error in size smaller than 5% can be achieved in most cases.