Rainbow refractometry using partial rainbow signals

Rainbow refractometry can offer simultaneous measurement of refractive index and size of droplets and has recently undergone interesting developments in spray measurement applications. Nevertheless, recording of incomplete rainbow signals from droplets with varying refractive index or at long working distances is often encountered, and these incomplete signals are usually considered invalid and are rejected. This study develops rainbow measurement using incomplete signals by systematically investigating the feasibility and accuracy. The partial degree of the rainbow signal was quantified by the newly defined dimensionless signal partial ratio (SPR). Simulations and inversions of typical incomplete standard rainbow and global rainbow patterns of droplets with three size distributions (normal, log-normal and bimodal normal) at various SPR were conducted. The retrieved refractive indices, size or size distributions and fitted signals were analyzed. SPR = 1 is the threshold for the deterioration of inversion quality. Inversion using signal fitting is far superior to the approaches using only specific characteristic points in terms of accuracy and precision. The above conclusions were also verified in laboratory experiments. For SPR <= 1, rainbow refractometry can achieve absolute and relative errors of refractive index and size within 6 x 10-4, 3% for monodisperse droplet and 2 x 10-4, 8% for spray droplets.