Search

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 (S P R). 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 S P R were conducted. The retrieved refractive indices, size or size distributions and fitted signals were analyzed. S P R = 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 S P R ≤ 1, rainbow refractometry can achieve absolute and relative errors of refractive index and size within 6 × 1 0 − 4 , 3% for monodisperse droplet and 2 × 1 0 − 4 , 8% for spray droplets. [Display omitted] • Study feasibility and accuracy of rainbow refractometry using incomplete signals. • Partial degree of rainbow signal is quantified by a newly defined variable (S P R). • S P R = 1 (primary peak position) is threshold for deterioration of inversion quality. • Inversion using full signal fitting is far superior to characteristic point methods. • Simulation conclusions are verified by experiments on monodisperse/spray droplets. [ABSTRACT FROM AUTHOR]

• Rainbow signal inversion algorithm based on ResNet and multi-objective regression. • The algorithm is comparable in accuracy to traditional ones but three times faster. • The structure and hyperparameters of the algorithm are determined in detail. • Loss competition relationship between droplet size and refractive index is studied. • An experimental validation system was built to verify the generalizability. Traditional standard rainbow inversion algorithms for retrieving droplet size and refractive index require time-consuming complex data pre-processing and multiple calculations, while optimized. This paper proposes a novel standard rainbow signal inversion algorithm based on residual networks and multi-objective regression. The algorithm requires only simple data pre-processing and is tested on a simulated data set covering representative signals from droplets with refractive indices of 1.33–1.35 and sizes of 60–240 μm. The average absolute error of the refractive index and average relative error of the droplet size are 9.16 × 10−5 and 0.55%, respectively. Experimental validations were carried under laboratory conditions on streams of mondisperse droplets and the robustness of the algorithm was verified under two conditions. In addition to its satisfactory inversion accuracy, the speed of each signal inversion is three times faster than traditional algorithms. The proposed algorithm meets the requirements of engineering applications and scientific research in terms of accuracy and real-time performance. [ABSTRACT FROM AUTHOR]