A method for scattering angle calibration in the rainbow region using a droplet stream

Abstract

Accurate quantification of scattering angle versus detector pixel strongly determines the measurement accuracy of rainbow refractometry. This is an emerging measurement technique operating at backscatter angles and characterizing droplets or complex droplets in terms of size and refractive index. A novel method for calibration of the rainbow scattering angle using a monodisperse droplet stream is introduced and the achievable accuracy is estimated. The assumption of a linear pixel-to-angle relation is derived, and a calibration procedure is proposed based on global fit of calibration data to the theoretically known rainbow signal. The accuracy of this method was examined by simulations and experiments, where the uncertainties of a priori parameters of droplets were also considered and validated using shadowgraphy as a ground truth. The results confirm the feasibility of this method with a maximum absolute error of 0.032°and 3.9E-5°/pixel respectively for the intercept and slope of the linear relationship. These values translate into maximum uncertainties in diameter and refractive index of approx. 0.67% and 2.8 × 10−4.