Planar rainbow refractometry

Three-dimensional rainbow refractometry

We propose a new, to the best of our knowledge, rainbow technique called three-dimensional rainbow refractometry (TDRR), with a cylindrical lens in the signal collecting system. With a TDRR model based on the ray transfer matrix developed, it is proved that the tilt angle of the rainbow signal is related to the axial position of the droplet, which helps to obtain the 3D position. By converting rainbow scattering angle calibration into the system parameter calibration, a new rainbow data processing program is written in combination with the model to obtain the refractive index and the particle size. With TDRR, we measured a monodisperse droplet stream of deionized water at room temperature for experimental validation and obtained the refractive index with an absolute error of less than 0.0015, the droplet size with an error within ±5%, and the axial position with an error within ±3%, which demonstrated a high accuracy of TDRR.

Droplet sizing in atomizing sprays using polarization ratio with structured laser illumination planar imaging

Previous research has shown that the polarization ratio technique allows the characterization of the surface mean diameter, D₂₁, of droplets forming dilute sprays. However, its application to optically dense sprays has posed significant challenges due to the presence of multiple light scattering. Additionally, errors in measurement can arise from the angular dependence of the signal. In this Letter, we present a novel, to the best of our knowledge, method that addresses these challenges. Our approach combines the use of a telecentric objective with structured laser illumination, to both optimize light detection and suppress the unwanted intensity from multiple scattering. This approach enables the utilization of the polarization ratio technique for measuring the droplet size of challenging atomizing sprays. The method offers a promising solution for accurate and comprehensive spray characterization. It is applied, here, to a hollow-cone water spray running at 30, 50, and 70 bar injection pressure, reaching an optical depth up to three.

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

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.

Synthetic aperture rainbow refractometry

This work proposed a synthetic aperture rainbow refractometry (SARR) by synthesizing rainbow signals of the same droplet with dual-wavelength laser beams, in order to increase the aperture of rainbow refractometry. In this way, the SARR can apply to long distance and small droplets measurement. An achromatic imaging system, which simultaneously records while separating the two rainbow signals in two channels of a color image, is elaborately designed. A data processing algorithm is developed to retrieve the optimal droplet refractive index and size. Numerical simulations of different droplet sizes from 10 μm to 200 μm certify the viability of the SARR. Proof-of-concept experiments of micron-sized ethanol droplets are performed with 1650 mm measurement distance. Results show that the SARR can accurately measure droplet refractive index and size with uncertainties of 2.3 × 10^-4 and 2μm, respectively. The feasibility and accuracy of the proposed SARR are successfully demonstrated, paving the way for rainbow refractometry applied to large-scale industrial applications.