An optimization scheme for the measurement of liquid jet parameters with rainbow refractometry based on Debye theory

Rainbow refractometry can be used to measure the radius and refractive index of a liquid jet. However, most existing algorithms are based on Airy theory or empirical formula from the angular spectrum of the rainbow. To apply the Airy formula, some characteristic information relevant to the radius and refractive index should be properly extracted from the rainbow. This is challenging for the liquid jet radius changing in a wide range because the rainbow structure, especially the ripple structure, is affected by the noise and the cone effect of a practical liquid jet. In this paper, a novel optimization scheme for the measurement of liquid jet parameters based on Debye theory (p=2) is proposed. First, an objective function is designed to quantify the deviation between the simulated rainbow with Debye theory (p=2) and the rainbow captured by a CCD camera. The liquid jet parameters are then determined by optimizing the objective function value. Experiments and numerical simulations are performed to evaluate the effectiveness of the scheme. Results indicate that the relative error of the radius is less than 12% and the absolute error of the refractive index is better than 1.1×10−3 when the real radius of the liquid jet is 25 μm. The measurement accuracy increases with the radius.