基于彩虹散射的液滴参数测量研究
Research on Droplet Parameter Measurement Based on Rainbow Scattering

本研究提出了一种结合几何光学理论和实验测量的综合方法，用于分析彩虹散射图案以表征液滴。首先，采用几何光学近似方法，通过追踪不同阶光线在液滴内的轨迹来计算其彩虹角，而艾里理论阐明了彩虹条纹的干涉机制。设计了一个实验系统来捕获液滴的彩虹散射图案。采集的图像经过滤波和归一化处理，提取第一和第二波谷的角度，以反演液滴粒径和折射率。实验结果表明，一阶彩虹角的测量值与理论预测之间的偏差小于0.25%，验证了光学反演模型在球形液滴参数测量中的可靠性。然而，研究也发现现有模型存在适用范围限制：当液滴椭球度超过0.66时，粒径反演误差显著增加至3.5%；而在椭球度小于0.5时，折射率误差则低于0.0004%。
This study proposes a comprehensive method combining geometric optics theory and experimental measurements for analyzing rainbow scattering patterns to characterize droplets. Firstly, the geometric optical approximation method is used to calculate the rainbow angle of the droplet by tracking the trajectories of different order rays inside the droplet, and Airy’s theory elucidates the interference mechanism of rainbow fringes. Designed an experimental system to capture rainbow scattering patterns of liquid droplets. The collected images are filtered and normalized to extract the angles of the first and second valleys, in order to invert the droplet size and refractive index. The experimental results show that the deviation between the measured value of the first-order rainbow angle and the theoretical prediction is less than 0.25%, which verifies the reliability of the optical inversion model in measuring the parameters of spherical droplets. However, research has also found that existing models have limitations in their applicability: when the droplet ellipsoid degree exceeds 0.66, the particle size inversion error significantly increases to 3.5%; When the ellipticity is less than 0.5, the refractive index error is less than 0.0004%.