A Precise and Fast Droplet Parameter Inversion Algorithm for Rainbow Scattering Detection

The rainbow scattering technique holds significant promise for simultaneously detecting micrometer-sized droplet size and refractive index. Reported here is a fast and lightweight deep-learning-based rainbow inversion algorithm containing a unique signal preprocessor and a novel signal inversion network. Rainbow signal is preprocessed based on scattering intensity, scattering angle, and its intensity-angle area to effectively preserve the physical features. A multilayer perceptron (MLP)-based rainbow inversion network is constructed for more effective inversion of droplet size and refractive index at the global sensory field level. The algorithm achieves a 50fold speedup compared with conventional methods without compromising accuracy. Extensive simulations demonstrate an average relative error of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${0}.{89}\%$ </tex-math></inline-formula> in droplet size estimation and an average absolute error of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${3}.{81}\times {10} ^{-{5}}$ </tex-math></inline-formula> in refractive index determination. Experimental validation further confirms the algorithm’s reliability. This work not only offers significant improvements in computational speed and accuracy but also opens new avenues for advanced droplet parameter inversion algorithms.