Inversion Algorithm of Rainbow Signal Based on Local Minimum

For a parametric inversion of standard or global rainbow signals,this study proposes a local minimabased general inversion algorithm,establishes a nonlinear optimized objective function with inequality constraints based on the complex angular momentum theory theory with correction coefficients and iteratively solves the function using sequential quadratic programming. Before the inversion, a different signal preprocessing, including the removal of the high-frequency structure and the inversion parameter range estimation, was performed for the standard and global rainbow signal. The rainbow signals of the droplets with different refractive indices and droplet size distributions (logarithmic and normal distributions) were numerically simulated based on the Lorenz-Mie theory. The proposed inversions with or without the size distribution were performed to verify the algorithm's effectiveness. The results show that the maximum absolute error of the refractive index of the standard rainbow signal inversion is less than 3x10(-4),and the maximum relative error of the droplet size is 1. 3%. Under various conditions,the error of the refractive index of the global rainbow signal inversion is less than 1x10(-4),and the relative error of the mean droplet size is less than 1. 67%. Finally,the algorithm was verified via the experimental standard and global rainbow data.

Automated summary

A local minimabased general inversion algorithm was proposed and tested on standard and global rainbow signals, with promising results indicating its effectiveness under different conditions. The algorithm is based on complex angular momentum theory with correction coefficients and iterative sequential quadratic programming.