An optimization tool for inverse problems of multilayered spherical particles

We present an optimization framework for retrieving the layer thicknesses and refractive indices of multilayered spherical particles from either angular scattering patterns or spectral scattering/extinction data. The forward problem is solved using the T-matrix formalism, with multiple recurrence schemes and analytical derivatives enabling efficient and accurate sensitivity analysis. The inverse problem is addressed within a global optimization setting that combines bound-constrained parameter estimation with optional data transformations for enhanced stability and reduced dimensionality. A MultiStart strategy is employed to explore the parameter space and identify distinct candidate solutions, followed by local refinement. As a point estimate, the minimum-residual solution is determined, while the associated uncertainties are computed using the covariance matrix approximation at the minimum-residual solution, and the marginal posterior expectation. The developed optimization tool is publicly available at https://github.com/DmitryEfremenko/MLSI .