Using global optimization for a microparticle identification problem with noisy data

We report some experience with optimization methods applied to an inverse light scattering problem for spherical, homogeneous particles. Such particles can be identified from experimental data using a least squares global optimization method. However, if there is significant noise in the data, the "best" solution may not correspond well to the "actual" particle. We suggest a way in which the original least squares solution may be improved by using a constrained optimization calculation which considers the position of peaks in the data. This approach is applied first to multi-angle data with varying amounts of artificially introduced noise and then to examples of single-particle experimental data patterns characterized by high noise levels.