Estimating quantitative features of nanoparticles using multiple derivatives of scattering profiles

Characterization of nanoparticles on surfaces is a challenging inverse problem whose solution has many practical applications. This article proposes a method, suitable for in situ characterization systems, for estimating quantitative features of nanoparticles on surfaces from scattering profiles and their derivatives. Our method enjoys a number of advantages over competing approaches to this inverse problem. One such advantage is that only a partial solution is required for the companion direct problem. For example, estimating the average diameter of nanoparticles to be 53 nm is possible even when a researcher's existing scattering data pertain to nanoparticles whose average diameters are in multiples of 5 nm. Two numerical studies illustrate the implementation and performance of our method for inferring nanoparticle diameters and agglomeration levels respectively.