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 53nm is possible even when a researcher's existing scattering data pertain to nanoparticles whose average diameters are in multiples of 5nm. Two numerical studies illustrate the implementation and performance of our method for inferring nanoparticle diameters and agglomeration levels respectively.