Noninvasive Imaging of Three-Dimensional Micro and Nanostructures by Topological Methods

Abstract

We present topological derivative and energy based procedures for the imaging of micro and nanostructures using one beam of visible light of a single wavelength. Objects with diameters as small as 10 nm can be located, and their position tracked with nanometer precision. Multiple objects distributed either on planes perpendicular to the incidence direction or along axial lines in the incidence direction are distinguishable. More precisely, the shape and size of plane sections perpendicular to the incidence direction can be clearly determined, even for asymmetric and non-convex scatterers. Axial resolution improves as the size of the objects decreases. Initial reconstructions may proceed by glueing together 2D horizontal slices between axial peaks or by locating objects at 3D peaks of topological energies, depending on the effective wavenumber. Below a threshold size, topological derivative based iterative schemes improve initial predictions of the location, size and shape of objects by postprocessing fixed measured data. For larger sizes, tracking the peaks of topological energy fields that average information from additional incident light beams seems to be more effective.