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We present topological derivative and energy based procedures for the imagingof micro and nanostructures using one beam of visible light of a singlewavelength. Objects with diameters as small as 10 nm can be located, and theirposition tracked with nanometer precision. Multiple objects distributed eitheron planes perpendicular to the incidence direction or along axial lines in theincidence direction are distinguishable. More precisely, the shape and size ofplane sections perpendicular to the incidence direction can be clearlydetermined, even for asymmetric and non-convex scatterers. Axial resolutionimproves as the size of the objects decreases. Initial reconstructions mayproceed by glueing together 2D horizontal slices between axial peaks or bylocating objects at 3D peaks of topological energies, depending on theeffective wavenumber. Below a threshold size, topological derivative basediterative schemes improve initial predictions of the location, size and shapeof objects by postprocessing fixed measured data. For larger sizes, trackingthe peaks of topological energy fields that average information from additionalincident light beams seems to be more effective.

Noninvasive imaging of three dimensional micro and nanostructures by topological methods