Angle of incidence averaging in reflectance measurements with optical microscopes for studying layered two-dimensional materials

Abstract

Reflectance spectrum measured using an optical microscope with a large numerical aperture objective lens is shown to get modified. The change is most prominent when there are optical interference related features in the spectrum. This modification is shown to arise primarily due to the wide range of angles of incidence involved in the measurement and a simple formulation is provided to correct for this in simulations. The importance of such analysis is brought out through a reflectance contrast spectroscopy based study for identifying mono-layer and bi-layer graphene and MoS2.