Optical contrast and clarity of graphene on an arbitrary substrate

A molecularly thin dielectric film on a multilayer substrate can be treated as an additive perturbation of the substrate reflection coefficient r, for which the perturbation depends only on r and the optical properties of the film. This general result is applied to the problem of graphene on arbitrary substrates that seek to maximize the film contrast. We define clarity to describe the graphene image quality in the presence of charge-coupled device noise. A substrate with r=1 produces the highest graphene clarity in most practical situations.