Curvature corrected impedance boundary conditions in an arbitrary basis

We present a generalization of the Rytov analysis for curvature corrections to the impedance boundary condition (IBC) that allows such boundary conditions to be written down using general coordinate systems and bases for vectors. This removes the need to base the analysis of IBCs on either principal curvature axes or on hypothetical orthogonal coordinate systems. As an application, we show how to write down high-order IBCs for surfaces that are the deformation of a plane. We also show how the use of such an IBC can be used to further reconcile Kirchhoff and small perturbation methods.