A model for the complex reflection coefficient of a collection of parallel layers

Reflectometry is a technique that uses the light reflected by a sample to determine properties of the sample. Interferometric reflectometry uses interference between two beams, one of which is incident on ---and reflected back by--- a sample and one of which is not, to obtain the complex electric field rather than merely its intensity. Since this interference allows one to retrieve an increased amount of information about the light, it also allows one to obtain more information about the sample, such as a thin layer. We will apply the methods derived here to the case of a planar lipid bilayer.