  Single molecule localization microscopy is a recently developed
superresolution imaging technique to visualize structural properties of single
cells. The basic principle consists in chemically attaching fluorescent dyes to
the molecules, which after excitation with a strong laser may emit light. To
achieve superresolution, signals of individual fluorophores are separated in
time. In this paper we follow the physical and chemical literature and derive
mathematical models describing the propagation of light emitted from dyes in
single molecule localization microscopy experiments via Maxwell's equations.
This forms the basis of formulating inverse problems related to single molecule
localization microscopy. We also show that the current status of reconstruction
methods is a simplification of more general inverse problems for Maxwell's
equations as discussed here.
