  Fluorescent Optical Tomography (FOT) is a new bio-medical imaging method with
wider industrial applications. It is currently intensely researched since it is
very precise and with no side effects for humans, as it uses non-ionising red
and infrared light. Mathematically, FOT can be modelled as an inverse parameter
identification problem, associated with a coupled elliptic system with Robin
boundary conditions. Herein we utilise novel methods of Calculus of Variations
in $L^\infty$ to lay the mathematical foundations of FOT which we pose as a
PDE-constrained minimisation problem in $L^p$ and $L^\infty$.
