  Adjoint field methods are both elegant and efficient for calculating
sensitivity information required across a wide range of physics-based inverse
problems. Here we provide a unified approach to the derivation of such methods
for problems whose physics are provided by Poisson's equation. Unlike existing
approaches in the literature, we consider in detail and explicitly the role of
general boundary conditions in the derivation of the associated adjoint
field-based sensitivities. We highlight the relationship between the adjoint
field computations required for both gradient decent and Gauss-Newton
approaches to image formation. Our derivation is based on standard results from
vector calculus coupled with transparent manipulation of the underlying partial
different equations thereby making the concepts employed here easily adaptable
to other systems of interest.
