Existence of invisible nonscattering objects and nonradiating sources

The radiation that is due to the scattering of an incoming light wave from an object or that is generated by a source distribution is considered. It is assumed that the field propagation can be described by the equation of radiative transport or, in the P1 approximation, by the diffusion equation. It is shown by explicit examples that there is a class of object (source) distributions that generate scattered (radiation) fields that are identically zero outside these distributions. The existence of these invisible object and source distributions leads to serious complications for the inverse, i.e., the reconstruction, problem.