Abstract
In this paper we propose and analyse a Gedankenexperiment involving three non-linear crystals and two objects inserted in the idler beams. We show that, besides the behaviour that can be extrapolated from previous experiments involving two crystals and one object, we are able to predict a new effect: under certain circumstances, one of the objects can be rendered undetectable to any single detection rate on the signal photons with discarded idler photons. This effect could find applications in future developments of quantum imaging techniques.