Imaging with undetected photons (IUP) enables the possibility of sensing changes in the phase and the transmission of a beam of light that need never be detected. This has led to the possibility of infrared sensing with visible silicon camera technology, for example. Relying on the interference of two identical pairs of photons, IUP was initially achieved using unidirectional paths through two nonlinear crystal pair sources. More recently, folded arrangements using bidirectional paths through a single-crystal have become common for their simplicity. Here, we theoretically model and experimentally implement a novel setup involving three interference paths through a single nonlinear crystal. This establishes two independent IUP sensing modes in addition to a third linear interference mode. We achieve this using a polarization state quantum eraser approach, with excellent agreement between experiment and theory. This system provides a new route to control and optimize IUP interference in a single-crystal folded arrangement by using controllable quantum erasure to balance the interferometer, opening the door to new implementations and applications for IUP.
