The effect known as ``induced coherence without induced emission'' has
spawned a field dedicated to imaging with undetected photons (IUP), where
photons from two distinct photon-pair sources interfere if their outputs are
made indistinguishable. The indistinguishability is commonly achieved in two
setups. Induced coherence IUP (IC-IUP) has only the idler photons from the
first source passing through the second, whilst nonlinear interferometry
(NI-IUP) has both signal and idler photons from the first source passing
through the second and can be simpler to implement. In both cases, changes in
the idler path between sources can be detected by measuring the interference
fringes in the signal path in a way that allows image information to be moved
between different wavelengths. Here we model and implement a novel setup that
uses a polarization state quantum eraser approach to move continuously between
IC-IUP and NI-IUP operation. We find excellent agreement between experiment and
theory in the low-gain or quantum regime. The system also provides a new route
for optimizing IUP interference by using controllable quantum erasure to
balance the interferometer