  Phase-grating moire interferometers (PGMIs) have emerged as promising
candidates for the next generation of neutron interferometry, enabling the use
of a polychromatic beam and manifesting interference patterns that can be
directly imaged by existing neutron cameras. However, the modeling of the
various PGMI configurations is limited to cumbersome numerical calculations and
backward propagation models which often do not enable one to explore the setup
parameters. Here we generalize the Fresnel scaling theorem to introduce a
k-space model for PGMI setups illuminated by a cone beam, thus enabling an
intuitive forward propagation model for a wide range of parameters. The
interference manifested by a PGMI is shown to be a special case of the Talbot
effect, and the optimal fringe visibility is shown to occur at the moire
location of the Talbot distances. We derive analytical expressions for the
contrast and the propagating intensity profiles in various conditions, and
analyze the behaviour of the dark-field imaging signal when considering sample
characterization. The model's predictions are compared to experimental
measurements and good agreement is found between them. Lastly, we propose and
experimentally verify a method to recover contrast at typically inaccessible
PGMI autocorrelation lengths. The presented work provides a toolbox for
analyzing and understanding existing PGMI setups and their future applications,
for example extensions to two-dimensional PGMIs and characterization of samples
with non-trivial structures.
