  The Neutron-star Interior Composition Explorer (NICER) is an X-ray
astrophysics payload that will be placed on the International Space Station.
Its primary science goal is to measure with high accuracy the pulse profiles
that arise from the non-uniform thermal surface emission of rotation-powered
pulsars. Modeling general relativistic effects on the profiles will lead to
measuring the radii of these neutron stars and to constraining their equation
of state. Achieving this goal will depend, among other things, on accurate
knowledge of the source, sky, and instrument backgrounds. We use here simple
analytic estimates to quantify the level at which these backgrounds need to be
known in order for the upcoming measurements to provide significant constraints
on the properties of neutron stars. We show that, even in the
minimal-information scenario, knowledge of the background at a few percent
level for a background-to-source countrate ratio of 0.2 allows for a
measurement of the neutron star compactness to better than 10% uncertainty for
most of the parameter space. These constraints improve further when more
realistic assumptions are made about the neutron star emission and spin, and
when additional information about the source itself, such as its mass or
distance, are incorporated.
