  Interest in the study of magnetic fields and the properties of interstellar
dust, explored through increasingly capable far-IR/submillimeter polarimetry,
along with maturing detector technology, have set the stage for a
transformative leap in polarization mapping capability using a cryogenic space
telescope. We describe the approach pursued by the proposed Probe far-Infrared
Mission for Astrophysics (PRIMA) to make ultra-deep maps of intensity and
polarization in four bands in the 91-232 micron range. A simple,
polarimetry-optimized PRIMA Polarimetric Imager (PPI) is designed for this
purpose, consisting of arrays of single-polarization Kinetic Inductance
Detectors oriented with three angles which allow measurement of Stokes I, Q,
and U in single scans. In this study, we develop an end-to-end observation
simulator to perform a realistic test of the approach for the case of mapping a
nearby galaxy. The observations take advantage of a beam-steering mirror to
perform efficient, two-dimensional, crossing scans. Map making is based on
'destriping' approaches demonstrated for Herschel/SPIRE and Planck. Taking
worst-case assumptions for detector sensitivity including 1/f noise, we find
excellent recovery of simulated input astrophysical maps, with I, Q, and U
detected at near fundamental limits. We describe how PPI performs detector
relative calibration and mitigates the key systematic effects to accomplish
PRIMA polarization science goals.
