  The Primordial Inflation Explorer (PIXIE) is an Explorer-class mission
concept to measure the gravitational-wave signature of primordial inflation
through its distinctive imprint on the linear polarization of the cosmic
microwave background (CMB). Its optical system couples a polarizing Fourier
transform spectrometer to the sky to measure the differential signal between
orthogonal linear polarization states from two co-pointed beams on the sky. The
double differential nature of the four-port measurement mitigates beam-related
systematic errors common to the two-port systems used in most CMB measurements.
Systematic errors coupling unpolarized temperature gradients to a false
polarized signal cancel to first order for any individual detector. This
common-mode cancellation is performed optically, prior to detection, and does
not depend on the instrument calibration. Systematic errors coupling
temperature to polarization cancel to second order when comparing signals from
independent detectors. We describe the polarized beam patterns for PIXIE and
assess the systematic error for measurements of CMB polarization.
