How does IXPE measure polarization?
Short answer: Electrons in the detector are preferential emitted in the direction of the polarization of the incident photon and then detected.
Quoting from NASA's IXPE: Polarization Detection page:
IXPE will have three identical X-ray telescopes, with polarization
detectors at each focus. The detectors, called Gas Pixel Detectors
(GPD) are based on proportional counters (see Mullard Space Science
Laboratory's Introduction to Proportional Counters). Polarized X rays
interacting with a gaseous medium create photoelectons that are
preferentially emitted in the polarization direction. Photoelectron
tracks mark the path of the photoelectron from the position of the
initial X-ray interaction to its stopping point. Analysis of the
distribution of the initial directions of the tracks gives the degree
of polarization and the position angle from the incident X ray.
Why does it have three identical X-ray telescopes?
Quoting from IXPE - Satellite Missions - eoPortal Directory:
Short answer: Redundancy and the three smaller systems could be accommodated better than one larger equivalent telescope.
These trades were completed and the result is the three telescope
system described here which meets science objectives and requirements
with margin while placing reasonable and achievable demands on the
spacecraft, launch vehicle, and the deployable optical bench.
Specifically, three identical systems provide redundancy, a range of
detector clocking angles to mitigate against any detector biases,
shorter focal length for given mirror graze angles (i.e., given energy
response) and thinner/lighter mirrors compared to a single telescope