  Precision polarimetry is essential for future e+ e- colliders and requires
Compton polarimeters designed for negligible statistical uncertainties. In this
paper, we discuss the design and construction of a quartz Cherenkov detector
for such Compton polarimeters. The detector concept has been developed with
regard to the main systematic uncertainties of the polarisation measurements,
namely the linearity of the detector response and detector alignment.
Simulation studies presented here imply that the light yield reachable by using
quartz as Cherenkov medium allows to resolve in the Cherenkov photon spectra
individual peaks corresponding to different numbers of Compton electrons. The
benefits of the application of a detector with such single-peak resolution to
the polarisation measurement are shown for the example of the upstream
polarimeters foreseen at the International Linear Collider. Results of a first
testbeam campaign with a four-channel prototype confirming simulation
predictions for single electrons are presented.

Instrumentation and Detectors;High Energy Physics - Experiment