A series of grooved dielectric quarter-wave plates was made for radio astro
nomical Zeeman splitting observations at millimeter wavelengths. To meet th
e stringent requirements on reflection and polarization purity, a design me
thod was formulated based on optimization of multiple reflections. The meth
od solves the problem of achieving low reflections for both polarization co
mponents while attaining high purity of circular polarization, Several plat
es have been manufactured, tested, and used successfully for astronomical o
bservations.