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The measurement of the poloidal magnetic field in a tokamak plasma from the Zeeman splitting and polarization of the magnetic dipole radiation from heavy ions is discussed. When viewed from a direction perpendicular to the toroidal field, the effect of the poloidal field on the circularly polarized radiation is detectable using a photoelectric polarimeter. The Zeeman splittings for a number of magnetic dipole transitions with wavelengths in the range 2300–9300 Å are presented. An imaging polarimeter is proposed that can measure the poloidal magnetic field with space and time resolution.