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The rotation of the plane of polarization of radiation propagating through a magnetized plasma (Faraday effect) yields the line integral of the electron density times the longitudinal magnetic field component. A commonly used technique for this measurement senses the change in intensity of a laser beam after passing through a linear polarizer. Two methods often employed to facilitate detection are 1) to mix the transmitted beam with a frequency-offset reference beam to allow heterodyne detection and 2) to oscillate the polarization direction of the laser beam. In addition to being sensitive to spurious amplitude variations, such amplitude measurements are sensitive to small polarization ellipticities introduced by optical components as well as by transverse magnetic fields within the plasma. By the addition of a quarter wave plate, the Faraday rotation can alternatively be sensed as a phase shift of the heterodyne beat of two frequency-offset input beams relative to the case of no plasma. This scheme has the advantage of phase modulation over amplitude modulation, i.e., independence of absolute amplitude and weak dependence on amplitude change. We demonstrate with Jones matrix algebra how the measured phase shift depends only weakly on imperfections and angular alignments of the optical components. Moreover, the phase shifts can be increased more than an order of magnitude by deliberate modifications in the basic optical configuration at a sacrifice of comparable amounts of the amplitude modulation of the carrier from which the phase shift is determined.