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We determined the extinction ratio of a polarization analyser on the basis of Malus' law by relating the transmitted light intensity to the analyser azimuth measured at only a small range of analyser azimuth angles around the minimum position, thus avoiding the requirement for an optical detector with a high dynamic range. To adjust the orientation of the analyser azimuth we manufactured a precise rotation stage which had an angular resolution of less than rad. The minimum value of the extinction ratio was , obtained for a polarization analyser of the Glan - Taylor type. To calibrate the apparatus we measured the Faraday rotation of a glass plate placed in a magnetic field in the optical path.

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We developed a technique for the high-sensitivity detection of the magnetically induced birefringence of gases. Elliptically polarized light from a GaAlAs diode laser was used to probe the change in ellipticity caused by the presence of oxygen gas in a transverse magnetic field. The change in ellipticity was analysed with a polarization analyser. By using high-quality optical elements with small optical anisotropies, we improved the light-extinction ratio of the polarization-analysis system to 1 × 10-9 so that the noise caused by intensity fluctuations of the light source was reduced to a level below that of shot noise. The minimum value that could be detected for the change in ellipticity was 6 × 10-9 rad, which was larger by a factor of 1.4 than the value expected at the shot-noise limit. The experimental value of the signal-to-noise ratio agreed with the theoretical prediction taking account both of the shot noise and of the residual noise caused by light-source-intensity fluctuations.