Optimum Half-Shade Angle in Polarizing Instruments

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Abstract
For visual instruments employing polarized light, half-shade devices have long been used to increase the precision of analyzer settings. Also when an object of small birefringence is to be detected against a uniform background a bias retardation has been used to increase the contrast. Assuming that Weber’s law is valid and that the polarization of the instrument is not perfect, optimum values are calculated for the half-shade angle and the bias retardation. In each case the sensitivity is shown to increase roughly as the square root of the extinction factor, the extinction factor (E) being defined as the ratio of the maximum to the minimum flux transmitted by the analyzer. For an interference microscope with E=35 the optimum half-shade angle is 19.2°. For a polarizing microscope with E=104 the optimum half-shade angle and bias retardation are each 1.1°.

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