Analysis of polarized light with two quarter-wave plates

The following method is proposed for the analysis of the elliptically polarized light leaving a transparent, birefringent and dichroic specimen (in which the direction of maximum absorption coincides with either of the principal axes of refractive index), oriented with its optic axis at +/-45 degrees relative to the transmission azimuth of the polarizer. Between the specimen and the rotatable analyser are two lambda/4 plates; that nearer the specimen is fixed with its slow axis at 90 degrees to the polarizer, while that nearer the analyser is rotatable. If the amplitude ratio of the components of light leaving the specimen is tan Y (Y being less than 45 degrees), and their relative retardation is Delta degrees, at compensation the azimuth of the rotatable lambda/4 plate will be Delta/2 (relative to its initial position orthogonal to the polarizer) and that of the analyser will be (45 degrees - Y), relative to the new azimuth of the rotatable lambda/4 plate. Apart from involving minimal calculations, the method is capable of high precision with suitable equipment, since all critical settings can be made with the aid of a Nakamura half-shade plate. Although so far used only in transmission polarization microscopy, the method is quite general and could be applied in any work involving polarized light.