Achromatic combinations of birefringent plates

Summary

An achromatic quarter-wave plate is obtained by superposing three birefringent plates of the same material; the first and last should have the same retardation 2δ₁ their fast vibration directions being parallel to one another but inclined at a specific anglec to that of the central plate—of retardation π. The desired range of achromatism determines the optimum values of 2δ₁ andc (which, in turn, will determine the orientation of the effective principal planes of the combination). As an example, using mica retardation plates prepared for Hg 5461, the range from 4100 Å to 6800 Å is covered with 2δ₁ = 115° 42′ andc = 69° 54′.

Further, for a particular wave-length, a birefringent compensator of variable retardation (0 to 2π) is obtained by interposing a half-wave plate that can be rotated in its own plane, between two quarter-wave plates that have their fast vibration directions parallel.

The results follow from the Poincaré sphere by geometrically compounding successive rotations.