Achromatic and apochromatic halfwave and quarterwave retarders

Achromatic half-wave and quarter-wave retarders are com- monly produced by combining two plates of different birefringent materi- als with properly chosen thicknesses. A theoretical analysis is presented leading to a systematic procedure for choosing a combination of materi- als that minimizes the residual variation of the retardation with wave- length. This analysis also shows how the residual variation of the retar- dation with wavelength can be almost completely eliminated with a combination of three birefringent materials.