Achromatic and apochromatic halfwave and quarterwave retarders

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