Customized retarders based on waveplates

Phase control is a critical parameter in polarization measurements. It is well known that a proper combination of wave plates allows to obtain achromatic phase shift, i.e., a constant retardation in certain spectral ranges. This paper is focused on a different, but more useful, goal, as it is to achieve customized variable retarders in broad spectral ranges. To do that, a merit function was used to measure the similarity between the overall phase shift of the wave plate combinations and the desired target. The control variables are the thicknesses and orientations of the wave plates. All possible combinations with four and five wave plates of quartz and MgF₂ were analyzed, but our approach can be perfectly extended to deal with more wave plates. The result of an optimization process determines the thicknesses and orientations of the wave plates, which results in the closest retarder to the desired one. Numerical results show deviations below 10% between the target and the obtained retardation. These systems are of special interest in those fields and instruments in which polarization control plays a fundamental role.