Polarized microscopy with the Berek compensator: a comprehensive tutorial for the modern reader

Abstract

Compensators are polarization microscopy accessories that enable precise measurements of optical retardation. The Berek compensator is a type of compensator invented in the early twentieth century. Despite being still widely in use today, a comprehensive description of its inner workings, derived from first principles, is absent from the modern literature, rendering this instrument inaccessible to students and researchers new to the field. In this tutorial article, we first establish through geometrical optics the fundamental relation giving the variable retardation induced by the compensator as a function of its tilt angle. We then shed light on the approximate relation that is still universally given in the manufacturers’ manuals—which seem to not have been updated since the slide rule era. We then discuss a third tilt–retardation relation, obtained within the more rigorous framework of wave optics. Lastly, we detail the principle of operation of the instrument. We hope that this article becomes a go-to resource for the new generation of scientists looking for an in-depth introduction to the Berek compensator.