The Plane-Parallel Plate

Abstract

16.1 Introduction There are two aspects that have to be dealt with when using a plane-parallel plate inserted in a converging or diverging beam. First, there are the aberrations, and second there is a relocation of the image. This relocation is a simple longitudinal shift if the plate is perpendicular to the optical axis. If the plate is tilted, as is the case with most beam splitters, there is a longitudinal and a lateral displacement, which is not too easy to assess because they interact. We shall address both cases. It should also be clear that most prisms behave like thick plane-parallel plates. This is indicated in Fig. 16.2 with a number of examples. The “unfolding” of the prism into an equivalent plane parallel plate is called the tunnel diagram. The first two examples are equivalent to plane-parallel plates inserted perpendicularly to the optical axis. The third one, the Dove prism, corresponds to a tilted plate, which of course introduces astigmatism and coma as will be pointed out further down in the text. For several reasons, such as cost and absorption, prisms are not much used in the infrared spectrum. However, wedges, which are thin prisms with a small apex angle, are employed in this region as beam-steering elements. The deviation of a ray exiting such a wedge is δ=(n−1)α, where n is the index of refraction, and α is the wedge angle. Details are shown in Fig. 16.1. A pair of counter-rotating wedges, known as Risley prisms, is used as a linear-scanning device.