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The distinction between a roof prism and a Porro prism is that for the roof prism the roof edge lies in the same plane as entrance and exit beam, while for a Porro prism the (left out) roof edge is orthogonal to the plane formed by the beams.
Porro prism and Perger prism binoculars and roof prism binoculars using the Abbe–Koenig roof prism do not use dielectric coatings because these prisms reflect with 100% reflectivity using total internal reflection in the prism rather than requiring a (dielectric) mirror coating.
These prisms are commonly used in binoculars as an image erecting system. The Schmidt–Pechan prism makes use of a roof prism section (from the German: "Dachkante", lit. roof edge). Binoculars designs using Schmidt–Pechan prisms can be constructed more compactly than ones using Porro or Uppendahl roof and Abbe–Koenig roof prisms.
In this way, since the 1990s, roof prism binoculars have also achieved resolution values that were previously only achievable with porro prisms. The presence of a phase-correction coating can be checked on unopened binoculars using two polarization filters.
Binoculars diagram showing an Abbe–Koenig prism. An Abbe–Koenig prism is a type of reflecting prism, used to invert an image (rotate it by 180°). They are commonly used in binoculars and some telescopes for this purpose. The prism is named after Ernst Abbe and Albert Koenig.
Image-erecting prisms for binoculars and spotting scopes include paired 45°-90°-45° Porro prisms (Fig. 14), the Porro–Abbe prism, the inline Koenig and Abbe–Koenig prisms, and the compact inline Schmidt–Pechan prism.