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Roof prisms make for slimmer binoculars, but they’re usually more expensive due to their more complicated manufacturing, allowing the prism to align with the eyepiece and the binocular tube.
The simplest roof prism is the Amici roof prism, with other common roof prism designs being the Abbe–Koenig prism, the Schmidt–Pechan prism and probably the best known being the roof pentaprism (pictured right).
A Schmidt–Pechan prism is a type of optical prism used to rotate an image by 180°. 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 using either a Schmidt–Pechan roof prism, Abbe–Koenig roof prism or an Uppendahl roof prism benefit from phase coatings that compensate for a loss of resolution and contrast caused by the interference effects that occur in untreated roof prisms.
Roof prism designs allow a simpler exterior, and are now common but they are more expensive to produce. Complicating production requirements make high-quality roof prism design binoculars relatively costly to produce compared to in optical quality equivalent Porro prism binoculars.
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 .