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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.
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 ).
A roof prism, also called a Dachkanten prism or Dach prism (from German: Dachkante, lit. "roof edge"), is a reflective prism containing a section where two faces meet at a 90° angle, resembling the roof of a building and thus the name.
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.
BAK-4 barium crown glass (glass code 569560) has a higher index of refraction than BK7, and is used for prisms in high-end binoculars. In that application, it gives better image quality and a round exit pupil. An achromatic doublet, which combines crown glass and flint glass.
Abbe-Koenig prisms are significantly longer than Schmidt–Pechan prisms, and were and are rarely used except in large roof prism type binoculars, where light weight, compact size and cost are less important than ultimate light-gathering power.
An Amici roof prism, named for its inventor, the Italian astronomer Giovanni Battista Amici, is a type of reflecting prism used to deviate a beam of light by 90° while simultaneously inverting the image. It is commonly used in the eyepieces of telescopes as an image erecting system.
Roof prisms use TIR at two faces meeting at a sharp 90° angle. This category includes the Koenig, Abbe–Koenig, Schmidt–Pechan, and Amici types (already mentioned), and the roof pentaprism used in SLR cameras; the last of these requires a reflective coating on one non-TIR face.
Prism sights are a type of telescopic sight with similar features and limitations. Most prism sights use roof prisms commonly seen in compact binoculars and spotting scopes.
A Perger prism or Perger–Porro prism system is a prism, that is used to invert (rotate by 180°) an image. The special feature of this prism is that, like a traditional double Porro prism system, it manages this with only four beam deflections and has neither a roof edge with the accompanying phase correction problems, a mirrored surface or ...