Schmidt-Pechan prism
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A Schmidt-Pechan prism is a type of optical prism used to rotate an image by 180°. They are commonly used in binoculars as an image erecting system.
The prism consists of two glass prisms separated by an air-gap. Multiple total internal reflections of the light cause a vertical flipping of the image; a "roof" section of the second prism also flips the image laterally, together causing a 180° rotation of the image. The image's handedness is not changed.
Compared to the double-Porro prism or Abbe-Koenig designs, the Schmidt-Pechan is much more compact. However, the large number of reflections and glass/air transitions of the light make the prism more lossy than the other designs. Some of the surfaces must be optically coated for efficient internal reflection, since the light is incident at an angle less than the critical angle.
The multiple internal reflections also cause a polarization-dependent phase-lag of the transmitted light, in a manner similar to a Fresnel rhomb. This must be suppressed by special phase-correction coatings to avoid unwanted interference effects on the image.