Schmidt–Pechan prism

The Schmidt-Pechan is based on the Pechan prism design: Both are a composite of two prisms, separated by an air gap. The Pechan will invert or revert (flip) the image, depending on the orientation of the prism, but not both at the same time. For the Schmidt-Pechan design, the upper prism from the Pechan design is replaced with a Schmidt roof prism, so the Schmidt–Pechan prism can both invert and revert the image and so act as an image rotator. The lower prism is known as a half-penta prism or Bauernfeind prism. The image's handedness is not changed by the Schmidt-Pechan.

The design of the two prisms is such that the entrance beam and exit beam are coaxial, i.e. the Schmidt–Pechan prism does not deviate the beam if centered on the optical axis. The "roof" section of the upper prism flips (reverts) the image laterally with two total internal reflections in the horizontal plane from the roof surface: once on each side of the roof. This latter pair of reflections can be considered as one reflection in the vertical plane. Both inversion and reversion together cause a 180° rotation of the image, but in doing so deviate the path by 45°. The lower prism corrects for this by interfacing the beam at 45° with the upper prism. The lower prism uses one total internal reflection, followed by a second reflection on the bottom surface to direct the beam into the second Schmidt prism. This second reflection in the lower prism happens at less than the critical angle, therefore the Schmidt–Pechan prism requires a reflective coating for this surface to be usable in practice. This is unlike other roof prisms, like the Abbe–Koenig prism, which use total internal reflection on all reflective surfaces.