A roof prism, also called a Dachkanten prism or Dach prism (from

German German(s) may refer to: * Germany (of or related to) **Germania (historical use) * Germans, citizens of Germany, people of German ancestry, or native speakers of the German language ** For citizens of Germany, see also German nationality law **Ger ...

: ''Dachkante'', lit. "roof edge"), is a reflective prism containing a section where two faces meet at a 90° angle, resembling the

roof A roof ( : roofs or rooves) is the top covering of a building, including all materials and constructions necessary to support it on the walls of the building or on uprights, providing protection against rain, snow, sunlight, extremes of temper ...

of a building and thus the name. Reflection from the two 90° faces returns an image that is flipped laterally across the axis where the faces meet. Characteristic for a roof prism is that the beam is split in half, with one half of the beam hitting first one face then the other face, while it is invert for the other half of the beam. Therefore, a roof prism can be used only with some distance to focal planes, or the "edge" of the roof would introduce slight distortions. Furthermore, the angle between the two faces has to be very close to 90°, or image quality would be degraded. The simplest roof prism is the

Amici roof prism 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 ...

, with other common roof prism designs being the

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. The prism is ...

, the

Schmidt–Pechan prism 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: ...

and probably the best known being the roof pentaprism (pictured right). A

Porro prism In optics, a Porro prism, named for its inventor Ignazio Porro, is a type of ''reflection prism'' used in optical instruments to alter the orientation of an image. Description It consists of a block of material shaped like a right geometric ...

is ''not'' a roof prism contrary to popular notion, as the Porro prism's two 90° faces usually don't meet and therefore don't form a roof edge.

Phase correction

The multiple internal reflections cause a polarization-dependent phase-lag of the transmitted light, in a manner similar to a

Fresnel rhomb A Fresnel rhomb is an optical prism that introduces a 90° phase difference between two perpendicular components of polarization, by means of two total internal reflections. If the incident beam is linearly polarized at 45° to the plane of inc ...

. This must be suppressed by multilayer ''phase-correction coatings'' applied to one of the roof surfaces to avoid unwanted

interference Interference is the act of interfering, invading, or poaching. Interference may also refer to: Communications * Interference (communication), anything which alters, modifies, or disrupts a message * Adjacent-channel interference, caused by extr ...

effects and a loss of contrast in the image. Dielectric phase-correction prism coatings are applied in a vacuum chamber with maybe thirty or more different superimposed vapor coating layers deposits, making it a complex production process. In a roof prism without a phase-correcting coating, s-polarized and p-polarized light each acquire a different

geometric phase In classical and quantum mechanics, geometric phase is a phase difference acquired over the course of a cycle, when a system is subjected to cyclic adiabatic processes, which results from the geometrical properties of the parameter space of the Ha ...

as they pass through the upper prism. When the two polarized components are recombined,

between the s-polarized and p-polarized light results in a different intensity distribution perpendicular to the roof edge as compared to that along the roof edge. This effect reduces contrast and resolution in the image perpendicular to the roof edge, producing an inferior image compared to that from a

porro prism In optics, a Porro prism, named for its inventor Ignazio Porro, is a type of ''reflection prism'' used in optical instruments to alter the orientation of an image. Description It consists of a block of material shaped like a right geometric ...

erecting system. This roof edge diffraction effect may also be seen as a

diffraction spike Diffraction spikes are lines radiating from bright light sources, causing what is known as the starburst effect or sunstars in photographs and in vision. They are artifacts caused by light diffracting around the support vanes of the secondary m ...

perpendicular to the roof edge generated by bright points in the image. In technical optics, such a

phase Phase or phases may refer to: Science *State of matter, or phase, one of the distinct forms in which matter can exist *Phase (matter), a region of space throughout which all physical properties are essentially uniform * Phase space, a mathematic ...

is also known as the Pancharatnam phase, and in quantum physics an equivalent phenomenon is known as the

Berry phase In classical and quantum mechanics, geometric phase is a phase difference acquired over the course of a cycle, when a system is subjected to cyclic adiabatic processes, which results from the geometrical properties of the parameter space of the ...

. This effect can be seen in the elongation of the

Airy disk In optics, the Airy disk (or Airy disc) and Airy pattern are descriptions of the best- focused spot of light that a perfect lens with a circular aperture can make, limited by the diffraction of light. The Airy disk is of importance in physics, ...

in the direction perpendicular to the crest of the roof as this is a

diffraction Diffraction is defined as the interference or bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a s ...

from the discontinuity at the roof crest. The unwanted interference effects are suppressed by vapour-depositing a special

dielectric coating A dielectric mirror, also known as a Bragg mirror, is a type of mirror composed of multiple thin layers of dielectric material, typically deposited on a substrate of glass or some other optical material. By careful choice of the type and thickne ...

known as a phase-compensating coating on the roof surfaces of the roof prism. These ''phase-correction coating'' or ''P-coating'' on the roof surfaces was developed in 1988 by Adolf Weyrauch at

Carl Zeiss Carl Zeiss (; 11 September 1816 – 3 December 1888) was a German scientific instrument maker, optician and businessman. In 1846 he founded his workshop, which is still in business as Carl Zeiss AG. Zeiss gathered a group of gifted practica ...

A. Weyrauch, B. Dörband: ''P-Coating: Improved imaging in binoculars through phase-corrected roof prisms.'' In: ''Deutsche Optikerzeitung.'' No. 4, 1988.
/ref> Other manufacturers followed soon, and since then phase-correction coatings are used across the board in medium and high-quality roof prism binoculars. This coating corrects for the difference in geometric phase between s- and p-polarized light so both have effectively the same phase shift, preventing image-degrading interference. From a technical point of view, the phase-correction coating layer does not correct the actual phase shift, but rather the partial polarization of the light that results from total reflection. Such a correction can always only be made for a selected wavelength and for a specific angle of incidence; however, it is possible to approximately correct a roof prism for polychromatic light by superimposing several layers. In this way, since the 1990s, roof prism binoculars have also achieved resolution values that were previously only achievable with porro prisms.Konrad Seil: Progress in binocular design. In: SPIE Proceedings. Band 1533, 1991, S. 48–60, doi:10.1117/12.48843 The presence of a phase-correction coating can be checked on unopened binoculars using two polarization filters.

References

External links

* https://www.knivesandtools.com/en/ct/binoculars-glossary-roof-prism.htm * https://lookforword.net/binoculars/roof-prisms/ * https://www.bestbinocularsreviews.com/blog/cheap-binoculars-roof-or-porro-prism-best-02/ {{DEFAULTSORT:Roof Prism Prisms (optics) de:Dachkantprisma