A Schmidt–Pechan prism is a type of optical prism

Prism (optics)

In optics, a prism is a transparent optical element with flat, polished surfaces that refract light. The exact angles between the surfaces depend on the application. The traditional geometrical shape is that of a triangular prism with a triangular base and rectangular sides, and in colloquial use...

 used to rotate an image by 180°

Degree (angle)

A degree , usually denoted by ° , is a measurement of plane angle, representing 1⁄360 of a full rotation; one degree is equivalent to π/180 radians...

. They are commonly used in binoculars

Binoculars

Binoculars, field glasses or binocular telescopes are a pair of identical or mirror-symmetrical telescopes mounted side-by-side and aligned to point accurately in the same direction, allowing the viewer to use both eyes when viewing distant objects...

 as an image erecting system. Compared to binoculars using a Porro

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....

 or Abbe–Koenig prism a binoculars using a Schmidt–Pechan "roof" (German Dach) prism is more compact.

Method of Operation

The Schmidt–Pechan prism is a merger of the designs of the Schmidt prism and the Pechan prism.

The Pechan prism is a composite of two prisms separated by an air gap. It will invert or revert (flip) the image depending up orientation of the prism but not both at the same time. By replacing the second prism in the Pechan design with a Schmidt prism the Schmidt–Pechan prism can both invert and revert the image and so act as an image rotator.

The Schmidt–Pechan prism consists of two glass prisms separated by an air-gap. The second, Schmidt, prism both reverts and inverts the image but in doing so deviates the path by 45°. The first prism corrects for this delivering a beam at 45° into the Schmidt prism. The design of the first prism 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 lower prism uses one total internal reflection

Total internal reflection

Total internal reflection is an optical phenomenon that happens when a ray of light strikes a medium boundary at an angle larger than a particular critical angle with respect to the normal to the surface. If the refractive index is lower on the other side of the boundary and the incident angle is...

 followed by a reflection from a mirrored surface to direct the beam into the second Schmidt prism so the orientation of the image is not changed.

The upper prism inverts the image by three total internal reflections in the vertical plane through the roof ridge. The "roof

Roof prism

A roof prism is in general any kind of reflective optical prism containing a section where two faces meet at a 90° angle...

" section of the Schmidt 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. The image's handedness

Handedness

Handedness is a human attribute defined by unequal distribution of fine motor skills between the left and right hands. An individual who is more dexterous with the right hand is called right-handed and one who is more skilled with the left is said to be left-handed...

 is not changed.

The reflection from the bottom surface of the first prism is not by total internal reflection since the light is incident at an angle less than the critical angle

Total internal reflection

Total internal reflection is an optical phenomenon that happens when a ray of light strikes a medium boundary at an angle larger than a particular critical angle with respect to the normal to the surface. If the refractive index is lower on the other side of the boundary and the incident angle is...

. This is unlike other roof prisms like the Abbe–Koenig prism. This surface of the Schmidt–Pechan prism requires a reflective coating for this prism to be usable in practice.

Glass–air transitions

All of the entry and exit surfaces must be optically coated

Optical coating

An optical coating is one or more thin layers of material deposited on an optical component such as a lens or mirror, which alters the way in which the optic reflects and transmits light. One type of optical coating is an antireflection coating, which reduces unwanted reflections from surfaces, and...

 to minimize losses, though the type of coating has to be carefully chosen as the same faces of the prism act both as entry faces (desiring good anti-reflection coating) and internally reflective faces (require a coating maximizing reflection). A paper, "Progress in Binocular Design", by Konrad Seil at Swarovski Optik

Swarovski Optik

Swarovski Optik is an Austrian manufacturer of sports optics, including binoculars, rifle scopes, telescopes, laser rangefinders and image intensifiers. Its headquarters are in Absam, Tyrol, where most of the products are developed and manufactured....

 shows that single-layer anti-reflective coatings on these surfaces maximized image contrasthttp://www.optics.arizona.edu/optomech/references/papers/Seil%201991.pdf.

Reflection losses

As the light is incident at a glass–air boundary with an angle less than the critical angle

Critical angle

Critical angle can refer to:*Critical angle the angle of incidence above which total internal reflection occurs*Critical angle of attack, in aerodynamics; the angle of attack which produces the maximum lift coefficient...

, total internal reflection

Total internal reflection

Total internal reflection is an optical phenomenon that happens when a ray of light strikes a medium boundary at an angle larger than a particular critical angle with respect to the normal to the surface. If the refractive index is lower on the other side of the boundary and the incident angle is...

 does not occur at that surface.

To mitigate this problem, a mirror coating is used on those surfaces. Typically an aluminum mirror coating reflectivity

Reflectivity

In optics and photometry, reflectivity is the fraction of incident radiation reflected by a surface. In general it must be treated as a directional property that is a function of the reflected direction, the incident direction, and the incident wavelength...

 of 87% to 93%) or silver mirror coating (reflectivity of 95% to 98%) is used.

The transmission of the prism can be improved by using a dielectric coating rather than a metallic mirror coating. This causes the prism surfaces to act as a dielectric mirror

Dielectric mirror

A dielectric mirror is a type of a 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 thickness of the dielectric layers, one can design an optical coating with specified...

. The dielectric multilayer coating increases reflectivity from the prism surfaces by acting as a distributed Bragg reflector

Distributed Bragg reflector

A distributed Bragg reflector is a reflector used in waveguides, such as optical fibers. It is a structure formed from multiple layers of alternating materials with varying refractive index, or by periodic variation of some characteristic of a dielectric waveguide, resulting in periodic variation...

. A well-designed dielectric coating can provide a reflectivity of more than 99% across the visible light spectrum. This reflectivity

Reflectivity

In optics and photometry, reflectivity is the fraction of incident radiation reflected by a surface. In general it must be treated as a directional property that is a function of the reflected direction, the incident direction, and the incident wavelength...

 is much improved compared to either an aluminum or silver mirror coating and the performance of the Schmidt–Pechan prism is similar to the Porro prism

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....

 or the Abbe–Koenig prism.

The requirement for a mirror coating makes the Schmidt–Pechan roof prism more lossy than the other image erectors using Porro prism

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....

 or Abbe–Koenig prism that rely only on total internal reflections.

Phase correction

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

Fresnel rhomb

A Fresnel rhomb is a prism-like device designed in 1817 by Augustin-Jean Fresnel for changing the polarization of light waves to be circularly polarized. Though the result is similar to that of using a wave plate, the rhomb does not depend on birefringent properties of the material...

. This must be suppressed by multilayer phase-correction coatings applied to one of the roof surfaces to avoid unwanted interference effects and a loss of contrast in the image.

In a roof prism without a phase correcting coating s-polarized and p-polarized light each acquire a different geometric phase

Geometric phase

In classical and quantum mechanics, the geometric phase, Pancharatnam–Berry phase , Pancharatnam phase or most commonly Berry phase, is a phase acquired over...

 as they pass through the upper prism. When the two polarized components are recombined interference 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. Giving an inferior image compared to that from a porro prism erecting system. This roof edge diffraction effect may also be seen as a diffraction spike

Diffraction spike

Diffraction spikes are lines radiating from bright light sources in reflecting telescope images. They are artifacts caused by light diffracting around the support vanes of the secondary mirror...

 perpendicular to the roof edge generated by bright points in the image.

This effect can be seen in the elongation of the Airy disk http://www.zbirding.info/zbirders/blogs/sing/archive/2006/08/09/189.aspx in the direction perpendicular crest of the roof as this is a diffraction

Diffraction

Diffraction refers to various phenomena which occur when a wave encounters an obstacle. Italian scientist Francesco Maria Grimaldi coined the word "diffraction" and was the first to record accurate observations of the phenomenon in 1665...

 from the discontinuity at the roof crest.

The unwanted interference effects are suppressed by vapour depositing

Chemical vapor deposition

Chemical vapor deposition is a chemical process used to produce high-purity, high-performance solid materials. The process is often used in the semiconductor industry to produce thin films. In a typical CVD process, the wafer is exposed to one or more volatile precursors, which react and/or...

 a special dielectric coating known as a phase-compensating coating on the roof surfaces of the roof prism. This coating corrects for the difference in geometric phase between s- and p-polarized light so both have effectively the same phase shift and no interference degrades the image.