Inverting prism

Dove prism ("turning prism") for axis reflection ( not a typical reflection prism because of the refractions on the entry and exit surfaces )

Porro prism (two half-cube prisms ) for complete image reversal, parallel beam offset

Schmidt-Pechan prism for complete image reversal, no beam offset, completely straight

Amici prism , an additional deflecting erecting prism with a pair of roof edges

Beam path in the Uppendahl prism (top view); the mirrored surface is hatched in blue, the roof edge is green.

An erecting prism is a reflecting prism that is used to change the position or to mirror the axis of a transmitted image, or both.

Function and application

The term erecting prism is not generally valid or firmly defined in the literature. The use of the term is therefore uncertain. Basically, two different functions can be assigned to an erecting prism:

"Image reversal" through an axis mirroring,
"Image reversal" in the form of an image rotation by 180 ° around the image vertical.

Prisms, which only cause an axis mirroring, exchange two opposite sides of an image for one another. The image is reversed in only one direction, that is, according to height or side. Prisms with such a function are sometimes referred to as "turning prisms". Examples are the Dove prism (also known as Dovean erecting prism) and its generalizations with other prism angles.

The second form of inverting prisms causes an image to be rotated by 180 °, which is also referred to as “completely” image reversing or “complete image reversal”. A requirement of the prism for this function is that at least two reflections must take place in different main sections of the prism. In a Porro prism , this is achieved by adding a second half-cube prism turned sideways against the first. In order to avoid the parallel offset that occurs between the incoming and outgoing light, prisms can be expanded by a pair of roof edge surfaces, for example the Schmidt-Pechan prism as a modification of the Pechan prism .

Prisms with complete image inversion are used primarily to erect an image that was previously upside down, for example to erect an upside-down image in telescopes . The optical axis in the corresponding optical imaging system is not or only slightly bent (45 ° or 90 ° with an Amici prism in an angle finder ).

In addition to binoculars and tubes, erecting prisms are also used in microscopes and single-lens reflex cameras .

In addition, deflection prisms , which only cause a beam deflection by 180 °, are sometimes referred to as erecting prisms. For example, they can be used as a special retroreflector .

Overview

Erecting prisms, a selection
designation	Number ^# of reflections	Roof edge pair	lateral offset ^†	angular misalignment	Comments / special features
Half-cube prism	2	No	0.5A	180 °
Abbe-König prism (Abbe prism type A)	4 (2)	Yes	0	0 °	cemented together from 2 parts
Amici prism	2 (2)	Yes	-	45 ° or 90 °
Brashear-Hastings prism (Abbe prism type B)	4 (2)	Yes	0	0 °	3 parts cemented together
Dove prism	1	No	0	0 °	2 distractions from refraction
Leman prism ( Sprenger prism )	4 (2)	Yes	3A	0 °
Daubresse prism 1st type ( Möller prism )	4 (2)	Yes	5.2A	0 °
Pechan prism	5	No	0	0 °	made of 2 parts with air gap
Roof pentaprism	3 (2)	Yes	-	90 °
Porro prism	4th	No	0.5A / 0.5A ^‡	0 °
Porro-Abbe prism (Porro prism of the second type)	4th	No	0.5A	0 °
Schmidt prism	4 (2)	Yes	-	45 °
Schmidt-Pechan prism	6 (2)	Yes	0	0 °	made of 2 parts with air gap
Uppendahl prism	6 (2)	Yes	0	0 °	of 3 parts, cemented

Remarks:

^# in brackets: of which number of reflections on roof edges

^† Beam offset in relation to the longest side (A) of the incidence surface

^‡ The beam is offset in both the x and y directions

Individual evidence

↑ ^a ^b Fritz Hodam: Technical optics . VEB Verlag Technik, Berlin 1967, p. 256.
↑ Heinz Haferkorn: Optics - physical-technical basics and applications . Barth, Leipzig 1994, ISBN 3-335-00363-2 , p. 475
↑ Heinz Haferkorn: Optics - physical-technical basics and applications . Barth, Leipzig 1994, ISBN 3-335-00363-2 , p. 474.
↑ ^a ^b Fritz Hodam: Technical optics . VEB Verlag Technik, Berlin 1967, p. 254.
↑ US Department of Defense (ed.): Optical design in Military Standardization Handbook , MIL-HDBK-141, 1962, from pages 13-25, PDF: Go to page 262
↑ Heinz Haferkorn: Optics: Physical-technical basics and applications . John Wiley & Sons, 2008, ISBN 978-3-527-62502-4 , pp. 472-487 .
↑ M. Bass, C. Decusatis, JM Enoch (eds.): Handbook of Optics. Volume I - Geometrical and Physical Optics, Polarized Light, Components and Instruments . 3. Edition. McGraw-Hill Professional Publishing, 2009, ISBN 978-0-07-162925-6 , pp. 19.3-19.25 .

[Hod256-1] Fritz Hodam: Technical optics . VEB Verlag Technik, Berlin 1967, p. 256.

[Haferkorn475-2] Heinz Haferkorn: Optics - physical-technical basics and applications . Barth, Leipzig 1994, ISBN 3-335-00363-2 , p. 475

[Haferkorn474-3] Heinz Haferkorn: Optics - physical-technical basics and applications . Barth, Leipzig 1994, ISBN 3-335-00363-2 , p. 474.

[Hodam254-4] Fritz Hodam: Technical optics . VEB Verlag Technik, Berlin 1967, p. 254.

[MIL-HDBK-141-5] US Department of Defense (ed.): Optical design in Military Standardization Handbook , MIL-HDBK-141, 1962, from pages 13-25, PDF: Go to page 262

[6] Heinz Haferkorn: Optics: Physical-technical basics and applications . John Wiley & Sons, 2008, ISBN 978-3-527-62502-4 , pp. 472-487 .

[7] M. Bass, C. Decusatis, JM Enoch (eds.): Handbook of Optics. Volume I - Geometrical and Physical Optics, Polarized Light, Components and Instruments . 3. Edition. McGraw-Hill Professional Publishing, 2009, ISBN 978-0-07-162925-6 , pp. 19.3-19.25 .