# Exit pupil

 The articles aperture , iris diaphragm , critical diaphragm , entrance pupil , exit pupil and light intensity (photography) overlap thematically. Help me to better differentiate or merge the articles (→  instructions ) . To do this, take part in the relevant redundancy discussion . Please remove this module only after the redundancy has been completely processed and do not forget to include the relevant entry on the redundancy discussion page{{ Done | 1 = ~~~~}}to mark. - Alturand … D 20:17, 11 Jun. 2018 (CEST)

The exit pupil (also eye circle , Ramsden 's circle or Biot 's circle ) is the image-side image of the aperture diaphragm of an optical system. It is conjugated to the entrance pupil , i.e. H. an object in the entrance pupil is imaged into the exit pupil by the system. With optical devices for direct visual observation - e.g. B. Telescopes and binoculars - the diameter of the beam that leaves the eyepiece is called the exit pupil or exit aperture .

## Lenses

The distance between the exit pupil and the image plane determines the angle θ at which the main rays strike the image plane:

${\ displaystyle \ theta = 90 ^ {\ circ} - \ arctan \ left ({\ frac {{\ text {distance}} _ {\ text {pixel to image center}}} {{\ text {distance}} _ { \ text {Exit pupil to image plane}}}} \ right)}$

In the case of lenses that are telecentric on both sides of the image , the exit pupil is at infinity, so that in the entire image plane d. H. the main rays strike the image plane perpendicularly everywhere. ${\ displaystyle \ theta = 90 ^ {\ circ}}$

Conversely, in the case of lenses that are telecentric on the object side, the exit pupil is in the focal plane and thus very close to the image plane. The main rays therefore quickly hit the image plane very flatly with increasing distance from the image center. If the image plane were also in the focal plane, d. H. the main rays would run parallel to the image plane and therefore never hit it. Therefore, with object-side telecentric systems, sharp images can only be achieved in the close range . ${\ displaystyle \ theta = 0 ^ {\ circ}}$

## Visual observation devices

As mentioned, with telescopes and binoculars, the diameter of the bundle of rays that emerges at the eyepiece is also referred to as the exit pupil (exit diaphragm). When the magnification of an instrument is increased, the exit pupil on the eyepiece is reduced.

### Determine the size of the exit pupil

The instrument is aimed at a bright surface, ideally in the daytime sky, but not in the immediate vicinity of the sun . It is focused on an object as far away as possible. With telescopes of the Maksutov or Schmidt-Cassegrain type , it should be noted that their focal length changes depending on the focus position. Therefore, telescopes of this type should be focused at "infinity". The size of the exit pupil can easily be roughly determined if you look at the instrument's eyepiece at a distance of about 30 cm. The exit pupil appears as a bright disk of light in the eyepiece.

### More precise determination of the size of the exit pupil

If the exit pupil is to be measured more precisely, a ground glass is held in front of the eyepiece. If there is enough light, a thin sheet of graph paper may be sufficient. The distance between the focusing screen or the paper and the eyepiece is changed until a light-colored disc with a sharply defined edge appears. When using graph paper, the value for the size of the exit pupil (in millimeters) is obtained by counting the millimeter lines. This value should be as large as the pupil of the eye - 1 to 2 mm in daylight vision, between 6 and 8 mm in night vision.

If the exit pupil is not adapted to the entrance pupil of the eye, an object appears darker when viewed with the optical device than with the naked eye.

The pupil of the eye forms the aperture diaphragm of the eye. A small exit pupil of an optical device does not fully illuminate it. It limits the aperture accordingly and reduces the diffraction-limited resolution.

### Sensible size of the exit pupil

With regard to the exit pupil of an instrument, it should be noted that the pupil of a young, healthy eye widens to a maximum of about 7 mm, and on the other hand, exit pupils smaller than 1 mm hardly provide any perception gain on the retina. 0.5 mm is the absolute limit here, which can only be used with a good eye and a very good instrument.

The exit pupil limits both the minimum and the maximum usable magnification of an optical instrument towards the eye.

With telescopes and binoculars, the exit pupil of a given eyepiece is determined by the aperture ratio (focal length / lens aperture) of the instrument.

The diameter of the exit pupil AP (in mm) is calculated as the quotient of the objective aperture D (in mm) and the magnification V of an instrument:

${\ displaystyle AP = {\ frac {D} {V}}}$

The geometric light intensity L G of an optical instrument is defined as the square of the diameter of the exit pupil (AP²). Example: An 8 × 40 binocular (8 × magnification and 40 mm entrance pupil) has a geometric light intensity of 25, corresponding to:

${\ displaystyle L _ {\ mathrm {G}} = \ left ({\ frac {40} {8}} \ right) ^ {2}}$