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In
optics Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultrav ...
, the exit pupil is a virtual
aperture In optics, an aperture is a hole or an opening through which light travels. More specifically, the aperture and focal length of an optical system determine the cone angle of a bundle of rays that come to a focus in the image plane. An ...
in an optical system. Only rays which pass through this virtual aperture can exit the system. The exit pupil is the
image An image is a visual representation of something. It can be two-dimensional, three-dimensional, or somehow otherwise feed into the visual system to convey information. An image can be an artifact, such as a photograph or other two-dimensio ...
of the aperture stop in the optics that follow it. In a
telescope A telescope is a device used to observe distant objects by their emission, absorption, or reflection of electromagnetic radiation. Originally meaning only an optical instrument using lenses, curved mirrors, or a combination of both to obse ...
or
compound microscope The optical microscope, also referred to as a light microscope, is a type of microscope that commonly uses visible light and a system of lenses to generate magnified images of small objects. Optical microscopes are the oldest design of microsc ...
, this image is the image of the objective element(s) as produced by the
eyepiece An eyepiece, or ocular lens, is a type of lens that is attached to a variety of optical devices such as telescopes and microscopes. It is named because it is usually the lens that is closest to the eye when someone looks through the device. The ...
. The size and shape of this disc is crucial to the instrument's performance, because the observer's eye can see light only if it passes through this tiny aperture. The term ''exit pupil'' is also sometimes used to refer to the
diameter In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle. Both definitions are also valid f ...
of the virtual aperture. Older literature on optics sometimes refers to the exit pupil as the ''Ramsden disc'', named after English instrument-maker
Jesse Ramsden Jesse Ramsden FRS FRSE (6 October 1735 – 5 November 1800) was a British mathematician, astronomical and scientific instrument maker. His reputation was built on the engraving and design of dividing engines which allowed high accuracy measurem ...
.


Visual instruments

To use an optical instrument, the
entrance pupil In an optical system, the entrance pupil is the optical image of the physical aperture stop, as 'seen' through the front (the object side) of the lens system. The corresponding image of the aperture as seen through the back of the lens system ...
of the viewer's eye must be aligned with and be of similar size to the instrument's exit pupil. This properly couples the optical system to the eye and avoids
vignetting In photography and optics, vignetting is a reduction of an image's brightness or saturation toward the periphery compared to the image center. The word '' vignette'', from the same root as ''vine'', originally referred to a decorative bord ...
. (The entrance pupil of the eye is the image of the anatomical pupil as seen through the
cornea The cornea is the transparent front part of the eye that covers the iris, pupil, and anterior chamber. Along with the anterior chamber and lens, the cornea refracts light, accounting for approximately two-thirds of the eye's total optical ...
.) The location of the exit pupil thus determines the eye relief of an eyepiece. Good eyepiece designs produce an exit pupil of diameter approximating the eye's apparent pupil diameter, and located about 20 mm away from the last surface of the eyepiece for the viewer's comfort. If the disc is larger than the eye's pupil, light will be lost instead of entering the eye. If the disc is too close to the last surface of the eyepiece, the eye will have to be uncomfortably close for viewing; if too far away, the observer will have difficulty maintaining the eye's alignment with the disc. Since the eye's pupil varies in diameter with viewing conditions, the ideal exit pupil diameter depends on the application.Hecht (1987), p. 152. An astronomical telescope requires a large pupil because it is designed to be used for looking at dim objects at night, while a microscope will require a much smaller pupil since the object will be brightly illuminated. A set of 7×50
binoculars Binoculars or field glasses are two refracting telescopes mounted side-by-side and aligned to point in the same direction, allowing the viewer to use both eyes (binocular vision) when viewing distant objects. Most binoculars are sized to be held ...
has an exit pupil just over 7.14 mm, which corresponds to the average pupil size of a youthful dark-adapted human eye in circumstances with no extraneous light. The emergent light at the eyepiece then fills the eye's pupil, meaning no loss of
brightness Brightness is an attribute of visual perception in which a source appears to be radiating or reflecting light. In other words, brightness is the perception elicited by the luminance of a visual target. The perception is not linear to luminance, ...
at night due to using such binoculars (assuming perfect
transmission Transmission may refer to: Medicine, science and technology * Power transmission ** Electric power transmission ** Propulsion transmission, technology allowing controlled application of power *** Automatic transmission *** Manual transmission ** ...
). In daylight, when the eye's pupil is only 4 mm in diameter, over half the light will be blocked by the iris and will not reach the
retina The retina (from la, rete "net") is the innermost, light-sensitive layer of tissue of the eye of most vertebrates and some molluscs. The optics of the eye create a focused two-dimensional image of the visual world on the retina, which the ...
. However, the loss of light in the daytime is generally not a concern since there is so much light to start with. By contrast, 8×30 binoculars, often sold with emphasis on their compactness, have an exit pupil of only 3.75 mm. That is sufficient to fill a typical daytime eye pupil, making these binoculars better suited to daytime than night-time use. The maximum pupil size of a human eye is typically 5–9 mm for individuals below 25 years old, and decreases slowly with age as shown as an approximate guide in the table below.Factors Affecting Light-Adapted Pupil Size in Normal Human Subjects
/ref> The optimum eye relief distance also varies with application. For example, a
rifle scope A telescopic sight, commonly called a scope informally, is an optical sighting device based on a refracting telescope. It is equipped with some form of a referencing pattern – known as a '' reticle'' – mounted in a focally appropriate ...
needs a very long eye relief to prevent recoil from causing it to strike the observer. The exit pupil can be visualized by focusing the instrument on a bright, nondescript field, and holding a white card up to the eyepiece. This projects a disc of light onto the card. By moving the card closer to or further away from the eyepiece, the disc of light will be minimized when the card is at the exit pupil, and the bright disc then shows the diameter of the pupil. A clear vial of milky fluid can also be used to visualize the light rays, which appear as an hourglass shape converging and diverging as they exit the eyepiece, with the smallest cross-section (the waist of the hourglass shape) representing the exit pupil.


Telescopes

For a telescope, the diameter of the exit pupil can be calculated by dividing the
focal length The focal length of an optical system is a measure of how strongly the system converges or diverges light; it is the inverse of the system's optical power. A positive focal length indicates that a system converges light, while a negative foc ...
of the eyepiece by the focal ratio (f-number) of the telescope. In all but the cheapest telescopes, the eyepieces are interchangeable, and for this reason, the magnification is not written on the scope, as it will change with different eyepieces. Instead, the f-number f=L/D of the telescope is typically written on the scope, as well as the objective diameter D and focal length L. The individual eyepieces have their focal lengths written on them as well. In the case of binoculars however, the two eyepieces are usually permanently attached, and the magnification and objective diameter (in mm) is typically written on the binoculars in the form, e.g., 7×50. In that case, the exit pupil can be easily calculated as the diameter of the objective lens divided by the
magnification Magnification is the process of enlarging the apparent size, not physical size, of something. This enlargement is quantified by a calculated number also called "magnification". When this number is less than one, it refers to a reduction in si ...
. The two formulas are of course equivalent and it is simply a matter of which information one starts with as to which formula to use.


Photography

The distance of the exit pupil from the sensor plane determines the range of angles of incidence that light will make with the sensor. Digital
image sensor An image sensor or imager is a sensor that detects and conveys information used to make an image. It does so by converting the variable attenuation of light waves (as they pass through or reflect off objects) into signals, small bursts of c ...
s often have a limited range of angles over which they will efficiently accept light, especially those that use microlenses to increase their sensitivity. The closer the exit pupil to the focal plane, the higher the angles of incidence at the extreme edges of the field. This can lead to
pixel vignetting In photography and optics, vignetting is a reduction of an image's brightness or saturation toward the periphery compared to the image center. The word ''vignette'', from the same root as ''vine'', originally referred to a decorative border ...
. For this reason, many small digital cameras (such as those found in cell phones) are image-space telecentric.


See also

*
Transmittance Transmittance of the surface of a material is its effectiveness in transmitting radiant energy. It is the fraction of incident electromagnetic power that is transmitted through a sample, in contrast to the transmission coefficient, which is t ...
*
Diaphragm (optics) In optics, a diaphragm is a thin opaque structure with an opening (aperture) at its center. The role of the diaphragm is to ''stop'' the passage of light, except for the light passing through the ''aperture''. Thus it is also called a stop (an ...
* Pupil magnification


References

* *{{cite book , first=Eugene, last=Hecht, year=1987, title=Optics, edition=2nd, publisher=Addison Wesley, isbn=0-201-11609-X


External links


A short definition of relative brightness
Optics Science of photography nl:Intree- en uittreepupil