Exit pupil

Last updated
The image side of the lens of an SLR camera; the exit pupil is the light area in the middle of the lens. Camera lens exit pupil.jpg
The image side of the lens of an SLR camera; the exit pupil is the light area in the middle of the lens.

In optics, the exit pupil is a virtual aperture in an optical system. Only rays which pass through this virtual aperture can exit the system. The exit pupil is the image of the aperture stop in the optics that follow it. In a telescope or compound microscope, this image is the image of the objective element(s) as produced by the eyepiece. 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 the aperture. The term exit pupil is also sometimes used to refer to the diameter 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.

Contents

Visual instruments

The aperture of this optical system is the edge of the objective lens. The exit pupil is an image of the aperture made by the optics following it; divergent rays from each point in the aperture plane come together again in the exit pupil. Exit Pupil raytrace.svg
The aperture of this optical system is the edge of the objective lens. The exit pupil is an image of the aperture made by the optics following it; divergent rays from each point in the aperture plane come together again in the exit pupil.

To use an optical instrument, the entrance pupil 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. (The entrance pupil of the eye is the image of the anatomical pupil as seen through the cornea.) 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 because there is no instrumental help to physically hold the eye position.

Average human eye
pupil diameter vs. age
Age
(years)
Day
(mm)
Night
(mm)
204.78
304.37
403.96
503.55
603.14.1
702.73.2
802.32.5

Since the eye's pupil varies in diameter with viewing conditions, the ideal exit pupil diameter depends on the application. [1] An astronomical telescope requires a large exit pupil because it is designed to be used for looking at dim objects at night, while a microscope will require a much smaller exit pupil since an object being observed will be brightly illuminated. A set of 7×50 binoculars 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 at night due to using such binoculars (assuming perfect 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. 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 here. [2] [3] [4] [5]

The optimum eye relief distance also varies with application. For example, a rifle scope needs a very long eye relief to prevent recoil from causing it to strike the observer. [1]

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 be used to scatter light rays exiting the eyepiece, making their paths visible. These rays 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

The small exit pupil of a 25x30 telescope and large exit pupils of 9x63 binoculars suitable for use in low light Nachtglaspupillep.jpg
The small exit pupil of a 25×30 telescope and large exit pupils of 9×63 binoculars suitable for use in low light

For a telescope, the diameter of the exit pupil can be calculated by dividing the focal length 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.

The exit pupil appears as a white disc on the eyepiece lens of these 8x30 binoculars. Its diameter is 30 / 8 = 3.75 mm. Exit Pupil.JPG
The exit pupil appears as a white disc on the eyepiece lens of these 8×30 binoculars. Its diameter is 30 ÷ 8 = 3.75 mm.

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. 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 sensors often have a limited range of angles over which they will efficiently accept light, especially those that use microlenses to increase their sensitivity. [6] 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. For this reason, many small digital cameras (such as those found in cell phones) are image-space telecentric, so that the chief rays strike the image sensor at normal incidence.[ citation needed ]

See also

Related Research Articles

<span class="mw-page-title-main">Optics</span> Branch of physics that studies light

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, ultraviolet, and infrared light. Because light is an electromagnetic wave, other forms of electromagnetic radiation such as X-rays, microwaves, and radio waves exhibit similar properties.

<span class="mw-page-title-main">Aperture</span> Hole or opening through which light travels

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 the bundle of rays that come to a focus in the image plane.

<span class="mw-page-title-main">Binoculars</span> Pair of telescopes mounted side-by-side

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 when viewing distant objects. Most binoculars are sized to be held using both hands, although sizes vary widely from opera glasses to large pedestal-mounted military models.

f-number Measure of lens speed

An f-number is a measure of the light-gathering ability of any optical system like a camera lens or even the human eye. It is calculated by dividing the system's focal length by the diameter of the entrance pupil. The f-number is also known as the focal ratio, f-ratio, or f-stop, and it is key in determining the depth of field, rate of light scattering, and exposure of a photograph. The f-number is dimensionless that is usually expressed using a lower-case hooked f with the format f/N, where N is the f-number.

<span class="mw-page-title-main">Circle of confusion</span> Blurry region in optics

In optics, a circle of confusion (CoC) is an optical spot caused by a cone of light rays from a lens not coming to a perfect focus when imaging a point source. It is also known as disk of confusion, circle of indistinctness, blur circle, or blur spot.

<span class="mw-page-title-main">Monocular</span> Optical device

A monocular is a compact refracting telescope used to magnify images of distant objects, typically using an optical prism to ensure an erect image, instead of using relay lenses like most telescopic sights. The volume and weight of a monocular are typically less than half of a pair of binoculars with similar optical properties, making it more portable and also less expensive. This is because binoculars are essentially a pair of monoculars packed together — one for each eye. As a result, monoculars only produce two-dimensional images, while binoculars can use two parallaxed images to produce binocular vision, which allows stereopsis and depth perception.

<span class="mw-page-title-main">Angular resolution</span> Ability of any image-forming device to distinguish small details of an object

Angular resolution describes the ability of any image-forming device such as an optical or radio telescope, a microscope, a camera, or an eye, to distinguish small details of an object, thereby making it a major determinant of image resolution. It is used in optics applied to light waves, in antenna theory applied to radio waves, and in acoustics applied to sound waves. The colloquial use of the term "resolution" sometimes causes confusion; when an optical system is said to have a high resolution or high angular resolution, it means that the perceived distance, or actual angular distance, between resolved neighboring objects is small. The value that quantifies this property, θ, which is given by the Rayleigh criterion, is low for a system with a high resolution. The closely related term spatial resolution refers to the precision of a measurement with respect to space, which is directly connected to angular resolution in imaging instruments. The Rayleigh criterion shows that the minimum angular spread that can be resolved by an image forming system is limited by diffraction to the ratio of the wavelength of the waves to the aperture width. For this reason, high resolution imaging systems such as astronomical telescopes, long distance telephoto camera lenses and radio telescopes have large apertures.

<span class="mw-page-title-main">Refracting telescope</span> Type of optical telescope

A refracting telescope is a type of optical telescope that uses a lens as its objective to form an image. The refracting telescope design was originally used in spyglasses and astronomical telescopes but is also used for long-focus camera lenses. Although large refracting telescopes were very popular in the second half of the 19th century, for most research purposes, the refracting telescope has been superseded by the reflecting telescope, which allows larger apertures. A refractor's magnification is calculated by dividing the focal length of the objective lens by that of the eyepiece.

<span class="mw-page-title-main">Optical telescope</span> Telescope for observations with visible light

An optical telescope is a telescope that gathers and focuses light mainly from the visible part of the electromagnetic spectrum, to create a magnified image for direct visual inspection, to make a photograph, or to collect data through electronic image sensors.

<span class="mw-page-title-main">Objective (optics)</span>

In optical engineering, an objective is an optical element that gathers light from an object being observed and focuses the light rays from it to produce a real image of the object. Objectives can be a single lens or mirror, or combinations of several optical elements. They are used in microscopes, binoculars, telescopes, cameras, slide projectors, CD players and many other optical instruments. Objectives are also called object lenses, object glasses, or objective glasses.

<span class="mw-page-title-main">Newtonian telescope</span> Type of reflecting telescope

The Newtonian telescope, also called the Newtonian reflector or just a Newtonian, is a type of reflecting telescope invented by the English scientist Sir Isaac Newton, using a concave primary mirror and a flat diagonal secondary mirror. Newton's first reflecting telescope was completed in 1668 and is the earliest known functional reflecting telescope. The Newtonian telescope's simple design has made it very popular with amateur telescope makers.

<span class="mw-page-title-main">Magnification</span> Process of enlarging the apparent size of something

Magnification is the process of enlarging the apparent size, not physical size, of something. This enlargement is quantified by a size ratio called optical magnification. When this number is less than one, it refers to a reduction in size, sometimes called de-magnification.

<span class="mw-page-title-main">Eyepiece</span> Type of lens attached to a variety of optical devices such as telescopes and microscopes

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 an optical device to observe an object or sample. The objective lens or mirror collects light from an object or sample and brings it to focus creating an image of the object. The eyepiece is placed near the focal point of the objective to magnify this image to the eyes. The amount of magnification depends on the focal length of the eyepiece.

<span class="mw-page-title-main">Telescopic sight</span> Sighting device for firearms

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 position in its optical system to provide an accurate point of aim. Telescopic sights are used with all types of systems that require magnification in addition to reliable visual aiming, as opposed to non-magnifying iron sights, reflector (reflex) sights, holographic sights or laser sights, and are most commonly found on long-barrel firearms, particularly rifles, usually via a scope mount. Similar devices are also found on other platforms such as Artillery, Tanks and even Aircraft. The optical components may be combined with optoelectronics to add night vision or smart device features.

The eye relief of an optical instrument is the distance from the last surface of an eyepiece within which the user's eye can obtain the full viewing angle. If a viewer's eye is outside this distance, a reduced field of view will be obtained. The calculation of eye relief is complex, though generally, the higher the magnification and the larger the intended field of view, the shorter the eye relief.

<span class="mw-page-title-main">Entrance pupil</span>

In an optical system, the entrance pupil is the optical image of the physical aperture stop, as 'seen' through the front of the lens system. The corresponding image of the aperture as seen through the back of the lens system is called the exit pupil. If there is no lens in front of the aperture, the entrance pupil's location and size are identical to those of the aperture. Optical elements in front of the aperture will produce a magnified or diminished image that is displaced from the location of the physical aperture. The entrance pupil is usually a virtual image: it lies behind the first optical surface of the system.

<span class="mw-page-title-main">Telecentric lens</span> Optical lens

A telecentric lens is a special optical lens that has its entrance or exit pupil, or both, at infinity. The size of images produced by a telecentric lens is insensitive to either the distance between an object being imaged and the lens, or the distance between the image plane and the lens, or both, and such an optical property is called telecentricity. Telecentric lenses are used for precision optical two-dimensional measurements, reproduction, and other applications that are sensitive to the image magnification or the angle of incidence of light.

<span class="mw-page-title-main">Observatory Naef Épendes</span> Observatory

Observatory Robert A. Naef is an astronomical observatory located at Épendes, Canton of Fribourg, Switzerland at 7.13938 degrees east of Greenwich and 46.76236 degrees north latitude. Its parallax constants are : ρ sin φ' = 0.68632 and ρ cos φ' = +0.72501.

<span class="mw-page-title-main">Newton's reflector</span> First successful mirror telescope

The first reflecting telescope built by Sir Isaac Newton in 1668 is a landmark in the history of telescopes, being the first known successful reflecting telescope. It was the prototype for a design that later came to be called the Newtonian telescope. There were some early prototypes and also modern replicas of this design.

References

  1. 1 2 Hecht (1987), p. 152.
  2. "Aging Eyes and Pupil Size". Archived from the original on 2013-10-23. Retrieved 2009-05-19.
  3. Factors Affecting Light-Adapted Pupil Size in Normal Human Subjects
  4. Ortiz, Estefan; Bowyer, Kevin W.; Flynn, Patrick J. (2013). "A linear regression analysis of the effects of age related pupil dilation change in iris biometrics" (PDF). 2013 IEEE Sixth International Conference on Biometrics: Theory, Applications and Systems (BTAS). pp. 1–6. doi:10.1109/BTAS.2013.6712687. ISBN   978-1-4799-0527-0. S2CID   14118454. Archived from the original (PDF) on 2014-10-06.
  5. "Astronomics - Outdoor Scientific & Astronomical Gear". Archived from the original on 2016-03-04. Retrieved 2016-10-05.
  6. Wisniewski, Joseph S. (December 6, 2003). "The Digital Lens FAQ". Archived from the original on July 5, 2008. Retrieved May 11, 2008.