entrance and exit pupil (original) (raw)

Author: the photonics expert (RP)

Definition: the apparent apertures of an optical system, seen from the object or image side

Categories: general optics, vision, displays and imaging

Related: optical aperturesimagingimaging with a lensobjectivesocular lenses

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DOI: 10.61835/1xf Cite the article: BibTex BibLaTex plain textHTML Link to this page! LinkedIn

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Contents

The Concept of Entrance and Exit Pupils

An optical imaging system may contain several optical apertures that restrict the passage of light rays. However, not all of these apertures directly determine the system's optical performance, since their effective influence can be altered by intervening optical elements. For example, in the human eye, the apparent pupil appears larger than the physical iris opening because the cornea acts as a refractive element that magnifies the iris when viewed from the outside. Similarly, the position of an aperture within an optical train affects how it limits rays arriving from off-axis directions.

To account for these effects, geometrical optics introduces the concepts of the entrance pupil and exit pupil, which we first consider only briefly, later in more detail:

• The entrance pupil is defined as the image of the aperture stop formed by the optical elements preceding it, as seen from the object side.
• Likewise, the exit pupil is the image of the same aperture stop formed by the elements following it, as seen from the image side.

These virtual images represent how the limiting aperture appears to an observer looking into or out of the optical system, and they play a key role in describing how the system transmits light and defines its field of view.

Entrance Pupil

We consider the effects of apertures at multiple positions in the beam path on the opening angle. We assume an imaging system which is focused on some object plane, and we consider rays starting from the center of the object plane. Figure 1 shows that apertures of different diameters at different locations can cause the same limitation of the opening angle. It is important to realize, however, that their effects are not the same for rays starting from a different (off-axis) location in the object plane. Therefore, it is not sufficient to know the maximum opening angle only.

Figure 1: An imaging system may be limited to the same open angle by apertures at different positions A1, A2 and A3. Their effects would be different, however, for light coming from other points in the object plane.

One solves that problem by constructing the so-called entrance pupil, which has a certain diameter and axial position. In Figure 2, this is shown for the system as above, but containing only the middle aperture (A2, now called A). That aperture is imaged onto the left side, i.e., considering only the optical elements left of it. The rays on the object side can then be projected back to find the edge of the entrance pupil — in this case a virtual image well behind the first and even second optical surface. The entrance pupil is the apparent aperture as seen from the object side.

Figure 2: Construction of the entrance pupil for the system as above, but only with the middle aperture.

With the knowledge of the entrance pupil, one can not only determine the maximum opening angle, but also correctly describe the limitations for rays emerging from other points in the object plane.

For an aperture in front of other optical elements, such as A1 in Figure 1, the entrance pupil is identical to that physical aperture, assuming that the lenses are large enough such that they do not set the limit. The construction of the entrance pupil for aperture A3 in Figure 1 would again lead to a different result. Indeed, those three apertures would also have different optical effects on the system performance.

In the case of a single thin lens with no additional apertures, the entrance pupil is simply the clear (transparent) area of the lens itself. In a multi-lens system, however, the entrance pupil — i.e., the image of the aperture stop as seen from the object side — may be located before, within, or after the optical assembly.

For any photographic objective, for example, one can construct the position and diameter of the entrance pupil based on the optical design. In the case of multiple apertures, the one causing the strongest limitation of light rays is considered. One can then specify those entrance pupil parameters instead of all the details of actual physical apertures and other optical elements; with those data only, the aperturing effects for the object side are sufficiently specified.

For a zoom lens, the entrance pupil generally depends on the zoom setting.

The opening of a photographic objective is usually specified with the f-number, which is defined as the ratio of focal length and diameter of the entrance pupil.

The axial location of the entrance pupil is also relevant as the camera's center of perspective.

For an objective which is telecentric with respect to object space, the entrance pupil lies at infinite distance from the objective. This leads to an orthographic view, i.e., with a magnification which is independent of the object distance.

For a microscope objective, the entrance pupil together with the focal length is directly related to the numerical aperture, which is the usual specification.

Some authors use the term entrance pupil for what should actually be called the diameter of the entrance pupil; note that the axial position of the entrance pupil is also an important parameter.

Exit Pupil

In an analogous way, we can construct the exit pupil of an optical system, this time imaging the relevant aperture to the right side, i.e., towards the image plane. In our example case (Figure 3), this again leads to a virtual image. That image is again in a conjugate plane of the physical aperture, when considering only the optics after that aperture. Also, one can see that the entrance and exit pupils lie in conjugate planes regarding the complete optical system.

Figure 3: Construction of the exit pupil for the system as above.

Depending on the system design, the exit pupil may be identical to a physical aperture on the side of the image plane, or some virtual image which may occur at any axial location. Frequently, it lies behind the optical system.

Ocular lenses of telescopes and microscopes are normally designed such that their exit pupil coincides with the pupil of the observing eye. (Note that the pupil diameter is assumed to be significantly larger for an astronomical telescope than for a microscope because the viewing conditions are usually relatively dark, leading to a wide pupil.) If the exit pupil were larger, not all exiting light could be utilized by the eye; one would lose image brightness. (That could happen in a telescope, for example, when using an ocular lens with too low magnification, i.e., with a too long focal length, or when using night vision glasses during the day.) A smaller exit pupil of the optical system is also not desirable; it would not allow one to make use of the full angular resolution of the eye. An axial position of the exit pupil away from the pupil of the observing eye would also not be desirable, since the transmission should work for a range of observing directions, and not only for objects in the center of the field of view. The distance between the exit pupil and the last optical surface (or the geometrical end of the ocular lens) is called the eye relief; it can be inconveniently small for some ocular lenses with a short focal length.

The axial position of the exit pupil is also relevant in photography. The closer it is to the image plane, the larger are the angles of incidence on the image sensor at its extreme edges. The objective design should avoid that condition, and possibly even be image-space telecentric, particularly for image sensors with microlenses, which imply a reduced acceptance angle of the detectors.

Frequently Asked Questions

This FAQ section was generated with AI based on the article content and has been reviewed by the article’s author (RP).

What is an entrance pupil?

The entrance pupil is the apparent aperture of an optical system as seen from the object side. It is the image of the system's actual limiting aperture (the aperture stop) formed by all optical elements preceding it.

What is an exit pupil?

The exit pupil is the apparent aperture of an optical system as seen from the image side. It is the image of the aperture stop formed by all optical elements that follow it. The entrance and exit pupils are located in conjugate planes.

How is the f-number of a camera objective related to its entrance pupil?

The f-number is defined as the ratio of the objective's focal length to the diameter of its entrance pupil. A smaller f-number corresponds to a larger entrance pupil, allowing more light to be collected.

Why is the exit pupil important for a telescope or microscope?

In visual instruments like telescopes or microscopes, the exit pupil should ideally coincide with the pupil of the observer's eye in both size and position. This ensures maximum image brightness and that the full field of view is visible.

What is an object-space telecentric lens?

An object-space telecentric lens is one where the entrance pupil is located at an infinite distance from the objective. This design results in an orthographic view, meaning the magnification is independent of the object distance.

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