core24 min studyLesson 205 in Physics

Aperture stops and field of view

Separate the admitted cone from the admitted scene, identify pupils, and calculate simple camera aperture and field limits.

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What you’ll understand

  • Distinguish aperture stop, field stop, and their optical images.
  • Calculate f-number and a paraxial angular field.
  • Explain chief rays, marginal rays, and off-axis vignetting.

Two cameras can have the same focal length yet admit different amounts of light and show different portions of a scene. Those differences arise from different boundaries in the accepted collection of rays. An aperture stop limits the cone from an axial object point; a field stop limits which object positions can contribute. Learning to separate these roles makes it easier to interpret pupil size, exposure changes, and darkened image corners without assigning every effect to a single hole in the housing.

Which opening actually limits the bundle?

Every lens rim, iris, or barrel can obstruct rays. The aperture stop is the element that limits the angular cone admitted from the axial object point for the chosen conjugates. It need not be the physically smallest opening because the intervening optics change apparent sizes and angles. One way to identify it is to trace the axial bundle and determine which clear aperture is reached first as the launch angle grows. The selected object position and focus setting matter.

The entrance pupil is the image of that stop through the optics preceding it, as seen from object space. The exit pupil is its image through the following optics, as seen from image space. A pupil can be real or virtual and can differ substantially from the physical iris diameter. In a simple thin lens with an iris at its plane and no other powered elements, the iris itself serves as both pupils, which is why elementary camera examples often hide the distinction.

N=fDEP,NA=nsin⁡α,NAimage≃12N(air, distant object, paraxial)N=\frac{f}{D_{\mathrm{EP}}},\qquad \mathrm{NA}=n\sin\alpha,\qquad \mathrm{NA}_{\mathrm{image}}\simeq\frac{1}{2N}\quad\text{(air, distant object, paraxial)}
N is f-number, D subscript EP is entrance-pupil diameter, and alpha is the appropriate marginal-ray half-angle. The final estimate assumes a simple distant-object imaging geometry and is not a universal finite-conjugate formula.↔ Scroll wide equations horizontally.

A different boundary selects the scene

A field stop limits the range of object points represented in the image. A detector edge or an opening near an intermediate image often supplies this role because different field points are spatially separated there. For a distant scene and a thin lens, the chief ray from field angle beta passes through the pupil center and reaches height approximately f times beta. An image-plane opening therefore translates directly into an angular field limit under this simple model.

The chief ray connects an off-axis object point to the center of the aperture stop, while the axial marginal ray runs from the on-axis object point through the stop edge. They describe different aspects of the accepted beam. Imaging the field stop through preceding or following optics gives entrance or exit windows, whereas imaging the aperture stop gives pupils. Calling a field stop a pupil confuses a boundary on object position with a boundary on ray direction.

h=ftan⁡β≃fβ,FoVfull=2arctan⁡ ⁣(hmax⁡f)≃2hmax⁡fh=f\tan\beta\simeq f\beta,\qquad \mathrm{FoV}_{\mathrm{full}}=2\arctan\!\left(\frac{h_{\max}}{f}\right)\simeq\frac{2h_{\max}}{f}
h max is an image-plane half-width and beta is the corresponding scene half-angle. The tangent relation is the ideal rectilinear camera model; the final expression requires small field angles in radians.↔ Scroll wide equations horizontally.

Changing one boundary need not change the other

Closing an iris reduces the admitted cone, generally reducing collected power and changing diffraction and aberration tradeoffs. If the detector and image scale are unchanged, it does not by itself narrow the geometric field boundaries. Cropping the detector narrows field while leaving the axial pupil diameter alone. In a real instrument, another aperture may begin clipping off-axis cones before the intended field boundary, producing gradual vignetting rather than a perfectly sharp field cutoff.

Pupil placement also matters for eye position in a telescope and for telecentric imaging. An eye outside the exit pupil can lose part of the bundle even when all glass diameters seem adequate. These effects require ray heights at several physical planes, so a single f-number is insufficient to describe the whole instrument. Whenever a scene corner darkens, distinguish reduced bundle area from loss of focus or a change in source radiance; those mechanisms demand different remedies.

A simple camera’s cone and scene

A thin camera lens in air has focal length 80 mm, an iris of diameter 20 mm at its plane, and detector half-width 8 mm in its focal plane. Assume no other clipping. Find f-number and paraxial full angular field.

  1. There are no preceding lenses that magnify the iris, so entrance-pupil diameter equals its physical diameter, 20 mm. The f-number is 80/20=480/20=4.

  2. The detector edge corresponds to half-angle β≃8/80=0.10\beta\simeq8/80=0.10 radians. The full field is approximately 0.20 radians, or 11.46 degrees.

  3. The exact ideal rectilinear value is 2arctan⁡(0.10)≃11.422\arctan(0.10)\simeq11.42 degrees, close to the paraxial estimate. The iris sets the axial cone, while the detector edge supplies the assumed field boundary.

The result

The camera is f/4 with an approximately 11.5-degree full horizontal field. The field calculation uses detector half-width, so it must be doubled to report the full field.

Explore the model

Interactive lab

Interactive lab · vectors

Separate ray length and direction

Use the vector only as a direction-and-scale analogy. Reset, set Angle = 10° and Magnitude = 1, and note its small y projection. For a fresh run Reset, set Angle = 10° and Magnitude = 2, and predict doubled projections with unchanged angle. For a third run Reset, set Angle = 20° and Magnitude = 1.

Separate ray length and directionPlayback traces a fixed vector and its projections. Angle and magnitude set the geometry; the moving marker does not change them. Current readings: x component: 1.393; y component: 0.975; Magnitude: 1.7. All parameters are adjustable with the labeled controls below.−7.46−3.7303.737.46−3.5−1.7501.753.5xyvvₓ = 1.39
Vectorx / y projectionsTrace marker
x component
1.393
y component
0.975
Magnitude
1.7
t = 0 s

Playback traces a fixed vector and its projections. Angle and magnitude set the geometry; the moving marker does not change them. Parameter changes pause playback and recompute the model at the current elapsed time. Reset restores both parameters and returns time to zero. Playback starts paused. Adjust either parameter, then choose Play or Step.

Look forChanging a direction and changing a scale are distinct operations. The diagram contains one vector, not an aperture, pupil image, ray cone, or camera field calculation.

Check your understanding

In the stated simple camera, what happens when iris diameter is halved while detector and focal length stay fixed?

Try it yourself

A second simple camera has f=100 mmf=100\,\mathrm{mm}, entrance-pupil diameter 10 mm, and detector half-width 5 mm. Find its f-number and paraxial full field. Then predict the effect of doubling detector width alone.

Take a moment to make a prediction or work it out on paper. Open a hint when you need one.

Give me a hint

Use diameter for f-number and half-width for the half-field angle.

Compare with the solution

The f-number is 100/10=10100/10=10. The half-field is 5/100=0.055/100=0.05 radians, so full field is approximately 0.10 radians or 5.73 degrees. Doubling detector width also doubles its half-width to 10 mm, giving full paraxial field 0.20 radians, while f-number remains 10. This prediction assumes the larger field is unvignetted and image quality remains acceptable.

Take it with you

  • The aperture stop controls a cone, and the field stop controls the represented scene.
  • Pupils are optical images of the aperture stop and can differ from the physical iris.
  • F-number alone cannot determine field of view or off-axis vignetting.

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