Stops, Pupils, and Field of View

An ideal lens bends every ray that reaches it, but no lens is infinite. It is the rims — the lens mounts, the iris of a camera, a hole in a baffle, the edge of a sensor — that decide how much light a system actually gathers and how wide a scene it can take in. The theory of stops and pupils is the bookkeeping that turns those finite edges into two apertures and their images, so that the light cone and the field of view of any instrument follow from paraxial ray tracing alone. It is the bridge from perfect-point image formation to the real questions of brightness, resolution, and design. Two apertures do the work. The aperture stop is the single opening that most tightly throttles the cone of rays from an on-axis object point; its image in the space before the system is the entrance pupil — the effective front window the world's light pours into — and its image in the space after is the exit pupil, the window from which converging light leaves toward the image. Two rays make the whole geometry legible: the marginal ray, drawn from the axial object point to the rim of the aperture stop, and the chief ray, drawn from an off-axis point through the centre of the stop. Every other ray lives between them. The field stop is a different gate: it limits the range of object angles that get imaged at all. Its images are the entrance and exit windows, and the half-angle the entrance window subtends at the pupil centre is the field of view. Because off-axis bundles are progressively clipped, the illumination fades toward the edge — vignetting — softened by the natural $\cos^4\theta$ falloff. Get the stops right and the rest is immediate: the numerical aperture, the $f$ -number, the throughput, and the diffraction-limited resolution all read straight off the pupils. This is the quiet architecture beneath every camera, microscope, and telescope.

Key takeaways

Every system has an aperture stop — the opening that most restricts the axial ray cone — and a field stop that limits the angular extent (field of view) it can image.
The entrance pupil is the image of the aperture stop formed by the optics in front of it; the exit pupil its image formed by the optics behind. Light enters as if filling the entrance pupil and leaves as if filling the exit pupil.
The chief ray goes through the centre of the aperture stop (and both pupil centres); the marginal ray grazes the stop edge from an axial point. These two rays define everything.
The pupils fix the numerical aperture $\mathrm{NA}=n\sin\theta$ , the $f$ -number $N=f/D=1/(2\,\mathrm{NA})$ , the throughput (etendue), and hence the light-gathering power and diffraction limit.
The field stop, imaged into object and image space, sets the entrance/exit windows and the field of view; off-axis illumination falls as $\cos^4\theta$ before hard vignetting.
Find the aperture stop by imaging every opening into object space and choosing the one that subtends the smallest angle at the axial object point — not the physically smallest hole.
Key idea: Image every aperture into object space and pick the one subtending the smallest angle at the axial object point; it is the aperture stop, its images are the entrance and exit pupils, and they fix the numerical aperture, $f$ -number, throughput, and resolution, while the field stop fixes the field of view.

The core insight

The aperture stop is whichever opening — imaged into object space — subtends the smallest angle at the on-axis object point. Its images are the entrance and exit pupils, which fix the numerical aperture $\mathrm{NA}=n\sin\theta$ , the $f$ -number $N=1/(2\,\mathrm{NA})$ , the throughput, and the diffraction-limited resolution. The field stop and its window images fix the field of view. All of instrument design is placing these two gates.

Where this lives today

Pupil engineering is everywhere the eye cannot see. A phone camera's fixed lens has an aperture stop whose $f$ -number sets both its low-light reach and its depth of field, and lens designers still fight the $\cos^4\theta$ falloff that darkens frame corners. In fluorescence and single-molecule microscopy the objective's NA sets the collection efficiency — a few percent, as the worked example shows — and drives the relentless push to higher-NA immersion optics; the back focal plane of that objective, which is its exit pupil, is where modern methods insert phase masks to engineer point-spread functions for three-dimensional localisation. Cold-atom and cavity-QED experiments live or die by pupil-matching high-NA collection optics to their detectors, constrained by the conserved etendue. Telescopes place their stops to control stray light and, in coronagraphs, apodise the pupil to suppress starlight and image exoplanets. Machine-vision metrology uses telecentric lenses — stop at the focal plane — so that measured feature sizes do not change with object distance. The two apertures Abbe formalised remain the levers of every imaging system built.

The physical picture

Stand at the on-axis object point and look toward the instrument. Every internal aperture appears, seen through whatever glass sits in front of it, at some apparent size and distance. The one that looks angularly smallest is the aperture stop, and the cone it subtends is exactly the light your point can send in. That apparent image of the stop is the entrance pupil — the effective front door of the whole instrument, and it is rarely the physical front rim.

Figure

Aperture stop, chief and marginal rays, and the two pupils: the marginal ray (blue) runs from the axial point to the stop rim, the chief ray (red) from an off-axis point through the stop centre; the entrance pupil is the stop imaged into object space, the exit pupil its image in image space

Now walk the object point off axis. Its chief ray — the one aimed at the pupil centre — eventually gets clipped by some other aperture; the first opening to vignette off-axis bundles is the field stop, and its image bounds the scene. Between full brightness (all rays pass) and darkness (chief ray blocked) is the vignetted zone where the field fades. Pupils are conjugate: a ray through the entrance-pupil centre passes through the exit-pupil centre, because both are images of the same physical stop centre. That is why you rest your eye at a telescope's exit pupil — put your pupil where the instrument's is, and you collect all the light it delivers. There is one conservation law behind all of it. Etendue — the product of area and solid angle a beam carries — cannot be reduced by any passive optic. Shrink the pupil to sharpen focus and you lose both light and, through diffraction, ultimate resolution. Stops are where that universal trade among brightness, field, and resolution is set.

Figure

Punchline — the f-number is the reciprocal of twice the numerical aperture, N = 1/(2·NA): a fast f/1.4 lens works at NA ≈ 0.36, a normal f/2 at NA = 0.25, a stopped-down f/4 at NA = 0.125; halving the pupil doubles N and quarters the light

The core equations

The pupils convert into the two numbers every instrument is rated by. The numerical aperture measures the half-angle of the cone the pupil admits at the object (or image) point, weighted by the local index:

\mathrm{NA}=n\sin\theta_m \qquad (1)

where: $n$ — refractive index of that space; $\theta_m$ — half-angle of the marginal-ray cone, set by the entrance (or exit) pupil. Immersion optics raise NA by raising $n$ : an oil objective with $n=1.52$ reaches $\mathrm{NA}\approx1.4$ where a dry lens caps near $0.95$ . For an object at infinity the same cone is captured by the $f$ -number, the ratio of focal length to entrance-pupil diameter, and the two measures are reciprocals:

N=\frac{f}{D_{\mathrm{EnP}}}=\frac{1}{2\,\mathrm{NA}} \qquad (2)

where: $N$ — $f$ -number (focal ratio); $f$ — effective focal length; $D_{\mathrm{EnP}}$ — entrance-pupil diameter; the image-space marginal angle obeys $\sin\theta\approx D_{\mathrm{EnP}}/2f$ in the paraxial limit, so a small $N$ (a "fast" lens) means a large NA, more light, and finer diffraction-limited detail. Marginal and chief rays are tied together by a conserved quantity, the Lagrange (optical) invariant, which propagates unchanged through refraction and transfer:

H=n\,(y_c u_m - y_m u_c) \qquad (3)

where: $y_c,u_c$ — height and angle of the chief ray; $y_m,u_m$ — height and angle of the marginal ray; $n$ — index; $H$ is constant through the whole system. At a pupil the marginal ray crosses the axis ( $y_m=0$ ), so $H=n\,y_c u_m$ ; at an image the chief ray crosses, giving image height times marginal angle. Squaring it gives the etendue $G\approx\pi^2 H^2$ , the area–solid-angle product that no passive optic can shrink. The field stop, imaged into object space as the entrance window, fixes the angular field of view through the angle its edge subtends at the pupil centre:

\tan\theta_{\mathrm{FOV}}=\frac{y_{\mathrm{EnW}}}{z_{\mathrm{EnP}}-z_{\mathrm{EnW}}} \qquad (4)

where: $y_{\mathrm{EnW}}$ — semi-diameter of the entrance window; $z_{\mathrm{EnP}},z_{\mathrm{EnW}}$ — axial positions of entrance pupil and entrance window; the chief ray, aimed at the pupil centre, defines this half-angle. Off-axis, illumination falls even before hard clipping, by the natural obliquity law:

E(\theta)=E_0\cos^4\theta \qquad (5)

where: $E(\theta)$ — image irradiance at field angle $\theta$ ; $E_0$ — on-axis value; the three factors of $\cos\theta$ (pupil foreshortening, inverse-square distance, image-plane tilt) multiply to $\cos^4\theta$ , the corner darkening of every wide-angle photograph.

Derivation AThe f-number as the reciprocal of twice the numerical aperture

We establish the working relation $N=1/(2\,\mathrm{NA})$ and, with it, the entrance/exit-pupil construction that gives it meaning — the owned result of this article. The strategy is to trace the marginal ray of an object at infinity: it enters parallel at the edge of the entrance pupil, is bent by the system to cross the axis at the focal point, and the half-angle of that converging cone is exactly what the numerical aperture measures; relating that angle to the entrance-pupil diameter and focal length yields the reciprocal law and shows why a "fast" lens and a high-NA lens are the same statement.

Step 1. Locate the pupils. The aperture stop, imaged by the optics in front of it, is the entrance pupil (diameter $D_{\mathrm{EnP}}$ ); imaged by the optics behind it, it is the exit pupil. A ray at the entrance-pupil edge emerges at the exit-pupil edge, because both are images of the same physical stop rim. Why this matters: NA and $N$ must be read at a pupil, where the whole admitted cone is defined by one diameter.

Step 2. Send in the marginal ray from an axial object at infinity: it arrives parallel to the axis at height $D_{\mathrm{EnP}}/2$ and the system focuses it to the axial image point at the back focal plane, a distance $f$ away. Why parallel-in: an object at infinity fills the entrance pupil with collimated light, so the marginal ray is the rim ray of that parallel bundle.

Step 3. The half-angle of the converging cone at the image satisfies $\tan\theta=\dfrac{D_{\mathrm{EnP}}/2}{f}$ , and in the paraxial regime $\sin\theta\approx\tan\theta$ , so the image-space numerical aperture is $\mathrm{NA}=n\sin\theta\approx \dfrac{D_{\mathrm{EnP}}}{2f}$ (with $n=1$ in air). Why the small-angle step: the $f$ -number is defined paraxially, so $\sin\theta$ and $\tan\theta$ are interchanged to first order.

Step 4. Invert: $N=\dfrac{f}{D_{\mathrm{EnP}}}=\dfrac{1}{2\,\mathrm{NA}}$ . A camera at $f/2$ therefore works at $\mathrm{NA}=0.25$ ; opening to $f/1.4$ raises it to $\mathrm{NA}\approx0.36$ and, since collected power $\propto\mathrm{NA}^2\propto1/N^2$ , doubles the light of $f/2$ . Why the reciprocal is useful: microscopists quote NA, photographers quote $N$ ; equation (2) translates between the two cultures. *Verified in verify_stops-pupils-field-of-view.py: $\mathrm{NA}=D_{\mathrm{EnP}}/2f$ paraxial, $N=1/(2\,\mathrm{NA})$ reproducing $f/2\!\to\!0.25$ , $f/1.4\!\to\!0.357$ , $f/4\!\to\!0.125$ ; and power $\propto1/N^2$ .*

Go deeper · Derivation B · 1 minFinding the aperture stop by angular subtense

Derivation BFinding the aperture stop by angular subtense

We determine which of several openings actually limits the axial ray cone, since the aperture stop is emphatically not always the smallest hole or the first lens. The strategy is to image every physical aperture into object space through whatever optics lie in front of it, compute the angle each image subtends at the on-axis object point, and pick the smallest: that aperture clips the axial bundle first and is therefore the stop, and its object-space image is by definition the entrance pupil.

Step 1. For each aperture $A_k$ (radius $a_k$ , position $z_k$ ), form its image in object space through the elements ahead of it with the thin-lens equation, giving an imaged radius $a_k'$ and position $z_k'$ . Apertures in front of everything image to themselves. Why image into object space: only there can all apertures be compared on the same footing — as seen from the object.

Step 2. Compute the half-angle each imaged aperture subtends at the axial object point $O$ : $\tan\theta_k=\dfrac{a_k'}{z_k'-z_O}$ . Why an angle, not a size: the object sends a cone, and the aperture that most restricts that cone is the one with the smallest angular radius, whatever its physical size.

Step 3. The aperture stop is $\arg\min_k\theta_k$ ; its object-space image is the entrance pupil, and imaging the same physical stop through the elements behind it gives the exit pupil. Why the minimum: whichever imaged aperture subtends the smallest angle is the first to cut off marginal rays, throttling the cone.

Step 4. Consistency check: the marginal ray drawn from $O$ to the entrance-pupil edge, when traced through the real system, must exactly graze the chosen physical stop and clear every other aperture. Why check: it confirms the identification and catches the common trap of a small nearby iris that subtends a larger angle than a big distant lens. *Verified in verify_stops-pupils-field-of-view.py: for a two-aperture example a small stop subtending a smaller angle wins over a larger, farther lens; the $\arg\min\theta$ criterion and the marginal-ray graze both agree.*

Go deeper · Derivation C · 1 minField of view from the field stop and its window

Derivation CField of view from the field stop and its window

We show how a second, distinct aperture — the field stop — sets the angular extent of the scene, independent of the aperture stop that sets brightness. The strategy is to identify the non-stop aperture that first clips off-axis chief rays, image it into object space as the entrance window, and read the field of view as the angle the window edge subtends at the entrance-pupil centre; where the field stop sits at an image plane, that boundary is sharp, and where it does not, the field fades through a vignetted zone.

Step 1. Among apertures that are not the stop, the field stop is the one subtending the smallest angle at the centre of the entrance pupil (through which every chief ray passes). Why the pupil centre: the chief ray defines the field edge, and it pivots about the pupil centre.

Step 2. Image the field stop through the elements in front of it to get the entrance window: semi-diameter $y_{\mathrm{EnW}}$ at position $z_{\mathrm{EnW}}$ . Why a window: it is to the field of view what the pupil is to the aperture — the object-space image of the limiting aperture.

Step 3. The half-field is $\tan\theta_{\mathrm{FOV}}=\dfrac{y_{\mathrm{EnW}}}{z_{\mathrm{EnP}}-z_{\mathrm{EnW}}}$ , the angle the window edge subtends at the entrance pupil. Why this angle: the chief ray from the extreme field point just grazes the window edge on its way to the pupil centre.

Step 4. If the field stop lies at an intermediate image plane, its edge images sharply onto the final image — a crisp field boundary (the eyepiece field stop); otherwise off-axis bundles are progressively clipped and the edge fades, with on-axis-region illumination following $\cos^4\theta$ . Why conjugate stops sharpen: an aperture at an image plane is reproduced in focus at every subsequent image. *Verified in verify_stops-pupils-field-of-view.py: $\tan\theta_{\mathrm{FOV}}=y_{\mathrm{EnW}}/(z_{\mathrm{EnP}}-z_{\mathrm{EnW}})$ on a worked window, and the $\cos^4\theta$ law from the product of three obliquity factors.*

Limiting cases

Case	Result	Meaning
stop is the first element	$D_{\mathrm{EnP}}=D_{\mathrm{stop}}$	entrance pupil coincides with the physical rim — no imaging needed
object at infinity	$N=f/D_{\mathrm{EnP}}=1/(2\,\mathrm{NA})$	the $f$ -number and NA are reciprocals; a fast lens is a high-NA lens
oil immersion, $n=1.52$	$\mathrm{NA}=n\sin\theta$ up to $\sim1.4$	raising the index raises NA past the dry-lens limit near $0.95$
off-axis, no vignetting	$E(\theta)=E_0\cos^4\theta$	natural corner darkening from pupil foreshortening, distance, tilt
chief ray blocked	no image	the absolute edge of the field of view — beyond it, darkness
stop at a focal plane	telecentric	chief rays parallel to the axis; magnification independent of defocus

Worked examples

1 · A camera lens at f/2 (confidence builder)

A $50\ \mathrm{mm}$ lens is set to $f/2$ . Find the entrance-pupil diameter, the image-space numerical aperture, the marginal half-angle, and how the light changes on stopping down to $f/4$ .

Step 1. Entrance pupil: $D_{\mathrm{EnP}}=f/N=50/2=\boxed{25\ \mathrm{mm}}$ — the effective front window through which the parallel light enters.

Step 2. Numerical aperture: paraxially $\mathrm{NA}=D_{\mathrm{EnP}}/(2f)=25/100=\boxed{0.25}$ , consistent with $N=1/(2\,\mathrm{NA})=1/0.5=2=f/2$ . The exact marginal half-angle is $\theta=\arctan(0.25)=14.0^\circ$ , giving $\sin\theta=0.243$ — essentially the paraxial value.

Step 3. Stop down to $f/4$ : $D_{\mathrm{EnP}}=50/4=12.5\ \mathrm{mm}$ , $\mathrm{NA}=0.125$ . That is two stops, and image irradiance scales as $1/N^2$ , so $E$ drops by $(2/4)^2=\boxed{1/4}$ — a quarter of the light.

Step 4. The trade is the whole point of a stop: $f/4$ gives a quarter the brightness but a smaller pupil, deeper depth of field, and (until diffraction bites) sharper corners. The pupil is the single knob controlling light, depth, and — through NA — diffraction-limited resolution.

2 · Light collection of a microscope objective (exam level)

A dry microscope objective has $\mathrm{NA}=0.5$ in air ( $n=1$ ). What half-angle cone does it collect, and what fraction of an atom's isotropic fluorescence does it gather? Compare a $7\times50$ binocular's exit pupil.

Step 1. Marginal half-angle: $\theta=\arcsin(\mathrm{NA}/n)=\arcsin(0.5)=\boxed{30^\circ}$ — the objective accepts a $30^\circ$ half-cone from each object point.

Step 2. Collected solid angle: $\Omega=2\pi(1-\cos\theta)=2\pi(1-\cos30^\circ)=2\pi(0.1340)=\boxed{0.842\ \mathrm{sr}}$ .

Step 3. Fraction of isotropic emission: $\Omega/4\pi=0.842/12.566=\boxed{6.7\%}$ . Even a respectable objective catches only a few percent of an emitter's light — which is why high-NA immersion optics matter so much in single-molecule and cold-atom imaging.

Step 4. For the binocular, the exit pupil is $d_{\mathrm{XP}}=D_o/M=50/7=\boxed{7.1\ \mathrm{mm}}$ , matched to the dark-adapted eye so no gathered light is wasted at the iris — the same pupil-matching logic, applied at the eye instead of the detector.

Physics of the portrait

The concepts of numerical aperture and the resolution it sets were forged by one man turning microscope design from craft into physics: Ernst Abbe, at the Zeiss works in Jena.

Origins · 1 minErnst Abbe and how this was discovered

Ernst Abbe

1840–1905 · Jena

Hired by Carl Zeiss to put microscope-making on a rational footing, Abbe realised in 1873 that image formation is a diffraction phenomenon: the objective must collect the light diffracted by fine object structure, and the finest resolvable spacing is set by the aperture of that collection. He introduced the numerical aperture $\mathrm{NA}=n\sin\theta$ as the governing quantity, showed that immersing the front element in oil raises $n$ and hence NA and resolution, and stated the sine condition that a lens must satisfy to image off-axis points as sharply as on-axis ones. With the chemist Otto Schott he engineered new optical glasses to realise apochromatic objectives that reached the diffraction limit his own theory had defined. His resolution bound — a spacing of order $\lambda/(2\,\mathrm{NA})$ — is a wave-optics result that the pupil analysis of this article feeds directly: fix the pupils, and you have fixed the NA that Abbe's limit depends on. A social reformer as well, he made the Zeiss foundation a model of profit-sharing and the eight-hour day.

History

1611

— Kepler analyses the telescope's field of view in Dioptrice

1873

— Ernst Abbe publishes his diffraction theory of the microscope and defines the numerical aperture

1873

— Abbe formulates the sine condition for aplanatic (sharp off-axis) imaging

1886

— Abbe and Otto Schott produce the first apochromatic objectives at Zeiss

1893

— August Köhler introduces Köhler illumination, separating the illumination and imaging pupils

Going further

Texts. Hecht, Optics, 5th ed., Ch. 5 (stops, pupils, field of view, vignetting) · Saleh & Teich, Fundamentals of Photonics, 3rd ed., Ch. 1 (ray optics, etendue) · Foot, Atomic Physics, appendices on optical collection · Demtröder, Laser Spectroscopy, on light-collection optics and etendue · Loudon, The Quantum Theory of Light, on mode/etendue in detection.

Provenance. Definitions and criteria follow Hecht Ch. 5 (aperture/field stops, pupils, windows, vignetting, $\cos^4$ law) and Saleh & Teich Ch. 1 (ray optics, etendue). verify_stops-pupils-field-of-view.py reproduces: $\mathrm{NA}=D_{\mathrm{EnP}}/2f$ and $N=1/(2\,\mathrm{NA})$ with $f/2\to0.25$ , $f/1.4\to0.357$ , $f/4\to0.125$ ; power $\propto1/N^2$ ; the stop-finding $\arg\min\theta$ criterion on a two-aperture example; the $30^\circ$ half-angle and $6.7\%$ collection fraction for $\mathrm{NA}=0.5$ ; the $7\times50\to7.1\ \mathrm{mm}$ exit pupil; the Lagrange invariant $H=n(y_c u_m-y_m u_c)$ ; and the $\cos^4\theta$ law from three obliquity factors. Standard constants (dark-adapted pupil $\sim7\ \mathrm{mm}$ , oil-immersion $\mathrm{NA}\approx1.4$ ) are from Hecht and Foot.

Builds on: Ray Model of Light · Image Formation and Magnification · Thin Lens Equation and Lensmaker's Equation · Refraction at a Spherical Surface. Leads to: Thick Lenses and Principal Planes · Circular Aperture Diffraction and the Airy Pattern · Etendue and Radiometric Throughput · Numerical Aperture and Resolution.

What is the difference between the aperture stop and the field stop, and between a pupil and a window?

The aperture stop limits the cone of rays from an on-axis point — it sets brightness, $f$ -number, NA, and resolution. The field stop limits the range of field angles imaged — it sets the field of view. Their images have matching names: the aperture stop's images are the entrance and exit pupils; the field stop's images are the entrance and exit windows. So "pupil" is always an image of the aperture stop, "window" always an image of the field stop. The half-field angle is the angle the entrance window subtends at the centre of the entrance pupil.

Why isn't the aperture stop simply the smallest opening in the system?

Because what throttles the axial cone is angular size at the object, not physical diameter. To compare fairly you must image each aperture into object space through the optics in front of it, then compute the angle each image subtends at the on-axis object point. A small iris sitting close to the object can subtend a larger angle than a big lens far away — in which case the big lens is the stop. Only after this imaging-and-compare step, choosing the smallest angle, do you know which aperture is the stop and hence where the entrance pupil lies.

Why does numerical aperture, not magnification, set a microscope's resolution?

Resolution is a diffraction phenomenon: to reproduce fine object detail the objective must collect the high-angle light diffracted by that detail, and the largest collection angle is exactly what NA measures. Abbe's limit puts the finest resolvable spacing at about $\lambda/(2\,\mathrm{NA})$ — depending on NA, not on how much you subsequently magnify. Piling on eyepiece magnification enlarges the image without adding detail ("empty magnification"). To resolve more you raise NA — a wider collection cone or a higher-index immersion medium — which is why oil-immersion objectives ( $\mathrm{NA}\approx1.4$ ) outperform dry ones ( $\mathrm{NA}\lesssim0.95$ ).

Why must I place my eye exactly at a telescope's exit pupil?

The exit pupil is the image of the aperture stop (the objective) formed by the eyepiece — the small bright disc where all the collected light is concentrated. Because pupils are conjugate, putting your eye's own pupil there captures the entire cone the instrument delivers; move forward or back (wrong eye relief) and the field dims or the edges vanish. Matching the exit-pupil diameter to your eye pupil matters too: a $7\times50$ binocular's $7.1\ \mathrm{mm}$ exit pupil fits a dark-adapted eye, so none of the gathered light is wasted on the iris.

What is etendue, and why does it limit what an optical system can do?

Etendue is the product of the beam's area and the solid angle it fills — roughly $G\approx\pi^2H^2$ in terms of the Lagrange invariant. No passive optic can reduce it: you can trade area for angle, but not shrink both. This is why you cannot simultaneously collect a wide field and a large solid angle onto a small detector — you would need a proportionally larger detector. It sets a hard ceiling on the throughput of spectrometers and light-collection systems, and it is the classical shadow of the fact that you cannot concentrate incoherent light beyond the brightness of its source.

What does it mean for a lens to be "telecentric," and when would I want that?

A telecentric lens has its aperture stop at a focal plane, which makes the chief rays parallel to the axis in object space (or image space, or both). The consequence is that magnification does not change as the object moves in and out of focus — an object that drifts nearer does not image larger. That is exactly what you want in machine-vision metrology, where a measured feature size must be independent of object distance, and in some lithography and inspection systems. It costs you a front element at least as large as the field, so telecentric lenses are bulky, but the constant magnification is worth it when you are measuring, not just imaging.