A Pupil Primer: How Big Should a Telescope's Exit Pupil Be?

"These lovely lamps, these windows of the soul" — to 16th-century poet Guillaume de Salluste, the eyes revealed a person's inner being. The rest of us look into the pupils of the eye and see only impenetrable blackness — but look out through them, and there's the world in all its sadness and glory. An astronomer looks at them and sees optical parts that need to be mated properly to any other optical instrument being employed, such as a telescope or pair of binoculars.

Understanding pupils is important for skywatchers who want to know which telescope eyepieces or binoculars to buy. It is also the key to some relatively unknown aspects of visual observing.

Pupils come in two types. The entrance pupil refers to the aperture through which light enters an optical instrument such as a telescope. The exit pupil is a small circle just behind a telescope through which all emerging light rays pass. You can see it as a little disk of light floating in the air behind the eyepiece when the instrument is pointed at a bright surface, such as a wall or the daytime sky. This disk is an image of the telescope's aperture. Its size equals the aperture divided by the magnifying power.

The size of the exit pupil is crucial because it must fit into the pupil of your eye (I explain why below). This simple fact governs your choice of optical systems. In practice, however, the matter is not always as simple as it seems.

For one thing, your eye's pupil shrinks in bright light and expands in the dark. Just how big it can get under a starry sky is the subject of much misunderstanding. The ancient dogma on this topic, printed in countless books, says "The human pupil dilates to a maximum diameter of 7 millimeters." Therefore 7 mm is supposed to be the ideal maximum size for the exit pupil of binoculars or a telescope.

This is the reasoning behind the popular 7x50 "night glass" binocular. Divide its 50-mm aperture by its 7-power magnification and you get an exit pupil 7.1 mm across, just about right.

But it ain't necessarily so. Everybody is different.

Some of us have night-owl pupils that enlarge to nearly 9 mm in the dark; others don't make it to 4 mm. After young adulthood there's a gradual downward trend with age — slowly at first, then more rapidly from about age 30 to 60, then slowly again in your later years. But even among people the same age there's a good 3 mm of scatter, so that some 70-year-olds outdo some teenagers.

The problem is that if the exit pupil of a binocular or telescope is too large to fit into your eye, you lose some of the instrument's incoming light. Imagine your eye's greatly magnified iris covering a telescope's front end like a prop in a horror movie, diaphragming the instrument down to a smaller aperture. For example, when a 4-inch (100-mm) telescope is used at 10x, its exit pupil is 10 mm across. If your eye's pupil is only ¾ this size, you're only looking through ¾ of the telescope's aperture — it's acting as a 3-inch, not a 4-inch. Clearly, 10x is too low a power to use on a 4-inch telescope if you want to take advantage of its full light-gathering abilities.

Similarly, if you're in late middle age and have a maximum pupil size of only 5 mm, your 7x50 binoculars are acting as 7x35's, and those big 10x70s you've been thinking of buying might as well be 10x50s.

The same goes for telescope eyepieces. If you have a 5-mm eye pupil and an 8-inch (200-mm) telescope, you should use no less than 40x. In all cases, the lowest power that allows full use of the aperture equals a/p, where a is the aperture and p is your eye pupil size.

Or to state it a different way: If you have a 5-mm eye pupil, you cannot use an eyepiece longer than 20 mm focal length on any f/4 telescope, or 30 mm on any f/6 scope, if you want full use of the aperture. This is true regardless of the telescope's size or anything else. The rule here is e = fp, where e is the eyepiece focal length, p is pupil size, and f is the telescope's f/number (focal ratio).

Clearly, "know thy pupil size" should be the watchword when buying. Two ways to measure your pupil are described at the end of this article.

Low-Power Lessons

Why would you want to employ your maximum pupil size, anyway?

By doing so you get the lowest power (minimizing the problems of an unsteady mount or lack of a clock drive), the widest possible field of view with a given eyepiece design (making objects easiest to find), and also what's called the "richest field." This means the most stars are packed into the view. A richest-field view has the maximum surface brightness — the density of light for each square degree of your field of view — that your eye can possibly receive when looking at a given scene.

This does not mean the stars themselves get brighter, contrary to misconceptions that have been spread by sloppy wording in books and tricky wording in ads. The amount of light you get from a star or any other object is governed by the instrument's effective aperture — not its f/ratio or exit-pupil size. Low power merely squeezes the same light into a smaller area.

For anyone who still isn't convinced of this (so entrenched are the misconceptions), consider that you use the maximum possible amount of your eye's pupil — all of it! — when you observe with the naked eye. Naked-eye viewing is thus the richest rich-field viewing possible. You see the greatest surface brightness on objects that you ever possibly can. No telescope of any size, power, or design can ever beat the naked eye in this regard — which puts the surface-brightness issue into its proper perspective.

If that's all you want, why bother with a telescope? In fact there are good reasons not to make much use of your telescope's lowest allowable power. For one thing, if the telescope's exit pupil is exactly the size of your eye's pupil, you must hold your eye rock-steady in exactly the right place or you'll cut off light. This may be practical if you arrange to clamp your head in a vise. Otherwise, a margin of a millimeter or so gives comfortable room for slight natural movements.

Another reason is that the optical quality of your eye is worst around the edges. This is why you'll discover that no eyepiece, no matter how perfectly designed, shows truly "pinpoint" stars at very low power. This is also why bright stars viewed with the naked eye have little points and flares on them. Whoever popularized the five-pointed "star" shape simply immortalized his or her particular eye aberrations.

In fact, the main reason our pupils open and close may not be to regulate light so much as to reduce aberrations by stopping down the eye's aperture whenever there's enough light to allow this. Alas, our eyes are so imperfect that nature has been reduced to a shoddy trick used by makers of the worst department-store telescopes — stop down the aperture to hide the aberrations.

There is no cure for this short of taking out your eyeballs and grinding and polishing a better optical figure on them, something we do not recommend. (However, vision can be corrected to a degree by laser "machining" of the cornea, and hard contact lenses are said to mold an irregular cornea to some degree.) At any rate, when you use a telescope or binoculars, a less-than-maximum exit pupil keeps light from passing through the eye's bad outermost zone.

This zonal problem may also help explain the so-called "scotopic Stiles-Crawford effect," whereby very dim light entering the edge of your pupil is not perceived as readily as the same amount of light entering near the center. Here is another reason to be conservative about using your lowest power, even when objects are too dim for your lens aberrations to show.

All this adds up to bad news for the 7x50 binocular as the traditional skywatching standard. The tradition should be rewritten more toward 8x50s or 10x50s, especially for folks who are no longer young.

With reflectors and Schmidt-Cassegrain telescopes, there's yet another reason to avoid the lowest possible power. These telescopes have a central obstruction — the secondary mirror — blocking their entrance pupils. The larger the scope's exit pupil, the larger is this black spot in the middle of it, and the more it blacks out the optically best zone in the center of your eye.

Lastly, of course, there's light pollution. When you increase the surface brightness to get a richest-field view, you increase the richness of the skyglow by an equal amount.

Some people love rich-field viewing despite all this. As for myself, the lowest power I use on my 12½-inch reflector is 60x, which gives an exit pupil of 5.3 mm. Even then stars show points and flares. (I know they're not the eyepiece's fault because they move when I rotate my head, and not when I rotate the eyepiece.) But since when is life perfect? In fact I usually find myself using 75x (a 4.2-mm pupil) as my basic "low" power.

High-Power Effects

At the other end of the scale, there is such a thing as too small an exit pupil. The basic limit is imposed by the diffraction inherent in any telescope's aperture. Use a magnification of more than 50x per inch of aperture, even in perfect atmospheric seeing, and you're just magnifying diffraction fuzz. This means the minimum useful pupil size for any telescope is 0.5 mm.

But even with a 1-mm pupil you're likely to notice some bothersome effects. You may see your retina's blood vessels superimposed on Jupiter, along with "floaters" — microscopic specks and strings of junk in your eyeball fluid. Floaters tend to increase with age. Other fine irregularities may be visible too.

Normally the neural network behind your retina does a remarkable job of image-processing all these things out of view. However, it tends to get thrown for a loop when the image is formed by narrow light cones from a tiny pupil. This is only logical. The eye never uses a 1-mm pupil in nature, so our visual processing system didn't evolve to fix whatever problems such a small pupil presents. If you keep glimpsing floaters, graininess, and blood vessels at very high power, ignore them.

A more pressing problem with small pupils is the issue of eye relief. This is how far the exit pupil floats behind the glass of the eyepiece. The amount of eye relief depends greatly on the eyepiece design. However, the smaller the exit pupil the closer to the glass it will probably be.

Since you have to get the exit pupil into your eye, you may have to crowd in mighty close. If you need to wear glasses while observing (to correct for astigmatism, say), you may not be able to get your eyes close enough to see the whole field of view. Check this before buying binoculars.

On a telescope, you can obtain good eye relief at high power by using a moderately long-focus eyepiece with a Barlow lens. Barlows once had a poor reputation, but modern, well-designed ones with multicoated lens elements do not degrade the image significantly. In my 12.5-inch, I really can't see the difference between the 180x view in a 10.5-mm eyepiece and the 180x view in a 26-mm eyepiece of the same design with a 2.5x Barlow — except that the latter gives more comfortable eye relief.

When all is said and done, you'll probably end up most pleased with a telescope's views when its exit pupil is from 2 to 5 mm across. By no coincidence, this is just about the everyday working size of the pupils that nature gave you.

Measuring Your Pupils

It's easy to find your pupil diameter and observe how it changes in varying light. For a quick test, hold a pencil vertically just in front of your eye, resting it against your cheek and eyebrow. Close the other eye. A standard pencil is about 7 mm in diameter. Against bright light you'll see a fuzzy fringe surrounding an opaque core. Block most of the light from view by cupping your hands, and watch the core narrow. If the core thins away completely in dim light, so that you can see a little light right through its center, your pupil has enlarged beyond 7 mm.

A better method is to use a pair of small slits in an opaque sheet with their inner edges separated by a measured distance. Look through the pair of slits while holding the paper against your eyebrow and cheek. (The holes should be about 14 mm in front of your eye, but this is not critical unless you are strongly nearsighted or farsighted and aren't wearing contact lenses.) You'll see two dim disks of light. If their edges barely touch, your pupil diameter equals the separation of the holes.

The pupil does most of its dilating in the first second or two after you enter the dark, but it takes a few minutes to reach its absolute maximum size. Pupil dilation should not be confused with true dark adaptation, a chemical process that happens more slowly in the retina.