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Of Pupils & Brightness

by Norman Sperling

Copyright © 1985, Griffith Observer magazine, January 1985

reprinted by permission

All you pupils in this short-course want to select telescopes. Great! You have an idea that skywatching can be a nice hobby. In fact, it is sensational. And you think that a telescope will show some impressive sights. In fact, the views can be awesome. If you pay moderate attention you can learn enough to buy acceptable telescopes. But it's a much brighter idea to learn the ins and outs and get a telescope tailored to your wants.

Selecting a telescope can bewilder the beginning astronomer. There are so many types -

"reflectors," "refractors," and "compound catadioptric" systems like Maksutovs and Cassegrains. Manufacturers cunningly select specifications to make systems sound too good to be true. So how do you choose?

At First Glance

You're likely to look first in a book or magazine. Most of these blithely recommend getting the fattest telescope - that is, the greatest aperture, or width - you can afford. That advice indeed achieves a lot of very useful light-gathering power. Unfortunately, it also limits portability, and it is heavily biased toward Newtonian reflectors that are not optimal for some uses. Other sources proclaim the unexcelled view through refractors, although that's true mostly for planets and double stars. Through the 1950s, those were the most popular targets for amateurs, but no longer. Still other authorities tout the benefits of Schmidt-Cassegrains and Maksutovs, the compound catadioptric types, especially for astrophotography. This advice, too, should be restricted, mostly to those needing extreme portability.

What a Telescope Does

Think of a telescope simply as a tool to funnel light. There are just 2 basic things the funnel can do: It can spread light out, or it can concentrate it. To spread light out is to magnify the image. This enlarges the object in view, which is usually good, but it dilutes the brightness, which isn't. High-power images also have tiny fields of view, and this makes targets hard to find. The other alternative is to concentrate light, to shrink the object in view. This is usually not so good, but it also makes the image bright and contrasty, which is. Low-power images have wide fields of view that take in lots of stars. In fact, telescopes designed for this are nicknamed "rich-field" telescopes.

The steepness of the funneling is the focal ratio. Many optical instruments, especially cameras, express this as an f/number. This is simply the focal length (how far away light focuses) divided by the diameter of the opening where light enters. For example, if the diameter is 100 mm, an f/4 reaches focus at 400 mm, while an f/15 reaches focus at 1500 mm. For most refractors and Newtonian reflectors, the focal length determines the tube length. That, in turn, affects the height of the mounting and, therefore, its weight.

Telescopes have dozens of qualities to optimize. But no telescope is best at all the things telescopes can do. You can optimize some but inevitably at the cost of others. Principles of optics and physics extract a price for every gain. So telescope design is an art of tradeoffs. To get the most-desired qualities, others must be sacrificed - preferably ones you can live without. The "3 Laws of Telescope Design" are:

1. Every time you gain something, you lose something.

2. Every time you gain much, you lose more.

3. There's no such thing as a free lunch.

If these look familiar, it's because they seem to be the laws of everything else, too.

So the first step is to define what the telescope must do. The dominant question is: What kind of objects do you most want to view? Other important questions include: Where will you observe from? What about carrying the telescope by car, or by muscle? How perfect must the system be? And, of course, how expensive?

The objects you want to see should determine the focal ratio. A behavioral look at optics provides a few quick answers. It turns out that for solar system observing, long-focal-ratio refractors are superior. For the galaxies, nebulae, and clusters - deep sky observing - use the shortest and fattest system possible, and that usually means a stubby Newtonian when other factors are accounted for.


And if you want to observe both within the solar system and beyond it, compromise. Get 2 telescopes: One each for the different types of viewing. If, however, it must be just one single telescope, there are choices to weigh. Only one configuration is both long and short - the Newtonian/Cassegrain - but only one small US producer has made them.

Or select a compromise focal ratio. Instead of the f/15 to 18 that shows the best detail on planets, or the f/4 to 6 that gives nebulae and galaxies the best contrast, try around f/10. Unfortunately, such systems usually deliver less-than-optimal images. To achieve the right magnifications for planets or for deep-sky objects, they require rather extreme eyepieces - either very short (less than 5 mm) or very long (more than 40 mm). Pushing optics to an extreme means a lot will have to be sacrificed to achieve even a little. Enormously long eyepieces are both expensive and heavy. Incredibly short ones are both difficult to construct and notoriously stingy on eye-relief, the ease with which you can see through them.

Poking Around the Neighborhood

Classic, long refractors are the "spyglass" type that leaps to most people's minds any time the word "telescope" comes up. Refractors team up lenses of at least 2 kinds of glass - commonly crown and flint - in a way that minimizes the chromatic aberration (spurious color) around bright images. This works best with focal ratios longer than f/11. New designs may work well at shorter ratios, but they will probably cost a lot. And their exotic, new types of glass may suffer problems of their own. So practical refractors are optically long. They deliver high magnification from conventional-length eyepieces, because magnifying power is simply the focal length of the objective divided by the focal length of the eyepiece.

Refractors are optimal for viewing the planets, Moon, and Sun. Their unobstructed light paths deliver the crispest and sharpest images. Planets appear quite small in the sky, as do details on the Moon and Sun, so you want to magnify them a lot. High magnification spreads out the image of an object, and that dilutes the light. But planets appear quite bright, so there's no problem. The classic long refractor need not be, therefore, too wide. The aperture gathers light, and the Sun, Moon, and planets offer plenty. This keeps the width, bulk, and cost of the telescope down.

Peering Far Beyond

Since the 1960s, observers have been flocking to deep-sky objects. This is due partly to the aperture explosion: Amateurs can now afford telescopes wide enough to gather enough light to make faint star clusters, nebulae, and galaxies impressive. Another stimulus was the incessant "Deep-Sky Wonders" column in Sky & Telescope magazine, written by Scotty Houston starting September 1946. Readers who initially passed over it eventually read a bit, then more and more until they were hooked. The star clusters, nebulae, and galaxies sought by amateurs have a lot in common: most appear much larger than planets, but vastly fainter. They are notoriously elusive, too. Some are so pale that it can take a long time to search them out.

The stubbier a telescope's focal ratio, the lower its magnifying power, so the better it concentrates the diffuse light of these objects. At first, it seems contradictory to use the lowest power on the farthest objects. But high magnification would produce a tangle of problems. The high-power field of view is tiny, and this makes it hard to locate and identify the right place in the sky. When you finally find it, only a small portion of the object may fit in at a time. And its light is so diluted, the image is washed out. You can scarcely tell anything is there at all. A short focal ratio delivers low power. The large field of view accommodates both the target and enough stars to facilitate identification. Also, it concentrates the diffuse light, enhancing contrast. This leads to an important supplementary principle to the laws of telescope design:

The bright ones are short, fat, and wide.

Novices find deep sky objects much more readily in short-ratio telescopes, and experienced amateur astronomers notice more detail through them.

Short-ratio telescopes are almost always Newtonians. That's mostly by elimination: It is difficult and expensive to build short refractors unless chromatic aberration grows objectionably. Compound telescopes gain most of their advantage by being compact. Compared to an already-compact reflector, they add little convenience, but they do cost a lot more. The remaining alternative is the Newtonian. There has been a gratifying flood of stubby Newtonians since the "Astroscan" appeared in 1976 and demonstrated that people would, indeed, buy a low-power telescope.


All this hints at limits to telescope capabilities that are only incidental to the optical pattern used. These limits are so remote from the beginning telescope purchaser that they are undreamt of. The truly limiting factors in designing a telescope for amateur skywatchers are not in the telescope itself! Instead, they result from phenomena beyond its ends.


On the top end, the limiting factor is the surface-brightness of the object viewed. Surface brightness is its apparent brightness divided by its apparent area. Nature provides surface brightnesses only in 2 radically different families: "high" - in the Sun, Moon, and planets, and "low" - for nebulae, clusters, and galaxies. There is virtually nothing in between. Only fleetingly will a bright comet straddle that interval.

The gap in surface brightness results from a void in distance: Our star brilliantly illuminates only its local neighborhood, so nearby planets appear bright. Then there's a huge gap to stellar realms beyond. Between us and the next-nearest system (alpha Centauri) yawns an abyss of more than 4 light years. Since light's intensity diminishes with the square of the distance, light from beyond the solar system invariably appears radically fainter.

For example, compare 2 popular targets for amateur astronomers' telescopes. The planet Jupiter shines at about magnitude -2. Because its diameter is about 2/3 arcminute, its angular area is about 0.35 square arcminute. By contrast, the Dumbbell Nebula, M 27, is much larger and dimmer. At magnitude 8, it is 10,000 times fainter than Jupiter. M 27 spans 8 arcminutes by 5 arcminutes, or 40 square arcminutes. This is 115 times larger in area than Jupiter. The Dumbbell Nebula's surface brightness is, therefore, about 1,150,000 times less than Jupiter's. No wonder different optical systems are needed to show each at its best.

So, on the top end, telescopes are constrained by the surface brightnesses of their targets.


On the bottom end, the limiting factor is not so much eyepieces as the human eye itself. The dark-adapted eye's pupil is rarely much over 6 mm wide. In young people the pupil can stretch to 7 mm, but the pupils of older folks don't exceed 5 mm. Also, smoking shrinks the pupil's ability to open widely. The telescope-and-eyepiece combination must be tailored to this. Any light that arrives wider than the pupil cannot enter the eye, and is thus sheer waste. So the telescope's exit-pupil must not exceed about 6 mm. The exit-pupil is simply the objective's diameter divided by the magnification. For any given telescope, the exit pupil enlarges as the power shrinks - that is, as the eyepiece lengthens. For a nice long eyepiece with low power and wide-field, contrasty views of deep-sky objects, the exit pupil must be large. Up to about 6 mm that's fine; beyond, there is no gain. The longest common eyepieces, used with conventional telescopes, deliver exit pupils around this size.

Therefore, in determining what telescope to make or buy, the paramount considerations are not in the telescope itself. The limiting factors are the surface-brightnesses of the objects you observe, and the entrance pupil of your dark-adapted eye. Tailor a telescope - a light-funnel - to fit between those objects and the eye, so that the second will receive the optimal view of the first.

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