The Seduction of Aperture

Jack Kramer

Aperture is seductive. Perhaps you already know that. And the quest for more aperture is often fueled by ads for telescopes that proclaim, for example, that an 8" scope has 77% greater light gathering than a 6". How is this light gathering figure derived and what does it mean in the real world of observing?

First of all, the result of larger aperture is really twofold: you get greater light-gathering, and with that comes improved resolution. The ability to gather more light simply means that you can see things that are fainter. Resolution refers to the ability to distinguish details, instead of seeing them as a blur. It's often measured in terms of being able to clearly split a double star system where the two components are separated from each other by a certain apparent distance, measured in seconds of arc. Larger optics will resolve objects that are closer to each other. Thus the resolution of a 6" scope may be stated as .76 arc sec, while the resolution afforded by a 4" is 1.14 arc sec.

In looking at how the comparison between scopes is measured, we'll simplify matters by ignoring the effects of the atmosphere and light pollution on larger telescopes. We'll also assume that all the telescopes have optics of uniformly good quality. But there is one thing that should be kept in mind -- it's inappropriate to directly compare a reflecting telescope with an unobstructed system, such as a refractor. When it comes to resolution, a refractor will usually outperform a reflector of like aperture.

The comparison of light gathering involves dividing the square of the radius of the larger optic by the square of the radius of the smaller. In our example of the 8" versus the 6", the calculation is 16 (42) divided by 9 (32), which equals 1.77. This means that the light gathering of the larger scope is 177% of the smaller, or 77% greater. Recalling high school geometry, you've probably realized that we're comparing the areas of the two mirrors. (Of course, the formula for the area of a circle is pr2, but for the ratio of one to the other, only the radius is different, so we can ignore p. Anyway, the result is the same.)

One aspect is that with large optics, the step up to the next larger size results in a less dramatic increase in light gathering. A move from an 8" scope to a 10" nets a 56% increase. Now let's jump a bit. Even though the difference in aperture is still two inches, going from a 14" to a 16" scope nets only about a 30% increase in light gathering. Actually, most people go up several inches at a time. Let's say you have an 8" scope and decide to go hog wild with a 16"; you'd get a 300% increase in light gathering! The diameter of the mirror has doubled, but the light gathering has quadrupled. To place it in perspective, if you have a small telescope, even a relatively minor increase in aperture will yield notable results. If you're already in the light bucket category, there are more factors to weigh in deciding on the value of a larger scope.

When it comes to the real world of observing, what can be expected? My most vivid recollection in moving from a 6" scope to an 8" was that globular clusters were much more dramatically resolved. With the move from the 8" to a 10", the big change was in the subtle details. The first object I observed with the 10" was the galaxy M31 in Andromeda; I was most impressed with how the dark lanes stood out. On one observing night, the Veil Nebula was seen especially well in my 10", but in Rich Burns' 13" (a 69% increase over the 10") it had a more three-dimensional look, appearing as a luminous, tangled braid. When it comes to the solar system (primarily the Moon and bright planets), I find the results of small percentage increases in aperture are more difficult to detect, with the ability to distinguish fine details increasing dramatically only with substantial increases in aperture.

Aperture certainly is only one of the many considerations in a move to a larger scope. But it becomes the item of overwhelming importance to most people. That's why there's a disease called "aperture fever"!

Published in the September 1995 issue of the NightTimes