Wild Card 001 - The Exit Pupil of a Telescope

OK. I’ve signed up to write a regular column for the New AstroMart. Some of you might have read my columns in Astronomy magazine from 1986 to 1997. Others might have a copy of my book Your Guide to the Sky, or the repackaged hardback version, Introduction to Astronomy. If you do, I hope you’ve found them useful. For those of you who don’t know me, I’ll just blow my own horn a bit:

I’m an astronomer, writer, teacher, and designer/builder of telescopes and sometimes, museum exhibits. I’ve won two merit awards at RTMC, and I’ve made more telescopes than I can remember.

Amateur Astronomy isn’t my only interest. I’ve played flying disk sports very seriously. I even placed 10th at the World Senior Flying Disk Championships in 1980. I’ve also been a baseball and softball umpire at many different levels, and I remain a serious student and fan of the game. I’m even pitching a book idea to a recently-retired MLB player. Finally, I’m a long-time fan of “hard” SciFi.

(Finally)^2, I have a rather warped sense of humor. (I tried standup comedy in the 80s, but the audiences’ general lack of mirth caused me to keep my day job, which was at NASA/JPL.) So, there are bad jokes lurking not very deep in my subconscious. They often make their way into what I write. So, if you think that our hobby ought to be a serious endeavor, devoid of any humor, you might want to avoid reading any of my columns, and just click on over to:

http://www.astronomy-oughta-be-serious-(dammit!).com

About what will I write? This column will take a look at the technical side of Amateur Astronomy, but it will also look into the people, history, and places that are part of our hobby. That’s why it’s called Wild Card. I’ll never know what it is I’m going to write, but I promise it won’t be boring. And, of course, if you want me to consider writing about a particular subject, just leave me a message here at AstroMart. Now, on to the show!

About the EXIT PUPIL of a Telescope:

I just wrote that this column won’t be boring. But I’m starting out by writing about the exit pupil. Am I daft? Well, yes, but that’s not why I’m writing this. It’s because I’ve noticed that quite a number of folks who post in the forums don’t have this concept down. I aim to correct that. So, please take a look at the figure, adapted from Your Guide to the Sky, and we’ll get this over with.

First, you’ll notice that the objective is small, and the eyepiece is big, sorta like it has a thyroid condition. (In actual fact this eyepiece played line in the NFL for a number of years….) The actual reason I drew it this way is so that you can clearly see what’s going on.

Let’s start with the fact that this is a Keplerian Telescope, vs. the Galilean Telescope, which was the first one to be used for studying the night sky. If you want to go deeper into this, take a look at:

http://hale.reed.edu/p101/lab4-optics.pdf

Let’s go quickly through this telescope before we all fall asleep:

Our telescope is looking “to the right” at a field of stars. In this case, I’ve drawn rays coming from just three stars. You can assume that one is exactly on the optical axis, and each of the other two is at the edge of the field of the telescope.

Let’s ignore the fact that the objective of our telescope is just a simple lens. It’s also the entrance pupil of our telescope. If it were a Newtonian reflector, the primary mirror would be the entrance pupil. It gets a bit more complicated with Maks and SCTs. For those catadioptric telescopes, the corrector is the entrance pupil.

As you might imagine, the objective is called that because it takes the light coming to it from the object in the field and focuses that light into an image of the object in the focal plane. If you trace the various rays, it should become obvious why this telescope presents an upside down image of whatever object it’s imaging.

Tracing the various rays should also reveal to you that the parallel bundles of light coming from the three stars in our field are turned into cones of light that end up converging at the focal plane.

Of course, we could stop here and place a sheet of film or a CCD-array at the focal plane of the objective lens, and we’d just have a camera. But, this is a telescope, so we need a bit more.

We could just look at the image with our naked eye. If you try it, you’ll notice that you can actually see what your telescope is imaging. The problem is that you won’t see a very bright image, because you can’t get your eye close enough to the image to get all the light coming from the objective into your eye. (Of course, if you’re an “old-bleep” like I am, you can’t get your eye very close to the image in any case!)

What we need is something that will allow us to get our eyes really close to the image our objective has formed. That, of course, is our eyepiece. An eyepiece is just a special-purpose magnifier that’s been designed for use with a telescope.

As you can see from the diagram, the light that’s been focused in the focal plane doesn’t “stay there”. That’s one thing light doesn’t do well at all. No, those photons blast on through and form diverging bundles of light until they run into the eyepiece. It’s the job of the eyepiece to bend those diverging bundles into bundles of parallel light. Our eyes really like to look at parallel light., so the eyepiece is doing just what we want it to.

The point where all those bundles of light converge is known as the eye point. That’s where you put your eye to get all the light coming from the objective into your eye. As you’ve probably noticed, if you put your eye a bit too close or too far from the eyepiece, you can’t get all the light coming through your scope into your eye. In those cases, you severely limit the field you can see.

What about the exit pupil? That’s the disk of light you see at the eye point. It is, literally, an image of the entrance pupil, which we’ve already seen is usually the objective. If you point your telescope at the sky during the day, you’ll see a bright disk if you stand back behind the eyepiece. That’s the exit pupil. The higher the power, the smaller the exit pupil will be. In fact there’s a simple relationship between the size of the exit pupil of a telescope, its aperture, and the magnifying power:

Power = (Aperture)/(Diameter of the Exit Pupil)

Another way of looking at the power of a telescope is that the angle between the various objects you see in the field is wider through a telescope than it is as seen by the naked eye. The ratio of the angles is the power. So, you can notice in the drawing that the angle the parallel bundles of light make with the optical axis as they come out of the eyepiece is greater than the angle the bundles made with the axis as they entered the objective. In this case the ratio is 2:1, so this is a 2X, or 2-power telescope. You’ll also notice that this telescope has an objective focal length that’s twice the focal length of the eyepiece. Again, that leads to a 2X telescope.

Now, a few extra thoughts about stops, vignetting, and illumination of the exit pupil:

Glare stops are just disks with holes in them that are placed in the tube of a telescope. They define the edge of the cone of light that will be allowed into the focal plane. They’re usually used in a refractor, but some folks put them in reflectors. They basically “stop” unwanted light from reaching the focal plane. Hence the name.

A field stop is one that’s placed in the focal plane of a telescope. There are three reasons you’d put a stop in the focal plane. First, you don’t want your eyepiece to be able to “see” a larger field than it can show with reasonable sharpness. Second, by placing the stop in the eyepiece, a lot of stray light that might reflect off the inside of the barrel is, well, stopped from doing that. If you see a nice sharp cutoff at the edge of the field of your eyepiece, it has a field stop. That’s one sign of a good eyepiece. Third, in the case of a Cassegrain telescope, a field stop will ensure that the eyepiece isn’t flooded with light that passes right by the secondary mirror and directly into the eyepiece.

Note that a field stop can only limit the field of view of your telescope. But, a glare stop, or any other kind of stop out of the focal plane, can limit the aperture of your telescope if it’s put in the wrong place or if its central hole is too small. This is a common “trick” used to conceal the defects of a telescope’s objective. Just put a stop somewhere in the telescope that will block the light coming from the periphery of the objective. A lens or mirror that’s been stopped-down will always present a sharper image than one that’s being used at full aperture. So, here are some places a stop might lurk in order to limit the aperture:

1. In a refractor, the first place to look is at the focuser. If the telescope has a “fast” objective lens, the cone of light can be stopped by a focuser that’s too long. That’s why many fast refractors have 2” or 2.7” focusers. If you can’t see the entire objective when you look into the focuser of a refractor at the distance where the eyepiece focuses, the focuser is limiting the aperture of the telescope.

2. In a Newtonian, simply making the diagonal too small can limit the aperture. If it can’t reflect rays coming from the edge of the mirror, they won’t get into the image plane. So, if you look into the focuser of a Newtonian and can’t see the entire mirror, the diagonal mirror is also functioning as an aperture stop. Such a telescope needs to have the spacing between the primary and secondary increased.

3. In a Cassegrain, the size of the secondary mirror can limit the aperture if it’s too small. If you look into the focuser of a Cass and you can’t see the edge of the corrector, the secondary is limiting the aperture of the telescope.

4. In binoculars, the aperture of the objective can be limited by using prisms that are too small for the cone of light coming from the objective. A little more about this later.

If a stop is lurking in your telescope or binocular, and either limits your field of view or, even worse, your aperture, we say that it’s either vignetting the field or the aperture. Vignetting of the field is a fact of life that designers face every day.

How can you determine if you have a stop that’s limiting the aperture of you objective? It’s fairly easy. Get a caliper and place it so that its jaws just touch the exit pupil as you see it from well behind your telescope. The diameter of the exit pupil you measure better be very close to the power divided into the diameter of your objective, as the equation above would indicate. If it is, the objective isn’t being vignetted by a stop inside your telescope or binocular. (Another way of doing this is to shine a laser beam into the very edge of the objective parallel to the optical axis. If the beam makes it out of the eyepiece and into the exit pupil, there is no vignetting of the aperture. Just be sure that your laser beam doesn’t enter yours or anyone else’s eye!)

Finally, you can get an idea how the field of your binocular or telescope is being vignetted by looking at the exit pupil as you move your view from on-axis farther and farther off-axis. Here’s how:

-When you’re on axis, the exit pupil should be perfectly circular. If you see any deviation from this, such as a straight line cutting the edge of the exit pupil, there’s something awry inside. This is common with cheap binoculars with small prisms.

-When you move your eye off axis, the exit pupil will appear to be more and more elliptical. That’s due to foreshortening. It’s no different than how my circular kitchen table looks when I’m looking at it from the doorway. I’m not directly over it, so the diameter in my line of vision looks shorter than the diameter at right angles to my line of vision. I know it’s a circular table, but, due to my perspective, it appears elliptical. This foreshortening of the exit pupil doesn’t mean that the exit pupil is being vignetted!

-As you continue to move your view off axis, you’ll likely see the elliptical exit pupil turn into a “cat’s eye”, as the exit pupil is finally vignetted by a stop inside the instrument. This isn’t any kind of disaster. Rather, it just means that, at some point in the field of your telescope, a stop inside is vignetting the field. Almost all telescopes, with the exception of fast, premium refractors, have modest vignetting of the outer half of their fields at low power. It’s the result of various design compromises their designeres had to make.

-As you move your view even farther off axis, the exit pupil gets really ugly. The “cat’s eye” is cut off by the edge of the eye lens of the eyepiece. Don’t be alarmed by this. You’d not want to pay for an eyepiece with lenses big enough to prevent this!

OK! Nap time is over! Wasn’t that exciting? Well, alright. It wasn’t something you’re going to discuss around the water cooler tomorrow. But I hope it’s sharpened up your understanding of the ins an outs of how a telescope operates and what the exit pupil is and isn’t.

I promise that the next column will be a bit more exciting. I’ll be venturing into the world of SETI, a “Big Ear”, and practical jokes. You might want to listen in….