How to select an eyepiece ?

The exit pupil (III)

The exit pupil of a scope or a binocular represents the all set of rays passing completely through the field stop. This is the diameter, in millimeters, of the light cone coming out the eyepiece from a focused pinpoint object.

Brightness is expressed by exit pupil. The larger the exit pupil, the more light reaches your eyes. This definition is expressed as the ratio between the diameter of the objective and the magnification. Another way to figure the exit pupil is to divide the scope f/ratio by the eyepiece focal length. For a 200 mm scope using a magnification of 100 or a f/7 scope using a 14 mm eyepiece the exit pupil is 2 mm. For highest magnifications the exit pupil could not be smaller than around 0.5 mm, the smallest size of the eye pupil  fully contracted (equivalent to an eyepiece providing a power of 50x per inch of aperture or 2x per mm). That can be a good lesson as at such high magnifications the image is often too dim to be comfortable. On the other hand for a specific eyepiece whatever the scope aperture the exit pupil is a constant. It only changes with the aperture ratio, becoming larger as the f/ratio decreases (with a faster scope).

 The exit pupil view from the eyepiece and the objective side in a 60 mm f/23 Stanley brass refractor. Document Stanley of London

This small bright circular image you can see at some distance of the eyepiece or from the film plane if you do astrophotography is defined as the exit pupil. If you image is not fully circular your optical system is defect, uncollimated or you probably use a cheap prism diagonal.

The exit pupil is also related to the eye's pupil diameter. It is easy to understand that at night while your eye pupil dilates more light reaches your retina with a maximum opening of ~7 mm for "youngs" between 20-50 years old. When the exit pupil of your eyes matches the one of your eyepiece, topla, you get the maximum brightness under your current conditions.

 In this drawing the exit pupil is smaller that the eye pupil of the observer in order to avoid blackouts and vignetting browsing the field. Drawing by T.Lombry.

This explain why childrens below 21 or observers older than ~65 cannot take advantage of very low eyepieces over ~40 mm, providing an exit pupil larger than 5 mm, as they can't yet or no more accomodate their eye pupil over 5.5 mm. On the contrary an observer of 30 observing at night a faint DSO has his/her eye pupils fully dilated and can take advantage of very fast scopes or very low focalseyepieces having an exit pupil as large as their own pupil. Unfortunately their power is so low that too few stars are visible. Binoculars exit pupils work the same way and this is a non-sense of using for example a 7x35 binocular having a 5mm exit pupil (35/7) when your eye dilates to 7 mm. Select rather a 10x60 or larger to get the most of it if you want to use them at night.

 The eye pupil pictured in the dark with a flash. The red area is the image of the retina lighted by the flash, hence the expression the "red eyes".

The best way to calculate your eye pupil is placing a millimeter ruler near your eye and picture your face in the dark with a flash - sorry for the super dazzle... Then ask to the photographer an enlargement of the negative showing your eye. Once you will have your prints back, you could measure the maximum size of your eye pupil and buy your low power eyepieces consequently.

If you are interested in planetaries observations which includes not only planets, but also the Sun and Moon, you need high power eyepieces (focals below ~10 mm) having a 0.5 to 1 mm exit pupil. For fainter objects like small galaxies or nebulosities, a 4 or 5mm exit pupil is recommended (eyepieces lower than ~30 mm).

Remark that under urban light-polluted sky, large exit pupils are useless as the sky background is bright, showing green or orange emissions lines under which you could never get a 7 mm or larger eye pupil, excepting using nebulae filters (UHC, OIII, etc) which darken the background in isolating lines in which these nebulae irradiate the most.

So the exit pupil is a excellent parameter to evaluate both the brightness your scope can support and the eyepieces to buy to fit with your favorites subjects. If you want to hunt faint galaxies for example that count by thousands or comets recently discovered you need a very large exit pupil to catch the maximum of light. This is because changing from a medium or high magnification eyepiece to a lower power one, the same amount of light fills into a smaller image, increasing the light per surface unit and its contrast against the sky background. DSO and all faint objects will appear smaller, but brighter. By using the next example you can find this way the eyepiece you should buy by selecting the one giving you an exit pupil of the same size of your largest eye pupil at dark (5 or 7 mm depending your age). This is the only way to optimize your choice.

Imagine you buy a 31 mm Nagler VI and want to use it with a f/10 scope. 31 / 10 = 3.1 mm. This is unsuited to search for the faintest objects as you must reach an exit pupil of ~7 mm. If you buy a focal reducer 0.63x, you reach 4.9 mm, not enough yet excepting under ligh-polluted skies. The best to do is buying a fast scope, open at f/4.5 for example as 31/ 4.5 = 6.9 mm. But you know that using such focal ratio aberrations appear at the edges of the field and that such a scope is very sensible to collimation. What to do ?

 Tele Vue Paracorr (2")

You have to know that using a medium to fast scope (f/4.5-6) can not acccomodate of cheap eyepieces, showing residual aberrations. To get a wide field free of aberrations with such scopes you must use eyepieces offering the best correction all over the field. Those eyepieces cost over \$100 each. So if you think to make a good deal buying a cheap russian scope or a dobsonian for example you will be disappointed when buying your eyepieces as only the most expensives will be suited to its fast f/ ratio.

Forget your Kellner and similar as you should have to invest in eyepieces using 5 to 8 lenses, all fully multicoated and corrected at a  few degrees off-axis too.

The optimized solution should be to select a f/6 scope for example which adapts to standard quality eyepieces like Plössl's. You win on both sides, on the scope and eyepieces prices without to mention the high contrast and crisp image that provides such a design. In the worst case you could always buy a Paracorr to correct the coma or using a Powermate to "slow down" a bit the scope without observing the defaults of barlow's.

Note that some observers don't care of the image quality off-axis and prefer moving their scope to center the object.. For these people a mid-range eyepiece is probably most that suited even if it displays some aberrations at a few degrees off-axis. Not all amateurs think this way.

Using an eyepiece giving a exit pupil larger that the maximum opening of your eye pupil, to say 7 mm on a large scope is like observing the sky not using the full aperture of that scope.

Imagine that you look through a 300 mm scope f/4 so open and fast it gives an exit pupil 10 mm wide using a 40 mm eyepiece. You can only catch 7/10 = 70% of the light reaching this scope. That means you are practically using a 210 mm scope ! The fast scope will display very wide stars fields but it’s a shame to not taking advantage of the its full aperture. Among the effects afecting the exit pupil there is the one caused by the central obstruction of the secondary mirror of telescopes. The percentage of obstruction gives also the size of the obstruction visible in the exit pupil. A scope presenting an obstruction of 35% by area, typical of Schmidt-Cassegrain designs for example, and using an eyepiece providing a 20 mm of exit pupil, will present an unilluminated central area of 33% or as large as 7 mm.

There is also the vignetting that occurs when the exit pupil matches the eye pupil. In these conditions the slightest movement of your head of your eye to look at an object off axis will causes a vignetting; the edges of the field dim and look like cut off. You can prevent this effect by using an eyepiece that yields an exit pupil larger or smaller than the eye pupil, the smaller being the best choice.

At last, the exit pupil or rather the brightness of the image is affected by the Kidney bean effect, a peculiar spherical aberration independent of the image quality. One of the downsides of using a very large exit pupil is that the eye pupil needs to be in the right place to intercept the light cone.

 The kidney bean effect occurs when the exit pupil is very large and close to the size of eye pupil. Looking at the edges of the field your eye pupil cuts off a part of the light cone; the medium field becomes dimmer with occasionally blackouts.

When you observe the edges of the field or the center of the image, the exit pupil of the eyepiece stays in the center of the field. Most eyepieces have an eyecup that will help you position your eye properly in the axis of the light one. But when the exit pupil is very large and close to the size of eye pupil, looking at the edge of the field your eye pupil will cut off a part of the light cone in the medium field region of the eyepiece. That medium field become dimmer while the center of the field of view is unaffected. You see blackout areas in the field When the exit pupil is small, the effect is less apparent as your eye pupil can more easily move inside the light cone, this last having more place to browse your eye pupil. The "blackout" effect mainly arises with eyepieces of large eye relief and exit pupil or barlowing a low focal eyepiece as a 35 mm.

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The brightness and the limit magnitude

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