Exit Pupil
Contents
Overview
An eyepiece's primary purpose is to magnify the view in a telescope, but how much magnification it provides, and the size of the aperture of the telescope, can influence how bright the view is. High magnification in a smaller aperture will result in a very dim view. Conversely, lower magnification will produce a brighter view.
The brightness of the view is best described by a property known as exit pupil. While strictly speaking, exit pupil is the diameter of a virtual aperture produced by the eyepiece in the telescope, it is easier to think of it as the size of the "beam" of light that leaves the eyepiece and enters the eye. The larger the exit pupil, the brighter the view will be. The smaller the exit pupil, the dimmer the view will be.
The useful size of the exit pupil is typically between 0.5mm and 7mm, though it varies from situation to situation. The upper size limit depends on how widely one's own pupils dilate. The average for most young adults is around 7mm. If the exit pupil exceeds this size, it means not all light from the telescope is entering the observer's eye, which reduces its effective aperture.
For these reasons, it can be just as important to consider the exit pupil that an eyepiece will produce, along with its magnification, since the two are inextricably linked. Too little exit pupil may render the view too dim for the object being viewed. Too much exit pupil and light is being wasted since it's not all fitting through the iris of the observer's eye.
Calculating Exit Pupil
Using aperture and magnification
One way to compute the exit pupil is to divide telescope aperture in millimeters, by magnification:
telescope aperture in mm / magnification
Examples:
- 200mm / 50x = 4mm exit pupil
- 127mm / 150x = 0.85mm exit pupil
Using telescope focal ratio and eyepiece focal length
A slightly more convenient method for computing exit pupil is to divide the eyepiece focal length by the telescope focal ratio
eyepiece focal length in mm / telescope focal ratio
Examples:
- 20mm eyepiece / F4.7 = 4.25mm exit pupil
- 5mm eyepiece / F10 = 0.5mm exit pupil
The interesting thing about this method is that it shows the same eyepiece will produce the same exit pupil in telescopes with the same focal ratio, regardless of aperture. A 1000mm aperture F/4 telescope produces the same view brightness as a 100mm aperture F/4 telescope. This demonstrates that it's ultimately the exit pupil, not the aperture, that governs view brightness.
Exit Pupil Effects and Considerations
Exit pupil generally influences the brightness of the view through the eyepiece + telescope combination, but not necessarily in the same way for all objects. Stars are unaffected by exit pupil since they are optical point sources. They cannot be magnified, so their light does not spread out. Thus star brightness is directly governed by telescope aperture.
Meanwhile any object that has a measurable surface area and can be magnified, does get dimmer with exit pupil. This includes the Moon, planets, nebulae, galaxies, and even light pollution and general sky glow.
Since exit pupil affects the brightness of light pollution, but not stars, one way to add contrast to star clusters is to increase magnification. By increasing magnification, the stars will remain the same brightness, but light pollution will get dimmer, thus the contrast of the view will increase.
However, this same trick does not work for galaxies and nebulae. Galaxies and nebulae will get dimmer equally as quickly as light pollution as magnification increases, so contrast does not change.
Exit Pupil and Astigmatism
If you have astigmatism in your vision, it typically becomes worse the larger the exit pupil is. Astigmatism in astronomy can be particularly annoying because it causes stars to have a spiky, irregular appearance. The larger the exit pupil, the more this problem will manifest itself.
This chart from Tele Vue indicates which levels of astigmatism will manifest at which exit pupils.
If seeing pinpoint-like stars is important to you, then consider choosing an eyepiece that provides enough eye relief to be used with glasses if that eyepiece will produce a large exit pupil in your telescope.
Exit Pupil and Nebula Filters
If you plan on using aggressive line filters like UHC/Narrowband, OIII, or H-Beta filters, then it's usually beneficial to have a large exit pupil. Line filters will dim the view quite a bit because they only permit a narrow spectrum of light to pass through them. If you are already starting off at a small exit pupil that is producing a dim view, adding a line filter could make the view too dim to be usable.
Generally any exit pupil larger than 2mm will work with line filters, but the larger the exit pupil, the better.
Minimum and Maximum Exit Pupil
The human eye is ultimately the limiting factor of how large or small an exit pupil can be. Though it depends on individual genetics, human pupils are typically around 7mm in diameter in our 20s, and then get smaller as we age. If an eyepiece and telescope combination produces an exit pupil larger than what our eye can accept, that light is effectively wasted. This can become especially problematic for reflectors and catadioptrics whose central obstruction starts occupying a larger and larger percentage of the light that does enter the pupil. The more oversized the exit pupil is in a telescope with a central obstruction, the more pronounced the secondary shadow will be, and it will often seem like there is a dark, out of focus blob floating in the center of the field of view. Refractors do not have this problem.
While there is some case to be made for breaking the largest usable exit pupil rule in order to achieve a wider true field of view in some cases, the general advice is not to exceed an exit pupil larger than what your own eyes can support. It is worthwhile getting your dilated pupils measured by an optometrist to get a better idea of what your personal maximum useful exit pupil will be.
For minimum exit pupil, it often depends on the target. The brighter the target, the smaller the exit pupil can be before the object becomes too dim. It should be noted that the dimmer the exit pupil, the less light the eye has to work with. This can rob the view of contrast and clarity. Given the rough rule of thumb of not to exceed 50x per inch of aperture, this translates to a minimum useful exit pupil of 0.5mm. However, this is not a hard and fast rule, and it depends entirely on the object. Some small faint objects can effectively disappear from your vision at 1mm exit pupil, while other small bright objects remain easily visible even as low as 0.3mm. Bright objects like planets and the moon can tolerate even smaller exit pupils, but at that point you would be pushing magnification well past the useful limit of the telescope's optics. You'd be sacrificing brightness for no additional detail.
Exit Pupil vs Magnification
Exit pupil and magnification are inextricably linked. Increasing magnification will decrease exit pupil, and vice versa. Thus a balance between magnification and exit pupil must be struck. It's generally beneficial to achieve higher magnification at the expense of exit pupil, since our eyes behave linearly with image scale, but non-linearly with brightness. That is, we can tolerate dimmer views better than we can tolerate smaller views. As an example, consider Messier 51 - the Whirlpool Galaxy. When looking at the night sky with the naked eye, you are effectively using a 7mm exit pupil since your eyes are fully dilated. When you look through say, a 6" telescope at 100x, the exit pupil is just 1.5mm - 22x dimmer. But despite the view being 22x dimmer than the naked eye, the fact that it is 100x larger is what makes M51 visible. Our eyes do not detect small, low contrast things very well, but do detect large low contrast things. Thus using magnification to enlarge low contrast objects is more beneficial than trying to preserve a bright exit pupil.
