# How does eyepiece exit pupil diameter affect image clarity and viewing experience?

This answer to Not Able to View Objects with Barlow Lens includes a calculation of exit pupil diameter as a way to address the limits of useful magnification when observing planets with a small telescope. A comment there cites Sky & Telescope's Stargazer's Corner: Adventures Under the Night Sky's Simple Formulas for the Telescope Owner for the math.

EXIT PUPIL

The exit pupil is the diameter of the "light pencil" that emerges from the eyepiece. The pupil of fully dark-adapted human eye can dilate to about 7 mm diameter, so an exit pupil in excess of 7 mm is passing more light than the eye can accept. On the other hand, as the exit pupil decreases below 7 mm, lack of light becomes the basic limiting factor to what you can see at night. Exit pupils of less than about 0.5 mm are so small and pass so little light to the eye that they are functionally useless. Actually, I like exit pupils of at least 1.0 mm for decent viewing.

Exit pupil can be calculated by dividing the telescope's clear aperture (in millimeters) by the magnification produced by the ocular in use. Thus:

APERTURE / MAGNIFICATION = EXIT PUPIL

For example, our 100 mm clear aperture telescope with a 10 mm ocular is operating at 100x magnification and therefore has a 1.0 mm exit pupil (100/100=1)

Another way to calculate exit pupil is to divide the eyepiece focal length in millimeters by the telescope's focal ratio (f/stop).

OCULAR FOCAL LENGTH / TELESCOPE FOCAL RATIO = EXIT PUPIL

Thus, a 10 mm ocular in our f/10 (100 mm clear aperture and 1000 mm focal length) telescope has a 1.0 mm exit pupil (10/10=1). Either formula results in the same answer.

I've always paid attention to eye relief of the exit pupil, which is how far it falls beyond the eyepiece. My reference point here are my binoculars which have large diameter eyepiece optics which allows them to have a long eye relief; passing them back and forth between an eyeglass-corrected vision person and someone without glasses is just a quick rotation of the eyecups to different distances.

But I never looked at the diameter of the exit pupil, as it seems not to be an independently adjustable parameter of the optics; the exit pupil diameter is "baked in" to the choice of objective aperture and desired magnification.

As a side note it's worth mentioning that our eye's entrance pupil diameter is often cited around 6 mm or 7 mm (in the block quote) so anything larger than that is wasted. That was the key behind the answers to:

Question: How does eyepiece exit pupil diameter affect image clarity and viewing experience?

The block quote relates small exit pupil diameters to "so little light to the eye that they are functionally useless." That might apply to extended objects differently than it would to unresolved objects like stars, asteroids or even distant planets in modest telescopes.

Astronomical seeing and diffraction may also come into play; these effects can spread even unresolved objects in to apparently extended objects.

Related:

Nikon Monarch 42 mm binoculars (for which I have some familiarity but no affiliation)

Magnification 10x 8x
Objective Diameter (mm) 42 42
Angular Field of View (Real) 5.5° 6.3°
Angular Field of View (Apparent) 51.3° 47.5°
Exit Pupil (mm) 4.2 5.25
Eye Relief (mm) 18.4 19.5

What it looks like when you are too far away from the eyepiece. From Wikipedia's exit pupil. If you were looking for something in a field of stars this "tunnel vision" would make it a lot more difficult.

Cropped and annotated from here

Exit pupil diameter is the determining factor of the apparent surface brightness (that is, brightness per unit area) of extended objects through a telescope or binoculars.

A 100,000,000,000,000,000mm aperture telescope operating a 2mm exit pupil will show an extended object at exactly the same brightness per unit area as a 100mm aperture telescope operating at a 2mm exit pupil. The difference of course, would be in magnification.

As exit pupil decreases in diameter, brightness decreases by the square (just like the telescope's aperture). A 2mm exit pupil contains 4x more light than a 1mm exit pupil.

The largest useful exit pupil is one that matches the observer's own dilated pupil. The smallest useful exit pupil is subjective and depends on the target. In some cases, an exit pupil smaller than 5mm may be too dim. In other cases, an exit pupil as small as 0.25mm is still acceptable.

When exit pupil gets small, however, floaters and other contaminants in the eye become very large proportional to the size of the pupil, and thus become more readily visible. When the exit pupil gets very small, there is so little light entering the eye that contrast perception suffers.

Exit pupil does NOT affect the perceived brightness of stars (at least not until the Airy pattern starts to become large enough for its light to be spread out). The light concentrated in the Airy pattern remains more or less constant in brightness regardless of how small the exit pupil gets (however, it will get dimmer once exit pupil starts to exceed your eye's entrance pupil).

For this reason, using higher magnifcation and smaller exit pupils can make star clusters appear more prominent, and will let you see fainter stars. If a telescope is sufficient aperture to barely see Pluto, the best chance of seeing Pluto will come from very high magnification, which will drop the exit pupil and dim the background skyglow, without making the ~15th magnitude speck of light dimmmer. The increase in relative contrast will make it easier to see.

Exit pupil should always be thought of as the other side of the magnification/brightness coin. You should strive to find the optimal balance of magnification and exit pupil against specific targets to achieve an optimum visual perception of them. This will vary from target to target, vary depending on light pollution levels, and vary from individual observer to individual observer. A zoom eyepiece is a useful tool in finding this optimal balance.

• "using higher magnification and smaller exit pupils can make star clusters appear more prominent" Do you mean in combination, or also separately? For example at constant magnification if I change from 2 mm to 1 mm exit pupil, will "star clusters appear more prominent"? What exactly does "prominent" mean in this context. Is there any chance that some of the adjectives can be supported with math?
– uhoh
Commented Jun 11, 2022 at 2:17
• @uhoh, in combination, since exit pupil and magnification are two sides of the same coin. When magnification goes up, exit pupil must go down. The increased magnification means there is greater separation between stars, letting the eye resolve more distinct stars. Simultaneously, the smaller exit pupil means the background is darker, improving the contrast of faint stars against that background. I'm sure there is math related to MTF and CTF curves, but trying to compute anything with respect to human vision (which can vary from person to person), is hard. Commented Jun 23, 2022 at 0:16
• Yes, got the first part; for a fixed objective diameter they're "two sides of the same coin". The exit pupil diameter is just the objective diameter divided by the magnification. But for "Simultaneously, the smaller exit pupil means the background is darker..." I think another way to say the same thing is that for higher magnification the surface brightness of extended objects (like background) decreases while the apparent brightness of unresolved objects (like stars) stays about the same. Have I got that right?
– uhoh
Commented Jun 23, 2022 at 0:42
• Yes, that's correct. The light from unresolved optical point sources remains concentrated in the Airy pattern. While the Airy pattern does get magnified by the eyepiece and therefore does have an apparent surface brightness, the typical working magnifications of a telescope keep the light concentrated enough on the retina that it's practical to say stars do not appear to get dimmer as magnification increases. Commented Jun 24, 2022 at 1:48