Concept

Exit pupil — where it appears

The small disc of light behind a telescope's eyepiece through which all the light from the image passes, equal to the aperture divided by the magnification. When it is wider than the eye's pupil some light is wasted; when narrower, extended objects appear dimmer.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Also named here as surface brightness — the same set of essays touches all of them, so they are one junction rather than several.

$How bright a nebula looks through a 200 mm telescope. The surface brightness of the image of an extended object — a nebula, a galaxy, the Moon — through a lossless 200 mm telescope, as a fraction of its brightness to the naked eye, against magnification on a logarithmic axis, for eye pupils of 7 and 5 mm. It is never above one. For a 7 mm pupil it is one up to a magnification of 28.6, where the exit pupil equals the eye's; below that magnification the exit pupil is wider than the eye's and part of the collected light falls on the iris; above it the image dims as the square of the exit pupil: 0.327 at 50×, 0.082 at 100×, 0.020 at 200×. The telescope makes the nebula larger, not brighter; at the magnification where its exit pupil matches the eye's it makes it as large as it can while keeping it as bright as it is.$

The nebula no telescope can brighten

A telescope eight metres across gathers a million times more light than the eye, and a star seen through it is a million times brighter. The Orion nebula seen through it is not brighter at all. It is bigger, and spread over a bigger patch of the retina, and the two exactly cancel: no instrument made of lenses and mirrors can show an extended object brighter than the naked eye sees it. What a telescope does is decided by the small disc of light behind its eyepiece, the exit pupil, and by whether that disc is larger or smaller than the pupil of the eye looking through it.

optics · Etendue

Magnifying past the brightest image to see more. How far above its threshold a small galaxy 1′ across, with a contrast of 0.6 against a dark sky, stands against magnification in a 200 mm telescope, by the model threshold. At low power it is below threshold: bright but too small for the eye to add up. Visibility rises steeply as it grows, keeps rising past 28.6×, where the image starts to dim, because growing still lowers the threshold faster than dimming raises it, and peaks at 128×, with a 1.6 mm exit pupil. It is above threshold only between 68× and 234×: invisible at the brightest image the telescope can give, and visible at a dimmer, larger one.

The faint thing more magnification shows better

No telescope can make a nebula's surface brighter than the naked eye sees it, and above a certain magnification every further step makes the image dimmer. Yet observers looking for the faintest small galaxies push the magnification up, and they are right to. The eye does not detect brightness. It detects contrast against a threshold, and that threshold falls steeply as an object grows. A dimmer, larger image can cross it where a bright, small one cannot.

optics · Etendue

Named alongside it

The objects these essays reach for when they reach for this one.

Etendue Magnification Surface brightness Contrast threshold Human eye Point source Radiance Spatial summation Telescope

All concepts