Mel Bartels On Exit Pupil And Surface Brightness

Mel Bartels On Exit Pupil And Surface Brightness:

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For extended objects, things are not as simple as stars. For starters, it is not possible to increase the surface brightness of an extended object by increasing the aperture. An example: take an object of 10 magnitude/ square arcsecond as seen by the unaided eye at night, exit pupil open to 7mm. Now, look at the object through a 10" scope. If there is no magnification to the image, the surface brightness will increase by the ratio of the scope's aperture to the eye's aperture squared, or, (10"/0.3")^2 =~ 1000x. However, in order to fit all of the light from the 10" aperture into the eye's exit pupil, we must use at least 33x. 33x will dilute the image brightness by 33^2 =~ 1000x, so we are back where we started. In fact, because of mirror coatings not reflecting 100%, and the small obstruction caused by a diagonal, the image brightness per area will actually be a little less than with the unaided-eye.

This leads to the interesting conclusion that the brightness of the sky glow as seen in the eyepiece is entirely dependent on exit pupil. At a given location on a given night, no matter the size of scopes, if they are giving the same exit pupil, then the sky glow brightness will be very similar.

So why then is aperture the dominant factor? If exit pupil or sky background brightness is kept constant, then as aperture increases so must the magnification. The object appears larger and is easier to see. It’s like moving in closer. If magnification is kept constant then the object and background brightness increase, also making the object easier to see.
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This lead me to the interesting (and false!) conclusion that the brightness of any extended object is entirely dependent on the exit pupil – not quite so:

… Nils shows that the best contrast comes when the background is dimmed below visual detection and the object is about one degree in apparent size.