APOD: Galaxy Cluster Abell 370 and Beyond (2017 May 06)

[Chris Peterson]

Back to telescopes with eyepieces ... Assuming a perfect instrument, I would consider the ratio of the area of the telescope aperture, to the area of the eyepiece exit pupil (especially if well matched to the area of the observer's pupil) to be a good measure of how much brighter objects appear in the telescope, compared with the unaided eye. Simply a measure of the increase in the number of photons per unit time, reaching the retina. So, Chris, where have I gone wrong?

You haven't. We're just talking about different kinds of "brightness". I'm considering surface brightness- photons per unit area. A telescope can't increase that (although it frequently decreases it). You're talking about the total signal- the photon count. As I noted, we can perceive a magnified image with the same surface brightness as apparently brighter because we involve more of the retina. We're getting more signal even though the surface brightness hasn't increased.

(The surface brightness of the retinal image decreases when the aperture and exit pupil aren't properly matched. No matter how large the aperture, the eye only sees photons collected by a diameter equal to the exit pupil times the magnification. If the exit pupil is larger than the eye, the full aperture isn't being utilized. If the projected aperture (exit pupil times magnification) is larger than the physical aperture, the surface brightness is reduced compared with the naked eye brightness. This is why you can't make a unit magnification telescope that gives you an unmagnified but brighter view. The largest aperture a unit magnification telescope can have is one which is the same size as your eye's pupil. It's also why the Moon will never damage your eye, no matter how large an aperture your telescope has.)

[Nitpicker]

I understand the exit pupil as the physical aperture divided by magnification. I don't understand how the exit pupil times magnification could be larger than the physical aperture.

...

Re brightness as total signal, versus signal per unit area, perhaps it is best to say that telescopes make objects appear brighter without increasing their surface brightness. One can certainly see dimmer objects with a typical telescope, than one can without (until the magnification is increased to the point that the exit pupil is too small in relation to the pupil of the eyeball).

[Chris Peterson]

I understand the exit pupil as the physical aperture divided by magnification. I don't understand how the exit pupil times magnification could be larger than the physical aperture.

Not the exit pupil, the entrance pupil of your eye.

[Nitpicker]

Ah, that makes more sense. If the "eye's entrance pupil times magnification" is larger than the physical aperture, the surface brightness is reduced compared with the naked eye brightness.

In most cases, smaller telescopes operating at recommended magnifications (and higher) give exit pupils that are significantly smaller than the typical night-time entrance pupil of the eye (i.e. the pupil diameter). This does cause some vignetting at the edges, but it normally isn't too significant and it doesn't noticeably affect the central portion of the image. Push the magnification to extremes and even the centralised image of a bright planet is noticeably degraded. If you don't push it too far, the scope is still better for small and bright things like planets (compared with a lower magnification and a perfectly matched exit/entrance pupil), though not so worthwhile for small and dim extended objects. One should not expect to see a small and dim extended object, highly magnified through a small telescope. That seems intuitive.