Aperture, Focal-Length, and F-Ratio Facts

by Robert J. Vanderbei
at Princeton University

Regarding prime-focus imaging, we have the following: So, ignoring ancillary factors like brightness of the source or size of the CCD chip, we can summarize as follows.

Here's how to determine how long it will take to get a "nice" picture:

Here's an anecdote:
My first telescope was an 3.5" f/15 Questar.
Thought it would be fun to do astrophotography with it.
Bright things, especially the planets and globular clusers, came out well but faint things took forever.
Why, you ask? Is it the small aperture of only 3.5" or is it the slow f-ratio of f/15?
Well, it's not easy to increase the aperture (without buying a whole new system) but it is easy to change the f-ratio with a focal reducer.
So, I bought a Meade 0.33x focal reducer. This is a positive lens.
It concentrates the light so that an area that was originally 9 (=3x3) times larger now actually falls on the CCD chip.
The result is a three times wider field of view and nine times as many photons per second landing on the chip.
So, it is the f-ratio that determines how long one must integrate.

Finally, for visual observation the basic facts are different as the eyepiece and human eye complicate the story. Simply put, as long as the magnification is sufficiently high that the exit pupil does not overfill your eye's pupil, then aperture determines image brightness (at a given magnification). In this regime, f-ratio is largely unimportant. See http://skyandtelescope.com/howto/visualobserving/article_1671_1.asp for a lengthier discussion of the relevant principles for visual observers.