Aperture ratio and aperture value (f-number)
The focal ratio is the ratio of the telescope aperture to the telescope focal length.
The reciprocal (1/V) is called the aperture value 'k' (f-number). From photography, the notation 'f:k' or 'f/k' and the terms "fast" and "slow" optics defined from it have become established. The smaller the number 'k' becomes, the "faster" the optic becomes and is synonymous with a brighter optic.
This refers to the fact that in astrophotography, comparable results can be achieved between equipment with different focal ratios with an increasingly shorter total exposure time.
For a better understanding, here is an overview table for night shots:
Source: https://www.digitipps.ch/fototechnik/belichtungstabelle-blendentabelle-verschlusszeitentabelle/ (translated)
The white fields arranged diagonally are decisive here. For each step of the upper aperture values, the exposure time doubles. As can be seen from the example marked in yellow, similar results can be achieved with f/4 optics and 30s exposure time as with f/22 optics and 16 min exposure time (neglecting the different noise components → see 'Basics' - 'Physical quantities' - 'Exposure time and noise').
But what effect do different aperture numbers have in addition?
Source picture aperture 1.8: NightWolf1223, CC BY-SA 4.0, via Wikimedia Commons
Source picture aperture 22: NightWolf1223, CC BY-SA 4.0, via Wikimedia Commons
The larger the aperture value (f-number) is selected, the more depth of field is achieved. This means that not only close objects are in focus, but also the background.
What does this mean for astrophotography? Here, all objects lie at infinity, so to speak, and there is no foreground or background. If an object is in focus, the surrounding objects are also in focus (prerequisite: flawless lenses and mirrors). For astrophotography, small aperture value, i.e. "fast" telescopes, are desirable. However, here the following must be considered. The "faster" a telescope becomes the smaller the margin in which the object is still perceived as satisfactorily focused.
|Range in which a point source is still perceived as focused (top: "slow" optics, bottom: "fast" optics)||In values:|
Source: https://www.intercon-spacetec.de/media/pdf/Astrofotografie-4_Fokussierung-Kapitelauszug.pdf (translated)
Even a "fast" optic with f4 requires an accuracy of +/-0.08mm with a medium focus, which must be set by hand on the telescope to be perceived as focused. If the temperature drops overnight, the telescope tube shortens and the focus point is no longer on the chip plane. So, without an electronic focusing device, an aperture number between f/4 and f/10 is best for astrophotography to get a good compromise between total exposure time and defocus.