Aperture Understanding

[tdinneen]

Apologies if I’m just rehashing questions and answers that already exists in likely multiple threads but I’d like to understand the roll / balance of aperture, focal length, resolution a little better. 
 

Assume I have a 5” refractor that has a fl of 900mm and an f-ratio of f/7.0. With a 3.8 micron camera that’ll give me an image scale of 3.8/(900/206) = 0.87”/px. 
 

Now assume I also have a 10” reflector with a central obstruction of 30%. With a reducer I can get this down to let’s say 1800mm at f/7.0 (rounding numbers to keep them the same). So if I bin the same camera at 2x2 I get the same image scale of 0.87”/px. That means I’ll have the exact same resolution as the refractor. So there’s no win but….am I right in saying that the reflector will gather light  ((10/2)^2 * 0.7 / (5/2)^2) = 2.8 times faster than the refractor . So although I’m not gaining on resolution (and loosing on FoV) I’m getting a much improved SNR (2.8 / sqrt(2.8) = 1.67 times) for the same exposure time by using the reflector. 
 

Tom. 

[vlaiv]

If you match the resolution between two scopes - then speed is ratio of aperture surfaces.

10" scope will be x4 as fast as 5" scope (minus central obstruction and mirror reflectivity) by having x2 aperture by diameter and that makes it x4 aperture by surface. There is x4 more photons captured in unit time.

Or in another words - if you image with 10" scope for 1h - you will need to image 4h with 5" scope to match SNR (because in one hour it will capture x4 more photons - same as imaging for x4 more time with base aperture).

This is irrespective of F/ratio. It plays no part in this equation (it is already included in equation as it is just ratio of aperture to focal length and we have aperture and focal length is included via resolution / sampling rate).

 

[tdinneen]

Thanks Vlaiv. So I’m correct (…ish,  I took central obstruction to be % of volume not diameter) albeit you explained everything I was trying to say in your first sentence 🤪 Also explains why everyone likes those big scopes even though they end up matching them with big pixels. 

Tom

Edited April 25, 2022 by tdinneen