Angular resolution vs seeing?

I think what you're looking at ("images labeled with 0.6" resolution") is not a measure of resolving power, but simply of image scale: the angular size of a pixel on the celestial sphere. As such, it is only determined by focal length and pixel size. It may under-sample, critically sample, or over-sample the resolving power and the seeing circle-of-confusion depending on the imager's choices, optics, and conditions, but the numeric value is independent from those.

the only thing you gain with a larger aperture is larger image scale if the F numbers are the same

I shan't think so.

Sean Mc:
Trying to understand a few things. 

let’s say seeing is (actually) 2”.  This means a 65-ish mm diameter scope would resolve as much as a 300mm diameter scope in those conditions right?

next up…

I see images labeled with 0.6” resolution. Is this even possible without drizzle?  I realize a large enough aperture can pull off 0.6 but can any reasonable atmospheric conditions support that angular resolution?  

is astrobin just using the aperture to determine the resolution rather than something like fwhm?

No, that is incorrect. With a 65mm aperture telescope you will have a diffraction limited fwhm of 1.78 arcseconds with no seeing. Seeing is fundamentally a convolution of an additional gaussian (approximately) on top of your original optical psf. This results in a 2.68 arcsecond theoretical fwhm from a perfect 65mm scope. The problem, however, is that if you actually measure the performance of a 65mm scope in those conditions you will find that it is significantly worse than that. For a normal scope of that aperture 3.5" fwhm might be reasonable. On the other hand, any decently well corrected 300mm scope will be almost exactly limited to the seeing conditions (assuming that magnitude of seeing). 

To your second question, that is simply the sampling of the imaging rig which has nothing to do with how much in the image is actually being resolved. The 0.6" in your example is in units of arcseconds per pixel, meaning one pixel's width accounts for 0.6 arcsec. When your seeing and/or optical resolution are much higher than your sampling, that is referred to as oversampling. So yes, astrobin is just using the focal length and the pixel size (though aperture is irrelevant) to calculate the sampling.

Arun H:

the only thing you gain with a larger aperture is larger image scale if the F numbers are the same

Andrea above is correct. 

It is completely true that the same F number results in the same irradiance, and hence same signal, on the image plane regardless of aperture. However, the larger image scale means different object space sampling;  you are gathering much more light from each square arc second of object with larger aperture. The important consequence of this is that if the images from two telescopes of differing apertures are normalized to the same viewing scale, the larger aperture scope will show better SNR.

A different way of saying this - if an object fits within the FOV of both scopes, but is presented at the same viewing scale, the SNR of the image acquired with the larger aperture scope will be better. This is important because it isn't often that we take images of objects that fit exactly within the FOV of our systems. It is by no means true that larger aperture is not useful in poor seeing.

Yes of course, I see this argument all the time but you would have to make a 4 frame mosaic of the object with the larger aperture scope to match the FOV of the smaller which to me, is apples to oranges and not a direct comparison.

Arun H:

Yes of course, I see this argument all the time but you would have to make a 4 frame mosaic of the object with the larger aperture scope to match the FOV of the smaller which to me, is apples to oranges and not a direct comparison.

Not really. A good example are the scopes I do own - 92 mm AP Stowaway that is 650mm with flattener or 490mm with reducer  and my ONTC 808 which is 920 with the Paracorr. Particularly with reducer, the difference in F number is not that different between both (F/4.6 vs F/5.3). Objects like M33 and the Owl Nebula would fit within both and are reasonable targets for both.  You see images of the Hercules cluster taken at wide ranges of focal lengths and then cropped. The notion of a four frame mosaic is a bit extreme and not relevant to many reasonable targets. 

In any case, the fundamental point here is that aperture matters for more than just resolution. It matters because it is THE fundamental determinant of how many photons are gathered from a given angular area of the object, and that is a critical concept to grasp.

Actually, the difference between 4.6 and 5.3 is larger than it seems, 4.5 to 5.6 would be a full stop and that would be very noticeable. I just think we are using different ways of saying the same thing that often confuses beginners. Of course, a larger aperture will collect more light. An 8" will collect 4 times the light of a 4" but if the F number is the same, it will deliver a quarter of the field using the same sensor. Yes, the resolution should be higher, hopefully with smaller stars and better detail but that's down to the seeing.