Can Drizzle Integration increase resolution beyond theoretical resolution of telescope? So I was wondering, if drizzle integration actually increases details in your image if the drizzled image results in higher resolution in terms of arcseconds / pixel than the telescope would allow (due to the uncertainty principle the telescope's resolving capability is dependent on its diameter, more commonly referred to as the diffraction limit 1, 2 )

In my case I have around 0.52" per px on my main camera and my GSO RC8" allows for around 0.5" resolution max due to the uncertainty principle. Drizzling an image would then give me 0.26" per px on the drizzled image when increasing width and height of the image by factor 2, which is higher resolving power than what the telescope would actually be able to do.

Apart from sharper and more defined stars when drizzle integrating, will drizzle integration actually increase my resolving capability?
Drizzling can't actually do any better than the theoretical resolving power of the combination of your telescope and the atmosphere. What it can do is at least partly compensate for having pixels that are too large to properly sample the resolution of your telescope + the atmosphere.

The Nyquist Sampling Theorem basically says that you should have at least 2 pixels per resolution element in order to properly sample the resolution. Or, conversely, if you want to achieve a resolution of X arcsec, you want pixels that are no more than X/2 arcsec in size. So if the theoretical combination of your telescope diameter and the atmosphere had a resolution of 0.5 arcsec (so we're talking about really good atmospheric conditions), you want pixels that are 0.25 arcsec or smaller; otherwise, the pixelization overwhelms the intrinsic resolution. But note that you don't really gain anything from going to even smaller pixels: you'll just have a nice blurry image without visible pixelization. Having pixels that are 0.1 arcsec in size won't make the image any sharper than pixels that are 0.2 arcsec in size, if the resolution of your system (telescope + atmosphere) is ~ 0.5 arcsec.

In your hypothetical case, 0.52-arcsec pixels are good enough for resolutions down to about 1 arcsec. Ideal drizzling would allow you to effectively have pixels that were about 0.25 arcsec in size, which would accommodate a resolution of about 0.5 arcsec. But you can never do better than the intrinsic resolution of your telescope + the atmosphere.