For me rather than debate maths, equations and optical limits I would much rather spend my time just getting out there on a very clear stable dark night and actually try to " see" what the limits of my scope and eyes are.
I may be very wrong but for years I thought Dawes and Raleigh limits are related to the ability of optics to resolve 2 similar "light point sources" and this serves as a good guide as to a telescopes ability to separate close double stars.
A telescopes ability to resolve a dark line on light background requires other considerations such as Edge Spread Function (ESF) as noted on web site below.
https://www.telescope-optics.net/tel...resolution.htm
Extract from web site below:
.... As mentioned, this limit applies to near-equally bright, contrasty point-object images at the optimum intensity level. Resolution limit for star pairs of unequal brightness, or those significantly above or below the optimum intensity level is lower. For other image forms, resolution limit also can and does deviate significantly, both, above and below the conventional limit. One example is a dark line on light background, whose diffraction image is defined with the images of the two bright edges enclosing it. These images are defined with the Edge Spread Function (ESF), whose configuration differs significantly from the PSF (FIG. 14). With its intensity drop within the main sequence being, on the other hand, quite similar to that of the PSF, resolution of this kind of detail is more likely to be limited by detector sensitivity, than by diffraction (in the sense that the intensity differential for the mid point between Gaussian images of the edges vs. intensity peaks, forms a non-zero contrast differential for any finite edge separation).
FIGURE 14: Limit to diffraction resolution vary significantly with the object/detail form. Image of a dark line on bright background is a conjunction of diffraction images of the two bright edges, described by Edge Spread Function (ESF). As the illustration shows, the gap between two intensity profiles at λ/D separation is much larger for the ESF than PSF (which is nearly identical to the Line Spread Function, determining the limiting MTF resolution). It implicates limiting resolution considerably better than λ/D, which agrees with practical observations (Cassini division, Moon rilles, etc.). Gradual intensity falloff at the top of the intensity curve around the edges can produce very subtle low-contrast features, even if the separation itself remains invisible.