I play the devil's advocate, here, because I enjoy the conversation and I have read extensively on this subject, but why do all the theories of vision, related to the visibility of objects in a telescope, ignore the physical number of photons gathered by the larger aperture? Why isn't the image of an extended object simply easier to see in the larger scope because the larger scope gathers more light? Raise the intensity of the light level, and we all see more and better.
The Moon is bright in a small scope, but it is a LOT brighter in a big scope. At double the power of a scope 1/2 the size, the brightness per unit area calculates to be the same. Yet, the image is brighter. Period. It's easy to calculate why a stellar point is brighter, but not so easy to understand why an extended object like the Moon is brighter. The size of the image is not the explanation that works. Image intensity is simply higher.
If you read the link to Tony Flander's page http://mysite.verizon.net/vze55p46/id18.html there are at least three kind of "brightness". Confusing them is fatal.
1) There is the total integrated brightness. The total amount of light collected by the scope. This increrases proportionally to the area of the collecting mirror or lens. In pointwise sources this is the factor that primarily determine visibility (I write primarily because, besides the amount of collected light there also is a cognitive aspecte, mainly influenced by backrgound contrast which make easiker to detect points against darker background, and that is why limiting magnitude increases with magnification, as well explained by a paper of Shaefler).
2) There i surfece brightness, that is the intensity per unit area of an extende object. It is the amount of collected light divided the apparent area. If you double the scope diameter and double the magnification you get 4 tomes the light divide four times the area and the surface brightness is the same (se "lowering rthe threshodls by bill ferris). Thi is the physical quantity that stimulate cones and rods. Each cone provides the same signal to the same surface brightness regardless of the fact that other cones may see the same source (if the area is large many cones respond if it is small lesser cones respond).
3) There is the "subjective" perception of brightness. This is where cognitive processes take place. If many cones/rod are simultaneously stimulated (that is you are looking a big area) the the area is further processed by the visual cortex in the barin and "recognized". This is the fundamental reason why we see better in bigger scopes (same brightness but bigger images, see again clark or ferris documents for a simple explanations, or you may search the visula neuro scientific literature for more rigorous frameworks). A surface twice the area is perceived as "brighter" (subjectively) because a "recognized" entity holds informaion of both its intrinsic surface brightnes and of its overall importance (or totasl brightness). That is why the moon appears brighter in a bigger scope even if the exit pupil is the same. Something similar happens for color recogntion. You need "real" signals from cones (for real colors). But that is not enough. You need the colour patch to be large enough (or the total brightness of the patch to bi bigger than a given amount - this is a variation of the concepts expressed by Clark about the optimal magnification and the detection of shapes). You may do a simple test: print two squares, the same color and lightness bou one larger that the other and look at them at distance. The larger is easier to detect (also its color), but the color is the same, the signal form cones is the same.
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