As I understand it*, it works like this:
The "circle of illumination" is the disk of light the lens projects. It's a property of the lens.
It does not change with aperture. It does change with focus distance. It is smallest at infinity, and increases in size as magnification increases. This is why in large format photography you'll see people using lenses designed for 4x5 film, for example, on 8x10 film. How is this possible? It's all a function of magnification: they're only able to do it at high magnification. It's also why lenses designed for macro will sometimes report a huge image circle, but that circle only is valid at 1:1 (for example). People who buy such a lens thinking the image circle is that size at infinity are in for a nasty surprise.
Within that circle of illumination, image quality is best in the centre at every aperture (again, a property of lenses), and generally declines as we go to the edge of the circle of illumination. Sometimes the decline is rapid, sometimes it's slow. And, importantly, the size of the circle of good definition tends to be closely tied to aperture. With most lenses, as you stop down, the size of the circle of good definition increases. The caveat is that as you stop down, you reach a point where any benefits from stopping down are lost to diffraction. Note that I said "generally" and "tends to" here because I've seen data for lenses where image quality across the frame was best wide-open and actually declines as you stop down; those are not common.
MTF charts are a great way to understand what this looks like for any given lens. Here's an example for the 150mm f/4.5 lens for the Mamiya 7 series. Without getting into the details of how MTF charts work, just look at the lowest solid line (which represents 40 lp/mm for the sagittal direction). The left-hand side of the chart is the centre, while the right-hand side is a corner. The numbers on the bottom axis of the chart are distance from centre (0mm at left, 44.5mm at right); this is the radius of the 90mm image circle of this lens, which is what's needed to cover 6x7 film.
Importantly, what this pair of charts is telling us is that the lens is very decent wide-open at f/4.5, and amazingly good at f/8. Notice how the lines are flat almost to the very corner at f/8. I have this lens in its Mamiya G (for the Mamiya 6) variant. The optics are almost the same. It really is this good on my GFX 50R. I can shift with a lens like this because the radius of the image circle needed to cover the GFX 50R sensor is 27.5mm, so if I were to mount this Mamiya 7 150/4.5 lens on my camera, the part of the image circle I use without shift is marked with the red line. The part of the image circle available to me for shift is everything to the right of the red line. This tells me that I should use at least f/8 if I'm planning to shift the
at least 17mm available to me with this lens. (I said "at least" because Mamiya isn't saying there's no usable image circle beyond r=44.5mm -- see below!)
So the take-away here is that the circle of illumination does not change with aperture, but the "circle of good definition" does "grow". That's just another way of saying that as we stop the lens down, the size of the circle
within the illuminated area that is good quality gets bigger. Even if you've never heard the phrase "circle of good definition", you know exactly what I'm talking about: we all have used lenses that are crappy wide-open, but get better as we close down. A nice example is my S-K Makro-Symmar 120/5.9. At infinity, the "circle of good definition" at infinity is quite small because it's a macro lens. However, at f/11, it's transformed into a killer lens at infinity with a big "circle of good definition" for shifting and stitching.
Now, here's where it gets trickier: the lens designer, Mamiya in this case, is only reporting MTF data for an image circle of 90mm (what's needed to cover 6x7 film). The circle of illumination at infinity is bigger than 90mm; I know this because I can shift my sensor 70mm on my camera, so I can see empirically where the edge of the circle is for any lens. Furthermore, I can see the circle of illumination growing as I focus on a closer and closer subject. BUT that doesn't mean that the image quality is necessarily any good in the expanded area of the circle. It might be, and it might not be -- you have to test to find out. Back to my S-K Makro-Symmar 120/5.9: at its design distances (under 2m), it's already excellent wide-open across the frame. As magnification decreases, you have to stop down more and more to get that image quality.
My final point in response to your question: image circle size at 6' to 14' will be more like infinity than it will be at 1:1. There are formulas you can use to calculate exactly how big it will be as a function of magnification, focal length, image circle at infinity. However, as a rough rule of thumb don't expect a big difference. If the lens is designed for "normal" (non-macro) work, then you likely won't see a huge difference in image quality as a function of aperture and magnification when used at your distances.
Rob
* I've learned it's always a good idea to use little caveats like that on a photo forum that has lots of more knowledgeable people than me...
