The circle of confusion numbers I refer to in the Depth-of-Field Calculator are actually the maximum acceptable diameters of the circle of confusion for any given point to render as sharp in an 8" x 10 or 8" x 12" print viewed from a normal viewing distance of about the diagonal of the print.
Acceptable circle of confusion is based on the fact that most people with normal eyesight can't see the difference between a point 1/100 of an inch and any point smaller from a normal viewing distance of around 12 inches. The Standard CoC in the Circle of Confusion Calculator is based on that. The Critical CoC number in the calculator is allowing for more critical or closer inspection and is like using 1/120 of an inch instead of 1/100 as the limiting factor.
A circle of confusion is present for any point of light recorded by film or sensors even at the exact point of focus. It happens because rays of light coming from one point on a subject pass through different parts of the lens. The rays that pass through the edge of the lens come to focus slightly in front of the rays that pass through the center of the lens. So instead of forming an exact point they form a tiny disk or circle of confusion.
As you stop down your aperture, the lens uses fewer and fewer rays from the edge of the lens elements. The circles of confusion at the point of focus get smaller as do the circles of confusion of points in front of and behind the point of focus, which produces more depth of field. It also usually produces sharper images (images with greater resolution) as long as you don't stop down too much.
When you stop down beyond f/11 or f/16 on lenses for FX and DX formats, diffraction can start to affect the sharpness of the image. The small openings created by stopping down the aperture make the light waves spread out as they pass through the opening. The spreading causes the light waves to interfere with each other. This interference forms diffraction disks, which are rings of light of diminishing intensities around each point of light. As the aperture gets smaller the diffraction disks get larger and at some point begin to reduce the sharpness of the image.
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