You need to understand that holding the f-number constant across formats is meaningless and bogus. †Once you figure that out, you'll realize the DOF claim is wrong.
Dear me! I don't quite know what to say, Craig!
What sort of nonsense are you trying to perpetrate!
The F stop is one of the great concepts of Photography precisely because it is
[/i] meaningful across formats. A 300mm lens at f8 will always require the same shutter speed in the same lighting conditions whether that lens is attached to a 35mm camera, a tiny digicam or a 12"x16" field camera, and it will always produce the same DoF from the same shooting position.
I've already mentioned in my response to Victor that 'only' changing the sensor size does not affect DoF. But you must realize that nobody designs and manufactures camera lenses without regard to the sensor size, film size, ie. format of camera the lens will be used with. However, it's true that lenses designed for a larger format can be and sometimes are used for a smaller format, the obvious example being the recent crop of DSLRs such as the D60, 10D and 300D.
So let's look at what happens when we take identical shots from the same position with a 50mm lens on a 1Ds and 10D. If the lens is the same and the F stop is the same and the distance to the central subject is the same . . . it follows that the exposure will be the same and the DoF will be the same. That's the beauty of the F stop system.
But something will be different, won't it? The 10D shot will be severely cropped. In oder to get the same angle of view with the 10D I'll have to step back a few paces. Consequently, the DoF will now be greater on the 10D shot because I've increased the distance between camera and subject. Alternatively, I could just whack on a 28mm lens to get the same field of view from the same position. That would also have the effect of increasing DoF for the 10D shot (at the same aperture).
Now you could argue that the increased DoF that the smaller format 10D seems to exhibit has nothing to do with its smaller sensor size and that the real
reason for the increased DoF is the fact that you either (a) had to step back to get a wider FoV or ( had to use a wider angle lens.
However, there are reasons behind reasons. If the 10D did not have a smaller size sensor than the 1Ds, there would be no reason to step back or to fit a wider angle lens. In this example (which extends across all formats), the size of the sensor could be viewed as the more 'primary' cause of the increased DoF.
Even from a purely mathematical point of view, there is a connection between sensor size, F stop and aperture if we're talking about standards lenses for the different formats. F stop is a relationship between the focal length of a lens and the physical dimensions of the aperture (F=FL/D). The focal length of a standard lens (as opposed to a telephoto or wide angle lens) is given by the diameter of the image circle the lens throws on the sensor. The size of the sensor or format bears a very direct relationship to the image circle. All 35mm lenses for example are designed to have an image circle a bit larger than the diagonal of the 36x24mm frame (about 43mm). The diagonal of an 8"x10" plate for a field camera is about 12.8"= 320mm. It's no accident that the standard lens for an 8x10 field camera is just that . . . 320mm.
Get my point?