I have shared some of your confusion over this.
There is a great description of DoF on this
Cambridge in Colour page with the added benefit of a Depth of Field Calculator. Here are a couple of result from that calculator. Both results assume an f/2 lens with a focal length of 50mm and a distance to the subject of 4 metres.
For a DSLR with a 1.5x crop factor (such as the D80) the results are
Closest distance of acceptable sharpness 3.74 m
Furthest distance of acceptable sharpness 4.299 m
Total Depth of Field 0.559 m
For a DSLR with a 1.0x crop factor (full-frame such as the D3) the results are
Closest distance of acceptable sharpness 3.622 m
Furthest distance of acceptable sharpness 4.466 m
Total Depth of Field 0.843 m
On the face of it this is nonsense. Let's assume that the 1.5x crop camera has been placed on a tripod at such a distance that an object of interest is nicely framed when it is 4 metres away (50mm lens at f/2 as above). After we take the picture we put a D3 (full frame) on the tripod and use the same lens so we are still at 4 metres with f/2 and a 50mm lens. There is no way
that the light falling on the central part of the sensor "knows" that there is more sensor at the periphery than before and so somehow magically increases it's depth of field.
The key to understanding this is the hidden assumption
that the full-frame print will be the same size as the 1.5x crop print. So if, for the sake of argument, both prints were 30cm wide then objects from the full frame camera's print would be about 1.5x smaller than the same objects on the 1.5x crop camera's print. That also means that any blurring caused by objects being out of focus is also 1.5x smaller. Hence, perceptually
, objects can be further from and closer to the point of optimum focus before blurring becomes obvious
To re-phrase, our eyes don't have infinitely good resolving power
. For each of us, when viewing an object like a print at a particular distance, there is a limit to how much fine detail we can see. If the out of focus blurring is smaller than this value we can't see it. Because the assumption was that the full-frame camera's print would be the same size as the cropped camera's print then the out of focus blurring drops below the eye's resolution limit more slowly as the distance of objects in the picture from the point of optimum focus increases.
Of course, if you can't get physically closer to an object when using a full-frame camera and so have to re-frame the picture by digitally zooming in post-processing then the full-frame depth of field reduces to the value calculated for the cropped sensor camera.
Right, I thought I had finished but there is one more thing to discuss. With the full-frame camera we can move closer to the subject so that the framing is the same as with the cropped sensor camera. So in the example above we can move in from 4 metres to about 2.7 metres with the 50mm lens. Still at f/2 we now have
Closest distance of acceptable sharpness 2.523 m
Furthest distance of acceptable sharpness 2.903 m
Total Depth of Field 0.38 m
So the act of re-framing by moving the camera with the identical 50mm lens closer to the subject has actually resulted in a decreased
depth of field. A similar result is seen if, instead of moving the camera closer to the subject, a 75mm lens is used at f/2 at the original 4 metres. Chances are though, that if you are using a 75mm lens you can only afford
a similar lens diameter so you are more likely to be working at f/2.8 where, at 4 metres, the total depth of field is pretty similar to the cropped sensor camera at f/2.
So, controversially perhaps, I will assert that this depth of field argument comparing full-frame versus cropped sensors is sterile. With a fixed print size and the cropped sensor as our benchmark you can end up with a smaller DoF if you re-frame by moving the full-frame camera closer to the subject, you can end up with a greater depth of field if you don't re-frame with the full-frame camera (and so objects in the final print are smaller) or you can end up with the same DoF if you re-frame with the full-frame camera by changing lenses but are operating to the same lens budget (which means you can only afford a slower lens).
P.S. Sorry the post was so long.
I had the time today because I'm also watching the latest space walk from the Space Station using NASA TV's Internet broadcast.