Originally posted by m42man "If you use the same lens on a small-sensor camera and a full-frame camera and crop the full-frame image to give the same view as the digital image, the depth of field is IDENTICAL"
I think that's just saying that a cropped image from a full-frame sensor will be identical to the full image from the smaller sensor (including DOF) - which is obviously exactly as you'd expect. It shouldn't be interpreted as "the DOF of the uncropped full-frame image will be the same as the DOF of the cropped image" (because it isn't).
Ok here we go again...
When you use a ff sensor, or crop sensor, for any shot, taken with the same lens, from the same point with the same level of magnification during printing/displaying the image, the common portion of the two images ARE IDENTICAL.
There are two things that people forget with respect to comparing FF and cropped sensors.
First, when using a cropped sensor, because you enlarge the image more to (for example print to 8"x10") this you would with a full frame sensor you are enlarging the image more. This has the effect of reducing dof because dof is defined traditionally as acceptable sharp when viewing an 8x10 print. This is why an aps-c camera has a circle of confusion that is smaller (at the sensor) than full frame. It is all relative to aa pure point of light appearing as less than 0.01" on an 8x10 print. That is the origin of the definition of DOF.
But......
This is counter intuitive to what every one claims where ff cameras have lower dof than crop sensors, so let's go to the second point....
With a subject at a set distance, to get the same image height in the view finder, with a crop sensor as full frame, you have two options, either put on a shorter focal length lens, which has more DOF, or move back, which, as you do, for any aperture DOF increases the further away you are.
when you go to a shorter focal length lens the impact on DOF is more than the loss of DOF from the different enlargement ratio so it appears that you get more DOF from a crop sensor than full frame when shooting from the same point ad compensating with changing focal length.
If you keep focal length the same, and move back to compensate for the crop sensor, the increase in DOF as you move back to keep the image on a crop sensor the same in proportion to the sensor, as the ff camera, the increased DOF of the lens is largely offset by the loss of DOF from the enlargement process, and you get relatively the same overall DOF
Set up some examples and play with your DOF calculator, it will surprise you