Or you can mostly keep discussing it whilst completely ignoring the linked articles that explain it far better then any of us.
What is dof? It is the distance at which a point is no longer a point but a circle (where something sharp is no longer sharp). The size of the circle or point is determined by the physical aperture (not the f stop value) and the subject magnification (not distance). Alone.
Depending on how you draw your comparison the sensor size can make a difference, or not.
Typical photo situations.
- Where you have different sensors and want to take exactly the same image from the same place. To do that you use a shorter focal length lens on a crop camera, this has a smaller physical aperture for the same framing and f stop value, if you use a 160mm @ f2.8 on your FF camera you are shooting through a 57mm aperture . Whereas for your same framed shot with a crop camera a 100mm @ f2.8 gives you an aperture of 35mm (to get the same dof you need the same 57mm aperture, with your crop sensor and 100mm lens that would be f1.8 ). The smaller the aperture, in absolute terms, the greater the dof. Think pinhole cameras where everything is sharp.
- Where you are focal length limited. If you are
shooting taking a picture of a bird with your two cameras, but you don't have a lens long enough to fill the frame even with the crop camera. If you crop both images to the same size, the dof is the same in both images. The physical aperture you shot through was the same, and the subject magnification is the same, so you get the same depth of field.
If you change either the physical aperture, not necessarily the f stop value (50mm f2 is the same as 100mm f4, they both equal 25mm), or the subject magnification, you change the dof characteristics.
Subject magnification is not limited to the size it is reproduced on the sensor, it continues through to final output size. Take a slightly blurry image and down size it to a thumbnail, it will look sharp, if you make something smaller the dof increases, conversely enlarging something more makes those points and circles easier to differentiate. Take a razor sharp image and enlarge it 400%, it will look blurry from the same place,
step back and it will regain its apparent sharpness. Look at a billboard from across the street, it looks sharp, now walk up to it and the "pixels" can each be two inches large.
You have to determine your specific image and comparison criteria to determine dof.