This thread seems to raise more questions than it answers. I'll try to summarise my take on DOF.
First the definition: DOF is the range of objectdistances from the camera in your scene , within which objects will be judged as acceptably sharp when viewed in the resulting image.
See
this page for some similar defintions.
As an example take the image with the domino stones on that page. I find the stones 4,5 and 6 (with 3 black dots) acceptably sharp.
Now back to the scene and measure the distance from your lens to stone 4 and stone 6, and you have the DOF.
That's basically what DOF is all about.
To give this a more theoretical framework the following:
The optical part.
Our lenses can't project everything in a scene equally sharp. To quantify this the Circle of Confusion (CoC) has been introduced. Points in the scene that are not at the focussed distance will be projected by the lens on the imaging plane behind it as circles (CoC's). The size of these circles depends on focal length, f/stop (relative aperture) and focussed distance of the lens plus the position of the point in the scene.
See
this page for a nice illustration.
The imaging/viewing part.
We define DOF by choosing a maximum size for all those CoC's, the CoC limit.
The CoC limit depends on a lot of factors in the imaging/viewing process, ao the sensor resolution, magnification, viewing distance, visual acuity, lighting conditions etc. etc.
You should decide on a CoC limit for your particular imaging /viewing situation.
DOF.
For each point in the scene the CoC diameter is known.
CoC diameter > CoC limit: outside DOF
CoC diameter < CoC limit: inside DOF
Comparing different situations.
Discussions around DOF usually are about the effect of a certain parameter.
The only way to show this effect is by keeping all other parameters the same.
To show the effect of different lens settings, keep the imaging/display part the same by eg. viewing all images on the same monitor at full screen. Now change only the parameter you are interested in.
You'll find that focal length, f/stop and focussed distance all influence DOF.
By changing 2 or more parameters, you can create images that look (or even are) the same, but you can't conclude that this is due to the changing of a single parameter.
Some examples Sensor size.
For different sensor sizes you end up with different sized images, having the same DOF.
Now if you compare different sensor sizes at the same image size, you'll see different DOF's, but this is due to different magnification to arrive at the same image size.
Constant magnification ratio.
You'll find claims that DOF is independant of focal length when keeping the magn. ratio the same.
This is usually shown with two images shot at different focal lengths showing the same scene.
What happens here is that for the different focal lengths to give the same magn. ratio you need to change the object distance and thus the focussed distance as well. You change TWO of the DOF parameters.
Also perspective is different.
At macro distances the comparison won't hold, same for distances where the focussed distance isn't small in relation to the hyperfocal distance. Lastly the distribution of the DOF in front and behind the focussed distance isn't constant.
Last example.
You can create equal images with exact same DOF for different focal lengths by chosing your settings carefully.
eg. a 25mm lens at f/2 and a 100mm at f/8. Focus at eg. 10 meter.
When cropping the 25mm image to have the same scene as the 100mm one and then magnifying it 4 times, you'll have two identical images, even the same perspective, but you had two change 3 parameters to create this result.
Finally.
In the above I didn't mention several assumptions/simplifications to keep the text readable.
eg. diffraction, CoC's looking like cat's eyes or having the shape of the diaphragm blades, sensors having enough pixels for large magnification etc.