The sensor has nothing to do with depth of field.
Agreed. As long as we're discussing just the depth of field projected by the lens, we can ignore the CoC effects of everything else, such as capture resolution, post processing, display medium, viewing conditions, acuity of vision, etc.
Given the same lens at the same subject distance, there is no difference in depth of field. The only difference is that the full-frame camera will capture a wider field of view.
Agreed again, given the same caveat.
The difference in Depth of Field comes into play when you *move the camera closer* to account for this increased field of view. Moving the camera closer while using the same lens and aperture will reduce DoF.
Agreed. That's one method (AKA "move in without zooming"). The other method is to use longer lenses ("zoom in without moving").
With the fastest lenses, yes, you will get that razor-thin DoF -- but then, I'm getting that with crop-sensor cameras at short distances, too.
For any given composition (angle of view and perspective), the lens with the largest physical aperture (not f/number) will project the thinnest DOF onto the sensor. In the case of comparing APS-C and 35mm systems, for most AOV (Angle Of View) circumstances, the 35mm has larger physical aperture available. At super telephoto, though, the apertures are equal.
To calculate the physical aperture, divide the focal length by the f/number. For example, given the same composition (AOV/perspective), 50mm f/2.0 has the same depth of field as 400mm f/16, and 50/2 and 400/16 both equal 25mm.
That's why "aperture and composition" is my preferred way to explain DOF which scales among all sensor sizes. Another way is "magnification ratio and f/number". Longer focal lengths and closer focus distances increase magnification, which makes DOF thinner.
That's not completely true. Depth of field also depends on the size of the circle of confusion, which is much smaller on APS-C cameras (higher pixel density).
Correct. This is what I meant above by capture resolution. It's helpful sometimes, though, to do as Mr. Bennett did above and assume that all formats to have the same resolution, processing, display size, viewing conditions, etc. just for the purpose of discussion. A more comprehensive
- discussion includes the effects of things like varied capture resolution, like you did.
Why is the circle of confusion different for the different cameras?
I'll add a little something here. APS-C must be enlarged (magnified) more than FF 35mm to be displayed at the same size. This scales in perfect balance with the f/number on FF35 for a given composition. So if both cameras have the same aperture and composition (as in the case of much wildlife photography), the one with higher resolution is capable of thinner DOF.
So, the simplest way to think about DOF, IMHO, is to break it into two things: A. DOF projected by the lens and B. DOF seen by the viewer.
A. DOF projected by the lens. Two simple but comprehensive
A1. Aperture determines DOF for a given composition.
A2. Magnification ratio and f/number determines DOF.
I prefer A1 ("aperture for a given composition") because composition (angle of view, perspective, and focus distance) is central to photography, and I think making it central to the discussion of DOF is most enlightening. (Allowing perspective or angle of view to vary with sensor size is not nearly as useful, IMHO.)
Both of those definitions let you abstract out the effect of sensor sizes, focal lengths. A1 lets you abstract out f/number. A2 lets you abstract out perspective and AOV.
B. DOF seen by the viewer.
Of course you have to start with "A. DOF projected by the lens", but there are many effects that occur after the light passes through the exit pupil. You can get very close by just assuming the CoC is determined only by the lesser of the capture resolution and display resolution. But to be accurate requires the consideration of subject size, pixel density, lens MTF, demosiac algorithm, sharpening, other PP, display size, resolution, viewing distance, environment lighting, eyesight, etc.
Aperture rules.
- I'm left out bellows factor on purpose; this post is long enough as it is.