Does entrance pupil size alone determine depth of field when comparing lenses?

Question

I’m trying to compare depth of field between two lenses and was told that I only need to compare entrance pupil size: the lens with the larger entrance pupil will have less depth of field and a blurrier background.

For example:
- Lens A: 100mm f/2
- Lens B: 200mm f/4

Both have a 50mm entrance pupil.

At the same focus distance, the 200mm lens appears to have shallower depth of field. But for the same subject framing, I’d need to move the 200mm lens farther back. In that case, it seems the 100mm f/2 may actually have less depth of field.

So what is the correct way to compare depth of field between lenses when framing is kept the same? Can entrance pupil size by itself be used to compare DOF, or is it really describing something else like background blur?

user75526 · Answer

What your friend told you is a way to estimate background blur, not depth of field. If you look at the DOF formula, you'll see it's inversely proportional to f²/N, not f/N. This corresponds with your statement, "focal length has an higher impact on DOF than the F-stop".

DOF = 2 u² N C / f²

N = aperture F-number
C = circle of confusion
u = distance to subject
f = focal length

Depth of Field (DOF), background blur, and bokeh are related, but different concepts. There is also subject-background isolation/separation.

Depth of field is based on focal length, aperture, distance, and a predefined acceptable sharpness level. It is concerned with what parts of the image are expected to be sharp, not what parts of the image will be blurry, or how blurry unsharp portions of the image will be.
Background blur – How blurry is the background? I think of it as something that can be quantified. How big are bokeh balls a given distance from the lens? Different lenses with the same focal lengths, apertures, and distances can create different, though similar, amounts of blur because of different amounts of distortion, aberration, and field curvature. (There's also foreground blur, but people tend to be less interested.)
Bokeh is a qualitative description of the blur that is produced. Are the bokeh balls round? Do they vary in shape throughout the frame? Are they smooth? Do they have edge highlights? Are they smeared? Some people refer to how lenses "render" images.
Subject-background isolation refers to (subjectively) how well the subject stands out from the background. This can be achieved with depth of field and background blur, as well as appropriate lighting (such as rim lighting and creative use of "glow"). The common formula is to try to use narrow depth of field with high background blur. However, some types of bokeh can achieve good subject isolation with high depth of field and low background blur. For instance, Sonnar lenses create bokeh balls with an edge highlight toward the center of the frame, but a smear toward the edge of the frame. This tends to emphasize the sharpness of the subject toward the center, while also emphasizing the blurriness of the background toward the periphery.

Does entrance pupil size alone determine depth of field when comparing lenses?

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