The purpose is that it's simpler. I could say things like "longer focal lengths with narrower f/numbers on larger sensors can have the same DOF, perspective, and FOV as shorter focal lengths with wider f/numbers on smaller sensors", but aperture, not f/number, intrinsically factors in those relationships.

If you keep aperture constant over a dozen different sensors, the DOF will also be constant (for a given FOV and perspective). F/number does not describe DOF for a given FOV/perspective like aperture does.

To answer the question of which camera system is capable of thinner DOF, one simply calculates which one has the widest aperture (not f/number) for the desired FOV.

In the case of FX-vs-DX, the lenses for the FX system are capable of thinner DOF for any given FOV+perspective except the extremes of super telephoto (smaller than 3.7 degree angle of view).

For the purpose of this thread (advising which system has thinner DOF), I prefer my simpler version: For any given perspective and field of view, the lens with a wider aperture (not f/number) will have thinner DOF.

Granted, it leaves out bellows factor and the various effects that sensor resolution, post-processing, display, etc. can have on CoC, but those factors are usually minor for typical shots (as in the case of bellows factor) or obvious (as in the case of many non-lens CoC factors).

Clearly your distinction between aperture and f/number is not represented in the formula for DOF as presented in the "American Cinematographers Manual." ACM uses F/number and not aperture. Can you please write the formula for DOF that you're using or link to a reference for it?

What magically happens at a FOV of 3.6 that changes a mathematical formula and allows it to fit your model for DOF?

Basically, what is failing to be recognized is the variability of DOF. If the subject size is kept constant, the FOV may be different, but the DOF is likely to be the same. This was my argument on keeping the size of a bird the same size and a subject's head the same size with different formats. The FOV may be different but is irrelevant in comparison to the importance of getting the size of the subject constant or as large as possible.

Conversely, if the FOV is determined to be the constant factor, then the DOF may change as a result of changing a variable in the formula for DOF (such as focal length of the lens.) What needs to be understood is that FOV is not an overriding factor and is in many cases not critical. Subject size is not an absolute either but for many scenes more important than FOV. The examples of the size of a head in a portrait or subject such as birds in wildlife photography fit the saying, size does matter.

My distinction is not intended to calculate DOF, but to compare it. For example, if you tell me the aperture of any 6 cameras/lenses, all with the same FOV/perspective, I can place them in order of shallowest DOF to greatest, but I can't tell you *what* the DOF is (e.g. inches in near+far DOF) without knowing the focal lengths.

So nothing is changed in the DOF formula. Aperture is a useful shortcut for knowing the relative DOF of different formats (chip sizes); it does not replace focal length. The shortcut works becase once you know the DOF for any aperture, you know it for all focal length/f/number combinations of that aperture. For example, with a 16.4-foot subject distance, all of the following camera/lens combinations will have the same 40 degree horizntal AOV and 6.7 feet DOF:

I used h/CoC=1200 for all of the above to arrive at 6.7 feet DOF. At 16.4 foot subject distance, bellows factor is not very significant, even for the 617 format lens. They all have approximately 15mm aperture despite the 7-stop difference in f/numbers.

I welcome you to try your own calculations. Can you find any two lenses/camera combinations with the same FOV+perspective+DOF, but different apertures? I can't. (With the exception of bellows factor).

Can you see now why I find that the aperture (not f/number) is a useful shortcut for comparing DOF of camera systems with different sensor sizes?

Aperture (AKA the "hole in space") correlates with DOF for a given FOV/perspective. A 100mm aperture, capturing a 6.5 degree cone, and displayed at a particular size, has the same DOF, no matter what the focal length, f/number, and sensor size are used to arrive at the 100mm aperture. It can be 300mm f/3 on FX, 200mm f/2 on DX, or 120mm f/1.2 on something smaller. Essentially, the scaling of the reproduction magnification cancels out the scaling of the f/number (smaller sensor size must be magnified relatively more for a given display size), leading to larger formats that get similar results from narrower f/numbers.

That's the point where the FX format no longer has any lenses available with focal lengths long enough to match the AOV of the DX format. An imaginary 750mm f/6 would have the same FOV and DOF on FX as the 500mm f/4 on DX.

For some purposes, such as wildlife photography, I certainly agree. This is another salient tangent, compared to the above discussion, but I'll say that I think for many other types of photography, the FOV is the central matter that should be kept constant. The reason is that FOV (and perspective) is one of the first and most important decisions I make in composition. I don't tend to change the FOV of my compositions just because I changed formats. For example, I would not purchase a 17-35 lens (designed as an "ultra wide") for DX and never shoot ultra wide angle just becase I was on a smaller format; I'd buy a 10-20 lens just for that purpose. Similarly, if I upgraded from DX to FX, I wouldn't stop shooting "normal" focal lengths just because my 17-35 became an ultra-wide; instead, I would buy a 24-70 and use it on FX in the same way that I used the 17-35 on DX. Those are the types of reasons why I think FOV is central for many types of photography.

Thanks again for the discussion, Jeff. I've already learned several new things, and I will continue to read your posts with the interest of learning more.

Why does this discussion conjure up images in my head of two guys wearing thick glasses and sporting pocket protectors wailing on each other with slide rules and American Cinematographers Manuals?

Bravo for wanting to thoroughly understand your craft. I just know I likes my backgrounds blurry and my subjects not.

[Thanks to the mods for moving this content into a new thread, by the way.]

I don't know about Jeff, but that doesn't describe me at all. I wear thin glasses (*extra* wide rim), high-water suspenders instead of pocket protectors, and my weapons of choice are manuals with highest nerdliness, which come from the chess club, astronomy group, and board-game meetings, which inflict +1 damage over the less-nerdly A.C. manuals.

I enjoy the technical parts almost as much as the creative parts, I have to keep my Nerd Cred up, you know.

Jeff *might* be too shy to mention it, but he is a photography instructor at the college level.

That's pretty close to me, but I haven't used a slide rule since the 7th grade (1969). I do however remember when Ti LCD calculators were 100's of dollars and only did basic mathematical functions. Pocket protectors were never my style, but I do like shirts with breast pockets. My glasses used to be thick, but with the advent of polymer lenses, they are now much thinner.

I do appreciate Chris stepping in and I'll post a bit of a response in the next day or two, but at the present time I'm tied up in family matters.