The Difficulty in Explaining Equivalence

If the transition, background blur and field compression are different then the dof is not the same according to the commonly accepted definition of dof.

Perhaps you are using a different definition of dof?

but they are discussing more dof to fit more faces in focus when changing sensor size. must admit so does all the calculators but in practice i cant see any difference in what is critically sharp.

If you're talking about the photos of the little plastic bottle, the DOF is not the same.

Maybe you're talking about some other photos.

If there's something you believe about equivalence that others here don't believe, state exactly what that is.

If there's something you don't believe about equivalence that others here believe, state exactly what that is.

Either way, I'm sure I can stage a practical demonstration that shows the reality.

define DOF

DOF = what is acceptably sharp infront of and behind the focal plane given that only what is at the focal plane is actually in focus.

Now, how do you define DOF?

Look at the equations can be quite instructive. damienfournier.co/dof-the-simplified-formula-to-understand-dof/

Take ASPC and FF. For the same FOV at a fixed distance d, then the "equivalent" focal length of the focal length on a FF for a focal length of f on an APSC is
1.5 f. So at the same f-number, N the DOF =2 (d/f)^2 N c, c the circle of confusion. So on the FF,
DOF_ff=2(d/1.5 f)^2 N_ff c_ff. DOF_apsc=2 (d/f)^2 N_apsc c_apsc

Hence DOF_ff/DOF_apsc=(1/1.5)^2 (N_ff/N_apsc) (c_ff/c_apsc).

Case 1 same sensor MP count, the c_ff/c_apsc)=1.5 for pixel peaking.
In this case DOF_ff/DOF_apsc=(1/1.5) (N_ff/N_apsc).
For printing to the same print size, there is a 1.5 enlargement ratio penalty for apsc which enlarges the c_apsc and hence
DOF_ff/DOF_apsc=(1/1.5)^2 (N_ff/N_apsc).

There are other conditions to consider but in general equivalence does not really hold up when considering DOF.

same

Can you elaborate? For low magnification (say, the distance to the subject is at least 10x the focal length used), Equivalence really does hold up with regards to DOF:

www.josephjamesphotography.com/equivalence/#dofderivation

It's a simplified formula, meaning it's not always applicable to reality. What does the unsimplified formula say?

The shorthand way in which most of us are accustomed to describing the principles of equivalence is indeed incomplete (because it's simplified). A question in another recent thread here prompted me to stage a practical test, and the results initially surprised me. It demonstrated that some of what we routinely say about equivalence is probably only strictly true at infinity focus. In order to avoid being surprised, we just have to be attentive to the terms we use.

another test. apsc vers FF equivalent fov same camera position.

same focal length moved camera for same fov. is my exif data showing ? because its not on my computer. 🤨but everyone elses is.

exif data is finally showing 😊
edit, no its not ,its intermittent 🤔

What do you see in those results?

What do you conclude from them?

Do you believe they disprove things that others here believe about equivalence? If so, what things?

Thanks GB, that is a great summary!

I had already responded to the other forum member (EZGritz) with this (which I hope I got right):

And this is his response:

😵 😵 😵

Remember when I said, "The problem is, no matter how well explained, 'they' simply refuse to change their preconceptions. That is, exposure is the be-all and end-all and noise is entirely a result of the sensor."? EZGritz response is a textbook example of that. Note how he says that the 4x greater amount of light is spread over 4x as much area (which is true), so it's all the same in the end (which is false).

He, and the rest of the anti-equivalence crowd, simply cannot let go of exposure as being central, when, in fact, it is completely irrelevant in cross format comparisons (except inasmuch as exposure is a component of total light: Total Light = Exposure x Sensor Area). The reason exposure is used, rather than Total Light, is because for a given format, exposure and Total Light are essentially interchangeable, like mass and weight are when in the same acceleration field. But when comparing different formats, the distinction is central, just as is the distinction between mass and weight if, say, you are comparing a person on the Moon vs a person on Earth.

So, EZGritz is uninterested in your "mathematical wizardry" -- he's only thinking about exposure. Thus, the question to pose to him is the following:

Consider the following three scenarios:

1) mFT at 25mm f/2.8 1/400 ISO 1600
2) FF at 50mm f/2.8 1/400 ISO 1600
3) FF at 50mm f/5.6 1/400 ISO 6400

How do the exposure, lightness, noise, perspective, [diagonal] framing, DOF, and motion blur compare for all three? I'll give you my answers first. The perspective, [diagonal] framing, lightness, and motion blur are the same for all three. The DOF and noisiness of (1) and (3) are the same, and the DOF and noisiness of (2) is half of that. The exposure of (1) and (2) are the same, but the photo in (2) is made with 4x as much light as the photo in (1), which is why it's half as noisy. The exposure of (3) is two stops lower than the exposure of (1), but both are made with the same total amount of light, and that's why they are equally noisy.

Quick prediction: he won't care. TC might step in, but not to tell EZGritz to stop arguing against the facts and/or just drop it, but to once again whine about how everyone already knows all this and is tired of hearing it over and over. What do I win? 😁

You are right, he won't care and will just shift his goalposts around to confuse the situation more than it already is.

Thankfully this debate isn't happening in the open forum. After TC locked the thread, EZGritz wanted to keep going so he sent me a PM to tell me I was wrong, didn't understand etc. So this has all been playing out in PMs. If it had been in the open forum, I think I'd have been put into the sandbox with you by now!

Ha ha, I am pretty sure you will win. If it was within my power, I would make you DPR m4/3 moderator for a week. That would be fun to watch.